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A photometric study of the open cluster NGC 7419 Thibault, Daniel 1984

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PHOTOMETRIC STUDY OF THE OPEN CLUSTER N G C 7419 by DANIEL THIBAULT B. Sc., Universite Laval, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES Department of Astronomy & Geophysics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1984 ® Daniel Thibault, 1984 In presenting this thesis in partial fulfilment ol' the requirements for an advanced degree at the The University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Astronomy & Geophysics The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: Angus: 1984 ABSTRACT A set of UBV plates of the heavily-extinguished open cluster NGC 7419, obtained at the Observatoire Astronomique du Mont Megantic by Anthony F. J. Moffat, were digitized by the Dominion Astrophysical Observatory PDS (Photometric Data Systems, Perkin-Elmer Corporation) machine. The data was subsequently processed by Greg Fahlman and Chris Pritchett's TOODEE Command Language, and later John Nicol's SUPERTOODEE Command Language. The resulting set of intensity indices were calibrated in the UBV system using Handschel and Sandage's magnitudes into a set of observed magnitudes. These were then de-reddened and de-extinguished with the help of an updated variation of Serkowski's (1956) method. Handschel's claim of differential reddening across the face of the cluster was examined and found valid. Using our own Zero-Age main sequence culled from several sources, the distance modulus was estimated at 13.9 ± 0.1 mag. Comparison of our color-magnitude diagram with those of other young clusters as well as with theoretical isochrones leads us to estimate the cluster as being as young as, or younger than, 10 million years, although serious problems with the photometry preclude any further analysis. Low-resolution Reticon spectra were obtained with the Dominion Astrophysical Observatory's 180 cm telescope of some of the cluster's stars in the hope of measuring radial velocities. The spectra were processed with Stephenson Yang's RETICENT Command Language. These were used to attempt to resolve the question of the possible membership of the fringe-dwelling carbon star. The low-weight determinations obtained for the carbon star and another possible cluster member are inconclusive and stress the need for a more careful study of the problem. In conclusion, the cluster's color-magnitude turnoff was observed, and its age and distance evaluated as 5 ± 5 Ma and 6.0 ± 0.3 kpc respectively! Average extinction was found to be A = 5.85, and reddening E(B-V) = v 1.77. ii Tahle of Contents ABSTRACT Table of Contents List of Tables List of Figures Acknowledgements 1. Introduction 2. The Raw Data 3. Data Reduction: From Digital Arrays to Flux Indices 3.1 TOODEE and SUPERTOODEE Processing 4. Data reduction: From Flux Indices to Magnitudes 4.1 The Virtual Plates 4.2 Calibration Theory 4.3 The Secondary Images 4.4 Calibration Results 4.5 The Carbon Star 5. The Color-Magnitude and Color-Color Diagrams 6. De-Reddening and De-Extinguishing 6.1 The Q method 6.2 The Serkowski method 6.3 Results 6.4 The distance modulus 7. Parting shots 7.1 Differential reddening 7.2 Age estimate 7.3 Conclusions BIBLIOGRAPHY iii APPENDIX A 144 A.1 Introduction 144 A.2 RETICENT 145 A.3 The Reticon 146 A.4 Spectrum Calibration 146 A.5 Bandhead Positions 148 A.6 The Radial Velocity 151 A.7 25/26 August 1982 ,....,..„..,.„„. 156 A.8 11/12 October 1982 163 A.9 Star 196 169 A.10 Star 183 171 A. 11 The carbon star's radial velocity 173 APPENDIX B 175 INDEX 232 iv List of Tables 1. The plates 6 2. The objects 11 3. The photometric standards 50 4. Raw photometry 80 5. The Zero-Age Main Sequence 110 6.1 Probable cluster stars, de-reddened and de-extinguished photometry 124 6.2 Probable field stars, de-reddened and de-extinguished photometry 128 7. The lines 152 8. The ultraviolet flux indices 175 9. The blue flux indices 180 10. The visual flux indices 193 11. Blue group 2 flux indices 206 12. Visual group 2 flux indices 219 v List of Figures I. Master finding chart 2.1 Finding chart, wide field 2.2 Finding chart, inner field 3. TOODEE density plot of frame after DOUBLT 4. Point-Spread Function contour plot 5. TOODEE density plot of TRIPLT situation 6. TOODEE density plot of 108-113 case 7. Correlation plot of B2ptl versus B2pt2 8. Correlation plot of B2pG versus B2pt2 9. Correlation plot of V2pt2 versus V2ptl 10. Correlation plot of V2pt3 versus V2ptl II. Correlation plot of V2pt4 versus V2ptl 12. Correlation plot of B2ptl versus B2mean 13. Correlation plot of B2pt2 versus B2mean 14. Correlation plot of B2pt3 versus B2mean 15. Correlation plot of V2ptl versus V2mean 16. Correlation plot of V2pt2 versus V2mean 17. Correlation plot of V2pG versus V2mean 18. Correlation plot of V2pt4 versus V2mean 19. Calibration of U group 1 20. Calibration of U group 2 21. Calibration of B group 1 22. Calibration -of B group 2 23. Calibration of B group 3 24. Calibration of V group 1 vi 25. Calibration of V group 2 68 26. Lg(F / F ) for U group 2 73 A B 27. Lg(F / F ) for B group 2 74 A B 28. Lg(F / F ) for B group 3 75 A B 29. Lg(F / F ) for V group 2 76 A B 30. Color-color diagram of the standards 97 31. Color-magnitude diagram of the standards .1 98 32. Color-color diagram of the standards (our data) 99 33. Color-magnitude diagram of the standards (our data) 100 34. Raw color-color diagram 101 35. Raw color-magnitude diagram 102 36. Color-color diagram of the faint stars 103 37. De-reddened color-color diagram 120 38. De-reddened color-magnitude diagram 121 39. Color-color diagram of the de-reddening sample 122 40. Color-magnitude diagram of the de-reddening sample 123 41. Extinction map —Handschel's data 134 42. Extinction map —Independent sample 135 43. Extinction map —Complete sample 136 44. First derivative of the bandhead region 150 45. 25/26 August 1982 iron-argon arc 159 46. Residuals of the polynomial fit to the 25/26 August 1982 iron-argon arc 160 47. 25/26 August 1982 spectrum of the carbon star 194 161 48. 25/26 August 1982 spectrum of TX Piscium 162 49. 11/12 October 1982 iron-argon arc 165 50. Residuals of the polynomial fit to the 11/12 October 1982 iron-argon arc 166 51. 11/12 October 1982 spectrum of the carbon star 194 167 vii 52. 11/12 October 1982 or TX Piscium 168 53. 11/12 October 1982 spectrum of star 196 170 54. 13/14 October 1982 spectrum of star 183 172 viii Acknowledgements I would like to express my gratitude to Harvey B. Richer for his guidance throughout these three long years, Universite de Montreal's Anthony F. J. Moffat for providing the substance of this work, the National Science and Engineering Research Council for providing my sustenance, and the Dominion Astrophysical Observatory staff —particularly the night assistants— for allowing me to lose my green horns. Further thanks and best regards go to the Astronomy & Geophysics faculty and staff for providing a homely atmosphere, University of British Columbia's Computing Centre staff for their unflinching patience, John^ Nicol and Stephenson Yang for introducing me to their respective brain childs, SUPERTOODEE and RETICENT, and the UBC Observers (Stephenson Yang, Chris Millward, Zoran Ninkov, Phil Bennett, Ed Chan, Gary Joslin, Dennis Crabtree, and more) for "introducing me to the life of the cosmopolitan observer" (Chris said it so well). No doubt there are more 1 owe to than I have managed to deal with here; to those my apologies and a dip of the hat. ix Quantification as such has no merit except insofar as it helps to solve problems. To quantify is not to be a scientist, but goodness, it does help. —Sir Peter Brian Medawar Advice to a young scientist x 1 Chapter 1 INTRODUCTION Open star clusters, studied for three centuries, have in the last decades assumed ever-increasing importance for several reasons. The early emphasis on the two types of stellar populations put them in the spotlight since they represent population 1 whereas globular clusters represent population I I . The increasing development of stellar evolution theory rests on star clusters, which furnish groups of stars presumably created from the same material at about the same time, and hence offer a chance to study evolutionary tracks in the Hertzsprung-Russell diagram. Open clusters, groups of dozens or hundreds of stars, seem to form the backbone of the Milky Way, whereas the great globular clusters, systems of thousands to hundreds of thousands of stars, act as beacon lights to indicate its overall dimensions in all directions. Open clusters mark out our Galaxy's spiral arms, and because of their intense concentration to its plane, have been used extensively to map out the ever so troublesome interstellar extinction. The youngest ones, finally, offer a unique opportunity to study stellar evolution in the high-metallicity range, as well as giving precious clues to the Galaxy's metallicity distribution. NGC 74]9, also known as Collinder 453 (Collinder 1931) or OCL-250 (Alter. Ruprecht, and Vanysek 1970), lies in Cepheus, at the equatorial coordinates (1950.0): a = 5 = 22h 52.3m +60° 34' 2 galactic coordinates: II 1 = 109.13° •9 II b = + 1 . 1 4 ° NGC 7419 is especially interesting in that it is rather distant (6 kpc or thereabouts); as a consequence of this and its low galactic latitude, it suffers from severe visual extinction (five to six magnitudes). Furthermore, it is one of the handful of young open clusters to include a carbon star as a (probable) member (Sandage 1958, Blanco 1965, Gordon 1968. Eggen 1974, Scalo 1976). The cluster's faintness is a major obstacle to obtaining its color-magnitude diagram; it caused early authors (Reinmuth 1926 to Collinder 1931) to underestimate the cluster's angular angular diameter fourfold. The modern value of .11' was first arrived at by Barhatova (1950). Handschel (1972) obtained the only color-magnitude diagram available prior to this work. It was our intention to build on Handschefs work to extend the diagram to fainter magnitudes, and thus hopefully define the cluster's turnoff more accurately. To this end deep U, B, and V plates of the cluster were secured by Anthony F. J. Moffat at the Observatoire Astronomiquc du Mont Megantic. In addition, a small effort was made to ascertain the physical membership of the cluster's carbon star; for this we obtained low-dispersion spectra of the star in the 350 to 600 nm range with a RET1CON solid-state detector. This last part of the work was unfortunately inconclusive; it is important that the matter of the carbon star's membership be settled as quickly as possible because of the tremendous import to theory a positive determination would have. Carbon stars are currently conceived as intermediate to low mass, highly evolved stars; its 3 membership in NGC 7419, however, would imply a relatively massive, young object —a picture quite at odds with the preceding one. 4 Chapter 2 THE RAW DATA The story begins with the U, B, and V plates taken al the Observatoire Astronomique du Mont Megantic by Anthony F. J. Moffat. Table 1 lists the plate number, date and duration of exposure, emulsion and filler used, estimated plate limit, and whether or not the Racine wedge was used. The seeing in all cases hovered in the two to three arc second range, with the exception of plaie 16, which had an exceptional night (seeing of one arc second), and plates 409 to 411, which had a bad one (seeing of about five arc seconds). The Racine wedge (Racine 1969) is a thin fused silica prism placed in the telescope's incoming parallel beam; it causes the appearance of secondary images of the brighter stars offset by a constant amount in position and magnitude (about 23 seconds of arc and four magnitudes in the case of the one used at the Observatoire Astronomique du Mont Megantic). Inspired by a similar device due to some of Astronomy's pioneers (Pickering 1891, Leavitt 1917), the Racine wedge is a simple and elegani way of extending one's photometric sequence to the faint end. A more complete discussion of the wedge's implications will be embarked upon in Chapter 3. A master finding chart was made from an enlargement of a contact prim of B plate 330. A B plate was chosen as a compromise between the very deep V plates and the comparatively shallow U plates. Plate 330 was chosen over plate 10, which is slightly deeper, because it was taken under superior seeing; as well, it sports secondary images whereas plate 10 does not. Some 233 objects were labeled on the master finding chart. Table 2 lists their corresponding catalog numbers (Bonner Durchmusterung, Henry Draper, Smithsonian Astrophysical Observatory, General Catalogue of "Variable Stars) as well as their Blanco et al. (1955) numbers (Iii), and Handschel (1972) numbers —the Hn numbers refer to Handschel's Karte V; those involving a roman numeral refer to his Karte III. As 5 Table 2 shows, five of the numbered objects turned out to be specks of dust on the master finding chart. Two turned out to be secondary images not recognized as such during the numbering phase. In addition, twenty-one X objects are shown; these are last-minute additions that were picked up while generating the PDS object-coordinate file. They are all very faint, as the false alarm XI, which turned out to be a figment of my imagination, attests. Finally, there are eleven objects labeled with "a, b, c...";these are even later additions, picked up during the processing of the PDS data frames. All but one arc faint V objects which do not appear on the U or B plates at all. The single exception, 142b, was recuperated on a B frame. Figure 1 is a reproduction of the master finding chart, without the identification numbers for the sake of legibility; note the numerous secondary images caused by the Racine wedge. Figures 2.] and 2.2 reproduce the finding chart at two different scales; the (X,Y) coordinates are taken directly from the PDS grid and reproduced in table 2. 6 TABLE 1 The Plates Plate Date Exposure Emulsion Filter Plate Limit Wedge 10 1 Jul 1978 35 min 103aO GG385 B^20 N 12 2 Jul 1978 . 81 min 103aO UG2 U=0 8 N 16 ~* Jul 1978 31 min 103aD GG495 V^2 1 N 162 24 Jul 1979 30 min IlaO GG385 B~19.5 N 326 8 Jul 1980 22 min IlaDt GG495 V^18.5 Y 327 8 Jul 1980 74 min IlaDt GG495 V=0 9 Y 328 8 Jul 1980 60 min IlaOt GG385 B=*2 0 Y 329 10 Jul 1980 65 min IlaDt GG495 8 Y 330 10 Jul 1980 83 min IlaOt GG385 B=-20 Y 333 11 Jul 1980 116 min IlaO UG2 U=*1 7 Y. 334 14 Jul 1980 65 min IlaO UG2 U~1 8 Y 335 14 Jul 1980 175 min IlaO UG2 U-l 8 Y 386 28 Jun 1981 45 min IlaDt GG495 V=1 8 Y 387 28 Jun 1981 50 min IlaOt GG385 B=20 Y 388 28 Jun 1981 80 min IlaOt UG2 U<*17.5 Y 409 2 Jul 1981 43 min IlaD GG495 V ^ l 8 Y 410 2 Jul 1981 43 min IlaO GG395 B^1 9 Y 411 2 Jul 1981 160 min IlaO UG1 U~17.5 Y t: Sensitized Notes: The plates in bold numbers were digitized; the plate in italic was digitized but the data lost due to plate misalignment on the PDS machine. 7 Facing page: Figure 1: Finding chart, wide field This is a reproduction of the central portion, considerably enlarged, of a contact print of blue plate 330. North is right and East up. and the bright objects in the northwest comer are stars 1 and 2. Note the numerous secondary images, oriented northeast, caused by the Racine wedge. 9 c3 o o o o o o o o Y cn o o o o o o o o o O o i r o O . O o o o 0 ° o o — Q ° e — c r 3> 6 o o ° o o _L I o o JL 15000 - 1 0 0 0 0 - 5 0 0 0 0 X 5000 10000 15000 Figure 2.1: Finding chart, wide field North is up and East left, and the scale is roughly 60 units = 1 arc second. The inner box gives the extent of Figure 2.2. The radii of the circles is given by a linear function of the B magnitude of each object (using the data from table 4), with a limiting magnitude of 22. Objects 1 and 2 lie about 13' WNW of the cluster, beyond the edge of the chart 10 o o o o o o h o r i ro o o o o o 8 o o o O ( O o o o O <£> O o O O r?0 CP O O o o O o o O O o o s ° o (3 O 0° . O o u 8 o ° o ° ° o o o *b o o CP o o o h o O w o o ° o O o O o O ° o ° O o -6000 -4000 -2000 J I L 0 X 2000 J L _ 4000 Figure 2.2: Finding chart, inner field This is an enlargement of the inner part of figure 2.1. TABLE 2 The objects )bject X Y Identification Object X Y Identification 1 (') 17 Non-existent 2 (2) 18 -2436 8124 Hn 21 3 7286 8950 Hn I B (3) 19 -1301 7217 Hn 22 4 7894 10760 Hn 27 20 -1000 6708 5 9797 11841 21 -478 7135 6 13833 12612 Hn 28 22 213 6944 Hn 23 7 12091 17062 23 -149 6215 8 Non-existent 24 141 5522 9 6457 15420 25 557 5347 10 4804 14013 Hn 17/Hn 1 11 26 2852 6887 11 5121 12576 Hn 16/Hn I 12 27 5078 6663 XI Non-existent 28 4628 5911 Hn 29 X2 -645 12659 29 4713 5429 Hn 30 12 1697 9130 Hn 25 30 5844 4205 Hn I 38 13 1370 9473 Hn 26 31 5611' 3456 14 1456 9911 32 6063 1609 Hn 13/Hn I Bl 5 15 367 10419 Hn 15/Hn I 21 33 7908 7225 16 -71 8285 Hn 24 34 10057 4598 Hn I 15 (') BD + 60°2453 A/HD 216572/SAO 20292/ADS 16334 (2) BD + 60°2453 B (3) BD + 60°2456/SAO 20306/HD 216721 TABLE 2 Die objects (4) Dbject X Y Identification Object X Y Identification 35 11544 3132 51 4101 -13614 36 11565 2790 52 3952 -1563.1 37 16297 -4973 Hn 57 53 1179 -12729 38 11051 -2197 54 1831 -8835 Hn 68 39 8041 -2085 55 1490 -8357 40 7524 -3843 Hn 12/Hn IV 56 196 -10071 16/ Bl e 41 7186 -1763 57 Non-existent 42 6764 -1751 Hn 56 (4) 58 -1057 -11632 43 10209 -1924 59 -1756 -11271 Hn 67 44 6835 -8388 Hn - 74 60 -2523 -9081 Hn 10/Hn III 37 45 7484 -8938 61 -3009 -8320 Hn 69 46 9084 -10050 Hn 59 62 -3560 -6312 Hn 71 47 11559 -10467 63 -3483 -5536 48 6285 -11057 64 -2731 -6381 X3 6066 -11118 65 8018 -15807 Hn 60 X4 6111 -11224 66 8604 -14653 Hn 58 49 4125 -10836 67 11222 -16902 50 3454 -11436 Hn IV 37 68 -2227 -5874 This star is : mislabeled as the western 6 on Handschel's Karte V 13 TABLE 2 The objects Object X Y Identification Object X Y Identification 69 -139 -5602 84 2578 4862 Hn 32 70 107 -5344 85 2364 5045 71 2458 -5388 86 1670 3229 72 4061 -4196 87 1182 3891 Hn 33/B1 3 X5 4064 -6283 87Bb 73 4920 -1700 Hn IV 19 88 863 2616 Hn 51/B1 d 74 4204 -801 X7 1130 2813 74b 89 1524 2704 Hn 50 75 3866 -1211 Hn 55 X8 500 3109 76 3332 -310 X8c 77 3438 1568 90 2459 2400 78 3289 1762 91 2707 1519 Hn 52 78b 92 2289 1028 Hn 53 79 3918 2574 93 2562 261 Hn 54 79b 94 2812 -657 80 4415 3079 95 2603 -735 81 4151 4218 Hn 31 96 1640 -387 Hn 80/B1 2 81b X9 1935 -326 82 3531 3238 97 1187 769 Hn 81 83 2987 3097 Hn 14/Hn I A / 98 1103 465 Bl f X6 2389 3408 99 959 318 14 TABLE 2 The objects Object X Y Identification Object X Y Identification 100 1023 170 118 -1420 -4104 101 1063 -911 119 -2081 -3778 Hn 73 102 1046 -1081 120 -2729 -4250 103 1021 -3440 Hn 11/Hn IV 24 121 -3288 -4097 104 55 -4228 122 -3491 -2968 Hn 93 104c 123 11911 105 277 -2753 124 -1964 -3006 106 628 -1420 Hn 78 125 -1677 -1891 Hn 91 107 567 -1683 Hn 79 126 -1965 -1549 Hn 92/B1 1 108 189 -1430 XI1 -2079 -1639 109 -144 -1158 127 -2625 -2573 110 -8 -1710 128 -2808 -2313 111 8 -1537 129 -2810 -1438 112 -8 -1374 XI2 -2355 -979 113 129 -1794 130 -2041 -901 Hn 90a/Bl c 114 -279 -1947 131 -1404 -723 Hn 90 X10 -450 -2216 132 -686 -628 Hn 89 (4) 115 -990 -1796 133 389 -442 Hn 83 116 -1272 -3052 134 435 48 Hn 82/B1 4 117 -1708 -3625 X13 516 267 (j) Two stars are labeled 89 on Handschel's Karte V; this is the southern one Object X Y TABLE 2 The objects Identification Object X Y Identification 135 136 137 X14 138 139 140 141 142 142b 142c 143 144 145 146 147 148 149 150 151 516 1186 213 1988 -374 2403 Hn 49 -199 2467 881) -531 4472 -1255 4118 -1092 3992 Hn 35 -1275 3523 Hn 34 •1496 4096 •2168 4691 Hn 38 •2040 4063 Hn 37 •2247 2999 •2521 2719 Hn 48 -2499 1952 Hn 47 •1675 1776 -1485 1992 •1226 1881 152 153 154 155 156 157 158 159 160 161 162 X15 163 164 165 166 167 168 169 170 52 1241 Hn 85 77 678 Hn 84 (s) -271 -675 -1071 -1854 1099 177 Hn 86 303 Hn 87 471 Hn 88 -2544 -3363 -3213 1302 808 Hn 46 927 Hn 45 -3787 1668 -3747 1139 Hn 44 -3690 1217 -4020 335 Hn 42 -3452 -623 -4018 -630 Hn 43 -3978 -1299 -3653 -1605 -4453 -2181 -3594 -2395 -4467 -2849 (') This star is mislabeled as the northern 89 on Handschel's Kartc V 16 Object X Y TABLE 2 The objects Identification Object X Y Identification 170b 186 171 -4629 -3508 Hn 94 187 172 -5474 -3421 Hn 9/Hn III 188 46/ Bl a 173 -6307 -3029 Hn 95 189 174 -6600 -2184 Hn 96 190 175 -6410 -1318 191 176 -7517 -2823 Hn 8/Hn III 17 192 177 Non-existent 193 178 -5356 -5393 194 179 -4728 -7477 Hn 70 195 180 -6188 -7515 196 181 -7081 -7577 Hn 101 197 182 -7909 -6267 198 183 -9138 -5027 Hn 98 199 184 -9987 -5917 Hn 102 200 185 -9760 -10638 Hn 66 201 X16 -8897 -10520 202 X17 -8952 -11730 203 -10620 -11701 Hn 65 -10583 -14646 Hn 64 -11493 -16244 Hn 63 -8607 -14719 -6297 -12879 -7122 -16899 Hn 62 -4755 -18014 Hn 61 -4651 -17502 -11982 -7602 Hn 8a/Hn III 12/ Bl g (7) -14801 -5731 -16297 -5284 Hn 103 -14538 -1186 -12977 -928 Hn 105 -12743 -1582 Hn 104 -13333 986 -13939 2502 -13858 5458 -11634 6455 Hn 2/Hn II 34 (7) GCVS 8803 17 TABLE 2 The objects Object X Y Identification Object X Y Identification 204 -13536 8950 Hn 1/Hn 11 20 219 -9182 8851 Hn 20 205 -12751 5394 X20 -8380 8978 206 -12069 3229 Hn 4/Hn 11 40 220 -13088 11278 Hn II 19 207 -11375 2441 221 -9467 14048 208 -9425 3327 Hn 5/Hn II 44 222 -12365 .17228 209 -9014 3994 223 -10536 17266 210 -8544 1.553 224 -9533 17677 211 -8233 -668 Hn 7/Hn III 11 225 -7877 18013 Hn 19 212 -7947 2702 226 227B 212b 227 -6813 14919 Hn 18 X18 -6961 2116 228 -5364 .11863 213 -6022 2203 Hn 40/Bl b C) 229 -5530 9181 214 -4986 .1300 Hn 41 X21 -5092 9157 215 -5416 2426 230 -4866 5130 Hn 6/Hn II O 216 -7819 4753 231 -3901 5148 Hn 39 217 -8229 6427 232 -3825 6102 X19 -7368 6615 Hn 11 32 233 -3685 6488 218 -7838 7559 Hn 3/Hn II 24 (8) This is Blanco et al.'s blue star b (Blanco et al. 1955, Fig. 1); it is not the same as their infrared star b. Our star 213 is not IRC + 60° 375/GCVS 8802 (Fawley and Cohen 1974) (9) Two stars are labeled 6 on Handschel's Karte V; this is the eastern one 18 The two U, five B, and five V plates mentioned in table 1 were digitized with the Dominion Astrophysical Observatory PDS machine over the period extending from July 23rd to August 1st 1982; one additional V plate was digitized at the time, but it later turned out it had been misaligned, thus rendering the data unusable. The scanning aperture used was square, 17 um on the side. Each plate was digitized in one continuous session, with the exception of B plate 387 and V plates 386 and 409, which were each done in two consecutive stretches, due to the orientation of the Racine wedge secondary images being different from that of the other plates, and with the further exception of B plate 410, which was digitized in two parts, for the same reason as above, but separated by three days. The end product of the PDS machine consisted of frames of the objects on the plates, each frame made up of forty by forty pixels, and each pixel an integer number between 0 (indicating lightness) and 1023 (indicating darkness). Through some quirk of the innards of the PDS, four of the plates had twelve frames skipped, as inspection later revealed. Ultraviolet plate 12 lost objects 1A/B to 9, inclusive, while ultraviolet plate 334 lost objects 19 through 30. Visual plates 329 and 386 both lost the same string of objects: 40 through 49. Because of the particular order in which the frames were, generated, the visual plates did not lose object 43, although they did lose objects X3 and X4 in the bargain. That these objects were missing came to light as the data reduction, detailed in the following chapters, was begun. Considering the losses as not being catastrophic, it was decided not to delay data reduction until time on the Dominion Astrophysical Observatory PDS machine could be secured anew, but to go ahead with what we had instead. 19 Chapter 3 DATA REDUCTION: FROM DIGITAL ARRAYS TO FLUX INDICES 3.1 TOODEE AND SUPERTOODEE PROCESSING TOODEE (Fahlman 1982) is a simple command language, written in FORTRAN IV by Dr. Gregory G. Fahlman, Dr. Dennis R. Crabtree, and Mr. John S. Nicol, designed to process two-dimensional images. It incorporates many of the features of RETICENT (see Appendix A for more details), a command language initially designed by Dr. Chris Pritchet to analyze one-dimensional spectra. TOODEE was specifically intended for data obtained with the 100 x 100 pixels BNR (Bell Northern Research) Charge-Coupled Device, but may be used with other data at the small cost of reformatting. Images are read into frames (or arrays if one-dimensional) which are in-core storage spaces in the program. Commands are issued to operate on these frames or on selected areas of frames; macros and do-loops can be used for oft-repeated sequences of commands. SUPERTOODEE (Nicol 1984), for which credit goes mostly to Mr. John S. Nicol, is an expansion and modification of TOODEE. It features dynamic memory management of the frames, which are now arbitrarily dimensioned (up lo hardware limitations — 1.7 Mbytes per frame) and can contain data in any of the ANSI FORTRAN numerical data types (integer to complex), optimized input/output operations on RAM files, compatibility with the FITS (Flexible Image Transport System (Wells and Greisen 1979)), CTIO, LAIR (Laboratory for Astronomical Image Reduction, UBC) and RETICENT data formats, as well as interfaces with the ISSCO Disspla graphics package and with MTS, the operating system of the University of British Columbia mainframe. Particular attention has been paid to improving the running times of SUPERTOODEE as compared to TOODEE; so far the ratio of execution speeds is 20 10:1 (input/output) to 20:1 (analytical routines). SUPERTOODEE is fast on it way to becoming a truly universal digital image processing package. As stated earlier, each object digili/.ed by the PDS machine appeared, in TOODEE terms, as a forty by forty array of pixels, each pixel being rated from 0 to 1023. If any of a star's pixels were found to bear the maximum value of 1023, the star was labeled saturated, and excluded from the sample. This docs not necessarily mean that the star image was saturated in the photographic sense of the word, only that the darkness of its inner pixels was beyond the dynamic range of the PDS machine's photoelectric cell. The procedure followed for each plate went like this: A simple density plot of each frame from the plate was obtained. Examples of such density plots are given by figures 3, 5, and 6. These plots were used to sort out the plate's data processing requirements: the frames were categoried as — Single stars — Two overlapping stars — Three overlapping stars — Crowded frame — Saturated star — Defective frame — No star The plots were also used to generate rough coordinates of the centers of each object, good lo + 0.5 pixel in each direction. An estimate of the star's peak flux (ie the largest value any of the star's pixels bear) was also recorded. An examination of the nearly-saturated frames yielded the size of the seeing disc, which was chosen as the aperture size. In the single star case, the program obtained a refined centroid by fitting a circularly symmetric gaussian function' to those pixels within a six pixel radius of the first approximation centroid, using the pixels' natural logarithms for the least-squares 21 evaluation (Fahlman 1982, p. 20). This particular shape was chosen over the alternative —a general quadratic function— because it was thought closer to the expected shape of the pixel intensity distribution; in any case the specific shape chosen is not critical to our results as long as the star image has circular symmetry, since we are only after the star's position. Those pixels outside the newly centered aperture were then used to determine the sky intensity level. The pseudomode —defined as three times the median minus twice the mean— of the sky pixels was computed along with its standard deviation. The median was calculated by sorting the set of pixel values in ascending order and looking up the middle value. Those pixels more than 3.5 standard deviations away from the pseudomode were then rejected, and the process repeated until no further pixels were rejected. An error flag was set if less than half the initial number of sky pixels then remained. The main purpose of the rejection algorithm was to avoid counting another star's fringe pixels as sky pixels. The flux index of the star was then computed as the sum of the intensities of the aperture pixels minus the sky intensity integrated over the same number of pixels, normalized to an arbitrary number of pixels kept the same for all objects on all plates. Note that because of the non-integer centering we made sure the number of aperture pixels was non-integer as well so as to avoid any "quantum effect" which might have arisen at the low flux end had the aperture routines counted in integer numbers of pixels only. In the two overlapping stars case, the brighter star had its center estimated, the sky intensity level surrounding it evaluated, then a point-spread function was fitted to the pixels within a variable radius of its centroid. The radius was chosen so as to vary linearly from four pixels for the faintest objects to the full seeing disc's radius for those approaching saturation, as a function of the logarithm of the net peak flux, as estimated by the centering routine (Ross 1936); that is to say 22 R = 4 + (R - 4 ) L g ( F - F ) (3.1) s e e i n g max sky The pixels outside this variable radius were used for the fit's evaluation of the sky level, using the value found beforehand as a first approximation. The fitted point-spread function was then subtracted from the initial frame, allowing the program to repeat the fit-and-subtract routine on the fainter star. These alternating subtractions and fits were repeated generally three times, after which the two star's parameters were reasonably disentangled. This then allowed the same procedure as for a single star to be applied to the two overlapping stars by subtracting each alternatively from the frame. Figure 3 illustrates the quality typically achieved; one notices the spots occupied by the stars previous to subtraction are now marked by a shallow depression with a central "peak", indicating the individual stars' profiles were sharper than the point-spread function's. The imperfection of the subtraction is sufficiently slight, we believe, that it should not affect seriously the validity of the flux indices thus obtained. The point-spread function was built up from the thirteen or so brightest unsaturated, single stars on the plate. Although some secondary images were quite bright, they were specifically barred from contributing to the point-spread function to avoid any shape effects (Blanco 1982). Each contributing star was centered, using its peak pixel as first approximation, using the same method as outlined in the single star case (see above). Its sky level was then computed and subtracted, and the whole array shifted so as to center it within the frame; finally, the resulting frame was added onto the accumulating point-spread function. Once all the contributing stars were included, the resulting point-spread function was normalized to just short of the saturation point. Finally, a cubic bi-spline was fitted to the empirical point-spread function to supply SUPERTOODEE with an analytical expression of the pixel flux as a function of the pixel position. Figure 4 is a contour plot of the point-spread 23 function profile of plate 16; this particular plate shows the largest departure from circular symmetry of all plates, because of the exceptional seeing it was taken under (see chapter 2) —that the exposure was trailed slightly is readily apparent. The other point-spread funtions are all wider, more spread out (larger seeing discs), and show smaller departures from circular symmetry (if any). In the case of three overlapping images, essentially the same procedure as with two overlapping images was followed. Having three stars overlap, simultaneously or not, complicates matters quite a bit. Indeed, obtaining a new fit to a single of the three stars entails subtracting two others instead of just one. So, wheretofore a loop of the two-star routine involved two fits and two subtractions, now a loop of the three-star routine involves three fits and six subtractions, making the process considerably more computer time consuming. Figure 5 illustrates a typical case, where one bright star complicates the separation of two strongly merged faint images. Near the center of the cluster, a particularly dense group, composed of stars 108 to 113, had to be cast aside because not only of multiple overlaps, which could have been handled, but mostly because of chained overlaps leading beyond the edge of the frame. Figure 6 illustrates the problem quite well. Experience has shown that a point-spread function fit should not be attempted if more than about 25% of a star's pixels are beyond the edge, and is simply impossible if the number of missing pixels is larger than 50%. Whenever a star was saturated, it was excluded from the sample. This also includes the cases where the saturated star was not the main star but simply an overlapper. This has the unfortunate side effect of causing some faint objects, such as XI1, to become unprocessable on the deeper plates because their bright, overlapping companion becomes saturated, and therefore cannot be fitted by the point-spread function any more. 24 1 0 1 5 20 25 ++XX + + + + + + + + : XX + + + + • + + + + ++XX XXXX++++ XX::++:: ++++:;++ :XX :++ ++++++ . X X : : + + : : : : : : + + : : + + X X S B + + + + : + + ; + + + + : + + + + + + + + XX ::::XX++::::XX++++++XX++XX ++++XX++::++::::::++++++&& ::++++++ : :xx++s*XX:: ::++::++::++++++::++ ++:;++++&X++::::::++ ++::++:: :XXXX:: : :::::::XX++XXXX XXXX++ ++ : : ::: :XX: XX++:.XX++++++: + + XX XX: ++::++++ : : ; ++XX++::++xX: :::: :XX::++ ++++XX::++++: ++++++XX++++++:::: ++ :++xx :++::XXXX++>s<:: XX++++ : :++++++XX::aaaa: ::++XX::++XX::XX++::::++ ::::++++++XX++++ XX::::++ :++::++ ++xxXXXXsa::++:: ::::++XX::++++++++ ::XX::++++++:: XXss?XX++XX++::++: + + ++XXaa: :+ + ++XX: : : :sss + +: :++: : : ::++:: : ++: : XX: : ++++++::++++ : ++++ .++++ :++ ::XXXX:: :++ an:: : :++ : + +: + + : XX + + + + + + ++XXXXB5S + + SJS: : ++ .++ . : ::++ :::::++++::++++++++: ++++ :XX::XX::XX::XXXX::XX XX++:: :XX++++ : : : : : :XX:: + +: + + • XXXX:::: ++++++++ ++::++++ XX :XX : ++XX::++ + + + + :++ ma :++++++++++ ++XXXXsssXX: : + + ++aaXX++++::XX ++++ :XX++XXXX++ ++++;•++ :XX: + + ++: : ++ + + :XX: ««?X: :XXj?«f?: + + : : :XX: + + + +: + + :++++++ + + + + + : : : ++: : + + + + + XX + + + + + + + + + + + + ++++++ ++++++ Intensity -45. -27. -9. 9. 27. 45. 63. 81. 99. 117. Pixel . : : : ++ XX an XX Figure 3: TOODEE density plot of frame after DOUBLT For technical reasons, only a 28 by 28 pixel portion of the full 40 by 40 frame is reproduced here. The object near the upper left was star 70, while the one near the lower right was star 69; their peak intensities before treatment were 191 and 453, respectively. This frame is taken from visual plate 327, the first plate in the visual group 2. 25 Figure 4: Point-Spread Function contour plot The point-spread function of plate 16. The contour lines start at the 200 pixel intensity level and follow each other by steps of 200. Note that not all the enure frame is encompassed by the figure, owing to the compact nature of this particular point-spread function. The last contour line is at the 800 level instead of 1000 because this point-spread function was normalized using the peak of its gaussian fit, which is noticeably higher than its actual peak. 26 15 20 25 30 35 40 25 • .XXXX++:: . . . :++XX*sXXXX . : : . . . : : :XXs?sXXXXXXXX: : : . . : : XXXX9 99999XX* a : : : . 20 . : + + ss«XX£$99XXs?£: : : . . . :++XXXXXXXX++ : : . 1 5 . . . 1 0 • • . . . : : : : : 5 . . . • Intensity 0. 65. 130. 195. 260. 325. 390. 455. 520. 585. Pixel . : : : ++ XX an XX 99 Figure 5: TOODEE density plot of TR1PLT situation For technical reasons, only a 28 by 28 pixel portion of the full 40 by 40 frame is reproduced here. The bright object near the center is star 48, while the elongated faint object to the lower right consists of stars X4 (the brighter part) and X3 (the fainter part). This frame is taken from visual plate 327, the first plate in the visual group 2. 27 10 15 20 25 30 35 40 : : : : : : : ; : : : ; : : + + : . : : + + ; : : : : ++:: . : : ; : . ++++++++XXXXXX++:::: : : : ; I : , + + XXXX»«j?«XXJ«siJSis + + + + : : : : . ; 35 i i . + + » K ? W ? W I W I W ? ? + + + + : : . ++>>XX$$9999999999MMXX++: l i X X X X X X 9 9 9 9 9 9 9 9 9 9 9 9 9 9 * * X X : : . ++XX> > $ $ 9 9 9 9 9 9 9 9 9 9 9 9 99MKXX: : • + + 9 9 9 9 9 9 9 9 9 9 9 9 ? 9 ? ? 9 ? ? « x x + + + + 30 + + XX ? 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 S S + + + + : : : XXs???9999999999XX+ + + +: ++««9X99««^^X?SSJ«XX : : : . ++: : ++XXXXasXXXX++++:: : . ; : : : X X ++xxXX++:::::: : : : : : : : 25 : ::++::: : : + + ++::::++++ :++++: : ++: : : : : : ++: : ++++XX++XX: • ++ :++++++++XXXXXXXX++: ++; : : + + + + BJSXX + + + + + + : : + + XXXXSBBSSJS3 + + + + : ++++XX: : : ++++XX++++++: : : : : ++: . X X X X 9 9 9 9 X X X X * * X X 20 •++XXXX++: : : : : : X X : :XXXX++: :++++xx?9999999« *xx++ : ++: .XX ; : + + X X : : : :++++:;H - + + +: : anJ?«999W9?X«»XX : ++: : ++: : : : + + + + £ J S B«XXB«X X X X + + ; I . i : • • « • . ; :++: :++XXXX++: : ++: : : : : : : > :++::++: : : : 1 5 : : : : : ++: * j l l 1 z • • '• : : • * • '- • .++::: • Intensity 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. Pixel . : : : ++ XX an XX 99 Figure 6: TOODEE density plot of the 108-113 crowded region For technical reasons, only a 28 by 28 pixel portion of the full 40 by 40 frame is reproduced here. To bring out the fainter objects, the contrast was increased, making star 108 appear saturated (its peak intensity is actually 480). To the lower right is 110, at mid-bottom is 111, and to the lower left is 112. Stars 109 and 113 lie beyond the edges of the figure (but not the frame), to the lower left and right respectively. This frame is taken from blue plate 330, the second plate in the blue group 2. 28 A very few frames had small "defects". That is to say a speck of dust which happened to be on the plate at the time of the PDS digitizing, or a defective emulsion grain. Luckily, in all cases the defective regions were never more than two or three pixels on the side, and appeared near the edge of the aperture, well away from the star itself. In turn, these stars all belonged in the medium-bright to faint part of the plate population, where the outer rings of the aperture are expected to contribute little signal if any at all. These frames were dealt with by replacing- the defective pixel values with the sky level intensify. This procedure, at worst, would have the effect of very slightly depressing the value of the star's flux index. We believe, however, that such an effect is just loo subtle to affect our results in any detectable way, owing to the above-mentioned considerations. Lastly, there were the cases where no star image could be detected by inspection. These were confirmed by the inability of the centering routine to obtain a solution. These frames were very simply ignored. Note, however, that evidence of absence is not absence of evidence, to paraphrase Albert Einstein; these non-detections put firm upper bounds on those objects' magnitudes. Note however that the absence of a (lux index entry for any object in tables 3 to 5 does not necessarily imply the object was undetectable on the plate in question; these no-entry cases also include saturated objects, and a few objects which were rejected outright for diverse reasons such as excessive pollution by a bright companion or a negative flux index —a phenomenon related to the numerical stability of the sky flux. The tables in Appendix B display the final set of flux indices obtained in the manner previously described. The weights come about as a result of certain stars' multiple appearances on a single plate, this either due to actual redundancy in the frames or to overlapping cases. The previously described algorithms spewed out flux indices for everything they dealt with, but the values for stars having more than a very few pixels missing from their aperture were rejected altogether because of the 29 skewing they would introduce —since fringe pixels are lost first and are the ones with the lowest intensities, losing a star's fringe would cause its mean flux to be overestimated. The aperture photometry approach was preferred over the alternative point-spread-function scaling ratio method initially because of the difference in computing times involved. It later turned out (Chan 1984) that the scaling ratio method somehow does not out-perform the aperture photometry method at the low flux end (although it would allow reduction of saturated images,' being able to ignore the invalid central pixels); thus wc are quite certain that a re-reduction of the digital frames within a point-spread-function formalism would not improve on the current reduction. 30 Chapter 4 DATA REDUCTION: FROM FLUX INDICES TO MAGNITUDES 4.1 THE VIRTUAL PLATES It was suggested by Stetson and Harris (1977) that virtual plates could be generated which would improve the systematic and internal precision of the data. The flux indices from several plates of same emulsion, filter combination, and telescope may be combined into a single set of flux indices of greater weights and improved overall quality. This, happily, applies to the middle three blue plates (328, 330, and 387) and all the visual plates save the first one (16). To quote Stetson and Harris on the method: (1) The deepest plate in each color is taken as defining the "standard" plate in that color and the iris readings from the remaining plates in the same color are transformed to the system of the standard plate. Any stars showing large residuals at this stage (due to plate flaws, intrinsic variability, or measuring errors) can easily be picked out. (...) (2) Following elimination of the large residual objects, the plate-to-plate transformations are repeated and for each star a mean iris reading on the system of the standard plate is computed. (3) Finally, each plate is retransformed to the averaged standard system determined in step (2) and a new mean iris reading for each star is computed. This last step is performed because the average of several plates provides a more precisely determined standard system than any one plate, so that the quality and uniformity of the reductions at every later stage are also 31 improved in general. It: is important to note that carrying out the plate-averaging process before reduction into magnitudes permits the use of all stars in common between plates, rather than only the photoelectric sequence stars. Internal and systematic errors in the subsequent calibration curves are, thus, reduced. Although our flux indices are of a slightly different nature than their iris readings, the method holds true. Taking as master plates the blue plate 330 and the visual plate 327, we proceeded to fit the other plates in each group to the power law At this stage was initiated the use of the logarithm of the flux indices as their weights in any fit. In this particular case, the weight of any datum pair was taken as the sum of the individual pair members' weights. That is to say One expects k to be about 1, failing on the lower side because of reciprocity failure. C takes the brunt of the normalization, representing the ratio of exposure times. The fit was obtained through use of the FORTRAN IV subroutine NL2SNO (Moore 1981). Any object more than three root-mean-square deviations in flux away from the fit was rejected, and the fit repeated until no more rejections occured. Figures 7 to 11 illustrate the fits obtained, highlighting the objects rejected at each step. k F, = CF 2 (4.1) (4.2) 32 Figure 7: Correlation of B plates 328 versus 330 The objects rejected (*) were (topside, top to bottom) 184 and X13, (underside, top to bottom) 106, 99, 151, 100, and 98. . , 1 1 1 1 1 1 1 1 1 1 2.0 2.4 2.6 8.2 9.6 4.0 4.4 4.8 3.2 9.6 6.0 LG(FLUX» B PLATE 330 Figure 8: Correlation of B plates 387 versus 330 The objects rejected (*) were (topside, top to bottom) 83B, 107, and 81, (underside, top to bottom) Xll, 94, 100, and 151. 34 Figure 9: Correlation of V plates 329 versus 327 The objects rejected (*) were (top to bottom) 149 and X15. 35 36 Figure 11: Correlation of V plates 409 versus 327 The objects rejected (*) were (top to bottom) 162, X15, and X9. 37 Noie thai that because the rejection criterion was in flux but the display is in log(flux), the "rejection envelope", so to speak, would appear to hug the fit very closely at the high flux end and then fan out quite strongly at the low flux end. The fit parameters were, as follows: 0 . 9 6 5 1 0 4 F = 1 . 4 4 0 0 7 8 * F ( 4 . 3 ) 3 3 0 3 2 8 root-mean-square deviation (in Lg(flux)) = 0.1.12 0 . 9 1 3 8 8 9 F = 3 . 1 7 9 6 9 7 * F ' ( 4 . 4 ) 3 3 0 3 8 7 root-mean-square deviation = 0.129 for the blue group, and 1 . 0 0 0 9 0 0 F = 3 . 5 7 5 3 4 8 * F ( 4 . 5 ) 3 2 7 3 2 9 root-mean-square deviation = 0.166 0 . 9 1 2 9 3 8 F = 5 . 9 0 0 3 1 6 * F ( 4 . 6 ) 3 2 7 3 8 6 root-mean-square deviation = 0.088 0 . 6 6 4 8 0 3 F = 1 2 9 . 1 9 8 0 3 8 * F ( 4 . 7 ) 3 2 7 4 0 9 root-mean-square deviation = 0.101 for the visual group. 38 A temporary virtual plate was then constructed, composed or the weighted mean of the transformed plates in each group, but including only the objects common to all the group members, and excluding any objects rejected in the first set of correlations. That is to say plates 328 and 387 were transformed to the system of plate 330 according to the above-described procedure, and the weighted mean of this triple set of numbers was taken as the temporary virtual plate. A similar procedure was conducted with the visual plates. Figures 12 to 18 illustrate this second step. 39 1 1 1 1 1 1 1 1 1 1 2.0 2.4 2.6 3.2 9.6 4.0 4.4 4.8 9.2 3.6 6.0 LGlFLUX) MEAN B GROUP 2 Figure 13: Correlation of B plate 330 versus mean group 2 No objects were rejected. 41 42 I 1 1 1 1 1 1 1 1 1 i .0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 8.6 6. LG(FLUX) MEAN V GROUP 2 Figure 15: Correlation of V plate 327 versus mean group 2 The rejected objects (*) were (top to bottom) 106 and 95. 43 Figure 16: Correlation of V plate 329 versus mean group 2 The rejected objects (*) were (top to bottom) 155 and 81. 44 45 .0 Figure 18: Correlation of V plate 409 versus mean group 2 No objects were rejected. 46 The entire group, including the master plate, was then transformed to the system of the temporary virtual plate. For ease of data processing, the transformed groups were not fused into a single-entry-per-object virtual plate; they were instead kept in the form of a virtual plate with several entries per object. Note that, of course, no object was excluded from the final virtual plate. The fit parameters were as follows: 0.969584 F = 1. 375347*F (4.8) mean 328 root-mean-square deviation (in Lg(flux)) = 0.061 1 .004578 F = 0.951824*F (4.9) mean 330 root-mean-square deviation = 0.067 0.911783 F = 3.242394*F (4.10) mean 387 root-mean-square deviation = 0.071 for the blue group, and 1.014035 F = 0.845592*F (4.11) mean 327 root-mean-square deviation = 0.030 0.907460 F = 8.544253*F (4.12) mean 329 root-mean-square deviation = 0.038 47 0.885735 F = 7.64 1143*F (4.13) mean 386 root-mean-square deviation = 0.027 0.699881 F = 94.877497*F (4.14) mean 409 root-mean-square deviation = 0.046 for the visual group. Note how, as predicted by Stetson and Harris (1977), the root-mean-square deviations for the second set of correlations have fallen with respect to the first set. In the blue, the mean r.m.s. deviation fell from 0.099 to 0.066; in the visual, from 0.107 to 0.036. Of course, a good fraction of the improvement is to be imputed to the restricted sample involved in the second set of correlations; this is especially true for the visual group. Once this process was concluded, one was left with the same two ultraviolet plates, a new set of three blue plates (composed of the old plates 10 and 410, and the new, virtual plate), and a new set of only two visual plates (old plate 16 and the new, virtual plate). From this point on, the plates, real or virtual, are going to be referred to as groups. Thus one has ultraviolet groups 1 (plate 12) and 2 (plate 334), blue groups 1 (plate 10), 2 (the virtual blue plate) and 3 (plate 410), and visual groups 1 (plate 16) and 2 (the virtual visual plate). Tables 11 and 12 in Appendix B give the object entries for the blue and visual virtual plates respectively. For ease of recognition, the multiple entries are tabulated as if the component plates were still separate. A more correct way of looking at the numbers is to consider each column as an independent plate-to-flux-indices reduction of the same plate. That is to say, we would have obtained qualitatively indistinguishable results if we had digitized the same plate several times, then obtained flux indices independently 48 for each set of digital arrays —save that instrumental variations would actually be larger if this hypothetical procedure was followed (drift of the PDS machine's response characteristics). 49 4.2 CALIBRATION THEORY Now begins the other part of the work: transforming the flux indices into magnitudes. Table 3 gives the entire set of photometric standards we had to work with. 1(1 Whenever two sources were available, we gave priority to: first, Sandage (1972), second, Handschel (1972), third, Blanco et al. (1955), and fourth, anything else. The photoelectric sequence of Sandage (1972) does not contain any ultraviolet magnitudes; whenever possible, this lack was corrected with the values of Handschel (1972). It was decided to include the color terms in the calibration itself, thus eliminating any intermediate steps. This is in the same spirit as the consolidation of several plates into a single virtual plate; it should reduce internal errors somewhat and increase consistency. We shall assume that the equation C = a + b L g ( F ) (4.15) i C i holds. That is to say, the magnitude of any object in a plate's color is a linear function of the logarithm of that object's flux index on the same plate. The task at hand is then to relate two ultraviolet colors, three blue colors, and two visual colors to the standard UBV colors. , ( lIt should be mentioned in passing that recently Vardanyan and Akhverdyan (1975) have measured 186 faint objects in and around NGC 7419 in the infrared; they claim (R-I) to an accuracy of ±0.5 magnitudes. Their objects' faintness in the infrared, combined with the known high reddening of the cluster, leads one to expect very little overlap between their object list and ours; as a consequence, we did not obtain their list, thinking it would be of too limited use to be of any help. The matter might be of interest to other researchers, however. 50 TABLE 3 Photometric Standards Object U B V Sou: 1A 8.02 7.50 1 2A 9.50 2 3A 8.88 8.62 3 4A 15.75 15.26 13.59 4 6 16.98 16.73 15.17 4 10A 14.53 14.27 13.41 3,4 11A 12.90 12.54 1.1.82 3,4 12 17.93 16.25 4 13 17.71 17.62 16.04 4 15 17.64 17.60 16.13 3,4 16 17.62 16.17 4 18 17.86 16.49 4 19 16.86 • 16.70 1.5.38 4 22 .17.68 16.19 4 28 17.05 15.07 4 29 18.07 16.65 4 30 19.27 17.55 3 32A 16.09 15.66 13.97 3,4 34 19.08 17.24 3 37A 16.85 15.98 14.85 4 40 17.17 13.77 3 42 16.99 16.52 14.81 4 R = 7.15 1 = 7.18 Sp = A2m (1) B = 8.75 V = 8.55 R = 8.42 1 = 8.55 Sp = A5 (1) R = 12.U 1 = 9.55 Sp = M3.5 (1) 51 TABLE 3 Photometric Standards Object U B V Soui 44A 15.17 15.04 14.31 4 46 17.48 16.38 4 50 19.19 17.53 3 54 17.22 16.94 15.37 4 59 17.84 16.12 3 60A 16.04 15.92 14.96 3,4 61 17.97 16.53 4 62 17.80 16.15 4 65 16.36 16.32 15.45 4 66 18.02 16.58 4 73 18.99 17.10 3 75 18.10 16.51 4 81 17.74 17.52 16.03 4 83A 13.17 11.82 10.57 3,4 84A 16.60 16.10 14.46 4 87A 16.00 15.56 14.03 4 88A 15.85 12.48 4 89 17.21 16.85 15.32 4 91 17.23 16.87 15.45 4 92 17.86 16.36 4 93 17.11 16.81 15.25 4 96A 15.61 15.28 13.65 4 B = 11.78 V = 10.6 Sp = G5 (1) R = 11.23 1 = 8.78 (1); Sp = M2Iab (5) Balmer line emission; Sp = OBIa(?) (6) 52 TABLE 3 Photometric Standards Object U B V Source Comments 97 16.17 16.02 14.57 4 103 17.36 17.36 15.69 3.4 106 17.63 17.36 15.84 4 107 17.62 17.36 15.84 4 119A 16.30 15.89 14.26 4 122 17.65 17.75 16.09 4 125 16.28 15.98 14.35 4 126A 15.07 14.63 12.98 4 Sp= "Early B" (5) 130A 16.06 12.49 4 R = 11.12 1 = 8.80 (1); Sp = M2Iab (5) 131 17.65 16.21 4 132A 15.98 15.74 14.19 4 133 16.59 16.40 15.04 4 134A 15.39 15.09 13.70" 4 137 17.62 17.33 16.07 4 141 16.14 15.74 14.31 4 142 17.04 16.84 15.34 4 144 16.10 15.89 14.30 4 145 16.16 15.90 14.28 4 147 17.17 17.01 15.74 4 148 17.11 17.01 15.74 4 152 17.01 16.92 15.65 4 153 16.75 16.72 15.25 4 154 17.16 17.09 15.85 4 53 TABLE 3 Photometric Standards Object U B V Source Comments 155 17.01 16.93 15.44 4 156 16.87 16.56 14.94 4 158 17.88 17.66 16.19 4 159A 15.55 1.5.46 13.98 4 162 16.90 16.70 15.29 4 163A 16.39 16.30 14.79 4 165 17.50 17.33 16.04 4 171 18.06 16.35 4 172A 16.21 12.98 3 R = 11.39 1 = 9.29 (1); Sp = M21ab (5) 173 17.07 17.15 15.53 4 174 18.00 16.53 4 176 18.09 16.66 3 179A .16.22 15.99 15.11 4 181 17.1.0 .16.71. 14.95 4 183A 15.81 15.46 13.98 4 184 18.16 16.44 4 185 16.65 16.30 15.23 4 186 17.60 16.99 15.81 4 187 17.49 16.37 4 188 16.45 16.44 15.26 4 191 17.72 17.16 16.27 4 192A 15.66 15.19 14.31 4 194 18.37 14.48 3 R = 12.68 1 = 10.3 Sp = N (1) TABLE 3 Photometric Standards Object U B V Source Comments 196 16.12 15.74 14.05 4 198 17.65 16.10 4 199 17.79 16.34 4 203 17.34 15.97 3 204A 13.94 13.65 12.97 3,4 206 . 18.78 16.02 3 208 18.58 16.43 3 211 16.47 16.10 14.50 3,4 213 17.38 17.23 16.01 4 214 17.48 17.26 15.90 4 X19 20.18 18.38 3 218 16.41 16.44 15.19 3,4 219 16.14 15.63 14.54 4 220 18.60 17.44 3 225A 15.83 15.48 14.49 4 227A 15.27 14.83 13.49 4 230 16.91 16.80 15.44 3,4 231 17.46 17.23 15.97 4 References: 1: Blanco, Nassau, Stock, and Wchlau 1955 2: Aitken 1932 3: Sandage 1972; photoelectric values 4: Handschel 1972; photographic values 5: Fawley and Cohen 1974 6: Moffat 1980 55 For any single set of pseudo-colors u, b, and v. the following relations (Henden and Kaitchuck 1982, p. 91) should hold: V = e(B-V) + v + $ (4.16) v (B-V) = u(b-v) + § (4.17) bv (U-B) = i^(u-b) + $ (4.18) ub inserting u = a + 6" Lg (F ) (4.19) u u u b = a + (3 Lg(F ) (4.20) b b b v = a + j3 Lg(F ) (4.21) v v v and working the equations a bit, one is left with U = 7Lg(F ) + SLg (F ) + 7?Lg(F ) + 9 u b v B = KLq (F ) + rjLq (F ) + £ b v V = pLg(F ) + 0Lg(F ) + r b v Note that the initial twelve parameters ( e , $ . u , $ , ^, $ , v bv ub a , a , a , j 3 , j 3 , | 3 ) have been condensed into only nine ( 7 , 6 , 7 7 , u b v u b v Q, K- 1 it Pr <t>, f). Note, as well, that the U and B equations share the (4.22) (4.23) (4.24) 56 parameter n, and that the B and V equations are independent of the U flux index. To solve, one must simultaneously minimize the three sums of the squares f = I w {jLq (F ) + 5Lg(F ) + r?Lg(F ) + 6 - U } 2 (4.25) u ubv u b v i i i i i f = I w {/cLg (F ) + rjLgCF ) + £ - B } 2 (4.26) b bv b v i i i i f = 2 w {pLg (F ) + 0 L g(F ) + r - V } 2 (4.27) v bv b v i i i i where the weights are defined as w2 = w 2 + w 2 + w 2 f 4_ 2 8) ubv u b v ; 2 = w2 + w2 (4.29) bv b v w = L g ( F ) (4.30) u u i i w = L g ( F ) (4.31) b b i i w = Lg (F •) (4.32) v v i i In practice, because of repeated entries (virtual plates and some single-plate cases where an object was digitized more than once), the tack was slightly different: 57 the flux indices were averaged using the simple weighing scheme of tables 8 to 12 (see Appendix B) (that is, the weight was taken as one-half, one, one and a half, or two), and then the weight in the calibration scheme was defined as the logarithm of the average flux, times the total weight in the tabulation scheme. We are dealing with two different samples of stars, the first one composed of those with known standard magnitudes in all three colors, U, B, and V, and the second one composed of those with known standard magnitudes in B and V only. The first sample is necessary for the ultraviolet solution, and the second one sufficient for the (simultaneous) blue and visual solutions. Since it turns out the population of the first sample is considerably less than that of the second one because of a lesser number of standards (see table 3) as well as because of the relative shallowness of the ultraviolet plates (see table 8), it was decided to solve the system in two parts. First the blue and visual solutions would be obtained, then the parameter TJ would be used in the ultraviolet solution as a known quantity; this was expected to worsen the fit less than the alternative, which was to solve all three colors with the first sample only. 58 Expressed in matrix form, the BV solution is ^ b v . V ^ b . * Iw, V.Lq(F ) bv. 1 ^ v . l l Iw, V. bv. I l l l Z w b v L 9 ( F K ) Lg( F„ ) £ w h „ L g ( F K ) v. bv 0 ^ b v . ^ b . ^ V * ^ b v . ^ V * ^ b v . ^ ^ b . ) I w b v . L 9 ( F , Iw, Lg(F ) bv. = v. I l Iw bv 59 and Zw, B . Lq ( F, bv . 1 ^ b. Zw, B . Lg ( F ) bv. 1 ^ v. l l Zw, B. bv. I l ^ b v . ^ ^ b . ) l l 2 w b v . L 9 ( F b . ) L 9 ( F v . ) ^ b v . ^ b . * l i i l l ^ b v . ^ ^ b . ^ g ^ v . ) Z w b v . L 9 2 < F v . > l l l l l Zw b v_Lg(F^ ^ b v . ^ ^ b . ) l l Zw bv where, of course, the matrices remain to be inverted. 60 The ultraviolet solution is then £ w u b v . { U i L 9 ( F u . ) " ^ g ( F )Lg(F )} 1 1 1 1 Iw , {U.Lg(F, ) - r?Lg(F, ) Lg (F )} ubv. I 3 b. ' ^ b . ^ v . Iw , {U. - rjLg (F ) } ubv. I ' ^  v. l l Iw , L g 2 ( F ) ubv . ^ u . I l ^ u b v . ^ ^ u . ^ g ^ b ^ ^ u b v . ^ ^ u ^ Iw , Lg ( F )Lg (F, )Iw , L g 2 (F, ) nh\7 ^ n K ubv. b-1 1 Iw , Lg(F, ) ubv. ^ b . Iw , Lg (F, ) ubv. ^ b. Iw , Lg(F ) ubv. ^ u. l l Iw ubv where, again, the matrix remains to be inverted. The problem with such a multi-color lit is that because of the number of colors initially available (seven), there are no less than six BV solutions and twelve U solutions! However, the lure of large-number statistics whittles the number of choices down. Of the three blue colors, group 2 stands out with its much larger number of entries; it carries considerably more weight. Similarly, the visual group 2 dwarfs its companion group 1 in importance. Thus we decided to limit the number of calibrations to five: 1. Ultraviolet group 1 was calibrated against blue group 2 and visual group 2 2. Ultraviolet group 2 was calibrated against the same selection 3. Blue group 1 was calibrated against visual group 2 —remember that the 61 blue and visual calibrations are ultraviolet.-independent 4. Blue group 2 was calibrated against visual group 2 —this was accomplished in the same computer run as the ultraviolet group 1 calibration 5. Blue group 3 was calibrated against visual group 2 6. Visual group 1 was calibrated against blue group 2 7. Visual group 2 was calibrated against blue group 2 —again, in the same computer run as the ultraviolet group 1 calibration Figures 19 to 25 illustrate our results. 62 THEORETICAL U HHGNITUOE Figure 19: Calibration of U group 1 63 Figure 20: Calibration of U group 2 Figure 21: Calibration of B group I Figure 2 2 : Calibration of B group 2 66 Figure 23: Calibration of B group 3 67 Figure 24: Calibration of V group 1 68 O Figure 25: Calibration of V group 2 69 4.3 THE SECONDARY IMAGES The role played by the secondary images consists of strengthening the low flux index end ol' the calibration curves as well as boosting the number statistics of the calibration overall. The Racine prism (Racine 1969) used at the Observatoire Astronomique du Mont Megantic was designed to generate secondary images dimmer by 4.00 magnitudes (in V) and separated by 23" from the primary images when used in conjunction with the observatory's 160cm telescope. It has an overall diameter of 233.4 mm, is 26.4 mm thick, while the prism proper is of fused silica, with a wedge angle of 50.4", and with its faces Hat to X/4 (Racine 1978). The major part of the magnitude differential comes from the ratio of the apertures between prism and telescope; however, the transmittivity of the prism also enters the equation, so that a slight dependence of Am on the observing color is expected. But that is not where caution stops! The prism's exact location in the incident beam is also expected to have a noticeable effect on the value of Am ; this is because the beam emergent from the prism strikes only a part of the primary mirror. Hence any non-uniformities in the primary mirror are going to affect the secondary-images. Also, the focal ratios of the prism and telescope are vastly different —1755 and 178 respectively—, thus it is crucial that the focus be as accurate as possible. For all these reasons, the secondary images were treated with circumspection. They were excluded from the point-spread functions as their structure is expected to differ from the primary images (Blanco 1982), all the calibrations were done without as well as with their contribution so as to spot any troublesome effects, and the value of Am was left as a free parameter in all cases (as Christian and Racine (1983) recommended recently). Tests were run with a second-order relation between the magnitudes and the logarithms of the flux indices. In the light of these tests, it is necessary to point out that the free parameter used was not Am proper, but the logarithm of the ratio of the flux indices between primary and secondary image. If 70 m = a + b L g ( F ) (4.33) then Am - b L g ( F ) - b L g ( F ) (4.34) A B Am = b L g ( F /F ) (4.35) A B but if m = a + b L g ( F ) + c L g 2 ( F ) (4.36) then Am = (b + 2 c L g ( F ) ) L g ( F /F ) - c L g 2 ( F /F ) (4.37) A A B A B which has a direct dependence on the .flux index of the primary image. Of course, (4.37) can be inverted to give Lg(F /F ) as a function of the fixed Am . The tests A B revealed that the effect of the introduction of the secondary images was always a dramatic straightening of the curve, thus indicating that the lower root-mean-square deviations obtained with a second-order fit were contrived, being entirely due to the extra degree of freedom provided by the coefficient c. Hence we adopted equation (4.33), and thus Am and Lg(F /F ) are equivalent, as (4.35) shows. A B Use of the known quantity Lg(F /F ) instead of the unknown Am allows A B one to incorporate the secondary image data into the fits readily. We evaluated the weighted mean of Lg(F /F ) in each color over all pairs for which both flux indices A B were available; standard magnitudes did not have to be known, allowing the use of a much larger sample than if they had. The entire set of secondary images for which the primary's magnitudes were known could then be used in the fit by replacing their log(flux) entries with Lg (F ) + <Lg(F /F )> (4.38) B A B These "artificial" primary (lux indices were, of course, weighted using their original, 71 unboosted values. Note that it was not necessary for the primary images' flux indices to be known, in effect extending the calibration at the high end if the primary images were saturated. The assumption or constant Lg(F /F ) v/as tested by examination of figures 26 A B to 29, which illustrate the observed sets of Lg(F /F ) values; no hint of any A B dependence on the primary's (lux, as would have been expected had the calibration curve not been linear, was detected. The scatter in Lg(F /F ) is large, though. Harris and Racine (1974) obtained, A B for an apparatus closely related to the Racine prism, a scatter in AB so low that they were able to establish a functional relationship between it and the (B-V) color index; their scatter was 0.02 magnitudes for a relation stretching over 1.9 magnitudes in (B-V). In contrast, our scatter is equivalent to, depending on the particular group, between 0.2 and 0.6 magnitudes over 1.1 magnitudes (excluding the M supergiants)! There was no point in trying to duplicate Harris and Racine's correction factors, as the graph is patternless, uniformly sprinkled with points. In any case the expected corrections would be so small (0.05 magnitudes or less) as to make no difference at all. This scatter is no doubt due to the fixed aperture used during the TOODEE processing; faint objects did tend to have their fluxes appear as a small difference between two large numbers (the total flux and the expected sky flux). This is of course a very dangerous situation, numerically unstable. It would have been interesting to compare these results with those one could obtain using standard iris photometry-techniques. It seems we chose a large, random scatter over a smaller, systematic scatter; 1 would tend to think the latter might have been preferable after all, since it could have been corrected for at least in part. Nevertheless, the agreement between the values found for Am and the predicted 4.00 is excellent: Ultraviolet group 2 Blue group 2 Blue group 3 Visual group 2 Observed Am 3.810 4.084 4.011 4 . 08 1 r.m.s. deviation 0.218 0.420 0.246 0. 576 _j , 1 1 1 1 1 1 1 1 I 4.0 4.13 4.8 4.43 4.8 4.73 4.9 3.03 3.7 3.83 3. U' LG(Ffl) Figure 26: Lg(F /F ) for U group 2 A B The sample is too small to warrant comment 74 e o CD O (9 <S> -ft Q o <5 1 1 1 1 1 1 1 1 1 I 4.0 4.13 4.8 4.43 4.6 4.73 4.9 3.03 3.2 3.83 3.3 B ' LG(pH) Figure 27: Lg(F /F ) for B group 2 A B Note, as expected, the conical envelope (axis along mean Lg(F./Fg) line, apex on the high Lg(F^) side). There is no systematic difference between the contributions of the different plates belonging lo the group. 75 O — — cr o „ , R . . T 1 1 1 ~" 7 7 . 7 . 2 < a 4.8 4.73 4.9 3.03 3.2 3.83 3.3 4 » A i A t B ' l M f l ) Figure 28: Lg(F /F ) for B group 3 A B 76 O o _Q O O O O O O , 1 1 1 1 1 1 1 1 I I 4.0 4.13 4.3 4.40 4.8 4.73 4.0 3.03 3.2 3.83 3.3 V L G l F R ) Figure 29: Lg(F /F ) for V group 2 A B There is no systematic difference between the contributions of the different plates belonging to the group. 77 4.4 CALIBRATION RESULTS The calibrations found were Ultraviolet group 1 U = 27.888219 - 1.849807Lg(F ) - 0.559089Lg(F ) - 0.308683Lg(F ) (4.39) ul b2 v2 r.m.s. deviation = 0.169 maenitudes Ultraviolet group 2 U = 29.059030 - 1.254033Lg(F ) - 1.440476Lg(F ) - 0.308683Lg(F ) (4.40) u2 b2 v2 r.m.s. deviation = 0.215 magnitudes Blue group 1 B = 30.785504 - 2.446742Lg(F ) - 0.760740Lg(F ) (4.41) bl v2 r.m.s. deviation = 0.179 magnitudes Blue group 2 B = 30.654326 - 2.995999Lg(F ) - 0.308683Lg(F ) (4.42) b2 v2 r.m.s. deviation = 0.203 magnitudes Blue group 3 B = 29.831006 - 2.942091Lg(F ) - 0.272089Lg(F ) (4.43) b3 v2 r.m.s. deviation = 0.196 magnitudes Visual group 1 V = 32.184752 - 0.568251Lg(F ) - 3.061888Lg(F ) (4.44) b2 vl r.m.s. deviation = 0.120 magnitudes 78 Visual group 2 V = 30.912374 - 0.282209Lg(F ) - 3.111401 Lg(F ) (4.45) b2 v2 r.m.s. deviation = 0.327 magnitudes If one compares the r.m.s. deviations of the calibrations before and after adding the secondaries, one can gauge the "worsening" effect of the large Am scatter: Before After Ultraviolet group 1 0.171 0. 1 69 Ultraviolet group 2 0.201 0.215 Blue group -1 0. 1 74 0. 179 Blue group 2 0 . 1 57 0.203 Blue group 3 0.162 0. 1 96 Visual group 1 0. 1 20 0.120 Visual group 2 0.120 0.327 The three group ones appear, although they have no secondary images, because of the secondaries' effect on the group(s) they were calibrated against. For example, ultraviolet group 1 has no secondaries, but since blue group 2 and visual group 2 do, the sums involved in the solution are altered somewhat by their introduction and therefore the lit is also affected. The seemingly huge increase in the r.m.s. deviation for visual group 2 is an artefact of the change in the calibration; in fact the r.m.s. deviations of the logarithms of the fluxes increased by about the same amount for blue group 2 and visual group 2, but the change in the calibration parameters "transferred", so to speak, most of the increase to the visual magnitudes. The V formula for visual group 2 without the secondaries was 79 V = 30.690643 - 0.120985Lg(F ) - 3.201981 Lg(F ) (4.46) b2 v2 As one can see, the addition of the secondaries increased the importance of the blue group 2 fluxes considerably, thus explaining in part the remarkable r.m.s. deviation inflation. It is of interest to compare the r.m.s. deviations of the blue and visual group 2 calibrations with those which one can predict from the correlation results. Assuming there are no cross-correlations, then (Bevington 1969, p. 60) K 2 O 2 b2 Lg(F ) b2 + r\2 a2 Lg(F ) v2 (4.47) and p2o2 + 4>2o2 V v2 Lg (F ) b2 Lg (F ) v2 (4.48) thus one predicts, for blue group 2, an r.m.s. deviation of 0.298, and for visual group 2, 0.333; this using the root-mean-square of the r.m.s. deviations of the first step of the correlations, which is a more representative sample (because it is much larger). The agreement is close, indicating very little of our calibration scatter is due to systematic errors in the sequence of standards. Table 4, which follows, lists the weighted mean of all the magnitudes obtained by applying the calibrations to the aforementioned color group combinations. That is, the U magnitudes, for example, are the weighted mean of the ultraviolet group 1 magnitudes (calibrated against blue and visual groups 2) with the ultraviolet group 2 magnitudes (calibrated against the same selection of groups). The color indices were obtained by simple subtraction of the appropriate magnitudes, the weights being added. 80 TABLE 4 Raw Photometry Object Magnitude Color Index Weights U B V U-B B-V U B V U-B B-V 2A 11.791 11.077 10.079 0.714 0.998 5.47 5.85 12.32 11.32 18.17 4A 15.701 15.437 13.605 0.264 1.832 4.14 36.12 25.74 40.26 61.86 5 18.363 16.935 1.428 18.32 20.94 39.26 6 17.002 16.762 15.177 0.240 1.585 3.70 20.75 14.04 24.45 34.79 7 18.223 16.687 1.536 18.51 21.31 39.82 9 18.634 17.004 1.629 17.85 16.71 34.56 10A 14.812 14.382 13.433 0.430 0.949 9.21 29.14 25.87 38.35 55.01 I1A 13.343 12.582 11.860 0.761 0.722 9.76 21.70 22.52 31.46 44.22 X2 19.097 17.669 1.427 17.15 15.91 33.06 12 18.132 18.0.10 16.298 0.122 1.712 6.77 18.80 21.91 25.57 40.71 13 17.900 17.793 16.172 0.107 1.621 6.94 19.18 22.09 26.12 41.27 14 19.145 16.883 2.262 16.92 21.19 38.11 15 17.937 17.760 16.312 0.177 1.448 . 6.88 19.24 21.84 26.12 41.08 16 17.784 17.581 16.200 0.203 1.381 7.01 19.54 22.00 26.55 41.54 18 18.106 17.954 16.601 0.152 1.353 6.73 18.97 21.40 25.70 40.37 19 16.861 16.724 15.398 0.137 1.326 3.93 20.86 18.43 24.79 39.29 20 18.717 17.329 1.387 17.77 16.29 34.06 21 19.029 19.312 17.720 -0.283 1.592 3.09 16.79 15.87 19.88 32.66 22 18.025 17.930 16.388 0.095 1.542 3.47 18.98 21.75 22.45 40.73 23 21.826 19.483 18.009 2.343 1.474 1.62 16.57 15.53 18.19 32.10 24 18.756 17.274 1.482 17.69 16.39 34.08 25 18.801 18.742 17.212 0.059 1.530 3.15 17.70 20.53 20.85 38.23 81 TABLE 4 Raw Photometry Object Magnitude Color Index Weights U B V U-B B-V U B V U-B B-V 26 18.116 18.574 16.897 -0.458 1.676 3.49 17.93 16.86 21.42 34.79 27 19.605 19.702 17.935 -0.097 1.767 2.84 16.16 15.67 19.00 31.83 28 17.275 17.067 15.068 0.208 1.999 3.73 20.19 18.90 23.92 39.09 29 18.617 18.323 16.676 0.294 1.648 3.20 18.34 21.36 21.54 39.70 30 19.281 17.692 1.589 16.89 15.96 32.85 31 18.957 19.003 17.499 -0.046 1.504 3.09 17.28 16.10 20.37 33.38 32A 15.985 15.733 13.845 0.253 1.888 8.32 31.19 25.41 39.51 56.60 33 18.459 18.722 16.803 -0.264 1.920 6.59 17.62 21.18 24.21 38.80 34 20.148 19.177 17.209 0.971 1.968 2.46 16.92 16.53 19.38 33.45 35 18.326 17.917 16.029 0.410 1.887 6.58 18.91 22.38 25.49 41.29 36 18.377 18.543 16.504 -0.165 2.039 6.67 16.08 21.69 22.75 37.77 37A 16.536 16.062 14.983 0.474 1.079 7.82 30.71 18.89 38.53 49.60 38 19.214 19.311 17.465 -0.097 1.846 3.00 16.76 1.6.24 19.76 33.00 39 19.648 19.093 17.559 0.555 1.534 2.75 17.19 16.08 19.94 33.27 40 19.270 17.168 13.785 2.102 3.383 2.60 19.72 5.15 22.32 24.87 41 19.183 19.369 17.368 -0.186 2.001 3.01 14.94 6.15 17.95 21.09 42 16.820 16.493 14.690 0.327 1.803 7.62 18.94 4.83 26.56 23.77 43 19.173 19.737 17.884 -0.564 1.852 3.06 16.04 15.71 19.10 31.75 44A 15.342 15.164 14.393 0.178 0.771 8.92 37.07 9.77 45.99 46.84 45 19.762 17.857 1.906 16.08 7.97 24.05 46 17.728 17.457 16.240 0.271 1.216 6.98 19.75 1.3.19 26.73 32.94 47 18.625 18.675 16.973 -0.050 1.702 3.23 17.81 12.60 21.04 30.41 82 Object Magnitude U B V TABLE 4 Raw Photometry Color Index U-B B-V U Weights B V U-B B-V 48 X4 X3 49 50 51 52 53 54 55 56 58 59 60A 61 62 63 64 65 66 67A 68 17.616 19.333 18.469 19.167 17.279 18.017 16.115 18.103 17.947 18.898 16.475 18.679 16.322 19.646 17.080 18.986 19.143 19.530 19.124 19.582 18.739 18.730 16.987 19.263 19.311 20.101 17.876 15.929 17.900 17.624 18.688 18.774 16.327 18.124 16.044 19.919 16.044 17.094 17.540 16.718 17.580 18.042 17.289 17.093 15.408 17.664 17.964 17.939 16.127 15.106 16.455 16.260 17.040 17.313 15.310 16.594 15.108 17.764 0.536 -0.197 -0.270 0.437 0.292 0.141 0.187 0.203 0.322 0.124 0.148 0.555 0.278 -0.273 1.036 1.892 1.603 2.811 1.544 1.540 1.450 1.637 1.579 1.599 1.347 2.162 1.749 0.823 1.444 1.364 1.648 1.460 1.017 .1.530 0.936 2.155 6.84 2.87 3.34 2.96 7.30 6.75 8.30 6.72 6.74 3.11 8.03 3.14 8.10 2.83 20.41 17.13 15.31 15.94 17.09 16.41 17.74 17.71 20.41 16.90 16.85 15.45 18.98 35.49 19.04 19.48 17.73 17.66 21.56 18.67 30.79 15.75 11.12 8.39 8.10 12.91 16.03 15.51 16.38 20.76 18.45 15.96 15.57 15.73 22.15 23.39 21.63 21.89 16.66 16.34 18.49 21.44 18.73 15.93 27.25 18.81 21.08 20.67 27.71 25.73 43.79 25.76 26.22 20.77 29.59 21.81 38.89 18.58 31.53 25.52 23.41 28.85 33.12 31.92 34.12 38.47 38.86 32.86 32.42 31.18 41.1.3 58.88 40.67 41.37 34.39 34.00 40.05 40.11 49.52 31.68 83 Object Magnitude U B V TABLE 4 Raw Photometry Color Index U - B B-V U Weights V U - B B-V 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83A X6 84A 85 86 87A 88A X7 18.430 19.736 19.094 19.376 18.890 18.755 18.783 18.422 17.828 19.372 18.305 17.600 17.722 12.877 19.126 16.418 17.548 19.229 15.944 18.015 18.944 18.264 19.054 I. 8.468 19.718 18.595 18.827 18.232 18.256 17.490 17.866 19.171 18.747 17.294 17.590 II. 567 19.598 16.062 16.916 19.125 15.593 1.5.802 18.560 16.518 17.447 16.987 17.991 16.710 17.229 16.532 16.665 16.154 16.594 17.475 17.004 15.819 16.065 10.298 16.996 14.572 15.383 17.393 14.188 12.834 17.184 0.166 0.682 0.626 •0.342 0.295 -0.072 0.551 0.165 0.338 0.201 -0.442 0.306 0.131 1.310 -0.472 0.356 0.632 0.104 0.351 2.213 0.384 1.746 1.607 1.481 1.727 1.885 1.598 1.700 1.591 1.337 1.272 1.695 1.743 1.475 1.525 1.269 2.603 1.490 1.533 1.732 1.405 2.968 1.377 6.47 2.71 2.97 2.95 3.06 3.19 6.08 6.49 3.40 2.89 3.44 7.04 7.08 9.62 3.05 7.99 7.02 2.98 8.31 3.1.0 3.09 16.50 17.21 18.14 16.12 17.83 17.57 18.45 18.45 19.67 19.08 17.00 17.65 19.94 17.49 22.87 16.13 30.60 20.54 17.07 31.61 30.70 18.00 21.60 16.25 16.73 15.57 21.32 12.38 21.58 17.11 19.84 15.00 14.18 20.94 18.07 15.60 18.31 21.06 19.43 13.87 16.31 24.82 21.64 8.27 22.97 19.92 21.11 19.07 20.89 20.76 24.53 24.94 23.07 19.89 21.09 26.98 24.57 32.49 19.18 38.59 27.56 20.05 39.92 33.80 21.09 38.10 33.46 34.87 31.69 39.15 29.95 40.03 35.56 39.51 34.08 31.18 38.59 38.01 33.09 41.18 37.19 50.03 34.41 33.38 56.43 52.34 26.27 84 Object Magnitude U B V TABLE 4 Raw Photometry Color Index U - B B-V U Weights B U-B B-V 89 X8 90 91 92 93 94 95 96A X9 97 98 99 100 101 102 103 104 105 106 107 114 16.940 19.230 18.844 17.247 18.042 17.059 17.405 17.825 15.617 16.224 17.899 18.992 17.321 19.067 19.026 17.112 17.234 18.208 16.834 19.387 19.206 16.997 18.062 16.814 17.265 17.344 15.328 18.583 15.994 18.451 17.806 18.130 18.753 19.025 16.983 19.195 19.353 16.950 16.942 18.188 15.284 18.043 17.480 15.402 16.354 15.183 15.668 15.947 13.562 16.395 14.493 17.258 16.288 16.564 17.490 17.518 15.302 17.645 17.604 15.669 15.562 16.516 0.106 •0.157 -0.362 0.250 -0.020 0.245 0.140 0.481 0.290 0.230 0.093 0.862 0.337 -0.128 -0.327 0.162 0.293 0.020 1.550 1.344 1.726 1.595 1.708 1.631 1.597 1.398 1.766 2.189 1.501 1.193 1.518 1.565 1.263 1.508 1.681 1.550 1.749 1.281 1.379 1.672 7.64 3.03 3.20 7.37 6.81 7.48 7.38 6.92 8.57 8.15 6.98 5.70 7.22 3.06 3.12 7.50 7.34 6.69 20.65 16.78 16.95 20.39 18.71 20.66 19.97 19.88 32.07 14.14 21.95 10.80 19.16 18.65 17.69 17.14 20.39 16.98 16.73 18.40 18.38 16.63 18.59 13.58 16.22 18.46 21.82 18.72 22.85 22.39 10.32 21.91 14.64 12.32 17.54 17.23 14.1.1 12.07 18.59 13.98 16.06 22.73 22.88 21.57 28.29 19.81 20.15 27.76 25.52 28.14 27.35 26.80 40.64 30.10 26.14 24.35 27.61 20.04 19.85 25.90 25.72 23.32 39.24 30.36 33.17 38.85 40.53 39.38 42.82 42.27 42.39 36.05 36.59 23.12 36.70 35.88 31.80 29.21 38.98 30.96 32.79 41.13 41.26 38.20 85 TABLE 4 Raw Photometry Object Magnitude Color Index Weights U B V U-B B-V U B V U-B B-V X10 19.076 19.774 18.418 -0.698 1.356 3.17 16.01 11.34 19.18 27.35 115 18.856 16.309 2.547 17.23 21.98 39.21 116 19.288 19.881 18.362 -0.593 1.519 3.05 15.95 11.38 19.00 27.33 117 18.442 18.807 17.213 -0.365 1.593 3.36 15.80 16.48 19.16 32.28 118 18.698 18.552 17.024 0.146 1.529 3.18 18.00 16.68 21.18 34.68 119A 16.184 15.947 14.160 0.237 1.787 8.17 30.76 24.93 38.93 55.69 120 18.461 18.290 16.711 0.171 1.579 6.46 18.40 17.06 24.86 35.46 121 19.210 17.936 1.274 17.04 11.73 28.77 122 18.042 17.820 16.220 0.223 1.599 6.74 19.12 22.00 25.86 41.12 124 19.223 17.659 1.564 16.95 15.93 32.88 125 16.256 16.000 14.385 0.256 1.615 8.12 19.66 14.74 27.78 34.40 126A 15.212 14.787 13.287 0.424 1.500 8.87 30.67 26.17 39.54 56.84 X l l 18.095 17.315 15.848 0.781 1.467 6.57 11.82 8.97 18.39 20.79 127 18.733 19.043 17.628 -0.310 1.415 3.24 17.22 15.98 20.46 33.20 128 18.708 18.367 16.824 0.341 1.543 6.22 18.27 16.93 24.49 35.20 129 18.507 18.554 17.080 -0.047 1.474 6.53 18.00 16.62 24.53 34.62 X12 19.446 17.541 1.905 9.80 14.17 23.97 130A 19.005 15.945 12.738 3.060 3.207 2.58 30.35 16.35 32.93 46.70 131 17.741 17.601 16.149 0.140 1.452 7.04 19.49 22.08 26.53 41.57 132A 15.981 15.765 14.084 0.216 1.681 8.33 31.18 25.02 39.51 56.20 133 16.728 16.493 15.056 0.235 1.437 7.76 21.20 18.84 28.96 40.04 134 A 15.525 15.163 13.600 0.363 1.563 6.52 32.49 25.71 39.01 58.20 86 TABLE 4 Object Ma gnitude Color Index Weights U B V U-B B -V U B V U-B B -V X13 19.058 18.579 16.717 0.479 1.862 2.99 14.47 12.72 17.46 27.19 135 19.119 19.031 17.293 0.088 1.738 3.02 17.22 16.43 20.24 33.65 136 19.704 17.826 1.878 16.14 15.81 31.95 137 17.684 17.171 16.089 0.513 1.082 6.99 20.25 19.91 27.24 40.16 X14 18.746 17.737 1.009 17.85 11.89 29.74 139 18.500 18.996 17.436 -0.496 1.560 3.35 17.31 16.22 20.66 33.53 140 18.019 17.963 16.317 0.056 1.646 3.32 18.86 13.03 22.18 31.89 141 15.968 15.765 14.231 0.203 1.534 6.22 22.30 14.87 28.52 37.17 142 17.014 16.713 15.444 0.301 1.269 3.79 20.89 18.49 24.68 39.38 142b 18.686 17.769 0.916 10.60 9.93 20.53 144 16.042 15.752 14.111 0.290 1.641 8.27 22.29 14.99 30.56 37.28 145 16.106 15.903 14.218 0.203 1.685 8.24 22.04 14.90 30.28 36.94 146 18.972 18.891 17.259 0.081 1.632 3.08 15.66 16.43 18.74 32.09 147 17.235 17.179 15.723 0.056 1.456 7.44 18.06 22.69 25.50 40.75 148 17.191 16.984 15.643 0.207 1.341 7.43 20.46 22.79 27.89 43.25 149 18.182 17.720 16.881 0.462 0.839 1.69 19.46 16.74 21.15 36.20 150 17.987 17.237 0.750 19.06 16.33 35.39 151 19.370 18.023 16.957 1,347 1.066 2.79 18.94 16.73 21.73 35.67 152 16.991 16.887 15.503 0.104 1.384 7.62 20.61 23.00 28.23 43.61 153 16.788 16.656 15.099 0.132 1.557 7.76 20.91 18.81 28.67 39.72 154 17.364 17.139 15.788 0.225 1.351 7.32 20.22 22.59 27.54 42.81 155 17.237 17.019 15.485 0.218 1.534 7.38 20.35 23.06 27.73 43.41 87 Object Magnitude U B V TABLE 4 Raw Photometry Color Index U - B B-V U Weights B U-B B-V 156 157 158 159 A 160 161 162 XI5 163A 164 165 166 167 168 169 170 171 172A 173 174 175 176 16.696 17.696 15.844 19.164 16.677 18.053 16.353 19.523 17.589 19.941 19.155 19.511 18.590 18.095 18.674 17.288 18.116 18.872 18.245 16.477 19.267 17.628 15.651 19.396 18.773 16.587 18.575 16.031 19.250 17.379 19.601 20.676 19.314 19.525 18.506 17.939 16.000 17.139 17.982 19.058 17.949 14.948 17.628 16.117 14.223 17.768 17.337 15.181 16.637 14.972 17.553 15.908 17.662 18.909 17.423 18.089 17.055 16.481 12.983 15.588 16.525 17.494 16.732 0.219 0.068 0.193 0.391 0.090 -0.522 0.321 0.273 0.210 0.340 -0.159 -0.014 0.085 0.156 2.674 0.150 0.134 -0.186 0.296 1.529 1.639 1.511 1.428 1.628 1.436 1.406 1.938 1.059 1.697 1.471 1.939 1.767 1.892 1.436 1.451 1.458 3.017 1.551 1.456 1.564 1.216 7.79 7.12 8.47 2.97 5.90 3.57 7.98 2.84 7.09 2.62 3.01 2.87 6.40 6.76 2.77 7.35 6.74 3.14 6.55 21.22 16.88 19.44 31.49 13.25 17.68 21.04 14.41 30.75 16.88 19.82 16.21 14.62 16.69 16.50 18.11 18.98 21.60 20.19 18.89 17.18 19.00 18.99 16.01 22.14 24.78 15.85 16.32 23.46 21.44 18.88 16.12 22.43 15.98 7.33 16.26 13.51 18.71 21.61 5.37 22.91 21.52 16.13 21.18 29.01 26.56 39.96 20.65 26.94 17.98 38.73 19.72 26.91 18.83 19.70 19.37 24.51 25.74 24.37 27.54 25.63 20.32 25.55 40.21 32.89 41.58 56.27 29.10 34.00 44.50 35.85 49.63 33.00 42.25 32.19 21.95 32.95 30.01 36.82 40.59 26.97 43.10 40.41 33.31 40.18 88 TABLE 4 Raw Photometry Object Magnitude Color Index Weights U B V U-B B -V U B V U-B B-V 178 18.681 18.633 16.922 0.048 1.711 3.19 17.84 21.00 21.03 38.84 179A 16.176 15.972 15.171 0.203 0.801 8.25 30.97 23.28 39.22 54.25 180 19.207 17.741 1.466 16.99 15.85 32.84 181 16.924 16.516 14.909 0.408 1.607 7.51 21.13 14.28 28.64 35.41 182 18.453 18.385 16.849 0.068 1.536 6.53 18.26 21.09 24.79 39.35 183 A 15.727 15.357 13.748 0.370 1.609 8.48 41.09 30.61 49.57 71.70 184 18.136 17.851 16.501 0.285 1.350 6.61 19.12 21.52 25.73 40.64 185 16.555 16.281 15.200 0.273 1.081 7.89 21.60 18.63 29.49 40.23 X16 20.192 19.389 18.052 0.803 1.337 2.51 16.76 11.64 19.27 28.40 X17 19.809 18.371 1.438 16.10 11.39 27.49 186 17.567 16.987 15.681 0.580 1.306 6.93 20.46 22.73 27.39 43.19 187 17.675 17.569 16.368 0.106 1.201 7.11 19.60 21.71 26.71 41.31 188 16.621 16.484 15.300 0.137 1.184 7.93 21.27 18.53 29.20 39.80 189 19.491 17.831 1.660 16.50 15.79 32.29 190 18.776 18.077 16.643 0.699 1.434 3.08 18.77 21.37 21.85 40.14 191 17.758 17.273 16.235 0.485 1.039 6.86 20.09 . 21.87 26.95 41.96 192A 15.636 15.306 14.374 0.330 0.932 8.59 41.47 19.58 50.06 61.05 193 18.874 17.296 1.578 17.50 16.38 33.88 194 19.120 14.621 4.499 16.43 14.79 31.22 195 19.146 18.285 16.410 0.861 1.875 2.89 18.35 21.79 21.24 40.14 196 16.017 15.686 14.032 0.331 1.654 8.24 22.40 15.06 30.64 37.46 197 19.023 18.708 17.051 0.315 1.657 3.02 17.74 12.54 20.76 30.28 89 TABLE 4 Raw Photometry Object Magnitude Color Index Weights U B V U-B B-V U B V U-B B-V 198 17.810 17.595 16.256 0.216 1.339 6.93 19.53 21.89 26.46 41.42 199 17.885 17.729 16.433 0.156 1.296 6.93 19.33 21.64 26.26 40.97 200 19.169 17.757 1.412 17.06 15.80 32.86 201 19.007 18.581 17.199 0.426 1.381 3.02 17.98 16.44 21.00 34.42 202 19.144 17.823 1.321 17.14 15.7.1 32.85 203 17.772 17.332 16.094 0.440 1.238 6.88 19.96 22.12 26.84 42.08 204A 14.264 13.708 13.142 0.556 0.566 9.22 20.34 26.23 29.56 46.57 205 19.663 18.028 1.635 16.27 15.57 31.84 206 18.718 15.977 2.741 17.46 22.56 40.02 207 19.241 17.740 1.501 16.95 15.87 32.82 208 18.743 18.415 16.408 0.328 2.006 3.12 18.09 21.80 21.21 39.89 209 18.968 18.898 .17.712 0.069 1.187 3.10 17.56 .1.5.84 20.66 33.40 210 18.564 18.985 17.405 -0.421 1.580 3.33 17.31 1.6.28 20.64 33.59 211 16.217 16.018 14.334 0.199 1.684 8.16 21.87 14.79 30.03 36.66 212 18.262 18.178 16.763 0.084 1.415 6.62 18.60 14.86 25.22 33.46 X18 19.097 19.675 18.587 -0.578 1.088 3.16 16.36 11.17 19.52 27.53 213 17.559 17.414 16.081 0.145 1.333 7.16 19.82 22.1.5 26.98 41.97 214 17.319 17.140 15.777 0.179 1.363 7.32 ' 20.22 22.60 27.54 42.82 215 18.813 17.468 1.345 17.64 16.14 33.78 216 18.791 19.158 .1.7.585 -0.367 1.573 3.21 17.03 16.03 20.24 33.06 217 19.316 18.805 17.757 0.511 1.048 2.92 17.74 15.78 20.66 33.52 X19 19.646 18.504 1.142 16.41 11.24 27.65 90 TABLE 4 Raw Photometry Objecl Magnitude Color Index Weights U B V U-B B-V U B V U-B B-V 218 16.609 16.438 15.179 0.1.71 1.259 7.92 21.32 18.68 29.24 40.00 219 16.022 15.660 14.483 0.362 .1.177 8.27 22.53 12.18 30.80 34.71 X20 19.412 18.076 1.336 16.71 11.64 28.35 220 18.958 18.987 17.438 -0.029 1.549 3.10 17.32 16.21 20.42 33.53 221 18.902 18.856 17.262 0.046 1.594 3.11 17.52 16.41 20.63 33.93 222 18.520 18.467 17.233 0.053 1.233 6.47 18.21 16.39 24.68 34.60 223 19.324 17.485 1.839 16.75 16.20 32.95 224 18.652 18.665 17.281 -0.013 1.384 3.23 17.86 16.38 21.09 34.24 225A 15.805 15.435 14.523 0.370 0.912 8.43 41.12 19.40 49.55 60.52 227A 15.469 15.099 13.566 0.370 1.533 8.66 32.64 20.61 41.30 53.25 228 19.414 19.462 17.904 -0.048 1.558 2.93 16.59 15.69 19.52 32.28 229 18.556 18.668 16.926 -0.111 1.742 6.46 17.78 16.83 24.24 34.61 X21 19.653 19.616 17.937 0.037 1.679 2.81 13.20 15.68 16.01 28.88 230 17.004 1.6.826 15.491 0.178 1.335 7.59 20.71 18.32 28.30 • 39.03 231 17.477 17.401 15.935 0.075 1.466 7.23 19.79 22.39 27.02 42.18 232 18.990 .18.679 17.299 0.311 1.380 6.00 .17.84 16.34 23.84 34.18 233 19.770 19.418 17.894 0.352 1.524 2.70 16.62 15.65 19.32 32.27 91 As an outside check, the data of table 4 were compared to those of table 3 to see if there were any remaining color terms. Specifically, we solved for V - V = aV + b (4.49) s ( B - V ) - ( B - V ) = c ( B - V ) + d (4.50) s (U-B) - ( U - B ) = e ( U - B ) + f (4.51) s We obtained V - V = 0 . 0 0 9 9 9 2 V - 0 .15672-9 (4.49') s ( B - V ) - ( B - V ) = 0.01 7 5 6 4 ( B - V ) - 0 . 019316 (4.50') s (U-B) - (U-B) = - 0 . 0 8 7 6 5 2 (U-B) + 0 . 023893 (4.51') s with r.m.s. deviations of 0.138, 0.156, and 0.145, respectively. We also solved lor V - V = a ' ( B - V ) + b ' (4.52) s (U-B) - (U-B) = e ' ( B - V ) + f (4.53) s For which we obtained V - V = 0 .006581 ( B - V ) - 0 . 0 1 0 4 6 2 (4.52') s (U-B) - (U-B) = 0 . 1 4 6 5 2 9 ( B - V ) - 0 . 203137 (4.53') s 92 with r.m.s. deviations of" 0.131 and 0.145 respectively. Since in all five cases the "correction", over the range of standards, is smaller than the r.m.s. deviation, we conclude that such corrections are unwarranted. That the corrections did not turn out to have null coefficients is most probably attributable to numerical instability. Further, such corrections could very well be disastrous because of the limited span of the standards in the color indices; the full range of (U-B), for example, is -0.698 to 3.060, whereas the standards span only -0.10 to 1.35 —thus iT the (U-B) correction is a fluke, its extrapolation would introduce an unjustifiably large distortion of our (U-B) distribution. Nevertheless, the (U-B) result is worrisome —more on that in chapter 5. 93 4.5 THE CARBON STAR By choice, star 194, the carbon star, was not used as a standard; this because . of its variability, but mostly because we wanted a totally independent confirmation of its place in the Hertzsprung-Russell diagram. A study of the carbon star's variability using this work's data can only be very-crude, of course; but it was attempted anyway: Date B V 1 July 1978 8 July 1980 10 July 1980 28 June 1981 2 July 1981 1 9 . 3 7 8 ( 1 1 ) 1 8 . 9 0 6 ( 1 1 ) 18.952 19.439 19.001 <15.931( 1 2 ) <15.171 ( 1 2 ) 14.953 14.681 14.643 ( n) Obtained using the average of Log(Flux(V2)) (13) Image was saturated The V magnitudes show no hint of variability, their r.m.s. deviation being 0.138, a number much smaller than the calibration's r.m.s. deviation in V (0.327). The B magnitudes, however, are another matter. The r.m.s. deviation of this set of B values is 0.226, slightly larger than the B calibration's r.m.s. deviation, 0.203. There are no U magnitudes available because, as a perusal of table 8 will show, the star simply did not appear at all on those plates. The best one can do is claim U>20, the approximate limiting magnitude, judging from table 4. To sum up, 1 would say the evidence for star 194's variability is inconclusive. 94 Chapter 5 THE COLOR-MAGNITUDE AND COLOR-COLOR DIAGRAMS Figures 30 and 31 present the color-color and color-magnitude diagrams, respectively, of Sandage (1972) and Handschel (1972). This is to be compared with our own color-color and color-magnitude diagrams for the same sample, figures 32 and 33, and for the complete set, figures 34 and 35. It is quite clear that the sample composed of the Sandage stars only is quite small, and certainly insufficient in the color-color plane, a fact which led us to ignore an alternate set of calibrations, obtained using the Sandage stars only —the initial reasoning being that photoelectric data should be superior in quality to photographic data (that is to say, Handschel's). Whereas in the color-magnitude plane there are no obvious discrepancies or systematic shift (a graphic way of confirming the conclusion arrived at in section 4.4), the color-color plane is another ball game entirely. There seems to be a rotation, counterclockwise, of the mass of stars representing (presumably) the cluster. Oddly enough, the correction to (U-B) found in section 4.4, if applied, does not remedy the situation; it does rotate the color-color points very slightly in the desired direction, but far from enough. The fact of the matter is that statistical analysis does not support the rotation impression —or more exactly, points out that such an effect is at or below the 1:1 signal-to-noise level (cf. the color term solution). Similarly, one might think our (U-B) problems stem from (4.40); one might justifiably hue and cry at having a U calibration equation where the pseudo-B flux coefficient is larger than the pseudo-U flux coefficient. Bafflingly, a recompilation of the raw photometry using only the U group 1 calibration (for which the pseudo-B flux coefficient is uncomfortably large, but not alarmingly so) fails to affect the color-color diagram in any significant way! 95 The best ] can do at this point is express my opinion that "there is something fishy with the (U-B) colors", that photoelectric determinations of the actual (U-B) colors of several of these stars would be of the utmost desirability, and issue a warning to any who would use our (U-B) values to proceed with great care and caution. This is of course a most unwelcome turn of events, since any and all further work on these data involves (U-B) at one step or another —I am thinking particularly about de-reddening and de-extinguishing— and since a chain is only as strong as the weakest of its links... With this in mind, we can take a look at. figure 34, our raw color-color diagram. The first thing that strikes an observer is that the elongated nature of the data evident in figure 30 (the standard color-color diagram) has been lost. Well, this can mean two things: either the evidence for differential extinction across the face of the cluster has been dealt a blow (not likely since the data clump has not lost its thickness), or we are now facing a much wider range of spectral types. The second hypothesis seems at first glance to be a natural consequence of a lower limiting magnitude: this should reveal a section of the cluster's main sequence that is later in type. Unfortunately, the reddening line running from the tip of our ZAMS (which corresponds to something in the 05 to BO range) neatly bisects the data clump. Comparing figure 30 or 32 with 34, one discovers that the data clump has expanded early- ward in going from the first to the second, a direction opposite to that expected. As figure 36 makes painfully clear, the largest part of the early-ward data clump is indeed due to the late-ward part of our main sequence! There definitely is a problem with our (U-B) colors! As every cloud has a silver lining, one takes comfort in the foreknowledge (assuming this is one's second reading) that the de-reddening algorithm to be described in chapter 6 will throw out the vast majority of the troublesome early-ward (in the color-color plane) stars. Thus, clinging to the hope that, while the extrapolation of the 96 standard sequence in (U-B) is definitely wrong, the interpolation might retain some validity, one forges onward... Turning our attention to figure 35, the raw color-magnitude diagram, we are on much firmer ground; both the standard data and our plates are much stronger in B and V than in U. This diagram is, in fact, the only part of this study which has no dependence whatsoever on the ultraviolet. In it, the main sequence stands out. While in Handschel's (1972) case (figure 31) there might have been some doubt as to whether the main sequence had been reached, there can be no doubt here. Further, there is what can be described as a turn-up in this diagram, rising to a brightness comparable to that of what might be termed a giant branch (formed out of the M3.5 star and the three M21ab stars); the carbon star, however, is better left for later discussion. Somewhat problematic is the rather large scatter in (B-V) (about 0.3 mag); this is not readily apparent in figure 35 because we used a wide scale so as to be able to take in the carbon star. When one plots figure 35 at the same scale as, say, Hagen's (1970) Atlas of open cluster colour-magnitude diagrams, the main sequence becomes barely twice as high as it is wide, taking on an appearance which can only be described as "stubby". The strong scatter is reminiscent of the "thick" appearance of NGC 2158 (Hagen 1970. Arp and CulTey 1962), where the main sequence ends abruptly in a stub. To the difference of NGC 2158, we shall see that our cluster is, if the results of the next chapter are to be trusted, much younger, and that the resemblance is probably no more than coincidence. 97 Figure 30: Color-color diagram of the standards. This diagram covers the entire Handschel (1972) sample; Sandage (1972) is not represented since he does not give any U magnitudes hence no U-B colors. The line is our ZAMS (tables 5.1 and 5.2). 98 ( £-V C O L 0 R INOEX. 0-0 0.5 1.1 l .J 2.0 2.5 3.0 8.3 4.0 4.5 1 1 1 I I I I I I I r> Figure 31: Color-magnitude diagram of the standards Sandage's (1972) points are represented by triangles, Handschel's (1972), by circles. Note the carbon star's position (the reddest star). 99 Figure 32: Color-color diagram of the standards (our data) This is the same sample as for figure 31, but using the data from table 4. 100 Figure 33: Color- magnitude diagram of the standards (our data) This is the same sample as for figure 32; the distinction between Sandage's and Handschel's points has been dropped, and the data from table 4 were used. Note how much redder the carbon star winds up. 101 Figure 34: Raw .color-color diagram This time all the points from table 4 are represented. 102 Figure 35: Raw color-magnitude diagram All the points from table 4 are represented. ) 104 Chapter 6 DE-REDDENING AND DE-EXTINGUISHING 6.1 THE O METHOD Since our color-magnitude diagram seems to include, in its main sequence region, mostly early-type stars, we decided to follow an algorithm closely related to the so-called Q method of Johnson and Morgan (1953) to de-redden and de-extinguish the cluster's photometry. A rapid review of the Q method is in order. The method hinges on the fact that if one defines a parameter Q such that Q = ( U - B ) - 0 . 7 2 ( B - V ) (6.1) then since E ( U - B ) / E ( B - V ) ~ 0 . 7 2 (6.2) (Johnson and Morgan 1953). the parameter Q will be reddening-independent: Q = ( U - B ) - 0 . 7 2 ( B - V ) (6.3) o o o introducing the color-excess defining equations: ( U - B ) = ( U - B ) + E ( U - B ) (6.4) o ( B - V ) = ( B - V ) + E ( B - V ) (6.5) equation (6.3) becomes: Q = ( U - B ) + E ( U - B ) - 0 . 7 2 ( ( B - V ) + E ( B - V ) ) 105 Q Q + E(U-B) - 0.72E(B-V) (6.6) and substituting equation (6.2), we get: Q - Q o Q.E.D. The approach is then to calibrate Q against spectral type, which in turn allows the un-reddened color indices to be known as soon as the reddened ones are measured. The catch is that for stars of type later than about AO, or earlier than about 05, the Q versus spectral type function flattens out at a constant value, making the extraction of the spectral type from Q impossible. As well, the method treads on insubstantial ground for types earlier than about BO because of the dearth of such stars. Hiltner and Johnson (1956) showed that, more accurately, E ( U - B ) / E ( B - V ) = 0.72 + 0.05E(B-V) (6.7) Although this curvature effect is very slight and is generally neglected, one can take it into account if one accepts that (B-V) = 0 . 332Q (6.8) o o as demonstrated by Johnson (1958) for main sequence stars of spectral type BO to AO. It then follows that (U-B) = ( 1 + 0. 72*0. 332)Q (6.9) o o Hence, inverting (6.6) and substituting (6.7), Q = Q - 0 .05E 2 (B-V) (6.10) which becomes, inserting (6.5) and (6.8), Q = Q - 0 . 0 5 { ( B - V ) - 0.332Q } 2 o o (6.11) Isolating Q , one finally gets o T ? ( B - V ) - 1 + y/ 1 - 2 T ? ( B - V ) + 0.332n2Q Q = (6.12) 0 . 332r? Where ri = 2*0 . 332*0.05 So the procedure one would follow would consist of computing Q from the color indices (B-V) and (U-B), extracting Q from Q with the help of (B-V), and o computing (U-B) and (B-V) from Q . The correction from Q to Q is O O O o non-negligible for heavily reddened cases, such as ours. 107 6.2 THE SERKOWSK1 METHOD The method we actually Followed was pioneered by Serkowski (1963). He finds (U-B) = (U-B) + X E ( B - V ) + 0 . 0 6 E 2 ( B - V ) (6.13) o where X = 0.58 - 0.33 (B-V) (6.14) o and (U-B) = 0.10 + 3.80(B-V) (6.15) o o for spectral types between 05 and B9. Of course, equation (6.15) is crucial to the analytical solution; it therefore provides the late-type bound. It might be of interest to mention here that Serkowski provides a means of extending the method to types as late as A4 through use of a graphic analog computer called a nomogram. This is of limited use when dealing with large quantities of data as is the case here. However, our main sequence extends very little later than AO, rendering this limitation of the method most inoffensive. Clearly, substitution of equations (6.14) and (6.15) into (6.13) shows that the color index (U-B) is a function of the color indices (B-V) and (B-V) only. One o makes short work of inverting the relation to find that (B-V) is given by T?,(B-V) ~ T ? 2 + T / ~ 7 7 3 ~ T? t(B-V) + ns(B-V)£ + 77 6 (U-B) 7?7 (6.16) 108 Where 7?, = 0 . 4 5 0 T J 2 = 3 . 2 2 0 r j 3 = 1 0 . 2 1 2 rin = 3 . 8 0 3 7?5 = 0 . 1 0 9 r?6 = 1 . 560 r?7 = 0 . 7 8 0 The color excesses flow from application of equations (6.4), (6.5) and (6.15). The procedure is then to obtain (B-V) from the observed color indices (U-B) and o (B-V), accepting only the cases where -0.08 < (B-V) < -0.33, these being the o bounding B9 and 05 cases, respectively. Thinking ahead to the evaluation of the distance modulus, we realized that a good Zero-Age Main Sequence (hereafter ZAMS) was essential. A survey of the litterature showed little agreement when it comes to the early part of the main sequence. We therefore built our own ZAMS as follows. Taking Schmidt-Kalcr (1982) as "standard", we fitted Turner's (1976) ZAMS in absolute magnitude by modeling the difference function A f ( ( B - V ) ) = M ( ( B - V ) ) - M ( ( B - V ) ) (6.17) v v SK T as a series of line segments. A similar treatment was inflicted on the Eggen (1976) values. More delicate was the matter or the (U-B) versus (B-V) relation. o o For (B-V) > -0.05, Eggen does not supply any values, so the Schmidt-Kaler curve o 109 was used; lor -0.05 > (B-V) > -0.30, Eggen supplies a great many more points o than Schmidt-Kaler does, so, even though the two curves diverge slowly —albeit by a small amount—, we decided to adopt Eggen's values altogether. For (B-V) < -0.30, o we beefed up Schmidt-Kaler's two points with Serkowski's (1963) —the two differ by 4} 0.04 and 0.05 as one goes bluer, so it was quite simple to correct Serkowski's two intermediate points to blend in with Schmidt-Kaler's— and then took a progressive mean between these numbers and an extrapolation of Eggen's curve (meaning that the weights shifted slowly from Eggen = l, Schmidt-Kaler = 0 for (B-V) =-0.30 to o Eggen = 0, Schmidt-Kaler =1 at (B-V) =-0.33). The resulting ZAMS is tabulated in 0 two parts, table 5.1 covering the range in (B-V) where it was possible to model the o color-color curve (see below), and table - 5.2 extending the main sequence for the purposes of the distance modulus calculation (see part 6.3). TABLE 5.1 The Zero-Age Main Sequence (B-V) (U -B ) M o o 0 . 3 3 - 1 . 3 1 5 - 5 . 2 0 . 32 - 1 . 2 7 2 - 4 . 7 6 0 .31 - 1 . 2 0 8 - 3 . 8 1 0 . 3 0 5 - 1 . 1 7 8 - 3 . 6 0 . 30 - 1 . 1 5 - 3 . 2 5 0 . 2 9 5 - 1 . 1 1 -3 . 07 0 . 2 9 - 1 . 1 0 2 -2 .88 0 . 2 8 5 -1 .075 - 2 . 7 4 0 . 2 8 -1 .04 - 2 . 6 0 . 2 7 - 1 . 0 0 5 - 2 . 4 0 0 . 2 6 - 0 . 9 7 - 2 . 2 3 0 . 2 5 5 - 0 . 9 3 - 2 . 1 7 0 . 2 5 - 0 . 9 0 9 - 2 . 1 0 . 245 - 0 . 8 9 - 2 . 0 6 0 . 2 4 -0 . 86 -1 .90 0 . 2 3 - 0 . 8 2 5 -1 .70 0 . 2 2 - 0 . 7 8 5 - 1 . 5 0.21 - 0 . 7 5 - 1 . 3 0 . 2 0 5 - 0 . 7 1 5 - 1 . 2 0 . 2 0 - 0 . 6 8 - 1 • 1 0 . 1 9 - 0 . 6 4 5 - 0 . 9 0 0 . 1 8 - 0 . 6 1 - 0 . 7 1 0 . 1 7 5 - 0 . 5 7 - 0 . 6 2 TABLE 5.1 The Zero-Age Main Sequence (B-V) (U-B) M o o V -0.17 -0.535 -0.53 -0.16 -0.50 -0.36 -0.15 -0.465 -0.2 -0.14 -0.43 -0.04 -0.135 -0.39 0.09 -0.13 -0.384 0 . 1 2 -0.125 -0.355 0.26 -0.12 -0.344 0.29 -0.115 -0.32 0.37 -0.11 -0.285 0.45 -0.10 -0.25 0.6 -0.09 -0.21 0.71 -0.08 - 0 . 1 8 8 0.82 -0.075 -0.175 0.85 -0.07 0.92 -0.065 -0.14 0.95 TABLE 5.2 The Zero-Age Main Sequence (B-V) (U-B) M o o 0.06 1 .02 0.05 - 0 . 105 1 . 1 0.04 1 .20 0.03' 1 .29 0.02 1 . 36 0.01 1 .44 0.00 0.01 1 .5 0.05 0.05 1 .7 0.10 0.08 1 .9 0.15 0.09 2. 1 0.20 0.10 2.4 0.25 0 . 07 2.55 0. 30 0 . 03 2.8 0.35 0.00 3. 1 0.40 -0.01 3.4 0.50 0.00 4. 1 0.60 0.08 4.7 0.70 0.23 5.2 0.80 0. 42 5.8 0. 90 0. 63 6.3 1 .00 0.86 6.7 1.10 1 . 03 7. 1 1 .20 1.13 7.5 TABLE 5.2 The Zero-Age Main Sequence (B-V) o 1 . 30 1 . 40 1 . 50 1 .60 1 .70 1 .80 1 .90 2.00 (U-B) o 1 . 20 1 . 22 1 . 1 7 1 . 20 1 . 32 1 . 43 1 . 53 1 . 64 M 8.0 8.8 10.3 12.0 13.2 14.2 15.5 16.7 114 Using our ZAMS, the (U-B) versus (B-V) relation is appropriately modeled o o by (U-B) = 0.107272 + 3 . 42242 (B-V) - 2 . 6 1 952 (B-V) 2 (6.18) o o o over the range -0.33 < (B-V) < -0.065, with a r.m.s. deviation of 0.010. We o substituted as well a more modern evaluation of the reddening equation (Gutierrez-Moreno and Moreno 1975) E(U-B) = (0 . 678 + 0 . 026(B-V) )E(B-V) + 0.063E 2(B-V) (6.19) o Substituting equations (6.18) for (6.15), and (6.19) for (6.13) and (6.14), the coefficients of equation (6.16) become TJ , = 0.100 T?2 = 2.744 773 = 8.640 ??„ = -6.455 Tjs = 0.661 77 6 = - 1 0 . 330 T7 7 = -5.165 The visual extinction, in turn, can be evaluated from A = V - V = {3 . 30 + 0. 28(B-V) + 0. 04E (B-V) } E (B-V) (6.20) v (Schmidt-Kaler 1982). The problem with the algorithm as it now stands is that it makes use of a star's colors only. Obviously, under the assumption that the star belongs to the main 115 sequence, its apparent magnitude bears some information. This can be handled by solving for the distance modulus in the color-magnitude plane; one has then a two-part exact solution yielding E(B-V) and (m-M ) as its two main parameters. v However, if one assumes the stars belong to a cluster, they should all lie at the same distance modulus. Substituting (U-B) = a + b(B-V) + c ( B - V ) 2 (6.18') o o o and E(U-B) = (d + e ( B - V ) ) E ( B - V ) + f E 2 ( B - V ) (6.19') o into (6.4), and replacing (B-V) with (B-V) - E(B-V), one has o (U-B) = a + b(B-V) + c ( B - V ) 2 + t h e o (e - 2 c ) ( B - V ) E ( B - V ) + ( d - b ) E ( B - V ) + (c - e + f ) E 2 ( B - V ) (6.21) Similarly, substituting A = {g + h ( B - V ) + i E ( B - V ) } E (B-V) (6.20') v into V = M + D + A (6.22) v v where D is the distance modulus (taken as constant) and M can be expressed as v z((B-V) ), a non- analytical function tables 5.1 and 5.2 can be considered to define, o one gets 116 V = z ( ( B - V ) - E ( B - V ) ) + (m - M ) + t h e o v g E ( B - V ) - (h - i ) E 2 ( B - V ) + h ( B - V ) E ( B - V ) (6.23) where (B-V) has once more been replaced by (B-V) - E(B-V). We therefore o propose to minimize the sum of the squares A 2 = ((U - B ) - (U-B) ) 2 + w 2 ( V - V ) 2 (6.24) t h e o t h e o in E(B-V) for each star, subject to the condition that -0.33 < (B-V) < -0.065 o —that is to say that if the sum of the squares is monotone increasing or decreasing across the allowed range of (B-V) , the star is rejected. o The w factor in (6.24) comes about because the color-color and color-magnitude deviations are of different nature; one should avoid having one deviation dominate the behavior of the sum of the squares. We chose w so that, for a true ZAMS star, a small error in E(B-V) causes equal contributions to the sum of the squares from the V and (U-B) deviations. A bit of thought will show that w is given by the ratio of the error slopes, in turn given, in either diagram, by the difference between the reddening and ZAMS slopes. 3 ( U - B ) a(u-B) 3 V av - ° - w{ - £ } (6.25) 3 E ( B - V ) 9 ( B - V ) BE(B-V) 3 ( B - V ) o o As might be expected from the non- trivial forms of the derivatives, w varies across the allowed (B-V) range; fortunately, the variation is tolerably small. We chose the o smallest value w attains (al the blue end) as our weighing factor, thus ensuring that if one of the deviations dominates, it will be the more trustworthy one: the color-color deviation. 117 As mentioned earlier, the dependence of M on (B-V) cannot be v approximated by a low-order polynomial over the range ol" interest here (the situation would be different for a redder (B-V) window, we suspect), making an analytical expression of the least-squares solution intractable. Therefore the solutions were obtained numerically, by evaluating the sum of the squares over a string of candidate E(B-V) values, until a minimum was found within the allowed (B-V) range o (otherwise the star was rejected). 6.3 RESULTS The algorithm's first pass retained 122 of the 190 stars submitted to it (that is to say all the stars from table 4 with full photometry); we immediately flagged out of the sample four obvious mistakes. Star 2 is quite far outside the physical limits of the cluster; it is associated with star 1, which is clearly far too bright to be a member. Star 83 is a known foreground G5 star (Blanco et al. 1955), while stars 130 and 172 are known to not belong on the main sequence, being M2Iab stars (Fawley and Cohen 1974). The sample now numbers 118. Figures 37 and 38 illustrate the de-reddened sample. Star X18 stands out like a sore thumb; this very blue object is barely caught by the reddening path and illustrates the dilemma presented by the (U-B)-blue objects in the sub-sample of figure 37. If one was to believe its reddening path, it would wind up earlier than the tip of our ZAMS —a peculiar enough position already—, and because it is so faint, would require an enormous distance modulus, completely at odds with the extinction solution. That is to say there is no way one is going to accept the combination of fairly "low" extinction (4.6 in its case) and extragalactic distance modulus (m-M = v 25 for (B-V) = -0.4); clearly this is not a main sequence object! One hesitates, o however, to label it as a white dwarf, because not only would it be too bright (if a cluster member), but this would seem to imply the rest of the (U-B)-blue objects of" 118 figure 37 are also white dwarf's: the cluster would then be ludicrously rich in these objects. As implied in the last chapter, the reasonable hypothesis is that something is deeply wrong with these objects' U magnitudes. The decision to reject the remaining 36 objects which, with X18, make up table 6.2 is based in part on the histogram (not shown) of the extinction solutions, which allows lopping off the objects with extremely high or low extinctions with respect to the cluster's mean, and in part on the main sequence's behavior in figure 35; one notes how, redward of (B-V) = -0.25, it suddenly goes wild, in strong o contrast with its rather sedate behavior in figure 38. The clue here is that these points are systematically blueward of the ZAMS in the color-color plane, and redward in the color-magnitude plane; clearly the algorithm is straining to obtain a fit. Also quite clearly, these stars arc most probably main sequence objects, judging from the color-color diagram: one then realizes that this is exactly what would be expected to happen if their real distance moduli were smaller than the one used. Thus we conclude these stars are foreground. Additional support for this conclusion is provided by figure 39, where, with the exception of X18, the rejected stars are seen to lie more or less in the reddening wake of the F5 knee of the color-color diagram. Figure 40 as well confirms our judgment, as we notice that all the "blue stragglers" are part of the rejected sample. There is a small chance, however, that at least some of these stars may be pre-main sequence; but this would imply an amazingly young age for the cluster, a claim I am not ready to put forward considering the severe problems the photometry is suffering from. The final sample, given in table 6.1 (where the absolute magnitudes are for a distance modulus of 13.9 (Handschel 1972)), numbers 81 objects. The mean extinction is <A > = 5.846, with a r.m.s. deviation of 0.462; the corresponding color excess is v <E(B-V)> = 1.779, with a r.m.s. deviation of 0.139. Table 6.2 gives the photometry 119 the algorithm came up with for the rejected stars; these values are supplied only lo allow identification of the points in figures 37 to 40. It remains now to consider the scatter at the blue tip of all four figures. Judging from figure 40, it seems a good fraction of the tip stars are probably beyond the turnoff, and hence evolved away from the main sequence; the more evolved a turnoff star is. the less the algorithm retains validity —thus the scatter. One final word of caution concerning the de-reddening; if one was to replot figures 37 and 38 using the cluster mean reddening and extinction for all the stars, one would obtain a totally random peppering of the figures' extent with points. This is because the scatter in (B-V) is so much larger than the expected span of (B-V) . From the turnoff to the photographic cutoff, we have about three o magnitudes; referring to table 5.1, this translates into a (B-V) span of only 0.07 o magnitudes, and thus an expected r.m.s. deviation of about 0.02. The run of (B-V), meanwhile, is expected to have an r.m.s. deviation of the same order as the run of U, B, or V: that is, about 0.2; however, the sample represented by table 6.1 is more ordered, and its r.m.s. deviation comes out as 0.128. Thus we would expect E(B-V) to have an r.m.s. deviation, from soaking up the scatter alone, of 0.126 (the square root of the difference of the squares). This is marginally lower than the observed 0.139. There is previous evidence (Handschel 1972) that the reddening (and hence the extinction) varies across the face of the cluster; so the remaining r.m.s. deviation in E(B-V) might just very well be real. This issue will be discussed in chapter 7. Figure 37: De-reddened color-color diagram Circles represent the probable cluster members (from table 6.1), and crosses the probable field stars (from table 6.2). Note the position of star X18 at the very top left 121 Figure 38: De-reddened color-magnitude diagram Circles represent the probable cluster members (from table 6.1), and crosses the probable Field stars (from table 6.2). Note the position of star X18 at the very lower left The distance modulus used was 13.9. 122 Figure 39: Color-color diagram of the de-reddening sample Circles represent the probable cluster members (from table 6.1), and crosses the probable field stars (from table 6.2). Note the position of star X18 at the very top left Figure 40: Color-magnitude diagram of the de-reddening sample Circles represent the probable cluster members (from table 6.1), and crosses the probable field stars (from table 6.2). 124 TABLE 6.1: Probable cluster stars De-reddened and de-extinguished photometry Object Absolute Magnitude Color Index M u M b M V (U-B) o (B-V) o 6 -6.587 -5.319 -4.995 -1.268 -0.324 15 -4.838 -3.647 -3.343 -1.190 -0.304 16 -4.588 -3.492 -3 . 199 -1.096 -0.293 18 -4.105 -2.985 -2.695 -1.120 -0.290 19 -5.275 -4.153 -3.849 -1.123 -0.304 22 -5.324 -3.952 -3.631 -1.371 -0.321 25 -4.433 -3.046 -2.736 -1.387 -0.310 29 -5.243 -3.983 -3.672 -1.260 -0.311 31 -4.140 -2.671 -2.361 -1.469 -0.310 39 -3.263 -2.430 - 2 . 193 -0.832 -0.237 53 -4.546 -3.456 -3.164 -1.091 -0.292 54 -6.250 -5.045 -4.727 -1.205 -0.318 61 -4.633 -3.475 -3.175 -1.157 -0.300 62 -4.185 -3.250 -2.989 -0.935 -0.261 64 -3.922 -2.671 -2.371 -1.251 -0.300 75 -5.306 -4.264 -3.963 -1.042 -0.301 76 -5.148 -3.809 -3.496 -1 .339 -0.313 79 -4.738 -3.342 -3.031 -1.396 -0.311 81 -5.3.12 -4.227 -3.924 -1.085 -0.303 82 -5.510 -4.195 -3.880 -1.315 -0.315 84A -6.638 -5.578 -5.261 -1.060 -0.317 87A -6.657 -5.670 -5.355 -0.987 -0.315 125 TABLE 6.1: Probable cluster stars De-reddened and de-extinguished photometry Object Absolute Magnitude Color Index M u M b M V (U-B) 0 (B-V) 0 X8 -3.028 -1.591 -1.281 -1.437 -0.310 91 -6.385 -5.120 -4.798 -1.265 -0.322 97 -6.909 -5.710 -5.389 -1.199 -0.321 99 -5.290 -3.945 -3.631 - 1.346 -0.314 103 -6.781 -5.521 -5.196 -1.260 -0.325 106 -4.704 -3.661 -3.375 -1 .043 -0.286 107 -5.075 -4.081 -3.799 -0.995 -0.282 118 -4.529 -3.230 -2.920 -1.299 -0.310 120 -5.035 -3.715 -3.404 -1.320 -0.311 122 -5.579 -4.289 -3.974 -1.290 -0.315 126A -7.912 -6.908 -6.588 -1.003 -0.320 128 -4.514 -3.412 -3.119 -1.102 -0.293 129 -4.432 -2.990 -2.680 - 1.443 -0.310 131 -5.083 -3.847 -3.537 -1.236 -0.310 133 -6.036 -4.905 -4.591 -1.131 -0.314 134 A -7.947 -6.822 -6.498 -1 .125 -0.324 X13 -5.971 -4.691 -4.373 -1.280 -0.318 146 -4.874 -3.403 -3.077 -1 .471 -0.326 147 -5.662 -4.329 -4.008 -1.333 -0.321 148 -4.967 -3.911 -3.619 -1.056 -0.292 152 -5.486 -4.273 -3.961 -1.213 -0.312 154 -4.822 -3.780 -3.493 -1.042 -0.287 126 TABLE 6.1: Probable cluster stars De-reddened and de-extinguished photometry Object Absolute Magnitude Color Index M u M b M V (U-B) 0 (B-V) 0 155 - 6 . 0 5 5 - 4 . 8 1 7 - 4 . 4 9 9 - 1 . 2 3 8 - 0 . 3 1 8 156 - 6 . 5 8 4 - 5 . 3 4 9 - 5 . 0 2 8 - 1 . 2 3 5 -0 .321 158 - 5 . 4 9 9 - 4 . 1 2 7 - 3 . 8 0 4 - 1 . 3 7 2 - 0 . 3 2 3 159A -6 .901 -5 .731 -5 .411 - 1 . 1 7 0 - 0 . 3 2 0 161 - 3 . 3 0 2 - 2 . 3 8 0 -2 . 128 - 0 . 9 2 2 - 0 . 2 5 2 162 - 5 . 9 3 9 - 4 . 6 8 8 -4 .371 . - 1 . 2 5 1 - 0 . 3 1 7 164 - 4 . 5 9 2 - 3 . 2 6 7 - 2 . 9 5 7 - 1 . 3 2 5 - 0 . 3 1 0 165 - 5 . 3 2 5 - 4 . 1 4 4 - 3 . 8 3 6 - 1 . 1 8 1 -0 . 308 169 - 3 . 182 - 1 .815 - 1 . 5 1 5 - 1 . 3 6 7 - 0 . 3 0 0 170 - 4 . 2 1 4 - 2 . 9 2 6 - 2 . 6 1 9 - 1 . 2 8 8 - 0 . 3 0 7 171 - 4 . 7 4 2 - 3 . 5 2 0 - 3 . 2 1 4 - 1 . 2 2 2 - 0 . 3 0 6 173 - 6 . 1 2 6 - 4 . 7 9 8 - 4 . 4 7 3 - 1 .328 - 0 . 3 2 5 174 - 4 . 7 2 0 - 3 . 4 7 7 - 3 . 1 6 9 - 1 .244 - 0 . 3 0 8 181 - 6 . 7 6 2 - 5 . 6 4 6 - 5 . 3 2 6 - 1 . 1 1 6 - 0 . 3 2 0 182 - 4 . 8 2 2 - 3 . 4 3 7 - 3 . 125 - 1 . 3 8 5 - 0 . 3 1 2 183A - 8 . 0 1 2 - 6 . 8 4 8 - 6 . 5 1 9 - 1 . 164 - 0 . 3 2 9 184 - 3 . 9 3 6 - 2 . 9 7 4 - 2 . 7 1 0 - 0 . 9 6 2 - 0 . 2 6 4 187 - 3 . 6 5 8 - 2 . 6 4 0 - 2 . 3 6 8 - 1 . 0 1 9 - 0 . 2 7 2 188 - 4 . 6 2 4 -3 .651 - 3 . 3 7 9 - 0 . 9 7 3 - 0 . 2 7 2 197 -4 .881 - 3 . 6 3 4 - 3 . 3 2 4 - 1 . 2 4 7 - 0 . 3 1 0 198 - 4 . 2 8 4 - 3 . 2 4 9 - 2 . 9 6 8 - 1 . 0 3 6 -0 .281 199 - 3 . 9 8 6 - 2 . 9 2 7 - 2 . 6 4 6 - 1 . 0 5 8 -0 .281 127 TABLE 6.1: Probable cluster stars De-reddened and de-extinguished photometry Object Absolute Magnitude Color Index M u M b M V (U-B) o (B-V) 0 209 -2.269 -1 .229 -0.962 -1.040 -0.267 212 -4.330 -3.078 -2.776 -1.252 -0 . 302 213 -4.566 -3.454 -3.160 - 1 . 1 1 2 -0.294 214 -4.996 -3.886 -3.585 - 1 . 1 1 1 -0.301 218 -5.088 -4.073 -3.788 -1.015 -0.285 220 -4.446 -2.941 -2.616 -1.505 -0.325 221 -4.739 -3.268 -2.943 -1 .471 -0.325 222 -3.019 -1.913 -1.633 - 1 . 1 0 6 -0 . 280 224 -3.801 -2.475 -2.168 -1.326 -0.307 227A -7.827 -6.740 -6.420 -1.087 -0.320 228 -4.028 -2.498 -2.175 -1.530 -0.323 230 -5.170 -4.082 -3.780 -1.088 -0.302 231 -5.445 -4.127 -3.812 -1.318 -0.315 232 -3.216 -2.257 -1.998 -0.958 -0.259 233 - 3.272 -2.212 -1.936 -1.060 -0.276 128 TABLE 6.2: Probable field stars De-reddened and de-extinguished photometryt Object Absolute Magnitude Color Index M u M b M V (U-B) 0 (B-V) 0 10 A -4.739 -4 . 335 -4.163 -0.404 -0.172 34 - 5 . 107 -4.283 -4.038 -0.824 -0.245 37A -3.706 -3.236 -3.060 -0.470 -0.176 44A -3.347 -2.826 -2.643 -0.522 -0 . 183 46 -3.547 -2.704 -2.461 -0.843 -0.243 48 -2.230 -1 .886 -1.746 -0.344 -0.140 60A -2.849 -2.294 - 2 . 109 -0.556 - 0 . 185 65 -3.719 -2.929 -2.696 -0.790 -0.233 66 -4.248 -3.413 -3.168 -0.836 -0.245 67A -3.244 -2.685 -2.496 -0.559 -0.189 70 -3.513 -2.750 -2.523 -0.763 -0.227 71 -3.433 -2.738 -2.523 -0.696 -0.215 77 -4.095 -3.211 -2.964 -0.884 -0.247 85 -5.395 -4.634 -4.389 -0.761 -0.245 X7 - 3 . 169 -2.300 -2.057 -0.869 -0.243 95 -4.408 -3.615 -3.370 -0.793 -0.245 100 -3.837 -3.328 -3.143 -0.509 - 0 . 185 X l l -4.230 -3.724 -3.536 -0.506 -0.188 137 -2.468 -2.052 -1.898 -0.416 -0.154 142 -4.545 -3.685 -3.440 -0.860 -0.245 149 -0.435 -0.210 -0.114 -0.225 -0.096 163A -3.940 -3.308 -3.100 -0.632 -0.208 129 TABLE 6.2: Probable field stars De-reddened and de-extinguished photometryt Objecl Absolute Magnitude Color Index M M b M V (U-B) 0 (B-V) o 176 -2.968 -2 . 160 - 1 . 9 3 0 -0.807 -0. 230 179A -2.629 -2.115 - 1 .940 -0.514 - o . 175 185 -3.914 -3.205 -2.984 -0.709 - o . 221 X16 - 1 . 1 7 4 -0.852 -0.722 -0.322 - o . 1 30 186 -3.967 -3.391 -3. 192 -0.575 - o . 1 99 190 -3.395 -2.833 -2.641 -0.562 - o . 1 92 191 -2 . 146 - 1 . 7 4 1 - 1 . 5 9 2 -0.405 - o . 1 49 192A -3.885 -3 . 385 -3.201 -0.500 - o . 1 84 195 -5.644 -4.792 -4.540 -0.852 - o . 252 201 -3.086 -2.263 -2.029 -0.823 - o . 234 203 -3.459 -2.793 -2.583 -0.666 - o . 210 217 -0 . 544 -0.173 -0.043 -0.371 - o . 1 30 219 -5.049 -4.330 -4.087 -0.719 - o . 243 225A -3.521 -3.093 -2.928 -0.429 - o . 1 65 t See text 130 6.4 THE DISTANCE MODULUS We "confirmed" independently Handschel's (1972) distance modulus by the following procedure: First, we used the modernized Serkowski algorithm (that is to say an exact solution for E(B-V) in the color-color plane for each star) lo de-redden as many stars as the algorithm would have. The mean values of E(B-V), E(U-B), and A were then applied to the entire raw v photometry data set. A histogram was then generated showing how many stars lay above (in the sense of brighter) the ZAMS as a function of the adopted distance modulus. We then hypothesized a gaussian distribution of the individual star points about the main sequence; the probability that a star lays between AV and AV+dAV away from the main sequence is given by - A V 2 / a 2 p ( A V ) d A V = Ae dAV (6.26) One then expects the histogram to model crf((m-M ) - (m-M ) ), as v v 0 the procedure used to generate it mimics the integration of (6.26) from AV = (m-M ) - (m-M ) to AV —> °°. v ° v We finally postulated that the distance modulus which generates the best ZAMS envelope is given by the point of strongest negative curvature on the erf((m-M ) - (m-M ) ) curve —this seems to contradict our v v° previous postulates, and indeed it does, but it generates fits pleasing to > the eye... What we thus have done is to formalize the old "slide-it-until-it-looks-good" method of distance modulus fitting. 131 The distance modulus obtained thusly was coincident with Handschel's, albeit with a large incertitude; a pleasant but not altogether unexpected result. Getting back to the color-color-magnitude solution, one can generalize the algorithm to extract the distance modulus from it too. This is done by computing the "r.m.s. deviation" of each fit (more exactly the root-mean-square of the individual stars' least squares) as a function of the D parameter, and pinpointing the minimum of thai curve. The problem with this approach is that as the candidate distance modulus changes, so does the sample of stars accepted by the algorithm —stars have their least squares solutions shift in and out of the allowed (B-V) range—, which o wouldn't be so bad except that it makes the curve jump now and then, giving it a somewhat disjointed appearance. Nevertheless a clear parabolic trend is apparent, and the distance modulus comes out as 14.7 ±0.2 . This is a surprisingly large value, and we feel it should be given little weight for several reasons. For one, the ZAMS has a very steep slope in the color-magnitude diagram in the region of interest (early-O tip to early B), so that a small shift in color will accomodate a large shift in magnitude. Also, we must remember that the sample is "contaminated" by turnoff stars, invalidating the algorithm's basic premise; this particular effect becomes more important as the distance modulus is increased, as the turnoff stars will be the last ones to drop out of the solution. There is finally our basic reluctance in promoting highly unusual claims (here a great distance, youth, and brightness for the cluster) on the basis of shaky photometry (those funny U-B colors again). 132 Chapter 7 PARTING SHOTS 7.1 DIFFERENTIAL REDDENING Handschel (1972) claimed to have detected differential reddening across the face of the cluster, ranging from E(B-V) = 2.0 in the southwest to E(B-V) = 1.5 in the northeast, the obscuring material taking the shape of a pincer surrounding the heart of the cluster (see Handschel's figure 7). Using the individual de-reddenings of table 6.1, we are in a position to check on that claim. Figure 41 reproduces Handschel's figure 7; it is a contour map, at the same scale as figure 2.1, of the extinction A , using v Handschel's data. Figure 42 repeats the procedure using those stars in table 6.1 which are not part of Handschel's sample (that is to say, those which do not appear in table 3), while figure 43 uses the entire sample of table 6.1. Though the contour-generating routines tend to introduce "noise detail", the general pattern of Handschel's figure 7 is still present in figure 41: there is a definite impression of generally increasing extinction from northeast to southwest. Only 39 out of 51 stars appear on this figure because of Handschel's imposing a radius condition on his figure 7 (roughly the region covered by the inner box of figure 2.1); this causes streaming of the contour lines from that radius to the figure's edges. Figure 42 uses a totally independent sample; indeed, although we used Handschel's photometry to calibrate these stars, nowhere do spatial terms have a chance a biasing our photometry. The PDS frames have no spatial bias, the SUPERTOODEE processing has no spatial bias; and, as long as the stellar population itself does not have a spatial bias, then it follows the calibrated stars cannot, in any way, end up being spatially biased. Thus it is most significant that Handschel's original pattern, the pincer, is reproduced. Figure 43, which uses the entire sample, is not without interest either, since the Handschel objects participating in it (51 out of 81) have had their photometry re-evaluated, and 133 the extinctions computed independently. Between figure 42 and figure 43, the only pattern alteration is the "clearing up" of the southeast quadrant. The apparent swing of the extinguishing mass from generally southerly to generally westerly is a streaming effect; one must compare the patterns only over the regions covered by the samples. We thus confirm, to the extent that the de-reddening can be trusted, HandschePs claim: there is definite evidence for differential extinction across the face of the cluster. If we were to be pressed for a physical model of the extinction, we would forward two: a) The cluster is partially imbedded in the side of a vast dust cloud which, over the small area we have mapped it, presents itself as a plane, tilted with respect to the plane of the sky so as to have its line of nodes run north-northwest to south-southeast, and approaching the observer to the southwest. b) The cluster's line of sight lies coincident with the ragged edge of a foreground dust cloud, and just happens to pass right between two of the cloud's edge blobs (small, semi-detached clouds). 134 Figure 41: Extinction map —Handschel's data The 39 stars from Handschel's (1972) figure 7 are used to reproduce his proposed extinction structure. The scale is identical to that of figure 2.1. Only the center quarter or so of the structure is significant because of the limited radius of Handschel's mapping sample. Figure 42: Extinction map —Independent sample The 30 stars from table 6.1 which are not part of Handschel's data were used to produce this map. This sample, though smaller in number, is more evenly spread across the face of the figure, lessening the contouring noise considerably. • 136 Figure 43: Extinction map —Complete sample All 81 stars from table 6.1 were used to produce this map. Note how little difference there is between this figure and the preceding one, apart from the southeast quadrant 137 7.2 AGE ESTIMATE Because of the high uncertainty associated with the de-reddening process, one hesitates to fit isochrones to the de-reddened color-magnitude diagram, for one. Comparison of said diagram (figure 38) with that of other young clusters, such as NGC 3293 (Turner et al. 1980), Trumpler 16 (Feinstein et al. 1973, Feinstein 1982), and Stock 14 (Turner 1982), indicates, at first glance, that NGC 7419 is as young, if not younger...and their ages range from 3 to 6 million years! This is, of course, entirely an artefact of the de-reddening algorithm (since aging off the main sequence is interpreted as extra reddening). Another very rough age can be estimated from the apparent turnoff in figure 40; estimating it at V +15.3 and applying extinction (5.85) and distance modulus (13.9), then M — -4.4. On the isochrone display of v Patenaude (1978), this requires extrapolation, leading to an age estimate of about 8 million years, possibly even younger. Note that this second estimate is only a function of the average values of A and E(U-B) because the turnoff point is picked on the v raw color-magnitude diagram. 138 7.3 CONCLUSIONS If we did this right, and once more 1 want to stress the importance of the (U-B) colors in obtaining this result, then NGC 7419 is an extremely young cluster, at 5 ± 5 million years, in which not only has the pre-main sequence been possibly detected (explaining the scatter of the fainter stars in iigure 38), but a sizable number of stars have been seen as already evolved to (the tip stars) or beyond (the four M supergiants) the turnoff point —which would make them all extremely massive. The carbon star is very unlikely to be a member, once one accepts the age arrived at for the cluster; however its radial velocity determination (see Appendix A) is tantalizingly inconclusive. One might also keep in mind that there is some, albeit very little, evidence some carbon stars may have evolved from stars as massive as 10 solar masses (Wallerstein 1973). At M = -5.1, star 194 would be "excessively v bright" (Gordon 1968); in fact it would lie a full 1.5 magnitudes beyond the usually-quoted maximum of -3.5. As a closing comment, 1 should point out that if the carbon star is to be a member, then it must have evolved quite rapidly, which in turn would imply it is very massive; this would be consistent with its high luminosity. There is so much more that has not been examined in this work. The question of duplicity has been completely ignored, and as well we did not attempt to gauge the cluster's metallicity. This restraint is in part due to time constraints, and in part due to the persistent high scatter of the data, which would have doomed any such efforts to inconclusiveness. It really is a shame we could not secure more and better data. 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D. dissertation (unpublished), (Vancouver: The University of British Columbia) 144 APPENDIX A A.l INTRODUCTION The Dominion Astrophysical Observatory was gracious enough to allow us a series of live observing runs in the period stretching from August 1982 to September 1983, totalling twenty-two nights. The telescope used was the 180 cm reflector —that venerable behemoth—, and the instrument configuration consisted of the 2131B blue spectrograph, the 300 lines/mm grating, blazed at 422.4 nm, used in first order, the EMI image lube, and University of British Columbia's 1872-Reticon solid-state detector. The configuration was chosen to give the best possible combined instrumental response curve, with an eye on sensitivity as the prime requisite. It turns out our observing window is sharply delimited by, at the blue end, the Reticon's response, and, at the red end, the image tube's response. The first few observing runs were devoted to obtaining a "good" spectrum or star 194, the carbon star. Accordingly, standard spectra were taken of TX Piscium (19 Piscium, HD 223075, BD+2°4709, SAO 128374, IRC +0.352), a bright (V = 5.04) type C62 carbon star, 58 degrees away from the cluster, as well as of iron-argon comparison arcs. Later on, spectra were also obtained of stars 1(1, 11, 32, 44, 87. 126, 134, 179, 183, 185, 196, 204, and 225; we intended to use these to attempt to gel some spectral type identifications of the bluer objects in the cluster. Lack of time prevented us from doing so, the task turning oul to be far from trivial. Unfortunately, this period coincided with my apprenticeship as an observer, the result being that the observing technique of the earlier runs leaves something to be desired; the' record keeping was sloppy (some exposure timings are missing and had to be interpolated), arcs were taken with less than the desirable frequency (that is to say immediately before and after each exposure, with the telescope in the same position), and some things were not done which I am now kicking myself for (such as 145 exposures of progressing durations of the same object so as to obtain good signal-to-noise over the entire spectral range; cases in point are the sodium D-line region of" TX Piscium and the red end of the iron-argon arcs). In addition, the Reticon was still undergoing teething pains, as it later turned out. Intrigued by the rather unexpectedly low signals we were getting from some objects, as well as a definite lack of repeatability between successive exposures, close monitoring of the instrument revealed, near the end of our observing runs, that it had been dumping its data at random intervals, triggered by electrical activity in the dome (such as guiding paddles and the telescope clock winding motor), because of some marginally defective chips in its electronics; the net result of which being that none of our long exposures actually achieved their full integration times —one hour for the cluster objects. A more accurate estimate of the longest times achieved would be of the order of 20 minutes. Nevertheless, we obtained a measurement of the radial velocities of stars 194 and 196. Before we detail the procedure followed, a word of explanation concerning RETICENT is in order. A.2 RETICENT RETICENT (Yang 1983a) is a command language written in FORTRAN IV designed to manipulate one-dimensional digital data. It was initially developed by Dr. Chris Pritchet, and has undergone a number of revisions and expansions at the hands of Mr. Stephenson Yang. Data, usually digital representation of spectra, are input from a variety of devices into in-core storage spaces in the program, called arrays or frames, depending on their structure. Commands, which can in turn be organized in do-loops and macros, are issued by the user to control the transformation of the data. Arrays are one-dimensional strings of numbers up to 200 elements in length, while frames can have up to 2048 elements and are accompanied by an 80 character comment block. The frames' odd length is dictated by the physical design of the 146 Reticon. A.3 THE RETICON The Reticon raw data, as collected al the telescope, consists of a trio of numeric strings representing respectively the read-out of the instrument after an exposure, after the immediately following baseline (a very short exposure used to approximate the instantaneous zero-signal instrumental profile), and the difference of the two. It is preferable to subtract from the raw exposure a dark exposure (that is to say an exposure taken with all the shutters closed) of matched length, taken as close as possible in time • (because the Reu'con's properties vary steadily as a function of a myriad of parameters, chief amongst them being the liquid nitrogen coolant level). Then, because of the wiring design of the instrument, an eight-pixel baseline pattern must be normalized out (one simple way to illustrate what is meant here is to think of the zero-signal display as reading 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8...). At this point, the Reticon's instrumental response can be considered ironed out; one now has to worry aboul the rest of the instrument —mostly the image tube. A.4 SPECTRUM CALIBRATION Because of the small dispersion used, the instrumental distortion introduced by the image tube's lenses and internal structure is quite large. It can be, for our purpose, properly modeled by a third-degree polynomial of the form X = a + bx + c x 2 + d x 3 (A.l) where x is the pixel number, measured from the blue end for convenience. This can be calibrated accurately using the iron-argon arcs. Magnetic effects between the image tube and the dome's metallic floor, as well as the imperfect steadiness of the high 147 voltage supply and nitrogen gas coolant flow are expected to cause this calibration to change slowly through the night, as well as making it totally irreproducible from night to night. One last instrumental hurdle must be surmounted. It has been shown (Ninkov 1983) that the image tube undergoes a shift whenever the 180 cm telescope passes within an hour of the zenith. This can be reasonably well modeled by replacing x in equation (A.l) by x + A x . However, this requires some means of measuring said shift. Proper observational technique, by taking iron-argon arcs immediately before and after the exposure proper, obviates the need for such a determination (unless the shift occurs in mid-exposure, which would usually ruin it, as did happen once). Needless to say, we ended up having to determine - A x after all. Luckily, the neighboring city of Victoria supplies very strong mercury emission lines for all our long exposures; it was thus possible to calibrate the shift in every case from the known wavelengths (and radial velocity, quite obviously) of those lines. As for TX Piscium, our standard, its shift was determined using as many atomic features as were reasonably free of continuum and blending problems. This is much harder to do than it sounds since the spectrum is crawling with molecular features. As table 7 shows, the sample of reliable atomic lines was always extremely small. The observed wavelengths of the atomic lines are derivable from the star's known radial velocity, +9.8 km/s (Walker 1979), and the observer motion at the time of the exposure, which, in our case, was computed by the SOS:OBRVEL program (Yang 1984). On the First of the two nights during which spectra of TX Piscium were taken, the spectral region included the sodium D lines; one must note that these are intrinsic (Schmidt-Kaler 1982, p. 3); they are not caused by interstellar absorption —one expects the interstellar lines to be negligible in comparison because of TX Piscium's small distance (128.8 pc from Eggen's (1972) distance modulus (m-M ) = 5.55). v 148 So far we have obtained the pixel-to-wavelength equations of star 194 and TX Piscium's spectra; now we wish to measure the former's radial velocity. Easier said than done. A.5 BANDHEAD POSITIONS The only recognizable and/or reliable features in star 194's spectra are the C2(0,0) and C2(0,1) Swan molecular bandheads at 51.6.52 and 563.55 nm, respectively. The catch is that these are not emission or absorption-like profiles, but a jump in the continuum; as such, accurate wavelengths of the features do not exist because there is no agreement on what part of the bandhead to measure the wavelength of. So we had to devise our own definition of some recognizable property of the bandheads which would allow a position, and therefore a wavelength, to be accurately measured. We settled on the shape of the first derivative of the bandhead region. As figure 44 shows, it is well represented, at least in TX Piscium's case, by a gaussian with its summit chopped off. The procedure was then to use the first derivative's flanks to interpolate the summit (dashed line in figure 44) using a gaussian fit (or more accurately a parabolic fit to the logarithm of the first derivative); said interpolation would then yield a position, which could be calibrated in wavelength using other, more orthodox features of the spectrum. Matters complicate themselves, however, when it turns out star 194's spectrum cannot be treated the same way because of its low signal-to-noise ratio; its first derivative is too noisy, and the bandhead cannot be seen. The position of the bandheads in star 194's spectrum had to be found from a sliding fit betwixt it and TX Piscium's spectrum. To do this, the fit I (x) = a + b l (x+Ax) TX Psc 194 (A.2) 149 (where the iwo degrees ol' freedom roughly correspond to the difference in noise level and the ratio of the integrated lights), evaluated over a short interval centered on the bandhead ", was executed over a range of Ax values and the r.m.s. deviations noted. These, in turn, were fitted by a parabola in Ax to obtain the shift for which the minimum r.m.s. deviation is attained. The positions of the bandhead features in star 194's spectra were then given by their positions in TX Piscium's spectra plus said shift. "Necessarily short (about 15 pixels) because of —the presence of mercury lines in one and their absence in the other —different continua due to the different pixel-wavelength zero-points (both because of differing shifts and different observer-relative radial velocities) over the far from trivial instrumental response curve 150 500.0 0.0 -500.0 1 1 — AMW / A / — \I\J 1 I 1 800 825 850 PIXEL n 875 900 Figure 44: First derivative of the bandhead region The spectrum of TX Piscium for the night of 25/26 August 1982 was derivated for a narrow region about the 516.52 nm C2(0,0) Swan molecular bandhead. The dashed line indicates the fitted parabola. 151 A.6 THE RADIAL VELOCITY All these quantities being known, one can then find star 194's radial velocity as follows. Since the Doppler-Fizeau shift is (neglecting rclativistic corrections whilst using rclativistic notation) X = ( 1 + 0 )X * (A.I) o it follows, since the bandhead has the same rest wavelength in both stars' spectra, that X X X = 194 = TX Psc (A.2) ( 1 + & ) ( 1 + /3 ) 194 TX Psc hence, isolating j3 , transforming to velocity, and correcting for the observer's 194 motion c ( X - X ) + v X v = 194 TX Psc TX Psc-194 - v (A.3) 0 194 X obs TX Psc It should be mentioned in closing that TX Piscium's radial velocity14 is reported to be variable, although it seems, from the quoted significant digits on its mean value, that such a variation must be very small, and in any case completely negligible when compared to our estimated accuracy. The following table 7 gives the wavelengths (in air) of the lines used in the fits detailed in the following pages; in addition to the two references given, line identifications were made possible by the help of Yang (1983b) (for the iron-argon arcs), Sanford (1950), and K.eenan and McNeil (1976) (for the carbon stars). 1 4I should point out here that TX Piscium's entry in the SAO catalog mistakenly gives the radial velocity as -11 km/s instead of +11 km/s (SAO staff 1966) TABLE 7 The Lines Wavelength Source Identification (nm) Iron-Argon arc, 25/26 August 1982 433.3560 1 Ar I 434.811 1 Ar 437.076 1 Ar II 440.102 1 Ar 443.948 1 Ar II 444.888 1 Ar II 446.146 1 Ar 447.477 1 Ar 11 448.183 Ar II 451.0733 1 Ar I 454.508 1 Ar 457.939 1 Ar 458.993 1 Ar II 460.960 1 Ar 11 463.725 1 Ar II 465.794 1 Ar 470.2316 1 Ar I 472.691 1 Ar 476.489 1 Ar 480.607 1 Ar 484.790 1 Ar 487.990 1 Ar TX Piscium, 25/26 August 1982 Star 194, 25/26 August 1982 Iron-Argon arcs, 11/12 October 1982 TABLE 7 The Lines Wavelength (nm) 4 8 8 . 9 0 6 4 9 0 . 4 7 5 4 9 6 . 5 1 2 5 0 0 . 9 3 5 501 .71 6 4 5 5 . 4 0 0 3 4 9 3 . 4 0 8 6 5 8 8 . 9 9 5 3 5 8 9 . 5 9 2 3 4 3 4 . 7 4 9 6 4 3 5 . 8 3 5 5 4 6 . 0 7 5 3 I 4 0 4 . 4 4 1 8 407 .201 410 .391 4 1 3 . 1 7 3 4 T 5 . 8 5 9 0 4 1 9 . 9 9 3 425 .9361 4 2 7 . 7 5 5 Source Identification Ar Ar II Ar Ar Ar II Ba II Ba II Na D, Na D, Hg I Hg 1 Hg I Ar I Ar II Ar Ar II Ar I Ar II Ar I Ar II TX Piscium, 11/12 October 1982 Star 194, 11/12 October 1982 TABLE 7 The Lines Wavelength (nm) 430.0100 433.3560 434.81 1 440.102 448.183 451.0733 454.508 457.939 458.993 460.960 465.794 472.691 476.489 480.607 484.790 487.990 496.512 501 .716 455.4003 404.6561 407.781 1 Source Identification Ar 1 Ar I Ar Ar Ar II Ar I Ar Ar Ar II Ar II Ar Ar Ar Ar Ar Ar Ar Ar II Ba II Hg I Hg 1 TABLE 7 The Lines Wavelength Source Identification (nm) 4 3 4 . 7 4 9 6 1 Hg I 4 3 5 . 8 3 5 1 Hg I Sources: (1) Phelps 1982 (2) Moore 1959 156 A.7 25/26 AUGUST 1982 Figure 45 is a reproduction of the iron-argon arc used that night, while figure 46 gives the residuals of the polynomial lit, using some 27 lines. The r.m.s. deviation, 0.011, is a fair estimate of the accuracy of the line-position fitting command. The fit obtained was X = 418.925 + 0.1176261x - 5.187517*10"4x2 + 9.413873*10-V (A.4) One is struck, however, upon looking at figure 47, a composite of the two different frames used to represent the same spectrum (because of a break in the pixel pattern mentioned earlier, which necessitated two separate normalizations), by the fact that the wavelength region covered by the iron-argon arc does not overlap al all the wavelength region where the spectrum of star 194 rises above the noise level. The nature of the polynomial fit to the arc is such that this situation would lead to a simple extrapolation being wildly off the mark. To remedy this, we conducted a merged fit of the arc and the mercury lines in figure 47, using as parameters the polynomial coefficients and the pixel shift. The unstated assumption here is that the radial velocities of the arc and the mercury lines are the same (zero), certainly a very reasonable one. This has the effect of pinning down the redward extrapolation of the arc fit; the interpolation is still somewhat unreliable, but this is the best one can do. The resulting fit was X = 418.763 + 0.1191937x - 9.516234*10"V + 3.614151 *lQ-7x3 (A.5) where the mercury lines are shifted by 157 x ( a r c e q u i v a l e n t ) = x ( m e r c u r y ) - 2.066 (A.6) The r.m.s. deviation is 0.020. The observer velocity for the TX Piscium spectrum of that night (figure 48) was -12.16 km/s. Once the atomic lines have their expected wavelengths computed, TX Piscium's shift is solved for and the answer comes out x ( a r c e q u i v a l e n t ) = x ( T X P i s c i u m ) + 14.160 (A.7) with an r.m.s. deviation of 0.026. Meanwhile the shift of the star 194 spectrum, figure 47, versus the TX Piscium spectrum (figure 48) turned out to be x( 194 ) = x ( T X P i s c i u m e q u i v a l e n t ) + 15.587 (A.8) for the 516 nm banhead, and x( 194 ) .= x ( T X P i s c i u m e q u i v a l e n t ) + 15. 304 (A.9) for the 564 nm one. That the two shifts disagree is quite evident; that they disagree by so much is surprising since the shift values are significant at better than the 0.01 pixel level — i t is possible, however, that the numerical significance level was more indicative of the shifting routine's reliability than the data's; thus the difference above might be a better candidate for the estimated error value. It was decided to carry through the two different shifts, hence using them to "stake out", so to speak, the effective error on the final radial velocity determination. 158 Meanwhile still, the bandheads were (bund to lie at 861.638 and 1282.939 pixels, respectively, in the T X Piscium spectrum. Using equations (A.7) and (A.5), one obtains the bandheads observed wavelengths: 516.712 nm and 563.650 nm, respectively. Application of equations (A.8) and (A.9) yields the bandhead positions in the star 194 spectrum, which, put through equations (A.6) and (A.5), become in turn the observed wavelengths of the bandheads in star 194: 516.641 nm and 563.547 nm. Putting the whole mess through equation (A.3) finally yields the radial velocity measurements: -31.6 and -45.7 km/s. An alternative treatment is possible; starting with the merged fit of all three spectra, one obtains X = 418.759 + 0.1192392x - 9.612585*10"4x2 + 3.661348*10-7x1 (A.5') x ( a r c e q u i v a l e n t ) = x ( m e r c u r y ) - 2 . 043 (A.6') x ( a r c e q u i v a l e n t ) = x ( T X P i s c i u m ) + 14.133 (A.7') with an r.m.s. deviation of 0.021. Going through the proper paces, the radial velocity measurements become -28.4 and -42.7 km/s. 159 Figure 45: 25/26 August 1982 iron-argon arc Note how fast the instrumental response kills the iron-argon lines as one goes redward (higher pixel number). 160 + + 8 i 1 1 1 1 1 1 1 ~i 1 P I X E L . 2 0 0 0 0 Figure 46: Residuals of the polynomial fit to the 25/26 August 1982 iron-argon arc 161 PIXEL « Figure 47: 25/26 August 1982 spectrum of the carbon star 194 This frame was reduced separately blueward of pixel 644 because of a discontinuity in the Reticon's baseline. A second such discontinuity is visible redward of pixel 1650. 162 PIXEL « Figure 48: 25/26 August 1982 spectrum of TX Piscium 163 A.8 11/12 OCTOBER 1982 Figure 49 is a reproduction of the iron-argon arc used that, night, while figure 50 gives the residuals of the polynomial lit, using some 26 lines. The r.m.s. deviation is 0.012. The fit obtained was X = 341.719 + 0.1186003x - 8.871904*10"4x2 + 3.326363*10" V (A.10) This time, even though there is still a lack of overlap, the extrapolation, being over a much smaller range in x, "feels" safe. This is confirmed by the magnitude of the x3 coefficient in equation (A.10), which is very comparable to that of equation (A.5). Fitting Ax between the cluster carbon star's mercury sky lines and the arc, we get x ( a r c e q u i v a l e n t ) = x( 194 ) - 6. 025 (A.ll) with an r.m.s. deviation of 0.025. This time the observer radial velocity for TX Piscium was +10.83 km/s, and the selection of atomic lines usable withered down to one! Ax can be immediately computed to be x ( a r c e q u i v a l e n t ) = x ( T X P i s c i u m ) + 5.835 (A.12) Meanwhile the shift of the star 194 spectrum, figure 51, versus the TX Piscium spectrum (figure 52) turns out to be x( 194) = x ( T X P i s c i u m e q u i v a l e n t ) - 1.143 (A.13) for the 516 nm banhead, which is the only one visible. 164 From a bandhead position of 1552.335 in the TX Piscium spectrum, and using equations (A.12) and (A.10), one obtains the bandhead observed wavelength: 516.890 nm. Application of equation (A.13) to the precedingly quoted bandhead position yields its position in the star 194 spectrum, which position, put through equations (A.11) and (A.10), becomes the observed wavelength of the bandhead in star 194: 516.759 nm. Putting the whole mess through equation (A.3) finally yields the radial velocity measurement: -54.2 km/s. The alternative treatment, starting with the merged Fit of the arcs and star 194 spectra, yields A = 341.570 + 0.1190734x - 9.347502*10'4x2 + 3.479733*10"7x3 (A.14) x ( a r c e q u i v a l e n t ) = x ( m e r c u r y ) - 6 . 0 0 9 (A.IF) x ( a r c e q u i v a l e n t ) = x ( T X P i s c i u m ) + 5 . 8 2 3 (A.12') with an r.m.s. deviation of 0.014. Going through the proper paces, the radial velocity measurement becomes -52.5 km/s. 165 Figure 49: 11/12 October 1982 iron-argon arc 166 -+ — ++ T 1 2 0 0 0 i r ~i 1 —r PIXEL • Figure 50: Residuals of the polynomial fit to the 11/12 October 1982 iron-argon arc 167 Figure 51: 11/12 October 1982 spectrum of the carbon star 194 168 PIXEL tf Figure 52: 11/12 October 1982 of TX Piscium 169 A.9 STAR 196 This star had an extremely weak spectrum (figure 53); however its H )3 and mercury sky lines were defined well enough that an attempt at reduction was warrantable. As it turns out, this spectrum was taken in close sequence with the second star 194 spectrum (11/12 October 1982), so that the same arc could be used. On the basis of its single, poor signal-to-noise line, the calculation comes out as v = -47 ± 35 km/s r 196 where the error was taken as 0.5 pixel. This determination has very low weight, but it is interesting to note how close to the median of the star 194 determinations it comes. 170 PIXEL « Figure 53: 11/12 October 1982 spectrum of star 196 171 A.10 STAR 183 This star is quite bright (V — 13.75) as the cluster goes, and its spectrum (figure 54) has a good signal as a consequence. Even more useful is the appearance of both sky mercury lines and the interstellar absorption calcium K line. Or so we 4! thought. The interstellar absorption line's intrinsic radial velocity can be taken as one half of the galactic rotation velocity of star 183 (Munch 1968); using the Oort formula (Freeman 1975) with A = +15.0 km/s (Allen 1976) and assuming the star to lie in the cluster at Handschel's (1972) distance of 6 kpc, this comes out as - 27.7 km/s. The surprise was that the Ca K line is completely discordant in radial velocity with the sky mercury lines, and by a large amount (about 110 km/s in excess rec/shift). It is most unlikely that the Ca K line's excess radial velocity comes from a greater galactic rotation term, hence a greater distance, because this would make the star intolerably bright (absolute magnitude in excess of -20!). Furthermore, the velocities given by the other lines (using the mercury lines as standards alone) are all wildly discordant (r.m.s. deviation of 70 km/s). Something is amiss. Much more probably, we simply misidentified this and several other lines, and/or the line shapes are poorer than they appear to the eye (an unlikely-conjecture). This spectrum (and several others left untouched during the course of this work) should be re-examined in the near future. In conclusion, the determination of star 183's radial velocity was a failure. 172 o o o o (0 0) CO CO 10 § w 100 300 500 700 900 1100 PIXEL ti 1300 1500 1700 Figure 54: 13/14 October 1982 spectrum of star 183 173 A.1.1 THF. CARBON STAR'S RADIAL VELOCITY The differenl measurements are: -31.6 km/s -45.6 km/s -28.4 km/s -42.7 km/s -54.2 km/s -52.5 km/s Giving all those entries the same weight (none is better than its peers), one concludes that v = -43 ± 10 km/s r 194 Meanwhile, Fawley and Cohen (1974) have measured v = -72 ± 5 km/s r 172 v = -61 ± 5 km/s r B l b v = -61 ± 6 km/s r 130 v = -64 ± 5 km/s r 88 and Moffat (1980) has found v = -74 ± 9 km/s r mean for 6 OB stars. 174 IT one had to decide the issue ol' the carbon star's membership on the basis of this data alone, one would probably declare that, on the one hand, things look bad for the pro-membership fans, but that, on the other hand, the radial velocity determination's reliability is sufficiently marginal that there is still a chance. Note, however, that we found v = -45 ± 30 km/s r 196 which might indicate that there is some systematic error causing the discrepancy between our radial velocities and those of Blanco et al.; this certainly sounds more likely than the possibility that the cluster itself has a large intrinsic velocity scatter. In conclusion, our radial velocity determinations do not allow us to confirm or infirm the carbon star membership hypothesis. In view of the theoretical importance of a positive resolution of this question, we urge ourselves and the interested astronomical community to endeavor to resolve the question as soon as possible through further and better observations of the cluster. 175 APPENDIX B TABLE 8 Ultraviolet Flux Indices Object IB 2B 3B 4A 6 10A 11A 11B 12 13 15 16 18 19 21 22 23 25 26 27 28 Plate 12 0.5117E+05 0.2017E+04 0.3454E+04 0.2701E+04 0.3126E+04 0.2878E+04 0.8542E+04 0.1239E+04 0.2921E+04 0.4164E+02 0.1397 E+04 0.3124E+04 0.6956E+03 0.5332E+04 Plate 334 0.5665E+05 0.1412E+05 0.4180E+05 0.1384E+05 0.5013E +04 0.3127E+05 0.7173E+05 0.3877E+04 0.2941E+04 0.2525E+04 0.2841E+04 0.3285E+04 0.1852E + 04 Object. 29 31 32A 33 34 35 36 37A 38 43 39 41 42 40 44A 46 47 48 49 52 53 Plate 12 0.1572E+04 0.1235E+04 0.1714E+05 0.1872E+04 0.2901E+03 0.1642E+04 0.2504E+04 0.1009E+05 0.1009E+04 0.1147E+04 0.5684E+03 0.1029E+04 0.7624E+04 0.3997E+03 0.3620E+05 0.3961E+04 0.1717E+04 0.2887E+041 0.7449E+03 0.2208E+04 0.9078E+03 Plate 334 0.1225E+05 0.2095E+04 0.2273E+04 0.1860E+04 0.667 2E+04 0.5473E+04 0.2311E+05 0.2407E+04 0.2566E+041 176 TABLE 8 Ultraviolet Flux Indices Object 54 59 60A 61 62 64 68 69 70 71 72 X5 65 66 67A 73 74 75 76 77 79 Plate 12 0.561 OF.+ 04 0.3100E+04 0.1753E+05 0.2633E+04 0.3107E+04 0.1288E+04 0.6836E + 03 0.1830E + 04 0.5098E+03 0.9246E+03 0.8961E + 03 0.1335E+04 0.1297E+05 0.1366E + 04 0.1420E+05 0.1156E + 04 0.1547E+04 0.7547E+03 0.1665E+04 0.3199E+0415 0.7838E+03 Plate 334 0.3570E + 04 0.1824E+04 0.1159E + 05 0.1983E+04 0.1790E+04 0.1620E+04 0.8354E + 04 0.8996E+04 0.1575E+04 0.1869E+04 0.2038E+0415 Object 80 81 82 83A 83B X6 84A 85 86 87A 88A X7 89 X8 90 91 92 93 94 95 96A Plate 12 0..2731E+04 0.4492E+04 0.4157E+04 0.1130E + 04 0.1045E+05 0.2631E + 04 0.9562E + 03 0.1678E+05 0.1268E+04 0.1244E+04 0.8598E+04 0.1075E+04 0.1597E+04 0.5350E + 04 0.3211E+04 0.6940E+04 0.5451E+04 0.2264E+04 0.2356E+05 Plate 334 0.2449E + 04 0.2900E+04 0.6824E+05 0.2897 E+04 0.9364E+04 0.4016E+04 0.1241E+05 0.5133E+04 0.431.9E+04 0.1998E + 04 0.4367E+04 0.4362E+04 0.3732E+04 0.1589E+05 177 TABLE 8 Ultraviolet Flux Indices Object 97 99 100 103 104 105 106 107 114 X10 116 117 118 119A 120 122 125 126 A X l l 127 128 Plate 12 0.1487E+05 0.2855E+04 0.2467E+03 0.5200E+04 0.1151E+04 0..1312E+04 0.6156E+04 0.3830E+04 0.2570E+04 0.1464E+04 0.1112E+04 0.2285E + 04 0..1517E+04 0.1514E+05 0.1819E+04 0.2771E + 04 0.1366E+05 0.2929E+05 0.9137E+03 0.1739E+04 0.1005E+04 Plate 334 0.9524E+04 0.3326E+04 0.2063E+04 0.3183E + 04 0.5135E + 04 0.5753E+04 0.1917E+04 0.9754E+04 0.1596E+04 0.2007E+04 0.9490E+04 0.2525E+05 0.4089E+04 0.1677E+04 Object 129 130 A 131 132A 133 134A X13 135 137 139 140 141 142 144 145 146 147 148 149 151 152 Plate 12 0.2160E+04 0.3838E+03 0.3837E + 04 0.1785E+05 0.9007E + 04 0.2502E+O5 0.9767E+03 0.1059E+04 0.3275E+04 0.2246E+04 0.1799E+0515 0.7440E+0415 0.1647E+05 0.1599E+05 0.1204E+04 0.6835E + 04 0.6056E+04 0.2387E+0415 0.6120E+03 0.8397E+04 Plate 334 0.1.599E + 04 0.2853E+04 O.1205E + O5 0.6506E+04 0.1749E+0515 0.2971E+04 0.2085E+04 0.1242E+05 0.5067E+0415 0..1123E + 05 0.1097E + 05 0.403 IE+04 0.4462E + 04 0.5040E+04 178 TABLE 8 Ultraviolet Flux Indices Object 153 154 155 156 158 159A 161 162 X15 163A 164 165 166 169 168 170 171 172A 173 174 175 Plate 12 0.8943E+04 0.4687E+04 0.6295E + 04 0.1074E+05 0.4247E+04 0.2205E+05 0.9290E + 03 0.8512E+0415 0.1241E+05 0.6873E+03 0.4339E + 04 0.4144E+03 0.7388E + 03 0.1023E+04 0.1938E+04 0.3134E+04 0.5956E+03 0.6238E+04 0.2385E+04 0.1396E+04 Plate 334 0.6445E+04 0.4452E + 04 0.3782E+04 0.5807E+04 0.3055E + 04 0.1354E+05 0.8472E+04 0.3686E+04 0.7808E+04 0.2849E+04 0.1296E+04 0.1822E+04 0.3569E+04 0.2274E+04 Object 176 178 179A 181 182 183A 184 185 X16 186 187 188 190 191 192A 195 196 197 198 199 201 Plate 12 0.2203E+04 0.1562E+04 0.1586E+05 0.6940E+04 0.2218E+04 0.2184E+05 0.2446E+04 0.1121E+05 0.3203E + 03 0.3840E+04 0.4546E+04 0.1092E+05 0.1216E+04 0.3549E + 04 0.2492E+05 0.7835E+03 0.1672E+05 0.1054E+04 0.3324E+04 0.3520E+04 0.1036E+04 Plate 334 0.1622E+04 0.1123E+05 0.4713E+04 0.1497E+04 0.1372E+05 0.1644E+04 0.6845E+04 0.2248E+04 0.2800E+04 0.7746E+04 0.2055E+04 0.I548E+05 0.1048E+05 0.2591E+04 0.2390E+04 179 TABLE 8 Ultraviolet Flux Indices Object Plate 12 Plate 334 Object Plate 12 Plate 334 203 0.3366E+04 0.2224E+04 219 0.1681E+05 0.1099E + 05 204A 0.4633E+05 220 0.1257E+04 204B 0.1685E+04 221 0.1282E + 04 208 0.1317E+04 222 0.2047E + 04 0.1436E+04 209 0.1263E+04 224 0.1716E + 04 210 0.2117E+04 225A 0.2100E+05 0.1287E+05 211 0.1467E+05 0.9878E+04 227A 0.2629E+05 0.1729E+05 212 0.2524E+04 0.1653E+04 228 0.8528E + 03 X18 0.1430E+04 229 0.2110E+04 0.1394E+04 213 0.4799E+04 0.3038E+04 X21 0.6530E+03 214 0.5952E+04 0.3527E+04 230 0.7159E+04 0.5494E+04 216 0.1606E+04 231 0.5688E+04 0.3037E+04 217 0.8328E+03 232 0.4539E+03 0.2179E+04 218 0.1060E+05 0.7827E+04 233 0.5059E+03 (,s) Half-weight (16) Triple half-weight (three half-weight entries) 180 Object 2B 4A 4B 5 6 7 9 10A 10B 11B X2 12 13 14 15 16 18 19 20 21 22 Plate 10 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.6263E+04 O.2011E+05 0.5309E+04 0.5641E+04 0.2241E+04 0.8080E+04 0.1146E+05 0.2725E+04 0.9189E+04 0.1086E+05 0.8727E+04 0.2014E+05 0.3446E+04 0.2568E+04 0.9344E+04 0.3709E + 05 0.268 IE+ 04 0.5125E+04 0.1381E+05 0.5238E+04 0.3U5E+04 0.3540E+04 0.1635E+05 0.3414E+04 0.5354E+04 0.5414E+04 0.2160E+04 0.6746E+04 0.7012E+04 0.6624E+04 0.1498E+05 0.3957E+04 0.1924E+04 0.5767E+04 0.3469E + 05 0.1460E + 04 0.43 5 IE+04 0.1428E + 05 0.5165E+04 0.4634E+04 0.4496E+04 0.1728E + 05 0.1933E+04 0.5827E+04 0.6732E+04 0.2374E+04 0.7492E+04 0.8339E + 04 0.6379E+04 0.1487E + 05 0.3426E+04 0.3466E+04 0.6225E+04 Plate 387 0.3618E+0515 0.2758E + 05 0.1233E + 04 0.2868E+04 0.9391E+04 0.3330E + 04 0.2735E + 04 0.5702E + 05 0.3592E + 04 0.1061E+05 0.2406E + 04 0.3724E + 04 0.4711E + 04 0.1233E + 04 0.4529E + 04 0.5538E+04 0.3807E+04 0.9962E+04 0.2990E+04 0.1678E + 04 0.4054E+04 Plate 410 0.3507E + 05 1 5 0.2522E+05 0.1178E+04 0.3042E+04 0.1027E+05 0.3959E + 04 0.1825E + 04 0.5467E+05 0.3763E+04 0.1214E+05 0.1982E+04 0.4091E+04 0.4636E+04 0.2581E+04 0.51.24E+04 0.6203E+04 0.4084E+04 0.1121E+05 0.2375E+04 0.1119E+04 0.4237E+04 181 Object 23 24 25 26 27 28 29 30 31 32A 32B 33 34 35 36 37A 37B 38 39 40 41 Plate 10 0.2529E+04 0.3670E + 04 0.4150E+04 0.5058E + 04 0.1703E+04 0.1384E+05 0.7189E+04 0.4035E+04 0.2641E+04 0.4092E+05 0.5556E+04 0.2247E + 04 0.1697E + 05 0.6248E+0415 0.3387E+05 0.2796E+04 0.4201E+04 0.1090E+05 0.3613E+04'5 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.1993E + 04 0.3433E+04 0.3160E+04 0.3448E+04 0.1919E+04 0.9756E+04 0.4698E+04 0.1902E+04 0.3723E+04 0.3056E+05 0.9797E+03 0.3768E+04 0.2885E+04 0.4804E+04 0.4122E+04 0.2546E+05 0.1342E+04 0.2148E+04 0.2900E+04 0.8603E+04 0.2587E+04 0.2708E+04 0.3515E + 04 0.3651E+04 0.4297E + 04 0.1907E+04 0.1044E + 05 0.4233E+04 0.2395E+04 0.3838E+04 0.2988E+05 0.1602E+04 0.4097E + 04 0.2229E + 04 0.4630E+04 0.3542E+04 0.2620E + 05 0.9833E+03 0.2487E+04 0.2734E+04 0.9685E + 04 0.2908E+04 Plate 387 0.1207E+04 0.2168E+04 0.3026E+04 0.2652E+04 0.9096E+03 0.8613E +04 0.2970E+04 0.1086E+04 0.1717E+04 0.2334E+05 0.2521E+04 0.1717E + 04 0.3167E+04 0.1988E + 04 0.1894E+05 0.1105E+04 0.1372E+04 0.6043E+04 0.9174E+03 Plate 410 0.1196E+04 0.2978E+04 0.1954E + 04 0.2526E+04 0.1315E+04 0.8233E+04 0.3052E+04 0.2007E + 04 0.1.633E+04 0.2338E+05 0.1119E+04 0.1808E+04 0.4069E + 04 0.2903E+04 0.1899E+05 0.1805E+04 0.1816E+04 0.6094E+04 0.1000E+04 182 TABLE 9 Blue Flux Indices Dbject Plate 10 Plate 328 Plate 330 Plate 387 Plate 410 42 0.2327E + 05 1 5 0.1686E+05 0.1725E+05 0.1157E + 05 0.1187E+05 43 0.2622E+04 0.1866E+04 0.1518E+04 0.1600E + 04 0.4659E + 03 44A 0.4531 E+05 0.4598E + 05 0.3542E + 05 0.3634E + 05 44B 0.2514E+04 0.3394E+04 0.1332E + 04 0.1650E+04 45 0.2545E+04 0.1109E+04 0.2749E+04 0.8834E+03 0.7556E+03 46 0.1180E + 05 0.9010E+04 0.8850E + 04 0.5524E+04 0.6903E+04 47 0.5336E+04 0.3849E+04 0.3934E+04 0.2388 E+04 0.1918E+04 48 0.1839E + 05 0.1111E+05 0.1290E+05 0.8902E+04 0.7359E+04 X4 0.6270E+04 0.3106E+04 0.4745E + 04 0.1369E+04 0.5153E+03 X3 0.2482E+04 0.1903E+04 0.3179E+04 0.4056E + 04'5 0.1285E+04 49 0.1875E+04 0.3046E+04 0.1766E+04 0.2015E+04 0.2154E+03 50 0.27 HE+ 04 0.2521E+04 0.2969E+04 0.1938E+04 0.1793E+04 51 0.2577E + 04 0.1939E+04 0.2166E + 04 0.1174E + 04 0.1071E+04 52 0.4965E + 04 . 0.3115E+04 0.2972E+04 0.2587E + 04 0.2588E+04 53 0.4293E+04 0.3311E+04 0.3397E+04 0.2090 E+04 0.2870E + 04 54 0.1704E + 05 0.1156E + 05 0.1191E+05 0.8127E+04 0.8911E+04 55 0.3080E+04 0.1831E+04 0.2930E+04 0.1541E + 04 0.1610E+04 56 0.2418E+04 0.2390E+04 0.2205E + 04 0.1715E+04 0.1791E+04 58 0.2122E+04 0.6831E+03 0.1586E+04 0.9497E+03 0.5510E+03 59 0.7475E+04 0.6672E+04 0.6558E+04 0.4030E+04 0.4516E+04 60A 0.3666E+05 0.2640E+05 0.2790E+05 0.2016E+05 0.1912E+05 183 Object 601$ 61 62 63 64 68 69 70 71 72 65 66 67A 67B 73 74 75 76 77 78 79 Plate 10 0.8082E+04 0.1017E + 05 0.4292E + 04 0.4306E+04 0.2275E+04 0.6668E+0415 0.6957E + 04 0.5069E+04 0.1867E + 04 0.2918E + 05 0.7779E + 04 0.3548E+05 0.3501 E +04 0.4003E+04 0.5988E+04 0.6909E+04 0.1276E + 05 0.8359E+04 0.2603E+04 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.1922E+04 0.6045E+04 0.7980E+04 0.4681 E+04 0.3320E+04 0.1006E+04 0.4536E+04 0.1861E+04 0.3709E+04 0.1997E+04 0.1994E+05 0.4962E+04 0.2487E+05 0.1074E+04 0.3418E+04 0.3079E+04 0.4277E+04 0.5264E+04 0.9343E+04 0.6537E+04 0.1384E+04 0.9884E+03 0.6826E+04 0.8280E+04 0.3968E+04 0.2334E+04 0.1459E+04 0.4904E+04 0.1487E + 04 0.4157E+04 0.2026E+04 0.2070E+05 0.5779E + 04 0.2729E + 05 0.1354E+04 0.3103E + 04 0.3048E+04 0.5421E+04 0.4768E+04 0.9939E+04 0.8107E+04 0.1809E+04 Plate 387 0.1016E + 04 0.4172E+04 0.5336E+04 0.2721E+04 0.3002E+04 0.1113E+04 0.3072E+04 0.2349E+04 0.2891E+04 0.1332E+04 0.1447E+05 0.3651E+04 0.1904E+05 0.3715E+04 0.2495E+04 0.2761E+04 0.3206E+04 0.5715E+04 0.4939E+04 0.3140E+04 Plate 410 0.4758E+04 0.5263E + 04 0.1449E+04 0.2420E + 04 0.7168E+03 0.3408E + 04 0.1572E+04 0.3594E+04 0.7098E+03 0.1440E+05 0.3462E+04 0.2010E+05 0.2651E+04 0.2242E+04 0.4308E+04 0.2988E+04 0.4405E+04 0.3482E+04 0.1788E+04 184 Object 80 81 82 83B X6 84A 84B 85 86 87A 87B X7 88A 88B 89 X8 90 91 92 93 94 Plate 10 0.5684E+04 0.1153E + 05 0.1763E+0515 0.3335E+04 0.3799E+05 0.2179E+05 0.3295E+04 0.3963E+05 0.8311E+04 0.2756E+05 0.1898E+05 0.4376E + 04 0.3253E+04 0.1613E + 05 0.6687E + 04 0.1907E+05 0.1876E+05 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.3657E+04 0.7186E+04 0.7564E+04 0.2971E+05 0.1757E+04 0.2470E+05 0.6370E+03 0.1.094E+05 0.2733E + 04 0.3205E + 05 0.2796E+04 0.2588E+04 0.2410E+05 0.1278E+04 0.1345E + 05 0.1268E + 04 0.2869E+04 0.1180E+05 0.5651E+04 0.1378E + 05 0.9218E+04 0.3046E+04 0.6862E + 04 0.7462E+04 O.2835E+05 0.1122E+04 0.2475E + 05 0.140 IE+04 0.1132E+05 0.3295E + 04 0.3148E+05 0.1126E+04 0.2474E + 04 0.2452E+05 0.1689E+04 0.1400E+05 0.1964E+04 0.1326E+04 0.1142E + 05 0.6043E+04 0.1323E+05 0.1044E+05 Plate 387 0.1167E + 04 0.9950E+04 0.4573E+04 0.2792E+05 0.1428E+04 0.1916E + 05 0.8601E+04 0.6669E+03 0.2403E + 05 0.8882E + 04 0.2011E+04 0.1442E+04 0.8344E + 04 0.3813E+04 0.9343E+04 0.3225E+04 Plate 410 0.3051E+04 0.8697E+04 0.5671E+04 0.2502E+05 0.6695E + 03 0.1851E + 05 0.9838E+04 0.2364E+04 0.2470E+05 0.2228E + 04 0.4569E+04 0.1805E + 05 0.1752E+05 0.9404E+04 0.1247E+04 0.2287E + 04 0.8957E+04 0.3578E+04 0.9541E+04 0.8556E+04 185 TABLE 9 Blue Flux Indices Object Plate 10 Plate 328 Plate 330 Plate 387 Plate 410 95 0.1633E+05 0.7468E+04 0.7656E+04 0.6078E+04 0.8549E+04 X9 0.2775E + 04 0.2695E+04 0.2007E + 04 0.5091E + 04 96A 0.4683E+05 0.3973 E+05 0.3894E + 05 0.3027 E+05 0.2984E+05 96B 0.3050E + 04 0.1058E+04 97 0.3307E+05 0.2438E + 05' 0.2500E + 05 0.1764E + 05 0.1822E+05 99 0.9738E+04 0.5324E + 04 0.8349E+04 0.3827E + 04 0.4977E+04 100 0.1051E+05 0.3708E+04 0.7594E+04 0.2594E+04 0.2938E+04 98 0.247 5E+04 0.6218E+04 0.3225E+04 101 0.2579E+04 0.3207E + 04 0.4153E+04 0.2193E+04 0.3721E+04 102 0.4142E+04 0.2840E+04 0.4066E+04 0.3189E+04 0.4985E+03 103 0.1551E + 05 0.1188E+05 0.1277E+05 0.7877E+04 0.8663E+04 104 0.3716E+04 0.2275E+04 0.2481E+04 0.2326E+04 0.1048E+04 105 0.3460E + 04 0.2189E+04 0.1712E+04 0.1459E + 04 0.1484E+04 106 0.2151E+0515 0.1018E+05 0.1376E+05 0.1131E + 05 0.6906E+04 107 0.2193E+0515 0.1194E+05 0.1199E + 05 0.1282E + 05 0.5777E+04 114 0.6806E+0415 0.5256E+04 0.6162E+04 0.2754E+04 0.3298E+04 X10 0.7358E+04 0.1535E+04 0.1601E+04 0.1034E+04 0.2849E+03 115 0.2842E+04 0.3074E+04 0.3869E+04 0.2914E+04 0.9786E+03 116 0.2522E+04 0.1242E+04 0.2067E+04 0.1097E+04 0.6329E+03 117 0.5431E+0415 0.3710E+04 0.3909E+04 0.1492E+04 0.2055E+04 118 0.5664E + 04 0.3556E+04 0.4125E+04 0.3103E+04 0.2270E+04 186 Object 119A 119B 120 121 122 124 125 126 A 126B X l l 127 128 129 X12 130A 130B 131 132A 132B 133 134 A Plate 10 0.3581E + 05 0.7000E+04 0.2437E+04 0.8265E+04 0.2372E+04 0.3470E + 0515 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.8241 E+04 0.1034E + 05 0.4555E + 04 0.2805E+05 0.1083E+05 0.3678E+05 0.2460E+05 0.4965E+05 0.2696E+05 0.1227E+04 0.4220E+04 0.2091 E+04 0.6639E+04 0.3003E+04 0.2407E+05 0.3551E+04 0.1508E+04 0.4308E+04 0.3281E+04 0.1668E+04 0.2401E+05 0.9807E+03 0.7535E+04 0.2917E + 05 0.1372E+04 0.1715E+05 0.4375E+05 0.2726E+05 0.9845E+03 0.5515E + 04 0.3945E + 04 0.6754E+04 0.2779E + 04 0.2417E +05 0.5167E+05 0.2954E + 04 0.1080E + 05 0.2367E+04 0.3601 E+ 04 0.3927E+04 0.1987E+04 0.2320E + 05 0.1029E + 04 0.8056E + 04 0.2932E + 05 0.1800E+04 0.1888E+05 0.4461E+05 Plate 387 Plate 410 0.I922E+05 . 0.1933E + 05 0.2834E + 04 0.1253E+04 0.4093E+04 0.1797E+04 0.1758E + 05 0.3958E+05 0.2737E+0415 0.3910E+04 0.2717E+04 0.3514E+04 0.2831E+04 0.1688E+05 0.3188E+04 0.2071E+04 0.5233E+04 0.1375E+04 0.1738E+05 0.4241E+05 0.2388E+04 0.9339E+04 0.9191E+03 0.1927E+04 0.3503E+04 0.1760E+04 0.1739E+05 0.5074E+04 0.5838E+04 0.2057E+05 0.2066E + 05 0.1150E+05 0.1189E+05 0.3517E + 05 0.3315E+05 187 Object 134B X13 135 136 137 X14 139 140 141 142 142b 144 145 146 147 148 149 150 151 152 153 Plate 10 0.6036E+04 0.3546E+04 0.2052E + 04 0.1854E+05 0.6858E+04 0.3727E+04 0.6409E+04 0.3853E+05 0.2368E+05 0.3905E+05 0.3319E + 05 0.4739E+0415 0.1594E+0515 0.1652E+05 0.1418E+05 0.1236E+05 0.1329E+05 0.1905E+05 0.2111E+05 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.251IE + 04 0.5935E+04 0.2878E+04 0.2473E + 04 0.9522E+04 0.2676E + 04 0.2365E+04 0.5038E+04 0.2817E + 05 0.1330E+05 0.2138E+04 0.2811E+05 0.2584E+05 0.1162E+05 0.5960E+04 0.5898E + 04 0.4171E+04 0.1323E+05 0.1537E+05 0.2615E + 04 0.2885E+04 0.2902E + 04 0.1463E + 04 0.1153E+05 0.4779E+04 0.2705E+04 0.6975E+04 0.2964E+05 0.1422E+05 0.3603E+04 0.2808E + 05 0.2487E+05 0.2947E+04 0.3784E + 04 0.1066E+05 0.1088E + 05 0.1262E + 05 0.8064E + 04 0.6209E+04 0.7941E + 04 0.1312E+05 0.1619E+05 Plate 387 0.1038E+04 0.1161E+04 0.7785E+03 0.5933E+04 0.1455E+04 0.2444E + 04 0.5766E+04 0.2275E+05 0.8806E+04 0.2114E + 05 0.1991E + 05 0.1628E+04 0.7355E + 04 0.8813E+04 0.6394E+04 0.3984E+04 0.2241E+04 0.8651E+04 0.1027E+05 Plate 410 0.2443E+04 0.1076E + 04 0.9234E+04 0.2694E+04 0.1907E+04 0.3325E+04 0.2007E+05 0.1327E+05 0.4524E+04 0.2227E+05 0.1921E+05 0.1999E+04 0.7077E+04 0.9004E+04 0.4051E+04 0.3927E+04 0.4344E+04 0.9476E+04 0.1048E+05 188 Object 154 155 156 157 158 159 A 159B 160 161 162 X15 163A 163B 164 165 166 167 169 168 170 171 Plate 10 0.1525E+05 0.1544E+05 0.2813E + 05 0.2823E+04 0.1098E+05 0.4350E + 05 0.473 IE+04 0.2388E+05 0.3622E + 04 0.2660E+05 0.2741E+04 0.1264E+05 0.2995E+04 0.1099E+04 0.2296E+04 0.3439E+04 0.6435E+04 0.9615E+04 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.1105E + 05 0.1178E + 05 0.1651E + 05 0.2211E + 04 0.7528E+04 0.3291E + 05 0.3184E+04 0.1533E+05 0.2173E+04 0.1814E+04 0.8986E + 04 0.2832E+04 0.1472E + 04 0.1668E + 04 0.1854E+04 0.4225E+04 0.1107E+05 0.1238E+ 05 0.1641E+05 0.2413E+04 0.8099E+04 0.3341E+05 0.2035E + 04 .0.1023E+04 0.2474E + 04 0.1885E + 04 0.3694E+04 0.1532E+05 0.3957E+04 0.3153E+04 0.1982E + 05 0.1974E+05 0.2148E+04 0.2029E+04 0.1054E+05 0.2625E+04 0.9450E+03 0.1398E+04 0.2694E+04 0.4085E+04 0.6204E + 04 0.5881E+04 Plate 387 0.7130E+04 0.6513E+04 0.1184E+05 0.1548E+04 0.4287E+04 0.2489E + 05 0.1213E+04 0.2242E+04 0.1285E+05 0.3162E+04 0.1391E+05 0.1786E + 04 0.5592E+04 0.7903E+03 0.6491E+03 0.2433E+04 0.1979E+04 0.2398E+04 0.3433E+04 Plate 410 0.8272E+04 0.9878E+04 0.1248E+05 0.1775E+04 0.5822E+04 0.2464E+05 0.1.624E+04 0.2241E+04 0.1052E+05 0.1369E+05 0.2189E+04 0.6246E+04 0.4046E+03 0.1934E+03 0.9893E+03 0.7643E+03 0.2770E+04 0.4741E+04 189 Object 172A 173 174 175 176 178 179A 179B 180 181 182 183A 183B 184 185 X16 X17 186 187 188 189 Plate 10 0.2467E+05 0.1581E + 05 0.7434E+04 0.2644E+04 0.7479E+04 0.5002E+04 0.3471E+05 0.2636E+04 0.2289E+05 0.5974E + 04 0.4794E + 05 0.7746E + 04 0.2726E+05 0.2954E + 04 0.2530E+04 0.1702E + 05 0.1192E+05 0.2497E+05 0.2211E+04 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.2189E + 05 0.1047E+05 0.6456E+04 0.2934E + 04 0.5496E+04 0.3840E+04 0.2488E+05 0.1583E + 04 0.3291E + 04 0.1744E+05 0.4771E+04 0.3705E+05 0.1446E+04 0.9983E + 04 0.2129E+05 0.1927E + 04 0.1470E+04 0.1246E + 05 0.8083E+04 0.1743E+05 0.1723E+04 0.2105E+05 0.1168E + 05 0.6505E+04 0.3474E+04 0.6864E+04 0.3556E+04 0.2676E+05 0.1699E + 04 0.1676E+04 0.1683E+05 0.3940E+04 0.3696E+05 0.2239E+04 0.6235E+04 0.2187E+05 0.1705E+04 0.1727E+04 0.1219E+05 0.8646E+04 0.1765E+05 0.1264E+04 Plate 387 0.157 IE+05 0.6952E+04 0.3895E + 04 0.1979E+04 0.4979E+04 0.2602 E+04 0.1883E+05 0.1677E + 04 0.1113E + 05 0.2575E+04 0.2795 E +05 0.1478E + 04 0.3602E+04 0.1509E+05 0.1839E+04 0.1015E+04 0.8366E+04 0.5264E+04 0.1276E+05 0.1764E+04 Plate 410 0.1578E+05 0.7362E+04 0.3934E+04 0.1627E+04 0.4392E+04 0.2218E+04 0.1788E+05 0.1935E+04 0.1225E+05 0.3665E+04 0.2723E+05 0.2112E+04 0.4.167E+04 0.1480E+05 0.1630E+04 0.1017E+04 0.9003E+04 0.5762E+04 0.1327E+05 0.1722E+04 190 Object 190 191 192A 192B 193 194 195 196 197 198 199 200 201 202 205 203 204B 206 207 208 209 Plate 10 0.7758E+04 0.1490E+05 0.5244E + 05 0.4238E+04 0.1346E+04 0.7392E + 04 0.4041 E+05 0.5711E+04 0.9936E+04 0.1079E+05 0.3480E+04 0.5212E+04 0.3371 E +04 0.3093E+04 0.1375E+05 0.3341E + 04 0.3389E+04 0.3953E+04 0.4885E+04 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.5373F. + 04 0.9912E+04 0.4079E + 05 0.2739E+04 0.2309E + 04 0.2386E+04 0.5206E+04 0.2992E+05 0.3640E+04 0.7853E+04 0.7142E+04 0.2928E+04 0.3889E+04 0.2U4E+04 0.8941 E+03 0.9627E+04 0.6992E+04 0.3263E+04 0.2330E+04 0.4037E+04 0.3379E+04 0.5625E+04 0.1065E+05 0.4029E+05 0.2615E+04 0.3400E+04 0.2530E+04 0.4395E+04 0.3064E+05 0.3586E+04 0.8576E+04 0.8146E+04 0.2534E+04 0.4923E+04 0.3136E+04 0.2119E+04 0.9670E+04 0.8251E+04 0.2132E + 04 0.2629E+04 0.4437E+04 0.3237E+04 Plate 387 0.3518E+04 0.6778E + 04 0.3139E+05 0.1359E + 04 0.2494E+04 0.9752E+03 0.2467E+04 0.2263E+05 0.2172E + 04 0.5658E+04 0.4086E + 04 0.2164E+04 0.3001 E +04 0.2409E+04 0.1235E+04 0.6279E+04 0.5221E+04 0.2673E + 04 0.1234E+04 0.2795E+04 0.2008E+04 Plate 410 0.4247E+04 0.7608E+04 0.3180E + 05 0.1531E+04 0.2044E+04 0.1679E+04 0.2988E+04 0.2185E + 05 0.1889E+04 0.5604E+04 0.5149E+04 0.1146E+04 0.1874E+04 0.1337E+04 0.1152E+04 0.7274E+04 0.4866E+04 0.2377E+04 0.1847E+04 0.3630E+04 0.1890E+04 191 Object 210 211 212 X18 213 214 215 216 217 X19 218 219 X20 220 221 222 223 224 225A 225B 227A Plate 10 0.3379E+04 0.3162E+05 0.6581E+04 0.1859E+04 0.1308E+05 0.1490E+05 0.4065E+04 0.2981E + 04 0.5000E + 04 0.2385E+04 0.2464E+05 0.4203E+05 0.2786E+04 0.3433E + 04 0.4166E+04 0.5845E+04 0.2816E+04 0.4602E + 04 0.4750E+05 0.5695E+05 TABLE 9 Blue Flux Indices Plate 328 Plate 330 0.2136E + 04 0.2364E + 05 0.4280E + 04 0.1593E+04 0.8782E + 04 0.1133E+05 0.3391E+04 0.2689E+04 0.3281E+04 0.1037E+04 0.1790E+05 0.3188E+05 0.2014E+04 0.2670E+04 0.2776E+04 0.4042E+04 0.2066E+04 0.3897E+04 0.3556E+05 0.2263E+04 0.4460E+05 0.3018E+04 0.2421E+05 0.5558E+04 0.1603E+04 0.902 IE+04 0.1188E+05 0.3318E + 04 0.3327E + 04 0.3741E+04 0.1513E+04 0.1881E+05 0.3243E+05 0.3269E+04 0.2881E + 04 0.4279E+04 0.5005E+04 0.1725E+04 0.4162E+04 0.3519E+05 0.2512E+04 0.4367E+05 Plate 387 0.1776E+04 0.1706E+05 0.4301E+04 0.1256E+04 0.6561E+04 0.6769E+04 0.2231E+04 0.1539E+04 0.1645E+04 0.1826E+04 0.1239E+05 0.2410E + 05 0.6666E+03 0.2290E+04 0.1945E + 04 0.2732E+04 0.1854E+04 0.1852E+04 0.2666E+05 0.1579E+04 0.3403E+05 Plate 410 0.2871E+04 0.1744E+05 0.3492E+04 0.1985E+04 0.6154E + 04 0.7865E+04 0.2467E+04 0.1448E+04 0.2980E+04 0.1554E+04 0.1422E+05 0.2459E+05 0.1691E+04 0.1918E+04 0.1842E + 04 0.2912E+04 0.1549E+04 0.2899E+04 0.2702E+05 0.1467E+04 0.3367E+05 192 TABLE 9 Blue Flux Indices Object Plate 10 Plate 328 Plate 330 Plate 387 Plate 410 227B 0.2681E + 04 0.3037E+04 228 0.3080E+04 0.1476E+04 0.2258E+04 0.1271E+04 0.1539E + 04 229 0.4973E+04 0.3251E+04 0.3124E+04 0.2995E+04 0.2196E + 04 X21 0.2780E+04 0.2094E+04 0.1389E+04 0.9729E+03 230 0.1850E+05 0.1373E+05 0.1419E+05 0.9578E+04 0.1000E + 05 231 0.1260E+05 0.8994E+04 0.8830E+04 0.6193E+04 0.6442E + 04 232 0.4343E+04 0.3715E+04 0.4083E + 04 0.2662E+04 0.2277E + 04 233 0.3138E+04 0.2626E+04 0.2889E+04 0.1506E+04 0.6291E + 03 (15) Half-weight 193 Object 2B 3B 4A 4B 5 6 7 9 10A 10B 11B X2 12 13 14 15 16 18 19 20 21 Plate 16 0.1976E+05 0.2442E+05 0.2065E + 05 0.1232E+05 0.3044E + 05 0.3723E + 05 0.2440E+05 0.2817E+05 0.3280E+05 0.2601E+05 0.1598E+05 0.1222E+05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.2619E+05 0.7091E+04 0.1305E+05 0.1785F. + 05 0.1297E+05 0.7040E+04 0.2859E+05 0.6684E+04 0.2509E+05 0.2330F. + 05 0.1707E+05 0.2155E+05 0.2491E+05 0.1985E+05 0.4310E+05 0.9193E+04 0.8040E+04 0.5015E+05 0.2349E+04 0.4184E + 04 0.1481E+05 0.4805E+04 0.4108E+04 0.5224E+05 0.2666E+04 0.7132E+04 0.2622E+04 0.5630E + 04 0.5934E+04 0.4660E+04 0.6041E+04 0.5884E+04 0.5040E+04 0.1068E+05 0.2928E+04 0.2302E+04 Plate 386 0.3942E+05'5 0.2766E + 04 0.4819E+04 0.1988E + 05 0.5883E+04 0.403 IE+ 04 0.3127E+04 0.9787E+04 0.2877E+04 0.7812E + 04 0.1056E + 05 0.6988E + 04 0.7982E+04 0.8770E+04 0.6028E+04 0.1651E+05 0.3807E + 04 0.2582E+04 Plate 409 0.2117E+0515 0.7312E+05 0.3689E + 05 0.1332E+04 0.6233E+04 0.1406E+04 0.3809E+05 0.3158E+04 0.2657E+04 0.2447E+04 0.7054E+03 0.2582E+04 0.2563E+04 0.1329E+04 0.5544E+04 194 Object 22 23 24 25 26 27 28 29 30 31 32A 32B 33 34 35 36 37A 37B 38 39 40 Plate 16 0.3068E+05 0.1017E+05 0.1792E+05 0.1659E+05 0.2129E+05 0.1103E + 05 0.2556E + 05 0.1335E+05 0.1525E+05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.2309E+05 0.1779E+05 0.3753E+05 0.2860E+05 0.1395E+05 0.1517E+05 0.2318E+05 0.5546E+04 0.1014E+05 0.9992 E+04 0.1542E + 05 0.6600E + 04 0.5120E+05 0.1815E+05 0.7479E+04 0.9651E+04 0.5094E+04 0.1594E + 05 0.1155E+05 0.2984E+05 0.2143E+05 0.1670E+04 0.8231E+04 0.8425E+04 0.5441E+04 0.1983E+04 0.2904E+04 0.3464E+04 0.3744E+04 0.2532E+04 0.1422E+05 0.4099E + 04 0.2217E+04 0.2648E+04 0.3890E+05 0.2702E+04 0.3835E+04 0.3980E+04 0.7566E+04 0.5329E+04 0.1825E+05 0.3455E+04 0.2170E+04 Plate 386 0.8959E + 04 0.2254E + 04 0.3961E+04 0.3722E+04 0.5227E + 04 0.1767E+04 0.2301E + 05 0.5995E + 04 0.3280E+04 0.2574E + 04 0.5004E+05 0.6123E + 04 0.3404E + 04 0.1030E + 05 0.7058E+04 0.2533E + 05 0.3489E+04 0.3498E+04 Plate 409 0.1396E+04 0.1151E+04 0.9180E+04 0.1841E+04 0.2579E+05 0.1545E+04 0.3500E + 04 0.2115E+04 0.1069E+05 0.3362E+05 195 TABLE 10 Visual Flux Indices Dbject Plate 16 Plate 327 Plate 329 Plate 386 Plate 409 41 0.1859E+0515 0.1075E+05 42 0.1193E+05 43 0.1109E+05 0.6046E + 04 0.2317E+04 0.2506E + 04 44A 0.1623E+05 44B 0.4636E+04 45 0.1311E + 05 0.7449E + 04 46 0.2779E+05 0.2153E + 05 0.3091E+04 47 0.2451E+05 0.1597E + 05 0.7875E+03 48 0.3700E+05 0.2642E+05 0.1887E+0415 X4 0.1788E+.05 0.1427E+05 X3 0.1332E+05 0.9979E+04 49 0.2402E + 05 0.1710E+05 0.2132E+04 50 0.1333E+05 0.7751E + 04 0.2382E + 04 0.3560E+04 51 0.9600E+04 0.4471E+04 0.194OE+04 0.2705E+04 52 0.1595E+05 0.1050E+05 0.3096E + 04 0.3931E + 04 53 0.1897E+05 0.1338E + 05 0.3408E+04 0.4286E+04 0.1175E+04 54 0.3973E+05 0.1149E+05 0.1633E+05 0.6186E+04 55 0.1278E+05 0.7166E+04. 0.3151E + 04 0.2275E+04 56 0.9940E+04 0.5185E+04 0.2851E+04 0.1505E+04 58 0.9699E+04 0.5756E+04 0.3070E+04 0.2094E+04 59 0.3266E+05 0.2666E+05 0.6893E+04 0.8979E+04 0.3183E+04 196 TABLE 10 Visual Flux Indices Dbject Plate 16 Plate 327 Plate 329 Plate 386 Plate 409 60A 0.5397E+05 0.1608 E+05 0.2198E+05 0.7490E+04 60B 0.1762E+04 61 0.2894E+05 0.2059E+05 0.5789E+04 0.7065 E+04 0.1599E+04 62 0.3218E+05 0.2275E+05 0.6722E+04 0.7373 E+04 0.2199E+04 63 0.1895E+05 0.1114E + 05 0.3865E+04 0.4795E+04 64 0.1494E + 05 0.9404E+04 0.3449E+04 0.3775E+04 65 0.4408E+05 0.1140E+05 0.1635E+05 0.6161E+04 66 0.2537E+05 0.1820E+05 0.4786E + 04 0.6705 E+04 0.1765E+04 67A 0.1526E+05 0.2111E+05 0.8990E+04 67B 0.2113E+04 68 0.1134E+05 0.6145E+04 0.3428E + 04 0.2452E+04 69 0.2469E+05 0.2213E+05 0.398 IE+ 04 0.7950E+04 0.2254E+04 70 0.1256E+05 0.1184E+05 0.1.894E+04 0.4874E + 04 71 0.1987E+05 0.1250E+05 0.4532E+04 0.4042E+04 72 0.1076E + 05 0.4687E + 04 0.2735E + 04 0.1620E+04 73 0.2417E+05 0.1533E+05 0.4805E+04 0.6716E+04 0.1591E+04 74 0.1794E+05 0.1234E+05 0.2535E+0415 0.4051E+041•, 74b 0.5774E + 04 0.2271E+04 75 0.2593E+05 0.1886E+05 0.4899E+04 0.6336E+04 0.2577E+04 76 0.2352E+05 0.1792E+05 0.4726E+04 0.5999E+04 77 0.2877E+05 0.2454E+05 0.5469E+04 0.1139E+05 0.2651E+04 197 Object 78 78b 79 79b 80 81 81b 82 83B X6 84A 84B 85 86 87A 87B 87Bb 88A 88B X7 89 Plate 16 0.2034E + 05 0.4376E + 04 0.1423E+05 0.1987E + 05 0.3845E + 05 0.1221E+05 0.3771E + 05 0.2104E+05 0.1528E+05 0.6229E+04 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.1707E+05 0.6247E+04 0.1010E+05 0.3853E+041 0.3408E+0415 0.1427E+05 0.3928E+04 0.3197E+05 0.6445E+04,J 0.3015E+051 0.1571 E+05 0.2769E+04 0.8890E+04 0.4693 E+04 0.6332E+04 0.2288E+05 0.3269E+04 0.2499E+05 0.1087E+05 0.3920E+04 0.3591E+05 0.7089E+03 0.5135E+03 0.1618E+0517 0.4494E+04 0.1340E+0515 0.1442E+0515 0.3238E + 0415 0.4691E+05 0.1290E+05 Plate 386 0.8455E + 04 0.2962E+04 0.1937E+04 0.4145E+04 0.1228E+05 0.3556E+04 0.9376E + 04 0.3392E+05 0.5141E+04 0.347 6E+05 0.1582E + 05 0.2938E + 04 0.4850E + 05 Plate 409 0.1524E+04 0.5112E+0415 0.1669E+05 0.1808E+04 0.1582E+05 0.6941E+04 0.2513E+05 0.7974E+05 0.4934E+0415 0.1796E+05 0.5856E+04 198 Object X8 X8c 90 91 92 93 94 95 96A X9 97 98 99 100 101 102 103 104 104c 105 106 Plate 16 0.1065E+05 0.2466E+04 0.1443E + 05 0.2854E + 05 0.3938E + 05 0.2822E+05 0.1473E+05 0.2761E+05 0.2300E+05 0.1287E + 05 0.1327E+05 0.1200E + 05 0.3177E+0415 0.1362E+05 0.3443E+05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.6617E +04 0.8192E+04 0.4190E + 05 0.20O3E+O5 0.4824E+05 0.3522E+05 0.2503E + 05 0.2426E+05 0.2028E+05 0.1273E+05 .2322E+05 0.1908E+05 0.1231E+05 0.1300E+05 0.4549E+05 0.7848 E + 04 0.1003E+04 0.7322E+04 0.3064E+05 Plate 386 0.3158E+0415 0.1103E + 04 0.3375E+04 0.1205E+05 0.6406E+04 0.1394E+05 0.1182E+05 0.9080E+04 0.4983E+05 0.6695E+04 0.2242E+05 .7271E + 04 0.6134E+04 0.3077E+04,J 0.1203E+05 0.3891E+0415 0.3260E+04 0.1584E + 05 0.6805E+04 0.1931E+05 0.1666E+05 0.1155E+05 0.6547E + 04 0.3160E+05 0.3821E + 04 0.7223E+04 0.5888E+04 0.2183E+04 0.1995E+04 0.1759E+05 0.2419E+04 Plate 409 0.5738E+04 0.2844E+04 0.7110E+04 0.3183E+04 0.4525E+04 0.3129E+05 0.4271E + 04 0.1444E+05 0.6771E+04 0.3405E+04 0.2478E+04 0.1083E+05 0.1426E+05 0.4693E+04 199 Object 107 114 X10 115 116 117 118 119A 119B 120 121 122 124 125 126A 126B X l l 127 128 129 X12 Plate 16 0.3920E+05 0.2719E+05 0.7596E+04 0.3190E+05 0.8758E+04 0.1934E+05 0.1908E+05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.2353E+05 0.1100E+05 0.3052E+05 0.1431E+05 0.9750E+04 0.2029E+05 0.1794E+05 0.1006E+05 0.3498E+05 0.2042E+05 0.3276E+04 0.2418E+05 0.4822E+04 0.1181E+05 0.1316E+05 0.2822E+04 0.1699E+05 0.5879E+04 0.2233E + 05 0.7738E + 04 0.1017E+05 0.8060E+04 0.1724E+05 0.1153E+05 0.1208E+05 0.1161E+05 0.4183E+04 0.6529E+04 0.3205E+04 0.3525E+04 0.2874E+05 0.2510E+04 0.4502E+04 0.5937E+04 0.2175E+04 0.2543E+05 0.5739E+05 0.3150E+04 0.1125E+05 0.2730E+04 0.4466E + 04 0.3979E+04 0.2510E+04 Plate 386 0.1811E+05 0.7152E + 04 0.2448E + 04 0.8488E+04 0.1842E+04 0.3431E + 04 0.4798E+04 0.3980E+05 0.5923E+04 0.2694E + 04 0.9170E+04 0.2812E+04 0.349 IE+05 0.2834E+04 0.3653E+04 0.4830E+04 0.4402E+04 0.4915E+0415 Plate 409 0.3494E+04 0.2259E+04 0.2490E+04 0.1865E + 05 0.3181E + 04 0.1529E+05 0.4940E + 05 0.2188E+04 200 Object 130A 130B 131 132 A 132B 133 134A 134B X13 135 136 137 X14 139 140 141 142 142b 142e 144 145 Plate 16 0.3301E+05 0.1580E+05 0.1133E+05 0.3343E + 05 0.1239E+05 0.1506E+05 0.4467E+05 0.1040E+05 0.8772E+04 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.1735E+05 0.2638E+05 0.3332E + 04 0.5233E+05 0.5862E+04 0.1282E+05 0.6063E+04 0.2743E+05 0.9362E + 04 0.8348E+04 0.4103E+05 0.7445E+04 0.3262E+04 0.5196E + 04 0.6271 E+04 0.3071E+05 0.2612E+04 0.1536E+05 0.4320E+05 0.3213E+04 0.4661E+04 0.3342E+04 0.2905E+04 0.5656E+04 0.2804E+04 0.5081E+04 0.2886E+05 0.1020E+0515 Plate 386 Plate 409 0.8094E+05 0.9004E + 04 0.2767E+04 0.3900E + 05 0.1921E+05 0.2040E + 05 0.7786E + 04 0.5561E + 05 0.3366E + 05 0.3405E+04 0.2643E+04 0.3278E + 04 0.2308E+04 0.9626E + 04 0.2166E + 04 0.3817E+04 0.6006E + 04 0.3584E + 05 0.1693E + 05 0.4027E+041S 0.3128E+0415 0.3606E+04 0.1884E+05 0.6391E+0415 0.3171E+05 0.2807E+05 0.4248E + 05 0.2013E+05 0.3948E+05 0.1907E+05 201 Object 146 147 148 149 150 151 152 153 154 155 156 157 158 159 A 159B 160 161 162 X15 163 A 163B Plate 16 0.1672E + 05 0.4590E+05 0.4151E+05 0.2.124E+05 0.1477E+05 0.1941E+05 0.4864E + 05 0.4125E+05 0.4379E+05 0.1361E+05 0.3237E + 05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.1195E+05 0.1570E+05 0.4392E+05 0.1865E+05 0.1124E+05 0.3436E+05 0.3416E+05 0.1847E+05 0.1403E + 05 0.1717E+05 0.3942E+05 0.5196E+05 0.3179E+05 0.4003E+05 0.5700E + 05 0.8980E+04 0.2448E+05 0.4098E+04 0.7028E+04 0.3034E + 04 0.7707E+04 0.8579E+04 0.1147E+04 0.1394E+04 0.1977E + 04 0.1068E+05 0.1477E+05 0.8040E + 04 0.9029E+04 0.1577E+05 0.2211E+04 0.7005E+04 0.3337E+05 0.1184E+04 0.2397E+04 0.9162E+04 0.3382E+04 0.4202E+05 0.1118E+05 0.1290E+05 0.1653E+04 0.1173E+03 0.1906E+05 Plate 386 0.4090E+04 0.1324E + 05 0.141 IE+05 0.6469E + 04 0.495 IE+ 04 0.5965E+04 0.1471E + 05 0.2017E+05 0.1187E+05 0.1720E+05 0.2356E+05 0.3071E + 04 0.9047E+04 0.445 3E +05 0.2758E + 04 0.3438E+04 0.1901E+05 0.3573E+04 0.2609E+05 Plate 409 0.4060E+04 0.5254E+04 0.4961E+04 0.7459E+04 0.4109E+04 0.6775E + 04 0.9034E+04 0.3337E+04 0.2047E+05 0.1359E+05 0.8833E+04 0.9571E+04 202 TABLE 10 Visual Flux Indices Objecl Plate 16 Plate 327 Plate 329 Plate 386 Plate 409 164 0.1313E + 05 0.8519E + 04 0.2766E+04 0.3487E+04 165 0.3591E+05 0.3009E + 05 0.7496E + 04 0.1057E+05 0.407 2E+04 166 0.1319E+05 0.8723E+04 0.2875E+04 0.2107E+04 167 0.7062E+04 0.320 IE+04 168 0.1275E+05 0.7515E+04 0.2731E+04 0.5361E+04 169 0.8726E+04 0.5358E+04 0.1898E + 0415 0.2473E+04 170 0.1956E+05 0.1300E+05 0.4103E + 0415 0.3855E+04 0.1249E+04 170b 0.5692E + 04 0.2389E + 04 171 0.2822E+05 0.1947E+05 0.5515E+04 0.6869E+04 0.1908E + 04 172A 0.7023E+05 173 0.4758E+05 0.3751E+05 0.1016E+05 0.1407E+05 0.4560E+04 174 0.2574E + 05 0.1779E + 05 0.4456E + 04 0.6616E+04 0.2477E+04 175 0.1412E+05 0.7362E + 04 0.3360E + 04 0.2883E + 04 176 0.2396E+05 0.1659E + 05 0.3902E + 04 0.6249E + 04 0.1263E+04 178 0.1952E+05 0.U82E+05 0.4639E+04 0.4992E+04 0.1545E+04 179 A 0.5000E + 05 0.1475E+05 0.I986E+05 0.7556E+04 179B 0.1865E+04 180 0.1103E+05 0.5808E + 04 0.3211E+04 0.2320E+04 181 0.1737E+05 0.2385E+05 0.8864E+04 182 0.2212E+05 0.1478E+05 0.3391E+04 0.5786E+04 0.1666E+04 183A 0.3924E + 05 0.5005E+05 0.2589E+05 203 Object 183B 184 185 X16 XI7 186 187 188 189 190 191 192A 192B 193 194 195 196 197 198 199 200 Plate 16 0.2773E + 05 0.9654E + 04 0.8664E+04 0.4125E+05 0.2908E+05 0.1000E+05 0.2429E+05 0.3182E+05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.1588E+05 0.2685E+05 0.1783E+05 0.3230E+05 0.2947E+05 0.1231E+05 0.4624E+04 0.1894E+05 0.4657E + 05 0.5537E + 04 0.4319E+04 0.3482E + 05 0.2173E+05 0.4635E+05 0.6655E+04 0.1746E+05 0.2421E+05 0.3430E + 04 0.1103E + 05 0.2009E + 05 0.1123E+05 0.2385E+05 0.2118E+05 0.8071E+04 0.2925E+04 0.5149E+04 0.123 IF+ 05 0.9237 E+04 0.5979E+04 0.1121E+05 0.2151 E+04 0.5084E+04 0.5321E + 04 0.2763E+05 0.2507 E+04 0.2592 E+05 0.5607E+04 0.3340E+05 0.4382E + 04 0.5552E+04 0.5307E+04 0.1697E+04 Plate 386 0.3057E+04 0.6705E+04 0.1841E + 05 0.2681E+04 0.2028E+04 0.1322E+05 0.7627E+04 0.1692E+05 0.3334E+04 0.6193E+04 0.8847E+04 0.3717E+05 0.4604E+04 0.3640E+05 0.6949E+04 0.4494E+05 0.8860E+04 0.6980E+04 0.2922E+04 Plate 409 0.1737E+04 0.6875E+04 0.4227E+04 0.1677E+04 0.6260E+04 0.1549E+04 0.2118E+04 0.1677E+05 0.1680E+05 0.3198E+04 0.2193E+05 0.2105E+04 0.1787E+04 204 Object 201 202 203 204A 204B 205 206 207 208 209 210 211 212 212b X18 213 214 215 216 217 X19 Plate 16 0.1730E+05 0.1209E + 05 0.3469E+05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.9940E+04 0.3897E + 05 0.1141E + 05 0.2967E+05 0.1208E + 05 0.1398E+05 0.2182E + 05 0.5526E + 04 0.7027E + 04 0.3628E+05 0.4034E+05 0.1460E+05 0.1241E+05 0.1299E+05 0.7096E+04 0.1169E+05 0.6215E+04 0.2767E+05 0.9870E+04 0.5842E+04 0.3142E+05 0.7763E+04 0.2327E+05 0.6907E+04 0.9038E+04 0.1725E+05 0.4540E+04 0.3902E + 04 0.2889E+05 0.3295E+05 0.7802E+04 0.6941E+04 0.7689E+04 0.4011E+04 0.2973E+04 0.1868E+04 0.6587E+04 0.6918E+05 0.2442E+04 0.1567E+04 0.8334E + 04 0.2231E+04 0.4635E+04 0.2043E + 04 0.3358E+04 0.2639E + 05 0.3690E + 0415 0.6511E+04 0.8626E+04 0.2416E + 04 0.3103E+04 0.1917E+04 Plate 386 0.3907E+04 0.2812E+04 0.941.1E+04 0.3448E+04 0.2989E+04 0.1149E + 05 0.3007E + 04 0.8417E +04 0.3173E+04 0.3660E+04 0.3682E + 05 0.5752E+04 0.1657E+04 0.9131E+04 0.1197E+05 0.407 8E+04 0.3058E+04 0.2471E+04 0.1888E+04 Plate 409 0.241.1E+04 0.5407E+05 0.4248E+04 0.2442E+04 0.1611E+05 0.2458E+04 0.3794E+04 205 Object 218 219 X20 220 221 222 223 224 225A 225B 227A 227B 228 229 X21 230 231 232 233 Plate 16 0.8826E + 04 0.1409E+05 0.1598E+05 0.1669E+05 0.1603E+05 0.1605E+05 0.9546 E+04 0.1989E+05 0.8252E+04 0.3684E+05 0.1616E+05 0.1117E+05 TABLE 10 Visual Flux Indices Plate 327 Plate 329 0.4909E + 05 0.5150E + 04 0.1034E+05 0.1078E + 05 0.1047E+05 0.1049E+05 0.1089E + 05 0.3439E+04 0.7735E+04 0.4138E+04 0.3987E+05 0.2844E+05 0.9679E+04 0.7645E+04 0.1362E+05 0.2227E+05 0.2929E+04 0.3263E+04 0.2817E+04 0.2682E+04 0.3186E + 04 0.2360E + 05 0.5325E+05 0.1896E + 04 0.6169E+04 0.2409E+04 0.1201E + 05 0.5019E +04 0.3103E+04 0.1075E+05 0.7436E+04 0.3005E+04 0.1755E+04 Plate 386 0.1921 E+05 0.3.155E+05 0.2942E + 04 0.3097E+04 0.3937E+04 0.4318E+04 0.2868E+04 0.3573E+04 0.3287E + 05 0.2636E+04 0.4865E + 04 0.2700E+04 0.1469E+05 0.1041E+05 0.3863E+04 0.2266E+04 Plate 409 0.6264E+04 0.1347E + 05'5 0.1408E+05 0.3940E+05 0.4956E+04 0.3909E+04 (l5) Half-weight Double weight (Two entries) 206 Object 2B 4A 4B 5 6 7 9 10A 10B 11B X2 12 13 14 15 16 18 19 20 21 22 TABLE 11 Consolidated Blue Flux Indices Part 1 Part 2 0.3704E + 05 0.2900E + 04 0.5436E + 04 0.1421E + 05 0.5552E+04 0.3354E+04 0.3797E+04 0.1674E+05 0.3666E+04 0.5671E+04 0.5733E+04 0.2352E+04 0.7096E+04 0.7367E+04 0.6971E+04 0.1538E+05 0.4230E+04 0.2102E+04 0.6095E+04 0.3464E+05 0.1437E+04 0.4303E+04 0.1420E+05 0.5.112E+04 0.4585E+04 0.4447 E+04 0.1720E+05 0.1905E+04 0.5771E+04 0.6672E+04 0.2341E+04 0.7428E+04 0.8272E+04 0.6320E+04 0.1479E+05 0.3385E+04 0.3424E+04 0.6167E+04 Part 3 0.4647E+0515 0.3628E + 05 0.2134E+04 0.4607E + 04 0.1359E+05 0.5279E+04 0.4412E+04 0.7036E+05 0.5657E+04 0.1519E+05 0.3925E+04 0.5846E+04 0.7244E+04 0.2134E + 04 0.6988E + 04 0.8394E+04 0.5965E+04 0.1434E+05 0.4785E+04 0.2826E+04 0.6316E+04 TABLE 11 Consolidated Blue Flux Indices Object 23 24 25 26 27 28 29 30 31 32A 32B 33 34 35 36 37A 37B 38 39 40 41 Part 1 0.2176E+04 0.3686E+04 0.3401E + 04 0.3702E+04 0.2097E + 04 0.1015E+05 0.4996E+04 0.2079E+04 0.3987E+04 0.3070E+05 0.1093E+04 0.4034E+04 0.3114E+04 0.5105E+04 0.4401E+04 0.2572E+05 0.1483E+04 0.2339E+04 0.3130E+04 0.8982E+04 0.2802E+04 Part 2 0.2673E + 04 0.3473E+04 0.3608E+04 0.4250E+04 0.1879E + 04 0.1037E + 05 0.4186E+04 0.2362E+04 0.3794E + 04 0.2981E+05 0.1577E+04 0.4051E + 04 0.2198E + 04 0.4581E+04 0.3500E+04 0.2613E+05 0.9659E+03 0.2453E+04 0.2698E+04 0.9614E+04 0.2871E+04 Part 3 0.2093E+04 0.3570E + 04 0.4838E+04 0.4290E + 04 0.1617E+04 0.1256E + 05 0.4756E+04 0.1901E + 04 0.2886E+04 0.3116E+05 0.4096E+04 0.2886E+04 0.5043E+04 0.3298E+04 0.2576E+05 0.193 IE+04 0.2352E+04 0.9090E+04 0.1630E+04 208 TABLE 11 Consolidated Blue Flux Indices Object 42 43 44A 44 B 45 46 47 48 X4 X3 49 50 51 52 53 54 55 56 58 59 60A Pan 1 0.1725E+05 0.2041E+04 0.4498E+05 0.2725E+04 0.1232E+04 0.9394E+04 0.4118E+04 0.1151E+05 0.3345E+04 0.2080E+04. 0.3282E + 04 0.2732E+04 0.2118E+04 0.3354E+04 0.3559E+04 0.1196E+05 0.2004E+04 0.2595E+04 0.7703E+03 0.7020E+04 0.2664E+05 Part 2 0.1717E + 05 0.1494E+04 0.4597E+05 0.3353E+04 0.2713E+04 0.8781E+04 0.3889E+04 0.1282E+05 0.4695E+04 0.3140E + 04 0.1739E+04 0.2931 E+04 0.2135E + 04 0.2934E+04 0.3356E+04 0.1183E+05 0.2893E+04 0.2174E+04 0.1561E+04 0.6498E+04 0.2783E+05 Part 3 0.1643E+05 0.2706E+04 0.4558E+05 0.2289E+04 0.1574E+04 0.8375E+04 0.3899E+04 0.1294E + 05 0.2347E+04 0.6319E + 0415 0.3339E+04 0.3223E+04 0.2041E+04 0.4194E+04 0.345 2E+04 0.1191E+05 0.2615E+04 0.2883E+04 0.1682E+04 0.6282E+04 0.2727E+05 209 TABLE 11 Consolidated Blue Flux Indices Object 60B 61 62 63 64 65 66 67A 67B 68 69 70 71 72 73 74 75 76 77 78 79 Part 1 0.2100E+04 0.6380E + 04 0.8351E+04 0.4979E+04 0.3568E+04 0.2029E+05 0.5268E+04 0.2514E+05 0.1195E+04 •0.1121E+04 0.4829E+04 0.2036E+04 0.3973E+04 0.2180E + 04 0.3670E+04 0.3317E+04 0.4562E+04 0.5579E+04 0.9730E+04 0.6882E+04 0.1528E+04 Pari 2 0.9710E+03 0.6765E+04 0.8213E+04 0.3923E+04 0.2302E+04 0.2062E+05 0.5723E+04 0.2722E+05 0.1332E+04 0.1436E+04 0.4853E+04 0.1463E+04 0.4111E+04 0.1997E+04 0.3064E + 04 0.3010E+04 0.5367E+04 0.4718E + 04 0.9867E+04 0.8041 E+04 0.1782E+04 Part 3 0.1789E+04 0.6484E+04 0.81.15E+04 0.4391E+04 0.4803E+04 0.2015E+05 0.5741 E +04 0.2588E+05 0.1944E+04 0.4905E+04 0.3840E+04 0.4641E+04 0.2289E+04 0.5833E+04 0.4057E+04 0.4450E+04 0.5100E+04 0.8639E+04 0.7562E+04 0.5004E+04 210 TABLE 11 Consolidated Blue Flux Indices Object 80 81 82 83B X6 84A 84B 85 86 87A 87B 88A 88 B X7 89 X8 90 91 92 93 94 Part 1 0.3919E + 04 0.7544E+04 0.7928E+04 0.2987E+05 0.1925E+04 0.2497E+05 0.7199E+03 0.1134E+05 0.2955E+04 0.3215E+05 0.3021E+04 0.2439E + 05 0.1414E + 04 0.2803E+04 0.1385E + 05 0.1403E+04 0.3097E+04 0.1220E+05 0.5976E+04 0.1418E+05 0.9604E+04 Part 2 0.3008E+04 0.6801 E+04 0.7398E+04 0.2828E+05 0.1103E+04 0.2467E+05 0.1378E+04 0.1125E+05 0.3255E+04 0.3142E+05 0.1107E+04 0.2444E + 05 0.1663E+04 0.2441E+04 0.1392E + 05 0.1935E+04 0.1304E+04 0.1134E+05 0.5986E+04 0.1315E+05 0.1037E+05 Part 3 0.2029E+04 0.1432E+05 0.7050E+04 0.3669E+05 0.2439E+04 0.2603E+05 0.1254E + 05 0.1218E + 04 0.3200E+05 0.2465E+05 0.3660E+04 0.1291E + 05 0.3333E+04 0.2461E+04 0.1220E+05 0.5973E+04 0.1352E+05 0.5127E+04 211 TABLE 11 Consolidated Blue Flux Indices Object 95 96A 96B X9 97 98 99 100 101 102 103 104 105 106 107 114 X10 115 116 117 118 Part 1 0.783 IE+ 04 0.3960E+05 0.3287E+04 0.2999E+04 0.2466E+05 0.2684E+04 0.5640E+04 0.3972E+04 0.3450E+04 0.3067E + 04 0.1228E+05 0.2473E+04 0.2383E+04 0.1057E+05 0.1234E+05 0.5571E+04 0.1689E+04 0.3312E+04 0.1375E+04 0.3974E+04 0.3814E+04 Part 2 0.7592E+04 0.3890E+05 0.1040E+04 0.2660E+04 0.2492E+05 0.6160E+04 0.8282E+04 0.7530E+04 0.4107E+04 0.4020E+04 0.1269E+05 0.2448E+04 0.1686E+04 0.1368E+05 0.1191E+05 0.6104E+04 0.1.576E+04 0.3825E+04 0.2037E+04 0.3864E+04 0.4079E+04 Part 3 0.9138E+04 0.3950E+05 0.3327E+04 0.2414E+05 0.5993E + 04 0.4204E+04 0.3607E+04 0.5075E+04 0.1157E+05 0.3806E+04 0.2488E + 04 0.1610E+05 0.1805E+05 0.4440E+04 0.1817E+04 0.4674E+04 0.1918E+04 0.2539E+04 0.4950E+04 212 TABLE 11 Consolidated Blue Flux Indices Object 119A 119B 120 121 122 124 125 126A 126B X l l 127 128 129 X12 130 A 130B 131 132A 132B 133 134A Part 1 0.2719E + 05 0.1359E+04 0.4503E + 04 0.2279E + 04 0.6987F. + 04 0.3237E + 04 0.2436E+05 0.3809E+04 0.1660E + 04 0.4594E+04 0.3528E+04 0.1831E + 04 0.2430E+05 0.1094E+04 0.7899E+04 0.2935E+05 0.1515E+04 0.1753E+05 0.4347E + 05 Part 2 0.2719E+05 0.9671E+03 0.5460E + 04 0.3900E+04 0.6693E + 04 0.2743E+04 0.2409E+05 0.5169E+05 0.2916E+04 0.1073E+05 0.2335E + 04 0.3558E+04 0.3882E+04 0.1958E+04 0.2312E+05 0.1011E+04 0.7990E+04 0.2925E+05 0.1773E+04 0.1880E+05 0.4459E+05 Part 3 0.2610E+05 0.4557E+04 0.2165E + 04 0.6372E+04 0.3008E+04 0.2407E+05 0.5044E+05 0.4415E + 0415 0.6112E+04 0.4385E + 04 0.5545E + 04 0.4553E+04 0.2319E + 05 0.7751E+04 0.2777E + 05 0.1634E+05 0.4529E+05 213 TABLE 11 Consolidated Blue Flux Indices Object 134B XI3 135 136 137 X14 139 140 141 142 142b 144 145 146 147 148 149 150 151 152 153 Part 1 0.2722E + 04 0.6267 E+04 0.3107E+04 0.2682E+04 0.9911E + 04 0.2895E + 04 0.2568E+04 0.5346E + 04 0.2837E+05 0.1370E+05 0.2329E+04 0.2831E+05 0.2609E+05 0.3179E+04 0.1106E+05 0.1202E+05 0.6293E + 04 0.6229E+04 0.4452E+04 0.1363E+05 0.1577E+05 Part 2 0.2580E+04 0.2848E+04 0.2865E+04 0.1440E+04 0.1145E+05 0.4729E+04 0.2670E+04 0.6913E+04 0.2957E + 05 0.1414E+05 0.3560E+04 0.2801E+05 0.2479E+05 0.3740E+04 0.1081E + 05 0.1254E+05 0.7998E+04 0.6151E+04 0.7876E+04 0.1304E+05 0.1611E+05 Part 3 0.1824E+04 0.2020E+04 0.1403E+04 0.8939E + 04 0.2481E+04 0.3982E + 04 0.8709E+04 0.3044E+05 0.1281E + 05 0.2847E+05 0.2696E+05 0.2749E+04 0.1087E + 05 0.1282E + 05 0.9570E+04 0.6217E+04 0.3679E+04 0.1261E+05 0.1474E+05 214 TABLE 11 Consolidated Blue Flux Indices Object 154 155 156 157 158 159A 159B 160 161 162 X15 163A 163B 164 165 166 167 168 169 170 171 Part 1 0.1.145E + 05 0.1218E+05 0.1690E+05 0.2406E+04 0.7892E + 04 0.3299E+05 0.2220E+04 0.2683E + 04 0.3426E+04 0.1573E + 05 0.4230E+04 0.2018E+05 0.2366E + 04 0.1986E+04 0.9370E + 04 0.3058E+04 0.1622E+04 0.2028E+04 0.1831E+04 0.4508E+04 0.6542E+04 Part 2 0.1100E + 05 0.1230E+05 0..1633E + 05 0.2380E+04 0.8033E + 04 0.3335E+05 0.1005E+04 0.1857E+04 0.3651E+04 0.1524E+05 0.3114E+04 0.1966E+05 0.2118E+04 0.2000E+04 0.1047E + 05 0.2590E+04 0.928 IE+03 0.2659E+04 0.1376E+04 0.4039E+04 0.5825E+04 Part 3 0.1057E+05 0.9732E+04 0.1678E+05 0.2626E+04 0.6647E+04 0.3304E+05 0.2102E+04 0.3681E+04 0.1808E + 05 0.5036E + 04 0.1944E+05 0.299.1 E+04 0.8469E + 04 0.1422E+04 0.1189E+04 0.3285E + 04 0.3965E+04 0.3913E+04 0.5428E+04 TABLE 11 Consolidated Blue Flux Indices Object 172A 173 174 175 176 178 179A 179B 180 181 182 183A 183B 184 185 X16 X17 186 187 188 189 Part ] 0.2222E+05 0.1087E+05 0.6800E + 04 0.3165E+04 0.5817E + 04 0.4109E+04 0.2515E+05 0.1740E+04 0.3538E + 04 0.1782E+05 0.5071E+04 0.3700E+05 0.1594E+04 0.1038E + 05 0.2162E+O5 0.2106E+04 0.1620E+04 0.1286E+05 0.8455E+04 0.1781E+05 0.1889E+04 Part 2 0.2097 E+05 0.1160E+05 0.6446E + 04 0.3432E+04 0.6803E+04 0.3514E+04 0.2669E+05 0.1673E+04 0.1650E + 04 0.1675E+05 0.3895E+04 0.3691E+05 0.2208E+04 0.6177E + 04 0.2179E+05 0.1679E+04 0.1701E+04 0.1211E + 05 0.8578E+04 0.1757E+05 0.1243E+04 Part 3 0.2172E+05 0.1033E+05 0.6090E + 04 0.3285E+04 0.7618E+04 0.4216E+04 0.2562E+05 0.2825E+04 0.1586E+05 0.4176E+04 0.3673E + 05 0.2517E+04 0.5671E+04 0.2094E+05 0.3072E+04 0.1787E+04 0.1223E+05 0.8015E+04 0.1797E+05 0.2958E+04 216 TABLE 11 Consolidated Blue Flux Indices Object 190 191 192 A 192B 193 194 195 196 197 198 199 200 201 202 203 204B 205 206 207 208 209 Part 1 0.5691E+04 0.1030E+05 0.4062 E+05 0.2961E+04 0.2509E+04 0.2590E+04 0.5519E+04 0.3008E+05 0.3901E+04 0.8222E+04 0.7499E+04 0.3159E+04 0.4160E+04 0.2303E+04 0.1002E + 05 0.7346E+04 0.1000E+04 0.3509E + 04 0.2531E+04 0.4313E+04 0.3630E+04 Part 2 0.5570E+04 0.1058E + 05 0.4026 E +05 0.2580E+04 0.3359E+04 0.2496E+04 0.4347E + 04 0.3058E + 05 0.3544E+04 0.8508E+04 0.8080E+04 0.2500E+04 0.4872E + 04 0.3097E+04 0.9599E+04 0.8184E+04 0.2089E+04 0.2102E+04 0.2594E+04 0.4389E+04 0.3197E+04 Part 3 0.5550E+04 0.1009E + 05 0.4083E+05 0.2332E+04 0.4056E+04 0.1723E + 04 0.4016E+04 0.3030E+05 0.3576E+04 0.8560E + 04 0.6362E+04 0.3564E+04 0.4802F.+04 0.3930E + 04 0.9413E+04 0.7955E+04 0.2137E+04 0.432 IE+04 0.2135E+04 ' 0.4500E+04 0.3329E+04 2 1 7 TABLE 11 Consolidated Blue Flux Indices Object 210 211 212 X18 213 214 215 216 217 X19 218 219 X20 220 221 222 223 224 225A 225B 227A Part 1 0.2327E+04 0.2393E + 05 0.4565E+04 0.17 5 IE+04 0.9163E+04 0.1173E+05 0.3642E+04 0.2909E+04 0.3528E+04 0.1155E+04 0.1828E+05 0.3199E+05 0.2198E + 04 0.2889E+04 0.3000E+04 0.4318E+04 0.2253E+04 0.4168E+04 0.3556E+05 0.2461E+04 0.4429E+05 Part 2 0.2980E+04 0.2413E+05 0.5503E + 04 0.1578E+04 0.8952E+04 0.1180E+05 0.3278E+04 0.3286E+04 0.3697E+04 0.1489E + 04 0.1873E+05 0.3237E+05 0.3229E+04 0.2844E+04 0.4232E+04 0.4953E+04 0.1699E+04 0.4116E+04 0.3514E+05 0.2478E+04 0.4365E+05 Part 3 0.2976E+04 0.2342E+05 0.6666E+04 0.2170E + 04 0.9798E+04 0.1008E + 05 0.3664E+04 0.2612E+04 0.2775E+04 0.3052E+04 0.1749E+05 0.3209E+05 0.1218E+04 0.3752E+04 0.3233E+04 0.4407E+04 0.3095E+04 0.3092E+04 0.3518E+05 0.2674E+04 0.4395E+05 TABLE 11 Consolidated Blue Flux Indices Object Pan 1 Part 2 Part 3 227B 0.2900E+04 0.2999E+04 228 0.1626E+04 0.2227E+04 0.2194E + 04 229 0.3496E + 04 0.3085E+04 0.4793E+04 X21 0.2282E+04 0.1367E + 04 0.1719E+04 230 0.1413E+05 0.1411E + 05 0.1383E+05 231 0.9378E+04 0.8762E+04 0.9295E+04 232 0.3979E + 04 0.4037E+04 0.4304E + 04 233 0.2843E + 04 0.2852E+04 0.2561E+04 (15) Half-weight 219 TABLE 12 Consolidated Visual Flux Indices Object 2B 3B 4A 4B 5 6 7 9 10A 10B 11B X2 12 13 14 15 16 18 19 20 21 Part 1 0.6791E+04 0.1260E + 05 0.1732E + 05 0.1253E+05 0.6741E+04 0.2792E+05 0.6396E+04 0.2446E+05 0.2269E+05 0.1655E+05 0.2096E+05 0.2428E+05 0.1929E+05 0.4233E+05 0.8836E+04 0.7713E+04 Part 2 0.8729E+05 0.1574E+06 0.9786E + 04 0.1652E+05 0.5203E+05 0.1874E+05 0.1625E + 05 0.1633E+06 0.1098E+05 0.2681E+05 0.108 IE+05 0.2163E+05 0.2269E+05 0.1822E+05 0.2306E+05 0.2252E + 05 0.1957E+05 0.3868E+05 0.1195E+05 0.9608E+04 Part 3 0.8990 E +0515 0.8545E+04 0.1397E + 05 0.4902 E+05 0.1667E+05 0.1193 E+05 0.9526E + 04 0.2617E+05 0.8848E+04 0.2143E+05 0.2799 E+05 0.1942E+05 0.2185E+05 0.2375E+05 0.1704E+05 0.4159E+05 0.1134E+05 0.8040E+04 Part 4 0.1011E+06'5 0.2407E+06 0.1491E+06 0.1459E + 05 0.4295E+05 0.1515E+05 0.1525E + 06 0.2669E+05 0.2365E+05 0.2233E+05 0.9348E+04 0.2318E+05 0.2306E+05 0.1456E+05 0.3957E+05 TABLE 12 Consolidated Visual Flux Part 1 0.2257E+05 0.5293E+04 0.9759E+04 0.9615E+04 0.1493E+05 0.6314E+04 0.5041 E +05 0.1761E+05 0.7168E+04 0.9282E+04 0.4856E+04 0.1544E+05 0.1114E+05 0.2916E+05 0.2084E+05 0.1567E+04 0.7899E+04 0.8088E+04 0.1397E+06 Part 2 0.2097E+05 0.8392E+04 0.1186E+05 0.1392E+05 0.1494E + 05 0.1O48E+05 0.5015E+05 0.1622E+05 0.9286E+04 0.1091E+05 0.1250E+06 O.llUE+05 0.1527E+05 0.1579E+05 0.2829E+05 0.2058E+05 0.6289E+05 0.1389E+05 0.9107E+04 Indices Part 3 0.2420E+05 0.7128E+04 0.1175E+05 0.1112E+05 0.1502E+05 0.5746E+04 0.5580E+05 0.1695E+05 0.9938E+04 0.8018E+04 0.1110E+06 0.1727E+05 0.1027E+05 0.2738E+05 0.1959E+05 0.6076E+05 0.1050E+05 0.1052E+05 Part 4 0.1507E + 05 0.1317E+05 0.5632E+05 0.1829E+05 0.1161E+06 0.1618E+05 0.2868E+05 0.2016E+05 0.6266E+05 TABLE 12 Consolidated Visual Flux Indices Object Part 1 Part 2 Part 3 Part 4 41 0.1036E + 05 42 0.6766E+05 43 0.5777E+04 0.9665E+04 0.7830E+04 44A 0.8392E+05 44B 0.4413E+04 45 0.7138E+04 46 0.2094E+05 0.2629E+05 47 0.1547E + 05 0.1010E + 05 48 0.2577E+05 0.1861E+051 X4 0.1380E+05 X3 0.9602E+04 49 0.1658E+05 0.2027E+05 50 0.7432E+04 0.9911E+04 0.1069E+05 51 0.4254E+04 0.8227E+04 0.8378E+04 52 0.1011E+05 0.1257E + 05 0.1167E+05 53 0.1293E+05 0.1372E + 05 0.1259E+05 0.1336E+05 54 0.3898E+05 0.4133E + 05 0.4119E+05 0.4273E+05 55 0.6864E+04 0.1278E+05 0.7187E+04 56 0.4944E+04 0.1167E+05 0.4984E+04 58 0.5496E+04 0.1248E+05 0.6678E+04 59 0.2601E+05 0.2599E+05 0.2425E+05 0.2684E+05 222 TABLE 12 Consolidated Visual Flux Object 60A 60B 61 62 63 64 65 66 67A 67B 68 69 70 71 72 73 74 74b 75 76 77 Part 1 0.5318E +05 0.1655E + 04 0.2002E+05 0.2215E+05 0.1.074E+05 0.9041 E+04 0.4331E+05 0.1766E + 05 0.1989E+04 0.5873E+04 0.2153E+05 0.1142E+05 0.1207E+05 0.4462E+04 0.1484E+05 0.1191E+05 0.2140E+04 0.1831E+05 0.1739E+05 0.2391E+05 Part 2 0.5607 E +05 0.2219E + 05 0.2541E+05 0.1538E + 05 0.1387E + 05 0.4104E + 05 0.1867E+05 0.5347E + 05 0.1379E+05 0.1580E + 05 0.8049E + 04 0.1777E+05 0.1124E + 05 0.1874E + 05 0.1049E+0515 0.1907E+05 0.1846E+05 0.2107E+05 Indices Part 3 0.5359E + 05 0.196 IE+ 05 0.2036E + 05 0.1391E + 05 0.1126E+05 0.41.23E+05 0.1872E+05 0.5170E + 05 0.7680E+04 0.2177E + 05 0.1411E + 05 0.1196E + 05 0.5320E+04 0.1875E+05 0.1198E+0515 0.1781E+05 0.1696E+05 0.2993E+05 Part 4 0.4885E+05 0.1658E+05 0.2072E+05 0.4261E+05 0.1776E+05 0.5550E+05 0.2108E+05 0.1652E+05 0.2315E+05 0.2361E+051 223 TABLE 12 Consolidated Visual Flux Indices Object 78 78b 79 79b 80 81 81b 82 83A 83B X6 84A 84B 85 86 87A 87B 87Bb 88A 88B X7 Part ]. 0.1655E+05 0.5972E+04 0.9720E+04 0.1380E+05 0.3127E+05 0.2947 E+051 0.1521E+05 0.2617E+04 0.8541E+04 0.4468E+04 0.2557E+06 0.1568E+0517 0.1395E+05,S Part 2 0.1533E+O515 Part 3 0.2299E+05 0.1372E+0515 0.9080E+04 0.6233E + 04 0.1560E+05 0.1223E + 05 0.2446E+0515 0.3200E+05 0.1068E+05 0.2407E+05 0.2519E+05 0.7722E+05 0.7869E+05 0.1321E+05 0.1480E + 05 0.8365E+05 0.8042E + 05 0.3930E+05 0.4004E+05 0.1558E+05 0.9014E+04 0.1162E+06 0.1080E+06 0.3300E+04 0.2463E+04 0.1763E+05 0.1310E+0515 0.1427E+0515 Part 4 0.1603E+05 0.3739E + 05'-s 0.8558E+05 0.1806E+05 0.8243E+05 0.463 IE+05 0.1 WOE+06 224 Object 89 X8 90 91 92 93 94 95 96A X9 97 98 99 100 101 102 103 104 104c 105 106 Part ] 0.4613 E+05 0.6331E+04 0.7861E+04 0.4114E+05 0.1946E+05 0.4746E+05 0.3450E+05 0.2440E+05 0.1971E+05 TABLE 12 Consolidated Visual Flux Part 2 0.4591E+05 0.1280E+05" 0.1360E+05 0.4315E+05 0.2432E + 05 0.4925E+05 0.4240E+05 0.3338E+05 0.1565E+06 0.2532E+05 0.7581E+05 0.1229E+05 0.2261 E +05 0.1853E+05 0.1188E+05 0.1256E+05 0.4471E+05 0.7526E+04 0.9345E+03 0.7015E+04 0.2995E+05 0.2728E+05 0.2338E+05 0.1250E + 0515 0.4309E+05 0.1547E+0515 0.1371E+05 0.3917E+05 Indices Part 3 0.4481E+05 0.3785E+04 0.9884E+04 0.4009E+05 0.1897E+05 0.4778E+05 0.4192E+05 0.3031E + 05 0.1833E+05 0.7391E+05 0.1138E+05 0.2000E+05 0.1669E+05 0.6929E+04 0.6398E+04 0.4399E+05 0.7589E+04 0.7752E+04 0.3653E+05 Part 4 0.4112E+05 0.4054E+05 0.2480E+05 0.4710E+05 0.2684E+05 0.343 3E+05 0.1329E+06 0.3297E+05 0.7733E+05 0.4552E+05 0.3522E+05 225 TABLE 12 Consolidated Visual Flux Object 107 114 X10 115 116 117 118 119A 119B 120 121 122 124 125 126 A 126B X l l 127 128 129 X12 Part 1 0.3426E+05 0.1985E+05 0.3103E+04 0.2356E + 05 0.4593E+04 0.1139E+05 0.127 IE+05 0.2668E+04 0.1647E+05 0.5615E+04 0.2173E+05 0.7419E+04 0.9789E+04 0.7733E+04 0.1672E+05 0.1112E+05 0.1166E+05 Part 2 0.4172E+05 0.1652E+05 0.2475E+05 0.1297E+05 0.1414E+05 0.9497E+05 0.1039E+05 0.1766E+05 0.2270E+05 0.9126E+04 0.8499E+05 0.1779E+06 0.1277E+05 0.4054E+05 0.1122E+05 0.1753E+05 0.1579E+05 0.1039E+05 Indices Part 3 0.4514E+05 0.1982E+05 0.7669E + 04 0.2307E + 05 0.5961E+04 0.1034E+05 0.1392E+05 0.9066E+05 0.1677E+05 0.8348E+04 0.2470E+05 0.8671E+04 0.8072E + 05 0.8731E+04 0.1093E+05 0.1400E+05 0.1290E+05 0.1422E+0515 Part 4 0.2865E + 05 0.2111E + 05 0.2260E+05 0.9250E + 05 0.2683E+05 0.8049E+05 0.1829E + 06 0.2064E+05 226 TABLE 12 Consolidated Visual Flux Indices Object 130A 130B 131 132A 132B 133 134A 134B X13 135 136 137 X14 139 140 141 142 142b 142c 144 145 Part 0.1683E+05 0.2573E+05 0.3157E + 04 0.5154E + 05 0.5599E + 04 0.1238E+05 0.5793E+04 0.2677E+05 0.9001E+04 0.8013E+04 0.4027E+05 0.7135E+04 0.3090E+04 Part 2 0.2011E+05 0.2386E+05 0.1009E+06 0.1078E + 05 0.5378E+05 0.1375E+06 0.1300E+05 0.1823E+05 0.1348E+05 0.1187E+05 0.2172E+05 0.1149E+05 0.1971E + 05 0.9533E+05 0.3710E+0515 Part 3 0.2431 E +05 0.8905E+05 0.5016E+05 0.1219E+06 0.1027E + 05 0.9932E + 04 0.7279E+04 0.2579E+05 0.6881E+04 0.1137E+05 0.1698E + 05 0.8263E+05 0.4252E+05 0.1192E+0515 Part 4 0.2584E+06 0.2433E+05 0.9443E + 05 0.5019E+05 0.1398E+06 0.2356E+05 0.2651E+0515 0.2929E+05 0.9316E+05 0.4371E+0515 0.1038E+06 0,9605E + 05 0.9296E+05 0.9002E+05 0.9758E+05 0.9395E+05 227 TABLE 12 Consolidated Visual Flux Object 146 147 148 149 150 151 152 153 154 155 156 157 158 159A 159B 160 161 162 XI5 163A 163B Part 1 0.1083E+05 0.3364E + 05 0.3344E+05 0.1793E + 05 0.1357E+05 0.1665E+05 0.3867E+05 0.5117E+05 0.3109E + 05 0.3928E+05 0.5621E + 05 0.8628E+04 0.2385E + 05 0.3894E + 04 0.6730E + 04 0.8806E+04 0.4126E+05 0.1246E+05 0.1551E+04 Part 2 0.1234E+05 0.2877E+05 0.3170E+05 0.5106E+04 0.6095E+04 0.8369E+04 0.3868E+05 0.5191E+05 0.2989E+05 0.3321 E+05 0.5509E+05 0.9263E+04 0.2638E + 05 0.1088E+06 0.5256E+04 0.9968E+04 0.1362E+05 0.4032E+05 0.6449E+03 0.6542E+05 Indices Part 3 0.1208E+05 0.3420E+05 0.3619E+05 0.1814E + 05 0.1431E+05 0.1688E+05 0.3755E+05 0.4966E+05 0.3105E+05 0.4312E+05 0.5698E+05 0.9375E+04 0.2441E + 05 0.1001E+06 0.8523E+04 0.1036E+05 0.4712E+05 0.1072E+05 0.6237E+05 Part 4 0.3182E+05 0.3811E+05 0.3661E+05 0.4871E+05 0.3209E+05 0.4553E+05 0.5569E+05 0.2774E+05 0.9873E+05 0.7412E+05 0.5482E+05 0.5799E+05 228 T A B L E 12 Consolidated Visual Flux Object 164 165 166 167 168 169 170 170b 171 172A 172B 173 174 175 176 178 179A 179B 180 181 182 Part 1 0.8179E + 04 0.2941 E+05 0.8378E+04 0.3031E+04 0.7203E + 04 0.5111E+04 0.1256E+05 0.2253E+04 0.1891E+05 0.2340E+06 0.3677E+05 0.1726E+05 0.7054E + 04 0.1608E+05 0.1140E+05 0.4921E+05 0.1753E+04 0.5546E+04 0.1430E+05 Part 2 0.1135E + 05 0.2805E+05 0.1176E+05 0.1122E+05 0.8065E+04,•, 0.1623E+0515 0.2123E+05 0.3696E + 05 0.1750E+05 0.1354E+05 0.1551E+05 0.1815E+05 0.5184E+05 0.1300E+05 0.6013E+05 0.1366E+05 Indices Part 3 0.1049E + 05 0.2802E+05 0.6715E+04 0.1536E+05 0.7738E+04 0.1147E+05 0.1913E+05 0.3610E+05 0.1850E+05 0.8865E + 04 0.1759E+05 0.1442E + 05 0.4898E+05 0.7313E+04 0.5760E+05 0.1643E+05 Part 4 0.3189E + 05 0.1394E+05 0.1876E + 05 0.345 IE+05 0.2252E+05 0.1405E + 05 0.1618E+05 0.4915E+05 0.5496E+05 0.1706E+05 Object 183A 183B 184 185 X16 X17 186 187 188 189 190 191 192A 192B 193 194 195 196 197 198 199 TABLE 12 Consolidated Visual Flux Part 1 Pari 2 0.1260E+06 0.1194E + 05 0.1995E+05 0.4400E+05 0.4402E+04 0.1839E+05 0.4579E+05 0.5284E+04 0.4107E+04 0.3410E+05 0.2114E+05 0.4557E+05 0.6367E+04 0.1693E+05 0.2359E+05 0.3251E+04 0.1063E+05 0.1952E+05 0.1082E+05 0.2323E+05 0.2060E+05 0.3390E+05 0.2285E+05 0.404] E + 05 0.9035E + 04 0.1972E+05 0.2055E+05 0.9163E+05 0.1038E + 05 0.8647E + 05 0.2155E+05 0.1088E+06 0.1723E+05 0.2136E+05 0.2050E+05 Indices Part 3 0.1111E+06 0.9337E+04 0.1872E + 05 0.4580E+05 0.8312E+04 0.6491E+04 0.3416E+05 0.2098E + 05 0.4250E+05 0.1O08E+05 0.1745E + 05 0.2393E + 05 0.8534E+05 0.1342E+05 0.8377E+05 0.1932E+05 0.1010E+06 0.2396E+05 0.1940E+05 Part 4 0.1164E + 06 0.1756E+05 0.4600E + 05 0.3273E+05 0.1714E+05 0.4308E+05 0.1621E+05 0.2018E+05 0.8587E+05 0.8598E+05 0.2693E+05 0.1036E+06 0.2009E+05 0.1792E+05 230 TABLE 12 Consolidated Visual Flux Object 200 201 202 203 204A 204B 205 206 207 208 209 210 211 212 212b X18 213 214 215 216 217 Part 1 0.7743E+04 0.1127E+05 0.5941 E+04 0.2701E+05 0.9496E+04 0.5579E+04 0.3072 E+05 0.7444E+04 0.2266E+05 0.6612E+04 0.8685E+04 0.1673 E+05 0.4321E+04 0.3706E+04 0.2822E+05 0.3224E+05 0.7482E+04 0.6645E+04 0.7372E+04 Part 2 0.7286E + 04 0.1212E+05 0.7949E + 04 0.2494E + 05 0.2107E+06 0.1014E+05 0.6778E+04 0.3088E + 05 0.9339E + 04 0.1813E+05 0.8622E+04 0.1353E+05 0.8789E+05 0.1474E+0515 0.2468E+05 0.3186E+05 0.1004E+05 0.1260E+05 0.8138E+04 Indices Part 3 0.8971E+04 0.1160E+05 0.8671E+04 0.2528E+05 0.1039E+05 0.9153E+04 0.3017E+05 0.9202E+04 0.2290E+05 0.9650E+04 0.1095E+05 0.8462E+05 0.1634E + 05 0.5428E+04 0.2461E+05 0.3128E+05 0.1205E+05 0.9340E+04 0.7733E+04 Part 4 0.2210E+05 0.1948E+06 0.3284E+05 0.2229E+05 0.8349E+05 0.2240E+05 0.3035E+05 TABLE 12 Consolidated Visual Flux Object X19 218 219 X20 220 221 222 223 224 225A 225B 227A 227B 228 229 X21 230 231 232 233 Pari 1 0.381 IE+04 0.4831E+05 0.4910E+04 0.9955E + 04 0.1038E+05 0.1008E+05 0.1010E + 05 0.1049E+05 0.3260E + 04 0.7416E+04 0.5896E + 04 0.1159E+05 0.3933E+04 0.3912E+05 0.2777E+05 0.9310E+04 0.7329E+04 Part 2 0.4823E+05 0.7535E + 05 0.1196E+05 0.1319E+05 0.1154E+05 0.1104E+05 0.1290E + 05 0.7942E+05 0.1662E + 06 0.8057E+04 0.1001E+05 0.1949E+05 0.1260E+05 0.3891E+05 0.2785E+05 0.1224E+05 0.7512E+04 Indices Part 3 0.6093E + 04 0.4756E+05 0.7380E+05 0.9025E + 04 0.9445E+04 0.1168E + 05 0.1268E + 05 0.8824E + 04 0.1072E+05 0.7653E+05 0.8189E + 04 0.1409E+05 0.8364E+04 0.375OE+O5 0.2764E+05 0.1149E+05 0.7162E+04 Part 4 0.4310E+05 0.7366E+051 0.7598E+05 0.1561E+06 0.3659E+05 0.3099E+05 ( , s) Half-weight (") Double weight INDEX Age estimate, 137 Age, Cluster, 137 Appendix A, 144 Appendix B, 175 Array, RETICENT, 145 Bandhead Positions, 148 Bibliography, 139 Calibration Results, 77 Calibration Theory, 49 Carbon star, 138 Cluster age, 137 Collinder 453, 1 Color terms, 49 Command, RETICENT, 145 Conclusions, 138 Data Reduction: From Digital Arrays to Flux Indices, Data reduction: From Flux Indices to Magnitudes, 30 De-Reddening and De-Extinguishing, 104 Differential reddening, 132 Flux Index, 21 Frame, PDS, 18 RETICENT, 145 TOODEE, 19 Groups, 47 Index, Flux, 21 Introduction, 1, 144 233 Main Sequence, Zero Age, 108 NGC 7419, Coordinates, Equatorial, 1 Coordinates, Galactic, 2 Diameter, Angular, 2 OCL-250, 1 Parting shots, 132 PDS, 3, 18 Frame, 18 Plate, Virtual, 30 Point-Spread Function, 22, 69 Racine Wedge, 4, 18, 69 Reddening, differential, 132 Results, 117 RETICENT, 19, 145 Array, 145 Command, 145 Frame, 145 Saturation, 20 Spectrum Calibration, 146 Star, Carbon, 2, 93 Star 183, 171 Star 196, 169 Star, carbon, 138 The Carbon Star, 93 The carbon star's radial velocity, 173 The Color-Magnitude and Color-Color Diagrams, 94 The distance modulus, 130 The Q method, 104 The Radial Velocity, 151 The Raw Data, 4 The Reticon, 146 The Secondary Images, 69 The Serkowski method, 107 The Virtual Plates, 30 TOODEE, 19 Frame, 19 TOODEE and SUPERTOODEE Processing, Wedge, Racine, 4, 18, 69 Weight, Fitting Scheme, 31 Tabulation scheme, 28 ZAMS, 108 11/12 October 1982, 163 25/26 August 1982, 156 

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