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

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PHOTOMETRIC STUDY O F T H E O P E N CLUSTER  NGC  by D A N I E L THIBAULT B. Sc., Universite Laval,  A THESIS SUBMITTED  1981  IN PARTIAL F U L F I L M E N T  THE REQUIREMENTS  FOR THE D E G R E E  MASTER OF  OF  SCIENCE  in T H E 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  T H E UNIVERSITY  OF BRITISH  August ®  COLUMBIA  1984  Daniel Thibault,  1984  OF  7419  In  presenting  this thesis  degree at the The  in partial  of  Department publication  this thesis or  by  and  for scholarly  his  or  her  purposes may  representatives.  permission.  Department of Astronomy &  Geophysics  The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5  1984  for  an  advanced  study. I further agree that permission for extensive  of this thesis for financial gain  Date: Angus:  requirements  University of British Columbia, I agree that the Library shall make  it freely available for reference copying  fulfilment ol' the  shall  be It not  granted is be  by  understood allowed  the that  Head  of  my  copying  or  without my  written  ABSTRACT A set of UBV plates of the heavily-extinguished open cluster N G C 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 T O O D E E 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 ± respectively! Average extinction was found to be A  = v  1.77.  ii  5 Ma and 6.0 ±  0.3 kpc  5.85, and reddening E(B-V)  =  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  4.  T O O D E E and S U P E R T O O D E E  Processing  Data reduction: From Flux Indices to Magnitudes 4.1  The Virtual Plates  4.2  Calibration Theory  4.3  The Secondary  4.4  Calibration Results  4.5  The Carbon Star  Images  5.  The Color-Magnitude and Color-Color Diagrams  6.  De-Reddening and De-Extinguishing  7.  6.1  The Q method  6.2  The Serkowski  6.3  Results  6.4  The distance modulus  method  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  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  ,....,..„..,.„„. 156  APPENDIX B  175  INDEX  232  iv  List of Tables  1. The plates  6  2. The objects  11  3. The photometric standards  50  4. Raw  80  photometry  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. T O O D E E density plot of frame after 4. Point-Spread  DOUBLT  Function contour plot  5. T O O D E E density plot of TRIPLT situation 6. T O O D E E 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 ) A B 27. Lg(F / F ) A B 28. Lg(F / F ) A B 29. Lg(F / F ) A B 30. Color-color  for U group 2  73  for B group 2  74  for B group 3  75  for V group 2  76  diagram of the standards  97  31. Color-magnitude diagram of the standards  .1  32. Color-color diagram of the standards (our data)  98 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 T X 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 thanks and best regards go to the Astronomy &  to lose my  green horns. Further  Geophysics faculty and staff for  providing a homely atmosphere, University of British Columbia's for their unflinching patience, John^ Nicol and Stephenson  Computing Centre staff  Yang for introducing me  their respective brain childs, S U P E R T O O D E E and RETICENT, and (Stephenson  the UBC  to  Observers  Yang, Chris Millward, Zoran Ninkov, Phil Bennett, Ed Chan, Gary Joslin,  Dennis Crabtree, and more) for "introducing me observer" (Chris said it so well). No  to the life of the cosmopolitan  doubt there are more 1 owe  managed to deal with here; to those my  to than I have  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  x  to a young scientist  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  a  =  1970), lies in Cepheus, at the equatorial coordinates (1950.0):  22h  5 = +60°  52.3m 34'  2  galactic coordinates: II 1  =  109.13°  •9  II b  NGC  =+1.14°  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 To  define the cluster's turnoff more accurately.  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 faint V objects which do not appear on the U exception, 142b, was  data frames. A l l but one arc  or B plates at all. The  single  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 reproduced in table 2.  grid and  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  the data lost due to plate misalignment on the PDS machine.  was digitized but  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  i O  o  c3  o o  r  o  O  .  o O  o o o o  o  o  3>  o 0°  6  o  o  o  — Q ° e — c r  o o  Y o  ° o  o  cn o o o  o o o o  o o  o _L  15000  Figure 2.1: Finding  -10000  chart,  -5000  0  X  5000  I 10000  JL 15000  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 o  o O <£> O  o o  o  O °  o  O O  o  oh o  o  r  O  o  ho  r?0  o ° o (3  o  o u  O  ° o  o o  8  -6000  -4000  Figure 2.2: Finding  0°  CP  o  o o  o  o  O  °  -2000  chart, inner  8  o *b o  o  w  O o  o o  O  o O  O ° O o  s  °  o  o  Oo  .O  i  ro o o o  °  CP  O o o  o  J  I  0  L  X field  This is an enlargement of the inner part of figure 2.1.  2000  J  L_  4000  TABLE 2 The  )bject  X  Y  Identification  objects X  Object  Y  Identification  1  (')  17  2  ()  18  -2436  8124  Hn 21  Hn I B ( )  19  -1301  7217  Hn 22  Hn 27  20  -1000  6708  21  -478  7135  22  213  6944  23  -149  6215  24  141  5522  25  557  5347  2  3  7286  8950  4  7894  10760  5  9797  11841  6  13833  12612  7  12091  17062  8  3  Hn 28  Non-existent  Non-existent  Hn 23  9  6457  15420  10  4804  14013  Hn 17/Hn 1 11  26  2852  6887  11  5121  12576  Hn 16/Hn I 12  27  5078  6663  Non-existent  28  4628  5911  Hn 29  29  4713  5429  Hn 30 Hn I 38  XI X2  -645  12659  12  1697  9130  Hn 25  30  5844  4205  13  1370  9473  Hn 26  31  5611'  3456  14  1456  9911  32  6063  1609  Hn 13/Hn I Bl 5  15  367  10419  16  -71  8285  Hn 15/Hn I 21  33  7908  7225  Hn 24  34  10057  4598  (') BD + 60°2453 A/HD 216572/SAO 20292/ADS 16334 ( ) BD + 60°2453 B ( ) BD + 60°2456/SAO 20306/HD 216721 2 3  Hn I 15  TABLE 2 Die objects Dbject  X  Y  Identification  Object  X  Y  35  11544  3132  51  4101 -13614  36  11565  2790  52  3952 -1563.1  37  16297 -4973  53  1179 -12729  38  11051  -2197  54  1831  39  8041  -2085  55  1490 -8357  40  7524 -3843  56  196 -10071  Hn 57  Hn 12/Hn IV  -8835  Identification  Hn 68  16/ Bl e 41  7186 -1763  42  6764 -1751  43  10209 -1924  44  6835 -8388  57 Hn 56 ( ) 4  Hn - 74  Non-existent  58  -1057 -11632  59  -1756 -11271  Hn 67  60  -2523  Hn 10/Hn III  -9081  37 45  7484 -8938  46  9084 -10050  47  61  -3009 -8320  Hn 69  62  -3560  -6312  Hn 71  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  68  -2227  Hn 59  Hn IV 37  -5874  : as the western 6 on Handschel's Karte V ( ) This star is mislabeled 4  13 TABLE 2 The  Object  X  Y  objects  Identification  Object  X  Y  Identification  Hn 32  69  -139 -5602  84  2578  4862  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  863  2616  Hn 51/B1 d  74  4204  X7  1130  2813  89  1524  2704  500  3109  Hn IV 19  -801  74b  88  75  3866 -1211  76  3332  -310  77  3438  1568  90  2459  2400  78  3289  1762  91  2707  1519  Hn 52  92  2289  1028  Hn 53  93  2562  261  Hn 54  94  2812  -657  95  2603  -735  96  1640  -387  1935  -326  97  1187  769  98  1103  465  99  959  318  Hn 55  X8c  78b 79  3918  2574  79b  80  4415  3079  81  4151  4218  X8  Hn 50  Hn 31  81b  X9  82  3531  3238  83  2987  3097  Hn 14/Hn I A / Bl f  X6  2389  3408  Hn 80/B1 2  Hn 81  14 TABLE 2 The  Y  objects  Object  X  Identification  100  1023  170  118  -1420 -4104  101  1063  -911  119  -2081 -3778  102  1046 -1081  120  -2729 -4250  103  1021 -3440  121  -3288 -4097  104  55 -4228  122  -3491 -2968  Hn 11/Hn IV 24  104c  Object  123  105  277 -2753  106  628 -1420  107  567 -1683  108  189 -1430  X  Y  Identification  -1964 -3006  Hn 78  125  -1677  Hn 79  126  -1965 -1549  -1891  -144  -1158  127  -2625 -2573  110  -8  -1710  128  -2808 -2313  129  -2810 -1438  8 -1537  112  -8  113  129 -1794  114 X10 115  -1374  XI2  Hn 91 Hn 92/B1 1  -2079 -1639  109  111  Hn 93  11911  124  XI1  Hn 73  -2355  -979  130  -2041  -901  Hn 90a/Bl c  -279 -1947  131  -1404  -723  Hn 90  -450  -2216  132  -686  -628  Hn 89 ( )  -990 -1796  133  389  -442  Hn 83  134  435  48  516  267  116  -1272  117  -1708 -3625  -3052  X13  4  Hn 82/B1 4  ( ) Two stars are labeled 89 on Handschel's Karte V; this is the southern one j  TABLE 2 The objects  Object  X  Y  Identification  Object  X  Y  Identification  Hn 85  135  516  1186  152  52  1241  136  213  1988  153  77  678  Hn 84 ( )  137  -374  2403  -199  2467  X14 138  Hn 49  881)  s  154  -271  177  Hn 86  155  -675  303  Hn 87 Hn 88  156  -1071  471  139  -531  4472  157  -1854  1099  140  -1255  4118  158  -2544  808  Hn 46  141  -1092  3992  Hn 35  159  -3363  927  Hn 45  142  -1275  3523  Hn 34  160  -3213  1302  142b  161  -3787  1668  142c  162  -3747  1139  -3690  1217  143  •1496  4096  144  •2168  4691  Hn 38  163  -4020  335  145  •2040  4063  Hn 37  164  -3452  -623  146  •2247  2999  165  -4018  -630  147  •2521  2719  Hn 48  166  -3978 -1299  148  -2499  1952  Hn 47  167  -3653 -1605  149  •1675  1776  168  -4453 -2181  150  -1485  1992  169  -3594 -2395  151  •1226  1881  170  -4467 -2849  X15  Hn 44  Hn 42  Hn 43  (') This star is mislabeled as the northern 89 on Handschel's Kartc V  16 TABLE 2 The objects Object  X  Y  Identification  Object  170b 171  -4629 -3508  Hn 94  172  -5474 -3421  Hn 9/Hn  III  X  Y  Identification  186  -10620 -11701  Hn 65  187  -10583 -14646  Hn 64  188  -11493 -16244  Hn 63  46/ Bl a 173  -6307  -3029  Hn 95  189  -8607 -14719  174  -6600 -2184  Hn 96  190  -6297 -12879  175  -6410 -1318  191  -7122 -16899  Hn 62  176  -7517  192  -4755 -18014  Hn 61  193  -4651 -17502  194  -11982 -7602  -2823  177 178  Hn 8/Hn III Non-existent  -5356 -5393  17  Hn 8a/Hn III 12/ Bl g ( ) 7  179  -4728  -7477  180  -6188  -7515  181  -7081  -7577  182  -7909  -6267  183  -9138  -5027  184  -9987  -5917  185  -9760 -10638  -14801 -5731  196  -16297 -5284  197  -14538 -1186  198  -12977  -928  Hn 105  Hn 98  199  -12743 -1582  Hn 104  Hn 102  200  -13333  986  Hn 66  201  -13939  2502  Hn 101  X16  -8897 -10520  202  -13858  5458  X17  -8952 -11730  203  -11634  6455  ( ) GCVS 8803 7  195  Hn 70  Hn 103  Hn 2/Hn II 34  17 TABLE 2 The  Object  X  objects  Y  Identification  Object  Hn 1/Hn 1120  219  X  Y  Identification  -9182  8851  Hn 20  -8380  8978  220  -13088  11278  221  -9467  14048  222  -12365  .17228  204  -13536  8950  205  -12751  5394  206  -12069  3229  207  -11375  2441  208  -9425  3327  209  -9014  3994  223  -10536  17266  210  -8544  1.553  224  -9533  17677  211  -8233  -668  225  -7877  18013  212  -7947  2702  X20  Hn 4/Hn 1140  Hn 5/Hn II 44  Hn 7/Hn III 11  226  212b X18  -6961  2116  213  -6022  2203  Hn 40/Bl b C)  214  -4986  .1300  Hn 41  215  -5416  2426  -6813  14919  228  -5364  .11863  229  -5530  9181  -5092  9157  -4866  5130  230  Hn 19 227B  227  X21  Hn II 19  Hn 18  Hn 6/Hn II O  216  -7819  4753  231  -3901  5148  217  -8229  6427  232  -3825  6102  -7368  6615  Hn 11 32  233  -3685  6488  -7838  7559  Hn 3/Hn II 24  X19 218  Hn 39  ( ) 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) ( ) Two stars are labeled 6 on Handschel's Karte V; this is the eastern one 8  9  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  3.1 TOODEE  REDUCTION: F R O M  AND  DIGITAL A R R A Y S TO F L U X  INDICES  SUPERTOODEE PROCESSING  TOODEE (Fahlman 1982) is a simple command language, written in F O R T R A N 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) storage spaces in the program. Commands  which are in-core  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 limitations  (up lo hardware  — 1.7 Mbytes per frame) and can contain data in any of the ANSI  F O R T R A N numerical data types (integer to complex), optimized input/output operations on R A M 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 —  Single stars  —  Two overlapping  —  Three overlapping  —  Crowded frame  —  Saturated star  —  Defective frame  —  No star The  requirements: the frames were categoried as  stars stars  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 —a  (Fahlman 1982,  p. 20). This particular shape was  general quadratic function—  because it was  the pixel intensity distribution; in any  chosen over the alternative  thought closer to the expected shape of  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 deviation. The order and  median was  looking up  computed along with its standard  calculated by sorting the set of pixel values in ascending  the middle value. Those pixels more than 3.5 standard  away from the pseudomode were then rejected, and further pixels were rejected. An  error flag was  of sky pixels then remained. The  the process repeated until  deviations no  set if less than half the initial number  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  the aperture pixels minus the sky intensity integrated  of the intensities of  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 aperture pixels was  we  non-integer as well so as to avoid any  might have arisen at the low  flux end  had  made sure the number of "quantum effect" which  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 to the pixels within a variable radius of its centroid. The  radius was  fitted  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)Lg(F  seeing  max  F  )  (3.1)  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 (see chapter 2) —that the exposure was  taken under  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 two-star routine involved two fits and two subtractions, now  a loop of the  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 ++XX  ++++++:  1 5  20  25  ++ + + ++XX  ::::XX++::::XX++++++XX++XX XXXX:::: ++++XX++::++::::::++++++&& ++++++++ ::++++++ xx++s*XX:: ++::++++ ::++::++::++++++ ++ XX XX :XX : ++:;++++&X++::::::++ ++XX::++ ++ ++::++:: :XXXX:: : XX + + + + :++ ma + + • XXXX++++ + + :::::::XX++XXXX XX::++:: :++++++++++ XXXX++ ++XXXXsssXX: : + + ++ ; ++ ++ : : ::: :XX: ++aaXX++++::XX + + ++++:;++ + + XX++:.XX++++++: ++ : :XX :++ + + + +: ++++ :XX++XXXX++ ++::++++ ++++++ . ++XX++::++xX: + + • ++++;•++ :++++++ X X : : + + : : XX :XX: :::: :XX::++ ++: : + + + + + : : : : : : + + : : + + + + X X : ++++XX::++++: ++ : ++: : + + X X S B + + + + : ++++++XX++++++:::: + + ++ ++ + + + ++ :++xx :++::XXXX++>s<:: ::++:: XX++++ : :++++++XX:: aaaa: : ++: : ::++XX::++XX::XX++::::++ XX: : ::::++++++XX++++ ++++++::++++ ++ XX ++ XX::::++ :++::++ ++++ .++++ :++ :XX: ++xxXXXXsa::++:: : : X X X X : : :++ ««?X: ::::++XX::++++++++ an:: : :++ : :XXj?«f?: + + ++ ::XX::++++++:: XXss?XX++XX++::++: ++ : ++ + + ++XXaa: :+ + ++XX: : : :sss + +: :++: : : + +: + + ++XXXXB5S + + SJS: : ++ .++ . : ++ + +: ::++ :::::++++::++++++++: ++++++ XX ++++ : X X : : X X : : X X : : X X X X : : X X : :XX: ++++++ ++ + + XX++:: :XX++++ : : : : X X :+:+ + +: ++ ::  ::  ::;  :  : :  Intensity  -45. -27. -9.  Pixel  Figure 3: TOODEE  .  :  9.  27.  ::  density plot of frame after  45.  ++  XX  63.  an  81.  99.  117.  XX  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  20  .XXXX++:: . . . :++XX*sXXXX . : : . . . : : :XXs?sXXXXXXXX: : : . . : : XXXX9 99999XX* a : : : . . : + + ss«XX£$99XXs?£: : : . . . :++XXXXXXXX++ : : .  15  . .. •  •  10  ...::::: 5  . ..  Intensity  0.  65.  Pixel  Figure 5: TOODEE  130. .  density  195. :  ::  plot of TR1PLT  260.  •  325.  ++  XX  390.  an  455. XX  520. 585. 99  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  40  20  25  30  35  : : :: : : : ;: :+ + : . : : + + ; : :: : ++:: . : : ; : . ;I : , ++++++++XXXXXX++:::: : : : . ; + + XXXX»«j?«XXJ«siJSis + + + + : : : : . 35 i i . ++»K?W?WIWIW??++++ : : l i ++>>XX$$9999999999MMXX++: . XXXXXX99999999999999**XX:: : ++XX> > $ $ 9 9 9 9 9 9 9 9 9 9 9 9 99MKXX: • ++999999999999?9??9??«xx++++ 30 + + : : : XX?999999999999999SS+++ + . ++: XXs???9999999999XX+ + + +: ++««9X99««^^X?SSJ«XX : : : . ; : : :XX : ++XXXXasXXXX++++:: : ++xxXX++:::::: : : : ::: : : : 25 :++ ::++::: ++::::++++ :++++: : ++:: : : : : ++: : ++++XX++XX: • ++ :++++++++XXXXXXXX++: ++; : : + + XXXXSBBSSJS3 + + + + + + + + BJSXX + + + + + + : : : ++++XX: : : ++++XX++++++: : : : ::++: . X X X X 9 9 9 9 X X X X * * X X 20 •++XXXX++: : : : : : X X : :XXXX++: : + + + + x x ? 9 9 9 9 9 9 9 « * x x + + : ++:. X X ; : + + X X : : : :++++:;H - + + + : anJ?«999W9?X«»XX : ++: : ++: : :: + + + + £ J S B « X X B « X X X X + + ; I . i . ;:++: :++XXXX++: : ++: : • •« • : : > :++::++:: : : : : : : 1 5 : ++:* j l l 1 z : :: : .++::: • '• •* • • • : : '- • :  :  : ;  :  Intensity  0.  Pixel  Figure 6: TOODEE  30.  60. .  90. :  ::  120. ++  150. XX  180.  an  210. XX  240. 270. 99  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 or three pixels on the side, and  two  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 was  object in tables 3 to 5 does not  necessarily imply the  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  manner previously described. The  weights come about as a result of certain stars'  multiple appearances on a single plate, this either due frames or to overlapping  in the  cases. The  to actual redundancy in 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 reduction.  would not improve on the current  30 Chapter 4 DATA  REDUCTION: F R O M F L U X INDICES TO  MAGNITUDES  4.1 THE V I R T U A L 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  Although  calibration curves are, thus, reduced.  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 visual plate 327,  we proceeded  and the  to fit the other plates in each group to the power law  k  F, = C F  (4.1)  2  At this stage was initiated the use of the logarithm of the flux indices as their weights in anyfit.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  (4.2)  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.  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.  . , 2.0  1 2.4  1 2.6  Figure 8: Correlation  1 8.2  1 9.6  1 4.0  1 4.4  LG(FLUX» B PLATE 330  of B plates  1 4.8  1 3.2  1 9.6  387 versus 330  The objects rejected (*) were (topside, top to bottom) 83B, 107, and 81, (underside, top to bottom) X l l , 94, 100, and 151.  1 6.0  34  Figure 9: Correlation  of V plates  The objects rejected (*)  329 versus 327  were (top to bottom) 149 and X15.  35  36  Figure 11: Correlation  of V plates  The objects rejected (*)  409 versus 327  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 thefitvery 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  3 3 0  (4.3) 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 '  3 3 0  (4.4) 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  3 2 7  (4.5) 3 2 9  root-mean-square deviation = 0.166  0 . F  =  9 1 2 9 3 8  5 . 9 0 0 3 1 6 * F  3 2 7  (4.6) 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  3 2 7  (4.7) 4 0 9  root-mean-square deviation = 0.101 for the visual group.  38 A temporary virtual plate was then constructed, composed o r 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 o f 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  2.0  2.4  1 2.6  Figure 13: Correlation  1 3.2  1 4.0  1  4.4 LGlFLUX) MEAN B GROUP 2  of B plate  No objects were rejected.  1  9.6  330 versus mean group 2  1 4.8  1 9.2  1 3.6  1 6.0  41  42  I  1  1  1  .0  2.4  2.8  3.2  Figure 15: Correlation The  1  1  1  1  i  4.0  4.8  5.2  8.6  6.  1 4.4 LG(FLUX) MEAN V GROUP 2  of V plate  rejected objects (*)  1  3.6  327 versus mean group 2  were (top to bottom) 106 and 95.  43  Figure 16: Correlation The  of V plate  rejected objects (*)  329 versus mean group 2  were (top to bottom) 155 and 81.  44  45  .0  Figure 18:  Correlation  of V plate  No objects were rejected.  409 versus mean group 2  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:  F  mean  0.969584 = 1. 3 7 5 3 4 7 * F 328  (4.8)  root-mean-square deviation (in Lg(flux)) = 0.061  F mean  1 .004578 = 0.951824*F 330  (4.9)  root-mean-square deviation = 0.067  F mean  0.911783 = 3.242394*F 387  (4.10)  root-mean-square deviation = 0.071 for the blue group, and  1.014035 F  = 0.845592*F mean  (4.11)  327  root-mean-square deviation = 0.030  F mean  0.907460 = 8.544253*F 329  root-mean-square deviation = 0.038  (4.12)  47 0.885735 F  =  7.64  (4.13)  1143*F  mean  386  root-mean-square deviation  =  0.027  0.699881 F  =  94.877497*F  mean  (4.14) 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  the restricted sample involved  imputed to  in the second set of correlations; this is especially true  for the visual group. Once this process was plates, a new  concluded, one  was  left with the same two ultraviolet  set of three blue plates (composed of the old plates 10 and a new  virtual plate), and  the new,  virtual plate). From this point on, the plates, real or virtual, are going to be has  two  visual plates (old plate 16  and  the new,  referred to as groups. Thus one  set of only  410,  ultraviolet groups 1 (plate 12) and  blue groups 1 (plate 10), 2 (the virtual blue plate) and groups 1 (plate 16) and  give the object entries for the blue and For  consider  we  had  12 in Appendix  B  more correct way  as if the component  of looking at the numbers is to  each column as an independent plate-to-flux-indices reduction  plate. That is to say, we  visual  visual virtual plates respectively.  ease of recognition, the multiple entries are tabulated  plates were still separate. A  2 (plate 334),  3 (plate 410), and  2 (the virtual visual plate). Tables 11 and  and  of the same  would have obtained qualitatively indistinguishable results if  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 characteristics).  machine's response  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 with.  standards we  had to work  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 whenever possible, this lack was It was  ultraviolet magnitudes;  corrected with the values of Handschel (1972).  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  +  bLg(F  i  )  (4.15)  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 hand is then to relate two ultraviolet colors, three blue colors, and to the standard UBV  ,(l  task at  two visual colors  colors.  It should be mentioned in passing that recently Vardanyan and Akhverdyan (1975)  have measured 186 faint objects in and around NGC (R-I) to an accuracy of ±0.5  7419  in the infrared; they claim  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 might be of interest to other researchers, however.  matter  50 TABLE 3 Photometric Standards  Object  U  1A  B  V  8.02  7.50  1  9.50  2  8.62  3  2A 3A  8.88  Sou: R = 7.15 1 = 7.18 Sp = A2m (1)  B = 8.75 V = 8.55 R = 8.42  1 = 8.55 Sp = A5 (1) 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  17.93  16.25  4  12 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  1.5.38  4  19  16.86  •  16.70  22  .17.68  16.19  4  28  17.05  15.07  4  29  18.07  16.65  4  30  19.27  17.55  3  15.66  13.97  3,4  19.08  17.24  3  15.98  14.85  4  17.17  13.77  3  32A  16.09  34 37A  16.85  40  R = 12.U 1 = 9.55 Sp = M3.5 (1)  42  16.99  16.52  14.81  4  51 TABLE 3 Photometric Standards U  B  V  15.17  15.04  14.31  4  46  17.48  16.38  4  50  19.19  17.53  3  16.94  15.37  4  17.84  16.12  3  15.92  14.96  3,4  61  17.97  16.53  4  62  17.80  16.15  4  16.32  15.45  4  66  18.02  16.58  4  73  18.99  17.10  3  75  18.10  16.51  4  Object 44A  54  17.22  59  60A  65  16.04  16.36  Soui  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  15.85  12.48  4  88A  B = 11.78  V = 10.6 Sp = G5 (1)  R = 11.23 1 = 8.78 (1); Sp = M2Iab (5)  89  17.21  16.85  15.32  4  91  17.23  16.87  15.45  4  17.86  16.36  4  92 93  17.11  16.81  15.25  4  96A  15.61  15.28  13.65  4  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)  16.06  12.49  4  R = 11.12 1 = 8.80 (1);  130A  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  18.16  16.44  4  184 185  16.65  16.30  15.23  4  186  17.60  16.99  15.81  4  17.49  16.37  4  187 188  16.45  16.44  15.26  4  191  17.72  17.16  16.27  4  192A  15.66  15.19  14.31  4  18.37  14.48  3  194  R = 12.68 1 = 10.3 Sp = N (1)  TABLE 3 Photometric Standards Object 196  U  V 14.05  4  198  17.65  16.10  4  199  17.79  16.34  4  203  17.34  15.97  3  13.65  12.97  3,4  206 .  18.78  16.02  3  208  18.58  16.43  3  13.94  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  20.18  18.38  3  X19 218  16.41  16.44  15.19  3,4  219  16.14  15.63  14.54  4  18.60  17.44  3  220 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: 2: 3: 4: 5: 6:  Source Comments  15.74  204A  16.12  B  Blanco, Nassau, Stock, and Wchlau 1955 Aitken 1932 Sandage 1972; photoelectric values Handschel 1972; photographic values Fawley and Cohen 1974 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 + $ v  (4.16)  (B-V) = u ( b - v ) + §  (4.17) bv  (U-B)  = i^(u-b) + $  (4.18) ub  inserting u = a  u  + 6" Lg (F ) u u  (4.19)  + (3 L g ( F ) b b  (4.20)  b  v  + j3 L g ( F ) v v  (4.21)  b = a  v = a  and working the equations a bit, one is left with  U = 7 L g ( F ) + SLg (F ) + 7?Lg(F ) + 9 u b v B  =  KLq  (F  )  b  +  rjLq (F  )  +  v  V = pLg(F ) + 0Lg(F ) + r b v  £  (4.22)  (4.23)  (4.24)  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  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  u  {jLq (F ubv  ) + u  i  f  = I  w  b  {/cLg ( F bv  = 2 v  rjLgCF  £ - B  v  }  2  (4.25)  i  } 2  (4.26)  }  (4.27)  i i  0Lg(F  ) + b  i  6 - U  i  ) +  i  ) + v  i  ) +  { p L g (F bv  r?Lg(F  b  b  w  ) +  i  i  f  5Lg(F  ) +  r - V  v i  2  i i  where the weights are defined as  w  =  2  w  2 +  ubv  2  w  u  ; bv 2  w  = w  2  +  w  b +  w  b  f _ ) 4  28  v  2  (4.29)  v  = Lg(F u  2  )  (4.30)  )  (4.31)  •)  (4.32)  u i  w  i  = Lg(F b  b i  w  i  = L g (F 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  ^bv.V^b.* Iw, V.Lq(F ) bv. 1 ^ v . l l Iw, V. bv. I l  bv  Z w  l  l  ^bv.^b.^V* ^bv.^^b.)  L  9  ( F  K  ) g ( „v. ) £ w bv „ Lg(F L  ^bv.^V* I w  bv.L9  ( F  ,  F  h  K  )  Iw, Lg(F ) bv. = v. I l Iw  bv  0  59  and  Zw, B . Lq ( F, bv . 1 ^ b. Zw, B . Lg ( F bv. 1 ^ v. l l  )  Zw, B. bv. I l  ^bv.^^b.) l l ^bv.^^b.^g^v.) l l l ^bv.^^b.)  2  w  bv. 9 L  (  F  l  Z w  b.  )  L  i  9  (  F  v.  bv. 9 < v.> l l L  l  2  F  l  where, of course, the matrices remain to be inverted.  )  ^ b v . ^ b . *  i  l  Zw _Lg(F^ b v  Zw  bv  l  60  The  £ w  ubv. 1  ultraviolet solution is then  { U  i 9 L  ( F  1  u.  )  " ^g(F  )Lg(F 1  1  Iw , {U.Lg(F, ) - r?Lg(F, ) L g (F ubv. I b. ' ^ b . ^ v .  )}  )}  3  Iw , {U. - rjLg (F ) } ubv. I ' ^ v. l l  Iw , L g ( F ) ubv . ^ u. I l 2  Iw nh\7 , L g^ ( nF Iw , L g ( F ) ubv. ^ u. l l  )Lg (F, K  ^ubv.^^u.^g^b^^ubv.^^u^ )Iw , L g (F, ubv. b2  1  1  Iw , L g ( F , ) ubv. ^ b .  )  Iw , L g (F, ) ubv. ^ b. 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 The  IMAGES  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 4.00  images dimmer by  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 secondaryimages. Also, the focal ratios of the prism and and  telescope are vastly different —1755  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 of  Am  was  effects, and  the value  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 = a  m  + bLg(F)  (4.33)  then Am  - bLg(F  ) - bLg(F  Am  )  (4.34)  B  A  = b L g ( F /F  )  (4.35)  B  A  but if m = a  + bLg(F)  + cLg (F)  (4.36)  2  then Am  =  (b + 2 c L g ( F  ))Lg(F A  /F  ) - c L g ( F /F B  A  )  2  A  (4.37)  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 A  Am  allows  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 B  /F A  )>  (4.38)  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 photometrytechniques. 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:  Observed  Am  r.m.s. deviation  Ultraviolet group 2  3.810  0.218  Blue group 2  4.084  0.420  Blue group 3  4.011  0.246  Visual group 2  4 . 08 1  0. 576  _j  4.0  ,  4.13  1  4.8  1  4.43  1  4.8  1  4.73  U' LG(Ffl)  Figure 26: Lg(F /F ) for U group 2 A B The sample is too small to warrant comment  1  4.9  1  3.03  1  3.7  1  3.83  I  3.  74  CD O  (9 <S>  -ft  e  Q  o  <5  o  1 4.0  4.13  1  1  1  1  1  1  1  1  4.8  4.43  4.6  4.73  4.9  3.03  3.2  3.83  B ' LG(pH)  Figure 27: Lg(F /F ) for B group 2 A B Note, as expected, the conical envelope (axis along mean L g ( F . / F g ) line, apex on the high Lg(F^) side). There is no systematic difference between the contributions of the different plates belonging lo the group.  I  3.3  75  O  —  —  cr  o  „  , A  Figure 28: Lg(F  .  R  7» 7 . 7 . 2 < a 4  i  A  /F ) for B group 3 A  B  .  fl) 4.8 B ' l M 4.73 t  T  1  4.9  3.03  1  3.2  1  3.83  ~"  3.3  76  O  o  _Q O  O O  ,  4.0  1  4.13  1  4.3  1  4.40  1  4.8  1  V  4.73  LGlFR)  1  4.0  1  O OO  3.03  1  3.2  I  3.83  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.  I  3.3  77 4.4 CALIBRATION  RESULTS  The calibrations found were Ultraviolet group 1 U  = 27.888219 - 1.849807Lg(F  ) - 0.559089Lg(F  )  (4.39)  1.254033Lg(F ) - 1.440476Lg(F ) - 0.308683Lg(F ) u2 b2 v2  (4.40)  ul  ) - 0.308683Lg(F  b2  v2  r.m.s. deviation = 0.169 maenitudes Ultraviolet group 2 U  = 29.059030 -  r.m.s. deviation = 0.215 magnitudes Blue group 1 )  (4.41)  = 30.654326 - 2.995999Lg(F ) - 0.308683Lg(F ) b2 v2  (4.42)  B = 30.785504 - 2.446742Lg(F  ) - 0.760740Lg(F  bl  v2  r.m.s. deviation = 0.179 magnitudes Blue group 2 B  r.m.s. deviation = 0.203 magnitudes Blue group 3 B  = 29.831006 - 2.942091Lg(F ) - 0.272089Lg(F ) b3 v2  (4.43)  r.m.s. deviation = 0.196 magnitudes Visual group 1 V  = 32.184752 - 0.568251Lg(F  ) - 3.061888Lg(F  b2 r.m.s. deviation = 0.120 magnitudes  vl  )  (4.44)  78 Visual group 2 V  =  30.912374 - 0.282209Lg(F b2  r.m.s. deviation  =  ) - 3.111401 Lg(F ) v2  (4.45)  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 formula for visual group 2 without the secondaries was  V  79 V  =  30.690643 - 0.120985Lg(F ) - 3.201981 Lg(F ) b2 v2  (4.46)  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  Lg(F  b2  +  2  b2  )  r\  2  a  2  Lg(F  v2  )  (4.47)  and p 2o 2 V  v2  Lg (F  b2  )  +  4> 2o 2  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  U  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  18.363  16.935  18.32  20.94  16.762  15.177  20.75  14.04  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  5 6  17.002  U-B  Weights  B-V  B  U  1.428 0.240  1.585  3.70  V  U-B  B-V  39.26 24.45  34.79  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  19.097  17.669  17.15  15.91  X2  1.427  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  19.145  16.883  16.92  21.19  14  2.262  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  18.717  17.329  17.77  16.29  20  1.387  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  18.756  17.274  17.69  16.39  18.742  17.212  17.70  20.53  24 25  18.801  1.482 0.059  1.530  3.15  34.08 20.85  38.23  81  TABLE 4 Raw Photometry Object  Magnitude  Color Index  U  B  V  U-B  26  18.116  18.574  16.897  -0.458  1.676  27  19.605  19.702  17.935  -0.097  28  17.275  17.067  15.068  29  18.617  18.323  16.676  19.281  17.692  30  B-V  Weights V  3.49  17.93  16.86  21.42  34.79  1.767  2.84  16.16  15.67  19.00  31.83  0.208  1.999  3.73  20.19  18.90  23.92  39.09  0.294  1.648  3.20  18.34  21.36  21.54  39.70  16.89  15.96  1.589  U-B  B-V  B  U  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  19.762  17.857  16.08  7.97  45  1.906  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  TABLE 4 Raw Photometry Object  Color Index  Magnitude  U  B  V  17.616  17.080  16.044  X4  18.986  17.094  X3  19.143  17.540  19.530  16.718  50  19.124  17.580  51  19.582  18.042  48  49  19.333  U-B  0.536  -0.197  B-V  Weights B  V  20.41  11.12  1.892  17.13  8.39  25.52  1.603  15.31  8.10  23.41  15.94  12.91  1.544  17.09  16.03  33.12  1.540  16.41  15.51  31.92  1.036  2.811  U  6.84  2.87  U-B B-V  27.25  18.81  31.53  28.85  52  18.469  18.739  17.289  -0.270  1.450  3.34  17.74  16.38  21.08  34.12  53  19.167  18.730  17.093  0.437  1.637  2.96  17.71  20.76  20.67  38.47  54  17.279  16.987  15.408  0.292  1.579  7.30  20.41  18.45  27.71  38.86  55  19.263  17.664  1.599  16.90  15.96  32.86  56  19.311  17.964  1.347  16.85  15.57  32.42  58  20.101  17.939  2.162  15.45  15.73  31.18  59  18.017  17.876  16.127  0.141  1.749  6.75  18.98  22.15  25.73  41.1.3  60A  16.115  15.929  15.106  0.187  0.823  8.30  35.49  23.39  43.79  58.88  61  18.103  17.900  16.455  0.203  1.444  6.72  19.04  21.63  25.76  40.67  62  17.947  17.624  16.260  0.322  1.364  6.74  19.48  21.89  26.22  41.37  18.688  17.040  17.73  16.66  63  1.648  34.39  64  18.898  18.774  17.313  0.124  1.460  3.11  17.66  16.34  20.77  34.00  65  16.475  16.327  15.310  0.148  1.017  8.03  21.56  18.49  29.59  40.05  66  18.679  18.124  16.594  0.555  .1.530  3.14  18.67  21.44  21.81  40.11  67A  16.322  16.044  15.108  0.278  0.936  8.10  30.79  18.73  38.89  49.52  68  19.646  19.919  17.764  -0.273  2.155  2.83  15.75  15.93  18.58  31.68  83  TABLE 4 Raw Photometry Object  Magnitude U  B  Color Index V  U-B  B-V  Weights U  V  U-B  B-V  69  18.430  18.264  16.518  0.166  1.746  6.47  16.50  21.60  22.97  38.10  70  19.736  19.054  17.447  0.682  1.607  2.71  17.21  16.25  19.92  33.46  71  19.094  I. 8.468  16.987  0.626  1.481  2.97  18.14  16.73  21.11  34.87  72  19.376  19.718  17.991  •0.342  1.727  2.95  16.12  15.57  19.07  31.69  73  18.890  18.595  16.710  0.295  1.885  3.06  17.83  21.32  20.89  39.15  74  18.755  18.827  17.229  -0.072  1.598  3.19  17.57  12.38  20.76  29.95  75  18.783  18.232  16.532  0.551  1.700  6.08  18.45  21.58  24.53  40.03  76  18.422  18.256  16.665  0.165  1.591  6.49  18.45  17.11  24.94  35.56  77  17.828  17.490  16.154  0.338  1.337  3.40  19.67  19.84  23.07  39.51  17.866  16.594  19.08  15.00  78  1.272  34.08  79  19.372  19.171  17.475  0.201  1.695  2.89  17.00  14.18  19.89  31.18  80  18.305  18.747  17.004  -0.442  1.743  3.44  17.65  20.94  21.09  38.59  81  17.600  17.294  15.819  0.306  1.475  7.04  19.94  18.07  26.98  38.01  82  17.722  17.590  16.065  0.131  1.525  7.08  17.49  15.60  24.57  33.09  83A  12.877  II. 567  10.298  1.310  1.269  9.62  22.87  18.31  32.49  41.18  X6  19.126  19.598  16.996  -0.472  2.603  3.05  16.13  21.06  19.18  37.19  84A  16.418  16.062  14.572  0.356  1.490  7.99  30.60  19.43  38.59  50.03  85  17.548  16.916  15.383  0.632  1.533  7.02  20.54  13.87  27.56  34.41  86  19.229  19.125  17.393  0.104  1.732  2.98  17.07  16.31  20.05  33.38  87A  15.944  15.593  14.188  0.351  1.405  8.31  31.61  24.82  39.92  56.43  88A  18.015  1.5.802  12.834  2.213  2.968  3.1.0  30.70  21.64  33.80  52.34  X7  18.944  18.560  17.184  0.384  1.377  3.09  18.00  8.27  21.09  26.27  84  TABLE 4 Raw Photometry Object  Magnitude  Color Index  Weights  U  B  V  89  16.940  16.834  15.284  0.106  1.550  7.64  20.65  18.59  28.29  39.24  X8  19.230  19.387  18.043  •0.157  1.344  3.03  16.78  13.58  19.81  30.36  90  18.844  19.206  17.480  -0.362  1.726  3.20  16.95  16.22  20.15  33.17  91  17.247  16.997  15.402  0.250  1.595  7.37  20.39  18.46  27.76  38.85  92  18.042  18.062  16.354  -0.020  1.708  6.81  18.71  21.82  25.52  40.53  93  17.059  16.814  15.183  0.245  1.631  7.48  20.66  18.72  28.14  39.38  94  17.405  17.265  15.668  0.140  1.597  7.38  19.97  22.85  27.35  42.82  95  17.825  17.344  15.947  0.481  1.398  6.92  19.88  22.39  26.80  42.27  96A  15.617  15.328  13.562  0.290  1.766  8.57  32.07  10.32  40.64  42.39  18.583  16.395  14.14  21.91  15.994  14.493  21.95  14.64  18.451  17.258  10.80  12.32  X9 97  16.224  98  U-B  B-V  B  U  2.189 0.230  1.501  8.15  1.193  U-B  B-V  36.05 30.10  36.59 23.12  99  17.899  17.806  16.288  0.093  1.518  6.98  19.16  17.54  26.14  36.70  100  18.992  18.130  16.564  0.862  1.565  5.70  18.65  17.23  24.35  35.88  101  18.753  17.490  1.263  17.69  14.1.1  31.80  102  19.025  17.518  1.508  17.14  12.07  29.21  103  17.321  16.983  15.302  0.337  1.681  7.22  20.39  18.59  27.61  38.98  104  19.067  19.195  17.645  -0.128  1.550  3.06  16.98  13.98  20.04  30.96  105  19.026  19.353  17.604  -0.327  1.749  3.12  16.73  16.06  19.85  32.79  106  17.112  16.950  15.669  0.162  1.281  7.50  18.40  22.73  25.90  41.13  107  17.234  16.942  15.562  0.293  1.379  7.34  18.38  22.88  25.72  41.26  114  18.208  18.188  16.516  0.020  1.672  6.69  16.63  21.57  23.32  38.20  85  TABLE 4 Raw Photometry Object  Magnitude U  X10  19.076  115  B  Color Index V  U-B  19.774  18.418  -0.698  18.856  16.309  B-V  1.356  Weights U  3.17  2.547  B  V  16.01  11.34  17.23  21.98  U-B  19.18  B-V  27.35 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  19.210  17.936  17.04  11.73  17.820  16.220  19.12  22.00  19.223  17.659  16.95  15.93  121 122  18.042  124  1.274 0.223  1.599  6.74  1.564  28.77 25.86  41.12 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  Xll  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  19.446  17.541  9.80  14.17  X12  1.905  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  X13 135  U  B  V  19.058  18.579  16.717  0.479  1.862  19.119  19.031  17.293  0.088  1.738  19.704  17.826  17.171  16.089  18.746  17.737  136 137  Color Index  Ma gnitude  17.684  X14  U-B  B-V  Weights B  V  2.99  14.47  12.72  17.46  27.19  3.02  17.22  16.43  20.24  33.65  16.14  15.81  20.25  19.91  17.85  11.89  U  1.878 0.513  1.082  6.99  1.009  U-B  B-V  31.95 27.24  40.16 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  18.686  17.769  10.60  9.93  142b  0.916  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  17.987  17.237  19.06  16.33  150  0.750  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  TABLE 4 Raw Photometry Object  156  Color Index  Magnitude U  B  V  16.696  16.477  14.948  19.267  17.628  157  U-B  0.219  B-V  1.529  Weights U  U-B  B  7.79  1.639  21.22  18.99  16.88  16.01  29.01  B-V  40.21 32.89  158  17.696  17.628  16.117  0.068  1.511  7.12  19.44  22.14  26.56  41.58  159 A  15.844  15.651  14.223  0.193  1.428  8.47  31.49  24.78  39.96  56.27  19.396  17.768  13.25  15.85  160  1.628  29.10  161  19.164  18.773  17.337  0.391  1.436  2.97  17.68  16.32  20.65  34.00  162  16.677  16.587  15.181  0.090  1.406  5.90  21.04  23.46  26.94  44.50  XI5  18.053  18.575  16.637  -0.522  1.938  3.57  14.41  21.44  17.98  35.85  163A  16.353  16.031  14.972  0.321  1.059  7.98  30.75  18.88  38.73  49.63  164  19.523  19.250  17.553  0.273  1.697  2.84  16.88  16.12  19.72  33.00  165  17.589  17.379  15.908  0.210  1.471  7.09  19.82  22.43  26.91  42.25  166  19.941  19.601  17.662  0.340  1.939  2.62  16.21  15.98  18.83  32.19  20.676  18.909  14.62  7.33  167  1.767  21.95  168  19.155  19.314  17.423  -0.159  1.892  3.01  16.69  16.26  19.70  32.95  169  19.511  19.525  18.089  -0.014  1.436  2.87  16.50  13.51  19.37  30.01  170  18.590  18.506  17.055  0.085  1.451  6.40  18.11  18.71  24.51  36.82  171  18.095  17.939  16.481  0.156  1.458  6.76  18.98  21.61  25.74  40.59  172A  18.674  16.000  12.983  2.674  3.017  2.77  21.60  5.37  24.37  26.97  173  17.288  17.139  15.588  0.150  1.551  7.35  20.19  22.91  27.54  43.10  174  18.116  17.982  16.525  0.134  1.456  6.74  18.89  21.52  25.63  40.41  175  18.872  19.058  17.494  -0.186  1.564  3.14  17.18  16.13  20.32  33.31  176  18.245  17.949  16.732  0.296  1.216  6.55  19.00  21.18  25.55  40.18  88  TABLE 4 Raw Object  Photometry  Color Index  Magnitude U  B  V  178  18.681  18.633  16.922  0.048  1.711  179A  16.176  15.972  15.171  0.203  0.801  19.207  17.741  180  U-B  B-V  Weights V  3.19  17.84  21.00  21.03  38.84  8.25  30.97  23.28  39.22  54.25  16.99  15.85  1.466  U-B  B-V  B  U  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  20.192  19.389  18.052  0.803  1.337  2.51  16.76  11.64  19.27  28.40  19.809  18.371  16.10  11.39  X16 X17  1.438  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  19.491  17.831  16.50  15.79 21.37  189  1.660  32.29  190  18.776  18.077  16.643  0.699  1.434  3.08  18.77  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  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  50.06  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  U  B  V  198  17.810  17.595  16.256  0.216  1.339  199  17.885  17.729  16.433  0.156  1.296  19.169  17.757  18.581  17.199  19.144  17.823  200 201  19.007  202  U-B  B-V  Weights B  V  6.93  19.53  21.89  26.46  41.42  6.93  19.33  21.64  26.26  40.97  17.06  15.80  17.98  16.44  17.14  15.7.1  U  1.412 0.426  1.381  3.02  1.321  U-B  B-V  32.86 21.00  34.42 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  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  18.813  17.468  1.345  17.64  16.14  X18  215  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  19.646  18.504  16.41  11.24  X19  1.142  27.65  90 TABLE 4 Raw Photometry Objecl  Magnitude  Color Index  U  B  V  218  16.609  16.438  15.179  0.1.71  1.259  219  16.022  15.660  14.483  0.362  .1.177  19.412  18.076  X20  U-B  B-V  Weights  U  B  V  U-B  7.92  21.32  18.68 29.24 40.00  8.27  22.53  12.18 30.80 34.71  16.71 11.64  1.336  B-V  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  19.324  17.485  223  16.75 16.20  1.839  32.95  224  18.652  18.665  17.281  -0.013  1.384  3.23  225A  15.805  15.435  14.523  0.370  0.912  8.43 41.12  227A  15.469  15.099  13.566  0.370  1.533  8.66  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  19.653  19.616  17.937  0.037  1.679  2.81  13.20 15.68 16.01  230  17.004  1.6.826  15.491  0.178  1.335  7.59 20.71  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  X21  17.86 16.38 21.09 34.24 19.40 49.55 60.52  32.64 20.61 41.30 53.25  28.88  18.32 28.30 • 39.03  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  (B-V)  s  - V = aV + b  (4.49)  -  (B-V) = c(B-V)  + d  (4.50)  -  (U-B) = e(U-B)  +  (4.51)  s  (U-B)  f  s  We  obtained V  - V = 0.009992V  -  0 .15672-9  (4.49')  s  (B-V)  -  ( B - V ) = 0.01 7 5 6 4 ( B - V )  -  0 . 019316  -  (U-B) = -0.087652 (U-B) + 0 .023893  (4.50')  s  (U-B)  s  (4.51')  with r.m.s. deviations of 0.138, 0.156, and 0.145, respectively. We also solved lor  V  -  V = a' (B-V) + b'  -  (U-B) = e ' ( B - V )  (4.52)  s  (U-B)  +  f  (4.53)  s  For which we obtained V  - V = 0.006581 (B-V) -  0.010462  (4.52')  s  (U-B)  s  (U-B) = 0. 1 46529(B-V)  -  0 . 203137  (4.53')  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 distribution. Nevertheless, the (U-B)  result is worrisome —more on that in chapter 5.  (U-B)  93 4.5 THE C A R B O N  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 verycrude, of course; but it was attempted anyway:  Date  B  V  1 July 1978  1 9 . 3 7 8  8 July 1980  18.906(  (  1  1  1 1  )  <15.931(  )  <15.171 ( ) 1  10 July 1980  18.952  14.953  28 June 1981  19.439  14.681  2 July 1981  19.001  14.643  )  12  2  ( ) Obtained using the average of Log(Flux(V2)) n  ( ) Image was saturated 13  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 T H E C O L O R - M A G N I T U D E A N D 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 — o r 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 color-color diagram in any significant way!  so) fails to affect the  95 The something (U-B)  best ] can do at this point is express my opinion that "there is fishy with the (U-B)  colors", that photoelectric determinations of the actual  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) about de-reddening  at one step or another —I am thinking particularly  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 N G C  2158 (Hagen 1970. Arp and CulTey 1962), where the main sequence ends  abruptly in a stub. To the difference of N G C  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  0-0  0.5  1  1  £-V C O L 0 R INOEX.  (  1.1  l.J I  1  2.0  2.5  3.0  8.3  I  I  I  I  4.0 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).  4.5 I  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 A N D  DE-EXTINGUISHING  6.1 T H E O M E T H O D 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)  -  0.72(B-V)  (6.1)  then since E(U-B)/E(B-V)  ~  0.72  (6.2)  (Johnson and Morgan 1953). the parameter Q will be reddening-independent:  =  Q  (U-B)  o  -  0.72  (6.3)  (B-V) o  o  introducing the color-excess defining equations:  (U-B)  =  (U-B)  +  E(U-B)  (6.4)  +  E(B-V)  (6.5)  o  (B-V)  =  (B-V)  equation (6.3) becomes: Q  =  (U-B)  +  E(U-B)  -  0.72((B-V)  +  E(B-V))  105  Q  and  Q  + E(U-B) -  substituting equation (6.2), we  0.72E(B-V)  (6.6)  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 stars. Hiltner and  because of the dearth of such  Johnson (1956) showed that, more accurately,  E(U-B)/E(B-V)  =  0.72  Although this curvature effect is very slight and into account if one  +  0.05E(B-V)  is generally neglected, one  (6.7)  can take it  accepts that (B-V)  =  0 . 332Q  o  (6.8) o  as demonstrated by Johnson (1958) for main sequence stars of spectral type BO  to  AO.  It then follows that (U-B)  =  (1  +  0. 7 2 * 0 . 3 3 2 ) Q  o  (6.9) o  Hence, inverting (6.6) and substituting (6.7), Q  = Q  -  which becomes, inserting (6.5) and (6.8),  0 . 0 5 E (B-V) 2  (6.10)  Q  = Q  o  -  0.05{(B-V)  -  0.332Q  o  }  2  (6.11)  Isolating Q , one finally gets o  T?(B-V)  Q  1 + y/ 1 - 2 T ? ( B - V )  -  + 0.332n2Q  =  (6.12) 0 . 332r?  Where ri = 2*0 . 3 3 2 * 0 . 0 5  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) O  and (B-V) from Q . The correction from Q to Q O  O  non-negligible for heavily reddened cases, such as ours.  o  is  107 6.2 THE SERKOWSK1 M E T H O D The method we actually Followed was pioneered by Serkowski (1963). He finds  (U-B)  = (U-B)  + XE(B-V) + 0.06E (B-V)  (6.13)  2  o  where X = 0.58 - 0.33 ( B - V )  (6.14) o  and (U-B)  = 0.10  + 3.80(B-V)  o  (6.15) 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)  T?,(B-V)  ~  T?2  +  T  /~77  3  ~  T? (B-V) t  + n (B-V) s  £  is given by  + 77 ( U - B ) 6  (6.16) 7?7  108  Where 7?,  =  0.450  TJ2  =  3.220  rj3  =  10.212  ri  =  3.803  7?  =  0.109  r? 6  =  1 . 560  r? 7  =  0.780  n  5  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 0 5 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  Af((B-V)  ) = M v  SK  ((B-V) ) - M ((B-V) ) v  (6.17)  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) o  For (B-V) o  relation.  o  > -0.05, Eggen does not supply any values, so the Schmidt-Kaler curve  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).  T A B L E 5.1 The Zero-Age Main Sequence (B-V)  (U-B) o  M  o  0.33  -1.315  -5.2  0 . 32  -1.272  -4.76  0.31  -1.208  -3.81  0.305  -1.178  -3.6  0 . 30  -1.15  -3.25  0.295  -1.11  - 3 . 07  0.29  -1.102  -2 .88  0.285  -1 . 0 7 5  -2.74  0.28  -1 . 0 4  -2.6  0.27  -1.005  -2.40  0.26  -0.97  -2.23  0.255  -0.93  -2.17  0.25  -0.909  -2. 1  0 . 245  -0.89  -2.06  0.24  -0 . 8 6  -1 . 9 0  0.23  -0.825  -1 . 7 0  0.22  -0.785  -1.5  0.21  -0.75  -1.3  0.205  -0.715  -1.2  0.20  -0.68  0.19  -0.645  -0.90  0.18  -0.61  -0.71  0.175  -0.57  -0.62  -  1  •  1  T A B L E 5.1 The Zero-Age Main Sequence (B-V) o  (U-B)  M  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  0.12  -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  -0.188  0.82  -0.075  -0.175  0.85  -0.07 -0.065  0.92 -0.14  0.95  T A B L E 5.2 The Zero-Age Main Sequence (B-V)  (U-B)  o  M o  0.06 0.05  1 .02 - 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  T A B L E 5.2 The Zero-Age Main Sequence (B-V)  o  (U-B) o  M  1  . 30  1  . 20  8.0  1  . 40  1  . 22  8.8  1  . 50  1.17  1  .60  1  . 20  12.0  1  .70  1  . 32  13.2  1  .80  1  . 43  14.2  1  .90  1  . 53  15.5  1  . 64  16.7  2.00  10.3  114 Using our ZAMS, the (U-B)  versus (B-V)  o  relation is appropriately modeled  o  by (U-B)  = 0.107272 + 3 . 42242 (B-V) o  - 2 . 6 1 952 (B-V)  2  o  over the range -0.33 < (B-V)  (6.18)  o  < -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 (B-V) 2  (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 , =  0.100  =  2.744  773 =  8.640  ??„ =  -6.455  =  0.661  TJ  T?  2  Tjs 776  T7 7  = - 1 0 . 330 =  -5.165  The visual extinction, in turn, can be evaluated from  A  = V - V  = {3 . 30 + 0. 2 8 ( B - V )  + 0. 0 4 E ( B - V ) } E ( B - V )  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  (6.20)  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) o  + c(B-V) o  2  o  (6.18')  and E(U-B) = (d + e(B-V)  )E(B-V) + fE (B-V) 2  o  into (6.4), and replacing (B-V)  with (B-V) - E(B-V), one has  (U-B)  + c(B-V)  (6.19')  o  = a + b(B-V)  2  +  theo (e - 2 c ) ( B - V ) E ( B - V ) (c  + (d-b)E(B-V)  + (6.21)  - e + f)E (B-V) 2  Similarly, substituting A  = {g + h ( B - V )  + iE(B-V) }E(B-V)  (6.20')  v into V = M v  + D + A v  (6.22)  where D is the distance modulus (taken as constant) and M  can be expressed as v  z((B-V)  o  one gets  ), a non- analytical function tables 5.1 and 5.2 can be considered to define,  116  V  = z((B-V)  - E(B-V))  theo gE(B-V)  where (B-V)  + (m - M ) + v - (h - i)E (B-V) + h(B-V)E(B-V)  (6.23)  2  has once more been replaced  by (B-V)  - E(B-V). We therefore  o  propose to minimize the sum of the squares  A2  = ((U-B)  - (U-B) ) theo  2  + w (V- V  )  2  2  (6.24)  theo  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. a(u-B)  3(U-B)  -  3E(B-V)  As  9(B-V)  av  3 V  -  ° - w{ o  BE(B-V)  £  3(B-V)  }  (6.25)  o  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 color-color deviation.  one: the  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 25 for (B-V)  = o  -0.4); clearly this is not a main sequence object! One  =  v hesitates,  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 The  magnitudes.  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 pre-main  be  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 is <A  mean extinction  > = 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 T A B L E 6.1: Probable cluster stars De-reddened and de-extinguished photometry  Object  Absolute Magnitude M  M u  Color Index M  b  V  (U-B)  (B-V)  o  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 T A B L E 6.1: Probable cluster stars De-reddened and de-extinguished photometry  Object  Absolute Magnitude M  M u  Color Index (U-B)  M b  V  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 . 1 2 5  -0.324  -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  X13  126 TABLE 6.1: Probable cluster stars De-reddened and de-extinguished photometry Object  Absolute Magnitude M  M u  Color Index M  b  (U-B) V  0  (B-V) 0  155  -6.055  -4.817  -4.499  -1.238  -0.318  156  -6.584  -5.349  -5.028  -1.235  -0.321  158  -5.499  -4.127  -3.804  -1.372  -0.323  159A  -6.901  -5.731  -5.411  -1.170  -0.320  161  -3.302  -2.380  -2 . 128  -0.922  -0.252  162  -5.939  -4.688  -4.371.  -1.251  -0.317  164  -4.592  -3.267  -2.957  -1.325  -0.310  165  -5.325  -4.144  -3.836  -1.181  -0 . 308  169  - 3 . 182  - 1 .815  -1.515  -1.367  -0.300  170  -4.214  -2.926  -2.619  -1.288  -0.307  171  -4.742  -3.520  -3.214  -1.222  -0.306  173  -6.126  -4.798  -4.473  - 1 .328  -0.325  174  -4.720  -3.477  -3.169  - 1 .244  -0.308  181  -6.762  -5.646  -5.326  -1.116  -0.320  182  -4.822  -3.437  - 3 . 125  -1.385  -0.312  183A  -8.012  -6.848  -6.519  - 1.164  -0.329  184  -3.936  -2.974  -2.710  -0.962  -0.264  187  -3.658  -2.640  -2.368  -1.019  -0.272  188  -4.624  -3.651  -3.379  -0.973  -0.272  197  -4.881  -3.634  -3.324  -1.247  -0.310  198  -4.284  -3.249  -2.968  -1.036  -0.281  199  -3.986  -2.927  -2.646  -1.058  -0.281  127 T A B L E 6.1: Probable cluster stars De-reddened and de-extinguished  Object  photometry  Absolute Magnitude M  M u  Color Index M  b  V  (U-B)  (B-V)  o  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  -1.112  -0.294  214  -4.996  -3.886  -3.585  -1.111  -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  -1.106  -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 T A B L E 6.2: Probable field stars De-reddened and de-extinguished photometryt Object  Absolute Magnitude M  M u  Color Index M  b  (U-B) V  0  (B-V) 0  10 A  -4.739  -4 . 3 3 5  -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  -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  Xll  129 T A B L E 6.2: Probable field stars De-reddened and de-extinguished photometryt Objecl  Absolute M  Magnitude  M  M b  (U-B) 0  V  176  -2.968  -2 . 1 6 0  -1.930  179A  -2.629  -2.115  - 1  185  -3.914  -3.205  -1.174  186  (B-V) o  -0.807  - 0 . 230  -0.514  - o . 175  -2.984  -0.709  - o . 221  -0.852  -0.722  -0.322  - o . 1 30  -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 . 1 4 6  -1.741  -1.592  -0.405  - o . 1 49  192A  -3.885  -3 . 3 8 5  -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  X16  t  Color Index  See text  .940  130 6.4 THE  DISTANCE M O D U L U S 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  of E(B-V), E(U-B), and A  mean values  were then applied to the entire raw v  photometry A  data set.  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 -AV /a 2  p(AV)dAV  2  = Ae  dAV  (6.26)  One  then expects the histogram to model crf((m-M ) - (m-M ) ), as v v the procedure used to generate it mimics the integration of (6.26) from 0  AV  =  (m-M  ) v  We  -  (m-M  °  ) to  AV  —>  °°.  v  finally postulated that the distance modulus which generates the best  Z A M S envelope is given by the point of strongest negative curvature on the erf((m-M ) - (m-M v  ) ) curve —this seems to contradict our 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 of thai curve. The  parameter, and pinpointing the minimum  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  somewhat disjointed appearance. Nevertheless the distance modulus comes out as and  we  and  then, giving it a  a clear parabolic trend is apparent, and  14.7 ±0.2  . This is a surprisingly large value,  feel it should be given little weight for several reasons. For one, the Z A M S  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 R E D D E N I N G 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  hesitates to fit isochrones to the de-reddened color-magnitude  process, one  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 (5.85) and distance modulus (13.9), then M  —  +15.3 -4.4. On  and applying extinction 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  raw  color-magnitude  v diagram.  and E(U-B) because the turnoff point is picked on the  138 7.3 CONCLUSIONS If we did this right, and once more 1 want to stress the importance of the (U-B) at 5 ±  colors in obtaining this result, then N G C  7419 is an extremely young cluster,  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 usuallyquoted 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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A., and  Johnson, Harold L., 1956, The  Hoffleit, Dorrit, and  Jaschek, Carlos, 1982, The  law of interstellar  absorption, The Astrophysical Journal, 122, 367 bright  star catalogue, 4th  edition, (New Haven, Connecticut: Yale University  Johnson, Harold L.,  1957, Photometric  distances  reddening  of galactic  and  revised  Observatory)  clusters, The  Astrophysical  Journal, 126, 121 Johnson, Harold L., 1958, Lowell Observatory Bulletin, 4, 37 Johnson, Harold L., and Morgan, William W., 1953, Fundamental stellar photometry for standards of spectral types on the revised system of the Yerkes spectral  Atlas, The Astrophysical Journal, 117, 313  14]  Keenan, Philip Childs, and  McNeil, Raymond C ,  1976, An atlas of spectra  of. the  cooler stars: Types G, K, M , S, and C, (Ohio State University Press)  Leavitt, Henrietta S., 1917, Annals of the Harvard College Observatory, 71. 47 Lindholm, E. Harry, 1957, Remarks  and  spectral  on the  variation  of E(U-B)/E(B-V')  with  class, The Astrophysical Journal, 126, 588  reddening  Moffat,  Anthony F. J.,  Moffat,  Anthony F. .1., and Vogt, N., 1973, An up-to-date picture of Galactic spiral features based on young open star clusters. Astronomy and Astrophysics  —A  1980, Private communication  with Harvey B. Richer  European Journal, 23.. 317  Moore, Charlotte E., 1959, A multiplet table of astrophysical interest; National of Standards technical note 36, revised edition, (Washington D.  Bureau C:  United States Department of Commerce, Oflice of technical services) Moore, Carolyn, 1981, UBC  CURVE;  Curve  fitting  routines. Internal document,  (Vancouver: UBC Computing Centre, The University of British Columbia), p. 114 W., and Harris, D. L., 1956, The galactic Vistas in Astronomy, 2, 1124  Morgan, William  cluster  M29  (NGC  6913),  Munch, Guido, 1968, Interstellar  absorption lines, Stars and stellar systems; Compendium of astronomy and astrophysics, Volume VII, Nebulae and interstellar  matter, edited by Barbara M. Middlehurst and Lawrence H. Aller (Chicago: University of Chicago Press), p. 365 Nicol, John S., 1.984, TOODEE  software  organisation:  Version J:  July  23 1984, Internal  document, (Vancouver: Department of Astronomy & Geophysics, The University of British Columbia) Ninkov, Zoran, 1983, Private communication Patenaude, M . , 1978, Age determination  —A  European Journal,  of open clusters.  wavelength  Phelps, Frederick M . , 1982, M.f.T.  Astronomy and Astrophysics  225 tables, Volume  element, (Cambridge, Massachusetts: MIT Press)  Pickering, Edward Charles,  2; Wavelengths  by  1891, Annals of the Harvard College Observatory, 26, XIV  Racine, Rene, 1969, Photometric  24, 1073  calibration  of direct  plates, The Astronomical Journal,  Racine, Rene, 1978, Le prisme  "de Racine", Internal document, (Sainte-Marie des Bois: Observatoire Astronomique du Mont Megantic)  Reinmuth, 1926, Abhandlungen der Heidelberger Akademie der Wissenschaften — Mathematisch-NaturwissenschafUiche Klasse, 13, 100 Ross, Frank E., 1936, Photographic  photometry,  The Astrophysical Journal, M,  241  142  Ruprecht, J., Balazs, B., and White, R. E., 1981, Catalogue of star clusters and associations; Supplement I, Part A, Edited by B. Balazs, (Budapest: Akademiai Kiado) Ruprecht, J.,  Balazs, B., and White, R. E., 1981, Catalogue of star clusters and associations; Supplement I, Part Bl, Edited by B. Balazs, (Budapest: Akademiai Kiado) 45  Sandage, Allan R., 1958, in discussion following Nassau, Jason J., 1958, Carbon and S-type stars, in Stellar populations; Proceedings of the conference sponsored by the Pontifical Academy of Science and the Vatican Observatory, edited by D. J. K.. O'Connell, (New York: lnterscience Publishers, Inc.), p. 1.91 Sandage, Allan R.,  1972,  Private communication  with G. Handschel  Sanford, Roseoe F., 1950, An atlas of spectra of 6 stars of classes Astrophysical Journal, U J (2), 262 Scalo, John M . , 1976, A composite Herlzsprung-Russell diagram giants. The Astrophysical Journal, 2M, 474  R and N, The  for the peculiar  Scalo, John M . , and Ulrich, Roger K., 1973, Studies of evolved stars I: Plume in S and N stars, The Astrophysical Journal, 18J, 171  red  mixing  Schmidt-Kaler, Th., 1982, Physical parameters of the stars, in Landolt-Bbrnslein, Numerical data and junctional relationships in science and technology; New series, K. Schaifers and H. H. Voigt, editors, (Berlin: Springer-Verlag), Group VI, Volume 2, Subvolume b, pp. 1.-34, 449-456 Serkowski, K.,  1963, Slopes of the reddening trajectories and intrinsic early-type stars. The Astrophysical Journal, J_3_8, 1035  colors of  Smithsonian Astrophysical Observatory staff, 1966, Smithsonian Astrophysical Observatory star catalog; Positions and proper motions of 258,997 stars for the epoch and equinox of 1950.0, (Washington D.C.: Smithsonian Institution) Stetson, Peter B., and Harris, William E., 1977, A photometric The Astronomical Journal, .82, 954 Turner, David G., 1976, Importance of random scatter The Astronomical Journal, i i i , 97  study of NGC  to variable- extinction  1904,  analyses,  Turner, David G., 1982, New UBV photometry for the open cluster Stock 14 and its cepheid-like variable V810 Centauri (=HR 4511), Publications of the Astronomical Society of the Pacific, 54, 655 Turner, David G., Grieve, G. R., I-Ierbst, W., and Harris, William E., 1980, The young open cluster NGC 3293 and its relation to Car OBI, The Astronomical Journal, JB5, 1193 Vardanyan, R. A., and Akhverdyan, L. G., 1975, Infrared observations the cluster NGC 7419, Astrophysics, I I , 374  in the region of  143  Walker, Alistair R., 1979, Photometry  and radial  velocities  of southern  carbon stars,  South African Astronomical Observatory, Circulars, 1, 112  Wallcrstein, George, 1973, The physical  properties  of carbon stars. Annual Review of  Astronomy and Astrophysics, i i , 115 Wells, Donald C , and Greisen, Eric W., 1979, FITS: A flexible image transport system, in Image processing in Astronomy, G. Sedmak, N. Capaccioli  and R. J. Allen, editors, (Trieste: Osservatorio Astronomico di Trieste), p. 445 Yang, Stephenson, 1983a, RETICENT  -  Version  (Jul 1983), Operation  Manual,  Internal  document, (Vancouver: Department of Astronomy & Geophysics, The University of British Columbia) Yang, Stephenson, 1983b, Private communication Yang, Stephenson, 1984, Precision  radial  velocities  with the hydrogen fluoride  absorption  cell, (Provisory title), Ph. D. dissertation (unpublished), (Vancouver: The University of British Columbia)  144 A  APPENDIX  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 1983, totalling twenty-two nights. The  telescope used was  the 180 cm  to September reflector —that  venerable behemoth—, and the instrument configuration consisted of the 2131B spectrograph, the 300 lines/mm grating, blazed at 422.4 nm,  blue  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, HD type C6  2  223075, BD+2°4709, SAO  128374, IRC  +0.352), a bright (V  179,  =  5.04)  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, 134,  Piscium (19  183,  185,  196,  204,  and 225;  we  11,  32,  44,  87.  126,  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 immediately  (that is to say  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 Reticon was  Piscium and the red end of the iron-argon arcs). In addition, the 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 and 196.  Before we  obtained a measurement of the radial velocities of stars 194  detail the procedure followed, a word of explanation concerning  RETICENT is in order.  A.2  RETICENT RETICENT (Yang 1983a) is a command  designed  language written in F O R T R A N  to manipulate one-dimensional digital data. It was  Chris Pritchet, and  IV  initially developed by  Dr.  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 78  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  + cx2  + dx3  (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 +  Ax.  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 spectra of TX  the First of the two nights during which  Piscium were taken, the spectral region included the sodium D  one must note that these are intrinsic  lines;  (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 distance modulus (m-M  Piscium's small distance (128.8 pc from Eggen's (1972)  ) = v  5.55).  148 So far we  have obtained the pixel-to-wavelength  Piscium's spectra; now  we  equations of star 194  and  TX  wish to measure the former's radial velocity. Easier said  than done.  A.5  B A N D H E A D POSITIONS The  only recognizable and/or reliable features in star 194's  C (0,0) and C (0,1) Swan molecular bandheads at 51.6.52 and 2  The  2  spectra are the  563.55 nm, respectively.  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 measured. We  therefore a wavelength, to be accurately  settled on the shape of the first derivative of the bandhead region. As  figure 44 shows, it is well represented, at least in TX with its summit chopped off. The  procedure was  Piscium's case, by a gaussian  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 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 bandheads in star 194's TX  spectrum  position of the  spectrum had to be found from a sliding fit betwixt it and  Piscium's spectrum. To do this, the fit  I  (x) TX  Psc  =  a  +  bl  (x+Ax) 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  1  500.0  1  —  —  AMW /  0.0 -500.0  800  A / \I\J  I  1  1  825  850  875  900  PIXEL n Figure 44: First derivative  of the bandhead  region  The spectrum of T X 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  R A D I A L 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 X X  hence, isolating j3  194  X  =  194 ( 1  in both stars' spectra, that  +  &  = 194  TX  )  +  ( 1  Psc /3  TX  (A.2) Psc  )  , transforming to velocity, and correcting for the observer's  motion v  = 0  c(X  194  -  X  TX  194  Psc  )  +  v  X Psc-194  TX  -  v  X  (A.3) obs  TX  Psc  It should be mentioned in closing that TX  Piscium's radial velocity  14  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  14  K.eenan and McNeil (1976) (for the carbon stars).  I should point out here that TX  the radial velocity as -11  km/s  Piscium's entry in the SAO  instead of +11  km/s  (SAO  catalog mistakenly gives 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 Ar II  448.183 451.0733  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  TABLE 7 The Lines Wavelength  Source  Identification  (nm)  TX  488.906  Ar  490.475  Ar II  496.512  Ar  500.935  Ar  501 .71 6  Ar II  455.4003  Ba II  493.4086  Ba II  588.9953  Na D,  589.5923  Na D,  434.7496  Hg I  435.835  Hg 1  546.0753  Hg I  Piscium, 25/26 August 1982  Star 194, 25/26 August 1982  Iron-Argon arcs, 11/12 October 1982I 404.4418  Ar I  407.201  Ar II  410.391  Ar  413.173  Ar II  4T5.8590  Ar I  419.993  Ar II  425.9361  Ar I  427.755  Ar II  TABLE 7 The  Lines  Wavelength  Source  Identification  (nm) 430.0100  Ar 1  433.3560  Ar I  434.81 1  Ar  440.102  Ar  448.183  Ar  451.0733  Ar I  454.508  Ar  457.939  Ar  458.993  Ar  II  460.960  Ar  II  465.794  Ar  472.691  Ar  476.489  Ar  480.607  Ar  484.790  Ar  487.990  Ar  496.512  Ar  II  501 .716 TX  Ar  Piscium, 11/12 October 1982  II  455.4003 Star 194,  Ba II  11/12 October 1982 404.6561  Hg  I  407.781 1  Hg  1  TABLE 7 The Lines Wavelength  Source  Identification  (nm)  Sources: (1) Phelps 1982 (2) Moore 1959  434.7496  1  Hg I  435.835  1  Hg I  156 A.7 25/26 A U G U S T 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" x 4  2  +  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  where the mercury lines are shifted by  +  3.614151 *lQ- x 7  3  (A.5)  157  x(arc  The  equivalent)  = x(mercury)  -  (A.6)  2.066  r.m.s. deviation is 0.020. The  observer velocity for the TX  was -12.16 km/s.  Piscium spectrum of that night (figure 48)  Once the atomic lines have their expected  Piscium's shift is solved for and  x(arc  wavelengths computed, TX  the answer comes out  equivalent)  = x(TX  Piscium)  +  (A.7)  14.160  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(  for the 516 nm  x(  for the 564 nm  194  ) = x(TX  Piscium  equivalent)  +  15.587  (A.8)  Piscium  equivalent)  +  15. 304  (A.9)  banhead, and  194  ) .=  x(TX  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 is possible, however, that the numerical significance level was  pixel level — i t  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  different shifts, hence using them to "stake out", so to speak, the effective error on the final radial velocity determination.  two  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" x 4  x(arc  x(arc  2  +  3.661348*10- x 7  (A.5')  1  e q u i v a l e n t ) = x ( m e r c u r y ) - 2 . 043  e q u i v a l e n t ) = x(TX  Piscium)  +  14.133  (A.6')  (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 0  1  1  1  1  PIXEL.  1  1  1  ~i  1 2  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 is 0.012. The  X =  fit obtained  341.719 +  r.m.s. deviation  was  0.1186003x - 8.871904*10" x 4  2  +  (A.10)  3.326363*10" V  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 x  3  coefficient in equation (A.10), which is very comparable to that of equation (A.5). Fitting we  Ax  between the cluster carbon star's mercury sky lines and the arc,  get x(arc  equivalent)  = x(  194  )  -  (A.ll)  6. 025  with an r.m.s. deviation of 0.025. This time the observer radial velocity for TX  Piscium was  the selection of atomic lines usable withered down to one!  +10.83 km/s,  Ax  can be  +  5.835  and  immediately  computed to be  x(arc  equivalent)  = x(TX  Meanwhile the shift of the star 194  Piscium)  spectrum, figure 51, versus the  (A.12)  TX  Piscium spectrum (figure 52) turns out to be  x ( 194)  for the 516 nm  = x(TX  Piscium  equivalent)  banhead, which is the only one visible.  -  1.143  (A.13)  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' x 4  x(arc  x(arc  equivalent)  equivalent)  2  (A.14)  + 3.479733*10" x  = x(mercury)  = x(TX Piscium)  7  3  -  6.009  +  5.823  (A.IF)  (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  -+ —  i  Figure 50:  r  ++  1  ~i  PIXEL  •  —r  T  1  2000  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 unlikelyconjecture). 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  CO  (0 0)  10  § o  CO  w  o o o  100  300  500  700  900  1100  PIXEL ti  Figure 54:  13/14  October  1982 spectrum of star 183  1300  1500  1700  173  A.1.1 THF. C A R B O N STAR'S R A D I A L 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  = r  -43 ±  10  km/s  194  Meanwhile, Fawley and Cohen (1974) have measured v  = r  -72 ±  5  km/s  172  v  =  -61 ±  5  km/s  r b  Bl v  r  =  -61  ±  6  km/s  =  -64 ±  5  km/s  =  -74  9  130  v  r 88  and Moffat (1980) has found v  r mean for 6 OB  stars.  ±  km/s  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  Plate 12  Plate 334  Object.  Plate 12  Plate 334  IB  0.5665E+05  29  0.1572E+04  2B  0.1412E+05  31  0.1235E+04  3B  0.4180E+05  32A  0.1714E+05  0.1225E+05  4A  0.1384E+05  33  0.1872E+04  0.2095E+04  6  0.5013E +04  34  0.2901E+03  0.3127E+05  35  0.1642E+04  0.2273E+04  11A  0.7173E+05  36  0.2504E+04  0.1860E+04  11B  0.3877E+04  37A  0.1009E+05  0.667 2E+04  10A  0.5117E+05  12  0.2017E+04  0.2941E+04  38  0.1009E+04  13  0.3454E+04  0.2525E+04  43  0.1147E+04  15  0.2701E+04  0.2841E+04  39  0.5684E+03  16  0.3126E+04  0.3285E+04  41  0.1029E+04  18  0.2878E+04  0.1852E + 04  42  0.7624E+04  19  0.8542E+04  40  0.3997E+03  21  0.1239E+04  44A  0.3620E+05  0.2311E+05  22  0.2921E+04  46  0.3961E+04  0.2407E+04  23  0.4164E+02  47  0.1717E+04  25  0.1397 E+04  48  0.2887E+04  26  0.3124E+04  49  0.7449E+03  27  0.6956E+03  52  0.2208E+04  28  0.5332E+04  53  0.9078E+03  1  0.5473E+04  0.2566E+04  1  176  TABLE 8 Ultraviolet Flux Indices Object  Plate 12  Plate 334  54  0.561 OF.+ 04  0.3570E + 04  80  0..2731E+04  59  0.3100E+04  0.1824E+04  81  0.4492E+04  0.2449E + 04  60A  0.1753E+05  0.1159E + 05  82  0.4157E+04  0.2900E+04  61  0.2633E+04  0.1983E+04  83A  0.6824E+05  62  0.3107E+04  0.1790E+04  83B  0.2897 E+04  64  0.1288E+04  X6  0.1130E + 04  68  0.6836E + 03  84A  0.1045E+05  69  0.1830E + 04  85  0.2631E + 04  70  0.5098E+03  86  0.9562E + 03  71  0.9246E+03  87A  0.1678E+05  72  0.8961E + 03  88A  0.1268E+04  0.1335E+04  X7  0.1244E+04  X5  Object  0.1620E+04  65  0.1297E+05  66  0.1366E + 04  67A  0.1420E+05  73  0.8354E + 04  89 X8  Plate 12  0.8598E+04  Plate 334  0.9364E+04  0.4016E+04  0.1241E+05  0.5133E+04  0.1075E+04  90  0.1597E+04  0.1156E + 04  91  0.5350E + 04  0.431.9E+04  74  0.1547E+04  92  0.3211E+04  0.1998E + 04  75  0.7547E+03  0.1575E+04  93  0.6940E+04  0.4367E+04  76  0.1665E+04  0.1869E+04  94  0.5451E+04  0.4362E+04  77  0.3199E+04  95  0.2264E+04  0.3732E+04  79  0.7838E+03  96A  0.2356E+05  0.1589E+05  0.8996E+04  15  0.2038E+04  15  177 TABLE 8 Ultraviolet Flux Indices  Plate 12  Plate 334  Object  Plate 12  Plate 334  97  0.1487E+05  0.9524E+04  129  0.2160E+04  0.1.599E + 04  99  0.2855E+04  0.3326E+04  130 A  0.3838E+03  100  0.2467E+03  0.2063E+04  131  0.3837E + 04  0.2853E+04  103  0.5200E+04  0.3183E + 04  132A  0.1785E+05  O.1205E + O5  104  0.1151E+04  133  0.9007E + 04  0.6506E+04  105  0..1312E+04  134A  0.2502E+O5  0.1749E+05  106  0.6156E+04  0.5135E + 04  107  0.3830E+04  0.5753E+04  135  0.1059E+04  114  0.2570E+04  0.1917E+04  137  0.3275E+04  0.1464E+04  139  0.2246E+04  116  0.1112E+04  140  117  0.2285E + 04  141  0.1799E+05  118  0..1517E+04  142  0.7440E+04  0.5067E+04  119A  0.1514E+05  0.9754E+04  144  0.1647E+05  0..1123E + 05  120  0.1819E+04  0.1596E+04  145  0.1599E+05  0.1097E + 05  122  0.2771E + 04  0.2007E+04  146  0.1204E+04  125  0.1366E+05  0.9490E+04  147  0.6835E + 04  0.403 IE+04  126 A  0.2929E+05  0.2525E+05  148  0.6056E+04  0.4462E + 04  Xll  0.9137E+03  0.4089E+04  149  0.2387E+04  151  0.6120E+03  152  0.8397E+04  Object  X10  127  0.1739E+04  128  0.1005E+04  0.1677E+04  X13  15  0.9767E+03  0.2971E+04  0.2085E+04 15  15  0.1242E+05 15  15  0.5040E+04  178 TABLE 8 Ultraviolet Flux Indices Object  Plate 12  Plate 334  Object  Plate 12  Plate 334  153  0.8943E+04  0.6445E+04  176  0.2203E+04  0.1622E+04  154  0.4687E+04  0.4452E + 04  178  0.1562E+04  155  0.6295E + 04  0.3782E+04  179A  0.1586E+05  0.1123E+05  156  0.1074E+05  0.5807E+04  181  0.6940E+04  0.4713E+04  158  0.4247E+04  0.3055E + 04  182  0.2218E+04  0.1497E+04  159A  0.2205E+05  0.1354E+05  183A  0.2184E+05  0.1372E+05  161  0.9290E + 03  184  0.2446E+04  0.1644E+04  162  0.8512E+04  185  0.1121E+05  0.6845E+04  15  X15  0.8472E+04 0.3686E+04  163A  0.1241E+05  164  0.6873E+03  165  0.4339E + 04  166  X16  0.3203E + 03  186  0.3840E+04  0.2248E+04  187  0.4546E+04  0.2800E+04  188  0.1092E+05  0.7746E+04  0.4144E+03  190  0.1216E+04  169  0.7388E + 03  191  0.3549E + 04  0.2055E+04  168  0.1023E+04  192A  0.2492E+05  0.I548E+05  170  0.1938E+04  0.1296E+04  195  0.7835E+03  171  0.3134E+04  0.1822E+04  196  0.1672E+05  172A  0.5956E+03  197  0.1054E+04  173  0.6238E+04  0.3569E+04  198  0.3324E+04  0.2591E+04  174  0.2385E+04  0.2274E+04  199  0.3520E+04  0.2390E+04  175  0.1396E+04  201  0.1036E+04  0.7808E+04  0.2849E+04  0.1048E+05  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  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  229  0.2110E+04  X18  0.1430E+04  213  0.4799E+04  0.3038E+04  214  0.5952E+04  0.3527E+04  216  16  0.1394E+04  0.6530E+03  230  0.7159E+04  0.5494E+04  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  233  0.5059E+03  0.7827E+04  ( ) Half-weight ( ) Triple half-weight (three half-weight entries) ,s  X21  0.1436E+04  180 TABLE 9 Blue Flux Indices  Object  Plate 10  Plate 328  Plate 330  2B  Plate 387  Plate 410  0.3618E+05  0.3507E + 05  15  4A  0.3709E + 05  0.3469E + 05  0.2758E + 05  0.2522E+05  4B  0.268 IE+ 04  0.1460E + 04  0.1233E + 04  0.1178E+04  5  0.6263E+04  0.5125E+04  0.43 5 IE+04  0.2868E+04  0.3042E+04  6  O.2011E+05  0.1381E+05  0.1428E + 05  0.9391E+04  0.1027E+05  7  0.5309E+04  0.5238E+04  0.5165E+04  0.3330E + 04  0.3959E + 04  9  0.5641E+04  0.3U5E+04  0.4634E+04  0.2735E + 04  0.1825E + 04  0.5702E + 05  0.5467E+05  10A 10B  0.3540E+04  0.4496E+04  0.3592E + 04  0.3763E+04  11B  0.1635E+05  0.1728E + 05  0.1061E+05  0.1214E+05  X2  0.2241E+04  0.3414E+04  0.1933E+04  0.2406E + 04  0.1982E+04  12  0.8080E+04  0.5354E+04  0.5827E+04  0.3724E + 04  0.4091E+04  13  0.1146E+05  0.5414E+04  0.6732E+04  0.4711E + 04  0.4636E+04  14  0.2725E+04  0.2160E+04  0.2374E+04  0.1233E + 04  0.2581E+04  15  0.9189E+04  0.6746E+04  0.7492E+04  0.4529E + 04  0.51.24E+04  16  0.1086E+05  0.7012E+04  0.8339E + 04  0.5538E+04  0.6203E+04  18  0.8727E+04  0.6624E+04  0.6379E+04  0.3807E+04  0.4084E+04  19  0.2014E+05  0.1498E+05  0.1487E + 05  0.9962E+04  0.1121E+05  20  0.3446E+04  0.3957E+04  0.3426E+04  0.2990E+04  0.2375E+04  21  0.2568E+04  0.1924E+04  0.3466E+04  0.1678E + 04  0.1119E+04  22  0.9344E+04  0.5767E+04  0.6225E+04  0.4054E+04  0.4237E+04  15  181  TABLE 9 Blue Flux Indices  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  23  0.2529E+04  0.1993E + 04  0.2708E+04  0.1207E+04  0.1196E+04  24  0.3670E + 04  0.3433E+04  0.3515E + 04  0.2168E+04  0.2978E+04  25  0.4150E+04  0.3160E+04  0.3651E+04  0.3026E+04  0.1954E + 04  26  0.5058E + 04  0.3448E+04  0.4297E + 04  0.2652E+04  0.2526E+04  27  0.1703E+04  0.1919E+04  0.1907E+04  0.9096E+03  0.1315E+04  28  0.1384E+05  0.9756E+04  0.1044E + 05  0.8613E +04  0.8233E+04  29  0.7189E+04  0.4698E+04  0.4233E+04  0.2970E+04  0.3052E+04  30  0.4035E+04  0.1902E+04  0.2395E+04  0.1086E+04  0.2007E + 04  31  0.2641E+04  0.3723E+04  0.3838E+04  0.1717E+04  0.1.633E+04  32A  0.4092E+05  0.3056E+05  0.2988E+05  0.2334E+05  0.2338E+05  0.9797E+03  0.1602E+04  Object  32B 33  0.5556E+04  0.3768E+04  0.4097E + 04  0.2521E+04  0.1119E+04  34  0.2247E + 04  0.2885E+04  0.2229E + 04  0.1717E + 04  0.1808E+04  35  0.1697E + 05  0.4804E+04  0.4630E+04  0.3167E+04  0.4069E + 04  36  0.6248E+04  0.4122E+04  0.3542E+04  0.1988E + 04  0.2903E+04  37A  0.3387E+05  0.2546E+05  0.2620E + 05  0.1894E+05  0.1899E+05  0.1342E+04  0.9833E+03  15  37B 38  0.2796E+04  0.2148E+04  0.2487E+04  0.1105E+04  0.1805E+04  39  0.4201E+04  0.2900E+04  0.2734E+04  0.1372E+04  0.1816E+04  40  0.1090E+05  0.8603E+04  0.9685E + 04  0.6043E+04  0.6094E+04  41  0.3613E+04'  0.2587E+04  0.2908E+04  0.9174E+03  0.1000E+04  5  182 TABLE 9 Blue Flux Indices  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  0.1686E+05  0.1725E+05  0.1157E + 05  0.1187E+05  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  Dbject 42  0.2327E + 05  43  0.2622E+04  15  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'  0.1285E+04  49  0.1875E+04  0.3046E+04  0.1766E+04  0.2015E+04  0.2154E+03  50  0.27 H E + 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  5  183  TABLE 9 Blue Flux Indices Object  Plate 10  601$  Plate 328  Plate 330  Plate 387  0.1922E+04  0.9884E+03  0.1016E + 04  Plate 410  61  0.8082E+04  0.6045E+04  0.6826E+04  0.4172E+04  0.4758E+04  62  0.1017E + 05  0.7980E+04  0.8280E+04  0.5336E+04  0.5263E + 04  63  0.4292E + 04  0.4681 E+04  0.3968E+04  0.2721E+04  0.1449E+04  64  0.4306E+04  0.3320E+04  0.2334E+04  0.3002E+04  0.2420E + 04  68  0.2275E+04  0.1006E+04  0.1459E+04  0.1113E+04  0.7168E+03  69  0.6668E+0415  0.4536E+04  0.4904E+04  0.3072E+04  0.3408E + 04  70  0.6957E + 04  0.1861E+04  0.1487E + 04  0.2349E+04  0.1572E+04  71  0.5069E+04  0.3709E+04  0.4157E+04  0.2891E+04  0.3594E+04  72  0.1867E + 04  0.1997E+04  0.2026E+04  0.1332E+04  0.7098E+03  65  0.2918E + 05  0.1994E+05  0.2070E+05  0.1447E+05  0.1440E+05  66  0.7779E + 04  0.4962E+04  0.5779E + 04  0.3651E+04  0.3462E+04  67A  0.3548E+05  0.2487E+05  0.2729E + 05  0.1904E+05  0.2010E+05  0.1074E+04  0.1354E+04  67B 73  0.3501 E +04  0.3418E+04  0.3103E + 04  0.3715E+04  0.2651E+04  74  0.4003E+04  0.3079E+04  0.3048E+04  0.2495E+04  0.2242E+04  75  0.5988E+04  0.4277E+04  0.5421E+04  0.2761E+04  0.4308E+04  76  0.6909E+04  0.5264E+04  0.4768E+04  0.3206E+04  0.2988E+04  77  0.1276E + 05  0.9343E+04  0.9939E+04  0.5715E+04  0.4405E+04  78  0.8359E+04  0.6537E+04  0.8107E+04  0.4939E+04  0.3482E+04  79  0.2603E+04  0.1809E+04  0.3140E+04  0.1788E+04  0.1384E+04  184  TABLE 9 Blue Flux Indices  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  80  0.5684E+04  0.3657E+04  0.3046E+04  0.1167E + 04  0.3051E+04  81  0.1153E + 05  0.7186E+04  0.6862E + 04  0.9950E+04  0.8697E+04  82  0.1763E+05  0.7564E+04  0.7462E+04  0.4573E+04  0.5671E+04  0.2971E+05  O.2835E+05  0.2792E+05  0.2502E+05  Object  15  83B X6  0.3335E+04  0.1757E+04  0.1122E+04  0.1428E+04  0.6695E + 03  84A  0.3799E+05  0.2470E+05  0.2475E + 05  0.1916E + 05  0.1851E + 05  0.6370E+03  0.140 IE+04  84B 85  0.2179E+05  0.1.094E+05  0.1132E+05  0.8601E+04  0.9838E+04  86  0.3295E+04  0.2733E + 04  0.3295E + 04  0.6669E+03  0.2364E+04  87A  0.3963E+05  0.3205E + 05  0.3148E+05  0.2403E + 05  0.2470E+05  0.2796E+04  0.1126E+04  87B X7  0.8311E+04  0.2588E+04  0.2474E + 04  0.2228E + 04  0.4569E+04  88A  0.2756E+05  0.2410E+05  0.2452E+05  0.1805E + 05  0.1752E+05  0.1278E+04  0.1689E+04  0.1898E+05  0.1345E + 05  0.1400E+05  0.8882E + 04  0.9404E+04  0.4376E + 04  0.1268E + 04  0.1964E+04  0.2011E+04  0.1247E+04  90  0.3253E+04  0.2869E+04  0.1326E+04  0.1442E+04  0.2287E + 04  91  0.1613E + 05  0.1180E+05  0.1142E + 05  0.8344E + 04  0.8957E+04  92  0.6687E + 04  0.5651E+04  0.6043E+04  0.3813E+04  0.3578E+04  93  0.1907E+05  0.1378E + 05  0.1323E+05  0.9343E+04  0.9541E+04  94  0.1876E+05  0.9218E+04  0.1044E+05  0.3225E+04  0.8556E+04  88B 89 X8  185  TABLE 9 Blue Flux Indices  Object 95  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  0.1633E+05  0.7468E+04  0.7656E+04  0.6078E+04  0.8549E+04  0.2775E + 04  0.2695E+04  0.2007E + 04  0.5091E + 04  0.3973 E+05  0.3894E + 05  0.3027 E+05  0.2984E+05  0.3050E + 04  0.1058E+04  X9 96A  0.4683E+05  96B 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  0.247 5E+04  0.6218E+04  98  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  TABLE 9 Blue Flux Indices  Object  Plate 10  Plate 328  Plate 330  Plate 387  119A  0.3581E + 05  0.2696E+05  0.2726E+05  0.I922E+05  . 0.1933E + 05  0.1227E+04  0.9845E+03  119B  Plate 410  120  0.7000E+04  0.4220E+04  0.5515E + 04  0.2834E + 04  0.3188E+04  121  0.2437E+04  0.2091 E+04  0.3945E + 04  0.1253E+04  0.2071E+04  122  0.8265E+04  0.6639E+04  0.6754E+04  0.4093E+04  0.5233E+04  124  0.2372E+04  0.3003E+04  0.2779E + 04  0.1797E+04  0.1375E+04  125  0.3470E + 0515  0.2407E+05  0.2417E +05  0.1758E + 05  0.1738E+05  0.5167E+05  0.3958E+05  0.4241E+05  0.2954E + 04  0.2737E+0415  0.2388E+04  0.1080E + 05  0.3910E+04  0.9339E+04  126 A 126B  0.3551E+04  Xll 127  0.8241 E+04  0.1508E+04  0.2367E+04  0.2717E+04  0.9191E+03  128  0.1034E + 05  0.4308E+04  0.3601 E + 04  0.3514E+04  0.1927E+04  129  0.4555E + 04  0.3281E+04  0.3927E+04  0.2831E+04  0.3503E+04  0.1668E+04  0.1987E+04  0.2401E+05  0.2320E + 05  0.9807E+03  0.1029E + 04  X12 130A  0.2805E+05  130B  0.1760E+04 0.1688E+05  0.1739E+05  131  0.1083E+05  0.7535E+04  0.8056E + 04  0.5074E+04  0.5838E+04  132A  0.3678E+05  0.2917E + 05  0.2932E + 05  0.2057E+05  0.2066E + 05  0.1372E+04  0.1800E+04  132B 133  0.2460E+05  0.1715E+05  0.1888E+05  0.1150E+05  0.1189E+05  134 A  0.4965E+05  0.4375E+05  0.4461E+05  0.3517E + 05  0.3315E+05  187  TABLE 9 Blue Flux Indices  Object  Plate 10  134B  Plate 328  Plate 330  0.251IE + 04  0.2615E + 04  Plate 387  Plate 410  X13  0.6036E+04  0.5935E+04  0.2885E+04  0.1038E+04  135  0.3546E+04  0.2878E+04  0.2902E + 04  0.1161E+04  0.2443E+04  136  0.2052E + 04  0.2473E + 04  0.1463E + 04  0.7785E+03  0.1076E + 04  137  0.1854E+05  0.9522E+04  0.1153E+05  0.5933E+04  0.9234E+04  0.6858E+04  0.2676E + 04  0.4779E+04  0.1455E+04  0.2694E+04  139  0.3727E+04  0.2365E+04  0.2705E+04  0.2444E + 04  0.1907E+04  140  0.6409E+04  0.5038E+04  0.6975E+04  0.5766E+04  0.3325E+04  141  0.3853E+05  0.2817E + 05  0.2964E+05  0.2275E+05  0.2007E+05  142  0.2368E+05  0.1330E+05  0.1422E+05  0.8806E+04  0.1327E+05  0.2138E+04  0.3603E+04  X14  142b  0.4524E+04  144  0.3905E+05  0.2811E+05  0.2808E + 05  0.2114E + 05  0.2227E+05  145  0.3319E + 05  0.2584E+05  0.2487E+05  0.1991E + 05  0.1921E+05  146  0.4739E+0415  0.2947E+04  0.3784E + 04  0.1628E+04  0.1999E+04  147  0.1594E+0515  0.1066E+05  0.1088E + 05  0.7355E + 04  0.7077E+04  148  0.1652E+05  0.1162E+05  0.1262E + 05  0.8813E+04  0.9004E+04  149  0.1418E+05  0.5960E+04  0.8064E + 04  0.6394E+04  0.4051E+04  150  0.1236E+05  0.5898E + 04  0.6209E+04  0.3984E+04  0.3927E+04  151  0.1329E+05  0.4171E+04  0.7941E + 04  0.2241E+04  0.4344E+04  152  0.1905E+05  0.1323E+05  0.1312E+05  0.8651E+04  0.9476E+04  153  0.2111E+05  0.1537E+05  0.1619E+05  0.1027E+05  0.1048E+05  188  TABLE 9 Blue Flux Indices  Object  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  154  0.1525E+05  0.1105E + 05  0.1107E+05  0.7130E+04  0.8272E+04  155  0.1544E+05  0.1178E + 05  0.1238E+ 05  0.6513E+04  0.9878E+04  156  0.2813E + 05  0.1651E + 05  0.1641E+05  0.1184E+05  0.1248E+05  157  0.2823E+04  0.2211E + 04  0.2413E+04  0.1548E+04  0.1775E+04  158  0.1098E+05  0.7528E+04  0.8099E+04  0.4287E+04  0.5822E+04  159 A  0.4350E + 05  0.3291E + 05  0.3341E+05  0.2489E + 05  0.2464E+05  159B  0.2035E + 04  .0.1023E+04  160  0.2474E + 04  0.1885E + 04  0.1213E+04  0.1.624E+04  161  0.473 IE+04  0.3184E+04  0.3694E+04  0.2242E+04  0.2241E+04  162  0.2388E+05  0.1533E+05  0.1532E+05  0.1285E+05  0.1052E+05  X15  0.3622E + 04  0.3957E+04  0.3153E+04  0.3162E+04  0.2660E+05  0.1982E + 05  0.1974E+05  0.1391E+05  0.1369E+05  0.2173E+04  0.2148E+04  163A 163B 164  0.2741E+04  0.1814E+04  0.2029E+04  0.1786E + 04  0.2189E+04  165  0.1264E+05  0.8986E + 04  0.1054E+05  0.5592E+04  0.6246E+04  166  0.2995E+04  0.2832E+04  0.2625E+04  0.7903E+03  0.4046E+03  167  0.1099E+04  0.1472E + 04  0.9450E+03  0.6491E+03  0.1934E+03  169  0.2296E+04  0.1668E + 04  0.1398E+04  0.2433E+04  0.9893E+03  168  0.3439E+04  0.1854E+04  0.2694E+04  0.1979E+04  0.7643E+03  170  0.6435E+04  0.4225E+04  0.4085E+04  0.2398E+04  0.2770E+04  171  0.9615E+04  0.6204E + 04  0.5881E+04  0.3433E+04  0.4741E+04  189  TABLE 9 Blue Flux Indices Object  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  172A  0.2467E+05  0.2189E + 05  0.2105E+05  0.157 IE+05  0.1578E+05  173  0.1581E + 05  0.1047E+05  0.1168E + 05  0.6952E+04  0.7362E+04  174  0.7434E+04  0.6456E+04  0.6505E+04  0.3895E + 04  0.3934E+04  175  0.2644E+04  0.2934E + 04  0.3474E+04  0.1979E+04  0.1627E+04  176  0.7479E+04  0.5496E+04  0.6864E+04  0.4979E+04  0.4392E+04  178  0.5002E+04  0.3840E+04  0.3556E+04  0.2602 E+04  0.2218E+04  179A  0.3471E+05  0.2488E+05  0.2676E+05  0.1883E+05  0.1788E+05  0.1583E + 04  0.1699E + 04  179B 180  0.2636E+04  0.3291E + 04  0.1676E+04  0.1677E + 04  0.1935E+04  181  0.2289E+05  0.1744E+05  0.1683E+05  0.1113E + 05  0.1225E+05  182  0.5974E + 04  0.4771E+04  0.3940E+04  0.2575E+04  0.3665E+04  183A  0.4794E + 05  0.3705E+05  0.3696E+05  0.2795 E +05  0.2723E+05  0.1446E+04  0.2239E+04  0.1478E + 04  0.2112E+04  183B 184  0.7746E + 04  0.9983E + 04  0.6235E+04  0.3602E+04  0.4.167E+04  185  0.2726E+05  0.2129E+05  0.2187E+05  0.1509E+05  0.1480E+05  X16  0.2954E + 04  0.1927E + 04  0.1705E+04  0.1839E+04  0.1630E+04  X17  0.2530E+04  0.1470E+04  0.1727E+04  0.1015E+04  0.1017E+04  186  0.1702E + 05  0.1246E + 05  0.1219E+05  0.8366E+04  0.9003E+04  187  0.1192E+05  0.8083E+04  0.8646E+04  0.5264E+04  0.5762E+04  188  0.2497E+05  0.1743E+05  0.1765E+05  0.1276E+05  0.1327E+05  189  0.2211E+04  0.1723E+04  0.1264E+04  0.1764E+04  0.1722E+04  190  TABLE 9 Blue Flux Indices  Object  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  190  0.7758E+04  0.5373F. + 04  0.5625E+04  0.3518E+04  0.4247E+04  191  0.1490E+05  0.9912E+04  0.1065E+05  0.6778E + 04  0.7608E+04  192A  0.5244E + 05  0.4079E + 05  0.4029E+05  0.3139E+05  0.3180E + 05  0.2739E+04  0.2615E+04  0.1359E + 04  0.1531E+04  192B 193  0.4238E+04  0.2309E + 04  0.3400E+04  0.2494E+04  0.2044E+04  194  0.1346E+04  0.2386E+04  0.2530E+04  0.9752E+03  0.1679E+04  195  0.7392E + 04  0.5206E+04  0.4395E+04  0.2467E+04  0.2988E+04  196  0.4041 E+05  0.2992E+05  0.3064E+05  0.2263E+05  0.2185E + 05  197  0.5711E+04  0.3640E+04  0.3586E+04  0.2172E + 04  0.1889E+04  198  0.9936E+04  0.7853E+04  0.8576E+04  0.5658E+04  0.5604E+04  199  0.1079E+05  0.7142E+04  0.8146E+04  0.4086E + 04  0.5149E+04  200  0.3480E+04  0.2928E+04  0.2534E+04  0.2164E+04  0.1146E+04  201  0.5212E+04  0.3889E+04  0.4923E+04  0.3001 E +04  0.1874E+04  202  0.3371 E +04  0.2U4E+04  0.3136E+04  0.2409E+04  0.1337E+04  205  0.3093E+04  0.8941 E+03  0.2119E+04  0.1235E+04  0.1152E+04  203  0.1375E+05  0.9627E+04  0.9670E+04  0.6279E+04  0.7274E+04  0.6992E+04  0.8251E+04  0.5221E+04  0.4866E+04  204B 206  0.3341E + 04  0.3263E+04  0.2132E + 04  0.2673E + 04  0.2377E+04  207  0.3389E+04  0.2330E+04  0.2629E+04  0.1234E+04  0.1847E+04  208  0.3953E+04  0.4037E+04  0.4437E+04  0.2795E+04  0.3630E+04  209  0.4885E+04  0.3379E+04  0.3237E+04  0.2008E+04  0.1890E+04  191  TABLE 9 Blue Flux Indices  Object  Plate 10  Plate 328  Plate 330  Plate 387  Plate 410  210  0.3379E+04  0.2136E + 04  0.3018E+04  0.1776E+04  0.2871E+04  211  0.3162E+05  0.2364E + 05  0.2421E+05  0.1706E+05  0.1744E+05  212  0.6581E+04  0.4280E + 04  0.5558E+04  0.4301E+04  0.3492E+04  0.1859E+04  0.1593E+04  0.1603E+04  0.1256E+04  0.1985E+04  213  0.1308E+05  0.8782E + 04  0.902 IE+04  0.6561E+04  0.6154E + 04  214  0.1490E+05  0.1133E+05  0.1188E+05  0.6769E+04  0.7865E+04  215  0.4065E+04  0.3391E+04  0.3318E + 04  0.2231E+04  0.2467E+04  216  0.2981E + 04  0.2689E+04  0.3327E + 04  0.1539E+04  0.1448E+04  217  0.5000E + 04  0.3281E+04  0.3741E+04  0.1645E+04  0.2980E+04  0.2385E+04  0.1037E+04  0.1513E+04  0.1826E+04  0.1554E+04  218  0.2464E+05  0.1790E+05  0.1881E+05  0.1239E+05  0.1422E+05  219  0.4203E+05  0.3188E+05  0.3243E+05  0.2410E + 05  0.2459E+05  0.2786E+04  0.2014E+04  0.3269E+04  0.6666E+03  0.1691E+04  220  0.3433E + 04  0.2670E+04  0.2881E + 04  0.2290E+04  0.1918E+04  221  0.4166E+04  0.2776E+04  0.4279E+04  0.1945E + 04  0.1842E + 04  222  0.5845E+04  0.4042E+04  0.5005E+04  0.2732E+04  0.2912E+04  223  0.2816E+04  0.2066E+04  0.1725E+04  0.1854E+04  0.1549E+04  224  0.4602E + 04  0.3897E+04  0.4162E+04  0.1852E+04  0.2899E+04  225A  0.4750E+05  0.3556E+05  0.3519E+05  0.2666E+05  0.2702E+05  0.2263E+04  0.2512E+04  0.1579E+04  0.1467E+04  0.4460E+05  0.4367E+05  0.3403E+05  0.3367E+05  X18  X19  X20  225B 227A  0.5695E+05  192  TABLE 9 Blue Flux Indices Object  Plate 10  227B  Plate 330  0.2681E + 04  0.3037E+04  Plate 387  Plate 410  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  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  X21  (15)  Plate 328  Half-weight  193  T A B L E 10 Visual Flux Indices Object  Plate 16  Plate 327  2B  Plate 329  Plate 386  Plate 409  0.2619E+05  0.3942E+05'5  0.2117E+0515  3B  0.7312E+05  4A  0.5015E+05  4B 5  0.1976E+05  0.3689E + 05  0.7091E+04  0.2349E+04  0.2766E + 04  0.1305E+05  0.4184E + 04  0.4819E+04  0.1332E+04  0.1481E+05  0.1988E + 05  0.6233E+04 0.1406E+04  6 7  0.2442E+05  0.1785F. + 05  0.4805E+04  0.5883E+04  9  0.2065E + 05  0.1297E+05  0.4108E+04  0.403 IE+ 04  0.5224E+05  10A  0.3809E+05  10B  0.7040E+04  0.2666E+04  0.3127E+04  11B  0.2859E+05  0.7132E+04  0.9787E+04  0.3158E+04  X2  0.1232E+05  0.6684E+04  0.2622E+04  0.2877E+04  12  0.3044E + 05  0.2509E+05  0.5630E + 04  0.7812E + 04  0.2657E+04  13  0.3723E + 05  0.2330F. + 05  0.5934E+04  0.1056E + 05  0.2447E+04  14  0.2440E+05  0.1707E+05  0.4660E+04  0.6988E + 04  0.7054E+03  15  0.2817E+05  0.2155E+05  0.6041E+04  0.7982E+04  0.2582E+04  16  0.3280E+05  0.2491E+05  0.5884E+04  0.8770E+04  0.2563E+04  18  0.2601E+05  0.1985E+05  0.5040E+04  0.6028E+04  0.1329E+04  0.4310E+05  0.1068E+05  0.1651E+05  0.5544E+04  19 20  0.1598E+05  0.9193E+04  0.2928E+04  0.3807E + 04  21  0.1222E+05  0.8040E+04  0.2302E+04  0.2582E+04  194  T A B L E 10 Visual Flux Indices Plate 16  Plate 327  Plate 329  Plate 386  Plate 409  22  0.3068E+05  0.2318E+05  0.5441E+04  0.8959E + 04  0.1396E+04  23  0.1017E+05  0.5546E+04  0.1983E+04  0.2254E + 04  24  0.1792E+05  0.1014E+05  0.2904E+04  0.3961E+04  25  0.1659E+05  0.9992 E+04  0.3464E+04  0.3722E+04  26  0.2129E+05  0.1542E + 05  0.3744E+04  0.5227E + 04  27  0.1103E + 05  0.6600E + 04  0.2532E+04  0.1767E+04  0.5120E+05  0.1422E+05  0.2301E + 05  0.9180E+04 0.1841E+04  Object  28  0.1151E+04  29  0.2556E + 05  0.1815E+05  0.4099E + 04  0.5995E + 04  30  0.1335E+05  0.7479E+04  0.2217E+04  0.3280E+04  31  0.1525E+05  0.9651E+04  0.2648E+04  0.2574E + 04  0.3890E+05  0.5004E+05  0.2579E+05  0.1545E+04  32A 32B  0.5094E+04  0.2702E+04  33  0.2309E+05  0.1594E + 05  0.3835E+04  0.6123E + 04  34  0.1779E+05  0.1155E+05  0.3980E+04  0.3404E + 04  35  0.3753E+05  0.2984E+05  0.7566E+04  0.1030E + 05  0.3500E + 04  36  0.2860E+05  0.2143E+05  0.5329E+04  0.7058E+04  0.2115E+04  0.1825E+05  0.2533E + 05  0.1069E+05  37A 37B  0.1670E+04  38  0.1395E+05  0.8231E+04  0.3455E+04  0.3489E+04  39  0.1517E+05  0.8425E+04  0.2170E+04  0.3498E+04  40  0.3362E+05  195  T A B L E 10 Visual Flux Indices Dbject 41  Plate 16  Plate 327  0.1859E+0515  0.1075E+05  Plate 329  Plate 386  42 43  Plate 409  0.1193E+05 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  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  0.3973E+05  0.1149E+05  0.1633E+05  0.6186E+04  54  0.2132E+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  T A B L E 10 Visual Flux Indices  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  Dbject  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  0.4408E+05  0.1140E+05  0.1635E+05  0.6161E+04  0.1820E+05  0.4786E + 04  0.6705 E+04  0.1765E+04  0.1526E+05  0.2111E+05  0.8990E+04  65 66  0.2537E+05  67A 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  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  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  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  0.2254E+04  0.1591E+04  0.2577E+04  0.2651E+04  197  T A B L E 10 Visual Flux Indices  Plate 16  Plate 327  Plate 329  Plate 386  78  0.2034E + 05  0.1707E+05  0.3853E+041  0.8455E + 04  78b  0.4376E + 04  0.6247E+04  79  0.1423E+05  0.1010E+05  0.3408E+0415  0.2962E+04  Object  79b  Plate 409  0.1937E+04  80  0.1987E + 05  0.1427E+05  0.3928E+04  0.4145E+04  0.1524E+04  81  0.3845E + 05  0.3197E+05  0.6445E+04,J  0.1228E+05  0.5112E+0415  81b  0.1221E+05  82  0.3771E + 05  0.3556E+04 0.3015E+051  83B X6  0.2104E+05  0.1571 E+05  84A  85 0.1528E+05  0.8890E+04  87A 0.4693 E+04  87B 87Bb  0.9376E + 04  0.2288E+05  0.3392E+05  0.1669E+05  0.3269E+04  0.5141E+04  0.1808E+04  0.2499E+05  0.347 6E+05  0.1582E+05  0.1087E+05  0.1582E + 05  0.6941E+04  0.3920E+04  0.2938E + 04  0.3591E+05  0.4850E + 05  0.2769E+04  84B  86  0.6332E+04  0.7089E+03 0.5135E+03  0.6229E+04  0.7974E+05  88A 88B X7 89  0.2513E+05  0.1340E+0515  0.1618E+0517  0.4494E+04  0.1442E+0515  0.3238E + 0415  0.4934E+0415  0.4691E+05  0.1290E+05  0.1796E+05  0.5856E+04  198  T A B L E 10 Visual Flux Indices Object  Plate 16  Plate 327  Plate 329  Plate 386  X8  0.1065E+05  0.6617E +04  0.3158E+0415  0.1103E + 04  X8c  0.2466E+04 0.8192E+04  0.3375E+04  0.3260E+04  0.4190E + 05  0.1205E+05  0.1584E + 05  0.5738E+04  0.20O3E+O5  0.6406E+04  0.6805E+04  0.2844E+04  0.4824E+05  0.1394E+05  0.1931E+05  0.7110E+04  90  0.1443E + 05  91 92  0.2854E + 05  93  Plate 409  94  0.3938E + 05  0.3522E+05  0.1182E+05  0.1666E+05  0.3183E+04  95  0.2822E+05  0.2503E + 05  0.9080E+04  0.1155E+05  0.4525E+04  96A X9  0.4983E+05 0.2426E+05  0.2028E+05  97  0.3129E+05  0.6695E+04  0.6547E + 04  0.4271E + 04  0.2242E+05  0.3160E+05  0.1444E+05  98  0.1473E+05  0.1273E+05  99  0.2761E+05  .2322E+05  .7271E + 04  0.7223E+04  100  0.2300E+05  0.1908E+05  0.6134E+04  0.5888E+04  101  0.1287E + 05  0.1231E+05  0.3077E+04,J  0.2183E+04  102  0.1327E+05  0.1300E+05  103  0.3821E + 04  0.1995E+04  0.4549E+05  0.1203E+05  0.1759E+05  0.3891E+0415  0.2419E+04  104  0.1200E + 05  0.7848 E + 04  104c  0.3177E+0415  0.1003E+04  105  0.1362E+05  0.7322E+04  0.3405E+04  0.2478E+04  106  0.3443E+05  0.3064E+05  0.1083E+05  0.1426E+05  0.6771E+04  0.4693E+04  199  T A B L E 10 Visual Flux Indices Object  Plate 16  Plate 327  Plate 329  Plate 386  Plate 409  107  0.3920E+05  0.3498E+05  0.1161E+05  0.1811E+05  0.3494E+04  114  0.2719E+05  0.2042E+05  0.4183E+04  0.7152E + 04  0.2259E+04  0.7596E+04  0.3276E+04  115  0.3190E+05  0.2418E+05  116  0.8758E+04  0.4822E+04  117  0.1934E+05  0.1181E+05  0.3205E+04  0.3431E + 04  118  0.1908E+05  0.1316E+05  0.3525E+04  0.4798E+04  0.2874E+05  0.3980E+05  X10  119A 119B  0.2448E + 04 0.6529E+04  0.8488E+04 0.1842E+04  0.2822E+04  0.2510E+04 0.4502E+04  120  0.2353E+05  0.1699E+05  121  0.1100E+05  0.5879E+04  122  0.3052E+05  0.2233E + 05  0.5937E+04  0.9170E+04  124  0.1431E+05  0.7738E + 04  0.2175E+04  0.2812E+04  125  0.2543E+05  0.349 IE+05  126A  0.5739E+05  126B  0.1017E+05  0.2694E + 04  0.3150E+04  0.3181E + 04  0.1529E+05 0.4940E + 05  0.2834E+04 0.2188E+04  127  0.9750E+04  0.8060E+04  0.2730E+04  0.3653E+04  128  0.2029E+05  0.1724E+05  0.4466E + 04  0.4830E+04  129  0.1794E+05  0.1153E+05  0.3979E+04  0.4402E+04  0.1006E+05  0.1208E+05  0.2510E+04  0.4915E+0415  X12  0.1865E + 05  0.5923E+04  0.1125E+05  Xll  0.2490E+04  200  T A B L E 10 Visual Flux Indices Object  Plate 16  Plate 327  Plate 329  Plate 386  130A  0.8094E+05  130B 131  Plate 409  0.3301E+05  0.1735E+05  0.5196E + 04  0.2638E+05  0.6271 E+04  0.9004E + 04  0.2767E+04  0.3071E+05  0.3900E + 05  0.1921E+05  132 A 132B  0.3332E + 04  0.2612E+04  133  0.5233E+05  0.1536E+05  0.2040E + 05  0.7786E + 04  0.4320E+05  0.5561E + 05  0.3366E + 05  0.4661E+04  0.3405E+04  0.2643E+04  134A 0.5862E+04  134B X13  0.3213E+04  135  0.1580E+05  0.1282E+05  0.3342E+04  0.3278E + 04  136  0.1133E+05  0.6063E+04  0.2905E+04  0.2308E+04  137  0.3343E + 05  0.2743E+05  0.5656E+04  0.9626E + 04  0.1239E+05  0.9362E + 04  0.1506E+05  0.8348E+04  X14  0.3128E+0415  0.2166E + 04 0.2804E+04  0.3817E+04  140  0.5081E+04  0.6006E + 04  0.3606E+04  141  0.2886E+05  0.3584E + 05  0.1884E+05  0.1020E+0515  0.1693E + 05  0.6391E+0415  139  142  0.4467E+05  0.4103E+05  142b  0.1040E+05  0.7445E+04  142e  0.8772E+04  0.3262E+04  0.4027E+041S  144  0.3171E+05  0.4248E + 05  0.2013E+05  145  0.2807E+05  0.3948E+05  0.1907E+05  201  T A B L E 10 Visual Flux Indices Object  Plate 16  Plate 327  Plate 329  Plate 386  146  0.1672E + 05  0.1124E+05  0.3034E + 04  0.4090E+04  147  0.4590E+05  0.3436E+05  0.7707E+04  0.1324E + 05  0.4060E+04  148  0.4151E+05  0.3416E+05  0.8579E+04  0.141 IE+05  0.5254E+04  149  0.2.124E+05  0.1847E+05  0.1147E+04  0.6469E + 04  150  0.1477E+05  0.1403E + 05  0.1394E+04  0.495 IE+ 04  151  0.1941E+05  0.1717E+05  0.1977E + 04  0.5965E+04  152  0.4864E + 05  0.3942E+05  0.1068E+05  0.1471E + 05  0.4961E+04  0.5196E+05  0.1477E+05  0.2017E+05  0.7459E+04  153  Plate 409  154  0.4125E+05  0.3179E+05  0.8040E + 04  0.1187E+05  0.4109E+04  155  0.4379E+05  0.4003E+05  0.9029E+04  0.1720E+05  0.6775E + 04  0.5700E + 05  0.1577E+05  0.2356E+05  0.9034E+04  156 157  0.1361E+05  0.8980E+04  0.2211E+04  0.3071E + 04  158  0.3237E + 05  0.2448E+05  0.7005E+04  0.9047E+04  0.3337E+04  0.3337E+05  0.445 3E +05  0.2047E+05  159 A 159B  0.4098E+04  0.1184E+04  160  0.1195E+05  0.7028E+04  0.2397E+04  0.2758E + 04  161  0.1570E+05  0.9162E+04  0.3382E+04  0.3438E+04  162  0.4392E+05  0.4202E+05  0.1118E+05  0.1901E+05  0.1359E+05  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0.5016E+05  0.5019E+05  0.1375E+06  0.1219E+06  0.1398E+06  0.1823E+05  0.1027E + 05  0.2356E+05  134A 134B  0.5599E + 04  X13  0.1300E+05  135  0.1238E+05  0.1348E+05  0.9932E + 04  136  0.5793E+04  0.1187E+05  0.7279E+04  137  0.2677E+05  0.2172E+05  0.2579E+05  X14  0.2651E+0515  0.6881E+04  0.9001E+04 0.1149E+05  0.1137E+05  140  0.1971E + 05  0.1698E + 05  0.2929E+05  141  0.9533E+05  0.8263E+05  0.9316E+05  0.3710E+0515  0.4252E+05  0.4371E+0515  139  0.8013E+04  142  0.4027E+05  142b  0.7135E+04  142c  0.3090E+04  0.1192E+0515  144  0.1038E+06  0,9605E + 05  0.9758E+05  145  0.9296E+05  0.9002E+05  0.9395E+05  227  T A B L E 12 Consolidated Visual Flux  Indices  Part 4  Object  Part 1  Part 2  Part 3  146  0.1083E+05  0.1234E+05  0.1208E+05  147  0.3364E + 05  0.2877E+05  0.3420E+05  0.3182E+05  148  0.3344E+05  0.3170E+05  0.3619E+05  0.3811E+05  149  0.1793E + 05  0.5106E+04  0.1814E + 05  150  0.1357E+05  0.6095E+04  0.1431E+05  151  0.1665E+05  0.8369E+04  0.1688E+05  152  0.3867E+05  0.3868E+05  0.3755E+05  0.3661E+05  153  0.5117E+05  0.5191E+05  0.4966E+05  0.4871E+05  154  0.3109E + 05  0.2989E+05  0.3105E+05  0.3209E+05  155  0.3928E+05  0.3321 E+05  0.4312E+05  0.4553E+05  156  0.5621E + 05  0.5509E+05  0.5698E+05  0.5569E+05  157  0.8628E+04  0.9263E+04  0.9375E+04  158  0.2385E + 05  0.2638E + 05  0.2441E + 05  0.2774E+05  0.1088E+06  0.1001E+06  0.9873E+05  159A 159B  0.3894E + 04  0.5256E+04  160  0.6730E + 04  0.9968E+04  0.8523E+04  161  0.8806E+04  0.1362E+05  0.1036E+05  162  0.4126E+05  0.4032E+05  0.4712E+05  0.7412E+05  0.1246E+05  0.6449E+03  0.1072E+05  0.5482E+05  0.6542E+05  0.6237E+05  0.5799E+05  XI5 163A 163B  0.1551E+04  228 T A B L E 12 Consolidated Visual Flux  Indices Part 4  Object  Part 1  Part 2  Part 3  164  0.8179E + 04  0.1135E + 05  0.1049E + 05  165  0.2941 E+05  0.2805E+05  0.2802E+05  166  0.8378E+04  0.1176E+05  0.6715E+04  167  0.3031E+04  168  0.7203E + 04  0.1122E+05  0.1536E+05  169  0.5111E+04  0.8065E+04,•,  0.7738E+04  170  0.1256E+05  0.1623E+0515  0.1147E+05  0.1394E+05  170b  0.2253E+04  171  0.1891E+05  0.2123E+05  0.1913E+05  0.1876E + 05  172A  0.2340E+06  0.3189E + 05  172B 173  0.3677E+05  0.3696E + 05  0.3610E+05  0.345 IE+05  174  0.1726E+05  0.1750E+05  0.1850E+05  0.2252E+05  175  0.7054E + 04  0.1354E+05  0.8865E + 04  176  0.1608E+05  0.1551E+05  0.1759E+05  0.1405E + 05  178  0.1140E+05  0.1815E+05  0.1442E + 05  0.1618E+05  179A  0.4921E+05  0.5184E+05  0.4898E+05  0.4915E+05  179B  0.1753E+04  180  0.5546E+04  0.1300E+05  0.7313E+04  0.6013E+05  0.5760E+05  0.5496E+05  0.1366E+05  0.1643E+05  0.1706E+05  181 182  0.1430E+05  T A B L E 12 Consolidated Visual Flux Indices Object  Part 1  183A  Pari 2  Part 3  Part 4  0.1260E+06  0.1111E+06  0.1164E + 06  183B  0.4402E+04  0.1194E + 05  0.9337E+04  184  0.1839E+05  0.1995E+05  0.1872E + 05  0.1756E+05  185  0.4579E+05  0.4400E+05  0.4580E+05  0.4600E + 05  X16  0.5284E+04  0.8312E+04  X17  0.4107E+04  0.6491E+04  186  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0.8824E + 04  224  0.1049E+05  0.1290E + 05  0.1072E+05  0.7942E+05  0.7653E+05  225B  Part 4  0.4823E+05  0.4910E+04  225A  0.7598E+05  0.3260E + 04 0.1662E + 06  227A  0.1561E+06  227B  0.7416E+04  0.8057E+04  228  0.5896E + 04  0.1001E+05  0.8189E + 04  229  0.1159E+05  0.1949E+05  0.1409E+05  0.3933E+04  0.1260E+05  0.8364E+04  230  0.3912E+05  0.3891E+05  0.375OE+O5  0.3659E+05  231  0.2777E+05  0.2785E+05  0.2764E+05  0.3099E+05  232  0.9310E+04  0.1224E+05  0.1149E+05  233  0.7329E+04  0.7512E+04  0.7162E+04  X21  (,s) (")  Part 3 0.6093E + 04  0.381 IE+04  219 X20  Part 2  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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