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Luminosity - velocity diagrams of virgo cluster spiral galaxies Woods, David 1990

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L U M I N O S I T Y - V E L O C I T Y D I A G R A M S OF V I R G O C L U S T E R SPIRAL G A L A X I E S by DAVID WOODS A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R 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 Geophysics and Astronomy We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A S E P T E M B E R 1990 © David Woods, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of GEOPHYSICS AND ASTRONOMY The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D a t e September 25/1990 DE-6(3/81) Abstract Luminosity-velocity diagrams for 12 spiral galaxies in the Virgo cluster are presented. Optical rotation curves obtained for the innermost portions of eight galaxies, complemented with velocity data from the literature, are coupled with luminosity growth curves to investigate the distance indication capabilities of the initial linear branch (ILB) feature and to delve into the physical basis for the T-F relation. Luminosity growth curves are obtained from Gunn r C C D images. The ILB feature is found to have a substantially larger dispersion in slope (~0.9) (and consequently, zero point) than previously thought. Plotting the magnitude and velocity of the final point in the ILB for all the galaxies in our sample yields a tight correlation (essentially an "inner T-F relation"), with the caveat that two galaxies are rejected from the fit (one is foreground, the other is a member of a binary pair). Ramifications of this relation are briefly discussed. - n -Table of Contents A B S T R A C T . i i LIST O F T A B L E S v LIST O F F I G U R E S vi A C K N O W L E D G E M E N T S viii 1. General Introduction 1 2. Inner Rotation Curves (a) Introduction 5 (b) Observations - 7 (c) Data Reduction 9 (d) Analysis 14 (e) Discussion 19 3. Surface Photometry (a) Introduction 41 (b) Observations 42 (c) Data Reduction 44 (d) Calibration 49 (e) Analysis and Discussion 53 - i i i -4. L - V Diagrams (a) Reduction Procedure 106 (b) Analysis and Discussion 109 5. Conclusions 120 R E F E R E N C E S 133 - iv -List of Tables 1. Properties Of Galaxies Wi th Rotation Curves 23 2. Emission Line Rotation Curves 24 3. Journal of Surface Photometry Observations 61 4. Parameters Of Galaxies Wi th Surface Photometry 62 5. ILB Parameters 122 6. ILB Spatial Extent 123 - v -List of Figures 1. (a)-(i) Velocity Profiles Without Corrections 29 2. (a)-(i) Final Rotation Curves 34 3. (a)-(d) Rotation Curves Compared With CdS Data 39 4. Calibration Plots 63 5. Surface Photometry Plots (Northern Set) 64 6. Surface Photometry Plots (Southern Set) 76 7. Luminosity Growth Curves (Northern Set) 82 8. Luminosity Growth Curves (Southern Set) 88 9. Composite Luminosity Growth Curves (Northern Set) 91 10. Smoothed Luminosity Growth Curves (Northern Set) 97 - vi -11. Luminosity Residuals Between Northern and Southern Data 103 12. Position Angle Residuals 104 13. Ellipticity Residuals 105 14. Final L - V Diagrams (Northern Set) 124 15. Final L - V Diagrams (Southern Set) 127 16. Histograms of ILB Slopes 128 17. Histograms of ILB Zero Points for Northern and Southern Data Sets . 129 18. Tully-Fisher Plot of Galaxies Overlapping With P T Sample 130 19. Overlay Plot of L - V Diagrams (Northern Set) 131 20. Last ILB Point T-F Plot 132 - vn -Acknowledgements This thesis is dedicated to the memory of Thomas E . Woods, my grandfather, who taught me more about life than I could ever describe. I was fortunate enough to have two co-supervisors for this thesis project, Greg Fahlman and Barry Madore. Greg, I am grateful for your herculean patience, all the insightful discussions and for the faith that you had in me. Barry, I thank you for the continual encouragement, boundless enthusiasm and for the scientific curiousity you have instilled in me right from the beginning. Wendy Freedman deserves my mega-kudos for pre-processing the data, several helpful discussions and for telling me how beautiful it was in Pasadena when it was raining in Vancouver. I am eternally indentured to Gerry Grieve for installing the IRAF facility and the GASP package on the U . B . C . V A X as well as for other software help. I am indebted to Vera Rubin and Mike Pierce for supplying me with tabulated velocities and luminosity growth curves, respectively. I offer my gratitude to my parents and family (in particular, my sister Ruth) for all the love and support over the years. Mucho gracias to Gordon Drukier, Claudia Mendes de Oliveira and the rest of my fellow graduate students for stimulating discussions and for some intense softball. Heaps of thanks to my roomies (and ex-roomies) Jana, Karen, Garry, Corrinne, Kathy, and Doug for the friendship, fun times and for helping me through the rough spots. I raise a pint to the kids from the formative years: Andy, Mike, Man Hoi, K i m and Mike R. Cheers to all the great people I have met in Vancouver. And for making the last few months, during the completion of this thesis, very enjoyable I offer my thanks to Kate. - vm — 1. G E N E R A L I N T R O D U C T I O N The Tully-Fisher relation (Tully and Fisher 1977), an empirical correlation between the total luminosity and maximum rotational velocity of spiral galaxies, has proven, so far, to be resistant to detailed physical interpretation. In one of the first infrared Tully-Fisher (hereafter T-F) studies Aaronson, Huchra and Mould (1979, A H M ) outlined a dynamical argument which yields a LccV4 power law, where L was some "total" luminosity and V was the maximum rotational velocity observed for the galaxy. In a more recent paper Pierce and Tully (1988) observe an "asymptotic" value for the slope of the T-F relation of ~ 8.0, as one goes to longer wavelengths. This is equivalent to a LoaV32 power law. The A H M result depends on the assumptions of a constant mean M/LH ratio and constant central mass surface density with the additional requirement that the rotation curves and mass profiles must each have a characteristic functional form for all galaxies. The second assumption is equivalent to "Freeman's law" (Freeman 1970, but see Souviron, Kormendy and Bosma 1989 and references therein). Burstein (1982) points out that the A H M argument leads to the conclusion that no variations in surface brightness are allowed among the galaxies, which is inconsistent with the A H M data. Dressier and Sandage (1983) have also presented, in general terms, a physical basis for the T-F relation in their velocity study of SO galaxies. They state that a T -F relation with no dispersion can be obtained for a sample of galaxies if four unique conditions are upheld: (i) constant M / L ratio for all the galaxies; (ii) a relation between the galaxy's total mass and the mass interior to the radius - 1 -where the rotational velocity peaks (RMAX)', (iii) a relation between (Rmax) and the radius (RT) where the "total" luminosity (LT) is measured; and finally (iv) a relationship between (LT) and (RT)-Another approach to delving into the physical nature of the T-F relation, on a more detailed, galaxy-by-galaxy level, is to produce so-called "luminosity - velocity diagrams", first introduced by Madore and Woods (1987, M W ) . The luminosity-velocity (hereafter L - V ) diagram of a galaxy is a plot of the accu-mulated luminosity (in the form of a magnitude) within a radius R against the logarithm of the local rotational velocity at that radius. A n individual spiral galaxy is represented by a detailed growth curve instead of just a single point in L - V space (e.g., an isophotal luminosity and maximum velocity width, for the T-F relation). The L - V diagrams calculated for a sample of 46 field spirals (MW) showed a characteristic initial linear branch (ILB) which appeared to have a low dispersion in its slope (±0.4) . If the ILB feature in the L - V diagrams for our Virgo sample is found to be constant in slope as well as having a mean slope which is consistent with the field sample, then the ILB has potential as a distance indica-tor. In this instance the Virgo data set could be used for a distance calibration. The ILB could be used as a distance indicator since the velocity measurements are independent of distance and the luminosity coordinate is distance dependent. The distance indication technique, which is similar to how the T-F relation is applied, is as follows. If the ILB is found to be constant in slope and zero point for a given sample of galaxies in a cluster (i.e., at the same distance), an "ILB relation" for these calibrators can be represented with the following equation: - 2 -M = 7 7 0 + C(log(Vrot)) (1) where M is the absolute magnitude measuring the luminosity inside the radius where the rotational velocity is Vrot. For a galaxy with an unknown distance, we represent its ILB relation by: with m being the cumulative luminosity, expressed as an apparent magnitude, measured at the same radius as Vrot, as in Eq.( l) . The zero point 77 in Eq.(2) is related to 7 7 0 from Eq.( l) as follows: where d is the unknown distance of the observed galaxy. Therefore, 77 corresponds to the ILB zero point and is the observable in this technique. The zero point in the calibrating relation, 7 7 0 5 is obtained by observing galaxies at a known distance. So, once 7 7 0 is determined, a measurement of 77 yields the distance d provided the slope ( is constant. One would like to have L - V diagrams for spiral galaxies in clusters in order to independently determine the dispersion in the slope and especially to find the scatter in the zero point of the ILB. The purpose of this thesis is to investigate the physical basis of the T-F relation by producing L - V diagrams for twelve spiral galaxies, which are members of the Virgo cluster. By examining galaxies at the same distance we can assess the viability of the ILB feature as a distance indicator for spiral galaxies. m = 77 + (,{log(Vrot)) (2) 77 = Vo + 5(log(d)) - 5 (3) - 3 -Chapter 2 consists of a detailed description of the data reduction and analysis required to produce rotation curves for our sample. Chapter 3 outlines the surface photometry profiles reduction and production, as well as the steps taken to obtain the final luminosity growth curve used for each galaxy. Chapter 4 presents the L— V diagrams and a comprehensive discussion of the results while Chapter 5 briefly gives the final conclusions. _ 4 _ 2. I N N E R R O T A T I O N C U R V E S (a) Introduction This chapter outlines the reduction and analysis of long-slit spectra from which accurate inner rotation curves are produced for nine spiral galaxies in the Virgo cluster. A l l are within the 6° core centered on M87 = N G C 4486. The number of published rotation curves for spiral galaxies has been growing steadily in recent years, due largely to the efforts of Rubin, her collaborators (Rubin, Ford and Thonnard 1980, Rubin et al. 1982 and Rubin et al. 1985) and a number of other groups (e.g., Bosma 1981, Albada et al. 1985 and Carignan and Freeman 1985). In the past, interest in rotation curves has been concentrated on the internal kinematics of field galaxies. Recently, shapes of rotation curves for field and cluster spirals have been compared to check for environmental dependences. In an optical study of spiral galaxies in the Virgo cluster and in Abell 1060, Chincarini and de Souza (1985, hereafter CdS) found the rotation curves for cluster galaxies and noncluster galaxies to be quite similar. Guhathakurta et al. (1988) ( G v G K B ) found similar results from a comparison of HI rotation curves for Virgo spirals with optical rotation curves for field galaxies. These two studies conflict with the results of Rubin, Whitmore and Ford (1988) (hereafter RWF) , and with Whitmore, Forbes and Rubin (1988, W F R ) who discuss velocity profiles for 21 galaxies in four large, spiral-rich clusters. R W F found significant differences between their field spirals and cluster spirals, including: (i) falling rotation curves for inner cluster galaxies, (ii) lower velocity amplitudes for Sa and Sb types, and (iii) a general absence of large, bright and massive spirals. Since the focus of this thesis is to elucidate the - 5 -relationship between the cumulative luminosity and the local rotational velocity for the inner regions of Virgo cluster spirals, the difference between field galaxy rotation curves and the rotation of galaxies in clusters will not be a central issue in our analysis. This is supported by W F R where no apparent environmental dependence was found for the inner velocity gradient (which is what our data essentially measure), even though a strong correlation is evident between the outer velocity gradients and the projected distance of those galaxies from the center of the cluster. Four galaxies from CdS overlap with our sample. Furthermore all nine spirals for which we present inner rotation curves have all been observed by G v G K B at 21 cm wavelength with substantially lower spatial resolution. We emphasize the need for high-spatial resolution inner rotation curves in order to produce accurate L - V diagrams. The two aforementioned studies (the CdS paper, in particular) serve as helpful external checks on general morphology and the reproducibility of the rotation curves presented here. In Section (b), we discuss how the observations were obtained, and Section (c) describes the subsequent steps required to reduce the data into rotation curves. The analysis of the results of the reduction are presented in Section (d), and Section (e) contains a brief discussion. - 6 -(b) Observations The 5 meter Hale telescope with the Double Spectrograph mounted at the Cassegrain focus, was used to obtain long-slit spectra of Virgo cluster galaxies on the night of 1987 March 15-16. A 1200 lines/mm grating was centered on the Ha line and imaged on to a TI 800x800 C C D detector. The spatial scale was 0."58 per pixel along the slit, and perpendicular to the slit the dispersion was ~ 0.8 A per pixel. The slit was opened to a width of only 1" in spite of the fact that the seeing was poor throughout the night, varying from 3-5". Hereafter, we will adopt an average seeing of 4" for the spatial resolution of the spectra. Wi th an adopted distance modulus of 31 mag for Virgo (e.g., Mould, Aaronson, and Huchra 1980), 4" is then equivalent to approximately 300 pc. The length of the slit on the sky is slightly less than 2 arcmin. and all the spectra had the slit visually centered on the nucleus of the galaxy. The forbidden lines of [Nil] (AA 6548, 6583) and [SII] (AA 6716, 6731) are commonly observed in the spectra, along with Ha emission; the [Nil] 6583 feature at times being more prominent than the Balmer emission. A l l the galaxy spectra had exposure times of 2400 s. Ten Virgo galaxies were observed. However, N G C 4647 was dropped from the sample retained here because of the complex and rather bizarre nature of its resultant rotation curve. N G C 4647 is a member of an interacting pair (Arp 116), and the velocities we obtained from the [Nil] and Ha lines radically disagreed with those derived from the [SII] lines. This is probably an artifact of the tidal interaction occurring between N G C 4647 and N G C 4649. The velocity field for this intriguing system warrants further, independent study. Another galaxy for which - 7 -we present an inner rotation curve, but which clearly is too peculiar to consider using for a L - V diagram, is N G C 4388. It has been well established (see Section (d)) that N G C 4388 is a Seyfert galaxy (the first one discovered in Virgo; Phillips and Malin 1982), and its rotation curve certainly reflects its abnormal status. We will discuss the morphology of its velocity profile in Section (d). - 8 -(c) Data Reduction The pre-processing (de-biasing and flatfielding) of the spectra was kindly done by Wendy Freedman at the Observatories of the Carnegie Institution of Washing-ton, using reduction programs developed by John Tonry and further modified by Robert Jedrzejewski. Additional reduction and analysis was completed using various IRAF packages and routines (predominantly the long-slit package). Each C C D spectrum was corrected for distortion and curvature using (a) calibration frames of "holes" (several circular apertures regularly spaced perpendicular to the dispersion axis), taken at the beginning and end of the night, and (b) the arc (He-Ne-Ar) exposures, which were obtained after each galaxy spectrum. The arcs have numerous lines of high S / N in the region surrounding the Ha and [Nil] lines but, regrettably, there were not enough arc lines to confidently define the longer wavelength region where the [SII] lines reside. For this reason, we use only the [Nil] and Ha lines for our final rotation curves. This is not a tremendous loss, because the [SII] lines are generally weak and appear over a much more limited region of the galaxies studied. Sky subtraction was performed on all the spectra where it was practical. Since each galaxy completely covered the C C D slit, we could only use the areas where there was no discernible galaxy emission (from any of the lines we were measuring) as the "sky" level to be removed. Three out of nine galaxies in the sample were not sky-subtracted, because there was continuous galaxy emission along the entire length of the slit; these were N G C 4501, N G C 4535 and N G C 4569. To check the effects of sky subtraction on the velocity information, we produced one galaxy's - 9 -rotation curves with and without sky subtraction (NGC 4192). There was no obvious difference between the two sets of rotation curves at the ±10 km/s level. To extract the emission-line positions, we set up apertures, seven pixel columns in width, across the C C D image perpendicular to the dispersion axis. The seven columns of each aperture were then summed to produce one-dimensional spectra for which the line centroids were measured using the IRAF center-finding algorithm. When there was emission in the outer regions of the galaxy, the aper-tures were placed side-by-side. In the innermost regions, close to the continuum peak, where there are consistently high S / N emission lines, the apertures were centered on each column. This intensive coverage of the nuclear regions smooths the positional information. It should be emphasized that the points in the inner-most regions are not independent of each other, as the apertures centered seven pixel columns apart in the outer regions are. We sampled the spectra in this way because it allowed the point of symmetry, i.e., the systemic velocity, of each curve to be determined with greater ease. The internal errors for the velocities, based on the wavelength solution fit, are about ± 2 km/s. The IRAF centering algorithm is most sensitive to the value of the parameter which estimates the width of the emission-line(s) being measured. Using a range of emission-line widths, where the width of the emission feature is measured at the continuum level, one can determine the accuracy of the line positions from the repeatability of the results. For each one-dimensional spectrum extracted, the line positions were measured by setting the emission-line width to three pixels for the lower S / N emission in the outer regions and a variety of widths, typically multiples of three pixels, which bracketed the real emission-line width, - 10 -for the strong emission in the vicinity of the nucleus. Any given line measurement which showed significant disagreement oyer a reasonable range of emission-line widths was not included in the final rotation curve. There are also parts of some galaxies which do not show spatially continuous emission due to the discrete nature of the emitting regions, or in some cases the HII regions do not have sufficient S / N to to provide accurate information. These two effects introduce breaks in some of the rotation curves presented. A conservative estimate of the error for a single measurement of an emission line with a good S /N; i.e., in the vicinity of the nucleus, is about ±10 km/s; For data points near the end of the slit, the errors are somewhat higher than this, ±15-20 km/s, primarily due to degradation of the S / N . The final velocity curves are presented in Figure 1. Systematic differences between the [Nil] and Ha line velocities are evident in N G C 4535, N G C 4388 (see also Fig. 2d) and possibly N G C 4206. Systematic shifts of this magnitude (~10-20 km/s) can also be seen between different lines in some of the rotation curves measured by the Rubin group (e.g., Rubin, Whitmore and Ford 1989: N G C 2558, W R 66; Rubin et al. 1982: N G C 7537, N G C 3054; Rubin et al. 1985: IC 724, N G C 3593). We do not understand the origin of this effect. Since our study will focus more on the gradient of the rotation curve rather than the systemic velocity it yields, systematic errors are not as much of a concern as are random errors. There appears to be a slight systematic difference between the gradients found from the [Nil] and Ha lines, for N G C 4206, ,4654 and 4689. The systemic velocity for each galaxy was found by iteration: a starting point for the center was chosen, the rotation curve was interpolated to find the systemic velocity, and then the velocities were folded across this position and replotted to see if the resulting rotation curve provided the expected degree of symmetry seen in most spirals. This fitting procedure was continued until a reasonable systemic velocity and symmetric rotation curve were found. The final systemic velocity adopted for each galaxy is a simple average of the systemic velocities determined from the [Nil] and Ha rotation curves when both data sets were available. The final systemic velocities are given in Table 1 (V©) along with physical data gleaned from other works, and the measured velocity profiles are tabulated in Table 2. Good agreement is found between the systemic velocities in this paper ( V o p f ) and those found by G v G K B with HI data. We find a mean difference of <Vopt-VHi> — 4 km/s and a standard deviation from the mean difference of a<vopt-vHi> — 28 km/s. Comparing our velocities with the Revised Shapley-Ames Catalog (Sandage and Tammann 1981, hereafter RSA) values yields a higher mean difference: <Vopt-VRSA> = 31 km/s with a standard deviation: c r < v o p t - v R S A > = 34 km/s. Eight galaxies were used for this comparison, because there is no R S A value for N G C 4206. At this point, the rotational velocities were corrected to edge-on, using the inclinations given by Pierce and Tully (1988) which are listed in Table 1. Their inclinations were determined by fitting ellipses to isophotes of the particular galaxy over a range of radii at which the disk dominated the light distribution, from which a characteristic axial ratio was derived. We assume that the rotational velocities we observed are confined to a plane, and that the emitting material is moving in circular orbits. Also, we consider the position angle that each spiral was observed at (see Table 1) to be the true position angle of the major axis. For completeness, - 12 -the relativistic corrections 1/(1 + zn) (Harrison 1974) were also applied to the velocities, where zq is the redshift of each galaxy calculated from its systemic velocity. The final rotation curves are shown in Figures 2 and 3. The plots in Figure 2 have the G v G K B HI measurements included, where they are shown as asterisks, and the diagrams in Figure 3 are identical except that the asterisks now correspond to the CdS optical data. Note that the velocities from G v G K B have not been corrected to our adopted inclination and position angle of the major axis for each galaxy, due to these parameters being derived in G v G K B in a multi-parameter fit. This could introduce small errors into our comparison of the radio data with our measurements. The CdS data, however, has had these two corrections applied. - 13 -(d) Analysis In this section, we look briefly at the characteristics of the individual rotation curves and how they compare with the HI curves of G v G K B . We also check the consistency between our data and the optical rotation curves from CdS, for the four galaxies in common. N G C 4192 - This galaxy has emission only in the nuclear and circumnu-clear regions. The velocity data from Ha are not included, because this line was partially blended with a night-sky line. A steep velocity gradient is seen, but the gradients on the opposing sides of the nucleus differ considerably. The rotation curve was formed assuming that the slight turn-over occurs at the same galacto-centric radius in the plane of the galaxy and then using these features to match the amplitudes of the two sides. It can be seen that the resolution of the HI rotation curve (45") degrades the inner velocity gradient found in the optical. G v G K B give their first velocity measurement as 31 km/s at a galactocentric radius of 15", and their velocities reach ~150 km/s only starting at 75". Our data show velocities greater than 150 km/s within a radius of 10". In addition to the beam smearing, a deficiency of HI gas in the central area of the galaxy could also contribute to the observed velocity differences. It is possible that the velocity gradients, which we observe, are even steeper, considering the spatial smoothing from our resolution of ~4". This effect could be most significant for N G C 4192 and 4216 (see Figs, l a and lc) , where there are a small number of independent velocity measurements for a compact region near the nucleus. N G C 4206 - The emission for this highly inclined Sc galaxy is continuous - 1 4 -and leads to a well-defined inner rotation curve with the scatter increasing with radius. The HI velocity profile, once again, shows a substantially flatter form due, at least in part, to lower resolution. Also, G v G K B mention being forced to use the optical center of the galaxy for their fitting procedure, perhaps introducing even more uncertainty for the inner velocities. N G C 4216 - This rotation curve is reminiscent of N G C 4192. Emission is observed in the nuclear regions only out to a radius of ~10", although the amplitude of the curve is ~50 km/s higher than in the case of N G C 4192. Once again, the Ha data were discarded because of blending with a night-sky line. In comparison to our optical data, the HI observations appear to significantly underestimate the amplitude and the gradient of the rotation curve for the inner regions. N G C 4388 - Phillips and Malin (1982) were the first to identify this galaxy as a Seyfert. Recently, detailed studies of this galaxy (Pogge 1988; Shields and Filippenko 1988) have suggested that N G C 4388, commonly classified as a Seyfert 2, is an example of a hidden Seyfert 1. The characteristic broad emission lines were very distinctive in many of our central spectra. The velocity profile obtained appears to reflect the peculiar nature of the galaxy, especially the kink in the rotation curve for the approaching side, apparent in Figure 1. The asymmetry seen in the final rotation curve in Figure 2d further demon-strates that this galaxy is peculiar. Corbin, Baldwin and Wilson (1988) have observed the velocity field of N G C 4388 with greater coverage and accuracy than this study and confirm the asymmetry we see in this Seyfert's rotation curve. The strikingly different form of the velocity curve on opposing sides of the major axis has also been seen by G v G K B . For this galaxy, the HI observations had a resolu-tion of 15" and appear to delineate the velocity gradient with greater success than in other galaxies. The HI gradient is still substantially shallower than that of our optical data again possibly due to a lack of HI in the central regions. Surprisingly, the velocity profile presented by CdS shows no evidence of the disparate velocity gradients on opposing sides of the nucleus and their velocity gradient appears to be comparable to, or even less than, the gradient shown by the HI data. Systematic differences (~10 km/s) between the [Nil] and Ha velocities are obviously present in our rotation curve of N G C 4388 but are not large enough to seriously effect the basic form of the profile. Since N G C 4388 is a Seyfert, it will not be included in future L - V diagram analysis. Nevertheless, this galaxy definitely warrants further study. Spectropolarimetric observations would help es-tablish a better understanding of the mechanism(s) behind this Seyfert's observed properties. N G C 4501 - The rotation curve, from either the Ha or [Nil] lines alone, is well defined. A combination of the data from the two lines, as presented in Figure 2e, however, exhibits scatter over the entire profile. The G v G K B HI curve (45" resolution) is similar to the optical curve at the radii for which HI and optical data are both available. However, the first two data points in the radio curve are still ~25 km/s lower than our optical velocities. N G C 4535 - Finding the symmetry point (i.e., the systemic velocity) for this rotation curve was not a simple task, due to the deficiency of velocity data on one side of the nucleus. A fit with considerably less scatter in the inner velocity gradient can be produced, but it yields a velocity profile of peculiar morphology, having very - 16 -different amplitudes for the velocities on opposite sides of the nucleus. The curve given in Figure 2f is a compromise fit. There appears to be a marked difference between the inner velocity gradients for the opposing sides traced by both the Ha and [Nil] lines. The HI curve of N G C 4535 overlaps with our optical data at only one point, at a radius of 45" , and the velocity they observe, ~137 km/s, is in good agreement with our optical value, ~135 km/s. Optical data presented by CdS show a shallower velocity gradient and an amplitude of the rotation curve which is noticeably lower than ours, scatter in the data being evident over the entire velocity profile. N G C 4569 - For this galaxy, the Ha data was not used, once again because of the superposition of a sky line. The G v G K B HI data, with a resolution of 15", are in reasonable agreement with the curve in Figure 2g but do not appear to resolve the plateau in velocity seen between ~ 15-50" in radius. The CdS velocities indicate that the curve flattens before its final rise around radius 60". N G C 4654 - The rotation curve is well defined with increasing scatter to-wards the outer regions. The HI data have a slightly shallower gradient but still show good agreement considering the difference in resolution. A substantial dif-ference in the HI kinematics is seen between the velocities measured on different sides beginning at a radius of 75". Our optical data do not have the spatial extent necessary to check this trend, and the CdS curve shows no evidence of it out to ~1.5 arcmin. The CdS rotation curve and our data have very similar velocities. N G C 4689 - The velocity profile for this galaxy agrees with the sparsely sampled HI rotation curve in G v G K B ; neutral hydrogen velocities which overlap with our results are: 80 km/s and 142 km/s at respective radii of 15 and 45". The scarcity of resolved points in the HI data is cited by G v G K B as a cause of the flattening of the velocity gradient. - 18 -(e) Discussion A general feature of the above comparisons between the G v G K B HI rotation curves and our optical data is that the inner velocity gradient measured in neutral hydrogen appears to be consistently shallower than the velocity gradient measured by the ionized gas. This effect is most easily explained by the poorer spatial resolution of the radio data, possibly in combination with holes in the neutral gas distribution toward the center of the galaxies in question (which would affect the highly inclined galaxies more strongly). This difference strikingly illustrates the necessity of obtaining high-resolution optical spectra if the rapid rise in rotational motion close to the nucleus is to be accurately determined. Differences between the CdS optical velocities and the rotation curves in this work, e.g., N G C 4388 and N G C 4535, could be a result of CdS using catalog values for their systemic velocities and/or their assumption that the optical center was coincident with the dynamical center. It is not immediately clear why the CdS and G v G K B data indicate no differ-ence between cluster and field galaxy rotation curves and why R W F and W F R find the opposite result. The approach taken by G v G K B for their comparison between cluster and field galaxies is to superpose the synthetic curves for field spirals of a given morphological type, given by Rubin et al. (1985), on the rotation curves for the cluster galaxies. The steeper inner velocity gradients, found here in sev-eral cases, should partly explain the discrepancy between the G v G K B results and those of the Rubin group. Also, the approximate nature of the comparison of a specific rotation curve with a mean rotation curve (for several different galaxies of - 19 -the same morphological type) has the potential to be misleading. The galaxy-by-galaxy gradient analysis adopted by W F R is probably a more physical description of the differences/similarities existing between cluster and field spirals. In W F R , a good correlation is found between the outer gradient of the rotation curve (defined as the change in velocity from 0.4i?25 to O.8.R25) and the projected distance of the galaxy from the center of the cluster. The inner velocity gradients (measured at O.I5.R25) were tested for a similar relation, with no conclusive result. There are insufficient numbers of galaxies in our sample with extensive enough spatial coverage to be able to obtain any kind of meaningful analysis of the inner velocity gradients, similar to that presented by W F R . It should be emphasized that the outer velocity gradient is used by W F R to conclude that there is a real difference between the rotation curves of field and cluster spirals. Studies of rotation curve gradients have become fairly common recently. One reason for this may be the close relationship that velocity gradients have with several other global and local physical properties of spiral galaxies. Specifically, Persic and Salucci (1986) have shown that the velocity gradient is directly related to a galaxy's specific angular momentum, kinetic energy and total mass. In another paper, Persic and Salucci (1988) analyse the rotation curves for 43 spirals collected from the literature (very similar to the sample used in M W ) . By comparing the logarithmic gradients of the circular velocities predicted by an exponential thin disk model with those observed, they calculate the dark-to-luminous mass ratio within the disk for each galaxy. Baiesi-Pillastrini (1987, 1988) has studied central velocity gradients in spiral galaxies and has found they correlate with Hubble type, bulge-to-disk ratio and the pitch angle of spiral arms. This is interpreted as - 20 -a confirmation that the luminous matter traces the underlying mass distribution in the central regions and that the Hubble classification system succeeds, to some degree, in describing intrinsic properties of galaxies. Recent detailed observational and modelling work (Fillmore, Boroson and Dressier 1986, hereafter F B D ; Kormendy and Westpfahl 1989, hereafter K W ) has suggested that emission-line rotation curves, which follow the gas motions, may not be tracing the true circular motion in the innermost regions of spirals having substantial bulge components. F B D found that constant mass-to-light models could be fit to their observations of six moderately inclined spirals with the three following caveats: (i) there were kinematic differences between the two sides of several of the galaxies, (ii) some of the bulges were flatter than would be expected from their observed rotation rates, and (iii) the emission-line rotation curves fell below the predicted circular velocity for R < 1 kpc. Absorption-line data were used as the tracer of stars close to the nucleus, and the emission-line data were used to delineate the motion at larger galactocentric distances. K W found a significant difference between the emission-line and absorption-line velocities for the central 35" of N G C 4594 (the Sombrero galaxy) and also interpreted it as the gas moving at less than the circular velocity. If emission-line velocities are, in fact, not representative of the true kinematics in the inner regions, this could call into question the interpretation of some of the velocities measured in our sample. The galaxies most likely to be affected by the difference in emission and absorption-line velocities are N G C 4388 and N G C 4569; both are Sab type galaxies, the earliest in our sample. N G C 4192 and N G C 4216, both Sb galaxies, may also be affected to a lesser extent. However, N G C 4388 is - 21 -a Seyfert and has for this reason been dropped from the sample. N G C 4569 is one of the galaxies in the F B D sample. The emission-line rotation curves given in F B D are in good agreement with our curve displayed in Figure 2. However, with constant mass-to-light models, F B D show that the expected circular velocity can be obtained in the inner parts only if the kinematics of the bulge, as measured by the absorption-line data, are included in the final fit. This suggests that our observed rotation curve for N G C 4569 is not measuring the true circular velocity. More absorption-line and emission-line rotation curves for late-type galaxies, in clusters, as well as the field, should help to establish over what range of morpho-logical types and scales this difference between absorption-line and emission-line velocities is prevalent (see, for example, Walker 1989). Also requiring further investigation is the environmental dependences for this phenomenon, along with those for velocity gradients and the general morphology of rotation curves. - 22 -T A B L E 1 Properties Of Galaxies With Rotation Curves Galaxy Type Vo Inclin. P .A, Rank (RSA) (km s"1) (degrees) (degrees) (1) (2) (3) (4) (5) (6) N G C 4192' - SMI: -115 86 152 10.92 9 N G C 4206 Sc(s) 719 90 0 12.79 6 N G C 4216 Sb(s) 159 90 19 10.97 5 N G C 4388 Sab 2449 83 92 11.83 1 N G C 4501 Sbc(s)II 2290 61 140 10.27 3 N G C 4535 SBc(s)I.3 1979 45 0 10.51 7 N G C 4569 Sab(s)I-II -185 63 a 23 10.23 2 N G C 4654 SBc(rs)II 1062 58 128 11.14 4 N G C 4689 Sc(s)IL3 1617 39 165 11.55 8 classification from R S A (Sandage and Tammann 1981); (2) this work; (3) Pierce and Tully (1988); (4) Warmels (1989); (5) R S A ; (6) Guhathakurta et al. (1989) a RC2 inclination - 23 -T A B L E 2 Emission-Line Rotation Curves Radius Velocity Radius Velocity Radius Velocity (arcsec.) (km/s) (arcsec.) (km/s) (arcsec.) (km/s) NGC 4192 -[Nil] -9.5 -278 -1.9 -155 5.1 36 -8.9 -287 -1.3 -146 5.6 41 -8.3 -282 -0.8 -132 6.2 50 -7.7 -278 -0.2 -123 6.8 55 -7.1 -269 0.4 -96 7.4 55 -6.6 -255 2.2 5 8.0 50 -4.2 -187 2.7 18 8.5 50 -3.7 -178 3.3 23 9.1 46 -3.1 -169 3.9 23 9.7 41 -2.5 -164 4.5 27 ... ... NGC 4206 -Ha -57.4 630 -8.7 672 1.7 740 -53.4 630 -4.6 685 2.3 749 -49.3 621 -4.1 690 6.4 763 -45.2 626 -3.5 690 10.4 781 -41.2 617 -2.9 694 14.5 786 -37.1 630 -2.3 699 30.7 795 -33.1 608 -1.7 704 34.8 795 -29.0 621 -1.2 708 38.9 795 -24.9 626 -0.6 713 42.9 818 -20.9 626 0.0 722 47.0 845 -16.8 653 0.6 726 51.0 845 -12.8 658 1.2 735 ... ... NGC 4206 -[Nil] -47.6 619 -2.9 692 2.3 738 -39.4 615 -2.3 697 2.9 742 -35.4 606 -1.7 701 3.5 751 -31.3 606 -1.2 706 4.1 756 -27.3 610 -0.6 710 8.1 765 -19.1 615 0.0 715 ' 12.2 783 -15.1 638 0.6 724 16.2 783 -11.0 647 1.2 729 44.7 838 -7.0 669 1.7 733 52.8 856 NGC 4216 -[Nil] -9.6 -64 -1.5 146 2.6 178 -5.5 -14 -0.9 150 3.8 332 -4.9 0 -0.3 155 4.4 342 -3.8 41 0.3 164 4.9 351 -3.2 68 0.9 168 5.5 360 - 2 4 -TABLE 2 — continued Radius Velocity Radius Velocity Radius Velocity (arcsec.) (km/s) (arcsec.) (km/s) (arcsec.) (km/s) -2.6 87 1.5 178 6.1 360 -2.0 105 2.0 182 6.7 364 NGC 4388 - Ha -38.3 2348 -1.7 2444 7.5 2526 -34.2 2357 -1.2 2448 8.1 2526 -30.2 2371 -0.6 2448 8.7 2526 -26.1 2371 0.0 2453 9.3 2531 -22.0 2385 0.6 2453 13.3 2558 -18.0 2412 1.2 2458 17.4 2586 -13.9 2430 1.7 2458 21.5 2608 -9.9 2426 2.3 2462 25.5 2627 -5.8 2403 2.9 2467 29.6 2659 -5.2 2407 3.5 2476 33.6 2659 -4.6 2412 4.1 2490 37.7 2663 -4.1 2417 5.2 2512 41.8 2668 -3.5 2426 5.8 2522 45.8 2672 -2.9 2430 6.4 2522 49.9 2654 -2.3 2435 7.0 2526 53.9 2649 NGC 4388 -[Nil] -38.0 2359 -0.9 2441 8.4 2536 -33.9 2368 -0.3 2445 9.0 2536 -29.9 2373 0.3 2445 9.6 .2536 -25.8 2377 0.9 2450 13.6 2564 -21.8 2382 1.5 2450 17.7 2591 -17.7 2404 2.0 2454 21.8 2609 -13.6 2436 2.6 2459 25.8 2628 -9.6 2427 3.2 2464 29.9 2659 -5.5 2400 3.8 2473 33.9 2659 -4.9 2404 4.3 2491 38.0 2669 -4.4 2409 4.9 2509 42.0 2669 -3.8 2413 5.5 2527 46.1 2678 -3.2 2418 6.1 2532 50.2 2673 -2.6 2423 6.7 2536 54.2 2641 -2.0 2427 7.3 2536 -1.5 2441 7.8 2536 NGC 4501 - Ha -54.2 2051 -4.3 2243 0.9 2311 -50.1 2056 -3.7 2247 22.4 2494 -46.1 2047 -3.1 2252 26.5 2499 -42.0 2056 -2.6 2252 30.5 2503 -37.9 2060 -2.0 2257 34.6 2508 - 25 -TABLE 2 — continued Radius Velocity Radius Velocity Radius Velocity (arcsec.) (km/s) - (arcsec.) (km/s) (arcsec.) (km/s) -33.9 2060 -1.4 2261 38.6 2508 -6.0 2229 -0.8 2266 42.7 2517 -5.5 2234 -0.2 2275 46.8 2522 -4.9 2238 0.4 2298 ... NGC 4501 -[Nil] -54.4 2045 -5.7 2222 1.9 2359 -50.3 2049 -5.1 2236 2.4 2359 -46.3 2054 -4.5 2240 3.0 2368 -42.2 2063 -3.9 2245 3.6 2359 -38.2 2054 -3.4 2250 4.2 2373 -34.1 2054 -2.8 2254 4.8 2377 -9.7 2177 -2.2 2263 22.2 2500 -9.2 2181 -1.6 2268 26.2 2495 -8.6 2177 -1.0 2268 30.3 2509 -8.0 2168 -0.5 2277 34.3 2500 -7.4 2190 0.1 2300 38.4 2518 -6.8 2222 0.7 2318 42.5 2523 -6.3 2213 1.3 2341 46.5 2509 NGC 4535 • - Ha -53.4 1873 -6.4 1900 1.2 1983 -49.3 1868 -5.8 1905 1.7 1992 -45.2 1878 -5.2 1919 2.3 2010 -41.2 1878 -4.6 1928 2.9 2028 -33.1 1896 -4.1 1937 3.5 2042 -24.9 1887 -3.5 1946 4.1 2056 -20.9 1882 -2.9 1955 4.6 2056 -15.1 1887 -2.3 1960 5.2 2056 -9.3 1887 -1.7 1960 5.8 2065 -8.7 1891 -1.2 1964 6.4 2069 -8.1 1891 -0.6 1969 51.0 2088 -7.5 1891 0.0 1973 -7.0 1891 0.6 1978 ... ... NGC 4535 -[NH1 -54.8 1899 -6.1 1931 0.3 1990 -50.8 1876 -5.5 1940 0.9 1999 -22.3 1890 -4.9 1949 1.5 2022 -10.7 1913 -4.4 1958 2.0 2045 -10.1 1913 -3.8 1958 2.6 2058 -9.6 1913 -3.2 1963 3.2 2058 -9.0 1913 -2.6 1963 3.8 2054 -8.4 1922 -2.0 1967 4.4 2067 TABLE 2 — continued Radius Velocity Radius Velocity Radius Velocity (arcsec.) (km/s) - (arcsec.) (km/s) (arcsec.) (km/s) -7.8 1913 -1.5 1972 4.9 2077 -7.3 1917 -0.9 1976 5.5 2081 -6.7 1922 -0.3 1981 49.6 2086 NGC 4569 -[Nil] -42.6 -50 6.7 -232 16.0 -273 -38.6 -59 7.3 -246 16.5 -273 -34.5 -73 7.8 -250 17.1 -278 -30.5 -87 8.4 -255 21.2 -273 -26.4 -77 9.0 -255 25.2 -278 -22.3 -73 9.6 -255 29.3 -278 -18.3 -114 10.2 -260 33.4 -273 -14.2 -132 10.7 -260 37.4 -291 -10.2 -123 11.3 -260 41.5 -296 2.6 -200 11.9 -260 45.5 -305 3.2 -200 12.5 -260 49.6 -310 3.8 -205 13.1 -260 53.7 -323 4.4 -214 13.6 -264 57.7 -360 4.9 -214 14.2 -264 61.8 -383 5.5 -219 14.8 -269 ... ... 6.1 -223 15.4 -269 ... NGC 4654 -Ha -52.5 959 -4.9 1037 4.4 1078 -48.4 955 -4.4 1042 4.9 1083 -44.4 955 -3.8 1042 5.5 1087 -40.3 955 -3.2 1042 6.1 1087 -36.3 950 -2.6 1046 6.7 1092 -32.2 950 -2.0 1051 7.3 1092 -28.1 959 -1.5 1055 11.3 1101 -24.1 959 -0.9 1060 15.4 1128 -20.0 973 -0.3 1060 19.4 1147 -16.0 1000 0.3 1064 23.5 1169 -11.9 1023 0.9 1069 27.6 1174 -7.8 1032 1.5 1069 31.6 1179 -7.3 1032 2.0 1069 35.7 1179 -6.7 1032 2.6 1074 39.7 1156 -6.1 1037 3.2 1074 ... ... -5.5 1037 3.8 1078 ... ... NGC 4654 -|NII] -52.8 975 -5.2 1043 3.5 1070 -48.7 943 -4.6 1043 4.1 1075 -44.7 965 -4.1 1047 4.6 1079 - 2 7 -TABLE 2 — continued Radius Velocity Radius Velocity Radius Velocity (arcsec.) (km/s) ' (arcsec.) (km/s) (arcsec.) (km/s) -36.5 952 -3.5 1047 5.2 1079 -32.5 965 -2.9 1052 5.8 1084 -28.4 965 -2.3 1052 6.4 1084 -24.4 965 -1.7 1056 7.0 1088 -20.3 975 -1.2 1056 11.0 1097 -16.2 1002 -0.6 1061 15.1 1120 -12.2 1020 0.0 1061 23.2 1161 -8.1 1034 0.6, 1066 27.3 1170 -7.5 1034 1.2 1066 31.3 1175 -7.0 1038 1.7 1066 35.4 1170 -6.4 1038 2.3 1070 ... -5.8 1038 2.9 1070 ... NGC 4689 - Ha -49.3 1535 -3.5 1571 3.5 1654 -45.2 1530 -2.9 1590 7.5 1667 -41.2 1539 -2.3 1590 11.6 1672 -33.1 1539 -1.7 1594 15.7 1672 -29.0 1544 -1.2 1599 19.7 1667 -24.9 1549 -0.6 1608 23.8 1676 -20.9 1549 0.0 1617 27.8 1686 -16.8 1553 0.6 1631 31.9 1690 -12.8 1562 1.2 1635 36.0 1699 -8.7 1571 1.7 1640 40.0 1713 -4.6 1581 2.3 1645 ... ... -4.1 1581 2.9 1649 ... NGC 4689 -[Nil] -48.7 1535 -2.3 1594 4.1 1648 -32.5 1539 -1.7 1598 8.1 1658 -28.4 1553 -1.2 1603 12.2 1671 -24.4 1557 -0.6 1607 16.2 1667 -20.3 1562 0.0 1617 20.3 1667 -16.2 1566 0.6 1621 24.4 1676 -12.2 1562 1.2 1626 28.4 1680 -8.1 1580 1.7 1635 32.5 1662 -4.1 1585 2.3 1639 36.5 1689 -3.5 1585 2.9 1644 40.6 1694 -2.9 1580 3.5 1644 - 28 -a (VI i • i • i 1 i • NGC 4192 POS A = 152 • i • i ~ o m • \ E -X • • a o - Q • a q 3 (VI 1 • • tNIIl a a i . i . i . i i . i , -60 -40 -20 0 20 40 60 | Radius (arcsec.) Fig. l . ( a ) Figure l.(a)-(i)—The velocity profiles, before any corrections have been applied to the velocities, and without the reflection about the point of symmetry. Each symmetry point (at zero radius) is that which yields the respective systemic velocity listed in Table 1. Note the good agreement between the Ha velocities (crosses) and the [Nil] data (black circles). - 29 -• 1 ' 1 ' 1 ' 1 ' 1 ' r NGC 420.6 POS A = 0 X X X X >" x H-alpha • [ N i l ] -60 -40 -20 • 20 40 60 Radius (arcsec.) Fig. l.(b) 1 1 1 NGC - — i | -4216 • ""1 •— 1 1 , , , POS A = 19 / • • / • • • • • • • * • • i i • < CNII3 i i -60 -40 -20 O 20 40 60 Radius (arcsec.) - 30 - Fig. l.(c) o o 03 | i ' i ' 1 ' — ~ i ' 1 ' 1 • r CVI L NGC 4388 POS A = 92 O * o L * 6 L * x H-alpha • CNII1 _ l i i _ -60 -40 -20 0 20 40 60 Radius (arcsec.) Fig. l.(d) o o CD I • I 1 T NGC 4501 POS A - 140 o e — a a a < x H-alpha * * * * * * • CNII1 - J • 1 i i i J i ' • • • • -60 -40 -20 0 20 40 60 Radius (arcsec.) - 31 -Fig. l.(e) , . ! r •, »' NGC 4535 1" > 1 • POS A = 0 I ' ^ x x X x * x * f I . I . I . X • i i H-a lpha [ N i l ] i i i - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 Radius (arcsec.) F i g . l . ( f ) i 1 i 1 i 1 NGC 4569 i 1 ' 1 ' 1 POS A = 23 -\ • « • I . I . I . • i . i . tNII] i . i - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 Rad lus (arcsec. ) F i g . l . ( g ) - 3 2 -• o E — o « o 1 i 1 ' 1 • r N G C 4 6 5 4 1 1 • T ' 1 P O S A = 1 2 8 X * X y r x x $ x n * * * • 1 . 1 . 1 — . X • 1 . 1 H - a l p h a C N I I 3 -60 -40 -20 0 20 Radius ( a r c s s c . ) 40 60 Fig. l.(h) e w o o 3> (B N G C 4 6 8 9 P O S A = 1 6 5 X X * * x H - a l p h a • [ N i l ] _ l _ -60 -40 -20 0 20 Rad ius (arcsec . ) 40 60 Fig. l.(i) - 33 -o o • ' • i 1 r i ' ' l m K a a • dP NGC 4192 • • * 5 POS A = 152 ] 1 i i l i i i 20 40 60 Radius (arcsec.) Fig. 2.(a) Figure 2.(a)-(i)—The final rotation curves with the velocities corrected for inclina-tion and relativistic effects. The black and open circles correspond to different sides of the Ha velocity profiles while the black and open squares are the opposing sides of the [Nil] rotation curves. Radio data points gleaned from Guhathakurta et al. (1989), uncorrected for our adopted values of the position angle of the major axis and the inclination, are denoted by the asterisks. - 34 -~ a n W \ E - ° I a 13 * n o 1 © © „ • o • « _ o © © • i$GC 420G * POS A = 0 20 40 60 Radius (arcsec.) Fig. 2.(b) a a i o • w f e • nm Q • • NGC 4216 POS A = 19 - I • • . 1 i . i L _ 20 40 60 Radius (arcsec.) Fig. 2.(c) - 35 -Q ~ O n CVJ 6 • _ l _ _I_ NGC 4388 POS A = 92 • !_ 20 40 Radius (arcsec.) 60 F i g . 2.(d) \ <3» « 3 NGC 4501 POS A = 140 • 1_ 20 40 Radius (arcsec.) 60 F i g . 2.(e) - 3 6 -• ~ o «< (VI •\ 6 o t x n D i om • aa aa man €D on _i_ o * NGC 4535 POS A = 0 _1_ 20 40 Radius (arcsec.) 60 Fig. 2.(f) o o o ~ o n (VI \ E NGC 4569 POS A = 23 20 40 Radius (arcsec.) 60 Fig. 2.(g) - 37 -• i ^ A 0 0 o NGC 46S4 POS A = 128 20 40 60 Radius (arcsec.) Fig. 2.(h) o i • • • 1 CI • o _ W • % • to o • • a o • a - O • _ m • • *m m o © m • OB> • • «• NGC 4G89 «1 m D POS A = 165 • I i i . . . i 20 40 60 Radius (arcsec.) Fig. 2.(i) - 38 -• ~ o n CU \ E • • * D NGC 4388 POS A = 92 • l_ 20 40 Radius (arcsec.) 60 Fig. 3.(a) a ~ o -«> W \ E "T~ • onnnn i ©m aa © © <T I -•9 CD on NGC 4535 POS A = 0 _ l _ _ l _ 20 40 Radius (arcsec.) 60 Fig. 3.(b) Figure 3.(a)-(d)—The same as Figure 2 except the asterisks are the velocities measured at optical wavelengths, as presented in Chincarini and de Souza (1985), corrected for the inclination and position angle of the major axis used in this paper. • ~ Q «> CU \ £ , , . • 1 • • * X • • • • y • • • * ** • K • y * NGC 4S69 POS A = 23 i . . . . 1 20 40 Radius (arcsec.) 60 Fig. 3.(c) o ~ o n m •\ e • a n a 4 X * X NGC 4654 POS A = 128 _ I _ 20 40 Radius (arcsec.) 60 Fig. 3.(d) - 40 -3. S U R F A C E P H O T O M E T R Y (a) Introduction Surface photometry studies of Virgo cluster galaxies have been common in the literature in the last couple of decades, as demonstrated by the bibliography compiled by Davoust and Pence (1982, see also Pence and Davoust 1985). One of the most recent, homogeneous studies, with a large sample, is that by Watanabe, Kodaira and Okamura (1982) where Schmidt plates taken in the V band were scanned and digitized to yield "projected profiles" and "generalized radial profiles" for twenty Virgo galaxies. Pierce and Tully (1988, hereafter PT) present B, RKC, and IKC C C D photometry of 34 Virgo spirals (which is a subset of a much larger survey). P T utilize this surface brightness data only to derive total magnitudes and accurate inclinations for application in the T-F relation. In this study, Gunn r surface photometry has been acquired for 12 spiral galaxies in Virgo which are within 6° of M87. Nine of the galaxies in our sample overlap with the P T data set. A comparison between the two sets of photometry will be made in Section (e) to check the consistency of our calibration. The observations and their characteristics are summarized in Section (b), and the data reduction is outlined in Section (c). The calibration used is described in Section (d). Finally, the resultant surface brightness profiles are presented in Section (e), along with the final luminosity growth curves that will be used for the L - V diagram analysis in Chapter 4. A discussion of accuracy and reproducibility of the photometry is also given. - 41 -(b) Observations Since the initial L - V diagram study (MW) was based mostly on Kent's (1986, 1984) Gunn r photometry, our observations were made through the same filter bandpass for comparison purposes. The surface photometry analysis is based on a combination of two different data sets. The first set, consisting of images for 6 galaxies, was obtained with the Las Campanas 40-inch Swope telescope during the period of 1987 February 21-28 by Barry Madore and Robert Jedrzejewski. A R C A C C D (330 x 512 pixels) was used in direct mode at f/7.0, resulting in a scale of 0."87 per pixel. The chip readout noise was 30 e~/pixel with a gain of 6 e ~ / A D U . Images of 12 galaxies obtained with the 60-inch telescope on Mt . Palomar, with re-imaging optics compressing the scale of the TI 800 x 800 C C D to l ."3 per pixel, comprise the second set of data. This collection of data was acquired during 1989 December 3-6 by Barry Madore. The TI chip has a readout noise of 8.7 e - / p ixe l and a gain of 1.6 e - / A D U . Hereafter, the Palomar data set will be referred to as the "northern set", and the Las Campanas images will be dubbed the "southern set". The former will be considered as our primary data source, due to its larger size, with the latter serving as checks on the photometry. The data used here is summarized in Table 3. The telescope used and the date of the observations are tabulated in columns 2 and 3, respectively. A n estimate of the seeing has been determined from the stellar profile of at least one coincident star on each frame, and is given in column 4. The exposure times for the images are shown in column 5. Note that some galaxies have had short and long exposure frames taken to compensate for saturation effects in the bright, nuclear region, - 42 -thereby extending the effective dynamic range of the observations. - 4 3 -(c) Data Reduction The galaxy images were de-biased and flat-fielded using the B A R F (Boro-son Astronomy Reduction Facility) reduction programs at the Observatories of the Carnegie Institute of Washington. The surface photometry was then fur-ther reduced and analysed with the G A S P (GAlaxy Surface Photometry) software package, written by Mike Cawson (GASP was kindly installed on the U B C V A X by Gerry Grieve). The various features and routines of G A S P have been outlined in considerable detail in Cawson (1984), Davis et al. (1985), and Cornell et al. (1987) so only a brief summary of the reduction routine will be given here. The main program in G A S P is known as P R O F (Cawson 1984). It is a F O R T R A N routine which assumes the isophotes in a galaxy image can best be described by ellipses. A n ellipse with a fixed major axis has its center, ellipticity, and position angle varied iteratively until the optimal fit for each isophote is found via a least squares regression. The intensity is sampled around a given ellipse as a function of the angle (6) from the major axis and can be represented as a Fourier series (see Jedrzejewski 1987 and Djorgovski 1985 for more general and complete treatments): 1(6) = IQ + asind + ficosd + 7 s i n 2 0 + £ cos 20 + ... (4) where I0 is the mean intensity. The coefficients a,/3,j and 8 will be zero for a perfect fit. In reality, the coefficients are non-zero and are directly related to errors in the ellipse parameters that have been adopted. The a and ft coefficients represent the magnitude of the error in the position of the center while 7 and - 4 4 -8 reflect the errors in the ellipse's position angle and ellipticity, respectively. In the P R O F program, these coefficients are changed by a specified amount until the largest coefficient is less than a certain threshold. This threshold depends on the ellipse size and a parameter entered by the user, which will be discussed later. Before P R O F can be applied to a galaxy image a few preliminary procedures must be performed. The D E V I C E and M A S K programs in the G A S P package are used to mask out foreground stars, HII regions and/or spiral arms which can perturb the smooth surface brightness profile and introduce spurious features into the ellipticity and position angle profiles. The masked regions are set to "don't know" values and are no longer incorporated into any of the ellipse fitting. Bad columns, rows and cosmetic defects of the particular C C D are also removed by masking. The estimation of a sky background for each C C D frame is an exceedingly important step in the reduction of surface photometry. G A S P has a program called B A C K which attempts to determine the background level of an image by finding the mode and mean for the histogram of the pixel intensities in the "margin" (typically 20 pixels wide) around the edges of the frame. However, this algorithm does run into problems when the galaxy extends right to the edge of the frame or when the margin is contaminated with bright stars that have not been masked. Instead of using B A C K , we used an interactive program called S K Y R E A D , which is part of the LIPS image display package written and implemented at U . B . C . by Gerry Grieve, to obtain mean intensity values for regions of the image (typically 50 pixels square) which appeared to be free of galaxy or star contamination. A n average of these independent sky level measurements was used as the background value for the frame. The error in the background was assumed to be the standard deviation of the several (typically eight) sky measurements. The images taken on the night of 1989 December 3/4 suffer from flat-fielding problems. Two approximately rectangular regions of the chip, which were located away from the position of the galaxy images (near the edge of the chip), showed a systematically higher and lower background (~2-3 % variation) than the adopted sky level. For the galaxies affected: N G C 4178, 4237, 4568 and 4579, the perimeter of each was masked at the faintest apparent light levels to ensure no contamination from the regions with deviant sky levels. It should therefore be emphasized that the sky background values determined for these images are not as accurate as those found for the rest of the sample. Nevertheless, since this study is primarily concerned with the surface photometry measurements in the innermost regions, small errors in the background determination shouldn't have a significant effect on our results. After finding a background and masking the frame, the galaxy center was determined, using the W I N D O W option in LIPS. The center was assumed to be the position of the pixel, found in the nuclear region, with the peak intensity. Extensive testing, using the I R A F image plotting package I M P L O T , showed that this center-finding approach was accurate enough for our purposes. Although P R O F can fit galaxy isophotes with ellipses with varying center positions, the centers of all the galaxies analysed were chosen and then fixed. The fixed centers cause the first order terms in Eq.(4) to be disregarded in the least squares regressions. This step was taken because all the galaxies in our sample are spirals and their isophotes can be irregular enough that ellipse fitting with a free center will not converge within - 46 -a reasonable number of iterations (less than 100). P R O F was executed on each galaxy image in three different modes. First, the position angle and ellipticity of the fitting ellipses were allowed to vary in the normal manner. The maximum number of iterations allowed per ellipse fit was set at 100, so some of the more irregular spiral galaxy isophotes would converge to a fit. The maximum residual factor (RESFACT) adopted was 10. This factor is used to set the threshold level for the residuals (coefficients), under which an individual ellipse fit is deemed acceptable. The threshold is given by: Threshold = RESFACT/VN (5) where N is the number of "samples" in the fit (Cawson 1984). One should note that for the innermost ellipse fits the samples are not independent pixel values, since there is a default of at least 40 samples per ellipse and bi-linear interpolation is used to evaluate intensities at non-integer pixel positions. This method of interpolation may cause some smearing near the galaxy center (Djorgovski 1985) where there is a significant intensity gradient. P R O F , in the free parameter runs, was typically set to analyse the galaxy's isophotes down to the background level. Generally, the algorithm would quit when the isophotes were a few percent above the sky. Any isophotes which appeared skewed, possibly due to a slow S / N ratio for the fit or from the influence of spiral arm structure, were deleted from the final profile. The second mode used for P R O F r i m s was with a fixed center, fixed position angle, and fixed ellipticity for the ellipses, essentially resulting in an intensity growth curve through elliptical apertures. The ellipticity and position angle used for each galaxy was found by inspecting the ellipticity (e) and position angle (p.a.) profiles from the first mode run. A n ellipticity is denned as e = 1 — b/a where b and a are the minor and major axes of the galaxy, respectively. Position angle profiles, to be discussed later, will follow the G A S P convention such that north is at 0° and east is at —90°. These profiles typically level off at some characteristic value once the disk of the galaxy begins to dominate the light profile, so, averages of these "constant" sections yielded the values Used for the intensity growth curves. These characteristic values of e and p.a. are listed in Table 4, in columns 2 and 3, respectively. Averages are given, of e and p.a., for those galaxies which are members of both the northern and southern samples. Note that the p.a. listed in Table 4 follow the regular convention such that north is at 0° and east is at +90° . The RSA morphological types of the observed galaxies, along with their radii (i^' 5 6) and total Gunn r magnitudes (rTb) (both with internal extinction and Galactic extinction corrections; see Tully 1988, Pierce and Tully 1988 and Dressier and Faber 1990), are also presented. Since seeing effects tend to circularize the isophotes at the smallest radii, P R O F was also executed so that mean intensities were found using circular apertures. Comparisons of the circular and elliptical aperture intensities are given, in the form of luminosity growth curves, with the final results in Section (e). - 4 8 -(d) Calibration The A P E R T program, in the G A S P package, was used to help determine a calibration for the surface brightness profiles. A P E R T is a simple circular aperture photometry routine which produces intensity growth curves for specified positions on C C D frames. The positions are marked, by the user, with an interactive cursor on a display screen. The southern sample was calibrated with frames of Landolt (1973, 1983) and Graham (1982) standards, taken at various times throughout the nights. Gunn standards (Thuan and Gunn 1976, Kent 1985) were observed for the calibration of the northern sample. In some cases, the standard stars were too bright for C C D exposures ex-ceeding a couple of seconds. To alleviate this saturation problem the brightest standards were de-focused. A P E R T was used to determine the total intensity of each standard star down to the background level. The sky background was deter-mined using the same technique as was described in the previous section, for the galaxy frames. It was discovered that the best way to distinguish between radii where photons were still being counted from the star and radii where it was at the background level, was by studying the variation of the mean intensity for each annuli in the aperture growth curve. Instrumental magnitudes were then taken from the point where the growth curves levelled off at the background (typically 10 - 15"). Since, the standard star observations did not have any one star observed over a wide range of airmass in a given night, extinction coefficients could not be determined directly. The mean extinction coefficients, kr = 0.10 and kr = 0.09, were adopted for the Las Campanas and Palomar data, respectively. The former coefficient was taken from the CTIO extinction table given in the I R A F package, and is known to be similar to the Las Campanas extinction value (Bob Hi l l , private communication, 1990). The latter coefficient was taken from Kent's (1985) observations of Gunn standard stars at Palomar. The total intensities obtained from A P E R T were corrected for exposure time to yield instrumental magnitudes and were then corrected for extinction. Since, the calibration stars for the southern sample were all Landolt and Graham standards, the following transformations from Bessell (1979) were used to obtain Johnson R magnitudes (Rj): (V-R)Kc = 0.73(V-R)j-0.03, (V - R)J < 1.0, (6) (V-R)KC = 0.62(V-R)j +0.08, 1.0 < (V - R)j < 1.7, (7) (note the typographical error in the original reference in Eq. 4), where the sub-script K C denotes the Kron-Cousins photometric system. The Rj magnitudes were then converted to Gunn r magnitudes (re) by applying the equation: rG = RJ + 0.43 + 0.15(5 - V)j (8) from Kent (1985). For the northern sample, observations of Gunn standards listed by Kent (1985), with accurate magnitudes, were used to obtain a calibration di-rectly. - 50 -The colour range of the standards used was restricted to stars with a (g — J " ) G > —0.56, where Kent (1985) lists this colour as corresponding to an AO spectral type. This is justified by the fact that a late-type galaxy's integrated spectrum will resemble a stellar spectrum no earlier than an A-type (Mihalas and Binney 1981). By limiting the colour range, we also diminish the importance of a colour term for our purposes in the calibration. Since, it is beyond the scope of this thesis to consider the added complication of colour gradients in spiral galaxies, the simplest approach is to have the calibration as a simple offset between the standard and instrumental magnitudes. A proper evaluation of a given galaxy's colour distribution would obviously require an image in another filter bandpass (besides rG)- Without this, one can only assume a mean colour for the galaxy. For the southern set, one night (February 21/22) had its zero point deviating ~0.25 mag, in the (re — r,-) vs. rG plot (where r,- is the instrumental magnitude), from the other two nights (which agreed to within ±0.02 magnitudes). The instru-mental magnitudes from this night were then differentially shifted to agree with the zero point for the remaining two nights. The northern set also had to have one night (Dec. 4/5) differentially shifted, 0.26 magnitudes, so, the zero points would agree. The night with the most data points was considered to give the "real" zero point. The final calibration equations used were the following: Northern set (10 standard observations): rG - n = 0.09X + 22.85(±0.07) (9) Southern set (16 standard observations): - 51 -rG - n = 0.10X + 21.63(±0.03) (10) where r,- are the instrumental magnitudes (inside the atmosphere) and X is the airmass. A n extra term, related to the C C D pixel scale, must be included in Eqs. (9) and (10) to convert rG to a surface brightness (fJ,r)- The calibrations, given by the above equations, are illustrated in Fig. 4, where the rG — r; coordinate has been corrected for extinction. - 52 -(e) Analysis and Discussion The final calibrated surface photometry is presented in Figs. 5 (northern set) and 6 (southern set). In the upper, lefthand corner of the plots, the surface brightness (Gunn r) profile, found by the "free solution" (varying e and p.a.), for each galaxy is shown. Surface brightness profiles obtained by fixing the e and p.a. (see Table 4 and Section 2(c)) are given in the lower, lefthand quadrants of Figs. 5 and 6. Errors in the surface photometry plots are a quadrature sum of the background error, calibration error and the standard deviations of the isophote fits (e.g., the F W H M of the histogram of intensities for each isophote fit). For the "fixed ellipse" or <fj.r> profiles, the errors in the isophote fits are replaced with errors. From the plots, one can see that the former errors are definitely more realistic. The dashed line in the surface photometry plots indicates the surface bright-ness of the background level (i.e., sky). A n apparent change in slope or "turning down" of some of the profiles, at large radii, is merely an artifact of the log scale used. This logarithmic scale is used so that the inner data points can be seen with less confusion. Ellipticity and position angle profiles, for each galaxy, are plotted in the upper and lower righthand corners of Figs. 5 and 6, respectively. Note that the e and p.a. data inside 10" have not been shown. The measures of e and p.a. at small radii are probably spurious because of seeing effects. Schweizer (1979) was the first to emphasize the importance of seeing effects on surface brightness measurements of the innermost parts of galaxies. Franx, Illingworth, and Heckman (1989) take the problem of seeing effects on surface photometry several steps further with their rigorous analysis of the light distribu-tions of seventeen ellipticals. They show, with a non-circular point-spread function treatment, that at radii as large as five times the F W H M of the seeing profile, the seeing can cause 10% errors in e and errors of several degrees for the p.a. Kent (1984) has found, empirically, that the e and p.a. values are meaningless for isophotes inside the radius equal to two times the seeing F W H M . We assume that this is also true for our data. For the final luminosity growth curves (see discussion below), at radii which are less than two times the seeing F W H M of the particular image, we use the surface brightness measurements taken from the fixed circular isophote P R O F runs (discussed in Section c). This is equivalent to the assumption that the observed innermost isophotes are circular due to a circularly symmetric seeing profile. A non-physical offset of the inner surface brightness data from the outer data is apparent in some of the intensity plots in Figs. 5 and 6 (extreme examples are: N G C 4192 and 4569 in Fig. 5). These discontinuous features in the profiles, which result from combining short and long exposure frames for the galaxy, are more evident in the fixed ellipse curves. The integration of the surface brightness profiles for production of luminosity growth curves, smooths these bumps. The more prominent bumps are probably due to images in the short exposures having low S / N ratios. The <fir> curves are probably not an accurate enough representation of the light distribution in the galaxies, for our purposes. The fixed elliptical isophote technique smooths over important details. As Kent (1984) comments, allowing "isophote twisting" (i.e.,.letting e and p.a. vary with radius) is the most realistic approach because a galaxy can have the bulge, disk, and potential bar or lens at different position angles. This inadequacy of the <fir> curves, with the physical structure of the galaxies being smeared out, leads us to use them for comparison purposes only. The luminosity growth curves further demonstrate that this is the proper approach. Integrating the fj.r, <fi,r>, and fixed circular isophote profiles for each galaxy yields the three luminosity growth curves given in Figs. 7 and 8. A simple inte-gration scheme has been applied. Each intensity measurement, at a given major axis radius Ri (of the fitting ellipse), is multiplied by the area (Ai) of an elliptical annulus, calculated using the following formula: At = w((Ri + (Ri+1 - Ri)/2)2 - (R{ - (Ri - J R i _ 1 ) / 2 ) 2 ) ( l - et) (11) where Ri+i, Ri-i are the major axis radii for the adjacent isophotes and ej is the measured ellipticity of the isophote at i?,-. The product of each intensity value and the area of the corresponding elliptical annulus is then summed as a function of radius to produce a luminosity growth curve. For the free solution, we make the assumption that the variation in the posi-tion angle of the isophotes with radius is not significant enough to consider it in our luminosity integration scheme. The position angle profiles, in Figs. 5 and 6, demonstrate the validity of this approximation for this particular sample, except perhaps for N G C 4535 and 4689. The p.a. variations seen for these two galaxies could be due to strong spiral arms (4535) or irregular (non-elliptical) isophotes - 55 -(4689). The errors displayed in Figs. 7 and 8 for the free solution curves, do not have the measurement errors of the isophote ellipticities folded in and consequently should be considered to be estimates or lower limits of the errors. A l l three luminosity growth curves shown asymptotically approach the total magnitude of the particular galaxy, as expected. It is interesting to observe the behaviour of the free solution growth curves with respect to the fixed growth curves, for different galaxies. As discussed earlier in this section, the most reasonable method in producing a luminosity growth curve is to use the fixed circular growth curve in the seeing dominated region and the free solution curve in the outer part. The composite luminosity growth curves for just the northern set are shown in Fig. 9. It should be emphasized that the circular growth data are used for radii less than two times the F W H M of the seeing profile measured for each galaxy. The transition between the circular growth and the free solution data is at a given luminosity, to avoid a contamination of excess luminosity (light sampled by both curves near the transition region). A plateau or discontinuity between the two data sets is apparent in most of the curves in Fig. 9. Total magnitudes from P T , for galaxies which overlap with their sample, are denoted by a dashed line in the plots in Fig. 9. These magnitudes have been uncorrected for Galactic and internal extinction and transformed to Gunn r magnitudes using the relation rG=-R;rc+0-36 (Dressier and Faber 1990), where RKC is the Kron-Cousins R magnitude from P T . Even though most of our luminosity growth curves are just beginning to level off at the total magnitude, it is encouraging to see signs of good agreement between our curves and the P T total magnitudes in Fig. 9. Since these discontinuities in the curves are non-physical, it is desirable to smooth them in some straightforward, reproducible manner. Two simple smooth-ing techniques are adopted and compared. First, a linear interpolation scheme is used with the caveat that a maximum of three data points are allowed to change on either side of the discontinuity. The points that are allowed to change in lumi-nosity, have their "smoothed" luminosities interpolated from the adjacent, fixed data points. The final luminosity growth curves for the northern set, which will be dubbed as the "smoothed" curves, are presented in Fig. 10. The P T magnitudes from Fig. 9 are also shown in Fig. 10. The second smoothing method is to offset the inner data points of the curves in Fig. 9, such that the discontinuity is no longer apparent. The offset used for each curve, is determined by finding an average offset of the circular growth curve from the free solution curve, in a radius range where both curves are well behaved. The offset is applied to all the data points interior to the discontinuity. Hereafter, we will refer to these curves as the "offset" luminosity growth curves. The offset luminosity curves are not shown due to space limitations but are similar to the plots in Fig. 10. The only difference in morphology of the smoothed curves and the offset curves is that the offset curves have inner data points with systematically lower luminosities. It would appear that the smoothed curves are more convincing a representation of the luminosity growth than the offset curves because fewer data points are altered and the smoothed data are interpolated while the inner offset data are extrapolations. On the other hand, the smoothed curves assume the inner isophotes are circular and this is not necessarily true. We use both the smoothed and offset luminosity growth curves in the production of L - V diagrams in Chapter 4 and compare the results. It is instructive to compare the luminosity growth and ellipse fitting parame-ters for those galaxies which are members of both the northern and southern sets. Residuals between the composite luminosity curves are displayed in Fig. 11, with the magnitude coordinate in the northern set minus southern set sense. Linear interpolation is used to match up luminosity, e, or p.a. measurements which are at non-coincident radii. It is very important to note that there will be errors in-troduced into the residual profile by the different seeing profiles of the two C C D frames. Also, since we are comparing the composite luminosity curves, there will be non-physical effects introduced into the residuals by the kinks in the growth curves which were discussed earlier in this section. These two effects suggest that the seeing dominated region (i.e., radius<10") should be ignored in the residual plots. Any discussion regarding the residuals should include the two aforemen-tioned caveats, with the realization that these plots are a simplified first-order comparison. The residuals in the 10"-100" region show that the luminosity growth curves agree reasonably well, except for some systematic problems which could be cal-ibration dependent. The galaxies N G C 4192, 4216, and 4535 have very good agreement between the northern and southern sets, except for some fluctuations at large radii. Luminosity residuals of both N G C 4501 and 4569 show a system-atic difference of approximately minus two or three-tenths of a magnitude. The N G C 4501 residuals show more of a trend of increasing disagreement between the growth curves with increasing radius. A systematic offset could have occurred for - 5 8 -N G C 4501 and 4569, due to a calibration problem, since these two galaxies were observed on the same nights for both the northern and southern sets. Also, for the southern set these two galaxies were observed on the same night which had the standard star's zero point differentially shifted 0.25 magnitudes (see Section d) to agree with the standards from other nights. By far, the worst case of disagreement between the luminosity curves is for N G C 4654. This galaxy's residuals show a systematic difference of ~0.6 magnitudes. The probable cause of this offset is a disagreement between the calibrations for the two data sets. We note that N G C 4654 was the only galaxy observed in our southern set on the night of Feb. 27/28. It should be noted that any calibration problems will only effect the ILB zero point comparison between data sets. The ILB slope determinations wil l be inde-pendent of any differences between the calibrations of the northern and southern data sets. We will average the ILB slopes obtained from the northern and southern sets in the final analysis, but the analysis of the ILB zero points will have to be segregated according to data set. Ellipticity and position angle residual plots are given in Figs. 12 and 13. The difference between the seeing profiles for the two C C D frames for each galaxy, must still be considered, especially for galaxies with strong spiral arm structure (NGC 4535 and 4654). The fluctuations seen in the e and p.a. residual profiles for these two galaxies are probably related to differential seeing effects. However, in general, the e and p.a. residual plots show little scatter. This agreement bodes well for our luminosity growth curves. For a sample of elliptical galaxies, Smith and Heckman (1989) have claimed that isophote fitting with G A S P gives position angle measurements good to within ±7° and ellipticities good to within ±0.04. Poorer seeing for our galaxy frames and the neglect of differential seeing effects between data sets both contribute to the higher scatter apparent in our residual plots. - 60 -T A B L E 3 Journal of Surface Photometry Observa ions Galaxy Telescope Date Seeing ( F W H M ") Exposure w N G C 4178 60 03/12/89 3.3 300 N G C 4192 60 05/12/89 3.9 30 + 200 40 25/02/87 2.6 240 N G C 4206 60 04/12/89 4.0 200 N G C 4216 M i l 60 04/12/89 3.8 30 + 200 40 25/02/87 1.9 60 N G C 4237 60 03/12/89 3.5 200 N G C 4501 60 05/12/89 3.5 30 + 200 40 21/02/87 2.3 120 N G C 4535 60 04/12/89 3.1 30 + 200 40 21/02/87 2.0 180 N G C 4568 60 03/12/89 3.0 200 N G C 4569 60 05/12/89 3.4 30 + 200 • • 40 21/02/87 2.3 10 + 180 N G C 4579 60 03/12/89 3.6 30 + 200 N G C 4654 60 04/12/89 2.9 200 40 27/02/87 3.0 90 N G C 4689 60 04/12/89 3.2 200 - 61 -T A B L E 4 Parameters Of Galaxies Wi th Surface Photometry Galaxy Type (RSA) € P .A. (degrees) •"-25 (arcsec.) rj (1) (2) (3) (4) (5) N G C 4178 SBc(s)II 0.73 33 120 11.08 N G C 4192 Sb l l : 0.80 149 198 9.53 N G C 4206 Sc(s) 0.80 180 111 11.67 N G C 4216 Sb(s) 0.80 200 171 9.23 N G C 4237 Sc(r)II.2 0.36 108 63 ... N G C 4501 Sbc(s)II 0.52 142 165 9.20 N G C 4535 SBc(s)I.3 0.32 197 186 9.91 N G C 4568 Sc(s)II-HI 0.62 24 132 ... N G C 4569 Sab(s)I-n 0.63 18 234 ... N G C 4579 Sab(s)II 0.11 65 159 9.30 N G C 4654 SBc(rs)II 0.46 122 132 10.24 N G C 4689, , Sc(s)IL3 0.29 156 111 10.86 (l) classification from R S A (Sandage and Tammann 1981); (2) and (3) this work; (4) Tully (1988); (5) Pierce and Tully (1988) and Dressier and Faber (1990) - 62 -22.5 | —l I l l 1 I l I l I i I l l I l l l l I I I I I j i i I I I I M I | I N 22.6 — 22.7 C 22.8 I 22.9 23 23.1 Northern Sample Calibration I I I I I I I I I I I I I I I I I I I I 1 I I I I l I I I I I I I I I I I L 9 9.5 10 10.5 11 11.5 12 r c 21.3 21.4 21.5 21.6 21.7 21.8 21.9 i — i — | — i — i i i | i i I i | i i i I | r n — I — i — i — i — i — I — i — r Southern Sample Calibration l 1 l I I l 1 I I I I I I I I i I i i i l I i i i i I i c 11 12 13 14 rG 15 16 Figure 4.—The calibration plots for the northern and southern sets L Gunn standard magnitudes are denoted by rG and r; are the instrumental magnitudes. 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T 16 18 20 22 24 16 18 20 22 24 ~ i — l l l l 11 l i 1 — l l l 1 1 l l NGC 4579 _ x x x +H • i i i 111 n i i i i 111 n i T 1 — i — I I i I I x x x > X X X x x X X X H—I I I 1 1 11 1—I—\ - x x x X X X x x x x x x x x X x X " J I x x X I X 10 100 Radius (") 10 100 Radius (") .8 .6 .4 .2 'o • l-l (X • r-t i—< W 50 7 - 0 - 5 0 o o Fig. 5-cont. 16 18 20 22 24 16 18 20 22 24 1 — I I I I 1 1 1 [ 1 — I I l I 1 1 1 1 NGC 4654 " i—r-o t - * f Hi F 8 « « . ****** *xxnr. I I I I 111 l l I I I I I I I i , x x 1 1—I—I I I I x . . x - H -< x x x x x x x x x x x x x x x ^ x x x x x x x x x x x x x 10 100 Radius (") 10 100 Radius (") .8 .6 .4 .2 • FN • r—i w H — h 50 o" 0 1—4 a o CO -50 £ Fig. 5-cont. 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I I 1. f r W - f X r I 'i v i 1 I v r i ' I ' I ' I ' I ' X X 11 i x: . t i , x X X O o cn o l I i i i I i i i I i i ro co oo Posit ion Angle (°) E l l i p t i c i t y CD 16 18 ^ 20 22 24 16 18 3 2 0 22 24 0 1 1 M I I H | 1 1 M i l l NGC 4535 If: 1 I I I I I I I H- x * * x * x x » ***** Xxx; -\ -1 I 1 1 l I i i ml i I i • X x X x x ' X ,x X 10 100 Radius (") J_L 10 100 Radius (") .8 .6 .4 .2 'o a, 3 50 a> i-H bo o J I L M - 5 0 o Fig. 6-cont. - 0 8 -P o s i t i o n Angle (•) E l l i p t i c i t y 16 18 20 22 24 16 18 20 22 24 1 i i i n i | i—i i i i m i NGC 4 6 5 4 * ****** ++ X X ' * * » B x ' x x x x < x x x x x ; **** ^ _n. -J—i i i i n i l 1 i i i 11 n i , , , x x I I I I I I I < x x x X - x x x x X X x A * x X X X X v v X X X X x xx x x x x x x x x x ' 10 100 Radius (") 10 100 Radius (") n r .8 .6 .4 .2 4-1 o a 50 C! o - 5 0 ° Fig. 6-cont. rH rt "1 1 I I I I 1 I 1 1 1 I I NGC 4178 J I i i i i i -J ' i i i i i i 1 0 Radius (-) 1 0 0 U — "1 I i I I I I I I I I I I I T T tltffi I I I 1 1 I NGC 4192 J I I ' i i i i I = I I i i i 1 0 1 0 0 Radius O Figure 7.—Luminosity growth curves for galaxies in the northern set . The lumi-nosity coordinate is in Gunn r magnitudes. Data points plotted as square boxes are the fixed circular growth, the x's denote the free solution and the triangles correspond to the fixed elliptical growth curves. - 82 -O U_ I I I I I I I I NGC 4206 J I ' ' ' i i i i i i i i 1 0 Radius (") 1 0 0 1 1 I I I I I I I I I I filiate NCC 4216 i i i i i i i i J I I 1 0 Radius (") 1 0 0 Fig. 7-cont. - 83 -Fig. 7-cont. - 8 4 -- i 1 — i — i i i i i I 1 1 — i i i i i i i i r o Li-eu NGC 4535 i i i i i i i i I - i I I I I I I ) 10 Radius (") 100 U -1 1 1—I I I I I I 1 1 I I I I ' ' 0 NGC 4568 I I I I I i i i I • I I I I I I I I I 1 1 L 10 Radius (") 100 Fig. 7-cont. - 85 -n 1 — i — i i i i i i I .••as* 1 NGC 4569 1 1 1 • 1 i i i i i 111 - i • ' ' 1 0 R a d i u s (") 100 .'1 1 I 1 1 1 1 | 1 1 1 i i i i | l 1 1 i W -I I — I -: i — ~. i NGC 4579 i i i i i i i 1 i i i 1 1 1 1 1 1 1 i i 10 R a d i u s (") 100 Fig. 7-cont. - 86 -Fig. 7-cont. - 8 7 -"1 I 1 1 — I I I ! "I 1 1 1—I I I I I1 I I **** NGC 4192 _J I I i i i i ' ' i i i t t 10 i I I I I i i i R a d i u s (") 1 1 1— i I I I I | 100 •I i I l I I i NGC 4216 i i i i i i i i i i i I I I I I 10 R a d i u s (") 100 Figure 8.—Luminosity growth curves for galaxies in the southern i set. The lumi-nosity coordinate is in Gunn r magnitudes. Data points plotted as square boxes are the fixed circular growth, the x's denote the free solution and the triangles correspond to the fixed elliptical growth curves. - 88 -Fig. 8-cont. - 89 -Fig. 8-cont. - 90 -NGC 4178 o t_l_ i i i i i i i i i i i i i i i I I I l _ 10 Radius (") 100 n 1 — i — i — i i i i | 1 1 — i — i — r r r T i i i r NGC 4192 j j i i i i i i i i I i i l l I I 1_ 10 Radius (") 100 Figure 9.—Composite luminosity growth curves for galaxies in the northern set The dashed line is the total magnitude for the galaxy, listed by Pierce and Tully (1988), which has been uncorrected for internal and Galactic extinction. ~ i i i i i i I I I i i — i — i — i i i i i 1 i r T t f i l H l 1 NGC 4206 J I I I i i i i J I I I I I i I I I L_ 10 Radius (") 100 " i 1 — i — i — i i i i I 1 1—i—i— i i i i | i 1—r . i U L I I -NGC 4216 J i i I I I I 1_ 10 Radius (") 100 F i g . 9-cont. - 92 -~ n i i i i i i i i i i i i i i i i i i i r t I u un H NGC 4237 J I I I I I I I I '-. I I I i i i i i I I I [_ 10 Radius (") 100 ~1 I I I I I I I I I I 1 I I I I I ~i—r I IS o Li-eu NGC 4501 i i i i i i i i I i i i i i i i i I 1 \ 1_ 10 Radius (") 100 F i g . 9-cont. - 93 -n 1—i—i i i i I 1 i i i i i i i -1 I I 1 1 NGC 4535 i i i I l M i i i i i i i i I l i _ 10 Radius (") 100 T 1 1 1 I I I I I 1 1 1 I I I I I I I I r I i 1 III o L i i i I I I I I NGC 4568 I : i l l 1_ 10 Radius (") 100 F i g . 9-cont. - 9 4 -"1 I I I M i l l I 1 1 1—I | I i ~\ r . i 1 i *1 NGC 4569 _ l l J i i i i J I I i i i i i I I I i _ 10 Radius (") 100 I I I I I I I I I I I I ~i 1— r n ' 1 ,1 *! o Ll_ NGC 4579 - I— I I I I I I d 1 I I i i i i i I i i i 10 Radius (") 100 F i g . 9-cont. - 9 5 -NGC 4654 -1-1 1 1 1—I I I I I I i I I i i i i i i 10 Radius (") 100 ""> I I 1 — I I I ! "1 I I I I I I I NGC 4689 1 1 1 ' ' * i 1 1 I i i i i i I 1 0 Radius (") 100 Fig. 9-cont. - 96 -10 ~~i i i i i i ' i i i i i i i i i r~r~ 12 16 NGC 4178 _i I I i ' ' ' _ i i i i i ' ' i i ' i i 10 100 : Radius (") n 1 1 1 i i i i | 1 1 , — i — i i i i - i 1 r 10 12 £ 14 16 - — J — 1 It II* 18 NGC 4192 —i 1 I i i i i i I -1 1 1 1 I L - i _ : Radius (") 100 Figure 10.—Final "smoothed" luminosity growth curves for galaxies in the northern set . The dashed line corresponds to the same value as in Fig. 9. - 9 7 -10 1 I I I I > I I I | i ] i i ! 12 14 -I — ! * « --16 - -18 "l 1 J i 1 1 NGC 4206 I I I 1 * t I r i i i i 1 1 i -1 10 . 100 Radius (") 10 _' 1 I I 1 • i i j i i i i i i I i | i i i . I " i 12 I I I z I I ' -14 I I — 18 -18 i 1 1 I t ( NGC 4216 i ' « 1 • i i i i t i i 1 i i 1 10 100 : Radius (") F i g . 10-cont. - 98 -" i i 1— i — i — r - r " i i — i — i — i i i 10 12 16 18 . 1 * I' NGC 4237 — i — i l i l l . 10 -1 1 1 I I L _ l _ Radius (") 100 10 12 ~ l I I I — I — I I I " 1 1 — I — I — I I I 1 1 r E I J J 11 NGC 4501 -J 1 — i i i i ' Radius (" Fig. 10-cont. - 99 -i I i i i i i r~ ~ i 1 r 12 14 16 18 NGC 4535 _l 1 1 I I L _L_1_L t 1 I I I I Radius (") ~~[ 1 1 1—I—i—I i i | 1 i 1—i—r 1 1 r 10 12 iH 18 NGC 4568 -I 1 I I I L_ —1 I I I ' ' ' I 100 Radius (") Fig. 10-cont. - 100 NGC 4569 -i 1 1 i I I I I I l l i ' i i i i I i i i 10 . 100 I Radius (") "i I I I I I l I I 1 1—i—i—i i i i 1 1 r 12 h , i J ! ! I. I I 16 1 8 NGC 4579 -l 1—i I I I i I i i i i i i i i I 10 . ; Radius (") Fig. 10-cont. 101 NGC 4654 - 1 1 1— ' i i i i I 1 1 i i i i i i I 10 100 ; Radius (") "i 1 1—i—i—r ~i 1 i—i—I I I I 12 III 14 16 IS NGC 4689 - 1 1 1 ' i i i . I 10 -* 1 1 ' ' ' ' Radius (") 100 Fig. 10-cont. - 102 -o w in I CO 1—1 cd • i — i c/i o 0.4 0.2 E-0.0 -0.2 E --0.4 0.4 0.2 0.0 -0.2 -0.4 0.4 0.2 0.0 -0.2 -0.4 i i i 111ii 1—i i 1 1 1 i n r i — i i 1111 i — i i i 11 M I 1 — n g NGC 4192 " A * * * A w * * * * NGC 4216 4 A A A A A * A M * * * * * * * * A A » * A * .*** A A * ^ NGC 4501 V A * N ^ ^ ^ NGC 4535 A A A A A A A * * * A * A -t-f I I Mill > I l | — H - f NGC 4569 " " ' " ' I K ' U l l ^ NGC 46j&4 A A * A J m i i i i i i nil i L m  I I I I 11 ll I I I I I I .4 .2 0 -.2 -.4 .4 . -3 .2 -= 0 -3 -.2 -.4 .8 .6 -3 ,4 .2 0 J I H 10 100 Radius (") 10 100 Radius (") Figure 11.—Magnitude (Gunn r) residual plots between the composite luminosity-curves for galaxies in the northern and southern sets • (in the north minus south sense). 20 J l l 1 1 1 1 1 1 1 1 ANGC 4192 1 1 _ _ 1 1 1 1 1 1 1 1 1 1 NGC 4216 1 1 1 _ 20 0 — A " A A A * A A A " A A a A A i A A A ± A A A A A A - A A A A A A A A A A A * A A A * A A A A A * A A A A A A A A A A A A A A 0 -20 "I 1 1 ! 1 M I N I 1 1 ~ 1 1 l l l l l l 11 I | - 2 0 20 0 J 1 1 A A i ! 1 1 1 II II NGC 4501 A A A A A * A A A A A A A A A * 1 A * A A A A ± 1 _ _ 11 A i A A 1 1 1 1 1 1 11 NGC 4535 A 4 A ^ k A A A A A A 1 1 A A A 20 0 -20 "i 1 1 1 1 1 II 1 1 1 1 1 1 " 1 1 1 1 1 1 1 1 1 1 1 1 - 2 0 20 J 1 1 1 1 1 1 1 1 1 1 NGC 4569 1 1 1 _ 11 1 1 1 1 1 1 1 1 A NGC 4654 1 1 20 0 -20 A A A A , A * ^ A A A \ A * A A A A I A , A A A A A A A A A * A A A * A < A - ' A A A * A A * A A * A A * A \ — 0 -20 " i i 11 "I 1 1 ~ " I I I l 1 1 1 1 1 l 1 1 1 1 " 10 100 10 100 Radius (") Radius (") Figure 12.—Position angle residual plots between the composite luminosity curves for galaxies in the northern and southern sets (in the north minus south sense). 0.4 0.2 0.0 -0.2 -0.4 0.4 0.2 0.0' -0.2 -0.4 0.4 0.2 0.0 -0.2 -0.4 FTTT"| r — i — i i i i 111 r NGC 4192 1—I -4-1 I I A A A 4 A ! 1 1 M i l l NGC 4216 • A A / A / V " A A 4 * A A A A A A A A A A A A A A A * A ^ A A A A A A A A A A -3 -4 .2 -=\ o NGC 4501 NGC 4535 A A A A A A A A A * * * \ A * * * " * * A A A A A A A A A A A A A A * A A A J * A . A A A K A " A A A A A I I I 1 I NGC 4569 H — H -' A A . A A A A A A A A A A ^ - - A A A a NGC 4654 A . . * A . . A . A A * A A A ^ A * • H i I I I I I 1 I 11 l l I I I I I J L 10 100 Radius (") 10 100 Radius (") F igure 13.—Elliptici ty residual plots between the composite luminosity curves for galaxies in the northern and southern sets (in the north minus south sense). 4. L - V D I A G R A M S (a) R e d u c t i o n Procedure Once the rotation curve and the luminosity growth curve of a galaxy have been determined, producing its L - V diagram is a straightforward procedure. Be-fore we can proceed to the combination of our velocity and luminosity data sets described in Chapters 2 and 3, respectively, some refinements and additions must be considered for our sample. Wi th the exclusion of the Seyfert galaxy N G C 4388, as discussed in Section 2(d), the number of galaxies in our sample with optical rotation curves is lowered to eight. Rotation curves of the four galaxies N G C 4178, 4237, 4568, and 4579, for which we obtained photometry were kindly provided by Vera Rubin (see Rubin et al 1989). Some smoothing of the rotation curves must be tolerated because the velocity measurements from different emission lines, and from different sides of a galaxy's nucleus for the same emission line, can cause significant scatter in the final rotation curves. This is demonstrated by some of the curves in Fig. 2. We take the simple approach of binning the data. For the rotation curves produced in Chapter 2, the velocities were averaged over 4" bins and the error was taken to be the standard deviation of the measurements occupying each bin divided by the root of the number of data points in the bin. Each velocity measurement was weighted equally since no errors are available for individual data points. The bin size was chosen to correspond to the maximum F W H M of the seeing profile for the rotation curve spectra. For the velocity profiles obtained from Rubin the bin size had to - 106 -be increased to 5" ( N G C 4568 and 4579) and 6" (NGC 4178) in order to yield a smooth final curve without non-physical discontinuities. A weighted mean for each velocity bin was calculated for the Rubin et al. (1989) data along with a variance of the mean using the measurement errors provided by Rubin. The velocities have already been corrected for inclination (i) but the luminos-ity growth curves have not. A correction scheme described by Tully and Fouque (1985) for inclination-dependent extinction (AlB) was adopted; we corrected to a face-on orientation using their Eq. (5). For galaxies with i>80°, a constant value of AB=AB° was assumed. Also, the Burstein and Heiles (1984) Galactic extinc-tion corrections were applied. Since our observations were made in the Gunn r bandpass, the sum of the two extinction corrections is multiplied by 0.56; i.e., A l r ^=0 .56A^ , (Dressier and Faber 1990). Following these corrections, the luminosity growth curves are then combined with the velocity profiles to yield L - V diagrams. Velocities are determined by us-ing a simple linear interpolation scheme applied to the rotation curve at the radii where there are corresponding luminosity curve data points. If just the binned (in-dependent) velocity measurements are used (interpolating the luminosity curve), the L - V diagrams which result are sparse. It should be noted that with the in-terpolation method we have adopted, the data points in the L - V diagrams are not, in general, going to be independent of each other. The limiting factor is the seeing for the rotation curve since this is almost always worse than the seeing for the surface photometry. The final L - V diagrams are shown in Fig. 14 for the northern set and Fig. 15 for the southern set, where the smoothed luminosity curves from Section 3(e) - 107 -have been used. The initial linear branch (ILB) is readily apparent in each L - V diagram. The last point of the ILB was defined to be the last point in the L - V growth curve before it turns up from the initial linear portion, at a reasonably large velocity (~100 km/s). This point is easily ascertained in our plots and is shown in Figs. 14 and 15 by a dotted line. Also, a linear regression to the points in the ILB is represented by a solid line in these diagrams. Asterisks denote the P T Tully-Fisher points for those galaxies which overlap with their sample. The P T magnitudes and extinction corrections have been transformed to the Gunn system, using the relations previously noted from Dressier and Faber (1990). Further analysis of the L - V diagrams is given in the following section. - 108 -(b) Analysis and Discussion Before discussing the implications of our L - V diagrams with respect to the physical basis of the T-F relation, we will first consider the viability of the ILB as a distance indicator. Parameters calculated from each galaxy's ILB are presented in Table 5 for the L - V diagrams produced using the two types of luminosity growth curves: smoothed and offset. A slope is determined from the linear regression of all the points, equally weighted, in the ILB. The final slope adopted is shown by the solid line in Figs. 14 and 15, except for N G C 4579. Values given in brackets for this galaxy, in Table 5, are used in the final analysis and represent the regression coefficients obtained when the first five data points are included. The unbracketed values tabulated for N G C 4579, are from the regressions which do not include the first five data points. These initial few data points mark a discontinuity which could be due to non-circular motions measured by the rotation curve. There is no distinct bar present in this galaxy. The zero points have been calculated for (logV r o* - 2.0) as the abcissa (following Freedman 1990), where Vrot is the rotational velocity. Calculating the intercept in this manner, greatly reduces slope correlated errors and is more representative of the data we are analysing than an intercept at log Vrot = 0. Galaxies in Table 5 with an "S" appended to their names are members of the southern data set and the slopes and zero points listed were determined from their respective L - V diagrams. Differences between the ILB slopes obtained from using the smoothed or offset luminosity curves are apparent in Table 5. Not surprisingly, the ILB slopes are systematically steeper for the L - V diagrams utilizing offset luminosity curves. - 109 -Comparing the slope (smoothed) determinations for galaxies which are in both the northern and southern data sets, we find an average difference of ~ 0.4. The ILB slopes for the "offset" L - V diagrams agree slightly better between the two data sets. It should be emphasized that any potential systematic error between the northern and southern calibrations will not have an effect on the ILB slopes calculated for a galaxy in both sets. This kind of error is just equivalent to a zero point shift for the magnitude coordinate. Obviously, the ILB zero points determined for a galaxy cannot be compared between the northern and southern sets since they depend on the absolute calibration. As another check on reproducibility, we produced L - V diagrams for three galaxies (NGC 4501, 4569 and 4654) with rotation curves from Rubin et al. (1989) instead of using our velocity profiles. The Rubin data was coupled with our smoothed luminosity growth curves from the northern set and the resultant L -V diagrams were then compared to our final diagrams. The agreement between the L - V diagrams with these independently measured velocities, was good and the difference in the ILB slopes was found to be only ~ 0.2 for the worst case. This test would suggest that our technique for obtaining the rotation curves is not influencing the value of the ILB slope to any significant degree. Two histograms of the distribution of the ILB slopes (smoothed) for the 12 galaxies in our set are shown in Fig. 16. The histograms axe shifted half a bin with respect to each other to demonstrate that there is no significant dependence of the distribution on the binning. It is a flat distribution with no distinctive peak but, of course, one cannot claim anything definitive since we are dealing with small number statistics. The galaxies which had L - V diagrams produced from - 110 -the northern and southern data sets, are represented by the average of the two ILB slopes. For all twelve galaxies, the average ILB slope is 2.51±0.87 for the "smoothed" and 2.79±1.06 for the "offset" L - V diagrams. A dispersion for the ILB slope this large is surprising in view of the results from M W . This point will be discussed later in this section. It should be emphasized that the slopes given above and any T-F slopes mentioned later in this section are not dimensionless values but have units of mag/dex. In other words, the slope of the T-F relation is not equal to the exponent (a) of the power law (LocV a ) discussed in the introduction. A histogram of the ILB zero points is plotted in Fig 17. The solid and dashed line histograms show the ILB zero point distributions for the northern and southern sets, respectively. Mean values for the two data sets are 13.29±0.90 mag for the north and 12.81i0.81 mag for the south. Wi th such a large dispersion in the "zero point", one is probably justified in dismissing the ILB in L - V diagrams as a distance indicator for spiral galaxies. However, one would still like to understand why the scatter in the ILB slope and zero point is so large and, to ascertain if this behaviour has any implications for the T-F relation. Since L - V diagrams are produced to probe the T-F relation on a more de-tailed level, it would be prudent to check how our sample behaves in a T-F plot. Magnitudes and line widths obtained from P T , for the nine galaxies which overlap with our sample, are plotted in Fig. 18 to demonstrate that the T-F relation is present. The dotted line is a linear regression with the errors solely in the mag-nitude coordinate and the dashed line is a fit with the errors in the line width dimension. The slope we calculate for the mean of these two regressions (double regression) is -6.54, slightly less steep than the P T slope value of-7.64±0.29 found - I l l -for the full Virgo sample of 34 galaxies. The rms dispersion for our nine galaxies is only 0.25 mag. This is well below the dispersion of 0.47 mag quoted by P T for their R-band T-F relation for all their Virgo galaxies. This suggests that our sample of galaxies is well behaved with respect to the T-F relation. The spatial extent of the ILB for each galaxy is summarized in Table 6. Isophotal, extinction-corrected radii (-R25) w e r e taken from Tully (1988) to scale the spatial parameters in order to show the relative spatial coverage for each galaxy in our sample. The first column in Table 6 gives the number of data points in the ILB and the second gives the F W H M of the seeing profile (cr) for the surface photometry scaled by R1^. The scaled radii of the first and last data point in the ILB are given in the third and fourth columns. In the fifth column the scaled radius corresponding to the last point in the L - V growth curve for each galaxy is tabulated. A perusal of the radii in the final column makes it immediately apparent that the two galaxies with the worst spatial coverage in their L - V diagrams are N G C 4192 and 4216. This is simply because these two galaxies had rotation curves which did not extend very far from their respective nuclei. The most important point to be made from the radii tabulated in Table 6 is that the total spatial extent (RjLB — RjLB) of the ILB for the galaxies in our sample, is, in general, only a few times the F W H M of the seeing profile. In four cases, the spatial extent of the ILB is less than twice the seeing F W H M estimated for the surface photometry data. In these cases the ILB data points are sampled only in the seeing dominated region. It is remarkable that the ILB slope doesn't exhibit even larger scatter than what we observe. In light of this sobering inspection of the spatial extent of the ILB, we decided - 112 -to re-analyse a subsample of the field galaxies studied in the initial L - V diagram study (MW) . L - V diagrams were determined for 36 galaxies, which appeared to have "normal" L - V growth curves, from the original sample of 46. Two basic conclusions were made from this re-analysis: (1) It was discovered that the technique used in M W to calculate the L - V growth curves was biasing the slopes of the ILB in a very subtle manner. Using the more objective method of determining the L - V growth that we have outlined and utilized in this work, the dispersion in the ILB slopes for the field galaxy L - V diagrams was found to be much larger than previously thought (at least comparable to the dispersion seen for Virgo L - V diagrams). (2) The typical scaled spatial extent of the ILB (R1^8 - RjLB) for the field L - V diagrams showed a smaller range in radius relative to the scaled seeing profile F W H M (for the surface photometry used) than in the Virgo sample. The probable reason for this is that the field galaxies studied are commonly at distances larger than that of the Virgo cluster, suggesting that an ILB for a galaxy which is a member of Virgo will , in general, be better resolved. It should be noted that the scaled ranges in radius for the ILB for field and Virgo cluster L - V diagrams were found to be similar. Since our sample of Virgo cluster galaxies has better spatial resolution than the field sample in M W , there is no evidence to support an ILB slope with a dispersion of less than ~0.9. In addition to the large dispersion in the slope there is also a large dispersion in the zero point of the I L B . As mentioned earlier, 0.9 mag scatter in the ILB zero point appears to nullify the potential of the ILB as a distance indicator. However, there is a different approach that we can take with - 113 -respect to L - V diagrams which proves to be useful. In Fig. 19, L - V diagrams determined for the northern set are offset in lu-minosity and log(velocity) such that the final point in the ILB is coincident for each galaxy (NGC 4579 is the "standard" to which the other galaxies are shifted). From this overlay plot, one can see that the morphology of the L - V growth curves are quite similar. The substantial scatter in the slope of the ILB is quite apparent from Fig. 19. It is immediately obvious that if we desire to characterize each galaxy with a physical feature that is well measured, the only feature in L - V dia-grams left to consider is the last point in the I L B . There is no clearcut similarity between the L - V growth beyond this point and and there is no other discernible common feature occurring in the curves. The last measured data point in the ILB has the positive attribute of being at a radius, for the galaxies in our sample, which is generally outside the seeing dominated region (two times the F W H M of the photometry seeing profile). Seeing-induced errors to the luminosities and velocities will therefore be minimized. There is also the added bonus that the final point in the ILB measures something physical in each galaxy, this being the termination of the solid-body part of a rotation curve where the velocity profile is beginning to level off. The velocity coordinate for this point does not correspond to the maximum rotation velocity in general, although it may for some galaxies (e.g., N G C 4192, 4216, 4579). The magnitude of the ILB termination point (rGLB) is plotted versus its ve-locity coordinate (log VjLB) for all the galaxies in the northern data set in Fig. 20. A mean (double) linear regression to 10 of the galaxies (filled boxes) is repre-sented by the solid line. Dashed lines mark the regressions with the errors solely - 114 -in the magnitude (shallow slope) and the velocity (steep slope) coordinates. Two of the galaxies in our sample of 12 (denoted in Fig. 20 by stars) are rejected for the following reasons. The rejected galaxy with a brighter r G L B magnitude is the well known fore-ground galaxy N G C 4569 (see Tolly and Shaya 1984 and references therein). Other workers are in agreement that N G C 4569 is at about half the mean cluster dis-tance. If one compares the magnitude we obtain for the ILB termination point for this galaxy to where it should be on our mean relation found for Virgo members, it appears that it should be even closer. It is possible that the VjLB value we have determined for N G C 4569 is in error since the galaxy has a substantial bulge. Our emission-line rotation curve may not be tracing the true circular velocity in the bulge-dominated region, as noted in Chapter 2. The other rejected galaxy is N G C 4568 which is a member of an interacting pair with N G C 4567. This galaxy was studied by G v G K B and they claim that its velocity field is not disturbed by the companion. However, they have insufficient resolution (45") to delineate the detailed velocity field. Also, Rubin et al. (1989) point out that the optical and 21 cm systemic velocities for N G C 4568 disagree by 50 km/s. Clearly the HI velocity measurements are uncertain. Both rejected galaxies were not included by P T in their T - F analysis of the Virgo cluster. A correlation coefficient of 0.95 is found for the mean relation shown in Fig. 20 for the remaining 10 galaxies, with a dispersion of 0.4 mag. The slope for the double regression is -6.59 which is in excellent agreement with the slope of the T - F relation (-6.54) plotted in Fig. 18 for the nine galaxies from P T which coincide with our sample. The dispersion of 0.25 mag found for the P T subsample - 1 1 5 -compared with our scatter of 0.4 mag suggests that the scatter in the T-F relation is increasing as the luminosity and velocity are sampled at smaller radii. This result must be treated as preliminary due to the small size of our sample. The true dispersion of the T - F relation has been a controversial issue among workers on the extragalactic distance scale. For the Ursa Major cluster, P T esti-mate the intrinsic dispersion (dispersion which excludes measurement uncertain-ties and depth of the cluster) in the T-F relation to only be ~0.25 mag. In a recent study, Fouque et al. (1990) calculated the intrinsic dispersion of the blue T-F relation for an "almost complete" sample of Virgo galaxies to be ~0.5 mag. Kraan-Korteweg, Cameron and Tammann (1988, K C T ) have found scatter in the blue and IR T-F relation as high as 0.7 mag. Burstein and Raychaudhury (1989) conclude that the K C T result is due to the use of inaccurate, older magnitudes and the inclusion of noncluster members in the Virgo sample. They agree with P T that the true scatter is less than 0.4 mag. It is justifiable to treat the luminosity-velocity relation that we have plotted in Fig. 20 as a specialized T-F relation. Bothun (1986) claims that the scatter in the T-F relation is minimized for apertures that correspond to the radius where the velocity profile of the galaxy begins to level off (i.e., at the maximum rotation velocity). Bothun states that "it becomes clear that the use of total magnitudes will increase the scatter" and the claim is made that the major source of scatter in the T-F relation is from variations in the light distribution of spirals which have the same HI velocity width. The scheme he adopts to reduce the dispersion is to scale the aperture with the surface brightness of the galaxy. Since the last point in the ILB is essentially the demarcation of the end of - 116 -solid-body rotation in a galaxy, our method is then measuring a feature of the velocity profile (like Vmax in the standard T-F relation) and the total luminosity inside the radius at which that feature occurs (not the total galaxy luminosity, as in the normal T-F) . It should be emphasized that the velocity at the final ILB point, for the galaxies in our sample, is not the maximum rotational velocity of the galaxy. Typically, the rotation curve is still rising, but at a reduced rate, towards the maximum rotational velocity after passing the radius at which the ILB terminates. Giraud (1987) obtained a. better correlation in the T-F diagram when frac-tional luminosities with an aperture ratio of log (A/D(0) )~ —0.6 were used in replacement of total luminosities. Giraud states that the aforementioned aperture ratio corresponds to the approximate position "where solid body rotation drops and the curve flattens out in many galaxies". Clearly, our method of analysing the actual velocity profile will be more accurate in discerning the region of solid body rotation for the galaxies we are studying. Also, for our T-F plot (Fig. 20), we use the velocity measured at the last point of the ILB, not the maximum velocity as Giraud does for his T-F plots. He concludes from his analysis that the outer parts of spirals are not "relevant" to what drives the T-F relation. This conclusion is put in a dubious light with the dispersion obtained by P T for the T-F relation in comparison to the dispersion quoted in Giraud (1987). P T refute the results of Giraud (1987) by using their growth curves to show that T -F relations for smaller aperture magnitudes have higher dispersion than those based on the total magnitudes. It is interesting to note, in the context of the Giraud result, that Bothun (1986) discovered that using a metric aperture of 5 - 1 1 7 -kpc for a sample of Pisces galaxies caused the scatter in the I-band T-F relation to decrease from 0.38 mag to 0.22 mag. From the point of view of this study, the P T result is not surprising since they are not scaling their aperture with the observed radius of some common physical feature of the galaxies velocity profiles (e.g., the end of the solid body part of the rotation curve). Our version of the T-F relation for the inner parts of spiral galaxies appears to have relatively low dispersion and this bodes well for the application of L - V diagrams as a tool for distance indication. Unfortunately, the major drawback for L - V diagrams is that detailed velocity and photometry profiles of individual galaxies are required for their production. Since large samples of this type of data can be time consuming to compile, the standard T - F relation is still a much more practical distance indicator to use than the final point in the ILB in L - V diagrams. Using L - V diagrams to probe the physical basis of the T-F relation is the application with the most potential. Wi th our small sample of 10 galaxies, it could be argued that the low disper-sion we observe for the "inner T -F" relation is merely fortuitous. Only a study based on a larger sample with similar or higher quality data could address this criticism. At the very least we have demonstrated that the scatter is comparable for the inner and outer parts of galaxies. In other words, the T-F relation ex-tends into the inner parts of spirals. This additional constraint will have to be incorporated into galaxy formation models. Persic and Salucci (1990, 1988) use the decrease in the scatter (as well as that of the residuals, nonlinearity and bias) of the T - F relation from the disk edge to smaller radii, for 58 galaxies, to show that dark matter must be present and that - 118 -the dark matter mass fraction must have a dependence on luminosity (but see Mould, Han and Bothun 1989). They work out an expression for the effect which dark matter has on the T-F relation as a function of radius. In order to do this the following assumptions are made: (i) an exponential disk mass distribution for the luminous matter in the galaxies; (ii) a negligible contribution to the circular velocity by the bulge and gas mass; and (iii) a constant stellar M / L ratio for all the galaxies in their sample. For the cases of no dark matter and a constant disk-to-dark matter mass ratio the T-F relation is expected to be unchanged at different radii in the galaxies. Collecting larger samples of L - V diagrams with greater spatial coverage would be desirable to help test the T-F relation's capabilities as a probe of spiral galaxy dark matter components. Any comparison of our results with those of Persic and Salucci (1990) has to be treated as inconclusive, due to the small size of our sample. - 119 -V . C O N C L U S I O N S The purpose of this thesis was to investigate the widely applied T-F relation by producing L - V diagrams (originally introduced by M W ) for a sample of 12 spiral galaxies from the Virgo cluster. Emission-line rotation curves for 9 Virgo galaxies were determined using longslit spectra observations. Comparisons with radio HI rotation curves from the literature showed that 21 cm observations typically do not define the velocity profile with the same accuracy as our optical rotation curves because of insufficient resolution in the radio data. The ability to accurately measure the inner velocity gradients with optical spectra was found to be crucial to the success of this project. A marked asymmetry in the rotation curve of N G C 4388 demonstrated the pe-culiar nature of the velocity field of this Seyfert galaxy and it was subsequently dropped from our sample. From a discussion of velocity profiles for early-type spi-rals with substantial bulges, measured and modeled by other workers, we conclude that velocity measurements for galaxies of this type should consist of absorption-line spectra for the inner parts and emission-line spectra for the outer parts of the optical disk. The reason this approach should be adopted is because emission-line rotation curves don't seem to trace the circular velocity in bulges. . Surface photometry observations for the full sample of 12 galaxies were re-duced and transformed into luminosity growth curves, with 6 being observed in the northern and southern hemispheres for comparison purposes. The method de-termined to best represent the luminosity growth was by using circular apertures in the seeing-dominated region (radius less than two times the F W H M of the pho-- 120 -tometry seeing profile) and then the free elliptical solution was utilized at radii exterior to this. Good agreement was obtained between the luminosity growth curves and Pierce and Tully (1988) total magnitudes. Residuals between luminos-ity growth measurements from the northern and southern sets showed generally good agreement, except in a couple of cases which suggested possible calibration problems. Rotation curves and luminosity growth curves were combined to yield L - V diagrams. The ILB feature of the L - V diagram was found to have a slope and zero point with a large dispersion (~0.9 mag), for our sample of Virgo galaxies, contrary to earlier results. Several checks were performed to explain this observed large scatter. A n alternative approach to the ILB method was attempted by using the last point in the ILB as a characteristic parameter for each galaxy. This is equivalent to a T -F relation for the inner parts of spiral galaxies. Wi th the rejection of a foreground galaxy ( N G C 4569) and a galaxy which is a member of an interacting pair (NGC 4568), a plot of the magnitude versus the log velocity of the last point in the ILB, for the 10 remaining galaxies, yielded a correlation (r=0.95) with a dispersion of 0.4 mag. This is more than the scatter observed for the standard T-F plot displayed in Fig. 18 which uses P T data for 9 of the 10 galaxies. If the dispersion in the T-F relation does decrease with radius in spirals galaxies this could be used to demonstrate the presence of dark mass fractions in disk galaxies, with a dependence of the nonluminous component on the luminosity of the host galaxy (Persic and Salucci 1990). - 121 -T A B L E 5 ILB Parameters Galaxy Slope Zero Point Slope Zero Point (Smoothed) (Smoothed) (Offset) (Offset) N G C 4178 -1.87 13.21 -1.93 13.19 N G C 4192 -2.25 13.15 -2.35 13.35 N G C 4192S -1.84 13.05 -1.90 13.22 N G C 4206 -3.69 13.64 -4.59 13.52 N G C 42i6 1 1 ' " -1.66 12.22 -1.69 12.34 N G C 4216S -1.23 12.16 -1.43 12.21 N G C 4237 -1.47 14.51 -1.51 14.67 N G C 4501 -3.53 12.56 -3.94 12.67 N G C 4501S -3.21 12.63 -3.50 12.70 N G C 4535 -2.68 14.17 -3.18 14.24 N G C 4535S -2.14 14.27 -2.97 14.27 N G C 4568 -1.93 14.26 -2.28 14.33 N G C 4569 -2.28 11.73 -2.07 11.77 N G C 4569S -1.83 12.03 -1.64 12.07 N G C 4579 -2.35 12.25 -2.50 12.29 (-3.14) (12.53) (-3.40) (12.60) N G C 4654 -2.64 13.33 -3.19 13.24 N G C 4654S -2.78 12.69 -3.17 12.62 N G C 4689 -4.02 14.17 -4.2C 14.22 - 122 -T A B L E 6 ILB Spatial Extent Galaxy # Ki 1 -"-25 TflLB 1 Tfi.b Kf 1K25 N G C 4178 23 0.028 0.058 0.469 0.830 N G C 4192 7 0.020 0.013 0.033 0.046 N G C 4192S 8 0.013 0.018 0.041 0.050 N G C 4206 17 0.036 0.023 0.195 0.461 N G C 4216 7 0.022 0.015 0.038 0.054 N G C 4216S ' 8 0.011 0.013 0.036 0.058 N G C 4237 7 0.056 0.040 0.104 0.610 N G C 4501 16 0.021 0.015 0.131 0.282 N G C 4501S 22 0.014 0.014 0.129 0.304 N G C 4535 6 0.017 0.014 0.041 0.275 N G C 4535S 9 0.011 0.012 0.033 0.269 N G C 4568 12 0.023 0.019 0.093 0.686 N G C 4569 7 0.015 0.011 0.043 0.264 N G C 4569S 8 0.010 0.010 0.042 0.235 N G C 4579 . , ,15 0.023 0.048 0.182 0.389 20 0.023 0.016 0.182 0.389 N G C 4654 18 0.022 0.019 0.164 0.387 N G C 4654S 22 0.023 0.017 0.177 0.380 N G C 4689 7 0.029 0.023 0.062 0.419 - 123 -10 12 14 16 18 10 12 14 16 18 - 1 1 1 1 11111 1 1 1 1 11111 I I I | 11 u ~ N G C 4 1 7 8 - * -1—1—1—1-1 M i l - 1 1 1 11111 1 1 1 II1 IT - i i I 1 11 l l | I I I 1 11 llj 1 | | | | I'Ti : .. N G C 4 1 9 2 ~ 1 1 1 1 1 1II I I I i i i I I i i i i i i rr i i i 1 1 1 1 1 1 1 1 11111 1 1 1 11111 f N G C 4 2 3 7 -r *r ~-- . i i I I i m l i i i i i m l i i i i i irr _ 1 1 1 1 l l l l 1 1 1 1 I N I 1 I - M l H i - « ~ = 1 1 1 1 l l l l l 1 1 1 i 1 m l i i n u n 10 12 14 16 18 10 12 14 16 18 10 100 Rot. Velocity 10 100 Rot. Velocity F igure 14 .—Fina l luminosity-velocity diagrams for galaxies in the northern set constructed using the smoothed luminosity growth curves. The solid line represents a linear regression to the points in the ILB. The horizontal, dotted line demarcates the point on the luminosity-velocity growth curve chosen to be the last point of the ILB. Asterisks, when shown, mark the Pierce and Tully (1988) Tully-Fisher point. F i g . 14-cont. F i g . 14-cont. to -4 O O o I I 1 1 I I I I I — i i 1 1 i n i j — r ~ i i i i i m N G C 4 5 3 5 * 1.0 12 14 16 18 10 12 14 16 18 10 12 14 16 18 " l — i I i 11 u| 1 i i 111111 1 — I I I I I N G C 4 5 6 9 nun i i imiir N G C 4 1 9 2 I I I I I I I 11 I I I I I I I 11 I I I I I I I7t~ I I I I I I 111 I I I I I I "I—I I I 11 l i j 1—I I I 11111 1—I l i l l i_n .. N G C 4 6 5 4 * 10 100 Rot. Velocity 10 100 Rot. Velocity Figure 15 .—Fina l luminosity-velocity diagrams for galaxies in the southern set constructed using the smoothed luminosity growth curves. The lines and asterisks are the same as in Fig. 14. n — i — i — i — I — i — i — r "i i i i i i i i i r 0 i i i I i i i I I I I I I I I I i I I I L U i I i i i L 0 1 2 3 4 5 6 ILB Slope ° | i i i i I i i i i i i i i — r i i i i i i i i i i i i i r J i i i I H i i i I i i i i i i i i i i i ILB Slope Figure 16.—Histograms of the slopes of the ILB for all the galaxies in the northern set. They are shifted half a bin with respect to each other to demonstrate there is no dependence of the distribution morphology on the binning. - 128 -11 12 13 14 15 16 ILB Zero Point Figure 17.—Histograms of the northern set (solid line) and southern s « t (dashed line) ILB zero points. ' I I I I I 1 I I I I I I I I I I I I I I I I I 2.3 2.4 2.5 2.6 2.7 log W R 1 2.8 2.9 Figure 1 8 .—A Tully-Fisher plot for the galaxies in our sample which overlap with the observations of Pierce and Tully (1988, P T ) . The ordinate is the extinction-corrected total Kron-Cousins R magnitude and the abscissa is the logarithm of the inclination-corrected HI profile width, where both have been taken from P T . The dotted line is a linear regression to the points, assuming the errors are solely in the magnitude coordinate, while the dashed line represents the fit with just the errors in the line width dimension. - 130 -i i i i i I r n—I I I " i — m -10 12 14 16 j i i i i i J I I I I I I i i i i i 10 100 Rot. Velocity Figure 19.—Overlay plot of all the L - V diagrams in the northern set. A l l the galaxies are offset to coincide with the final data point in the ILB of N G C 4579. 1.6 1.8 2 2.2 2.4 2.6 I , A r ILB log Vf Figure 20.—Plot of the magnitude versus the log velocity of the final data point of the ILB for all the galaxies in the northern set . R E F E R E N C E S Aaronson, M . , Huchra, J . , and Mould, J . 1979, Ap. J., 229, 1. (AHM) Albada, T. S. van, Bahcall, J . N . , Begeman, K . , and Sanscisi, R. 1985, Ap. J., 295, 305. Baeisi-Pillastrini, G . C. 1987, Astr. Ap., 172, 375. Baeisi-Pillastrini, G. C. 1988, Astr. Lett. Comm., 27, 27. Bessell, M . S. 1979, P. A. S. P., 91, 589. Bosnia, A . 1981, A. J., 86, 1791. Bothun, G . 1986, in Galaxy Distances and Deviations from Universal Expansion, ed. B . F . Madore and R. B . Tully (Dordrecht: Reidel), p. 87. Burstein, D. 1982, Ap. J., 253, 539. Burstein, D., and Heiles, C. 1984, Ap. J. Supp., 54, 33. Burstein, D., and Raychaudhury, S. 1989, Ap. J., 343, 18. Carignan, C , and Freeman, K . C. 1985, Ap. J., 294, 494. Cawson, M . 1984, GASP Users Manual. Chincarini, G. , and de Souza, R. 1985, Astr. Ap., 153, 218. (CdS) Corbin, M . R., Baldwin, J . A . , and Wilson, A . S. 1988, Ap. J., 334, 584. Cornell, M . E . , Aaronson, M . , Bothun, G. , and Mould, J . 1987, Ap. J. Supp., 64, 507. Davis, L . E . , Cawson, M . , Davies, R. L . , and Illingworth, G . 1985, A. J., 90, 169. Davoust, E . , and Pence, W. D. 1982, Astr. Astrophys. Suppi, 49, 631. Djorgovski, S. B . 1985, Ph.D. thesis. University of California, Berkeley. Dressier, A . , and Faber, S. M . 1990, Ap. J. (Letters), 354, L45. - 133 -Dressier, A . , and Sandage, A . 1983, Ap. J., 265, 664. Filmore, J . A . , Boroson, T. A . , and Dressier A . 1986, Ap. J., 302, 208. (FBD) Fouque, P., Bottinelli, L . , Gouguenheim, L . , and Paturel, G . 1990, Ap. J., 349, 1. Franx, M . , Illingworth, G. , and Heckman, T. 1989, A. J., 98, 538. Freeman, K . 1970, Ap. J., 160, 811. Freedman, W . L . 1990, Ap. J. (Letters), 355, L35. Giraud, E . 1987, Astr. Ap., 180, 57. Graham, J . A . 1982, P. A. S. P., 94, 244. Guhathakurta, P., van Gorkom, J . H . , Kotanyi, C. G . , and Balkowski, C. 1989, A. J., 96, 851. ( G v G K B ) Harrison, E . R. 1974, Ap. J. (Letters), 191, L51. Hi l l , B . 1990, (private communication). Jedrzejewski, R. I. 1987, M. N. R. A. S., 226, 747. Kent, S. M . 1984, Ap. J. Supp., 56, 105. Kent, S. M . 1985, P. A. S. P., 97, 165. Kormendy, J. , and Westpfahl, D. J . 1989, Ap. J., 338, 752. (KW) Kraan-Korteweg, R. C., Cameron, L . M . , and Tammann, G. A . 1988, Ap. J., 331, 620. (KCT) Landolt, A . U . 1973, A. J., 78, 959. Landolt, A . U . 1983, A. J., 88, 439. Madore, B . F. , and Woods, D. 1987, Ap. J. (Letters), 323, L25. (MW) Mihalas, D., and Binney, J . 1981, Galactic Astronomy, second edition, (San Fran-cisco, C A : Freeman), p. 297. Mould, J . , Aaronson, M . , and Huchra, J . 1980, Ap. J., 238, 458. - 134 -Mould, J . , Han, M . , and Bothun, G . 1989, Ap. J., 347, 112. Pence, W . D. , and Davoust, E . 1985, Astr. Astrophys. Suppl, 60, 517. Persic, M . , and Salucci, P. 1986, M. N. R. A. S., 223, 303. Persic, M . , and Salucci, P. 1988, M. N. R. A. S., 234, 131. Persic, M . , and Salucci, P. 1990, Ap. J., 355, 44. Phillips, M . M . , and Malin, D. F . 1982, M. N. R. A. S., 199, 905. Pierce, M . J . , and Tully, R. B . 1988, Ap. J., 330, 579. (PT) Pogge, R. W. 1988, Ap. J., 332, 702. Rubin, V . C., Burstein, D. , Ford, W. K . , Jr., and Thonnard, N . 1985, Ap. J., 289, 81. Rubin, V . C., Ford, W. K . , Jr., and Thonnard, N . 1980, Ap. J., 238, 471. Rubin, V . C., Ford, W. K . , Jr., Thonnard, N . , and Burstein, D. 1982, Ap. J., 261, 439. Rubin, V . C., Kenney, J . D. , Boss, A . P., and Ford, W . K . , Jr. 1989, A. J., 98, 1246. Rubin, V . C., Whitmore. B . C., and Ford, W. K . , Jr. 1988, Ap. J., 333, 522. (RWF) Sandage, A . , and Tanrmann, G. A . 1981, A Revised Shapley-Ames Catalog of Bright Galaxies, (Washington, D. C.: Carnegie Institution of Washington). (RSA) Schweizer, F. 1979, Ap. J., 233, 23. Shields, J . C , and Filippenko, A . V . 1988, Ap. J. (Letters), 332, L55. Smith, E . P., and Heckman, T. M . 1989, Ap. J. Supp., 69, 365. Souviron, J . , Kormendy, J . , and Bosma, A . 1989, DAO preprint. - 135 -Thuan, T. X . , and Gunn, J . E . 1976, P. A. S. P., 88, 543. Tully, R. B . 1988, Nearby Galaxies Catalog, (Cambridge, England: Cambridge University Press). Tully, R. B . , and Fisher, J . R. 1977, Astr. Ap., 54, 661. Tully, R. B . , and Fcnique, P. 1985, Ap. J. Supp., 58, 67. Tully, R. B . , and Shaya, E . J . 1984, Ap. J., 281, 31. Walker, M . F. 1989, P. A. S. P., 101, 333. Watanabe, M . , Kodaira, K . , and Okamura, S. 1982, Ap. J. Supp., 50, 1. Whitmore, B . C , Forbes, D. A . , and Rubin V . C. 1988, Ap. J., 333, 542. (WFR) - 136 -


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