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Mon. Not. R. Astron. Soc. 328, 1151-1160 (2001)

Gas-rich galaxies and the H I mass function
J. I. Davies,1P W. J. G. de Blok,2 R. M. Smith,1 A. Kambas,1 S. Sabatini,1 S. M. Linder1 and S. A. Salehi-Reyhani1
1 2

Department of Physics and Astronomy, Cardiff University, Queen's Buildings, PO Box 913, Cardiff CF24 3YB ATNF, PO Box 76, Epping, NSW 1710, Australia

Accepted 2001 August 22. Received 2001 August 22; in original form 2001 April 9

ABSTR A CT

We have developed an automated cross-correlation technique to detect 21cm emission in sample spectra obtained from the H I Parkes All Sky Survey. The initial sample selection was the nearest spectra to 2435 low-surface-brightness galaxies in the catalogue of MorshidiEsslinger, Davies and Smith. The galaxies were originally selected to have properties similar to Fornax cluster dE galaxies. As dE galaxies are generally gas poor it is not surprising that there were only 26 secure detections. All of the detected galaxies have very high values of (MH/LB)(. Thus the H I selection of faint optical sources leads to the detection of predominately gas-rich galaxies. The gas-rich galaxies tend to reside on the outskirts of the large-scale structure delineated by optically-selected galaxies, but they do appear to be associated with it. These objects appear to have relative dark matter content similar to that of optically-selected galaxies. The H I -column densities are lower than the `critical density' necessary for sustainable star formation and they appear, relatively, rather isolated from companion galaxies. These two factors may explain their high relative gas content. We have considered the H I mass function by looking at the distribution of velocities of H I detections in random spectra on the sky. The inferred H I mass function is steep, though confirmation of this result awaits a detailed study of the noise characteristics of the H I survey. Key words: techniques: photometric - catalogues - surveys - stars: formation - galaxies: luminosity function, mass function - radio lines: galaxies.

1

I NT R O DU CTION

It is believed that galaxies evolve via star formation from initially a gas-dominated to finally stellar- (and stellar-remnant) dominated states. Although the average star formation rate of the Universe possibly had a peak value somewhere between z ? 1-2 (Madau et al. 1996; Lilley et al. 1996), individual galaxies can have very different star formation histories. Star formation seems to have either started at different times and/or has proceeded at different rates at different places in the Universe. Elliptical galaxies appear to have formed very early and converted their gas into stars very quickly, whilst galaxies like the giant low-surface-brightness (LSB) galaxy Malin 1 (Bothun et al. 1987; Impey & Bothun 1989) still have huge reservoirs of gas and seem to be forming stars at a (constant?) slow rate. The globally averaged star formation rate of galaxies has been determined using rather high-surface-brightness galaxies, measuring either the ultra-violet and/or the far-infrared luminosity density (Blain et al. 1999). What is not clear from these measurements is whether there is a significant population of
P

E-mail: jid@astro.cf.ac.uk

galaxies, similar to Malin 1, that have continued to form stars at very much lower rates over longer periods of time. These galaxies would be very difficult to detect in the ultra-violet, because of their LSB, and in the far-infrared, because of their low gas-phase metallicity (hence low dust content) and because of the large average distance between the stars the dust would be very cold. Given their hypothesized large relative gas mass the most fruitful region of the spectrum to detect them would seem to be 21 cm. Malin 1 is different from other spiral galaxies in a number of ways. For example its ðMH / LB Þ( of 5 (Bothun et al. 1987; Impey & Bothun 1989) is much higher than the 0.1 for a `typical' spiral galaxy and very much more than 0.01 for a `typical' elliptical. While there does seem to be a systematic increase in ðMH / LB Þ( from < 0.05 for early-type spirals to < 1 for very-late-type irregulars (Knapp 1990), galaxies with values as high as Malin 1 are quite extraordinary. A large value of (MH/LB)( indicates either a galaxy that is very young or one that has been forming stars at a very low rate, for its mass, compared with other galaxies. If we can find larger numbers of galaxies with these properties then we shall gain a much better understanding of the factors that govern galaxy and star formation rates.

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Morshidi-Esslinger, Davies & Smith (1999a). Where required, we have used H 0 ? 75 km s21 Mpc21 . 2 T H E D ATA

The reasons why galaxies form stars at different rates is not totally clear, but there are two very likely prime factors. These are the initial conditions (the gas density at formation) and the frequency of galactic interactions. High density and/or a large number of encounters are both thought to promote star formation. Thus elliptical galaxies formed at places of high initial overdensity and subsequently had many interactions and mergers with smaller galaxies, while Malin 1 probably formed at a spatially large, but small overdensity, in a very isolated environment. By studying relatively isolated gas-rich galaxies we have the opportunity of studying galaxies that have not had rapid star formation induced by interactions, undergone mergers and have not been tidally stripped. As long as they have not suffered significant expulsion or accretion of gas the mass function of these galaxies should reflect the initial mass function of galaxies at their time of formation. Gas-rich galaxies are thus the best galaxies to compare with the initial density fluctuations (Press & Schechter 1974) assumed in recent numerical models of galaxy formation (Frenk et al. 1996; Kauffman, Nusser & Steinmetz 1997). There are two fundamental ways of detecting atomic hydrogen in gas-rich systems, either by absorption or emission. QSOabsorption-line studies indicate large numbers of gas-rich systems (from the damped Lya systems to the Lya forest) most of which have no identifiable optical counterparts. Observations at 21 cm have predominately concentrated on, and therefore almost always appear to be associated with, optical systems. In addition, the QSO data tends to sample the distant Universe while the 21-cm observations have concentrated on rather nearby objects. QSOabsorption-line observations are generally sensitive to much lower column densities (down to < 1012atoms cm22) than 21-cm observations (at best < 1018atoms cm22), but even where the two regimes overlap there are many objects that have no optical counterparts. Some damped Lya systems, for example, which were generally believed to arise in the discs of `typical' large spiral galaxies have now, after much closer scrutiny, been found to arise from absorption in dwarf and LSB galaxies (Cohen 2000; Bowden, Tripp & Jenkins 2000). If further observations confirm this for other damped Lya systems then we will have to move away from the view that the majority of hydrogen absorption lines occur in huge gas haloes around `typical' galaxies to one in which the gas is clumped into much smaller, previously undetected clouds. So we might speculate on the possibility of H I -rich clouds like this existing nearby and thus being accessible to 21-cm observation at column densities of < 1018 atoms cm22 or above (for an alternative view, see Rao & Briggs 1993). As 21-cm observations become more sensitive and extensive we will be able to test this hypothesis. A start can be made using the first 21-cm all sky survey (Barnes et al. 2001). So is there a large local population of galaxies that have converted only a small fraction of their gas into stars? If so, what is their spatial distribution? What is the form of their H I mass function and how does such a population relate to current numerical models of galaxy formation? To try and answer these questions we have used 21-cm data taken from the H I Parkes All Sky Survey (H I PASS)1 to study the H I properties of a sample of LSB galaxies. The extracted H I spectra are those closest to the optical positions of the 2435 galaxies in the LSB galaxy sample of

The optical data are taken from the photographic survey for LSB galaxies carried out by Morshidi-Esslinger et al. (1999a) and Morshidi-Esslinger, Davies & Smith (1999b). The survey covered approximately 2000 deg2 using data obtained from APM scans of UK Schmidt telescope survey plates. Galaxies were selected to be `similar' to previously detected dE galaxies in the Fornax cluster. We use the word `similar' because the APM automated detection routine is optimized to select rather smooth looking images like dE galaxies, rather than dI or spiral galaxies. The latter tend to have a `lumpy' appearance which the APM classifier often splits into separate or `noise' images. The photometric selection criteria was a central surface brightness in the B band fainter than 22.5 Bm and an exponential scale length greater than 3 arcsec. Full details of the optical survey data are given in Morshidi-Esslinger et al. (1999a). The optical data were originally used to study the total numbers, numbers in different environments and the clustering scales of LSB dwarf galaxies. Given that we tried to optimize the galaxy selection to dE galaxies we actually might not expect any H I detections. Previous observations of dE galaxies in clusters indicate H I masses of less than 107 M( (Impey et al. 1988) while our sensitivity (see below) is only below 107 M( for velocities less than about 1500 km s21. Thus we do not expect to be able to detect the numerically dominant dE galaxies in this sample. Rather, we are trying to detect `interlopers', that is objects that appear similar to LSB dE galaxies yet contain larger amounts of H I . In fact Malin 1 was discovered in a similar way. It was originally thought to be a dwarf galaxy in the Virgo cluster, but was later discovered to be a giant LSB galaxy in the background (Bothun et al. 1987). Our models and observations (Morshidi-Esslinger, Davies & Smith 1999a; Morshidi-Esslinger, Davies & Smith 1999b), indicated some `background' contamination of the optical sample by more distant objects, not necessarily dE galaxies. We were hoping that some of these might be gas-rich galaxies like Malin 1. The H I data comes from the 388 88 Â 88 survey data cubes of the H I PASS 21-cm southern sky survey (Barnes et al. 2001). The angular resolution of the data is 15.5 arcmin after the data have been gridded. The grid spacing in each cube is 4 arcmin and the spectrum used is the nearest spectrum to the optical position. The channel spacing is 13.2 km s21 and the velocity resolution is 27 km s21 after smoothing. There are 1024 channels, but we initially considered only velocities in the range 400-12000 km s21 . The lower limit was set to avoid local hydrogen, the upper limit by the proximity of the velocity cut-off. The typical noise fluctuation in each spectrum after smoothing is 0.006 Jy beam21. The identification of sources in the H I data is described below. 3 H I DETE CTION

1

The Parkes telescope is part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.

The automated detection to well-defined selection criteria of images on, for example, CCD frames has become much more sophisticated over the last few years - see for example Bertin & Arnouts (1996). Numerous computer packages exist to select galaxies automatically to well-defined selection criteria (isophotal size and magnitude for example). This does not appear to be the case for H I detections, yet the two problems are very similar. For example Kilborn (2001) discusses an automated galaxy finder for use on H I PASS data cubes, but then resorts to selection by eye. In
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Gas-rich galaxies and the H I mass function
none of the papers on blind H I surveys we have come across do we find objective selection criteria for H I sources (Zwaan et al. 1997; Schneider et al. 1998). These papers supply information about the observing setup and the data reduction, but say little about the detection of objects from the spectra obtained. In the main, objects appear to be identified by eye and there is no explanation of the selection criteria except to say (incorrectly) that there is some lower mass limit at each distance. We have previously been involved with techniques for the detection of LSB galaxies in imaging data (Phillipps & Davies 1991; Davies, Disney & Phillipps 1994; Kambas et al. 2000). A number of years ago it had become clear that LSB galaxies were very much under-represented in optically- (by-eye-) selected samples taken from imaging data. The lesson learnt was that only when a full analysis of the selection process had been carried out could you then define the sorts of galaxies you would and would not be able to detect (Disney 1976; Disney & Phillipps 1983; Davies 1990). Carrying out deeper observations with better-understood selection criteria has led to the detection of numerous LSB galaxies. An optical image of a galaxy is detected against a systematically varying background level with the addition of random noise fluctuations. Detection of the H I signal is very similar - the varying background is the baseline ripple and in addition there are random noise fluctuations. For optical image detection there is no well-defined magnitude or size limit - sample selection is always a combination of magnitude and size. For example one can always think of a galaxy that is bright enough to be part of a magnitudelimited sample, but fails to get in because it is too large (its surface brightness is less than or close to the survey isophotal limit). In a similar way, large-velocity-width galaxies with low central intensities will be missed or assigned to baseline ripples even though they contain sufficient hydrogen, in total, to be detected in a `mass-limited' survey. In this section we describe how we have applied some of our previous techniques of surface photometry to the detection of H I sources. Having 2435 spectra to inspect was another strong motivation for employing an automated technique. As mentioned above there are two important factors that influence our ability to detect `H I objects' in H I spectra. The first is random noise; the second is baseline fluctuations. The signal is the integral over the linewidth, so large signals can arise from large peak values and/or large velocity widths. The problem with identifying large velocity widths without large peak values is that they can look the same as baseline fluctuations (see also Section 6 and Fig. 1). The problem with the random noise is that the expectation (Gaussian) is one single channel 3s (s is the standard deviation of the data values) fluctuation in the 1000+ channels. Thus 3s detections (see Fig. 1) are not reliable unless they have sufficiently large velocity widths; but even then, if the velocity width is too large, they can resemble baseline fluctuations. By `hiding' simulated galaxies in real spectra it became clear that an initial 4s detection was required, because even 3s peak values with quite large velocity widths were not convincingly different from the noise. So the initial object identifier was simply one of peak value at the 4s level. At 4s we would expect one false detection in every 30 spectra or about 80 false detections in the sample as a whole. So the second requirement was that the initial peak value detection also had a `resolved' velocity width (Fig. 2), i.e. a velocity width greater than 27 km s21. With these criteria we would not expect any detections by chance (see also Section 6 below). The lowest signal-to-noise ratio for detection is about 10, a value that would be readily accepted in imaging data.
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Figure 1. A 3s fluctuation in an H I spectrum at <6700 km s21.
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Figure 2. A 4s detection with a velocity width that is just resolved ðDv < 38 km s21 Þ.

Our selection criteria do not lead to an integrated flux-limited sample (see above), so we shall use the term `survey limits' to indicate our two minimal-selection criteria. This is analogous to what would be referred to (incorrectly) as the magnitude limit for a magnitude-limited imaging survey sample. There are two other points. First, our selection criteria will lead to the preferential selection of face-on, rather than edge-on, disc galaxies as these will have higher central intensities and narrower line profiles. Secondly, `spikes' in the data like that illustrated in Fig. 2 are very similar in velocity width but, lower in amplitude, to the confirmed detection of an apparently isolated H I cloud by Kilborn et al. (2000). Given the noise in the data it is difficult to measure the velocity width and flux integral accurately. To minimize this problem we have cross-correlated the data with templates and used the bestfitting template to derive the central velocity, velocity width and


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intensity. Substituting into equation (1) and integrating gives sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2as at ; ð2Þ Cst ? a2 1 a2 s t which obviously has a maximum when as ? at . By convolving with different Gaussian templates over a range of velocities we can determine the best-matching template and the central velocity from the maximum value of Cst. To determine the flux integral we also need to know the central intensity. To do this we use a second convolution, but with a different normalization: Ð Gs ðxÞGt ðxÞ dx Ast ðxÞ ? Ð 2 : ð3Þ Gs ðxÞ dx For the Gaussian case this reduces to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi It 2a2 t ; Ast ? I s a2 1 a2 s t ð4Þ

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7 -10

-11

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Figure 3. The H I mass against the absolute B-band magnitude.

flux integral. Inspection of a small part of the data indicated that by far the majority of the sources appeared as single `spikes' rather than `double horned'. The exact form of the template used is not critical, but the maximum gain in signal to noise is obtained for an `optimum filter', this is one that has the same shape as the object being measured, this is an example of matched filtering (Irwin et al. 1990). We have chosen Gaussian templates as they appear `similar' to the profile shapes we are trying to measure and they are relatively easy to interpret. The cross-correlation program will also measure `double horned' profiles (but not so accurately) by fitting Gaussians around the central velocity. Essentially we use a technique similar to one we have used before to detect and measure LSB galaxies (Davies et al. 1994; Phillipps & Davies 1991). We have used this method to derive the best-fitting exponential central surface brightness and scale length of LSB galaxy images (photometry). Here we shall derive the central intensity and velocity width of the best-fitting Gaussian to the H I spectrum. The cross-correlation technique for surface photometry is fully described in Phillipps & Davies 1991 (hereinafter PD). Below we shall briefly describe our method using similar notation to PD. The correlation coefficient of a spectrum Gs and a model template spectrum Gt is defined in general by the convolution Ð G ðxÞGt ðx 1 r Þ dx Ð 2 s 1=2 Ð 2 Cst ðr Þ ? ð Gs ðxÞ dxÞ ð Gt ðxÞ dxÞ

which implies Ast ? I t /I s when as ? at . So once we have selected the correct template (at), Ast is just the ratio of the unknown intensity Is to the known normalization of the model, It. The velocity profile will not be a perfect Gaussian so the crosscorrelation will find a closely-matching Gaussian model. This will be the `best'-fitting model in the sense of minimizing the weighted sum of the deviations. In practice we shall always have a noisy image. For example, if the noise per pixel is everywhere Gaussian with a fixed amplitude s (this assumes the signal is not large compared with the noise) then ð ð G2 ðvÞ dv ? ?I s exp 2 ðv/ as Þ2 1 N 1=2 dv; ð5Þ s while the other terms remain unchanged. N represents a Gaussian random error term with mean zero and standard deviation s. As the cross-terms have an expectation value of zero, equation (2) becomes sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2as at pffiffiffi Cst ? ; ð6Þ pffiffiffiffi 2 1 a2 Þ?1 1 ð 2x s 2 / pa I 2 Þ ðas ss t t

1=2

;

ð1Þ

where r is the shift between the spectrum and template and the integrals are taken over their intersection. In practice the integrals are taken as sums over the digitized data. C2 # 1 regardless of the st form of Gt or Gs and there is a maximum when Gt ? aGs , where a is a positive constant (see PD). If the data substantially exceeds the scale size of the Gaussians used we can ignore the limits on the integrals of equation (1). So, if the velocity profile of the template and galaxy are both Gaussians then Gt ðvÞ ? I t exp 2 ðv/ at Þ2 and Gs ðvÞ ? I s exp 2 ðv/ as Þ2 , where v and a are velocities and I is an

where xt is the intersection of the spectrum with the template. The `correction' term involves only the parameters of the noise and the spectrum and so the maximum still occurs at as ? at . As one might expect, the effects of the noise are minimized for large values of as I 2 (large velocity widths and peak values). During the crosss correlation process we kept the intersection, xt, the same for each template so that we could compare the correlation coefficients of different templates. We have used Gaussian templates with full-width-halfmaximum values from 25 to 500 km s21 at 12.5 km s21 intervals. We reject those that are not velocity resolved ðv , 27 km s21 Þ. The largest detected velocity width in the sample is 337.5 km s21 - some way below the largest template size. The detection process has been fully tested on a wide range of simulated and real data. Using simulated Gaussian profiles, in real data, with central intensities of 4s we find that we can estimate profile parameters and H I masses to about a factor of three. As confirmation of this, one of the galaxies in the final sample (see below) has a previous 21-cm measurement. For F300-026, Matthewson & Ford (1996) measured an H I mass of 8 Â 108 M( (using our derived distance of 11.3 Mpc) while the value derived from our cross-correlation
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Gas-rich galaxies and the H I mass function
program is 6 Â 108 M( . We have also excluded regions in each spectra that contain known sources of noise (H I PASS web page). In summary, the automated H I detection process involved firstly the identification of a 4s or higher value, then finding the maximum correlation coefficient with a template of velocity width (full width at half-maximum) greater than 27 km s21, the velocity resolution of the data (in practice the width of the smallest `resolved' template of 37.5 km s21). This is what we define as our `sample limits'. After carrying out the template matching we had a list of 155 H I detections. We then needed to carry out other checks to see how secure these detections were. The main problem is one of reliably assigning the optical and H I detections to the same object. Typically, the galaxies in the optical sample have diameters of 0.3 arcmin. The H I resolution is 15.5 arcmin. To overcome this problem we have used the optical Digital Sky Survey (DSS) to inspect the area around each H I detection. We have also used the NASA/IPAC Extragalactic Database (NED) to find known objects within 10 arcmin of the position of the H I spectra. We have removed objects from our initial list if NED has a similar redshift for another object within 10 arcmin or if there is a more prominent galaxy within the field of view. For strong nearby signals ðv , 2000 km s21 Þ we searched NED for galaxies of similar redshift at up to 18 away (by looking at spectra at random positions around nearby galaxies - such as NGC 1365 and 1291 - it is clear that they can affect spectra up to 30 arcmin away from their optical centre). As an indication that some of our optical and H I detections come from the same object we can compare the measured H I velocities with previously determined (optical) velocities obtained from NED; these are available for 10 galaxies in our sample (see Table 1). In all cases the optical and H I velocities are in good agreement. The above procedure resulted in a reduction to 84 detections, but it was clear from inspection of the images from the DSS that for the most distant objects (greater than about 6000 km s21) confusion was still a problem. The large beam size covered many faint objects that, although not listed in NED, were nevertheless distinctly possible sources of the H I emission. In fact, the H I emission could arise from the combination of a number of sources in the same group. A simulation (see below) of the expected number of sources in a set of random beams indicated that contamination of the sample was possible at a level better than about 1 in 4 for a sample limited to 5000 km s21, but that this drops quickly to about 1 in 2 or worse beyond 6000 km s21. Given that our data are not from a set of random sight lines, we should expect to do better than this and so (rather arbitrarily) we set a maximum velocity limit of 5500 km s21. This fits in well with the previously measured galaxies of Table 1, which all have confirmed redshifts below this limit. This final sample consists of just 26 objects, out of an initial sample of 2400, that have both a reasonably secure optical and H I detection. Given the above discussion and that our sample consists of relatively isolated galaxies (see below) we believe that our detections are secure and not due to other nearby objects. In Fig. 3 we have plotted H I mass against the absolute B-band magnitude. As one might have hoped, there is a correspondence between the two - supporting our contention that the optical and H I detections belong to the same objects. At our sample limits, we should expect to be able to detect < 2 Â 107 M( of hydrogen at our minimum veloc ity of 400 km s21 and < 3 Â 109 M( of hydrogen at our maximum velocity of 5500 km s21. Given that a `typical' M* galaxy (like the
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Milky Way) has M H i < 1010 M( (Zwaan et al. 1997), we can detect galaxies that are gas poor compared with M* over our full range of velocities. Although the low number of combined optical and H I detections is disappointing, it is what we might have expected if our original, optical, selection was sound. The optical selection was designed to select gas-poor dE galaxies - and this is what it appears to have predominately done. The only other explanation for the low number of H I detections would be that most of the undetected galaxies are at large distances ðv . 12000 km s21 Þ, but this is unlikely given the way the optically detected galaxies appear to cluster around nearby brighter galaxies (Morshidi-Esslinger et al. 1999a).

4 T HE SP A T IA L D IST R I B UTI O N O F T HE GAS- RICH GA LAXIES In Fig. 4 we have plotted the positions of the detected objects compared with the positions of the four major groups/clusters in the survey area. The spatial distribution of our detections is very
Table 1. A comparison of line-of-sight velocities ob tained from NED and measured H I velocities. Name F115-001 F303-023 F304-013 F353-003 F362-027 F410-001 F418-059 F481-018 F483-019 F548-020 NED velocity (km s21) 1131 4485 2250 3739 1344 1545 1673 2087 4128 1961 H I velocity (km s21) 1305 4412 2098 3922 1332 1558 1758 2079 4017 1958

Figure 4. The position of the H I -rich galaxies in relation to nearby groups and clusters. Triangles mark galaxies with velocities less than 2250 km s21, squares those with velocities greater than 2250 km s21.


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different from that of the complete optical sample (see fig. 8 in Morshidi-Esslinger et al. 1999a). The optical galaxies cluster about the group/cluster centres while the H I detections appear to avoid the cluster centres almost completely. This segregation of gas-rich galaxies from the gas poor has of course been known for some time. It is in low-galactic-density environments that we would expect to find galaxies like this (Solanes et al. 2000). It is possible that the effect has been enhanced in this case by increased `optical confusion' due to the higher density of galaxies in the group/cluster centres. In Fig. 5 we have plotted a histogram of the line-of-sight velocities. The detections cluster at about the velocities expected for the bright galaxies. Fornax, Dorado, NGC 1400 and Sculptor groups/clusters all have redshifts below 2000 km s21. Both Jones & Jones (1980) and Fairall (1998) show that over this region of sky there is a peak in the number density of galaxies at about 1500 km s21 and then a void out to about 4000 km s21. This shows that, although these galaxies avoid group/cluster centres, they are still associated with the larger-scale structure defined by the brighter galaxies.

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Figure 5. The distribution of galaxy velocities.

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M ASS-T O -LIGHT RA TIOS

H I masses can be derived using ð M H i ? 2:4 Â 105 d 2 Sv dv;

ð7Þ

where MH I is the mass of H I in solar units, d is the distance to the galaxy in Mpc, Sv is the flux density and the integral is over velocity. The flux integral is solved using the Gaussian parameters of the best-fitting template as described above. Distances are obtained by converting line-of-sight velocities to velocities relative to the Local Group (Yahil, Tammann & Sandage 1977). We have calculated stellar masses from the absolute blue magnitude of the galaxy assuming a stellar mass