Baryonic Tully–Fisher relation for extremely low mass Galaxies

Monthly Notices of the Royal Astronomical Society, May 2008

We study Tully–Fisher (TF) relations for a sample that combines extremely faint (MB < −14) galaxies along with bright (i.e. ∼L*) galaxies. Accurate (∼10 per cent) distances, I-band photometry and B−V colours are known for the majority of the galaxies in our sample. The faint galaxies are drawn from the Faint Irregular Galaxy GMRT survey (FIGGS), and we have H i rotation velocities derived from aperture synthesis observations for all of them. For the faint galaxies, we find that even though the median H i and stellar masses are comparable, the H i mass correlates significantly better with the circular velocity indicators than the stellar mass. We also find that the velocity width at the 20 per cent level (W20) correlates better with mass than the rotation velocity, although the difference is not statistically significant. The faint galaxies lie systematically below the I-band TF relation defined by bright galaxies, and also show significantly more intrinsic scatter. This implies that the integrated star formation in these galaxies has been both less efficient and also less regulated than in large galaxies. We estimate the intrinsic scatter of the faint galaxies about the I-band TF to be ∼1.6 mag. We find that while the faint-end deviation is greatly reduced in Baryonic Tully–Fisher (BTF) relations, the existence of a break at the faint end of the BTF is subject to systematics such as the assumed stellar mass-to-light ratio. If we assume that there is an intrinsic BTF and try to determine the baryonic mass by searching for prescriptions that lead to the tightest BTF, we find that scaling the H i mass leads to a much more significant tightening than scaling the stellar mass-to-light ratio. The most significant tightening that we find, however, is if we scale the entire baryonic mass of the faint (but not the bright) galaxies. Such a scenario would be consistent with models where dwarf (but not large) galaxies have a large fraction of dark or ‘missing’ baryons. In all cases, however, the minimum in the χ2 curve is quite broad and the corresponding parameters are poorly constrained.

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Baryonic Tully–Fisher relation for extremely low mass Galaxies

Jayaram N. Chengalur 1 I. D. Karachentsev 0 M. E. Sharina 0 0 Special Astrophysical Observatory, Nizhnii Arkhys 369167, Russia 1 National Centre for Radio Astrophysics , Post Bag 3, Ganeshkhind, Pune 411 007, India 2 Institute of Astronomy, University of Cambridge , Madingley Road, Cambridge CB3 0HA A B S T R A C T We study Tully-Fisher (TF) relations for a sample that combines extremely faint (MB < 14) galaxies along with bright (i.e. L ) galaxies. Accurate (10 per cent) distances, I-band photometry and B V colours are known for the majority of the galaxies in our sample. The faint galaxies are drawn from the Faint Irregular Galaxy GMRT survey (FIGGS), and we have H I rotation velocities derived from aperture synthesis observations for all of them. For the faint galaxies, we find that even though the median H I and stellar masses are comparable, the H I mass correlates significantly better with the circular velocity indicators than the stellar mass. We also find that the velocity width at the 20 per cent level (W20) correlates better with mass than the rotation velocity, although the difference is not statistically significant. The faint galaxies lie systematically below the I-band TF relation defined by bright galaxies, and also show significantly more intrinsic scatter. This implies that the integrated star formation in these galaxies has been both less efficient and also less regulated than in large galaxies. We estimate the intrinsic scatter of the faint galaxies about the I-band TF to be 1.6 mag. We find that while the faint-end deviation is greatly reduced in Baryonic Tully-Fisher (BTF) relations, the existence of a break at the faint end of the BTF is subject to systematics such as the assumed stellar mass-to-light ratio. If we assume that there is an intrinsic BTF and try to determine the baryonic mass by searching for prescriptions that lead to the tightest BTF, we find that scaling the H I mass leads to a much more significant tightening than scaling the stellar mass-to-light ratio. The most significant tightening that we find, however, is if we scale the entire baryonic mass of the faint (but not the bright) galaxies. Such a scenario would be consistent with models where dwarf (but not large) galaxies have a large fraction of dark or 'missing' baryons. In all cases, however, the minimum in the 2 curve is quite broad and the corresponding parameters are poorly constrained. - One of the stringent tests of galaxy formation models is their ability to reproduce the tightness of the TullyFisher (TF) relation, i.e. the fact that the rotation velocity and absolute magnitude of bright spiral galaxies are tightly correlated. For such galaxies, the intrinsic scatter in the I-band TF has been estimated to be as small as 0.2 mag (e.g. Sakai et al. 2000), while Verheijen (2001) argues that there is probably no intrinsic scatter in the K -band TF relation. This implies that the dark and visible (i.e. stellar) matter content of galaxies is tightly correlated, or, if one assumes that the visible matter traces the bulk of the baryons, that the non-baryonic and baryonic content of galaxies are tightly correlated. Theoretically, one would not expect this correlation to hold all the way down to dwarf galaxy masses. Reheating prior to the epoch of reionization would lead to small haloes having a reduced baryon fraction (e.g. Gnedin 2000), and small dark matter haloes are also expected to easily lose baryons because of energy input from the first burst of star formation and supernova winds (e.g. Efstathiou 2000; Dekel & Woo 2003; Tassis, Kravtsov & Gnedin 2008). Large galaxies on the other hand are more able to keep their original share of baryons. Consistent with this expectation, observations show that dwarf galaxies with rotation velocities less than 90 km s1 lie below the TF relation defined by brighter galaxies (Matthews et al. 1998; McGaugh et al. 2000; Begum & Chengalur 2004; McGaugh 2005), that is, they are under luminous for the velocity width. On the other hand, Geha et al. (2006) using an independent Sloan Digital Sky Survey (SDSS) based sample of dwarf galaxies did not find any break in the I-band TF relation, although, in agreement with earlier studies they find an increased scatter about the TF relation at low luminosities. Further, as first noted by McGaugh et al. (2000) the break seen at the faint end of the B-band TF relation is removed if one works with the total baryonic mass (i.e. the sum of stellar and gas) instead of the luminosity. Accurate extensions of the TF relation to faint dwarf galaxies pose a number of practical problems. First, dwarf galaxies are largely a field population, and very few of them have accurately known distances. Secondly, being faint, and largely of low surface brightness, accurate photometry is difficult. Finally, in contrast to the situation for bright spirals, the peak rotational velocities of faint (MB > 14) dwarf galaxies are generally comparable in magnitude to the velocity dispersion of the gas (e.g. Begum, Chengalur & Hopp 2003; Begum & Chengalur 2004). In such a situation, it is unclear if the velocity width (e.g. at the 20 per cent level, W20, which is the commonly used indicator of the circular velocity in TF relations) is a good tracer of the circular velocity. In this paper, we discuss the TF relation using a data set which address all of the above issues. Accurate (10 per cent) tip of the red giant branch (TRGB) distances are known to most of the galaxies in our sample, and we also use accurate I-band magnitudes. Finally, all of the galaxies have been observed in H I using the Giant Meterwave Radio Telescope (GMRT) as part of the Faint Irregular Galaxies GMRT Survey (FIGGS) (see Begum et al. 2008). Pressure corrected rotation curves are available for all of the galaxies; these can be compared with W20 to see which is the better observable to use for TF studies. As a comparison sample, we use the sample of bright galaxies for which Cephied distances were measured as part of the Hubble Space Telescope (HST) key project on the extra galactic distance scale (Sakai et al. 2000). 2 T H E D WA R F G A L A X Y S A M P L E The dwarf galaxy sample is a part of an H I imaging study of faint dwarf galaxies with the GMRT the FIGGS (Begum et al. 2008). The FIGGS sample is a systematically selected subsample of the Karachentsev et al. (2004) catalogue of galaxies within 10 Mpc (see Begum et al. 2008 for details on the sample selection and observations). The FIGGS galaxies represent the extreme low mass end of the dIrr population, with a median MB 13 and a median H I mass 3 107 M . Our GMRT observations show that, contrary to the general belief that extremely faint dIrr galaxies have chaotic velocity fields (Lo, Sargent & Young 1993), most of them have coherent large-scale velocity gradients (see e.g. Begum et al. 2006). For many galaxies, these large-scale gradients are consistent with the systematic rotation. Rotation curves were derived using a tilted ring model, details can be found in Begum et al. (in preparation). For the current study, we have considered only those galaxies from the FIGGS sample which are well resolved (i.e. are more than six independent beams across) and for which tilted ring analysis gave sensible fits to the data. Examples can be seen in, for example, Begum et al. (2003), Begum & Chengalur (2004), Begum, Chengalur & Karachentsev (2005) and Begum et al. (2006). The galaxies from the FIGGS sample selected for the current study are given in Table 1. The columns are as follows. Column (1) the name of the galaxy, Column (2) Vrot, the rotation velocity at the last measured point of the rotation curve, corrected for the pressure support (see e.g. Begum et al. 2003; Begum & Chengalur 2004), Column (3) Vder, the derived rotation velocity at the last measured point of the rotation curve, Column (4) Verr, the error on the derived velocity, Column (5) the absolute B magnitude, Column (6) the absolute I magnitude, Column (7) the H I mass derived from the GMRT data, Column (8) the luminosity in B band, Column (9) the extent of the H I disc at a level of NH I = 1 1019 cm2, normalized to the Holmberg radius of the galaxy, Column (10) the B V colour, Column (11) the velocity width of the global H I profile at 20 per cent level, derived from the GMRT data, Column (12) the distance to the galaxy from Karachentsev et al. (2004) and Column (13) the method used to derive the distance e.g. the tip of the red giant branch (rgb), TF relation, the Hubble relation (H) and the member ship of the group (grp). 22 of the 29 galaxies in our sample have independent distances measured using the TRGB. In our analysis below, where appropriate, we treat the galaxies with independent distances separately from those which do not. The sources of the absolute magnitudes of our sample galaxies are listed in the table. The photometry for those galaxies for which there is no separate notation is from an HST (WFPC2 and ACS) survey of local volume dwarf galaxies. The photometry of galaxies with large angular diameters was done using SDSS images. The HST photometry was done using the recipes and equations given in Holtzman et al. (1995) and Sirianni et al. (2005). Details on both the HST and SDSS based photometry can be found in Sharina et al. (2007). Photometry for the few galaxies in our sample that are not also in Sharina et al. (2007) was done using SDSS images and an identical procedure to that followed by Sharina et al. (2007). Transformation to the standard JohnsonCousins system was done using the empirical colour transformations given by Jordi, Grebel & Ammon (2006). Note that these magnitudes are those measured within a limiting diameter (tabulated in Sharina et al. 2007). In principle, one could instead use extrapolated total magnitudes derived from assuming an exponential stellar disc. However, in practice, the surface brightness distribution is poorly fit by an exponential disc, and there is substantial uncertainty in the scalelength and location of centre of the stellar disc. Consequently, the errors in the extrapolated total magnitudes are large, and, in fact, will agree within the errorbars with those listed in Table 1. We hence use the magnitudes as tabulated by Sharina et al. (2007). As a comparison bright galaxy sample, we use a sample of 21 galaxies with Cepheid distances taken from Sakai et al. (2000). Rotation curves are available in literature for only few galaxies in this sample, hence, we use the inclination corrected velocity widths at 20 per cent level of the peak emission (W20), given in Sakai et al. (2000). The velocity widths were corrected for the line broadening due to the turbulent velocity dispersion using the prescription given in Verheijen & Sancisi (2001). Note that although there exist several intermediate-mass dwarf galaxies samples (e.g. Schombert, Pildis & Eder 1997) that could have been used as templates, we have restricted our analysis here to galaxy samples with accurate, Hubble flow independent distance estimates. 3 R E S U LT S A N D D I S C U S S I O N Table 2 lists the correlation coefficients between different indicators of the mass and the circular velocity. We use either Vrot or W20 after correction for the line broadening due to the turbulent velocity dispersion using the prescription given in Verheijen & Sancisi (2001). The stellar mass, M, was computed using the stellar mass-to-light ratio given by Bell et al. (2003) for the case of a diet Salpeter initial mass function (IMF). Two estimates of the total baryonic mass were used; the first (Mbar) was computed using the sum of the stellar mass and 1.33 times the H I mass to correct for primordial He (Cote, Carignan & Freeman 2000; Ott et al. 2001). No 14.31 12.42 12.13 13.35 14.06 15.65 11.85 12.30 14.90 14.75 14.29 14.27 15.08 13.14 13.13 14.06 12.59 14.16 15.49 12.26 12.98 13.03 13.17 12.42 11.83 13.69 14.54 13.72 11.09 15.07 13.53 12.84 14.06 15.27 15.71 13.03 13.23 16.00 15.49 15.57 15.95 16.23 13.85 13.94 14.77 14.32 15.24 16.46 13.30 13.99 13.90 13.97 13.27 12.54 14.87 16.14 14.32 11.90 log(Vrot) 0.505 (0.15) 0.459 (0.16) 0.683 (0.10) 0.631 (0.12) 0.665 (0.11) log(W20) 0.629 (0.10) 0.596 (0.11) 0.733 (0.07) 0.732 (0.08) 0.741 (0.07) FIGGS+HST log(W20) 0.931 (0.01) 0.928 (0.02) 0.910 (0.01) 0.942 (0.01) 0.943 (0.01) correction for the molecular gas was made, which is probably justifiable for the FIGGS sample, since dwarf galaxies do not seem to have a substantial reservoir of molecular gas (Taylor, Kobulnicky & Skillman 1998). While the molecular gas probably makes a substantial contribution to the total gas mass in the case of the bright spirals in the Sakai et al. (2000) sample, the baryonic mass of these systems is dominated by the stellar contribution, and the error we make in ignoring the molecular gas is likely to be subsumed by the uncertainty in the stellar mass-to-light ratio. The second estimate of the baryonic mass (Mbar1 ) uses the same estimate of the total gas mass as before, but the stellar mass was computed from Bell et al. (2003) for a Bottema IMF. For a given B V colour, the mass-to-light ratio for the Salpeter lite IMF and Bottema IMF differ only by a multiplicative constant, so the correlation between the stellar mass computed using a Bottema IMF and the circular velocity indicators is identical to that computed using the Salpeter lite IMF. These two IMFs were chosen as being representative of two extremes of the stellar mass-to-light ratio (Bell et al. 2003). The correlation coefficient errorbars were computed using bootstrap resampling. The listed values are for the entire FIGGS sample; if one uses only the subsample of 22 galaxies with TRGB distances, the computed correlation coefficients agree within the errorbars with the tabulated values. For the galaxies in the FIGGS sample alone, a few interesting points emerge. The first is that even though the H I and stellar masses of these galaxies are comparable (the median ratio of the H I to stellar mass is 1.25), the H I mass is significantly better correlated with the circular velocity indicators than the stellar mass. In fact, the H I mass correlates with the circular velocity indicators at least as well the baryonic mass estimates. The second is that the errorbars in the correlation coefficients are significantly larger for the FIGGS sample than for the combined HST+FIGGS sample. This is partly because of the substantially larger baseline of the combined sample, but as shown below, it is also partly because of genuinely increased scatter in the low-mass range. Finally, W20 correlates better with the mass indicators than Vrot, although the correlation coefficients overlap within the errorbars. The best-fitting regression of log(MI ) on log(W20) computed using a bivariate least-squares fit for the data from Sakai et al. (2000) gives log(MI ) = 8.66 (0.67) log(W20) + 0.231(1.7) and is shown in Fig. 1 as a solid line. The errorbars account for errors in both the distance measurement and the photometry. The two different panels show where the FIGGS galaxies lie with respect to this line, in Panel (A) W20 is used as the estimator of the circular velocity and in Panel (B) one uses Vrot. As can be seen, relative to the TF relation for bright galaxies, the FIGGS galaxies are underluminous for their velocity width. However, the offset is significantly larger when one uses Vrot (0.93 0.06 mag) than when one uses W20 (0.31 0.06) mag. If one does a regression fit using W20 to the entire FIGGS+HST sample, the best-fitting relation is log(MI ) = 8.77 (0.1) log(W20) + 0.741(0.3). The scatter of the FIGGS galaxies about this relation is 1.6 mag, while that of the HST sample galaxies is 0.36 mag. The scatter for the FIGGS galaxies is much larger than the typical estimated total measurement error of 0.37 mag (from the errors in the distance measurement, the photometry and the error in the velocity width scaled by the TF slope), and indicates that essentially all of the observed scatter at the faint end are intrinsic. The systematic deviation from and the increased scatter around, the TF relation set by bright galaxies, imply that dwarf galaxies have been relatively less efficient at forming stars, and that there has also be considerably more stochasticity in their integrated star formation efficiencies. Lee et al. (2007) find that dwarf galaxies (i.e. with MB > 15) show a larger scatter in the specific star formation rate as compared to bright galaxies. They suggest that this could be because the processes that regulate star formation in bright spirals are not operative in dwarfs, consistent with the finding of Begum et al. (2006) of a lack of a simple relationship between gas column density and star formation rate in dwarf galaxies. Fig. 1 indicates that even integration over time is not sufficient to remove this scatter, i.e. even the integrated star formation rate of dwarf galaxies shows substantially more scatter than that of bright spirals. In a recent study using a sample of SDSS galaxies, Geha et al. (2006) found a similar increase in scatter around the I-band TF relation at low luminosities. However, in contrast to what we find here they do not find that faint galaxies are systematically underluminous. The reason for this discrepancy is unclear, though we do note that we are using galaxies with accurately measured distances, while Geha et al. (2006) used Hubble flow based distances for their galaxies. As mentioned in the introduction, the deviation of dwarf galaxies from the B-band TF relation was one of the primary motivations for searching for a relation between the total baryonic mass and the velocity width, i.e. the Baryonic TullyFisher (BTF) relation (McGaugh et al. 2000). The BTF relation for the HST sample is shown in Fig. 2 as a solid line. As can be seen, the FIGGS sample deviates much less from this relation that it does from the I-band TF relation. The average deviation of the FIGGS galaxies from the BTF relation set by bright spirals is 0.16(0.02), 0.11(0.02) for the Salpeter lite and Bottema IMFs and using Vrot as the circular velocity indicator, and 0.09(0.02), 0.09(0.02) for the same two IMFs but with W20 as the circular velocity indicator. Clearly, whether one sees a deviation from the BTF at the faint end seems dominated by systematic uncertainties (IMF, choice of circular velocity indicator). On the other hand, the increased scatter about the BTF at the faint mass end is independent of the choice of IMF or circular velocity indicator. Fig. 3 compares the scatter about the combined best-fitting BTF for the HST and FIGGS galaxies, the difference in scatter is striking. Different choices of IMF or circular velocity indicator do not qualitatively change the plot. As discussed above, systematic uncertainties limit the measurement of the BTF. Numerous authors (e.g. McGaugh 2005; Pfenniger & Revaz 2005) have tried to approach this problem along the reverse direction, viz. to use the BTF itself to determine one or both of the scaling of the H I mass to the total gas mass and the stellar massto-light ratio. In this approach, one assumes that an intrinsic BTF relation exists, and that the right choice of stellar mass-to-light ratio and/or H I mass scaling will minimize the scatter of the observed data about the relationship. Pfenniger & Revaz (2005) found that the BTF relation is optimally improved when the H I mass is multiplied by a factor of 3; however, the actual best-fitting value is poorly constrained, and scalefactors of up to 11 lead to a tightening of the BTF. Allowing a free scaling of the H I mass is prompted by models which have a dark baryonic component whose distribution is correlated with that of H I (e.g. Hoekstra, van Albada & Sancisi 2001). These models in turn are based on the possibility that some of the dark matter in the haloes of galaxies may be in the form of cold, dense gas clouds (Pfenniger & Combes 1994; Gerhard & Silk 1996). Many observations based on dynamical and stability analysis indicate that galactic discs may be more massive than inferred from its luminous mass (Fuchs 2003; Masset & Bureau 2003; Pfenniger & Revaz 2005). Further, from theoretical modelling and N-body simulations, Pfenniger & Revaz (2004) found that if discs are marginally stable with respect to bending instabilities, the mass within the H I discs must be a multiple of that detected in H I and stars. We note that since the stellar mass and H I mass are highly correlated [correlation coefficient 0.91 between log(Mstar) and log(MH I)], simultaneous minimization of both the stellar mass-to-light ratio and the scalefactor for the H I mass is degenerate. So instead we first allow the H I mass scalefactor to vary keeping the mass-to-light ratio of the stellar disc fixed (Fig. 4) and then allow the stellar mass-to-light ratio to vary keeping the H I mass scalefactor fixed (Fig. 5). In the case of a variable H I mass scalefactor (Fig. 4), there is a broad minimum in the 2, around a scalefactor of 6.7. The minimum 2 is 357.2, as compared to 402.3 for the case in which the H I mass scalefactor is kept at 1.33. Since the number of parameters has been increased, a decrease in the 2 is to be expected. The significance of the decrease can be estimated using the F-test. For nested models with 1 and 2 degrees of freedom, respectively (p = 1 2, being the extra number of parameters in the second model) and 2 values 12 and 22, respectively, the F-test looks at the value F = Large values of F indicate a statistically significant improvement in the fit. Applying the F-test to the 2 numbers above indicates that this decrease is significant at the 2 per cent level, i.e. there is a 2 per cent probability that a H I scalefactor of 6.7 does not provide a better fit to the data. The horizontal line in Fig. 4 indicates the threshold value of 2 for a 5 per cent significance. As can be seen, this leads to a relatively broad range in the scalefactor, i.e. from 3.0 to 13.5. If one excludes the FIGGS galaxies without TRGB distances, the minimum 2 occurs at an H I mass scalefactor of 5 and has a 5 per cent significance. For models with a fixed H I mass scalefactor of 1.33 but variable stellar mass-to-light ratio, we follow the parametrization of Bell et al. (2003) and assume that the stellar mass-to-light ratio is given by log( ) = + (B V ), where and are free parameters. Fig. 5 shows contours of the resulting 2. The minimum 2 (356.3) corresponds to = 1.51, = 1.20. For comparison, = 0.549, = 0.824 correspond to the Salpeter lite IMF and = 0.749, = 0.824 correspond to the Bottema IMF. The decrease in the 2, however, is significant only at the 7 per cent level (as compared to the 2 per cent level for a variable H I mass scalefactor). Since the H I mass forms a much larger fraction of the total baryonic mass in the case of galaxies from the FIGGS sample, the greater sensitivity of the goodness of fit to the H I mass scalefactor suggests that models in which one has a scalefactor for the total baryonic mass of dwarf galaxies would probably significantly improve the fit. While this (like the earlier two models) is a phenomenological model, it would correspond to galaxy formation models in which dwarf galaxies have a larger fraction of dark (e.g. highly ionized) or missing baryons. For example models which account for the reheating and ionization of the gas during the epoch of recombination predict that large galaxies should have essentially the cosmic baryon fraction, while small galaxies (with circular velocity in the 20 km s1 range) could lose up to 90 per cent of their baryons. Of course, in such a situation, when applying the BTF relation with the observed velocity widths, we have to make the further assumption that the baryon loss does not affect the observed velocity width. The 2 curve for a model in which the scalefactor of the baryonic mass of the FIGGS galaxies is a free parameter (but the scalefactor for the baryonic mass of the HST sample is kept at 1.0) is shown in Fig. 6. Once again, the 2 curve shows a broad minimum, however the minimum 2 (289.6, for a scalefactor of 9.18) is substantially lower than in the case that only the H I mass was rescaled. The F-test gives a probability of 2 104 that this reduction in 2 is by chance. The horizontal line in Fig. 6 indicates the threshold value of 2 for a 1 per cent significance. As can be seen this leads to a relatively broad range in the scalefactor, i.e. from 2.0 to 28.8. If one includes only those FIGGS galaxies with TRGB distances, the minimum 2 occurs at a mass scalefactor of 7.56 and corresponds to a significance of 103. The best-fitting BTF relation after the baryonic mass of the FIGGS galaxies has been scaled by a factor of 9.18 is shown in Fig. 7. For reference, the original BTF relation without this rescaling is also shown. Rescaling by a factor of 9.18 implies that over 90 per cent of the original baryonic mass is dark or missing. To summarize, we present TF relations for a sample combining extremely faint dwarf irregular galaxies from the FIGGS survey and large spiral galaxies. For the FIGGS sample alone, we find that though the median H I mass and stellar mass are comparable, the H I mass correlates with the velocity width much better than the stellar mass. Distances are accurately known for the bulk of the galaxies in our sample, and we find that the extremely faint dwarfs show substantial intrinsic scatter about both the I-band TF and the BTF relations. Deviations from the BTF at the faint end are sensitively dependent on systematics, e.g. the assumed stellar mass-to-light ratio. If one assumes that there is an intrinsic baryonic TF relation, one could try to determine the total baryonic mass by searching for the prescription that leads to the tightest BTF. We find that changing the scalefactor of the total H I mass leads to a more significant tightening of the BTF than changing the stellar mass-to-light ratio. Finally, the most significant tightening that we find is when we allow the entire baryonic mass of the faint (but not the bright) galaxies to scale by a constant factor. This best-fitting relation is for a scalefactor of 9. The exact value is, however, poorly constrained, any value between 2 and 28.8 leads to a significant tightening of the BTF. The observations presented in this paper were made with the Giant Metrewave Radio Telescope (GMRT). The GMRT is operated by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. This paper has been typeset from a TEX/LATEX file prepared by the author.


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Ayesha Begum, Jayaram N. Chengalur, I. D. Karachentsev, M. E. Sharina. Baryonic Tully–Fisher relation for extremely low mass Galaxies, Monthly Notices of the Royal Astronomical Society, 2008, 138-144, DOI: 10.1111/j.1365-2966.2008.13010.x