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The discovery of a substantial population of LSB galaxies at z = 0 is relevant to a number of cosmological issues. These issues are enumerated below; those issues that are only briefly discussed here are covered in more detail in Impey and Bothun (1997).

QSO absorption lines: Increasing the number density of galaxies is a very good first step towards understanding the origin of QSO absorption lines. In addition, the discovery of Malin 1, which has 105 kpc2 of gaseous cross section at a level of Nh geq 3 x 1019 cm-2 is a helpful addition to the zoology of objects that might produce damped Lyalpha systems.

Large Scale Structure (LSS): To date, most studies of LSS are based on redshift surveys of optically selected samples, which, by definition, do not contain many LSB galaxies. If LSB galaxies are better tracers of the mass distribution, then the linear biasing factor between mass and light has a surface brightness dependence. This would be an ugly complication to the various sophisticated attempts to determine bOmega0.6, where b is the (scale-independent) linear bias parameter (see Strauss & Willick 1995). In an attempt to shed light on this, Bothun et al. (1985, 1986) performed a redshift survey of approx 400 LSB disk galaxies, primarily selected from the UGC. Few of these galaxies were in the CFA redshift survey at that time. That data, coupled with a thorough analysis of the clustering properties of LSB galaxies by Bothun et al. (1993) and Mo et al. (1994) provides the following insights:

(1) On scales geq 5 h100-1 Mpc LSB galaxies trace the identical structure as HSB galaxies.
(2) LSB galaxies generally avoid virialized regions.
(3) On scales leq 2 h100-1 Mpc LSB galaxies are significantly less clustered. In fact, there is a significant deficit of companions within a projected distance of 0.5 h100-1 Mpc indicating that LSB disks are generally isolated. In general, the correlation function has a lower amplitude for LSBs (see Mo et al. 1994) resulting in them being less clustered on all scales, compared to the HSB galaxies contained in the CFA redshift survey.
(4) Whether in groups or clusters, LSB galaxies are usually near the edge of the galaxy distribution. The results of O'Neil et al. (1997a) show that, in the cluster environment, there is a limiting value of µ 0 which depends on local galaxy density. If one considers that the highest surface brightness galaxies of all, ellipticals, tend to occur in virialized regions then we have the surface brightness extension of the morphology-density relation of Dressler (1980). That is, the local galaxy density limits the surface mass/luminosity density of galaxies.
(5) LSB galaxies are not preferentially found in large scale voids. For instance, there are none in either the CFA bubble (Bothun et al. 1992) or the Bootes Void (Aldering et al. 1997).

The following scenario can be advanced. Given a Gaussian initial spectrum of density perturbations which will eventually form galaxies, there should be many more low density perturbations than high density ones. Many of these low density perturbations are subject to disruption or assimilation into other perturbations and hence will not produce individual galaxies. However, if a substantial percentage of them do survive to produce individual galaxies then we would expect them to dominate the galaxy population. We tentatively identify the LSB galaxy population with these 1-2sigma peaks in the initial Gaussian perturbation spectrum. If that is the case, we expect LSB galaxies to (1) have formed in isolation, and (2) be fair tracers of the mass distribution on large scales. This isolation on small scales must clearly affect their evolution since, compared to HSB galaxies, LSB galaxies have experienced fewer tidal encounters with nearby galaxies over a Hubble time. Tidal encounters are effective at clumping gas and driving global star formation. Without this external hammer, LSB galaxies would continue to evolve slowly and passively.

The Faint End Slope of the Galaxy Luminosity Function: In recent years, a lot of different values have appeared for the faint end slope, alpha, of the Schechter luminosity function. The canonical value of alpha approx -1.25 for HSB field galaxies can be compared with observations of nearby clusters that show alpha of approx -1.1 (but see Wilson et al. 1997 for significantly steeper values for more distant clusters). However, alpha = -1.9 has been determined for low mass irregular galaxies in the CFA redshift survey (Marzke et al. 1994). The safest thing to then conclude is that recent surveys have now produced a variety of different values of alpha indicating that its a) uncertain and b) may evolve with time.

In general, corrections for incompleteness to the galaxy luminosity function have been erroneously applied in the past based on apparent magnitude only. This is conceptually incorrect since galaxies are selected on the basis of a combination of surface brightness and luminosity. This is best illustrated in the Virgo and Fornax clusters, where the diffuse and fairly large LSB dwarf were missed in earlier surveys but detected using the Malin method. The integrated luminosity of these galaxies is brighter then many of the Binggeli et al. (1984) dwarfs due to their large scale length. The surveys in Virgo (Impey et al. 1988) and Fornax (Bothun et al. 1991) revealed LSB galaxies that were up to 3 magnitudes brighter than the nominal magnitude limit of the Binggeli et al. (1984) survey but which were missed by that survey.

Figure 8 (adapted from Figure 10 in Impey et al. 1988) illustrates the basic point for the Virgo cluster. When these "missing galaxies" are properly accounted for, there is a significant increase in the faint end slope of the luminosity function relative to that which is obtained simply by applying a correction for incompleteness based on apparent flux. The correlation between surface brightness and magnitude that seems to hold for dwarf elliptical galaxies (e.g., Sandage et al. 1985; Binggeli et al. 1985; Caldwell and Bothun 1987; Bothun et al. 1989) has been shown to break down below µ 0 approx 24.5 (e.g., Bothun et al. 1991) indicating that corrections for apparent flux do not mimic the more proper correction based on surface brightness selection effects (see also Sprayberry et al. 1997; Impey and Bothun 1997). Combining the Virgo and Fornax cluster sample of dwarfs yields alpha = -1.55 ± 0.05 after these proper corrections are made. Such a steepening indicates that LSB galaxies dominate numerically in clusters. If stellar/baryonic M / L increases with decreasing surface brightness for this cluster population then they contain a significant fraction of the baryonic material in clusters (which might exacerbate the fb problem in clusters). It is interesting to speculate that cluster LSB galaxies might represent the results of a phase of intense baryonic blow-out at higher redshifts. These relic galaxies then might be the source of the gas seen in clusters as well as the enrichment of that gas. In the case of the Virgo cluster, there are approximately twice as many dwarfs as brighter galaxies.

Figure 8
Figure 8. The luminosity function of the Virgo cluster galaxies showing the difference between corrections based on apparent magnitude from those based on surface brightness selection effects. The solid circles/squares give the raw counts and error bars as a function of apparent magnitude. The filled circles are the result of applying an incompleteness correction based only on apparent magnitude. The open circles are the result of applying a correction based on surface brightness. These galaxies are missed not because of reduced apparent flux, but because too much of their flux is below the night sky background. As a result, the correction correction for incompleteness based on surface brightness considerations sets in at a substantially brighter magnitude than corrections based only on apparent flux. These are the galaxies in Virgo that were discovered by Impey et al. 1988.

The APM survey of Impey et al. (1996) allows the contribution of LSB galaxies to the field galaxy luminosity function to be estimated. This has been done in detail by Sprayberry et al. (1997) who find a faint end slope of alpha = -1.42 compared to alpha = -1.09 for all disk types in the CFA redshift survey. It is too soon to tell if there is a significant difference between the cluster and field faint end slopes but in both cases, the discovery of LSB galaxies in both environments yields the same result: the faint end slope steepens.

The Faint Blue Galaxy Connection: One immediate result from various deep surveys of galaxies (e.g., Lilly et al. 1991, Lin et al. 1997, Odewahn et al. 1996, Driver et al. 1996, Glazebrook et al. 1995) was the discovery of an apparent excess, relative to local observations, of faint galaxies with blue colors. These enigmatic faint blue galaxies (FBGs) are the subject of much research. Since the FBG population apparently does not exist at z = 0, reasons for their absence from galaxy catalogs of the local universe must be found. Two possible approaches involve either a very large merger rate since z approx 0.7 or rapid fading of this FBG population (Efstathiou et al. 1991; Colless et al. 1990). This faded population is potentially an important constituent of the total baryonic content of the universe (see Cowie 1991; Bouwens and Silk 1996). However, arguments presented above suggest that these faded remnants have not yet been detected in large numbers (see also Dalcanton 1993).

A number of explanations for the FBG ``problem'' have a natural linkage with LSB galaxies at z = 0. Some of the possible explanations are the following:

If optically selected LSB galaxies do have normal UV fluxes, then this population can become conspicuous in faint galaxy surveys when this light is redshifted into the ground based filter set. This would occur, in general, over the redshift range 0.5-1. It is possible that some of the FBGs are in fact LSB galaxies! For example, the median luminosity of the FBGs in Lilly et al. (1991) is identical to the LSB sample of McGaugh & Bothun (1994) and both samples are dominated by late type galaxies which are weakly clustered.

The FBGs are a population of star bursting dwarf galaxies located at modest redshift. This suggestion takes advantage of the fact that in any GLF with alpha leq -1, low mass dwarf galaxies dominate the space density. To produce the FBGs, however, these dwarf galaxies have to be at least an order of magnitude brighter at modest redshifts which requires a fairly significant star formation rate. Subsequent heating of the ISM by massive stars and supernova should be sufficient to heat it beyond the escape velocity of these low mass systems (see Silk et al. 1987; Wyse and Gilmore 1992) and hence such galaxies have a significant phase of baryonic blowout after which they fade to very low absolute luminosities and hard to detect at z = 0. This mechanism gives the universe a channel for making baryons ``disappear'' with time. This hypothesis has been investigated in detail by Phillips and Driver (1995) and Babul and Ferguson (1996).

The number density of galaxies is not conserved and the FBGs merge with other galaxies. It is difficult to support this hypothesis because (1) the FGBs are already weakly clustered, and (2) the required merging rate is significantly higher than the inferred rate at modest redshift by Patton et al. (1997). The merger idea works best if the FBGs are predominately at higher redshift, where the merger rate is higher owing to the smaller volume of the universe.

The FGBs represent an entirely new population of galaxies - one defined by a star formation history or an initial mass function that allows only a limited window of visibility before the galaxies fade to extremely low surface brightness levels by z = 0. As an example, an IMF which forms no stars less than 1 Msmsun produces a galaxy that is destined to have a very bright phase and then fade into mostly white dwarf remnants at z = 0. A collection of 1011 white dwarfs distributed in a disk with scale length of 2 kpc would have a central surface brightness of µ 0 = 27.5 which would be below the current detection threshold of LSB galaxies. This situation illustrates the kind of extreme fading which would be necessary to hide this component from being detected locally. Interestingly, the latest MACHO results (see Sutherland et al. 1996) strongly suggest that halo white dwarfs are the main cause of the 8 observed lensing events towards the LMC. In that sense, the Galactic halo might be regarded as a LSB galaxy.

The FBGs are an artifact of uncertainties in the determination of the local galaxy luminosity function. In particular, the faint end slope has been seriously underestimated from nearby samples. Alternatively, the local normalization, Phi(0), of the galaxy luminosity function could be too low. This would result if, for instance, deep surveys were more efficient at selecting galaxies than nearby surveys. Driver et al. (1994a, b) have explored this possibility and concluded that the local normalization may well be seriously underestimated. However, the effect of increasing the space density at z = 0 can only partially offset the excess FBG counts. A much larger lever arm is provided by steepening alpha.

Sprayberry et al. (1997) have considered the effects of increasing alpha (due to LSB inclusion) and increasing Phi(0) on the ability for LSB galaxies to explain the FBG excess. The conclude that the CFA survey has missed about 1 / 3 of the total galaxy population at z = 0. While this helps to resolve the apparent difference between the large numbers of FBGs and the local galaxy population, this effect by itself is not large enough to completely resolve the issue (see also Ferguson and McGaugh 1995). For additional assistance we turn to the Lilly et al. (1995) redshift survey of approx 500 faint galaxies. Their sample has excellent quality control and is fairly free from selection effects and is primarily aimed at determining the galaxy luminosity function up to a redshift approx 1.

Lilly et al. detect a change in the luminosity function of blue galaxies by approximately one magnitude between z approx 0.38 and z approx 0.62, and another magnitude between z approx 0.62 and z approx 0.85. Moreover, many of these galaxies have been observed with HST in order to measure characteristic surface brightnesses. Schade et al. (1995) find that the disks of these blue galaxies are approx 1 magnitude higher in surface brightness at z = 0.8 than z = 0.3. These studies provide rather strong evidence for luminosity evolution in the FBGs. In a 15 Gyr old universe, there are approximately 3.3 billion years between z = 0.85 and z = 0.38. The data indicates that a typical FBG would decline in luminosity by a factor of six (e.g., 2 mags) over this time period. This modest decline is quite consistent with standard population synthesis models involving a normal IMF which fades after a significant burst of star formation has occurred to make these objects visible at higher redshift. The decline in luminosity is primarily a reflection of the disappearance of the upper main sequence. By z = 0, these galaxies will certainly not have faded to levels that preclude their detection, and indeed many of them are likely to be represented by the z = 0 red LSB population which has now been discovered.

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