THE SMALL SCALE ENVIRONMENT OF LOW SURFACE BRIGHTNESS DISK GALAXIES

Authors: Gregory D. Bothun, Department of Physics, University of Oregon

James M. Schombert , IPAC/JPL, Cal. Inst. of Technology

Christopher D. Impey and David Sprayberry , Steward Observatory, University of Arizona

Stacy S. McGaugh, Department of Astronomy, University of Michigan
ABSTRACT
We use a sample of 340 low surface brightness (LSB) disk galaxies with measured redshifts in combination with the Center for Astrophysics redshift survey to test the hypothesis that LSB galaxies have a deficit of nearby companion galaxies compared to high surface brightness (HSB) disk galaxies. We find a very strong statistical deficit of galaxies located within a projected radius of 0.5 Mpc and within a velocity of 500 km/s around LSB disk galaxies compared to HSB ones. Furthermore, comparing LSB and HSB disk galaxies which are located in the same portion of the sky indicates that the average distance to the nearest neighbor is 1.7 times farther for LSB disk galaxies. A Komologorov-Smirnoff test rules out, at greater than the 99% confidence level, the hypothesis that the distribution of nearest neighbor distances is the same for HSB and LSB disk galaxies. We speculate that LSB disk galaxies have relatively long formation timescales and therefore must form in relative isolation. In addition, the lack of tidal interactions over a Hubble time serves to suppress the overall star formation rate as no external trigger is available to help clump the gas. The observed low surface densities of H I in combination with the low probability of tidal interactions effectively prevents these disk galaxies from evolving very rapidly.

1. INTRODUCTION

The evolutionary processes which determine the surface brightnesses of galactic disks remain enigmatic. Over the last five years, sufficient data in a variety of wavelengths has been gathered (eg McGaugh 1992; Knezek 1992; Schombert etal 1992; Peletier and Willner 1992;) to effectively dispel the once popular notion that the central surface brightnesses of disk galaxies are a constant (see Freeman 1970; van der Kruit 1987). Instead, central surface brightness (B(0)) spans a large continuum of values with no clear indication of any hard lower limit on B(0). Moreover, the space density of galaxies as a function of B(0) remains unknown due essentially to 50 years of selection effects associated with the cataloging of galaxies. An intensive effort to alleviate this selection effect has been pursued by Schombert etal (1992) and Impey etal (1993). That effort has now detected hundreds of new disk galaxies whose contrast with the night sky background is only a few percent. This new class of galaxies, named low surface brightness (LSB) galaxies, has properties which are quite distinct from those that define the Hubble sequence (see McGaugh 1992).

The role that environment plays in the evolution of galaxies also remains enigmatic. The present arrangement of galaxies into clusters, low density but large scale walls, or shells surrounding large scale voids means that a wide range of environments exists. The existence of the morphology-density relation (eg Dressler 1980 Postman and Geller 1984) and the Butcher-Oemler effect (Butcher and Oemler 1978; see also Bothun and Dressler 1986; Dressler and Gunn 1990; Lavery etal 1992) are the two most obvious examples of environmental influences on galaxy evolution. The physics of this influence, as well as its duration and at which redshift it is most effective, however, is not at all clear from the available data. For instance, the role of merging and galaxy evolution is now under intense scrutiny. Some extreme positions (eg Schweizer etal 1990, Lavery etal 1992, Carlberg and Charlot 1992) suggest a rather larger merging rate which has lead to the general galaxy population. Others acknowledge that merging is occurring now but downplay its overall prominence (eg Mihos etal 1992, Majewski etal 1993, Zepf 1992). A balanced perspective is offered by Hernquist (1992).

Clearly, mergers or interactions between galaxies will have the greatest probability of occurring in a low velocity dispersion environment in which several galaxies are embedded. The frequency of occurrence of galaxies in this type of environment depends both upon the unknown details of galaxy formation and large scale structure formation (eg the exact shape of the power spectrum). For instance, excess power on large scales is conducive to delayed infall of galaxies, which may have formed in relative isolation, towards denser structures. Furthermore, if the mean surface brightness of a galaxy is related to the amplitude of the initial density perturbation from which it formed, then there may well be a difference in the spatial distribution of high and low surface brightness galaxies. In particular, at a given mass, high surface brightness (HSB) galaxies would form more rapidly, from higher density perturbations and might be more strongly clustered and thus experience more interactions over a Hubble time. LSB galaxies, on the other hand might be more weakly clustered and experience less interactions. To date, the clustering properties of LSB galaxies compared to HSB galaxies have been studied only on a scale of 5-10 Mpc (see Bothun etal 1986; Thuan etal 1987; Schneider etal 1990) and little is known about the smaller scale clustering properties.

Recent observations by van der Hulst etal (1993) and McGaugh (1992) vividly show that the surface densities of H I throughout LSB disks are at or below the threshold criterion for star formation established in Kennicutt (1989) (see also Impey and Bothun 1989). Without a mechanism to clump this gas (eg Mihos, Bothun and Richstone 1993), star formation is unlikely to proceed on a large scale in these disks and hence their evolutionary progress is temporarily static. Indeed, it is unlikely that the star formation rate in the past in these galaxies was ever very high since this would leave, as a trace, a HSB red component of the stellar population. In general, such a component is not seen in LSB disks with the possible exception that some of these galaxies do contain normal bulges. Hence, there must be some mechanism which is operative in HSB disks but missing in LSB disks to account for the difference in star formation rates averaged over a Hubble time.

A possible clue to this mechanism comes from the recent work of Zaritsky and Lorrimar (1992) who have searched for companion galaxies around the LSB sample of Impey etal (1993) and found a significant deficit compared to a control sample. They speculate that the lack of tidal interactions in LSB disks acts to suppress star formation and to keep the systems relatively static. Such speculation does have some theoretical basis (see Lacey and Silk 1991) and indeed, the tendency for some giant LSB disks to be isolated has been emphasized previously by Bothun etal (1990) and may provide a key to their formation and/or survival (see also Hoffman, Wyse and Silk 1992). While better statistics are required to further progress in this area it has been our general impression, based on repeated visual inspection of images of LSB galaxies, that there is seldom another conspicuous galaxy nearby.

In this paper, we seek to further quantify our visual impression by using redshift surveys to compare the clustering properties of LSB and HSB disk galaxies on a scale of 0-2 Mpc in order to statistically assess any differences, should they exist. Section 2 describes the LSB sample and the available control samples of HSB disks as well as our procedure for identifying companion galaxies. Section 3 presents the results of this comparison where it can be seen that the statistics strongly bear out our visual impression. Section 4 then discusses these results and suggests possible reasons why LSB galaxies inhabit sparser small-scale environments that HSB galaxies. All distances and scales are derived using a Hubble constant = 100.

2. Sample Characteristics and Reduction Technique

2.1 LSB Sample

Almost by definition, redshifts of LSB galaxies are difficult to obtain by optical means, unless they have a well-defined nucleus or bulge. Fortunately, however, many of these LSB disks are rich in H I, as measured by the distance independent ratio of hydrogen mass to blue luminosity and thus redshifts can be obtained at 21-cm . In fact, the distributions of H I masses for LSB and HSB disk galaxies are nearly identical (see Schombert etal 1992) with the caveat that LSB disks have lower central column densities and larger H I extents (see van der Hulst etal 1993). To date, the largest redshift surveys of LSB disk galaxies are those of Bothun etal (1985), Schombert etal (1992) and Impey etal (1993). The survey of Bothun etal (1985) comes exclusively from the UGC and the large scale clustering characteristics of that sample have been discussed by Bothun etal (1986; see also Schneider etal 1990). Most of those redshifts now appear in the redshift catalog maintained by the Center for Astrophysics (hereafter denoted ZCAT ). Furthermore, owing to the relatively poor plate material, the UGC sample does not go to nearly as low of surface brightness levels as those of Schombert etal (1992) and Impey etal (1993) (see discussion in Schombert and Bothun 1988). Hence, we form our LSB sample from the latter two recent surveys.

The Schombert etal (1992) sample is derived from visual inspection of the plates of the Second Palomar Sky Survey (POSS-II) and is confined to a narrow declination strip located at 20 +/- 10 degrees. The spatial distribution of those galaxies with measured redshifts, together with the redshift distribution, is shown in Figure 1. The Impey etal (1993) survey is a machine selected equatorial strip generated by APM analysis of UK Schmidt plates.

Figure 2 displays the spatial and redshift distributions for that sample. The appearance of 'holes' in the spatial distribution for declinations < 0 is a reflection of the inability to obtain H I redshifts from Arecibo at those declinations. As Impey etal (1993) discuss, the characteristics of this machine selected sample are similar to the POSS-II sample. In particular, CCD surface photometry of galaxies in both samples (eg McGaugh 1992, Impey etal 1993) shows that both select disks with B(0) > 23.0 mss and that the light profile can be easily detected out to 4 scale lengths (B ~ 27.5 mss ). The lowest values of B(0) which appear in either survey are ~ 25.0 mss . Both surveys also have a similar depth and both surveys have similar redshift distributions, although the APM sample does have a larger percentage of galaxies with v > 12,000 km/s. Most of these higher velocity galaxies have had their redshifts determined from optical spectroscopy instead of at 21-cm.

2.2 HSB Comparison Sample

To form a comparison sample, we have searched through the electronic version of ZCAT as it was distributed in 1991 October. Several criterion are established to produce the desired end product, namely a sample of HSB disk galaxies with measured redshifts. To begin with, a magnitude and diameter must be tabulated, to compute a surface brightness which we parameterize as a surface magnitude defined as

surface mag = apparent mag + 5 * log (diameter)

where D is the diameter measured in arcseconds. Magnitudes and diameters generally come from the Zwicky catalog, the UGC and the ESO catalog. Next we use the morphological information in ZCAT and only select objects which are tagged as having T > 1. Finally, since the relation between velocity and distance can become particularly contorted in the Local Supercluster, we restrict our analysis of both the HSB and LSB samples to objects with velocities > 2000 km/s. This velocity cut also eliminates true dwarf galaxies from either sample. This leads to a sample of 5704 disk galaxies. We now apply one additional velocity cut based on the empirical observation that few galaxies in the Zwicky, UGC or ESO catalogs have velocities > 12,000 km/s. After applying this last criterion we are left with a sample of 5493 disk galaxies. The distribution of surface magnitudes for that sample is shown in Figure 3 . It is remarkably Gaussian which is a likely manifestation of the selection effects first pointed out by Disney (1976) combined with large random errors in the tabulated magnitudes and diameters. To further obtain a sub-sample of HSB disk galaxies, we then select only those galaxies with mean surface brightness higher than the median shown in Figure 3. This leaves a sample of 2627 galaxies which have a mean surface brightness of 23.75 +/- 0.61 mss . Curiously, this level of mean surface brightness is identical to the mean surface brightness of a Freeman disk (eg B(0) = 21.65) within the B=25.0 mss isophote (equivalent to the mean surface brightness within ~ 3 scale lengths). By comparison, the mean surface brightness within 3 scale lengths for the typical LSB galaxy in our sample is 1.5- 2.0 mss less. In addition to this global sample of HSB spirals culled from ZCAT , we further divide it into two subsamples which have the same sky coverage as the POSS-II and APM surveys. These two samples contain 870 and 137 galaxies respectively. The sparseness of the APM HSB sample renders it of little use as a comparison sample. We include it here only for the sake of completeness.

Rest of Document still Under Construction

At the suggestion of the referee we consider two additional samples. We use only the POSS search area in the construction of these samples since, as the rest of this paper discusses, this area contains the most reliable data. The first sample, called Subset A, consists of a HSB comparison sample now restricted to morphological types of Sb and later. There are 790 galaxies in this sample, compared to the 870 galaxy sample discussed above. The referee has suggested this comparison sample is more appropriate in the comparison of disk surface brightnesses as including spirals with large bulge-to-disk ratios in the HSB comparison sample clearly elevates its mean SB level. This is certainly a valid concern. However, we note two items in this regard 1) the actual number of type Sa and Sab galaxies is small (about 20% of all disk galaxies in ZCAT ) and 2) the major point of this study, as well as that of Zaritsky and Lorrimar (1992), is to investigate the relation between mean galaxy surface brightness and the small scale environment. Without detailed surface photometry for all the galaxies, one can not make a valid comparison between {\it disk} surface brightness and small scale environment. The referee has also suggested considering a sample of LSB galaxies which is independent of our new samples, namely, those LSB galaxies that were in ZCAT prior to the more recent redshift surveys of Schombert etal (1992) and Impey etal (1993). In the POSS area, this sample of ZCAT LSB galaxies, not coincidentally, consists mostly of UGC galaxies whose redshifts were obtained by Bothun etal (1985). The referee suggests defining a ZCAT LSB galaxy as one with mean SB fainter than 25.75. In the velocity range 2-12,000 km/s, there are 185 galaxies that define this criteria. However, 8 of those galaxies are cD's or peculiar interacting galaxies with LSB extensions. Upon excluding these, this sample, called Subset B consists of 177 galaxies, only 25 of which have velocities $\geq$ 7000 km/s, which indicates the high degree of incompleteness for this ZCAT LSB sample at high velocities. Moreover, the median redshift of the Subset B sample is 4600 km/s which is significantly lower than our POSS LSB and HSB samples. Hence Subset B is a less representative sample of LSB galaxies as it lacks the important class of large LSB disk galaxies that have been discovered by Schombert etal (1992) and Impey etal (1993). \bigskip \leftline{\bf 2.3 Finding Nearby Galaxies} \bigskip Each individual HSB or LSB galaxy is cross-referenced with the entire contents of {\it ZCAT} to search for other galaxies which are located within a certain velocity range and projected radius (in Mpc). These radius and velocity parameters are somewhat arbitrary but are uniformly applied to both samples. Here, we are not interested in applying any ``friends-of-friends'' algorithm for purposes of group identification as others (eg Ramella etal 1990) make that a specific focus of {\it ZCAT} analysis. Rather, we wish to roughly estimate the number of galaxies that are located in the same phase space element as an individual LSB or HSB galaxy. A more detailed treatment of the autocorrelation function of LSB compared to HSB disk galaxies is beyond the scope of this paper but can be found in Mo etal (1993). Based on properties of known groups, we searched in a cylinder of projected radius 2.4 Mpc and depth $\pm$ 500 km/s. Thus, for each LSB or HSB galaxy, we cycle through {\it ZCAT} and count the number of galaxies that are located within a projected radius of 2.4 Mpc and have a velocity within 500 km/s of that given galaxy. This yielded a sufficient number of `hits' per galaxy that we are able to bin the radius parameter in units of 0.5 Mpc and to then compare the mean number of nearby galaxies in 4 radius intervals. In addition, we also record the actual distribution of projected separations for purposes of doing a nearest-neighbor analysis and to compare the cumulative distributions between the HSB and LSB samples using the KS test. Care is taken to ensure that the search galaxy is not counted twice. In the case of HSB spirals this is easily done as the velocity of the search galaxy is identical to the listing in ZCAT (since it was culled from {\it ZCAT} in the first place). For the individual LSB galaxy, determining if it already has an entry in {\it ZCAT} is considerably more difficult for two reasons: 1) if it is in {\it ZCAT} then, in most cases, its velocity does not come from the H I detections of Schombert and Bothun (1988), Schombert etal (1992) or Impey etal (1993) and hence the velocity in {\it ZCAT} is not identical to that listed in those sources. Furthermore, there are small positional discrepancies between {\it ZCAT} and our master LSB catalog. Hence, we have assumed that any {\it ZCAT} hit which has a positional difference of $\leq$ 10 \arcm and a velocity difference of $\leq$ 100 km/s is a real match to the search galaxy and does not represent another nearby galaxy. Approximately 10 % of the total LSB sample meet this criterion and inspection of the available image does not reveal another nearby galaxy. 2) A small number of galaxies selected to be LSB are, in fact, HSB galaxies which pronounced LSB extensions (see Schombert and Bothun 1988 for more detail). In general, these galaxies have very peculiar morphologies and some seem to be of early type but have pronounced shell structure around them. The {\it ZCAT} entry for these galaxies can consists of 2 (or more) measurements as different knots of emission have been observed. A total of 8 LSB galaxies in the combined POSS + APM sample have been removed on this basis. \bigskip \leftline{\bf 3.0 Search Results} \bigskip \leftline{\bf 3.1 Possible Biases} \bigskip For our comparisons to be valid, we must ensure that there is no significant difference in either the redshift distribution or the sky coverage of {\it ZCAT} relative to the POSS-II and APM LSB surveys. For instance, if the median redshift of the LSB samples was significantly higher than that of {\it ZCAT}, this would lead to an artificial reduction in the number of 'hits' found in {\it ZCAT} for that LSB sample. Similarly, inadequate sky coverage in {\it ZCAT} in the LSB survey fields would also bias the comparison. The strip of sky corresponding to the POSS-II search (see Figure 1) contains 4482 entries in {\it ZCAT} in the velocity range 2,000 - 12,000 km/s and covers \app 14% of the sky. This yields a surface density of \app 0.8 {\it ZCAT} galaxies per square degree. The strip of sky corresponding to the APM search contains 1051 entries in {\it ZCAT} and corresponds to about 5% of the sky. This yields a surface density of \app 0.5 {\it ZCAT} galaxies per square degree. This reduced surface density is a reflection of the lower mean galactic latitude of the APM survey. Hence, the spatial distribution of the POSS-II LSB galaxies better matches the current sky coverage of {\it ZCAT}. We will take this factor into consideration in the subsequent analysis. As discussed in $\S$ 2, we have restricted the velocity search range to 2000 $\leq$ v $\leq$ 12000 km/s for all samples. In the POSS search area, the median redshift of the {\it ZCAT} sample is 6850 km/s which, not surprisingly, is the approximate median redshift of the Great Wall (see Geller and Huchra 1989). For the LSB sample the median redshift is 5850 km/s. The median redshift of the {\it ZCAT} sample in the APM search area is 5750 km/s which reflects the Perseus-Pisces Supercluster. The median redshift of the APM sample is 7200 km/s; significantly higher than {\it ZCAT} and hence incompleteness in the {\it ZCAT} sample will be more significant in this sample. This coupled with the reduced surface density coverage of {\it ZCAT} in the APM search area indicates that the ensemble average of companion galaxies in the APM LSB sample will be artificially less than the POSS-II sample. This is indeed borne out in the analysis (see below) but we can partially compensate for this bias by velocity filtering the data. \bigskip \leftline{\bf 3.2 Comparison of Mean Number of Companions} The simplest statistic which can be formulated just involves counting companions out to a specified radius (\app 2.4 Mpc in this case). While this statistic carries virtually no spatial information, it does provide a rough test of the hypothesis that LSB galaxies have, on average, fewer nearby galaxies than HSB disk galaxies. Table 1 presents the results of these raw counts. In table 1, column 1 specifies the sample and column 2 gives the velocity range. Column 3 gives the projected radius out to which the counts were made while column 4 gives the number of galaxies used in formulating the sample mean (column 5). In general, mean quantities are calculated after one cycle of 2.5 $\sigma$ rejection. The number of rejected galaxies is given in parenthesis in column 4. The first 6 rows of Table 1 refer to all companions contained within a projected radius of 2.4 Mpc and the means are formed without any rejection. Error bars on these means represent root N counting noise. For the remaining entries in this table mean counts are given in annuli of width 0.5 Mpc. Error bars are $\sigma$/$\sqrt N$. The basic result is that the combined APM + POSS LSB sample is deficient in companions at the 5.6 $\sigma$ level compared to HSB spirals in {\it ZCAT}. Note also, that since there are \app 36,000 galaxies contained in ZCAT , 50% of them are located within a projected radius of 2.4 Mpc from some HSB spiral. This is consistent with the well established correlation length of galaxies of 5-10 Mpc. The next level of analysis involves binning the data by radius and velocity. To account for possible velocity bias and differential incompleteness effects in sample comparisons, we subdivide each HSB and LSB sample into two velocity regimes. The low velocity regime is defined by 2000 $\leq$ V $\leq$ 7000 km/s and the high velocity regime is defined by 7000 $\leq$ V $\leq$ 12000 km/s. Table 2 summarizes the differences between the means, in units of $\sigma$, in the comparison of various LSB and HSB samples. The POSS and APM samples are compared at radii of 0.5,1.0,1.5 and 2.0 Mpc to the total HSB sample as well as to the respective HSB sample that covers the equivalent area of sky. The values in parenthesis are those obtained by considering Subset B in comparison to the POSS HSB sample. Figure 4 graphically summarizes the information contained in Table 2. The plotted error bars are $\pm$ 2$\sigma$ in length. The statistically poor APM HSB sample is omitted from these Figures as are Subsets A and B because they seem to provide redundant information. In particular, the entries in Table 2 for Subset A are only slightly reduced from those in the POSS LSB/HSB comparison. Hence, the elimination of type Sa and Sab galaxies from the comparison sample has made little difference. The consideration of Subset B (drawn exclusively from ZCAT ), actually yields slightly higher levels of significance (in the most relevant 2-7000 km/s slice) owing to its larger size. In any case, consideration of Subset B confirms the result obtained by using the LSB sample of Schombert etal (1992) which, as argued, is a more representative sample of LSB disk galaxies than is Subset B (see also discussion in Bothun etal 1986). A fuller discussion of these results is presented in the next section. We briefly note here that 1) in all velocity cuts and at all radius bins, there is a highly significant difference in the mean number of companion galaxies between the HSB and LSB samples, 2) the APM and POSS samples generally track each other very well, and 3) {\it ZCAT} exhibits a more clustered behavior in the POSS search region than over the whole sky. The differences are particularly significant at the high velocity end which means that the POSS search region has been more thoroughly covered by {\it ZCAT}. \bigskip \leftline{\bf 3.3 Nearest Neighbor Distribution} Another statistical test for investigating differences in the small scale environment between HSB and LSB samples involves determining the mean projected distance to the closest galaxy. However, in addition to noting the mean difference we can also apply the KS test on the respective cumulative distribution functions. This was done by binning the distance to the nearest projected galaxy in bins of width 0.2 Mpc from 0 to 2.4 Mpc. These results are summarized in Table 3 and graphically shown in Figure 5. In table 3, column 1 gives the sample, column 2 gives the number of galaxies which have at least 1 companion within a projected radius of 2.0 Mpc, column 3 gives the velocity range and column 4 gives the mean projected distance and its error to the nearest companion. Column 5 and 6 give the KS statistic $D_{max}$. The number in parenthesis is the confidence level that $D_{max}$ exceeds. For very large samples, $D_{max}$ asymptotically approaches a value of .163 at the 99% confidence interval. Clearly, the KS test strongly rejects the hypothesis that the distribution of nearest neighbor distances is the same for the HSB and LSB samples. Importantly, the KS test also shows that the nearest neighbor distributions for all the various HSB samples are consistent with one another and that the APM and POSS LSB samples are consistent with each other. \bigskip \leftline{\bf 4 Discussion} \bigskip \leftline{\bf 4.1 A Lack of Nearby Companions} The statistical results presented in $\S$ 3 strongly show that there is a deficit of other galaxies around LSB galaxies as compared to HSB galaxies. This deficit appears to be quite real. We can not account for any selection effect which would result in such a pronounced difference. For instance, both the visual search of the POSS and the machine search of the APM were blind to the presence of other galaxies; that is, we did not look only where there were no other galaxies. Since the median redshifts of the various HSB and LSB samples are roughly similar, this deficiency of galaxies nearby to LSB samples is also not the result of redshift incompleteness in ZCAT . Moreover, although the difference in mean number of companions is very significant between all the LSB and HSB samples, it is most pronounced between the POSS LSB sample and the ZCAT HSB sample which is located in the POSS search area. We emphasize that this area of the sky has been the most heavily surveyed for inclusion in ZCAT and hence represents the fairest comparison, especially in the 2000 -- 7000 km/s velocity range. From the data in Table 1 for the POSS LSB and HSB samples, we see that the deficit in the number of galaxies grows from 0.89 $\pm$ 0.08 at r =0.5 Mpc to 2.71 $\pm$ 0.40 at r = 2.0 Mpc. The best fit linear slope for the POSS HSB sample to the 4 data points plotted in Figure 4 is 3.08 $\pm$ 0.18 compared to 2.42 $\pm$ 0.24 for the LSB sample; a marginally significant (2.4 $\sigma$) difference. Hence, normalized to the r =0.5 Mpc bin, the LSB sample would appear to contain a deficit of galaxies at larger radii in comparison to the HSB sample. However, to draw this conclusion from examining the data in this manner is quite erroneous since the r =2.0 Mpc data point represents 16 times more projected area. Therefore, the relevant quantity to plot is surface density of galaxies. This is shown in Figure 6, where the surface density now includes the search galaxy itself. This Figure makes it quite clear that, in all velocity intervals, the deficit between HSB and LSB galaxies occurs primarily at small radii. At progressively larger radii, the surface density around LSB galaxies smoothly mergers with that around HSB galaxies, although the apparently small differences at r = 2.0 Mpc remain significant. This behavior is consistent with the results of the nearest neighbor analysis shown in Figure 5, where the largest difference also occurs at the smaller radii. It is also consistent with the assertions of Schombert etal (1992), Thuan etal (1987) and Bothun etal (1986) that, on scales $\geq$ 5 Mpc, there is no difference in the spatial distribution of HSB and LSB galaxies. Hence, the principle difference between the environments of HSB and LSB galaxies is that LSB galaxies are isolated on small scales. This result is also highly consistent with the visual search results of Zaritsky and Lorrimar (1992), conducted for the APM sample. Comparing the POSS HSB and LSB samples indicates that, on average, the nearest neighbor to a LSB disk galaxy is located 1.7 times farther than the typical separation between a HSB galaxy and its nearest neighbor. Interestingly, there is also a difference in the mean velocity separation of companions between the POSS HSB and LSB samples. In particular, the 6740 galaxies found around the POSS HSB spirals have a mean velocity difference of -10 $\pm$ 3 km/s. Conversely, the 625 companions found around the POSS LSB spirals exhibit a significant peculiar velocity of 207 $\pm$ 6 km/s. Since our use of a projected radius at some mean velocity means that the volume we sample is really a cone, the high velocity half of the cone contains a greater volume than the low velocity half. Recall that our velocity limits are $\pm$ 500 km/s ($\pm$ 5 Mpc) so that, in each cone, there is a high probability that the galaxies are separating from one another with the Hubble flow. As there should be more galaxies in the high velocity half (more volume) then the positive peculiar velocity found for the LSB companions strengthens the isolation argument as it shows that most of the detected companions are more distant objects not physically associated with the LSB galaxy itself. \bigskip \leftline{\bf 4.2 LSB Galaxies in Diverse Environments} The results discussed above show that, on average, LSB disk galaxies lack nearby companions. But, does this imply that all LSBs are situated in locally sparse environments? Figure 7 shows the distribution of the number of companions within r = 0.5 and r = 2.0 Mpc for the combined APM and POSS LSB sample within the 2--7000 km/s velocity range. This Figure demonstrates that, while LSB isolation on a scale of 0.5 Mpc is common, it is rare on a scale of 2.0 Mpc as 80 % of the sample have at least one other galaxy located within that radius. Moreover, \app 20 % of the sample are located in populous environments of 8 galaxies or more. Tables 4 and 5 list the 38 most isolated LSBs and the 37 most populous LSBs. A populous LSB is defined as one having either 3 or more companions within a projected radius of 0.5 Mpc or 8 or more companions with a projected radius of 2.0 Mpc. An isolated LSB is one defined as having zero companions in ZCAT out to a projected radius of 2.0 Mpc. Of course, there could be nearby projected galaxies that are not in ZCAT and therefore we performed a visual inspection of the plate material for all the galaxies listed in Table 4. The results of that inspection are listed in the comments column. In most cases, this visual inspection also revealed the galaxy to be isolated. In a few cases, small galaxies were located nearby but these all appear to be background based on their HSB and small angular size. However, two galaxies (F893-11 and F683-1) definitely appear to be associated with companions whose redshifts are not (yet) in ZCAT . For the populous LSB galaxies, either the name of the brightest galaxy within 2.0 Mpc or that of a known structure near the galaxy is listed in Table 5. The mean redshift of the isolated LSBs 3975 $\pm$ 520 km/s while that of the popular LSBs is 3084 $\pm$ 480 km/s; no significant difference. The distribution on the plane of the sky of the isolated and populous LSBs is shown in Figure 8 in velocity strips 1000 km/s wide. Most of the populous LSBs are associated with known large scale structures such as the Cancer or Pegasus, or are located near groups associated with the Perseus-Pisces Supercluster, Coma-A1367 structure, or the A194-A400 complex. Figure 9 shows the spatial distribution around the populous LSBs listed in Table 5. For those in clusters (eg the F495 or F677 objects) only one example is shown. In general, the LSB sits on the edge of the distribution and only in a few cases (eg F544-1 in the NGC 772 group) does it appear to be a real member of a group. In most cases, although there are a large number of galaxies located within a projected radius of 2.0 Mpc, the LSB remains isolated on a scale of 0.5 Mpc. In a very few cases, (eg F611-1) the LSB is a true dwarf irregular galaxy which is a member of a small group. The distribution of the most isolated LSB galaxies in the lowest three velocity slices is somewhat sporadic with only a loose association with known structures. However, in the highest two velocity slices there is a clear clustering of objects with 150 $\leq$ ra $\leq$ 200 and declination \app 20$^o$. This clustering is particularly apparent in the highest velocity slice. The dominant structures in this part of the sky are the Coma Supercluster (at mean redshift \app 7000 km/s) as well as the Great Wall. Most of the isolated LSBs are part of the Great Wall structure, once again, indicating that they are reliable tracers of structure on large scales. Most importantly, however, is that we can discern no difference in the overall morphology or mean surface brightness between the isolated and populous LSBs. Hence, if environment and surface brightness are linked, then it would appear to be the small scale environment (eg r $\leq$ 0.5 Mpc) which is the most important. \bigskip \leftline{\bf 4.3 Possible Reasons for LSB Isolation} In this subsection we consider possible reasons behind the observed paucity of other galaxies within 0.5 Mpc and within 500 km/s of our sample of LSB disk galaxies. Two basic options spring to mind. The first appeals to some intrinsic formation scenario while the second involves the effects of a limited number (or none) of tidal interactions over a Hubble time. Although the mass-to-light ratios of LSB disk galaxies are still not well known, the available data is consistent with the idea that, at a given mass, LSB galaxies represent lower initial density fluctuations (see McGaugh 1992; Mo etal 1993). For any Gaussian filtering of a CDM power spectrum, lower density fluctuations correspond to lower $\sigma$ and hence more common fluctuations. For instance, at a mass scale of $10^{10}$ M\solar, a typical LSB disk forms from a 0.5$\sigma$ fluctuation whereas a typical HSB disk forms from a 2.5$\sigma$ fluctuation (see Mcgaugh etal 1993 for more details). The key to successful galaxy formation, however, is that a fluctuation is isolated and therefore allowed to collapse free from external perturbations. Most low $\sigma$ peaks are located on the ''shoulders'' of higher $\sigma$ peaks and hence will quickly merge into the formation of a single, denser object. Unfortunately, current N-body simulations lack the resolution to determine the statistics of isolated peaks on a scale of 1 Mpc, but we note here that potentially, the existence of these isolated LSB galaxies can help constrain such higher resolution simulations. In this sense, the existence of isolated LSBs is not a confirmation of biased galaxy formation because the scales are much too small. Biasing, in the context of current generation N body simulations, suggests that objects which formed from \app 1$\sigma$ peaks should be less clustered on large scales (5-10 Mpc) than objects which formed from the much more rare 3$\sigma$ peaks. Those simulations, however, can not be easily extrapolated to smaller scales to predict that, on a size scale of 1 Mpc, lower $\sigma$ peaks would preferentially be devoid of nearby objects which formed from higher $\sigma$ peaks (eg HSB galaxies). Furthermore, as demonstrated above, the overall surface density environment of LSB galaxies, on a scale size of 2.0 Mpc, is not very different than that of HSB spirals. Since there is unlikely to be any physical difference between the formation of structure on 2.0 and 0.5 Mpc scales, it seems quite improbable that isolated LSB galaxies result from some fundamentally different manner of the collapse of initial density perturbations. A more likely scenario, in the context of galaxy formation, appeals to an extension of the argument for the existence of the morphology density relation (eg Dressler 1980; Postman and Geller 1984). Here it is suspected that the longer formation timescales of disks, relative to spheroids, makes it quite difficult for a disk to form in a high density environment. Since a lower initial density contrast naturally leads to longer formation (collapse) time then LSB disks are particularly prone to being destroyed in dense environments (though remember, they are found in clusters such as Cancer and Pegasus). Hence, it seems likely that these objects did initially form in relative isolation and like other galaxies, have since migrated to inhabit larger scale structures. This scenario then suggests that, since LSB galaxies are observed to have the same large scale clustering properties as the rest of the galaxy population, they were more weakly clustered at higher redshift. Hence, they may be related to the weakly clustered population of faint, blue galaxies observed by Lilly etal (1991) although we stress that our sample of LSB objects are unlikely to be the faded remnants of a higher redshift population (see Babul and Rees 1992) because they are still quite blue. Finally, we consider the obvious. Our sample of LSB galaxies tends to avoid the group environment. It is this low velocity dispersion environment which is most conducive for strong tidal interactions. Although LSBs are also found in clusters, that environment is not conducive to interactions due to the high relative velocities of the potential participant galaxies. The lack of tidal disturbances over a Hubble time may have two important effects on the evolution of LSB disks. Mihos etal (1991,1993) have studied the effects of an interaction on both the stellar and gaseous distributions in disk galaxies. They find that most interactions result in an increase in the star formation rate as the gas is perturbed and becomes more clumped. McGaugh etal (1993) and van der Hulst etal (1993) show that, in general, the H I surface density in LSB disks is below the suspected threshold for star formation to occur. In addition, LSB disks appear to be highly deficient in molecular material (Schombert etal 1990; Knezek 1992). Hence, without an external agent to modify the gas distribution, these LSB galaxies will continue to evolve slowly as the time averaged star formation rate remains low. A similar conclusion has been reached by Zaritsky and Lorrimar (1992). Our LSB sample also contains no examples of inner bars, a feature that usually does arise in a tidal encounter and which can dynamically channel gas into higher density regions thus facilitating star formation. Of course, the ability for tidal interactions to actually facilitate star formation depends sensitively on the encounter parameters. Weak encounters which gradually modify the gas distribution are probably better suited to stimulating star formation than those strong, slow encounters that often result in stellar bars and tails (see also Mihos etal 1993). In addition to perturbing the star formation rate, tidal interactions also cause mass to be lost from galaxies. Hence, isolation from tidal interactions aids the survivability of systems with low surface mass density and hence low gravitational restoring force. This seems especially critical in the case of the very large LSB disks such as Malin 1 whose scale lengths are larger than 10 kpc. Indeed, most of these very large objects are quite isolated (see Knezek 1992). However, we emphasize here that, on average, our sample galaxies have only a factor of 4 less surface mass density (assuming similar M/L as HSB spirals- see McGaugh 1992). In a purely exponential mass distribution, the 1/2 mass radius occurs at 1.7 scale lengths, which corresponds to a surface brightness of 23.5 mss for a Freeman disk. Tidal damage can be expected to occur mostly at radii beyond the 1/2 mass point and this is borne out both in simulations and observations of real interacting galaxies (see Mihos 1992). Since the typical central surface brightness of our sample LSB galaxies is 23.0 mss , then most of our sample galaxies would easily survive a tidal encounter and would not be totally destroyed if located in the group environment. We thus believe that the lack of exposure to tidal interactions is more effective at suppressing the global star formation rate and the overall evolutionary timescale of the disk than it is in preserving these objects to be discovered at the present epoch. \bigskip \leftline{\bf 5 Summary} We have used a sample of \app 340 LSB galaxies with measured redshifts to investigate their small scale clustering characteristics in comparison with samples of HSB spirals culled from the Center for Astrophysics redshift survey catalog. Care has been taken to minimize any possible bias due to incompleteness in redshift in either the HSB or LSB samples. In addition to a whole sky comparison sample of HSB spirals, we have formed subsamples which duplicate the sky coverage of the LSB samples. This is particularly important in the case of those LSB spirals selected from the POSS-II survey since that region of the sky shows the highest degree of clustering in ZCAT . To form our analysis we have searched through our master LSB catalog in combination with ZCAT to find all galaxies which are located within a projected radius of 2.4 Mpc and within a velocity of 500 km/s of individual HSB and LSB spirals. Based on a comparison of the relative populations in this phase space we conclude the following: 1. There is a pronounced and highly significant deficit of galaxies with projected separations less then 0.5 Mpc in the LSB sample. The mean projected distance to the nearest neighbor is \app 1.7 times farther for LSB than HSB spirals which are located in the same portion of the sky. A KS test rejects, at greater than the 99% confidence level, the hypothesis that the distribution of nearest neighbor distances is same for HSB and LSB spirals. 2. Although there remains a significant deficit of galaxies around LSB galaxies out to r = 2.0 Mpc, the respective surface densities of HSB and LSB galaxies being to merge at larger radii. This is consistent with earlier observations (Bothun etal 1986, Thuan etal 1987, Schneider etal 1990, Schombert etal 1992) that, on scales $\geq$ 5 Mpc, LSB galaxies trace out the same structures as HSB galaxies. 3. Although LSB disks have a pronounced deficit of nearby galaxies, not all LSBs are confined to that regime. In particular, several LSBs are found in loose clusters or on the periphery of groups. However, LSB disks are very rarely found inside groups. There appears to be no difference between the appearance or mean surface brightness of the most isolated LSBs compare to the ones which are found in or near the densest regions. 4. If LSB disks are the result of initial density perturbations of relatively low amplitude, then their relative isolation on small scales has a natural explanation on two grounds: 1) For any Gaussian filtered power spectrum, most low density contrast, low $\sigma$ peaks will not be isolated and hence are destined to merger early on with the rarer higher density perturbations which eventually make luminous galaxies. To avoid this merger, would require a low $\sigma$ peak that is well isolated. 2) Low density contrast perturbations will have longer collapse times and hence are more prone to disruption in dense environments. Hence, the observation that many LSB disks are relatively isolated is an additional manifestation of the well established density--morphology relation, but is not, by itself, a manifestation of biased galaxy formation as LSB disk galaxies encompass a wide range of galactic masses. 5. The data are consistent with the notion that LSB disk galaxies have experienced fewer tidal encounters, over a Hubble time, compared to HSB spirals. While the net effect of this on the physical evolution of this systems is not clear, we have argued that the lack of tidal interactions serves to suppress the overall star formation rate as an external trigger to clump the H I is not available. Without such a tidal trigger, the low observed surface densities of H I in these systems renders their evolutionary rate rather slow. For galaxies with a normal IMF, the mean surface brightness is a direct reflection of the average star formation rate over a Hubble time. Hence, it may well be that the distinguishing characteristic between HSB and LSB disk galaxies is the net number of tidal interactions that each has experienced over a Hubble time. This difference may well reflect the initial conditions of galaxy formation which allowed for these low surface mass density systems to form in relatively isolated locations. We close by emphasizing that there likely exist two distinct and unrelated classes of LSB galaxies; only one of which has been discussed here. These two classes are characterized by substantial differences in their $M/L$ ratios and present day gas content. The quiescent H I rich LSB disks of this sample appear to have relatively normal $M/L$ values and are found in small scale low density environments. In contrast, is the population of LSB galaxies which are found in high density environments (eg Impey etal 1988). These galaxies are uniformly H I poor and devoid of any current star formation. In addition, their mean surface brightness is at least 1 mss lower than the typical H I rich LSB disk contained in this sample and they are 1-2 orders of magnitude lower in total luminosity. Many of their properties suggest that they have high $M/L$ values. These cluster LSB dwarfs likely have a very different formation and evolutionary scenario than we have outlined for our sample of LSB disks. \bigskip \bigskip We thank John Huchra and the CFA Redshift Team for continuing to provide an extremely valuable service to the astronomical community which helped to make this project feasible. We are also grateful for comments from Dennis Zaritsky. We further thank the referee for suggesting we consider some other kinds of comparison samples. The research described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Work at the University of Oregon on LSB galaxies is supported by NSF Grant AST90-5115. \eject \input environ.ref \eject \input tables.tex \eject \input environ.fig \end