5 Discussion and conclusions

   
5.1 Companion properties

It is interesting to examine the properties of the found disturbing galaxies and to describe in more detail the relative fractions of various combinations of BCGs with their partner galaxies.

In Fig. 2 the distributions of blue absolute magnitude differences, the relative projected distances and the relative radial velocities are shown.

One can see that the general distribution of the projected distances for suggested disturbing galaxies spreads upto ${\sim}400$ kpc, which is consistent with conclusions by Zaritsky et al. (1994, 1997) on the distribution of companions around massive spirals. However, if we limit the group of disturbing galaxies by "dwarfs'' ( $M_{B} \geq -$18 $.\!\!^{\rm m}$5), then the distribution of the projected distances is much narrower, with the median $D_{\rm proj} \sim 90$ kpc. The distribution of the relative radial velocities of the partner galaxy and the BCG peaks at $\Delta V=0$, with ${\sim}93\%$ of this value in the range ${\pm}250$ km s$^{\rm -1}$. The latter value is typical for these studies, considering possible physical neighbours of field galaxies.

In Fig. 2 the full range of total magnitude differences is shown for BCGs with identified disturbing partners. Its asymmetric (relative to zero) and bimodal appearance at least partly is caused by selection effects. It is more difficult to measure the redshifts for the fainter candidate neighbours. However, even if all remaining BCGs without identified disturbing galaxies would appear to have fainter companions after a more careful search, this distribution will be still bimodal, with the prominent peak at $\Delta B$ around -2 $.\!\!^{\rm m}$5. Accounting for the mean brightening of BCGs due to a SF burst of the order $\Delta B$ = 0 $.\!\!^{\rm m}$75-1 $.\!\!^{\rm m}$0 (e.g., Papaderos et al. 1996; Lipovetsky et al. 2001), the full interval of the mass ratios of the BCG progenitor and its disturbing galaxy ranges from ${\sim}1/400$ to ${\sim}25$. The peak in the distribution of $\Delta B$ indicates that the most common brighter disturbing galaxies are more massive than the BCG progenitors by a factor of 10-25.

5.2 The problem of a control sample

For confident conclusions on the results of statistical studies like this, it is quite important to compare them to the results of a similar study on a control sample. The objects of the latter should be separated to have a complimentary property relative to that of the main sample. In our case, it should be a sample of gas-rich, low-mass galaxies with no SF bursts. However, while there is no problem in obtaining a large, well-selected BCG sample in the considered volume, it is very difficult to form such a sample of LSB dwarfs or Im galaxies. We postpone the similar study of control samples to the time when such samples will be available, hopefully after SDSS (Sloan Digital Sky Survey) data will be distributed. For the purposes of illustration, we undertook the study of the environments for the sample of LSB dwarfs by Pildis et al. (1997). We separated from their 110 LSB dwarfs, 56 objects with $V_{\rm hel}< 6\,000$ km s$^{\rm -1}$ and $V_{\rm Vir} >2\,000$ km s^-1, that is, with the same criteria as for our general field (GF) BCG group (see next subsection).

Figure 3: Distributions of two compared samples - 49 BCGs from the general field (GF) region with M(HI) data (see 5.3) (solid line) and 56 LSB galaxies from Pildis et al. (1997) (dashed line), selected in the same velocity range. Upper panel: distribution of radial velocity; Middle panel: distribution of absolute B-band magnitude; Lower panel: distribution of M(HI) (in solar masses).

Before comparing this group of LSB galaxies with BCGs for the presence of disturbing neighbours, it is reasonable to check how similary they are distributed in space (that is, in radial velocity), and how similar are their ranges of global parameters, like luminosity and gas mass. In Fig. 3 we show distributions of $V_{\rm r}$, L_B, and HI mass for both samples. We note that $V_{\rm r}$ and L_B distributions for BCGs and LSB galaxies are similar. The null hypothesis on the same distribution of both samples can not be rejected, according to the Kolmogorov-Smirnov D statistic, even on the significance level 0.37 and 0.31, respectively. This makes the comparison of distances to the disturbing galaxy secure for the two samples.

For M(HI), despite the closeness in the total range of this parameter for both samples, their distributions have larger differences, which is also reflected in the Kolmogorov-Smirnov D statistic (significance level for rejection of the null hypothesis is 0.03). This difference, however, is only of the general interest. The amount of HI in the considered galaxy samples can be the result of the difference of their distances to the disturbing neighbours, but can not be the reason for this difference.

To compare the distributions of LSB galaxies and BCGs according to the distance to the most disturbing galaxy, we proceeded the same way as for BCGs, but have checked potential disturbers at the projected distances upto 3 Mpc. First, we checked potential neighbours in UZC (Falco et al. 1999), then looked at possible fainter neighbours in NED. Finally, we selected the most tidally disturbing galaxies, assuming mass to be proportional to L_B, and the tidal force proportional to the cubed inverse projected distance $D^{\rm -3}$.

The search for the strongest disturbing galaxies for this LSB subsample have been made in UZC and NED, taking the limiting difference in radial velocity $\vert \Delta V \vert \leq 500$ km s$^{\rm -1}$. Its results are illustrated in Fig. 4 along with the results of a similar search for BCGs from the GF group. For BCGs from Table 3 with no identified real tidal disturbers, the strongest disturbers are found to be at the distances 600-2000 kpc, which leads to the long tail. BCGs with a merger morphology were excluded from the comparison with LSB galaxies.

Summarizing, we draw the following conclusion. BCGs/H II-galaxies significantly more often have the strongest disturbing neighbours at a distance of tens to a few hundred kpc than LSB dwarfs have. E.g., ${\sim}76\%$ of BCGs have such neighbours at $D_{\rm proj} < 400$ kpc while for LSB dwarfs this fraction is only ${\sim}46\%$. The median and mean values of $D_{\rm proj}$ - 270 and 384 kpc for BCGs, and 560 and 728 kpc, respectively for LSB dwarfs, differ by about factor of two. In addition, ${\sim}1/5$ of BCGs show merger morphology. If these 11 BCGs from the general field are included in the first bin $D_{\rm proj} < 100$ kpc, the difference between BCGs and LSB dwarf distributions becomes striking.

Bothun et al. (1993) made a comparison of the local environment of a large LSB disk galaxy sample to that of HSB (high surface brightness) disks, and arrived a similar conclusion on the significant statistical deficit of galaxies from the CfA redshift survey within a projected radius of 0.5 Mpc from LSB galaxies.

Figure 4: Distribution of projected distances between the studied galaxies and their the most important disturbing neighbour, as found in NED. Upper panel: 49 BCGs from the general field group (see 5.3). Lower panel: 56 LSB galaxies from Pildis et al. (1997). Median values are 270 kpc for BCGs and 560 kpc for LSBDs.

Other than this exercise on brighter neighbouring galaxies, we can cite the results of the search for HI-rich low-mass companions for the small LSB dwarf sample by Taylor (1997). It is shown that the control sample of LSB dwarfs has a significantly lower fraction of low-mass companions than the sample of BCG/H II-galaxies. However, several low-mass HI-companions do exist around LSB dwarfs, and they do not trigger SF bursts in these galaxies. This clearly indicates that the presence of a sufficiently close disturber cannot be the only factor determining enhanced SF in gas-rich galaxies. One plausible interpretation of this conclusion by Mihos et al. is mentioned in Sect. 5.5. On the other hand, ${\sim}40\%$of their BCG sample have no detected companions. While the effect of incompletness probably affects this number, one can expect that some fraction of "isolated'' BCGs are not triggered by interactions with low-mass companions.

Another sample, interesting for comparison, is the Local Volume sample (LV) (e.g., Karachentsev & Makarov 1999), that is galaxies with radial velocities relative to the centroid of Local Group $V_{\rm LG} < 500$ km s$^{\rm -1}$. Among 335 galaxies currently known in the LV (Makarov 2000), the class of BCG (or post Star-burst) can be assigned to the following objects: NGC 1569, NGC 1560, SBS 1123+576, Mkn 178, VII Zw 403, Arp 211, NGC 6789. Of them SBS 1123+578 is probably tidally disturbed and Mkn 178 is a merger, as shown in Table 3. The post Star-burst dwarf NGC 1569 interacts with UGCA 92 at a distance of ${\sim}40$ kpc, or with a low-mass HI companion (Stil & Israel 1998). The post Star-burst dwarf NGC 1560 is in the group Maffei/IC 342 at a distance of ${\sim}300$ kpc from IC 342, which could disturb it, accounting for the time elapsed since beginning of the SF burst. For Arp 211, the situation is uncertain. Its photometrical distance of 2.8 Mpc (Nordic Optical Telescope - NOT data, Makarova et al. 1998), after obtained HST data changed to 6.7 Mpc (Crone et al. 2001). Its probable strongest disturber, IC 3687, from the NOT photometry of 3 brightest blue stars is at about 3.0 Mpc. However, this estimate is probably not reliable, since from the estimate on the brightest red star, the distance is close to that of HST for Arp 211 (Makarova et al. 1998), and Arp 211 can be disturbed by IC 3687. The remaining BCGs, VII Zw 403 and NGC 6789 are probably well isolated. So, summarizing, we conclude that the data on a very limited number of star-bursting dwarfs in the LV do not contradict the results of the study on 86 BCGs above.

   
5.3 Effect of global environment

One of the important points of this study is to determine if the results obtained for the discussed BCG sample are representative of the general situation with BCGs. It is evident that some bias in the fraction of BCGs with the galaxy-interaction-induced SF burst must be present in our sample, since a significant number of our BCGs fall into the Local Supercluster, which is not typical of the general field. In paricular, besides the environments of the Virgo cluster, the galaxies of the UMa poor cluster (Tully et al. 1996) (with the center at ${\rm RA}\sim12^{\rm h}$, Dec. ${\sim}$ $49^{\circ}$, the angular diameter of ${\sim}13^{\circ}$ and the radial velocity range $V_{\rm hel}$ of 640 to 1150 km s$^{\rm -1}$) can appear among the BCGs of our sample.

The simplest way to check how much the effect of Local Supercluster contributes to the various types of interactions is to divide our sample by radial velocity. Roughly, the BCGs with the Virgo infall-corrected velocity $V_{\rm Vir} < 2\,000$ km s$^{\rm -1}$( $D_{\rm Vir} <26.67$ Mpc) are considered constituents of the Local Supercluster volume, and all remaining as the galaxies of general field. The respective total numbers for these two groups are: 26 and 60 BCGs.

For the 26 BCGs within the "borders'' of the Local Supercluster volume, we have the following statistics. 14 of them ( ${\sim}54\pm14\%$) have significantly brighter disturbing neighbours ( $\Delta B \leq-1$ $.\!\!^{\rm m}$5). 5 BCGs ( ${\sim}19\pm8\%$) have neighbours of similar or lower luminosity, and 3 ( ${\sim}11.5\pm6.5\%$) have no neighbours but have a merger morphology. 4 more BCGs ( ${\sim}15.5\pm8\%$) have neither evident companions (or have possible candidates with unknown velocities) nor show evidence of a recent merger.

For the remaining 60 BCGs in the general field, only 19 ( ${\sim}31.5\pm7\%$) have significantly brighter disturbing neighbours. 18 BCGs ($30\pm7\%$) have neighbours of similar or lower luminosity. 11 BCGs ( ${\sim}18.5\pm6\%$) have no disturbing neighbours, but have more or less clear indication of merger morphologies. The remaining 12 BCGs without evident companions or merging correspond to 20%.

Comparing these two groups of BCGs from our sample, we see that the fraction of BCGs probably triggered by interactions with other galaxies is similar ( ${\sim}84.5\pm18\%$ and $80\pm12\%$, respectively) in the Local Supercluster volume and outside of it. The fractions of BCGs with various types of disturber and merger morphology differ in the two groups. However, only the difference in the fractions of BCGs with significantly brighter disturbing galaxies ( ${\sim}54\pm14\%$versus ${\sim}31.5\pm7\%$) is seemingly real (while it is still within 1.5$\sigma$ of the combined uncertainty). This can quite naturally be interpreted as an indication of the more important role of interactions of BCGs with massive neighbours in the regions of higher galaxy density. The differences in the fractions of other categories (low-mass neighbours and mergers) are within the statistical uncertainties accounting for the small numbers of BCGs involved in the comparisons.

Thus, we conclude that in the general field, the role of galaxy interactions to trigger SF in BCGs is as important as in the Local Supercluster volume. ${\sim}80\%$ of all BCGs are probably either tidally disturbed or result from recent mergers. At least ${\sim}60\%$ of field BCGs experience a tidal disturbance from other galaxies. Mergers and probable mergers constitute ${\sim}1/5$ of all BCGs.

Some fraction of the remaining ${\sim}20\%$ of "non-interacting'' BCGs can in fact also be interacting. Several of them have massive galaxies at projected distances of ${\sim}500$-600 kpc, and can be their distant companions. On the other hand, for several "non-interacting'' BCGs, there are close candidate faint companions without radial velocities.

5.4 On the results of complimentary approach

Telles & Maddox (2000) made an attempt to address the problem of faint companions of H II-galaxies through the 2D statistical analysis of their environment using the APM galaxy catalog of the southern sky. They did not find an excess of faint galaxies around studied BCGs, and concluded that "tidal interactions cannot be the only factor that triggers their burst of star formation''. We also do not generalize interactions as the only trigger of SF bursts in BCGs, but our results seem rather to contradict than to support each other. Therefore this requiress some discussion. Their conclusion is drawn from only one point on their cross-correlation function, corresponding to the minimal sampled distance of 120  $h^{\rm -1}$ kpc. This is about twice the typical distance between low-mass companions and BCGs in Taylor et al. (1995) and the median distance between BCGs and low-luminosity neighbours, in our sample (see Sect. 5.1). The presented uncertainty of this point is so high that it is difficult to trust any conclusion made on this basis. The auto-correlation function of the same H II-galaxies, determined by Iovino et al. (1988) and used by Telles & Maddox (2000) as an argument, was measured only for distances larger than 350  $h^{\rm -1}$ kpc. Its extrapolation to the distances of interest, ${\sim}50{-}80~h^{\rm -1}$ kpc, is questionable in the frame of this problem, since its value is the subject of the study. To indicate possible caveats of their analysis, we note that about a half of our 32 BCGs with neighbours fainter than M_B=-18 $.\!\!^{\rm m}$5 (see Table 3) are within the projected distances closer than 80 kpc (60 h^-1 kpc). 3 more such faint companions at larger distances are significantly fainter than M_B=-15, the limit for APM galaxies at the typical redshift of their H II-galaxies. Therefore, about 60% of faint companions found for SBS BCGs would probably not enter the cross-correlation function of H II and APM galaxies, discussed by Telles & Maddox.

   
5.5 Trigger mechanism and BCG progenitors

The question of the trigger mechanisms of BCG SF bursts has another interesting aspect relating to the evolutionary links of BCGs to other types of low-mass galaxies. What are BCGs in the periods between the episodes of enhanced SF activity? We do not know other gas-rich low-mass galaxies without SF bursts other than dwarf spirals Sd-Sm, dwarf irregulars, including Im, and LSB dwarfs. Here we separate LSB dwarfs, as low-mass disks with roughly the same morphology classification, but with the central blue surface brightness $\mu_{\rm0}(B) \geq$ 23 $.\!\!^{\rm m}$5/sq arcsec (e.g. Dalcanton et al. 1997), with the SF rates many times lower than their "normal'' cousins. Unlike more typical Sdm and dIs, the HI surface density in LSBDs (almost) everywhere is below the threshold density of gravitational instability, resulting in global suppression of SF (van der Hulst et al. 1993; van Zee et al. 1997), and their dim optical appearance.

Evidently, either some or all types of gas-rich low-mass galaxies (in various proportions) can be progenitors of BCGs/H II-galaxies picked up by ELG surveys thanks to their strong emission lines. If, as we conclude, the main trigger mechanism of SF bursts in BCGs is external, then some consequences of BCG in relation to other galaxies can be derived.

As Mihos et al. (1997) showed in N-body simulations of collisions of equal mass high-surface (HSB) and low-surface brightness (LSB) disk galaxies, their response during a close approach is qualitatively different. While in the HSB disk a bar structure was generated, which caused its gas to sink into the center, in the LSB disk only weak spirals were induced. Therefore even relatively strong tidal action of a neighbouring galaxy would cause only a small disturbance of the matter in a LSB galaxy. This leads to the conclusion that LSB dwarfs can hardly be progenitors of the main part of BCGs. Only the merger of LSB dwarfs with any type of low-mass galaxy will result in the strong disturbance and the loss of gas stability with subsequent collapse. In this case, their high HI mass content is the important factor in providing material for a strong SF burst.

The merging of any type of gas-rich dwarf with an other dwarf will lead to a strong SF burst and an appearance of the BCG phenomenon. However, among the field BCGs of merger origin namely the fraction of LSB dwarf progenitors should prevail. This follows from the fact that the number density of LSB galaxies is several times higher than that of their HSB analogs (e.g., Dalcanton et al. 1997; O'Neil & Bothun 2000). This should be the main factor determining the rate of merger BCGs, since, unlike the case of weak tidal trigger, the rate of merging is proportional to the square of the number density of galaxies under the question. Moreover, being the most abundant and stable type of galaxy in the general field, LSB dwarfs can constitute a significant, or even the main fraction of galaxies, exerting tidal action on BCG progenitors and triggering SF bursts in the majority of them.

Salzer & Norton (1999) argued that BCG progenitors are not typical dwarf irregulars, but rather are objects from the extreme tail in their distribution on the central mass concentration. While these authors seemingly appreciate the important feature distinguishing the essential fraction of BCGs, their BCG sample seems to be randomly identified, and therefore the claimed results can be biased due to selection effects. The real fraction of this type of BCG should be confirmed on a BCG sample with well-defined selection criteria. If, however, Salzer & Norton are right and such untypical dIrrs are the progenitors of the majority of observed BCGs, then such galaxies will be the most easily triggered by the tidal interactions from external galaxies. These authors suggest an intrinsic trigger mechanism, based on settling down of the cold ambient gas ejected from the disk during the previous SF burst. Unlike this, if interactions are the main trigger mechanism, the SF history, metal enrichment, gas consumption and the duty cycle of BCGs should noticebly depend on their environment. Some evidence for this come from the results of Izotov & Guseva (1989) of the study of Virgo cluster BCGs. These have higher metallicities (mean 12+log(O/H) ${\sim}\ 8.3$) than their typical general field analogs with a mean of 12 + log(O/H) ${\sim}\ 8.0$ (e.g., Kniazev et al. 2001c). The systematic increase of a BCG parameter M(HI)/L_B with the decrease of galaxy density from a cluster through supercluster and general field to void environments (Pustilnik et al. 2001b) also supports the interaction-triggered SF bursts as the main mechanism.

New results of the blind HI survey for low-mass gas-rich galaxies, presented by Schneider & Rosenberg (2000), clearly demonstrate a steeply rising HI mass function of HI-rich field dwarf galaxies for masses < $10^{\rm 9}~M_{\odot}$. This indicates once more the importance of low-mass companions of field dwarfs (often not seen without dedicated observations, e.g., Pisano & Wilcots  1999) as probable triggers of SF activity. The hypothesis of infall of gas clouds from the intergalactic medium was recently discussed as an option for triggering SF bursts in "isolated'' BCGs (e.g., Crone et al. 2001). By its essence such hypothesis is equivalent to the trigger due to sinking satellite if a gas-rich dwarf galaxy is considered as a massive component. Thus, this mechanism can in principle trigger SF bursts in some of BCGs of our sample without identified disturbing galaxy.

Summarizing the results of this study and the discussion above, we suggest that BCG progenitors are a mixture of various types of gas-rich low-mass galaxies with a wide range of surface densities and degrees of mass concentration. All of them, being isolated, are in a metastable state with various levels of "quasistationary, equilibrium'' star formation rate. Some occasionally can "spontaneousely'' leave it (i.e. due to some intrinsic processes) and undergo enhanced gas collapse, igniting SF burst. However, most reach the phase of SF burst by an external trigger consisting of various strength interactions with other galaxies. In particular, the disks with the highest central gas concentration are the least stable against gas collapse, and can be ingnited to SF burst by relatively weak tidals. On the other hand, LSB dwarfs are the most stable, and can be transformed to BCGs only by a merger with another galaxy.

Finally, we note some interesting implications of the described results for cosmological evolution of gas-rich low-mass galaxies. If galaxy interactions are the main trigger of enhanced SF in a significant number of gas-rich galaxies during the modern epoch, then their role at earlier times becomes dominant due to the significant increase of galaxy density. This is consistent with much observational data on the morphology and environment of faint high-z galaxies discovered with the HST (see, e.g., review by Ferguson et al. 2000). Therefore, for most low-mass gas-rich galaxies with a sufficiently high surface mass density, such as normal dIs, galaxy interactions during at least several first Gyr in the life of the Universe seemingly were the main driver of their cosmological evolution.

The same is applicable to the problem of the existence of local truly young galaxies. Such objects, if they are not disks of too low surface density, could survive to the modern epoch as protogalaxies, only if they populated relatively low galaxy density regions. Therefore, the general field environment, or even voids, are the most suitable regions to search for these very rare objects.

5.6 Conclusions

Summarizing the results and discussion presented above we draw the following conclusions:

1.

The fraction of BCGs in the well-defined sample of 86 galaxies which either have the interacting neighbours with strong enough tidal action or have merger morphology is ${\sim}80\%$. This conclusion remains valid for BCG populating both the Local Supercluster volume and general field;

2.

Fractions of BCGs with significantly brighter disturbing galaxies ("non-isolated'' BCGs) vary from $54\pm14\%$ for the Local Supercluster volume to ${\sim}31.5\pm7\%$ in the general field. This is consistent with the expectation that large mass galaxies play a more important role in the regions of higher galaxy density;

3.

Among the so called "isolated'' BCGs (without bright neighbouring galaxy) in both the Local Supercluster volume and in the general field, ${\sim}43\pm10\%$ are disturbed by dwarf galaxies and ${\sim}26\pm8\%$ have a merger morphology;

4.

The whole BCG dataset discussed in the paper implies that galaxy interactions with both massive and dwarfs neighbours and with the full range of the disturbance amplitude (from weak tidals to mergers), is very important, and probably the main mechanism that triggers SF bursts in BCG progenitors. These are the mixture of all known low-mass gas-rich galaxy types with proportions which still are unknown. Depending on the quiescent level of SF of various BCG progenitors, their stability against various interaction-induced disturbances and their type of environment, interactions may be the main driver of their cosmological evolution. Future high quality N-body simulations of gas collapse in gas-rich galaxies due to the tidal action of external galaxies are necessary in order to support more certain conclusions.