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Astron. Astrophys. 342, 655-664 (1999)

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5. Discussion

The structural parameters of the modeled disks appear to be independent from the star formation activity. In this section we will discuss the appearance of the stellar disk of LSB galaxies, and the ISM in LSB galaxies.

5.1. Stellar disk

LSB galaxies are flatter than normal HSB galaxies (cf Fig. 2). From a study of the catalog of edge-on galaxies by Karachentzev et al. (1993), Kudrya et al. (1994) concluded that galaxies become increasingly thinner towards later Hubble types, with the very thinnest galaxies having major over minor axis ratios of 20. Our model galaxies have axial ratios of 15, that is, almost as flat as the flattest galaxies in the Karachentzev et al. catalog. The top panel in Fig. 5 shows the edge-on view of mass distribution in LSB galaxy L.

[FIGURE] Fig. 5. Edge-on views of the mass and light distribution in LSB galaxy L. The top panel shows a linear grey-scale representation of the projected mass surface density. The bottom panel shows a grey-scale representation of the projected V-band surface brightness. Here, the star particles formed during the run-time of the simulation are assigned a V-band flux according to their age following Charlot & Bruzual (1993). The contrast has been adjusted to a dynamic range of 5 magnitudes. This view resembles the so-called "chain galaxies" described by Cowie et al. (1995)

Our model LSB galaxies support claims made by Dalcanton & Shectman (1996) that some of the extremely flat galaxies ("chain galaxies") detected in medium-redshift HST images (Cowie et al. 1995) are simply edge-on LSB galaxies. Cowie et al. present HST wide-I band observations of these chain galaxies which they describe as "extremely narrow, linear structures... with superposed bright `knots'." A few of these galaxies were found to lie at a redshift [FORMULA]. As an I-band view of that redshift corresponds approximately to a V-band view locally, we have attempted to simulate a V-band observation of model L edge-on, by assigning to each stellar particle the I-band flux corresponding to its age (Charlot & Bruzual 1993). This is shown in the bottom panel of Fig. 5, where the dynamic range of the picture has been adjusted to correspond approximately with the contrast that the observed chain galaxies have with respect to the sky-background. Comparison with any of the galaxies in Fig. 20 of Cowie et al. will show the resemblance.

How will the edge-on surface brightness distributions of LSB galaxies compare with those of HSB galaxies of similar scale length? Compared to an equally large HSB galaxy, the scale height of an LSB galaxy is smaller. Due to the low dust content in LSB galaxies (McGaugh 1994), effects of edge-brightening will be stronger in the LSB galaxy compared to the dust-rich HSB galaxy. An edge-on LSB might have a higher apparent surface brightness than an edge-on HSB galaxy of the same size. For example, for HSB galaxies in the Ursa Major cluster, Tully et al. (1997) find a differential extinction in the B-band going from face-on to edge-on of 1.8 mag arcsec-2. The LSB galaxies in their sample are found to be almost transparent with a differential extinction of only 0.1 mag arcsec-2. The almost two magnitudes extra extinction in the HSB can thus easily compensate the few magnitudes difference in intrinsic surface brightness, making edge-on LSB galaxies as bright in surface brightness as edge-on HSB galaxies.

Hence it is much more difficult to distinguish between edge-on LSB and HSB galaxies than between face-on LSB and HSB galaxies. A smaller number of star forming regions, extreme flatness and blue colors will be the only easily visible distinguishing characteristics.

The reason why the stellar disks of LSB galaxies are so thin is that they are very stable to local instabilities (Fig. 1). As a consequence, bars and spiral structure, which are the most efficient methods for heating a stellar disk (Sellwood & Carlberg 1984), are unlikely to develop spontaneously in LSB galaxies. Thus there is no natural way to make the disks thick.

This explanation is supported by the rarity of barred LSB galaxies. In the LSB galaxy catalog by Impey et al. (1996), only 4 percent of the galaxies are barred, while the frequency of barred galaxies in the RC2 is some 30 percent (Elmegreen et al. 1990). Sellwood & Wilkinson (1993) give a fraction of 2/3 for barred HSB galaxies. The stability of LSB disks is confirmed in a numerical study of the dynamical stability of these systems by Mihos et al. (1997). Whereas we adopted the "most likely" solution for the mass-to-light ratio of stellar disk, these authors considered the "worst case" scenario of maximum disk. However their conclusion is the same as ours: the disks of LSB galaxies are extremely stable.

The lack of truly LSB edge-on galaxies (Schombert et al. 1992) could tell us something about the existence of very LSB galaxies. As shown above, the presently known population of LSB galaxies, when turned edge-on, brightens to surface brightnesses comparable to those of similar-sized HSB galaxies. In principle, the edge-on counterparts of the currently known LSB galaxies should thus already be in the conventional galaxy catalogs, showing up as "streaks on the sky". As truly LSB edge-on galaxies seem to be lacking from the LSB catalogs, this suggests that galaxies with face-on surface brightnesses [FORMULA] mag arcsec-2 are probably very rare.

5.2. Blue and red LSB galaxies

Fluctuations in the SFR as shown in Fig. 3, may very well explain why most of the LSB galaxies detected in surveys are blue. As McGaugh (1996) argues, the selection effects against finding red LSB galaxies on the blue sensitive plates on which surveys have been carried out are quite severe. It will be very hard to find LSB galaxies with colors [FORMULA] or redder. So if the absence of red LSB galaxies from the current catalogs is caused purely by these selection effects, the blue LSB galaxies could simply be the bursting tip of a proverbial iceberg.

In order to explain the colors of the bluest LSB galaxies in the sample of de Blok et al. (1996), van den Hoek et al. (1997) had to invoke bursts with a duration of between 0.5 and 5 Myr and an amplitude between 1 and 5 [FORMULA]/yr. The fluctuations found in our simulation L have an amplitude of 0.15 [FORMULA]/yr, with a duration of about 20 Myr. This duration is determined by the lifetime for OB stars and the collapse time for molecular clouds, which are both of the order of a few [FORMULA] yr. They are therefore slightly milder than the bursts invoked by van den Hoek et al. (1997), but keep in mind that the latter bursts were used to explain the bluest galaxies. Our models attempt to simulate an average LSB galaxy, and it should not come as a surprise that the fluctuations we find are milder. Given the many assumptions and uncertainties in both modeling and observations, it is actually quite encouraging that the parameters agree to within an order of magnitude.

Assuming that blue LSB galaxies are currently undergoing a period of enhanced star formation, implies that there exists a population of red, non-bursting, quiescent LSB galaxies. These should then also be metal-poor and gas-rich, and share many of the properties of the galaxies we have been modeling.

We can estimate the fraction of red LSB galaxies by calculating the distribution of the birthrate parameter b for simulation L. The b parameter is the ratio of the present SFR over the average past SFR and is a useful tool for studying the star formation history of galaxies. Birthrate parameters have been determined for a large sample of spiral galaxies by Kennicutt et al. (1994). The trend is that early type galaxies have small values for b, thus most star formation occurred in the past, while late type and irregular galaxies have large values for b, often exceeding 1, indicating that those galaxy are still actively forming stars, and more so than in the past. Here we apply this analysis to simulation L in order to estimate the fractions of blue and red LSB galaxies.

In Fig. 6a we plot the distribution of b values for simulation L (solid line), where we have followed the value of b over the duration of the simulation in steps of 15 Myr. Thus if the SFR peaks in a particular time interval, the corresponding value of b will be high. If the SFR is low in this time interval b is also low. In total we have 200 b values.

[FIGURE] Fig. 6. a Distribution of the birthrate parameter b, the ratio of the current SFR to the average past SFR. Solid line shows the b values derived for simulation L, dotted line shows the b distribution for a simulation of an Sc galaxy (Gerritsen & Icke 1998). On the top are average b values for different types of galaxies (Kennicutt et al. 1994). The bottom panel shows the cumulative distribution for the two simulations. Less than 20% of the b values for the LSB galaxy are below [FORMULA], hence we expect at most 20% of LSB galaxies to be "red"

Also shown in Fig. 6a are the b distribution for a simulation of an HSB Sc galaxy (Gerritsen & Icke 1998, dotted line) and the mean values for different galaxy types (from Kennicutt et al. 1994). Due to the low average SFR the distribution for the LSB simulation is much broader than the distribution for the HSB simulation, and the average b value is larger.

Also it is clear that the LSB galaxy has b values larger than the average for early type galaxies for most of the time. "Classical" LSB galaxies are blue compared to HSB galaxies, they thus have an excess of recent star formation or equivalently a higher b value. We now define a LSB galaxy to be "blue" if its birthrate parameter b exceeds the average value of b for a HSB late-type galaxy (see Kennicutt et al. 1994 for relations between birthrate parameter and color). Fig. 6a shows that this requires that [FORMULA].

LSB galaxies that do not meet this requirement are "red": non-bursting, but nevertheless still gas-rich. From Fig. 6b (which shows the cumulative b distribution) we can see that over 80 percent of the fluctuations result in blue LSB galaxies. Less than 20 percent of the fluctuations therefore results in red LSB galaxies.

We can estimate colors of the red population using the burst models from van den Hoek et al. (1997). For example, a 5 Myr burst with an amplitude of 3 [FORMULA]/yr superimposed on a 13 Gyr old population which has undergone an exponentially decreasing SFR with a timescale of 4 Gyr changes colors and surface brightnesses by [FORMULA], [FORMULA], [FORMULA] and [FORMULA] (cf. Table 5 in van den Hoek et al.). Using these values together with the measured colors of the bluest LSB galaxies in de Blok et al. (1995), yields [FORMULA], [FORMULA] and [FORMULA] for the red population.

A recent CCD survey (O'Neill & Bothun 1997) has picked up a class of LSB galaxies which have [FORMULA] and [FORMULA]. If some of these galaxies are indeed the non-bursting counterparts of the blue LSB galaxies, they should be metal-poor and gas-rich, and share many of the properties of the galaxies we have been modeling.

In summary, if the blue colors found in LSB galaxies are the result of fluctuations in the star formation rate, then this implies that the red gas-rich LSB galaxies constitute less than 20% of the gas-rich LSB disk galaxies. This does not rule out the existence of a population of red, gas-poor LSB galaxies. These must however have had an evolutionary history quite different from those discussed here and possibly have consumed or expelled all their gas quite early in their life.

5.3. ISM

The SFRs from both simulations are larger than the observed rate of about [FORMULA]/yr. This latter value is probably correct within a factor of 2. Especially the high SFR of simulation H ([FORMULA]/yr) is almost an order of magnitude larger than what is needed and it seems impossible to reconcile this value with the observations. Instead the global SFR is consistent with the global SFR for equal-luminosity galaxies (e.g. Kennicutt 1983). For instance the Sc galaxy NGC 6503 with a maximum rotation velocity of [FORMULA] km s-1 has a total measured SFR of [FORMULA]/yr, and a simulated SFR of [FORMULA]/yr (Gerritsen & Icke 1997, 1998). In general the SFRs of equal-luminosity galaxies differ by a factor 10 between LSB and HSB galaxy (van den Hoek et al. 1997, and Kennicutt 1983), despite the copious amounts of gas available in the LSB galaxies (de Blok et al. 1996).

SFRL approaches the correct value and the physical reason is shown in Fig. 4. The essential information to retain from this phase diagram is that we need a different ISM for LSB galaxies, where the bulk of the gas is not directly available for star formation, as it is too warm (of order [FORMULA] K). The simulations do not include phase transitions from neutral to molecular gas, but as an estimate for the H2 mass we can consider all star forming gas ([FORMULA] K) to be molecular. This gas represents less than 2% of the total gas mass. In this respect it is interesting to note that for a small sample of LSB galaxies CO is not detected, yielding an limit of M(H2)/M(H I ) [FORMULA] 30 percent (de Blok & van der Hulst 1998b, Schombert et al. 1990). A few galaxies have upper limits less than 10%.

As discussed in the previous section the warm ISM may be caused by a low metallicity for the gas. Below [FORMULA] K, cooling is dominated by heavy elements like C+, Si+, Fe+, O. If these elements are rare then it is difficult for the gas to radiate its energy away.

Direct observational support for a low metallicity ISM in LSB galaxies comes from oxygen abundance measurements of H II regions in LSB galaxies. Those studies yield metallicities of approximately 0.5 times solar metallicity (McGaugh 1994). Measurements of the oxygen abundance in F563-1 (de Blok & van der Hulst 1998a) give an average oxygen abundance of 0.15 [FORMULA] (compare with the difference in metallicity between models H and L).

A point of concern is the IMF. Our premise is that the IMF is universal, however it can differ from our adopted Salpeter IMF (see 2.1). Especially a low upper-mass cutoff could easily lead to an underestimation of the SFR (e.g. an upper mass cutoff at 30 [FORMULA] reduces the measured SFR by 2-3; Kennicutt 1983). However current determinations of the IMF in external galaxies point towards a universal IMF (Kennicutt 1989; Kennicutt et al. 1994). Furthermore, observations suggest that massive stars are present in the H II regions of LSB galaxies (McGaugh 1994).

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999