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5.1. The Role of the Halo Gas: Understanding High SN

New clues emerging from the recent surveys (Blakeslee 1997; Blakeslee et al. 1997; Harris et al. 1998) show rather clearly that SN for these large galaxies displays a continuum of values from the ``normal'' SN0 appeq 3-4 up to 15 and more. More importantly, SN is clearly correlated with the luminosity of the BCG, and with the total mass of the surrounding galaxy cluster as measured by the velocity dispersion of the galaxies or the temperature and luminosity of the hot X-ray gas in the cluster potential. Larger BCGs are found in more massive potential wells, and have higher specific frequencies.

Let us go back to the definition of SN. To obtain an unusually high ratio Ncl / Lgal, we really have only two ways to do it. (a) First, we can increase Ncl at a given Lgal. This route remains arbitrary, since we have no physical theory for predicting the formation efficiency e. (b) Second, we can decrease Lgal for the same number of clusters. The most obvious way to take this second path, following the clues mentioned above for NGC 5128 and NGC 4472, is to leave a lot of the original gas supply unused. To put this another way, we can assume that Ncl is proportional to the original protogalactic gas mass; but that in certain galaxies (the BCGs in particular), for whatever reason a large amount of the gas ended up not being converted to stars.

This latter option is raised by Blakeslee (1997) and Harris et al. (1998) and pursued extensively by McLaughlin (1999). Summarizing their arguments, suppose now that we redefine the globular cluster formation efficiency as a mass ratio,

Equation 4

where M* is the mass now in visible stars, while Mgas is the remaining mass in the galactic halo which was originally part of the protogalaxy. We now explicitly assume that epsilon is constant, and thus the total number of globular clusters is directly proportional to the original protogalactic mass. (We do not expect, of course, that epsilon can be precisely the same in all environments, since cluster formation must at some level be a stochastic process. We are, however, using this hypothesis to reduce the order-of-magnitude differences in SN down to much smaller levels that can more easily be accommodated within the observational scatter.) In most galaxies, Mgas is much smaller than M*: their halos do not contain much leftover gas. However, the BCGs usually have quite large amounts of high-temperature X-ray gas, and the amount goes up dramatically with luminosity (MX ~ Lgal2.5). For the very biggest BCGs, Mgas is larger than M*, which would require us to assume in this picture that most of their protogalactic gas is still unconverted.

McLaughlin (1999) tests this idea quantitatively by showing that in three well studied galaxies (M87 and NGC 4472 in Virgo and NGC 1399 in Fornax), the ratio of mass densities rhocl / (rho* + rhogas) throughout the halo is equal to appeq 0.0025 in all three galaxies. That is, the addition of the X-ray gas mass makes this ratio much more nearly consistent with the hypothesis that there is a quasi-universal cluster formation efficiency epsilon. By using the fundamental plane relations for E galaxies which relate the mass-to-light ratio, scale radius, and internal velocity dispersion to Lgal, McLaughlin (1999) also shows that the ratio Mgas / M* scales as Lgal1.5, leading to the following scaling for the specific frequency:

Equation 5

There are two principal effects acting to define the shape of this relation: first is that the mass-to-light ratio increases gradually with luminosity (M/L ~ L0.3), so that bigger ellipticals have more clusters per unit light. Second is that bigger BCGs have much more surrounding halo gas, thus (by hypothesis) they generated many more clusters at early times. Combining both of these effects, McLaughlin shows that the overall relation between Ncl and Lgal matches the BCG pattern remarkably well (Figure 12). In the graph, the solid line representing the epsilon = constant = 0.0025 model continues to steepen at higher luminosity because of the progressively increasing relative amounts of halo gas.

Figure 12

Figure 12. Relation between specific frequency and galaxy luminosity for giant E galaxies (BCGs are shown by filled circles, other giant ellipticals by open circles. The dashed line indicates SN = 3.5 shown previously in Figure 7. The solid line is from the model of McLaughlin (1999), in which a constant globular cluster formation efficiency epsilon per unit initial gas mass is assumed. The curve ramps up steeply at high luminosity to account for the observation that more luminous BCGs have considerably more high-temperature halo gas (see text).

This model provides, for the first time, a plausible and quantitative view of the specific frequencies in BCGs, and as such, gives us a partial solution to the overall problem of understanding the global galaxy-to-galaxy scatter in specific frequency. Clearly, interesting anomalies still remain above and below the mean line. Do all the E galaxies with very lowSN values represent merger remnants? And do the few remaining normal ellipticals with anomalously high SN represent cases of genuinely more efficient cluster formation? In addition, for the BCGs themselves, it is still not certain how the large amounts of halo gas were left in place: the gas might have been ejected and heated during the earliest star formation phase by the first round of supernovae, as we speculated earlier for NGC 5128 (this phase would have had to be particularly violent and short-lived to distinguish it from other, more normal ellipticals, perhaps involving a major galactic wind; see Harris et al. 1998). Alternately, the protogalactic SGMCs may have been stripped of much of their gas in the deep central BCG potential well before star formation could begin in earnest (Blakeslee 1997). Whatever the answer, these large central galaxies represent an extreme set of conditions which still needs to be modelled in detail.

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