5. THE BARYONIC MASS FUNCTION OF FIELD GALAXIES

The baryonic mass function is presented in figure 4. This is the sum of the functions in the three previous figures, where the masses in gas functions are multiplied by 1.33 to take into account the presence of helium. The error bars are small enough that Schechter or any other analytical fits to the data are formally poor, however we show our best fit values on the plot.

Figure 4. The field galaxy baryonic mass function. The data points are for all galaxies, while the lines show spine fits by Hubble Type. The lines are as in figure 2. The CDM mass spectrum from the numerical simulations of [Weller et al. 2004] is also shown. Overlaid are parameters for a Schechter fit to the total mass function.

In table 3, we present the total mass density of the Universe in baryons within galaxies, in different forms. Typical errors are 10%. For the stellar masses the uncertainty mainly comes from our lack of knowledge of the mass-to-light ratios. For the gas components the error primarily comes from the uncertainty in the scaling of optical luminosity to gas mass for galaxies of a given Hubble Type.

Table 3. The baryonic mass density of galaxies. Typical errors are ~ 10%.

	b	*	HI	H2
E	0.00064	0.00064	~ 0	~ 0
S0	0.00073	0.00068	0.00003	0.00001
Sa+Sab	0.00036	0.00032	0.00001	0.00002
Sb+Sbc	0.00056	0.00040	0.00004	0.00008
Sc+Scd	0.00072	0.00047	0.00010	0.00008
Sd+Sdm+Sm	0.00037	0.00021	0.00007	0.00005
Irr+dIrr	0.00013	0.00007	0.00003	0.00001
dE	0.00002	0.00002	~ 0	~ 0
total	0.0035	0.0028	0.00029	0.00026

A comparison with the CDM mass function is also shown in figure 4. The normalisation for the baryonic component in galaxies is very much lower, reflecting the fact that galaxy masses are dominated by dark matter, not baryons.. Additionally, the baryonic mass function has a very different shape from the dark mass function. This suggests that the collapse of baryons into galaxies and the ability of the galaxies to retain the gas once star formation has begun is very much a scale-dependent process. At the very low mass end, where galaxies are heavily dark-matter dominated, the baryonic mass function is still very much shallower than the CDM mass function - this is the classical missing satellites problem [Moore et al. 1999].

Finally, notice that there is a slight bump in the baryonic mass function at ~ 10⁹ M. This corresponds to a similar dip in the stellar mass function (see figure 2) and a dip in the luminosity function at M_R ~ - 17 (see figure 1). The dip is much less significant in the baryonic mass function than in the stellar mass function. It is caused by a transition at this point in galaxy type from ellipticals and spirals to dwarfs. The fact that it is less pronounced in the full baryonic mass function than in the stellar mass function highlights the fact that the gas mass fraction in dwarf irregulars is much larger than in ellipticals and spirals. A similar dip in the luminosity function was recently found by [Flint et al. 2003] suggesting that it is not simply the result of incompleteness or poor overlap in the surveys used.

There are a number of baryonic mass components which we have not included in the above analysis because they comprise only a tiny fraction of the total mass in baryons within galaxies.
Field halo stars: In the Milky Way and M31 there is a faint spheroidal stellar population of stars which lie neither in the disc nor bulge components of the galaxy [Gilmore et al. 1989]. While the total mass of this component is quite uncertain and estimates range from ~ 10⁸ [Binney & Merrifield 1998] to ~ 10⁹ M [Freeman & Bland-Hawthorn 2002], this is still only ~ 0.1 - 1% of the total baryonic mass and, therefore, a negligible Galactic mass component. Because of the low surface density of these halo stars, they are difficult to resolve in galaxies much further away than M31. Perhaps other galaxies have a much more significant stellar halo and we are missing an important baryonic mass component. This is probably not the case, however, because stars from these halos would generate a high extragalactic background light in galaxy clusters, which is not observed [Zibetti et al. 2005].
MACHOs and stellar remnants: Limits can be placed on massive compact halo objects (MACHOs) of any form, which may or may not be made of baryonic matter, from microlensing experiments (e.g. [Alcock et al. 2000]). Current data ([Afonso et al. 2003]) suggests that the contribution of MACHOs to the total baryonic mass of the Galaxy may be small, and we neglect this contribution here. A more stringent constraint can be placed on the total mass in MACHOs that are the endpoints of stellar evolution (neutron stars and black holes) due to the lack of large amounts of heavy elements in the Universe (e.g. [Freese et al. 2001]). [Fukugita & Peebles (2004)] estimated the cosmological density in the remnants to be _remnants ~ 0.00001, which is far less than the sums in Table 3, and we ignore this contribution here.
Hot gas: Early type galaxies contain hot ionised gas. However, most observational evidence (e.g. [O'Sullivan et al. 2001], [Mathews & Brighenti 2003] and [Goudfrooij 1999]) suggests that less than 1% of the baryonic mass of these galaxies is in the hot gas component, and we neglect it here.
Dust: In the Milky Way, a dust-to-gas ratio by mass is about 1/200 [Gilmore et al. 1989]. There does not seem to be any evidence for this ratio being different in the majority of external normal galaxies (see e.g. the review by [Young and Scoville 1991]), and we neglect the contribution of dust to the baryonic mass density of the Universe.