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.
![]() |
![]() |
![]() |
![]() |
|
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 |
About 8% of the baryons in the Universe are in atomic gas and about 7% are in molecular gas. In the Milky Way about 12% of the baryons are in atomic gas and a further 12% in molecular gas. This suggests that the Milky Way is slightly more gas-rich than typical galaxies in the Universe, as is appropriate for its Hubble Type of Sbc.
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 MR ~ - 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.