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2.1. Low luminosity galaxies

CDM simulations predict a vast excess of dwarf halos (Fig. 1). Input of baryonic physics helps resolve the dwarf excess. Only halos of mass gtapprox 105 Modot trap baryons that are able to undergo early H2 cooling and eventually form stars. Reionisation reinforces this limit by ejecting the baryons in the lowest mass systems that have not collapsed prior to the reionization epoch, and hence suppressing star formation. Reionisation gives an inevitable feedback for the lowest mass dwarfs. An abrupt increase of the sound speed to ~ 10-20 km/s at z ~ 10 means that dwarfs of mass ~ 106 - 107 Modot, which have not yet collapsed and fragmented into stars, will be disrupted. However more massive dwarfs are unaffected, as are the high sigma peaks that develop into early collapsing, but rare, low mass dwarfs.

Figure 1

Figure 1. The theoretical mass function of galaxies compared to the observed luminosity function

The accepted solution for gas disruption and dispersal in intermediate mass and massive dwarfs (~ 108 - 1010 Modot) is by supernova feedback. Supernovae expel the remaining baryons in systems of mass up to ~ 108 Modot, leaving behind dim remnants of dwarf galaxies (Dekel & Silk 1986). Presumably the luminous dwarfs accrete gas at later epochs. Most gas is ejected by the first generations of supernovae for systems with escape velocity ltapprox 50 km/s, leaving dim stellar remnants behind. Multiphase simulations (Powell et al. 2010) confirm the effectiveness of supernova-driven winds in yielding an acceptable fit to the low mass end of the galaxy luminosity function for the classical dwarfs. A factor of two uncertainty in abundance remains at intermediate luminosities due to the observed variance at the LMC / SMC level. This is due to the small number statistics both locally in the MWG / M31 complex and observed more widely in the SDSS (Guo et al. 2011). The discovery of a population of ultrafaint dwarfs in the MWG halo verifies this expectation, and even provides a quantitative fit to the feedback expectations (Koposov et al. 2009) at the ultra-faint end.

Tidal disruption also plays a role in disrupting satellites whose orbits intersect the disk or bulge. Dramatic discoveries due to deep imaging of nearby galaxies with very small, wide field of view, telescopes confirm the ubiquity of tidal tails that trace dwarf disruption in the remote past (Martínez-Delgado et al. 2010). Simulations provide a convincing demonstration that we are seeing tidal disruption in action (Cooper et al. 2010). An independent confirmation of disruption in action comes from studies of the tidal tails around the outermost MWG globular star clusters such as PAL31. Gaps in the tails (Grillmair 2009) indicate the presence of dark satellites. Numerical simulations (Yoon et al. 2010) find that high M/L satellites of mass ~ 107 Modot are required, again a prediction of the CDM model.

In summary, the low luminosity end of the luminosity function seems to be understood in the context of CDM. However other problems remain unresolved. Most notably, for the dwarf galaxies, there is the question of the apparent persistency of dark matter cores. The simulations prefer cusps, although feedback via, most plausibly, bulk gas motions driven by supernovae can soften the cusps (Mashchenko, Wadsley and Couchman 2008).

2.2. Disk galaxies

In addressing star-forming galaxies, the problem reduces to our fundamental ignorance of star formation. Phenomenology is used to address this gap in our knowledge. Massive star feedback in giant molecular clouds, the seat of most galactic star formation, implies a star formation efficiency of around 2%. This is also found to be true globally in the MWG disk, for a star formation efficiency (SFE) defined to be star formation rate/gas mass × dynamical or disk rotation time.

Remarkably, a similar SFE is found in nearby star-forming disk galaxies. Indeed, star formation rates per unit area in disk galaxies, both near and far, can be described by a simple law, with star formation efficiency being the controlling parameter:

Equation 2

The motivation comes from the gravitational instability of cold gas-rich disks, which provides the scaling, although the normalisation depends on feedback physics. For the global law, in terms of star formation rate and gas mass per unit area, supernova regulation provides the observed efficiency of about 2% which fits essentially all local star-forming galaxies. One finds from simple momentum conservation that SFE = [sigmagas vcool m*SN] / [ESNinitial] approx 0.02. This is a crude estimator of the efficiency of supernova momentum input into the interstellar medium but it reproduces the observed global normalization of the star formation law.

The fit applies not only globally but to star formation complexes in individual galaxies such as M51 and also to starburst galaxies. The star formation law is known as the Schmidt-Kennicutt law (Kennicutt et al. 2007), and its application reveals that molecular gas is the controlling gas ingredient. In the outer parts of galaxies, where the molecular fraction is reduced due to the ambient UV radiation field and lower surface density, the star formation rate per unit gas mass also declines (Bigiel et al. 2010).

For disk instabilities to result in cloud formation, followed by cloud agglomeration and consequent star formation, one also needs to maintain a cold disk by accretion of cold gas. There is ample evidence of a supply of cold gas, for example in the M33 group. Other spiral galaxies show extensive reservoirs of HI in their outer regions, for example NGC 6946 (Boomsma et al. 2008) and UGC 2082 (Heald et al. 2011). Recent data extends the Schmidt-Kennicutt law to z ~ 2, with a tendency for ultraluminous starbursts at z ~ 2 to have somewhat higher SFE (Genzel et al. 2010).

A more refined theoretical model needs to take account of star formation in a multi-phase interstellar medium. One expects self-regulation to play a role. If the porosity in the form of supernova remnant-driven bubbles is low, there is no venting and the pressure is enhanced, clouds are squeezed, and SN explosions are triggered by massive star formation. This is followed by high porosity and blow-out, and the turbulent pressure drops. Eventually halo infall replenishes the cold gas, the porosity is lowered and the cycle recommences. Some of this complexity can be seen in numerical simulations (Agertz et al. 2011). Supernovae provide recirculation and venting of gas into fountains, thereby reducing the SFE and prolonging the duration of star formation in normal disk galaxies.

2.3. Spheroidal galaxies

The baryon fraction is far from its primordial value in all systems other than massive galaxy clusters. Supernovae cannot eject significant amounts of gas from massive galaxies. Baryons continue to be accreted over a Hubble time and the stellar mass grows. One consequence is that massive galaxies are overproduced in the models, and that the massive galaxies are also too blue.

A clue towards a solution for these dilemmas comes from the accepted explanation of the Magorrian relation, which relates supermassive black hole mass to spheroid velocity dispersion. This requires collusion between black hole growth and the initial gas content of the galaxy when the old stellar spheroid formed. One conventionally appeals to outflows from the central black hole that deliver momentum to the protogalactic gas. When the black hole is sufficiently massive, the Eddington luminosity is high enough that residual gas is ejected. An estimate of the available momentum supply come from equating the Eddington momentum with self-gravity on circumgalactic gas shells, LEdd / c = GMMgas / r2. Blowout occurs and star formation terminates when the SMBH-sigma relation saturates. This occurs for MBH propto sigma4-5, the observed slope (Graham et al. 2011), and gives, at least in order of magnitude, the correct normalisation of the relation. This is the early feedback quasar mode.

There is also a role for AGN feedback at late epochs, when the AGN radio mode drives jets and cocoons that heat halo gas, inhibit cooling, resolve the galaxy luminosity function bright end problem and account for the red colours of massive early-type galaxies. AGN feedback in the radio mode may also account for the suppression in numbers of intermediate mass and satellite galaxies. Feedback from AGN in the host galaxies also preheats the halo gas that otherwise would be captured by satellites.

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