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• A long-standing problem is that CDM models predict
too many low-mass dark haloes.
mass function of dark haloes at low-mass end: n(m) ~ M^{-2}
Observed luminosity function faint end: \phi (L) ~ L^{-1}
• One of the biggest challenges in galaxy formation is
to understand the physical origin of this strongly
nonlinear relationship:
to lower star formation efficiency in low mass haloes
• One possibility: feedback from supernova explosions
Question: whether such high efficiency are realistic?
• other mechanisms: preheating
* photoionization heating by the UV backgroud:
efficient in dark matter haloes with M< 10^10/h M_{Sun}
* vigorous energy feedback associated with the formation of
stars in old ellipticals and bulges and with AGN at redshifts of
2 to 3. (Mo & Mao 2002)
* the collapse of pancakes and filaments heats the gas (in this
paper)
Observational constraints:
The CLF allows one to compute the average relation between
halo mass and the luminosity of the central galaxy.
The standard model:
• Simplifying assumption: each dark matter halo
forms a single disk galaxy.
Yang et al (2005) show that in haloes with M< 10^12/h
M_{Sun} the fraction of late-type galaxies is larger than
60%.
• The model of MMW98:
1) baryons have the same specific angular momentum as the
dark matter
2) they conserve their specific angular momentum when they
cool
3) they form an exponential disk
4) the halo responds to the gas cooling by adiabatically
contracting
1) and 4) are supported by numerical simulations. 2) is
required to obtain the right size. 3) is equivalent to
assuming a particular distribution of specific angular
momentum in the proto-galaxy.
• Halos are modelled as NFW spheres with a
concentration that depends on the halo mass and
spin parameter.
• One free parameter: md, defined as the disk mass
divided by the total virial mass.
Since radiative cooling is very efficient in low mass halos
with M< 10^12/h M_{Sun} , they start by setting md=0.17.
• They assume that the disk mass inside the radius
with surface density lower than the critical value
turns into stars.
• They assume that the gas surface density e.q. the
critical density inside the critical radius and the
gas surface density e.q. the disk density outside
the critical radius.
Observational constraints:
The CLF allows one to compute the average relation between
halo mass and the luminosity of the central galaxy.
Supernova feedback:
• ‘retention’ model: part of the cold gas is assumed to
be heated by SN to halo virial temperature and is
added to the hot gas for cooling in the future.
* the feedback efficency must be high enough to keep a large
amount of gas in the hot phase.
• Difficulties:
* the slope at low-mass end is much too steep.
* the HI-mass function is unchanged from the standard model
* this model predicts fairly extensive haloes of hot, X-ray
emitting gas
• ‘ejection’ model: the reheated gas is assumed to be
ejected from the current host halo.
Difficulties:
* the observed mass outflow rate in starburst galaxies is
about twice the star formation rate.
* the mass loss rate in quiescent disk galaxies are much
lower than those observed in starburst galaxies.
* the feedback effeciencies are completely unphysical.
* permanent ejection has a drastic impact on the stellar
masses but leaves the gas mass basically unchanged.
Three fundamental problems for SN feedback:
• The efficiency needed seems unphysically
• Unless the hot gas is expelled from the halo it
predicts haloes of hot gas which are inconsistent
with observations
• It overpredicts the abundance of systems with low
HI masses by almost an order of magnitude.
Reionization and preheating:
The gas in the IGM is preheated to a high specific
entropy that not all of this gas will be accreted into
the halo.
• Photoionization heating by UV background:
the strength of the effect fails to reconcile the models with the
data.
• This paper: the IGM around low-mass haloes is
preheated to a temperature corresponds to a larger Mc.
• The mass-metallicity relation