contraction becomes less efficient [132, 52].
The rotation curve decomposition of disks within contracted ΛCDM halos
are in general consistent with observations [82, 45, 132] (nearly–flat total rotation curves; maximum disk for high–surface brightness disks; submaximum
disk for the LSB disks; in more detail, the outer rotation curve shape depends
on surface density, going from decreasing to increasing at the disk radius for
higher to lower densities, respectively). However, there are important non–
solved issues. For example, from a large sample of observed rotation curves,
Persic et al. [95] inferred that the rotation curve shapes are described by an
“universal” profile that (i) depends on the galaxy luminosity and (ii) implies
a halo profile different from the CDM (NFW) profile. Other studies confirm
only partially these claims [123, 132, 25]. Statistical studies of rotation curves are very important for testing the ΛCDM scenario.
In general, the structure and dynamics of disks formed within ΛCDM halos
under the assumption of detailed AM conservation seem to be consistent with
observations. An important result to remark is the successful prediction of the
infrared Tully–Fisher relation and its scatter16. The core problem mentioned
in §4.2 is the most serious potential difficulty. Other potential difficulties are:
(i) the predicted disk size (surface brightness) distribution implies a P (λ)
distribution narrower than that corresponding to ΛCDM halos by almost a
factor of two [74]; (ii) the internal AM distribution inferred from observations of dwarf galaxies seems not to be in agreement with the ΛCDM halo AM
distribution [122]; (iii) the inference of the halo profile from the statistical study of rotation curve shapes seems not to be agreement with CMD halos.
In N–body+hydrodynamical simulations of disk galaxy formation there was
common another difficulty called the ’angular momentum catastrophe’: the
simulated disks ended too much concentrated, apparently due to AM trans-
ference of baryons to DM during the gas collapse. The formation of highly
concentrated disks also affects the shape of the rotation curve (strongly de-
creasing), as well as the zero–point of the Tully–Fisher relation. Recent nu-
16 In §4.1 we have shown that the basis of the Tully–Fisher relation is the CDM halo
M − Vm relation. From the pure halo to the disk+halo system there are several
intermediate processes that could distort the original M − Vm relation. However,
it was shown that the way in which the CDM halo couples with the disk and the
way galaxies transform their gas into stars “conspire” to keep the relation. Due
to this conspiring, the Tully–Fisher relation is robust to variations in the baryon
fraction fB (or mass–to–luminosity ratios) and in the spin parameter λ [45].
Understanding Galaxy Formation and Evolution
41
merical simulations are showing that the ’angular momentum catastrophe’,
rather than a physical problem, is a problem related to the resolution of the
simulations and the correct inclusion of feedback effects.
4. Star formation and feedback. We are coming to the less understood and
most complicated aspects of the models of galaxy evolution, which deserve
separate notes. The star formation (SF) process is studied at two levels (each
one by two separated communities!): (i) the small–scale physics, related to the
complex processes by which the cold gas inside molecular clouds fragments and
collapses into stars, and (ii) the large–scale physics, related to the disk global
instabilities that give rise to the largest unities of SF, the molecular clouds.
The SF physics incorporated to galaxy evolution models is still oversimpli-
fied, phenomenological and refers to the latter item. The large-scale SF cycle
in normal galaxies is believed to be self–regulated by a balance between the
energy injection due to SF (mainly SNe) and dissipation (radiative or turbu-
lent). Two main approaches have been used to describe the SF self–regulation
in models of galaxy evolution: (a) the halo cooling-feedback approach [130]), (b) the disk turbulent ISM approach [44, 124].
According to the former, the cool gas is reheated by the “galaxy” SF feed-
back and driven back to the intrahalo medium until it again cools radiatively
and collapses into the galaxy. This approach has been used in semi–analytical
models of galaxy formation where the internal structure and hydrodynamics
of the disks are not treated in detail. The reheating rate is assumed to depend
on the halo circular velocity Vc: ˙
Mrh ∝ ˙
Ms/V α
c , where
˙
Ms is the SF rate
(SFR) and α ≥ 2. Thus, the galaxy SFR, gas fraction and luminosity depend
on Vc. In these models, the disk ISM is virtually ignored and the SN–energy
injection is assumed to be as efficient as to reheat the cold gas up to the virial
temperature of the halo. A drawback of the model is that it predicts hot X-ray
halos around disk galaxies much more luminous than those observed.
Approach (b) is more appropriate for models where the internal processes
of the disk are considered. In this approach, the SF at a given radius r is
assumed to be triggered by disk gravitational instabilities (Toomre criterion)
and self–regulated by a balance between energy injection (mainly by SNe)
and dissipation in the turbulent ISM in the direction perpendicular to the
disk plane:
v
Q
g (r)κ(r)
g(r) ≡
< Q
πGΣ
crit
(15)
g (r)
Σg(r)v2
γ
˙
g (r)
SN ǫSN Σ∗(r) + ˙
ΣE,accr(r) =
,
(16)
2td(r)
where vg and Σg are the gas velocity dispersion and surface density, κ is
the epicyclic frequency, Qcrit is a critical value for instability, γSN and ǫSN
are the kinetic energy injection efficiency of the SN into the gas and the
SN energy generated per gram of gas transformed into stars, respectively,
˙
Σ∗ is the surface SFR, and ˙
ΣE,accr is the kinetic energy input due to mass
42
Vladimir Avila-Reese
accretion rate (or eventually any other energy source as AGN feedback). The
key parameter in the self–regulating process is the dissipation time td. The
disk ISM is a turbulent, non-isothermal, multi-temperature flow. Turbulent
dissipation in the ISM is typically efficient (td ∼ 107−108yr) in such a way that
self–regulation happens at the characteristic vertical scales of the disk. Thus,
there is not too much room for strong feedback with the gas at heights larger
than the vertical scaleheigth of normal present–day disks: self–regulation is
at the level of the disk, but not at the level of the gas corona around. With
this approach the predicted SFR is proportional to Σn
g (Schmidt law), with
n ≈ 1.4 − 2 varying along the disk, in good agreement with observational
inferences. The typical SF timescales are not longer than 3 − 4Gyr. Therefore,
to keep active SFRs in the disks, gas infall is necessary, a condition perfectly
fulfilled in the ΛCDM scenario.
Given the SFR radius by radius and time by time, and assuming an IMF,
the corresponding luminosities in different color bands can be calculated with
stellar population synthesis models. The final result is then an evolving inside–
out luminous disk with defined global and local colors.
5. Secular evolution
The “quiet” evolution of galaxy disks as described above can be disturbed by
minor mergers (satellite accretion) and interactions with close galaxy com-
panions. However, as several studies have shown, the disk may suffer even
intrinsic instabilities which lead to secular changes in its structure, dynam-
ics, and SFR. The main effects of secular evolution, i.e. dynamical processes
that act in a timescale longer than the disk dynamical time, are the vertical
thickening and “heating” of the disk, the formation of bars, which are efficient
mechanisms of radial AM and mass redistribution, and the possible formation
of (pseudo)bulges (see for recent reviews [71, 33]). Models of disk galaxy evolution should include these processes, which also can affect disk properties,
for example increasing the disk scale radii [117].
5.2 Spheroids
As mentioned in §2, the simple appearance, the dominant old stellar popu-
lations, the α–elements enhancement, and the dynamically hot structure of
spheroids suggest that they were formed by an early (z > 4) single violent event
∼
with a strong burst of star formation, followed by passive evolution of their
stellar population ( monolithic mechanism). Nevertheless, both observations
and theory point out to a more complex situation. There are two ways to de-
fine the formation epoch of a spheroid: when most of its stars formed or when
the stellar spheroid acquired its dynamical properties in violent or secular
processes. For the monolithic collapse mechanism both epochs coincide.
In the context of the ΛCDM scenario, spheroids are expected to be formed
basically as the result of major mergers of disks. However,
Understanding Galaxy Formation and Evolution
43
• if the major mergers occur at high redshifts, when the disks are
mostly gaseous, then the situation is close to the monolithic collapse;
• if the major mergers occur at low redshifts, when the galaxies
have already transformed a large fraction of their gas into stars, then
the spheroids assemble by the “classical” dissipationless collision.
Besides, stellar disks may develop spheroids in their centers (bulges) by
secular evolution mechanisms, both intrinsic or enhanced by minor mergers
and interactions; this channel of spheroid formation should work for late–
type galaxies and it is supported by a large body of observations [71]. But the picture is even more complex in the hierarchical cosmogony as galaxy
morphology may be continuously changing, depending on the MAH (smooth
accretion and violent mergers) and environment. An spheroid formed early
should continue accreting gas so that a new, younger disk grows around.
A naive expectation in the context of the ΛCDM scenario is that massive
elliptical galaxies should be assembled mainly by late major mergers of the
smaller galaxies in the hierarchy. It is also expected that the disks in galaxies
with small bulge–to–disk ratios should be on average redder than those in
galaxies with large bulge–to–disk ratios, contrary to observations.
Although it is currently subject of debate, a more elaborate picture of
spheroid formation is emerging now in the context of the ΛCDM hierarchical
scenario (see [106, 46, 39] and the references therein). The basic ideas are that massive ellipticals formed early (z > 3) and in a short timescale by the
∼
merging of gas–rich disks in rare high–peak, clustered regions of the Universe.
The complex physics of the merging implies (i) an ultraluminous burst of SF
obscured by dust (cool ULIRG phase) and the establishment of a spheroidal
structure, (ii) gas collapse to the center, a situation that favors the growth of
the preexisting massive black hole(s) through an Eddington or even super–
Eddington regime (warm ULIRG phase), (iii) the switch on of the AGN activ-
ity associated to the supermassive black hole when reaching a critical mass,
reverting then the gas inflow to gas outflow (QSO phase), (iv) the switch off
of the AGN activity leaving a giant stellar spheroid with a supermassive black
hole in the center and a hot gas corona around (passive elliptical evolution).
In principle, the hot corona may cool by cooling flows and increase the mass
of the galaxy, likely renewing a disk around the spheroid. However, it seems
that recurrent AGN phases (less energetic than the initial QSO phase) are
possible during the life of the spheroid. Therefore, the energy injected from
AGN in the form of radio jets (feedback) can be responsible for avoiding the
cooling flow. This way is solved the problem of disk formation around the
elliptical, as well as the problem of the extended bright end in the luminosity
function. It is also important to note that as soon as the halo hosting the
elliptical becomes a subhalo of the group or cluster, the MAH is truncated
(§4). According to the model just described, massive elliptical galaxies were
in place at high redshifts, while less massive galaxies (collapsing from more
common density peaks) assembled later. This model was called downsizing or
44
Vladimir Avila-Reese
anti-hierarchical. In spite of the name, it fits perfectly within the hierarchical
ΛCDM scenario.
5.3 Drivers of the Hubble sequence
• Disks are generic objects formed by gas dissipation and collapse inside the
growing CDM halos. Three (cosmological) initial and boundary conditions
related to the halos define the main properties of disks in isolated halos:
1. The virial mass, which determines extensive properties
2. The spin parameter λ, which determines mainly the disk surface
brightness (SB; it gives rise to the sequence from high SB to low SB
disks) and strongly influences the rotation curve shape and the bulge–
to–disk ratio (within the secular scenario). λ also plays some role in
the SFR history.
3. The MAH, which drives the gas infall rate and, therefore, the
disk SFR and color; the MAH determines also the halo concentration,
and its scatter is reflected in the scatter of the Tully–Fisher relation.
The two latter determine the intensive properties of disks, suggesting a
biparametrical sequence in SB and color. There is a fourth important param-
eter, the galaxy baryon fraction fB, which influences the disk SB and rotation
curve shape. We have seen that fB in galaxies is 3–5 times lower than the uni-
versal ΩB/ΩDM fraction. This parameter is related probably to astrophysical
processes as gas dissipation and feedback.
• The clustering of CDM halos follows an spatial distribution with very
different large–scale environments. In low–density environments, halos live
mostly isolated, favoring the formation of disks, whose properties are driven
by the factors mentioned above. However, as we move to higher–density envi-
ronments, halos form from more and more clustered high–peak perturbations
that assemble early by violent major mergers: this is the necessary condition
to form massive ellipticals. At some time, the larger scale in the hierarchy col-
lapses and the halo becomes a subhalo: the mass aggregation is then truncated
and the probability of merging decreases dramatically. Elliptical galaxies are
settled and continue evolving passively. Thus, the environment of CDM halos
is another important driver of the Hubble sequence, able to establish the main
body of the observed blue–red and early–type morphology sequences and their
dependences on density.
• Although the initial, boundary and environmental conditions provided
by the ΛCDM scenario are drivers of several of the main properties and cor-
relations of galaxies, astrophysical processes should also play an important
role. The driving astrophysical processes are global SF and feedback. They
should come in two modes that drive the disk and elliptical sequences: (i)
the quiescent disk mode, where disk instabilities trigger SF and local (nega-
tive) feedback self–regulates the SFR, and (ii) the bursting mode of violent
mergers of gaseous galaxies, where local shocks and gravothermal catastrophe
trigger SF, and presumably a positive feedback increases its efficiency. Other
Understanding Galaxy Formation and Evolution
45
important astrophysical drivers of galaxy properties are: (i) the SN–induced
wind–driven outflows, which are important to shape the properties of dwarf
galaxies (M < 1010M
< 80km/s), (ii) the AGN–induced hydrodynamical
∼
⊙, Vm ∼
outflows, which are important to prevent cooling flows in massive ellipticals,
(iii) several processes typical of high–density environments such as ram pres-
sure, harassment, strangulation, etc., presumably important to shape some
properties of galaxies in clusters.
6 Issues and outlook
Our understanding of galaxy formation and evolution is in its infancy. So far,
only the first steps were given in the direction of consolidating a theory in
this field. The process is apparently so complex and non–linear that several
specialists do not expect the emergence of a theory in the sense that a few
driving parameters and factors might explain the main body of observations.
Instead, the most popular trend now is to attain some description of galaxy
evolution by simulating it in expensive computational runs. I believe that
simulations are a valuable tool to extend a bridge between reality and the
distorted (biased) information given by observations. However, the search of
basic theories for explaining galaxy formation and evolution should not be
replaced by the only effort of simulating in detail what in fact we want to get.
The power of science lies in its predictive capability. Besides, if galaxy theory
becomes predictive, then its potential to test fundamental and cosmological
theories will be enormous.
Along this notes, potential difficulties or unsolved problems of the ΛCDM
scenario were discussed. Now I summarize and complement them:
Physics
• What is non–baryonic DM? From the structure formation side, the preferred
(and necessary!) type is CDM, though WDM with filtering masses below ∼
109M⊙ is also acceptable. So far none of the well–motivated cold or warm non–
baryonic particles have been detected in Earth experiments. The situation is
even worth for proposals not based on elemental particles as DM from extra–
dimensions.
• What is Dark Energy? Dark Energy does not play apparently a signif-
icant role in the internal evolution of perturbations but it crucially defines
the cosmic timescale and expansion rate, which are important for the grow-
ing factor of perturbations. The simplest interpretation of Dark Energy is the
homogeneous and inert cosmological constant Λ, with equation of state pa-
rameter w = −1 and ρΛ =const. The combinations of different cosmological
probes tend to favor the flat-geometry Λ models with (ΩM , ΩΛ)≈(0.26, 0.74).
However, the cosmological constant explanation of Dark Energy faces serious
theoretical problems. Several alternatives to Λ were proposed to ameliorate
46
Vladimir Avila-Reese
partially these problems (e.g. quintaessence, k–essence, Chaplygin gas, etc.).
Also have been proposed unifying schemes of DM and Dark Energy through
scalar fields (e.g, [81]).
Cosmology
• Inflation provides a natural mechanism for the generation of primordial
fluctuations. The nearly scale–invariance of the primordial power spectrum is
well predicted by several inflation models, but its amplitude, rather than being
predicted, is empirically inferred from observations of CMBR anisotropies.
Another aspect of primordial fluctuations not well understood is related to
their statistics, i.e., whether they are Gaussian–distributed or not. And this
is crucial for cosmic structure formation.
• Indirect pieces of evidence are consistent with the main predictions of
inflation regarding primordial fluctuations. However, more direct tests of this
theory are highly desirable. Hopefully, CMBR anisotropy observations will
allow for some more direct tests (e.g., effects from primordial gravitational
waves).
Astrophysics
• Issues at small scales. The excess of substructure (satellite galaxies) can
be apparently solved by inhibition of galaxy formation in small halos due to
UV–radiation produced by reionization and due to feedback, rather than to
modifications to the scenario (e.g., the introduction of WDM). Observational
inferences of the inner volume and phase–space densities of dwarf satellite
galaxies are crucial to explore this question. The direct detection (with gravi-
tational lensing) of the numerous subhalo (dark galaxy) population predicted
by CDM for the Galaxy halo is a decisive test on the problem of substruc-
ture. The CDM prediction of cuspy halos is a more involved problem when
confronting it with observational inferences. If the disagreement persists, then
either the ΛCDM scenario will need a modification (e.g., introduction of self–
interaction or annihilation), or astrophysical processes involving gas baryon
physics should be in action. However, there are still unsolved issues at the
intermediate level: for example, the central halo density profile of galaxies is
inferred from observations of inner rotation curves under several assumptions
that could be incorrect. An interesting technique to overcome this problem
is being currently developed: to simulate as realistically as possible a given
galaxy, “observe” its rotation curve and then compare with that of the real
galaxy (see §§4.1).
• The early formation of massive red elliptical galaxies can be accommo-
dated in the hierarchical ΛCDM scenario (§§5.2) if spheroids are produced by
the major merger of gaseous disks, and if the cold gas is transformed rapidly
into stars during the merger in a dynamical time or so. Both conditions should
be demonstrated, in particular the latter. A kind of positive feedback seems
Understanding Galaxy Formation and Evolution
47
to be necessary for such an efficient star formation rate (ISM shocks produced
by the jets generated in the vicinity of supermassive black holes?).
• Once the elliptical has formed early, the next difficulty is how to avoid
further (disk) growth around it. The problem can be partially solved by con-
sidering that ellipticals form typically in dense, clustered environments, and
at some time they become substructures of larger virialized groups or clusters,
truncating any possible accretion to the halo/galaxy. However, (i) galaxy ha-
los, even in clusters, are filled with a reservoir of gas, and (ii) there are some
ellipticals in the field. Therefore, negative feedback mechanisms are needed to
stop gas cooling and accretion. AGN–triggered radio jets have been proposed
as a possible mechanism, but further investigation is necessary.
• The merging mechanism of bulge formation within the hierarchical model
implies roughly bluer (later formed) disks as the bulge–to–disk ratio is larger,
contrary to the observed trend. The secular scenario could solve this problem
but it is not still clear whether bars disolve or not in favor of pseudobulges. It
is not clear also if the secular scenario could predict the central supermassive
black hole mass–velocity dispersion relation.
• We lack a fundamental theory of star formation. So far, simple models,
or even just phenomenological recipes, have been used in galaxy formation
studies. The two proposed modes of star formation (the quiescent, inefficient,
disk self–regulated regime, and the violent efficient star–bursting regime in
mergers) are oversimplifications of a much more complex problem with more
physical mechanisms (shocks, turbulence, etc.). Closely related to star forma-
tion is the problem of feedback. The feedback mechanisms are different in the
ISM of disks, in the gaseous medium of merging galaxies with a powerful en-
ergy source (the AGN) other than