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Galaxy counts

Evolution of galaxies: observational evidences

Over many years, galaxy counts, i.e., the plot of the observed number of galaxies at the limiting magnitude, have been considered to be an impor tant cosmological test. In par ticular, in the 1930s, Hubble tried to apply them to estimate the curvature of space. It became clear later that practical application of this test is so difficult (photometric errors, the account for k -correction, the evolution of galaxies with time) that "any attempt to do so appears to be a waste of telescope time" (Sandage 1961). Presently, deep counts are regarded not as a cosmological test but rather as a test of galaxy formation and evolution.

Galaxy counts

Galaxy counts

Figure summarizes modern results of differential galaxy counts. (Only data obtained after 1995 are shown.) With each filter, the results of about twenty projects (including 2MASS, SDSS, HDF, CDF, NDF, etc.) are summarized; with filter B , counts in the SDF, VVDS, and HUDF fields are added.

Main result: good agreement between the results of different works. For example, for B 25m , the count dispersion is only about 10% (accounting for the photometry, different selection of galaxies, etc., this dispersion must be even smaller), which clearly illustrates the homogeneity and isotropy of large-scale galaxy distribution. The solid lines in the figure show predictions of a semianalytic model of galaxy formation (Nagashima et al. 2002). However, the model predictions are not fully definitive due to many parameters characterizing galactic proper ties and their evolution with z (including spatial density evolution). For fur ther progress in this field, both observational data and theoretical understanding of galaxy evolution must be improved.


Galaxy distribution

Galaxy distribution

The distribution of galaxies in the nearby volume of the Universe is highly inhomogeneous. When passing to the hundred Megaparsec scale, the density fluctuations smoothen and the distribution becomes more homogeneous.

Galaxies tend to cluster. This means that the probability of finding a galaxy at some point P is highest when P is known to be close to another galaxy. We saw a hint of this in the Local Group because there are 2 big galaxies, not one. The clustering of galaxies is usually described in terms of two-point correlation functions (r) and (). The former function describes the joint probability of finding two galaxies separated by a distance r, and the latter characterizes the joint probability of detecting two objects at the angular distance . To calculate (r), spatial distances between galaxies should be known, and in practice it is therefore more convenient to measure the (angular) two-point correlation function ().

Galaxy distribution

Galaxy distribution

From (), one can then estimate (r) because both functions are related through the Limber integral equation. If (r) can be represented as a power law (r) = (r/r0 )- , the angular correlation also takes a power-law form () 1- .
The angular correlation function for 0.5 million galaxies from the 2MASS survey (+APM, SDSS). At angular scales 1 < < 2.o 5, this function is well fit by a power law with 1 - =­0.79±0.02. The amplitude of () depends on the sample depth ­ for brighter and closer objects, the clustering amplitude increases (this, in par ticular, explains the systematic shift between different survey data).

The spatial correlation function (r) calculated in different papers. In the range 0.1 Mpc r 20 Mpc, this function follows a power law with the exponent 1.7 - 1.8, and then tends to zero. The characteristic clustering scale (correlation length) r0 for nearby galaxies is 5-7 Mpc. The correlation length depends on the proper ties of galaxies, such as their luminosity and morphological type, but is independent of the sample depth.


Galaxy distribution

Galaxy distribution

Modern survey data allow determining the density fluctuations in the Universe as a function of the scale of averaging. (The power spectrum of the SDSS galaxies, which has been used to plot this figure, is based on data on 2·105 galaxies.) Figure shows that different kinds of data, from galaxy density fluctuations to cosmic microwave background anisotropy, form a unique smooth dependence described by the CDM model.

Examples of large-scale structure at high redshifts LAEs

Sky distribution of 43 LAE candidates at z = 4.86 (Shimasaku et al. 2003). LAE candidates are shown by circles. Brighter candidates are shown by larger circles. Progenitor of a cluster of galaxies?

Galaxy distribution
Ouchi et al. (2005) carried out extensive deep narrowband imaging in the 1 sq.deg. sky of the Subaru/XMM-Newton Deep Field and obtained a cosmic map of 515 Ly emitters (LAEs) at z 5.7 in a volume with a transverse dimension of 180 Mpc в 180 Mpc and a depth of 40 Mpc in comoving units. This cosmic map shows filamentary LSSs, including clusters and surrounding 10­40 Mpc scale voids, similar to the present-day LSSs.

Galaxy distribution

Shimasaku et al. (2006): angular correlation function of LAEs at z = 5.7. The filled and open circles correspond to the whole sample (N = 89) and a bright sample (N = 53), respectively.


Galaxy distribution

Galaxy distribution

Examples of large-scale structure at high redshifts LBGs
Ouchi et al. (2004) calculated angular two-point correlation functions of LBGs, and found clear signals for LBGs at z = 4 and 5. The correlation length of L L LBGs is almost constant, 7 Mpc, over z 3 - 5.

Ouchi et al. (2004): sky distributions of z 5 LBGs detected in the SDF.

Galaxy distribution

Luminosity function evolution

Correlation length and galaxy­dark matter bias as a function of redshift. A bias factor b is defined by (r)ga or
2 2 b2 = 8 (galaxies)/8 (mass). laxies

= b2 (r)mass ,

The luminosity function (LF) is the dependence of the number of galaxies within a unit volume on their luminosity. It is one of the most impor tant integral characteristics of galaxies. The LF allows estimating the mean luminosity density in the Universe. The LF form is one of the main tests of galaxy formation models. The standard form of the LF is the so-called Schechter function (L)dL = (L/L ) exp(-L/L ) d(L/L ), where (L)dL is the number of galaxies with the luminosity from L to L + dL per unit volume, and , L and are parameters.

(b = 1 ­ light does not follow mass.)


Luminosity function evolution

Luminosity function evolution
The luminosity density of galaxies is L (L) dL = L =
0

The parameter yields the normalization of the LF, L is the characteristic luminosity, and determines the slope of the weak wing (L < L ) of the LF: the weak wing of the LF is flat for = -1, the LF increases with decreasing L for < -1, and decreases at > -1. The Schechter function fits well the real LF of field galaxies and clusters and has convenient analytical proper ties.

= L
0

y (y )dy = y
0 1+ -y

= L

e

dy =

= L ( + 2) and the galaxy density is = L /L = ( + 2).

Luminosity function evolution

Luminosity function evolution

The local LF of galaxies is relatively well studied. According to many projects (including the 2dF and SDSS surveys), within the luminosity range -15m M (B ) -22m , the LF can be described with the following values of parameters: -(1.1 - 1.2), M (B ) -20.m 2 (L (B ) = 1.9 · 1010 L,B ), and (0.5 - 0.7) · 10-2 Mpc-3 . Therefore, the luminosity density of galaxies at z = 0 is L (B ) = L ( + 2) 1.3 · 108 L,B /Mpc3 and the galaxy density is = L /L = ( + 2) 10-2 Mpc-3 . The LF of local galaxies depends on their morphological type and environment.

Croton et al. (2005): direct comparison of the earlyand late-type galaxy populations in the cluster environment and void regions of the 2dF survey. The void population is composed almost exclusively of faint late-type galaxies, while in the cluster regions the galaxy population brighter than ­19m consists predominantly of early types.


Luminosity function evolution
Numerous deep field studies performed over the last ten years have enabled the evolution of the LF with z to be determined. In solving this problem, the so-called `photometric redshifts' inferred from multicolor photometry are used instead of spectroscopic ones for the most distant objects. Such a photometry allows a kind of a low-resolution spectrum and hence z of an object to be obtained. Photometric estimations of z are being made with 10%­20% accuracy, which is quite sufficient to derive the LF for large samples of galaxies.

Luminosity function evolution
Observations suggest a differential (depending on the galaxy type and the color band) evolution of the LF. Different papers give somewhat different results, but the qualitative picture emerging is as follows: the value of M increases with z , while decreases. The evolution of the LF slope is much less definitive.

Luminosity function evolution

Evolution of the galaxy structure
Morphological evolution

By considering different types of objects separately, the space density of elliptical and early spiral galaxies almost stays constant or slightly decreases toward z 1, while their LF evolution can be described as a change in the luminosity of galaxies (they become brighter). In contrast, the space density of late spiral galaxies with active star formations notably increases toward z 1. The change in the LF of galaxies alters the luminosity density they produce: from z = 0 to z 3, the value of L increases, with the strongest growth being in the UV region (by about 5 times).

One of the main goals of the deep field galaxy studies is the origin and evolution of the Hubble sequence. In the local Universe, the optical morphology of the vast majority of bright galaxies can be described in terms of a simple classification scheme suggested by Hubble. Only about 5% of nearby objects do not fit this scheme and are related to irregular or interacting galaxies.


Evolution of the galaxy structure
Morphological evolution

Evolution of the galaxy structure
Morphological evolution

The deep HST fields for the first time allowed us to see the structure of distant galaxies. The very first studies revealed that the fraction of galaxies that do not fit the Hubble scheme increases for fainter objects. At z 1 (where the age of the Universe is about half the Hubble time), the fraction of such galaxies reaches 30%­40%.

Evolution of the galaxy structure
Morphological evolution

Evolution of the galaxy structure
Morphological evolution

Fraction of interacting and merging galaxies
The statistics of objects in some deep fields also suggests that the fraction of interacting galaxies and merging galaxies increases with z . With the (1 + z )m growth assumed, observational data suggest m 2 - 4 for z 1. The evolution of the merging rate is likely to depend on the mass of galaxies ­ it is most pronounced for massive objects. It is much more difficult to draw definitive conclusions on the structure evolution for objects at z 1 due to the increasing effects of the k -correction, the cosmological diming of surface brightness and degradation of the resolu- tion.

Kar taltepe et al. (2007):


Evolution of the galaxy structure
Morphological evolution

Evolution of the galaxy structure
Morphological evolution

Abraham & van den Bergh (2001):

Evolution of the galaxy structure
Radial surface brightness of spiral galaxies

Evolution of the galaxy structure
Radial surface brightness of spiral galaxies


Evolution of the galaxy structure
Radial surface brightness of spiral galaxies

Evolution of the galaxy structure
Radial surface brightness of spiral galaxies

Evolution of the galaxy structure
Radial surface brightness of spiral galaxies

Evolution of the galaxy structure
Ver tical surface brightness distribution

Surface brightness
Barden et al. (2005): strong evolution in the magnitude-size scaling relation for galaxies with MV -20m , corresponding to a brightening of µ(V ) 1 in reast-frame V band by z 1.


Evolution of the galaxy structure
Ver tical surface brightness distribution

Evolution of the galaxy structure
Ver tical surface brightness distribution

Evolution of the galaxy structure
Ver tical surface brightness distribution

Sizes of galaxies
Ferguson et al. (2004): half-light radii vs. redshift (GOODS projects). The solid blue curve shows the expected trend if physical sizes do not evolve. The dashed red curve shows the trend if sizes evolve as H-1 (z ).


Kinematics of distant spirals

Kinematics of distant spirals

Kinematics of distant spirals

Chemical evolution
Example: MK ­metallicity relation for the intermediate-z (z = 0.4 - 1) starburst galaxies (red symbols) and local spirals (blue stars) ­ Liang et al. (2005). (The oxygen abundances are derived from R23 = [OI I ]3727/H + [OI I I ]4959, 5007/H .)


Chemical evolution
Rodrigues et al. (2008):

Optical colors
Rudnick et al. (2003): the cosmic rest-frame color of all the visible stars that lie in galaxies with LV > 1.4 в 1010 L . (Solid lines ­ a model with an exponentially declining SFH with = 6 Gyr and zstart = 4.0.)

Conclusions: The predominant population of z 0.6 starbursts and luminous IR galaxies (LIRGs) are on average, two times less metal rich than the local galaxies at a given stellar mass; the metal abundance of the gaseous phase of galaxies is evolving linearly with time, from z = 1 to z = 0 and after comparing with other studies, from z = 3 to z = 0.

Optical colors

Fundamental plane evolution

Kormendy relation
The color evolution of early-type galaxies in clusters out to z 0.9 (blue curve ­ purely passive evolution model). Ziegler et al. (1999): KR for distant galaxy clusters (z = 0.4 - 0.55. An average brightening of of distant ellipticals by = 0.m 42 at z = 0.4 and = 0.m 73 at z = 0.55. The luminosity evolution of early-type galaxies since intermediate redshifts as derived from the Kormendy relations is compatible with passive evolution models.


Fundamental plane evolution

Fundamental plane evolution
Edge-on projection of the FP in the three clusters. Dots are galaxies in the nearby Coma cluster. The solid line is a fit to Coma.

Fundamental plane
van Dokkum & van der Marel (2007): new spatially-resolved Keck spectroscopy of early-type galaxies in three galaxy clusters at z 0.5.

3C 295 ­ z = 0.46, CL 0016+16 ­ z = 0.55, CL 1601+42 ­ z = 0.42.

Fundamental plane evolution

Fundamental plane evolution

Evolution of the zeropoint of the FP can be interpreted as a systematic change of the mean M/L ratio with redshift. The conversion of zeropoint offsets to offsets in M/L ratio assumes that early-type galaxies form a homologous family and that the FP is a manifestation of an underlying relation between the M/L ratio of galaxies and other parameters. Star ting from the empirical FP relation and assuming M 2 r 2 and L Ie re , this underlying relation is M/L
2+a -(1+b)/b re e

.


Fundamental plane evolution

Evolution of the mean M/LB ratio of field galaxies with M> 1011 M (blue symbols) compared to that of cluster galaxies (red symbols). The age difference between massive field (zf = 1.95) and cluster (zc = 2.23) galaxies is small at 4%.