Evolution of galaxies and dark matter halos

Yipeng JingShanghai Astronomical Observatory

Main Collaborators:Chunyan Jiang (姜春艳） , Cheng Li（李成） , Donghai Zhao（赵东海） , Lan Wang （王岚）…… .

Taken from S. Faber

Theoretical framework for understanding evolution of galaxies and dark matter halos

Taken-away conclusions• The mass accretion history and the structure evolution of

halos established by Zhao et al. (2009) is universally valid not only for LCDM, but also for WDM, HDM (Zhao et al. 2012);

• A reliable stellar mass-halo mass is directly measured from SDSS, putting useful constraints both on galaxy formation and on cosmology (Li, Cheng et al. 2012);

• The merger time scale of galaxies is about two times longer than previously thought ( Jiang et al. 2008);

• Merger leading to a increase of 50-100% in stellar mass of massive galaxies (Wang & YPJ 2010) from z=1 to z=0, consistent with our recent analysis of CFHT data (YPJ 2012)

The universal mass accretion history of dark matter haloes

N-body cosmological simulations

• Assumption: MAHs are well simulated with pure dark matter (incomplete, 1024**3)

model ni Γ σ8 Ω0 Λ0 Np L NNQ η zi

SF1 1 K cut 1 1 0 5123 160 512 0.016 1481.3

SF2 0 1 1 0 5123 160 512 0.016 363.2

SF3 -1 1 1 0 5123 160 512 0.016 75.0

SF4 -2 1 1 0 5123 160 512 0.016 11.3

LCDM1 1 0.2 0.9 0.3 0.7 2563 25 512 0.0025 72

LCDM2 1 0.2 0.9 0.3 0.7 5123 100 512 0.01 72

LCDM3 1 0.2 0.9 0.3 0.7 5123 300 512 0.03 36

OCDM1 1 0.2 1.0 0.3 0 2563 50 256 0.02 72

SCDM1 1 0.5 0.55 1 0 2563 25 512 0.0025 72

SCDM2 1 0.5 0.55 1 0 5123 100 256 0.02 72

Choosing proper variables for modeling

• Given cosmology and power spectrum, after extrapolated linearly to z=0,

linear mass variance of given volume σ is determined by M, and

linear critical collapse overdensity δc by z.

Growth rate as a function of scaled “mass”

D.H. Zhao et al. (2010)

Universal differential relation w-p determines

growth rate of halo of mass M

D.H. Zhao, et al. ApJ (2009)

• LCDM

Much more accurate than van den Bocsh (2002) or Wecshler et al. (2002)

– SCDM & OCDM

Another universal correlationt: universe age

of final halo t0.03: universe

age when main progenitor mass is 4% of final halo massImportant Finding!

Evolution of halo density profile• Combined with

MAHs model we presented in part I, c-t correlation can be used to predict the evolution of halo density profile

– LCDM1-3

Evolution of halo density profile

– SCDM1-3

Prada et al. (2012) does not work!

Zhao et al. (2009) for HDM, without any tuning the parameters, universal indeed

Zhao et al. (2009) for Warm DM, without any tuning the parameters, universal indeed (Zhao et al. 2012)

Taken from S. Faber

Relation between the stellar mass of the central galaxy and host dark matter halo

Group catalog of SDSS DR7 (Yang et al. 2008)

Sky coverage: 4514 deg^2

Galaxies with redshifts: 369447 (408119)

Groups selected: 301237 (300049)

Measure the redshift cross correlation function for groups with a given central stellar mass (Li et al. 2012

Velocity dispersion – stellar mass relation

Halo mass-stellar mass relation

Luminosity – halo mass relation

Velocity dispersion – stellar mass relation

Constraint on cosmology

Sigma_8=0.88 \pm 0.04

Consistent with WMAP7 <2sigma

Taken from S. Faber

Galaxy merger timescale

Using ln(m_h/m_sub) for Coulomb logarithm (c.f. Navarro et al. (1994)

Predicted friction timescale

Measured merger timescale

repeated Navarro et al. 1994

But our conclusion is different from theirs

Fitting formula

Merger timescale for all mergers

arXiv:1204.6319

Summary• The Chandrasekhar formula, as is usually used,

under(over)-estimates merger time for minor(major) mergers ;

• If the Coulomb logarithm is replaced ln(1+lambda), the mass dependence is accounted for correctly; but underestimate

• The dependence on the circularity is much weaker than the 0.78 power;

• We have presented a fitting formula and circularity distribution which are sufficient for modeling the merger rate;

• the scatters are 40%

Evolution of the stellar mass and halo mass relation with Halo Occupation Model

• Halo (and subhalo) catalog from an high resolution N-body simulation

• Galaxies in halos (central) and subhalos (satellites) are determined by the host halos at infall (Lan Wang et al. 2006),

Using the mass functions and correlation functions from SDSS and VVDS (z=0.8)Linear interpolationUnified model

Jing & Suto (2000)

HOD method: assuming N galaxies in halo of mass M；

First applied to Las Campanas Redshift survey ，getting alpha ＝0.09

Jing, Mo, Boerner 1998, ApJ, 494, 1

Fitting to SDSS (Wang & YPJ 2010)

Fitting to VVDS

The stellar mass –halo mass relation

Stellar mass functions at high redshift

How many mergers

CFHT and COSMOS (preliminary)

Remarks

• Well understood for the evolution of dark matter halos

• Still very poorly for evolution of galaxies• Combining deep catalogs of galaxies with

the dark matter model can yield important clues to the evolution of galaxies