halo merger histories

Transcription

1 Physics 463, Spring 07 Lecture 5 The Growth and Structure of Dark Mater Halos z=7! z=3! z=1! expansion scalefactor z=0! ~milky way M>3e12M! /h c vir ~13 ~virgo cluster M>3e14M! /h, c vir ~6 halo merger histories extract merger histories from simulations get merger histories analytically from Extended Press- Schechter selected mass accretion histories mass of most massive progenitor expansion scalefactor a=1/(1+z) RW et al 2002 time

2 ] a universal mass accretion history MAH well fit by: M(z)=M 0 e -Sa c z where a c is scalefactor where dlogm/dloga=s mass of most massive progenitor expansion scalefactor a=1/(1+z) average mass accretion history M>3x 13 M! /h! average MAH M>1-4x 12 M! /h! } scatter M(z)=M 0 e -Sa c z RW et al 02 "#time individual MAH is quite lumpy mass accretion depends on definition 14 Mpc Mpc 0 kpc kpc R200 Rvir M(<r) [ M ] kpc 1 kpc M 12 M(<r) [ kpc 0 kpc 40 kpc a = 1 / (1+z) 0.1 kpc Diemand et al a = 1 / (1+z) Diemand et al 2006

3 rapid mass accretion slow mass accretion definitions of formation time Zhao et al 2002 a c (M,z) σ[m (a)] = δ c /D(a) } scatter is 0.13 in logac collapsing today rms mass fluctuations,! collapsed early "#1 for collapse RW et al 02 formation time set by mass, independent of z ac is the time that dlogm/dloga = 2 one can also define a formation time as the time when FM = M* f(σ, P S) = mass scale M low mass halos form early, when the universe was denser 2 δ c π σ exp( δ2 c 2σ 2 ) ν = δ c σ(m)

4 a c (M,z) } scatter is 0.13 in logac how is the mass accreted? RW et al 02 formation time set by mass, independent of z ac is the time that dlogm/dloga = 2 one can also define a formation time as the time when FM = M* for F ~ these definitions are equivalent. Lacey & Cole 1993 Merger rate of DM halos merger statistics Li et al 2007 Li et al 2007 merger rate goes as (1+z) 3 Gottloeber et al 2000 Wechsler 2001

5 mmp upsizing vs. total mass downsizing halo density profiles )* ! 7!!!"(!&!&"( (!&! &# (!&! %!'!!"#!"$!"% &"' )*+,&-./ )* ! 5!!!"(!&!&"( (!&! % (!&! &#!'!!"#!"$!"% &"' )*+,&-./ dark matter halos in N- body simulations found to have a Universal density profile Neistein et al 2006 Navarro, Frenk & White 1996, 1997 halo density profiles Navarro, Frenk & White 1996, 1997 halo density profiles roughly self-similar form: small radius large radius M vir 4π 3 virρ b R 3 vir Also: Dubinsk 1991, Moore et al 1999 Fukushige & Makino 1999 Klypin 2001 Bullock 2001 Jing & Suto 2001 Power et al 2003 Navarro et al convenient parameterization: ρ(r) ρ crit = δ c (r/r s )(1 + r/r s ) 2 Navarro, Frenk & White 1996, 1997(NFW) concentration parameter: %(r) %~r -1 %~r -2 R s %~r -3 r/r vir * virial radius with respect to the background density; $ vir =337 at z=0 note: concentrations depend on definition of the density threshold used to define halos

6 lots of mass definitions... halo concentrations Bullock et al 2001 B01: measured in LCDM for thousands of halos 2x 11 <M<few x 14 0<z<5 M vir 4π 3 virρ b R 3 vir ρ vir = vir ρ b ρ vir = δ vir ρ c ρ b /ρ b 0.3 M 200 = 200(4π/3)ρ c r vir 333 δ vir 0 ρ(r) ρ crit = } 68% intrinsic scatter in halo population δ c (r/r s )(1 + r/r s ) 2 c vir 9(M/M ) 0.13 M = (4π/3)ρ r 3 NFW use 200 Bullock 2001 uses vir. σ(logc vir ) = 0.14 halo concentrations Bullock et al 2001 B01: measured in LCDM for thousands of halos 2x 11 <M<few x 14 0<z<5 halo rotation velocities r vmax = 2.163r s } 68% intrinsic scatter in halo population log rotation velocity c vir ~1/(1+z) V c (r) = 4πGρ s rs 3 f(r) r f(r) = ln(1 + r/r s ) r/r s 1 + r/r s log radius Navarro, Frenk & White 1996, 1997

7 Physics of halo formation M and c vir evolution what is the reason for the correlation between concentration c and halo mass M? what determines the time dependence of c(m, z)? what is the source of the scatter in the relation? how does c(m,z) depend on cosmology & power spectrum? average MAH expansion scalefactor a average concentration c vir evolution by formation time early forming! $late forming expansion scalefactor a RW et al 02 concentration vs. formation time c vir =c 1 a obs /a c concentration vs. formation time fit to density profiles and mass accretion histories of z=0 halos c vir ~1+z c details of merger history relatively unimportant WBPKD02 concentration formation scalefactor recent major merger for all masses and redshifts! scatter at a given mass and redshift caused by scatter in mass accretion histories! correlated with galaxy type? RW et al 02 concentration scaled formation scalefactor z=0 z=1 z=2

8 ] a c (M,z) σ[m (a)] = δ c /D(a) } scatter in cvir collapsing today rms mass fluctuations,! collapsed early "#1 for collapse simply inverting this plot gives you c(m,z) + scatter. the same model for formation time based on M* applies. this means that we can understand how concentrations depend on the power spectrum! RW et al 02 c vir = K a a c 9(M/M ) 0.13 mass scale M low mass halos form early, when the universe was denser reducing mass fluctuations on galaxy scales (low! 8, tilt) reduces concentrations M(a) predicts %(r) note: the z dependence of concentration is mostly due to definiton assuming: 1. NFW %(r) 2. M~e -2a c z 3. c vir ~a/a c M 12 M(<r) [ kpc 0 kpc 40 kpc a = 1 / (1+z) 400 kpc R200 Rvir Diemand et al 2006

9 non-standard inflation models mass variance halo concentration Warm Dark Matter mass variance halo concentration Zentner & Bullock 2002; 2003 Zentner & Bullock 2002; 2003 two problems with profiles (?) the inner slope CDM predicts cuspy halos many dwarf galaxies have cores the concentrations too high for low mass galaxies (?) too low for clusters (?)

10 cluster concentrations are they too high because of a selection effect? ah, the inner slope (the cusp/core problem aka cuspy halo crisis ) halo phase space density a diversity of inner slopes? close to a simple power law insight into the reason for the profile?

11 triaxial halos triaxial halos wide distribution of shape parameters, but all halos fairly triaxial and prolate Jing & Suto 2002 Jing & Suto 2002

12 halo shapes s = 0.54Mvir/M* major caveat shape = shortest axis/longest axis halos get rounder with time & further out in radius low mass halos are the most spherical early forming halos more spherical Allgood et al 2005 we have only discussed dark matter! next time halo substructure angular momentum in halos