Dark Halo Properties & Their Environments

Transcription

1 Dark Halo Properties & Their Environments Andrew R. Zentner The University of Chicago The University of Pittsburgh 1

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4 Collaborators Andrey Kravtsov The University of Chicago James Sinclair Bullock The University of California, Irvine Risa Wechsler Stanford University 4

5 Dark Matter Halos δρ/ρ 200 For MW: Rvir 250 kpc Mvir 1012 M Diemand et al

6 Halo Properties Concentration: cvir Rvir/rs 6

7 02 Halo Properties CONCENTRATION AND HALO ASSEMBLY HISTORY Wechsler et al Formation Time: af cvir-1 7

8 Property-Dependent Halo Clustering 6 WECHSLER, ZENTNER, BULLOCK, & KRA Sheth & Tormen 2004, Gao et al. 2005, Wechsler et al. 2006, Betz et al. 2006, Harker et al. 2006, Wetzel et al. 2006, Berlind et al

9 Property-Dependent Halo Clustering ER, ZENTNER, BULLOCK, & KRAVTSOV elected by quarcompared to the Sheth & Tormen 2004, Gao et al. 2005, Wechsler et al. 2006, Betz et al. 2006, Harker et al. 2006, Wetzel et al. 2006, Berlind et al Fig. 4. Relative bias as a function of normalized concentration, log(! cvir )/σ(log! cvir ), for various values of halo mass scaled c" 8

10 Great Talks to Come! Charles Shapiro Doug Rudd 9

11 It cold is also useful to think of amodel, window 2as(k) having a particular eguments. standard, dark matter (CDM) increases with wavw Some Preliminaries The window volume small can bescale obtained operationally normalizing W( til some exceedingly determined by the by physics of the prod maximum value of but unity is dimensionless. Call this newwith dimen the early universe), we and observe the density field smoothed som 3! tion W (x). The volume is given by integrating to give V = d xw W re, a quantity of physical interest is the density field smoothed on a pa e thinks of thethe window weighting points in the space by different amou smoothed density field:! "!!! ear that W (x) = W. Roughly the )δ(" smoothed field is δ("x(x)/v ; RW )W d3 x! Wspeaking, ( "x! "x ; R x ) W 3 density fluctuation in a region of volume VW RW. The Fourier trans ction W (x; RW ) is the window function that weights the density field And it s Fourier transform: d field is elevant for the particular application. According to the convention use δ("k; RW ) W ("k; RW )δ("k), dow function (sometimes called filter function) has units of inverse v R ) is the Fourier thethink window alwarguments. It istransform also usefulof to of afunction. window as having a parti natural choice of window function is probably a simple sphere in rea VW. The window volume can be obtained operationally by normalizin function is then has a maximum value of unity and is dimensionless. Call this new d 3 " (x R )! 3 W function W (x). The volume is4πr given by integrating to give V = 10 d W W

12 Halo Formation in Excursion Set Theory Random walks of the smoothed density field: Bond et al. 1991, Lacey & Cole 1993 Smoothed Density δ(m) Merger M3 M2 time δc M3 M2 MASS Mass M1 at z=0 11

13 Let s Understand MassDependent Halo Clustering Random walks of the smoothed density field: 12

14 al to the dark matter overdensity and is a function of halo mass th amics that can map the initial Lagrangian volume to the final Eu moothed density fluctuation (dictated by the linear theory) is dient needed to Eulerian relate thespace abundance of just halos to the matter δdshift represent the variables corresponding to the densi Lagr z, corresponds to an object that has virialized with namics map initial the final E and δ0.that Thecan final halothe abundance between mass and smoothing scalelagrangian is is set by thevolume volume to of the Let s Understand MassDependent Halo Clustering 3 Bias from δ represent the Eulerian space variables corresponding to the Lag Mass-Dependent Halo the relative ple, the relationship is M = 4πρ R /3 for a tophat window M δ0, S0 ) N (M 1. δhalo abundance = halos: is overdensity of Vaussian and δ. The final halo 0 0 )V window. Further, any(dn(m region)/dm that exceeds the critical will meet that threshold when discussion smoothed on larger scale N (M δ0, S 0 )some White [38] give an extensive of the mapping from Lagra 1. δhalo = (dn(m )/dm )V mulative probability for a region to have a density dinates and use a spherical collapse model smoothed to determine the appropr tional occupied by virialized objects larger White [38]limit give discussion from ely. In volume the ofana extensive small overdensity δ0of"the 1, Vmapping #than V0 (1the + δ), Lagra δ# Yields a bias relation ating Eq. (15), this probability is! model to " determine the appropr dinates and use a spherical collapse 2 ν 1 # " δhalo overdensity =ν 1 + δ1, V # V0 (1 + δ), δ # vely.!in the limit of a 1small δ " 0 δc (16) M) = P (δ; R)dδ = erfc, " 2 δc 2b! δ. 2 h ν 1 δhalo = 1 + δ Kaiser 1984, Mo & White 1996, entary error function, and ν δc /σ(m ) δisc the heightsheth of&the Tormen verabundance is proportional to bthe matter overdensity and always δ. h 13 dard deviation of the smoothed density distribution. In this

15 Let s Understand MassDependent Halo Clustering Simulations by Jeremy L. Tinker 14

16 Correlations Between Scales window functions 15

17 Correlations Between Scales Uncorrelated 16

18 Correlations Between Scales 16

19 Correlations Between Scales 17

20 Correlations Between Scales Half-mass scale 17

21 Formation Times in Different Environments ARZ

22 Formation Times in Different Environments 6 WECHSLER, ZENTNER, BULLOCK, & Wechsler et al

23 Consider the Global Mass Function Press & Schechter 1974, Bond et al. 1991, Sheth & Tormen 1999, Jenkins et al

24 Environmental Effects in the Low-mass Regime Environmental Dependence of Cold Dark Matter Halo Formation ure 3. The ratio between initial mass, Mi, and the final mass a Sandvik functionetofal.halo Wang et al. 2006,Malso see 2006formation redshift. Left pane h as mass halos with h M" > Mh > h M", while right panel is for halos with Mh > h three curves in each panel represent the median, 20 and 80 percentiles. 21

25 Do We Understand Halo Properties in Different Environments? It is intriguing to speculate the environmental dependence of halo properties stems from two things The statistics of the density field for the largest mass objects Truncated growth for smaller mass objects 22