Arcetri, February 2009 Galaxy Halo Assembly Simon White Max Planck Institute for Astrophysics
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below ● They form at high redshift and thus are dense and resistant to later tidal disruption
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below ● They form at high redshift and thus are dense and resistant to later tidal disruption
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below ● They form at high redshift and thus are dense and resistant to later tidal disruption ● The mass is primarily in small halos at redshifts z ≥ 20
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below ● They form at high redshift and thus are dense and resistant to later tidal disruption ● The mass is primarily in small halos at redshifts z ≥ 20
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below ● They form at high redshift and thus are dense and resistant to later tidal disruption ● The mass is primarily in small halos at redshifts z ≥ 20 ● Structure builds up from small (e.g. Earth mass) to large (e.g. Milky Way halo mass) by a sequence of mergers
Halo assembly for neutralino ΛCDM ● Typical first generation halos are similar in mass to the free- streaming mass limit – Earth mass or below ● They form at high redshift and thus are dense and resistant to later tidal disruption ● The mass is primarily in small halos at redshifts z ≥ 20 ● Structure builds up from small (e.g. Earth mass) to large (e.g. Milky Way halo mass) by a sequence of mergers
Overdensity vs smoothing at a given A position If the density field is smoothed using B a sharp filter in k- space, then each y t i step in the random s n e walk is independent d r of all earlier steps e v o l a A Markov process i t i n i The walks shown at variance of smoothed field positions A and B mass are equally probable spatial scale
Overdensity vs smoothing M A (τ 1 ) M A (τ 1 ) M B (τ 1 )? τ 1 at a given A position B At an early time τ 1 y t A is part of a quite i s n massive halo e d r e v B is part of a very o l low mass halo or a i t no halo at all i n i variance of smoothed field mass spatial scale
Overdensity vs smoothing M A (τ 2 ) M B (τ 2 ) at a given A τ 2 position B Later, at time τ 2 y t A 's halo has grown i s n slightly by accretion e d r e v B is now part of a o l moderately massive a i t halo i n i variance of smoothed field mass spatial scale
Overdensity vs smoothing at a given A M B (τ 3 ) M A (τ 3 ) position τ 3 B A bit later, time τ 3 y t A 's halo has grown i s n further by accretion e d r e v B 's halo has merged o l again and is now a i t more massive than i n i A 's halo variance of smoothed field mass spatial scale
Overdensity vs smoothing at a given A position M A (τ 4 ) M B (τ 4 ) τ 4 Still later, e.g. τ 4 B Y X A and B are part of y t halos which follow i s n identical merging/ e d accretion histories r e v o l On scale X they are a i t embedded in a high i n i density region. variance of smoothed field On larger scale Y in mass a low density region spatial scale
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 Angulo et al 2009 free-streaming cut-off The linear power spectrum in “power per octave” form Assumes a 100GeV wimp following Green et al (2004)
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 Angulo et al 2009 free-streaming cut-off Variance of linear density fluctuation within spheres containing mass M, extrapolated to z = 0 As M → 0, S(M) → 720
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 If these Markov random walks are scaled so the maximum variance is 720 and the vertical axis is multiplied by √720, then they represent complete halo assembly histories for random CDM particles. An ensemble of walks thus represents the probability distribution of assembly histories
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 Angulo et al 2009 Distribution of the masses of the first generation halos for a random set of dark matter particles The median is 10 -2 M ⊙ For 10% of the mass the first halo has M > 10 7 M ⊙ Direct simulation will M f.s. become possible around 2035
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 Angulo et al 2009 Collapse redshift distribution of the first generation halos for a random set of dark matter particles The median is z = 13 For 10% of the mass the first halo collapses at z > 34 For 1% at z > 55
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 Angulo et al 2009 Collapse redshift distribution for first generation halos split by their mass The high redshift tail is entirely due to matter in small mass halos For first halo masses below a solar mass, the median collapse redshift is z = 21
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 Angulo et al 2009 Total mass fraction in halos At z = 0 about 5% (Sph) or 20% (Ell) of the mass is still diffuse Beyond z = 50 almost all the mass is diffuse Only at z < 2 (Sph) or z<0.5 (Ell) is most mass in halos with M > 10 8 M ⊙ The “Ell” curve agrees with simulations
EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ω m = 0.25, Ω Λ = 0.75, n=1, σ 8 = 0.9 Angulo et al 2009 The typical mass element in a “Milky Way” halo goes through ~5 “infall events” where its halo falls into a halo bigger than itself. Typically only one of these is as part of a halo with M > 10 8 M ⊙
EPS halo assembly: conclusions ● The typical first generation halo is much more massive than the free-streaming mass limit ● First generation halos typically form quite late z 13 < ~ ● Most mass is diffuse (part of no halo) beyond z = 20 ● Halo growth occurs mainly by accretion of much smaller halos ● There are typically few (~5) “generations” of halos Low mass “first” halos are little denser, and so not much more resistant to tidal destruction than more massive “first” halos
The Aquarius halos Springel et al 2008
“Milky Way” halo z = 1.5 N 200 = 3 x 10 6
“Milky Way” halo z = 1.5 N 200 = 94 x 10 6
“Milky Way” halo z = 1.5 N 200 = 750 x 10 6
How well do density profiles converge? Aquarius Project: Springel et al 2008 z = 0
How well do density profiles converge? Aquarius Project: Springel et al 2008
How well does substructure converge? Springel et al 2008 N ∝ M -1.9
How well does substructure converge? Aquarius Project: Springel et al 2008 Convergence in the size and maximum circular velocity for individual subhalos cross-matched between simulation pairs. Biggest simulation gives convergent results for V max > 1.5 km/s r max > 165 pc Much smaller than the halos inferred for even the faintest dwarf galaxies
How uniform are subhalo populations? Springel et al 2008 For the six Aquarius halos, the scatter in subhalo abundance is Poisson at high mass and ~20% at low mass The Via Lactea simulations differ significantly, at least VL-I
Solar radius 4 kpc 40 kpc 400 kpc Aquarius Project: Springel et al 2008 ● A ll mass subhalos are similarly distributed ● A small fraction of the inner mass in subhalos ● <<1% of the mass near the Sun is in subhalos
Substructure: conclusions ● Substructure is primarily in the outermost parts of halos ● The radial distribution of subhalos is almost mass-independent ● Subhalo populations scale (almost) with the mass of the host ● The subhalo mass distribution converges only weakly at small m ● Subhalos contain a very small mass fraction in the inner halo
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