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Clumps within Lumps

or, why adding small scale substructure increases the small scale power spectrum…

Effects of halo substructure on the power spectrum and bispectrumDolney, Jain, and Takada [DJT] astro-ph/0401089published in MNRAS

discussion lead by Stephen Bailey

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Halo Model

Instead of full N-body simulations, track clumps of dark matter (haloes)

Does a pretty good job of matching N-body simulationswith a lot less work

See Corray and Sheth (2002) Phys. Rep. 372, 1 for a review

From Cooray and Sheth, 2002

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Basic Ingredients

Mass functions How many halos there are of a given mass

Halo density profile How the matter is distributed within a halo Spherically symmetric Smoothly decreasing with radius

Bias prescription [?]

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The Problem

N-Body simulations have halo substructure 10%-ish of halo matter is in a sub-halo clump This shouldn’t be too surprising

the halo model is a pretty severe limit which works surprisingly well adding substructure is a first order correction back toward the truth

Several recent papers discuss halo substructure DJT try to quantify the size of the effect and relate it to future

measurements

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What DJM do

Standard halo model, plus Sub-halos within each halo, with their own density distributions,

mass functions, etc. Sub-halo density follows the parent halo density They ask: How does this affect the power spectrum?

power spectrum [2 point correlation] bispectrum [3 point correlation] reduced bispectrum [3 point normalized by 2 point squared]

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Figure 1 – How do sub-halos affect power?

Bigger Smaller

sub-halos increasesmall scale power(no surprise)

Questions:- Why Smith et al. (2003)?- Normalization between 0%, 10%, 20%?- What size scales are galaxies, clusters, superclusters, etc.?- What size does weak lensing probe?

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Figure 2 – What contributes what?

smooth:smooth

within clump

smooth:clump

clump:clump

halo:halo

Interesting, but no surprises.Details reflect the specificsof their model

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Figure 3 – What size sub-halos contribute?

Is this interesting, or just areflection of their model inputs?

Smaller stuff contributes at smaller scales

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Figure 4 – comparison with other models

No substructure

Vary halo density profile [?]

varying the halo density profile might be part of the picture

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Figure 6 – other cosmological effects

Other cosmological parameters mimic substructure

But they each affect different measures in different ways spectrum (2 point) bispectrum (3 point) reduced bispectrum

(3 point / 2 point) So there is hope for

disentangling this

Side notes:• yay! for model error bars!• they might spoil the day…

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Figure 10 – can we measure substructure?

With CMB Input

Just weak lensing

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Questions and Comments

I don’t see anything deep, subtle, or surprising in their results But it is important to make quantitative comparisons between

models and relate simulations to observations

Their claim: with SNAP-like weak lensing and Planck-like CMB, we should be able to measure halo substructure It would be nice to be able to test models against data rather

than against each other…

DJM aren’t the first authors to use sub-halos in their halo models What have they done which is new? and/or Why didn’t the other authors do it first?

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Movie(from Ma & Bertschinger)