Baryon oscillationsTheory

Martin WhiteUC Berkeley

Outline

• Linear theory– Stability– Physics– Weird stuff at z~103

• Beyond linear theory– Dark matter– Redshift space distortions– Galaxy bias

Linear perturbation theory• Key to the BAO method is the fact that the (linear) theory

of perturbations is well understood and the sound horizoncan be inferred from z~103 physics.

• However the physics is not completely trivial - no analyticmodel exists.

Numerical stability Seljak, Sugiyama, W

hite & Zaldarriaga (2003)

Recombination

Non-standard scenarios• Our method hinges on being able to predict the

sound horizon, s:

– Recombination (atomic physics) is very robust.– Remaining dependence is on ρB/ργ and zeq.

• We can get ρB/ργ from CMB (peaks & damping)• The CMB also fixes zeq very well (from high l)

– Potential envelope depends on zeq (Hu & White 1997)

– s is relatively insensitive to zeq.• Decreasing zeq by 500 decreases s by 5%

Extra radiation?• For 3 relativistic ν species, knowing ργ (from Tγ)

gives ωrad=Ωradh2.• Knowing zeq gives ωm.• What if ωrad was different?• As long as zeq is still known reasonably well it

doesn’t matter! Misestimate ωm– Comparing rulers at z~103 and z~1.– Same ωm prefactor enters H, dA as s.– All DE inferences go through unchanged!– Misestimate H0. Eisenstein & White (2004)

Decaying “X” ?A non-relativistic (massive) particle which undergoes a momentum

conserving decay into massless neutrinos with lifetime τ leads to excesssmall-scale power and a shift in sound horizon.

Beyond linear theory …• Unfortunately we don’t measure the linear theory

matter power spectrum in real space.• We measure:

– the non-linear– galaxy power spectrum– in redshift space

• How do we handle this and what does it mean forthe method?

BAO surveys are always in the sample variance dominated regime.Cannot afford to take a large “hit” due to theoretical uncertainties!

Numerical simulations• Our ability to simulate structure formation has

increased tremendously in the last decade.• Simulating the dark matter for BAO:

– Meiksin, White & Peacock (1999)• 106 particles, 102 dynamic range, ~1Gpc3

– Springel et al. (2005)• 1010 particles, 104 dynamic range, 0.1Gpc3

– Huff, Schulz, Schlegel, Warren & White (in prep)• Many runs of 109 particles, 104 dynamic range, several Gpc3

• Our understanding of galaxy formation has alsoincreased dramatically.

Non-linearities (easy part)

White (2005)

0.1 1.0

Current accuracy is a few percent among the better codes.

Updated from Heitmann et al. (2005)δ P

(k)/P

(k)

Galaxy bias• The hardest issue is galaxy bias.

– Galaxies don’t faithfully trace the mass• Here we use large numerical simulations with ad-

hoc galaxy recipes.– Rather than try to predict the unique “right” answer for

galaxy formation we want to explore a range ofplausible alternatives.

– We do this by assigning galaxies to the halos found indark matter simulations using phenomenological rules.

– The resulting catalogs exhibit scale-dependent,stochastic, non-linear bias of the galaxies wrt the darkmatter. Huff, Schulz, Schlegel, Warren, White.

Eisenstein, Seo, White.

A slice, 10Mpcthick, through a1Gpc3 simulation.

Each panel zooms inon the previous 1 bya factor of 4.

The color scale islogarithmic, fromjust below meandensity to 102xmean density.

Points mark galaxypositions.

An example

A slice, 10h-1 Mpcthick, through a1h-3Gpc3 simulation.

Each panel zooms inon the previous 1 bya factor of 8.

The color scale islogarithmic, fromjust below meandensity to 102xmean density.

Points mark galaxypositions.

An example

Insight vs Numbers• Trying to learn from these simulations

– What range of behaviors do we see?– Which D/A algorithms work best?– How do we parameterize the effects?

• Can we gain an analytic understanding of theissues?

• Are there shortcuts for describing thecomplexities?– Bias on large scales, excess power on small scales.

Toy model I• We can understand the main features with a

simple “toy” model: halo model.• There are two contributions to the 2-point function

of objects:

2-halo

1-halo

2-halo

1-halo

Toy model II• If the halos form a biased tracer of the linear

theory density field, with a bias depending on theirmass, then

• Definite predictions for Pgal(k) which depend onthe number of galaxies in halos of mass M, N(M),and how they are spatially distributed.– However on the scales of interest only N(M) matters.

M

N(M)

central

satellite

Toy model IIIIf we work on scales much larger than the virial radius of atypical halo, the halo profile is sub-dominant. Then

With a similar expression for the dark matter with thereplacement of Ngal with Mhalo.

The tradeoff between the 1- and 2-halo terms occurs atdifferent k for the galaxies and DM, leading to a scale-dependent bias.

Schulz & White (2005)

Scale-dependent bias

Wavenumber

Pow

er ~

k3 P

(k)

In our model scaledependence of bias isenhanced when:

At fixed ngal, biasincreases.

At fixed bias, ngaldecreases.

Scale dependenceincreases faster with bfor rarer objects.

Perhaps a real spacedescription is better!

Schulz & White (2005)

Bias + shot-noise decompositionReal space

k (h/Mpc) Huff et al.

Real space descriptionBut the 1-halo term is confined to small-r in real space!

Measuring ξ( r) in periodic boxes is problematic -- instead measure

which is insensitive tolow-k modes, meandensity estimate etc.

Look at residual scaledependence and anysystematic shifts in thepeaks.

Huff et al.

Conclusions• Baryon oscillations are a firm prediction of CDM models

relying (mostly) on linear physics.• For DE inferences method is surprisingly robust to

uncertainties in physics at z~103

• Both precision and systematic mitigation are dramaticallyimproved with Planck data.

• Understanding structure and galaxy formation to the levelrequired to maximize our return on investment will be anexciting and difficult challenge for theorists!

• We need a “turn-key” method for extracting DE science frommock data to evaluate the effects of various choices a real-world survey needs to make.