baryon oscillations theory
TRANSCRIPT
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Baryon oscillationsTheory
Martin WhiteUC Berkeley
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Outline
• Linear theory– Stability– Physics– Weird stuff at z~103
• Beyond linear theory– Dark matter– Redshift space distortions– Galaxy bias
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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.
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Numerical stability Seljak, Sugiyama, W
hite & Zaldarriaga (2003)
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Recombination
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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%
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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)
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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.
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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!
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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.
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Non-linearities (easy part)
White (2005)
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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)
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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.
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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
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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
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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.
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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
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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
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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)
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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)
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Bias + shot-noise decompositionReal space
k (h/Mpc) Huff et al.
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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.
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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.