The Baryon Acoustic PeakThe Baryon Acoustic Peak

Nick Cowan

UW Astronomy

May 2005

Nick Cowan

UW Astronomy

May 2005

Outline

• Acoustic Peak• Statistical Methods• Results from SDSS• Summary

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Acoustic Peak

• Quantum fluctuations led to density variations in the early universe.

• These density fluctuations generated sound waves.

• Those sounds waves are responsible for the large-scale structure of the universe.

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Density Fluctuations

• Given an initial density fluctuation, how does it evolve?

• Point-like pertubations are easy to follow.

• An arbitrary density distribution can always be decomposed into point-pertubations.

• Let’s look at point-pertubations!

Point-like Pertubation

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(comoving)

(r2)

Plasma Sound Wave

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Neutrinos stream offAt the speed of light

Dark Matter stays put

Sound wave propagates through plasma

Perturbation at Decoupling

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Photons Break Free

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Photons streamoff at speed of light

Intermission: Sound Speed

Before recombination, have relativistic plasma

After recombination, have baryonic gas

Sound Wave Stalls

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Dark Matter and Baryons Flirt

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Baryons fall back intocentral potential DM falls

into shell

Dark Matter and Baryons Merge

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Nowadays we expect baryons and DMto track each other.

Density Pertubation Today

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The central peak dominatesbecause of CDM

A faint shell due to the propagating sound waveshould still be visible.

Statistical Methods

• The specific density distribution of our universe is hard to obtain and contains loads of useless information.

• The statistics of galaxy distribution should contain all the useful information.

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Power Spectrum vs Correlation Function

Fourier Transform

Power Spectrum

Contain all the useful information if fluctuations are isotropic.

Correlation Function

Average over directions

Exact representation of density pertubations

2-point Correlation Function

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Correlation and CovarianceStatistical Correlation

Covariance

Where the Covariance Matrix is:

and the variance is given by:

The diagonal terms in the covariance matrix quantify the “shot noise”

StandardDeviation

Observations• Size matters.• Good redshifts don’t

hurt, either.• SDSS provides the

largest catalogue of spectroscopic galaxies.

• Use Luminous Red Galaxies to get a (nearly) complete sample out to z=0.47

• SDSS is “more bulk than boundary”.

Flashback

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The central peak dominatesbecause of CDM

A faint shell due to the propagating sound waveshould still be visible.

Correlation Function

Results from SDSS

CorrelationFunction for46,748 LRGs

Points looktoo highbecause the covariance is “soft” w.r.t.shifts in .

Holy S**t!There’s the peak!

Systematics• Radial Selection: even if

you ignore redshift data, still get a peak.

• Selection of LRGs is sensitive to photmetric calibration of g,r and i bands.

• Calibration errors in SDSS (along the scan direction) should not be important.

• Different redshift slices all exhibit the acoustic peak.

Low zHigh z

Peak is still there!

Covariance Matrix• The covariance matrix is constructed from the

sample of LRGs.• It shows considerable correlation between

neighboring bins (off-diagonal terms) and an enhanced diagonal from shot noise.

2 = 16.1/17 which is reasonable.• Check the matrix by comparing jack-knifed

samples to each other. • Compare to a covariance matrix based on the

Gaussian approximation.• Other fancy statistical tricks

Summary

• Sound waves stall at recombination.• They should always be found the same

distance from the central CDM peak.• We can still see the signature of these

sound waves in the distribution of galaxies as a baryon acoustic peak.

• The position and size of the peak is consistent with the WMAP cosmology.

References

• Eisenstein et al, astro-ph/0501171

• Eisenstein, “What is the Acoustic Peak?”

• Peacock, Cosmological Physics (1999)

• Ryden, Introduction to Cosmology (2003)