On the signature of the baryon-dark matter relative velocity in the two- and three-point galaxy correlation functions

Citation:

Slepian Z, Eisenstein DJ. On the signature of the baryon-dark matter relative velocity in the two- and three-point galaxy correlation functions. Monthly Notices of the Royal Astronomical Society. 2015;448 :9-26.

Date Published:

March 1, 2015

Abstract:

We develop a configuration-space picture of the relative velocitybetween baryons and dark matter that clearly explains how it can shiftthe baryon acoustic oscillation (BAO) scale in the galaxy-galaxycorrelation function. The shift occurs because the relative velocity isnon-zero only within the sound horizon and thus adds to the correlationfunction asymmetrically about the BAO peak. We further show that inconfiguration space the relative velocity has a localized, distinctivesignature in the three-point galaxy correlation function (3PCF). Inparticular, we find that a multipole decomposition is a favourable wayto isolate the relative velocity in the 3PCF, and that there is a strongsignature in the l = 1 multipole for triangles with two sides around theBAO scale. Finally, we investigate a further compression of the 3PCF toa function of only one triangle side that preserves the localized natureof the relative velocity signature while also nicely separating linearfrom non-linear bias. We expect that this scheme will substantiallylessen the computational burden of finding the relative velocity in the3PCF. The relative velocity's 3PCF signature can be used to correct theshift induced in the galaxy-galaxy correlation function so that nosystematic error due to this effect is introduced into the BAO as usedfor precision cosmology.

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