## [1005.2416] Relative velocity of dark matter and baryonic fluids and the formation of the first structures

 Authors: Dmitriy Tseliakhovich, Christopher Hirata Abstract: At the time of recombination, baryons and photons decoupled and the sound speed in the baryonic fluid dropped from relativistic to the thermal velocities of the hydrogen atoms. This is less than the relative velocities of baryons and dark matter computed via linear perturbation theory, so we infer that there are supersonic coherent flows of the baryons relative to the underlying potential wells created by the dark matter. As a result, the advection of small-scale perturbations (near the baryonic Jeans scale) by large-scale velocity flows is important for the formation of the first baryonic structures. This effect involves a quadratic term in the cosmological perturbation theory equations and hence has not been included in studies based on linear perturbation theory. We show that the relative motion suppresses the abundance of the first bound objects, even if one only investigates dark matter haloes, and leads to qualitative changes in their spatial distribution, such as introducing scale-dependent bias and stochasticity. We discuss the possible observable implications for high-redshift galaxy clustering and reionization. [PDF]  [PS]  [BibTex]  [Bookmark]

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Antony Lewis
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### [1005.2416] Relative velocity of dark matter and baryonic f

This is a very interesting paper, which looks at the second-order effect of baryon velcoties on the small-scale matter power spectrum and halo formation. The basic idea is that in regions of space where the baryon velocity was large at the end of recombination the fast bulk flow of the baryons relative to the small-scale dark matter perturbations washes away any baryon overdensity and hence suppresses growth of structure. The effect is therefore a bit like local non-Gaussianity, where here the small-scale matter perturbations are modulated by the large-scale baryon velocities. The paper finds a large effect on the bias, which become scale-dependent.

I was confused by Fig 2, but I think this is $\Delta_m^2$ rather than $\Delta_c^2$, so there is a fall-off in the linear result about the Jeans scale though I can't quite reproduce the same shape for the linear result.