Analytic Prediction of Baryonic Effects from the EFT of Large Scale Structures

TL;DR

The paper extends the Effective Field Theory of Large Scale Structures to a two-fluid description of baryons and dark matter, showing that long-distance baryonic backreaction can be captured by a small set of parameters in an effective stress tensor. The authors derive the two-fluid Eulerian EFT, perform linear and one-loop perturbative calculations, and implement IR resummation to account for large-scale displacements and the relative baryon–dark matter velocity. They demonstrate that the leading baryonic effect on the total and baryon power spectra scales as $\Delta P^A(k) \propto (k/k_{NL})^2 P_{11}^A(k)$ with two time-independent counterterms, and that simulations with varied baryonic physics are described to percent accuracy up to $k \sim 0.3$–$0.6\,h$ Mpc$^{-1}$ (and higher for certain observables). This provides a predictive analytic framework that interfaces cleanly with simulations and enhances the interpretation of forthcoming large-scale structure data.

Abstract

The large scale structures of the universe will likely be the next leading source of cosmological information. It is therefore crucial to understand their behavior. The Effective Field Theory of Large Scale Structures provides a consistent way to perturbatively predict the clustering of dark matter at large distances. The fact that baryons move distances comparable to dark matter allows us to infer that baryons at large distances can be described in a similar formalism: the backreaction of short-distance non-linearities and of star-formation physics at long distances can be encapsulated in an effective stress tensor, characterized by a few parameters. The functional form of baryonic effects can therefore be predicted. In the power spectrum the leading contribution goes as $\propto k^2 P(k)$, with $P(k)$ being the linear power spectrum and with the numerical prefactor depending on the details of the star-formation physics. We also perform the resummation of the contribution of the long-wavelength displacements, allowing us to consistently predict the effect of the relative motion of baryons and dark matter. We compare our predictions with simulations that contain several implementations of baryonic physics, finding percent agreement up to relatively high wavenumbers such as $k\simeq 0.3\,h\, Mpc^{-1}$ or $k\simeq 0.6\, h\, Mpc^{-1}$, depending on the order of the calculation. Our results open a novel way to understand baryonic effects analytically, as well as to interface with simulations.

Figures (13)

• Figure 1: $\epsilon_{s<}^{\rm rel}$ and $\epsilon_{s>}^{\rm rel}$ at redshift $z=40$ are plotted in red and blue respectively. This plot shows that at redshift $z=40$ the effect of infrared relative motions becomes large at $k\approx k_J$, while the effect from short relative displacement is always perturbative.
• Figure 2: IR resummation of the total matter power spectrum at $z=40$. The dashed black line is the total linear power spectrum, and the solid black line is the tree-level IR resummation. The solid blue curve shows the tree-level cross correlation $\langle \delta^{(1)}_b \delta^{(1)}_c \rangle$ contribution to the total power spectrum, and the dotted blue line shows the same contribution but after IR resummation. The suppression of this contribution is the reason for the advection effect.
• Figure 3: Equation (\ref{['eq:lambdaIR']}) as a function of $\Lambda=\Lambda_{\rm Resum}$ for $\sigma=c,b,bc$. The solid line is the curve for dark matter, the dotted line is the curve for baryons, and the dot-dashed curve is the one for the cross correlation.
• Figure 4: We use the dark-matter-only simulation to determine the speed of sound $\bar{c}^2_{c,w_b=0} \simeq 7.9 \,k_{\rm NL}^{-2}$ for the WMAP7 data, and $\bar{c}^2_{c,w_b=0} \simeq 9.6 \,k_{\rm NL}^{-2}$ for the WMAP3 data. We do this by plotting the ratio of the EFT total matter power spectrum with $w_b = 0$, $P^A ( k ; 0 , \bar{c}^2_{c,w_b=0} , 0)$, to the simulation data for the same quantity. The black dots are the data points, and the surrounding red region is the error due to the cosmic variance of a box size $L = 100 \, h^{-1} \rm Mpc$. The green region is the size of the theoretical error, which we have calculated by estimating the size of the two-loop corrections that we have not included, using Eq. (\ref{['estimate11']}), and the green dashed line is this error added in quadrature with a $1\%$ error for unknown systematics.
• Figure 5: We fit to the simulation that includes baryons and determine $\Delta \bar{c}_A^2 \simeq 1.32 \,k_{\rm NL}^{-2}$. In these plots, we compare the ratio of the adiabatic power spectra in the presence of baryon effects and in their absence, $R = P^A_{\rm with \, baryon} / P^A_{\rm DM\, only}$, as calculated in the EFT to the same quantity calculated from the data. The solid line in the left panel is $R_{\rm EFT}$, and the points are from the simulation data. The fit starts deviating near $k \approx 0.7 \ h \rm Mpc^{-1}$. The green region is the size of the theoretical error, which we have calculated by estimating the size of the two loop corrections that we have not included, using Eqs. (\ref{['estimatedelta1']}) and (\ref{['estimatedelta2']}). The dashed line is the same theoretical error after adding in quadrature a 1% error for unknown systematics.