Baryonic Features in the Matter Transfer Function

Abstract

We provide scaling relations and fitting formulae for adiabatic cold dark matter cosmologies that account for all baryon effects in the matter transfer function to better than 10% in the large-scale structure regime. They are based upon a physically well-motivated separation of the effects of acoustic oscillations, Compton drag, velocity overshoot, baryon infall, adiabatic damping, Silk damping, and cold-dark-matter growth suppression. We also find a simpler, more accurate, and better motivated form for the zero baryon transfer function than previous works. These descriptions are employed to quantify the amplitude and location of baryonic features in linear theory. While baryonic oscillations are prominent if the baryon fraction exceeds $Ω_0 h^2 + 0.2$, the main effect in more conventional cosmologies is a sharp suppression in the transfer function below the sound horizon. We provide a simple but accurate description of this effect and stress that it is not well approximated by a change in the shape parameter $Γ$.

Figures (7)

• Figure 1: Comparison of the physical scales as functions of $\Omega_0 h^2$ and the baryon fraction $\Omega_b/\Omega_0$. (a) The equality scale vs. the sound horizon: $k_{\rm eq}s/\pi$ (unlabeled contours at $0.1$ increments). (b) The sound horizon vs. the Silk scale: $k_{\rm Silk}s/\pi$ (unlabeled contours $2$ and $3$). The factors of $\pi$ have been included to facilitate comparison with the acoustic scale.
• Figure 2: Suppression factors for (a) the CDM ($\alpha_c \Omega_c/\Omega_0$) and (b) the baryonic acoustic oscillations ($\alpha_b \Omega_b/\Omega_0$).
• Figure 3: Four examples of the fit compared to numerical results. The larger plots show the numerical result (solid) and the fit (dashed). The smaller subplots show the residuals, defined as the difference between the two divided by a non-oscillatory envelope. Note that in the fully baryonic models, the oscillations have alternating sign in the transfer function. Also shown is the zero baryon case (dotted); note the strong suppression on scales below the sound horizon due to the baryons.
• Figure 4: The location of the first peak in Mpc$^{-1}$ as a function of cosmological parameters.
• Figure 5: The fractional enhancement of power due to (a) the first valley and (b) the first peak relative to non-oscillatory CDM portion of the transfer function, $(T/T_c)^2-1$, at the appropriate wave vector from the fit. Unlabeled contours are at (a) -0.8, 0, 1, 3 and (b) 8.0, 16.0