The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters

TL;DR

This paper develops a parameter-free analytic model for the SZ angular power spectrum $C_\ell$ using a halo-model framework built on universal dark-matter and gas-pressure profiles. It demonstrates that $C_\ell$ scales as $C_\ell \propto \sigma_8^7 (\Omega_b h)^2$ and is largely insensitive to other cosmological parameters, with the dominant contribution arising from gas at about $0.2-0.4\,r_{\rm vir}$, making core gas physics less critical. The model agrees with diverse hydrodynamic simulations to within a factor of two around $\ell \sim 3000$ and yields a non-Gaussian covariance in line with simulations, enabling robust parameter estimation from SZ data. Applying to CBI/BIMA data yields $\sigma_8 (\Omega_b h/0.035)^{2/7} = 1.04 \pm 0.12$ (statistical) with ~10% theoretical uncertainty, and future surveys (e.g., ACT/AMIBA) could reach a few-percent precision, making SZ power a powerful, selection-bias-free probe of $\sigma_8$ in the near term.

Abstract

The angular power spectrum of the SZ effect, C_l, is a powerful probe of cosmology. It is easier to detect than individual clusters in the field, is insensitive to observational selection effects and does not require a calibration between cluster mass and flux, reducing the systematic errors which dominate the cluster-counting constraints. It receives a dominant contribution from cluster region between 20-40% of the virial radius and is thus insensitive to the poorly known gas physics in the cluster centre, such as cooling or (pre)heating. In this paper we derive a refined analytic prediction for C_l using the universal gas-density and temperature profile and the dark-matter halo mass function. The predicted C_l has no free parameters and fits all of the published hydrodynamic simulation results to better than a factor of two around l=3000. We find that C_l scales as (sigma_8)^7 times (Omega_b h)^2 and is almost independent of all of the other cosmological parameters. This differs from the local cluster abundance studies, which give a relation between sigma_8 and Omega_m. We also compute the covariance matrix of C_l using the halo model and find a good agreement relative to the simulations. We estimate how well we can determine sigma_8 with sampling-variance-limited observations and find that for a several-square-degree survey with 1-2 arcminute resolution one should be able to determine sigma_8 to within a few percent, with the remaining uncertainty dominated by theoretical modelling. If the recent excess of the CMB power on small scales reported by the CBI experiment is due to the SZ effect, then we find sigma_8(Omega_b h/0.029)^0.3 = 1.04 +- 0.12 at the 95% confidence level (statistical) and with a residual 10% systematic (theoretical) uncertainty.

Figures (14)

• Figure 1: Comparison between the predicted SZ angular power spectra (solid) and the simulations (dashed; see table \ref{['tab:simulations']} for the meaning of the labels shown in each panel, and for the cosmological parameters used). The dotted lines indicate r.m.s. errors of the simulated power spectra. The bottom-right panel scales all the power spectra by $\sigma_8^7\left(\Omega_{\rm b}h\right)^2$. The agreement between the scaled power spectra indicates that this combination of cosmological parameters controls the amplitude of $C_l$.
• Figure 2: Dependence of the SZ angular power spectrum on $\sigma_8$. From top to bottom, the lines indicate $\sigma_8=1.2$, 1.1, 1.05, 1.0, 0.95, 0.9, and 0.8, as shown in the figure.
• Figure 3: Dependence of the SZ angular power spectrum on $\Omega_{\rm m}$. From top to bottom, the lines indicate $\Omega_{\rm m}=0.97$, 0.77, 0.57, 0.47, 0.37, 0.27, and 0.17, as shown in the figure. While varying $\Omega_{\rm m}$, we have assumed a flat universe, i.e., $\Omega_{\Lambda}=1-\Omega_{\rm m}$, and $w=-1.0$.
• Figure 4: Dependence of the SZ angular power spectrum on the equation of state of the dark-energy component, $w$, the baryon density $\Omega_{\rm b}$, the Hubble constant in units of $100~{\rm km~s^{-1}~Mpc^{-1}}$, $h$, and the primordial power-spectrum slope $n$. Values of each parameter are shown in each panel of the figure. While varying $\Omega_{\rm b}$ or $h$, we have $\Omega_{\rm b}h=0.035$ fixed. The panels for $\Omega_{\rm b}$ and $h$ are to show any residual dependence of $C_l$ on these two parameters. This figure is to be compared with figure \ref{['fig:sigma8']}, showing how insensitive $C_l$ is to $w$, $\Omega_{\rm b}$, $h$, or $n$ compared to $\sigma_8$.
• Figure 5: Redshift distribution of $C_l$. We plot $d\ln C_l/d\ln z$, equation (\ref{['eq:dlncldlnz']}), for a given $l$. From left to right it is shown $l=500$, 1000, 3000, 5000, 10000, and 20000, as indicated in the figure.