Simulations of the Sunyaev-Zel'dovich Power Spectrum with AGN Feedback

TL;DR

This study uses large-volume hydrodynamical simulations with diverse gas physics, including a self-regulated AGN feedback model, to predict the thermal and kinetic SZ power spectra and compare them to X-ray pressure profiles and SZ observations from ACT and SPT. The results show that AGN feedback mitigates the classic overcooling problem, bringing simulated cluster pressure profiles into agreement with the universal X-ray profile within $R_{500}$ and reducing high-$\ell$ SZ power, while leaving low-$\ell$ power relatively unchanged; high-$\ell$ measurements are thus powerful probes of intracluster gas physics. By fitting SZ templates to CMB data via MCMC, the work finds that AGN-informed templates yield SZ amplitudes and $\sigma_8$ in better agreement with primary CMB constraints, though some degeneracies with dusty galaxy foregrounds remain. The paper highlights the necessity of resolving gas physics in cluster outskirts (up to ~4$R_{200}$) and advocates stacking rotated simulational clusters to inform semi-analytic pressure models for precision cosmology.

Abstract

We explore how radiative cooling, supernova feedback, cosmic rays and a new model of the energetic feedback from active galactic nuclei (AGN) affect the thermal and kinetic Sunyaev-Zel'dovich (SZ) power spectra. To do this, we use a suite of hydrodynamical TreePM-SPH simulations of the cosmic web in large periodic boxes and tailored higher resolution simulations of individual galaxy clusters. Our AGN feedback simulations match the recent universal pressure profile and cluster mass scaling relations of the REXCESS X-ray cluster sample better than previous analytical or numerical approaches. For multipoles $\ell\lesssim 2000$, our power spectra with and without enhanced feedback are similar, suggesting theoretical uncertainties over that range are relatively small, although current analytic and semi-analytic approaches overestimate this SZ power. We find the power at high 2000-10000 multipoles which ACT and SPT probe is sensitive to the feedback prescription, hence can constrain the theory of intracluster gas, in particular for the highly uncertain redshifts $>0.8$. The apparent tension between $σ_8$ from primary cosmic microwave background power and from analytic SZ spectra inferred using ACT and SPT data is lessened with our AGN feedback spectra.

Figures (4)

• Figure 1: Shown are $f_{\mathrm{b}}$ (dashed lines) and $f_{\mathrm{star}}$ (solid lines) normalized to the universal value ($f_{\mathrm{b}}=0.13$) assumed in our simulations of our cluster g676 with $M_{500} = 6.8 \times 10^{13}\,h^{-1}\,M_{\sun}$. The blue lines are for the simulation with radiative cooling and star formation while the red and orange lines are for our AGN feedback model ($\varepsilon_{\mathrm{r}} =2\times 10^{-4}$, $\dot{M}_{\star} \geqslant 5\,\mathrm{M}_{\sun}/$yr) and that by 2008MNRAS.387.1403S, respectively. The data points are observations by 2007ApJ...666..147G and 2007MNRAS.378..293A. $f_{\mathrm{star}} (<R_{500})$ from X-ray measurements also agrees well, but the errors are large. Our sub-grid model matches the results from 2008MNRAS.387.1403S in this high resolution simulation well.
• Figure 2: Top: Comparison of fits to normalized average pressure profiles from analytic calculations, simulations and observations, scaled by $(r/R_{500})^3$. For a cluster of $M_{500} = 2 \times 10^{14}\,h^{-1} M_{\sun}$, we show fits to our SPH simulations (red), and compare them with the analytic KS profile (green), the semi-analytic S10 average profile (light green), and a fit to AMR simulations 2007ApJ...668....1N. Our feedback model matches a fit to X-ray observations 2009arXiv0910.1234A within $R_{500}$ well; only the dark grey part is actually a fit to the data, with the light grey their extrapolation using older theory results unrelated to the data. We illustrate the 1 and 2 $\sigma$ contributions to $Y_{\Delta}$ centered on the median for the feedback simulation by horizontal purple and pink error bars. 2nd panel: We compare fits to our AGN model at redshift $z=0$ (red solid) to all our three models at redshift $z=1$ (blue). Shown are the 1$\sigma$ error bars of the cluster-by-cluster variance of the weighted averages in our AGN models using corresponding lighter colors. 3rd panel: We show the effective adiabatic index $\Gamma$ for our simulations, comparing it with KS (dash-dotted) and with a constant 1.2 (light green). Bottom: The distribution of kinetic-to-thermal energy in percentile decades is indicated by the dots for the feedback case, with the median shown for all three models; thus, there are significant additions to pressure support even in the cores of simulated clusters, and even more so in the SZ-significant outer parts.
• Figure 3: Predictions for the tSZ power spectrum at 30 GHz from our simulations (red and purple symbols), simulations by 2001ApJ...549..681S (orange triangles), simulations by 2005ApJ...626...12B (orange pluses), semi-analytical simulations by S10 (dark green) and analytical calculations by KS (light green). The 256$^3$ power spectra (red symbols) are averages over 12 translate-rotate tSZ maps and 10 separate hydrodynamical simulations for each of the 33 redshift bins, the power spectra of which are then added up to yield the total spectrum; the error bars show the variance among the power in all maps. The full-width half-max values appropriate for Planck, ACT and SPT show which part of the templates these experiments are sensitive to. At low-$\ell$, the discrepant higher power in the semi-analytical calculations can be traced to the enhanced pressure structures assumed beyond $R_{200}$ over what we find.
• Figure 4: Our 150 GHz tSZ adiabatic and feedback ($A_{\mathrm{SZ}}=1$) power spectra computed with $\sigma_8 = 0.8$ (long dashed lines) are contrasted with the dark grey band indicating the $1\sigma$ range in multiplicative amplitude, $A_{\mathrm{SZ}}$$=0.75 \pm 0.36$, allowed by the SPT$_{\mathrm{DSFG}}$ power spectrum for the feedback template shape. The light grey band is the $2\sigma$ upper limit region. The $A_{\mathrm{SZ}}=1$ S10 tSZ power spectrum (dashed line) and the KS tSZ spectrum (dash dotted line) are shown for contrast; their allowed $1\sigma$ band is determined by multiplying these by their $A_{\mathrm{SZ}}$ values given in Table 1, but cover a similar swath to the grey bands. We also show the averaged kSZ power spectra computed for our simulations by dotted lines. The kSZ spectra were calculated in the same was as the tSZ spectra were, and have similar shapes. However, kSZ is underestimated at low $\ell$ because of missing bulk velocities in the simulations. There should be an additional (rather uncertain) kSZ template from inhomogeneous re-ionization as well. To show the tension with the CMB data, we plot the tSZ + 0.46 kSZ power (solid lines) since this can be directly compared with the SPT$_{\mathrm{DSFG}}$ grey bands.