Atacama Cosmology Telescope: Modeling the gas thermodynamics in BOSS CMASS galaxies from kinematic and thermal Sunyaev-Zel’dovich measurements

The thermal and kinematic Sunyaev-Zel’dovich effects (tSZ, kSZ) probe the thermodynamic properties of the circumgalactic and intracluster medium (CGM and ICM) of galaxies, groups, and clusters, since they are proportional, respectively, to the integrated electron pressure and momentum along the line of sight. We present constraints on the gas thermodynamics of CMASS (constant stellar mass) galaxies in the Baryon Oscillation Spectroscopic Survey using new measurements of the kSZ and tSZ signals obtained in a companion paper [Schaan et al.]. Combining kSZ and tSZ measurements, we measure within our model the amplitude of energy injection $\epsilon M_{\star }{c}^2$, where $M_{\star }$ is the stellar mass, to be $\epsilon =(40\pm 9)\times {10}^{-6}$, and the amplitude of the nonthermal pressure profile to be ${\alpha }_{\text{Nth}}<0.2(2\sigma )$, indicating that less than 20% of the total pressure within the virial radius is due to a nonthermal component. We estimate the effects of including baryons in the modeling of weak-lensing galaxy cross-correlation measurements using the best-fit density profile from the kSZ measurement. Our estimate reduces the difference between the original theoretical model and the weak-lensing galaxy cross-correlation measurements in [A. Leauthaud et al., Mon. Not. R. Astron. Soc. 467, 3024 (2017)] by half (50% at most), but does not fully reconcile it. Comparing the kSZ and tSZ measurements to cosmological simulations, we find that they underpredict the CGM pressure and to a lesser extent the CGM density at larger radii with probabilities to exceed ranging from 0.00 to 0.03 and 0.12 to 0.14, for tSZ and kSZ, respectively. This suggests that the energy injected via feedback models in the simulations that we compared against does not sufficiently heat the gas at these radii. We do not find significant disagreement at smaller radii. These measurements provide novel tests of current and future simulations. This work demonstrates the power of joint, high signal-to-noise kSZ and tSZ observations, upon which future cross-correlation studies will improve.

Figure 1

Constraints on the polytropic index, $\mathrm{\Gamma }$, the amplitude of the nonthermal pressure profile, ${\alpha }_{\text{Nth}}$, the feedback efficiency parameter, $\epsilon$, and the amplitudes of the two-halo terms of the density and pressure profiles, $A_{\mathrm{k}2\mathrm{h}}$ and $A_{\mathrm{t}2\mathrm{h}}$, obtained by fitting the OBB model to combined kSZ and tSZ measurements by [18]. The radial data have large correlations (see Fig. 7 in [18]) that are accounted for in the analysis. The triangle plot shows one and two dimensional projections of the posterior probability distributions of the free parameters. We assume uniform priors within the following: $1<\mathrm{\Gamma }<5/3$, $0<{\alpha }_{\text{Nth}}<0.8$, $-4.8<{\log }_{10}\epsilon <-4.0$, $0<A_{\mathrm{k}2\mathrm{h}}<5$, $0<A_{\mathrm{t}2\mathrm{h}}<5$. The top right panels show the observed kSZ and tSZ profiles (points) with the best-fit and the $2\sigma$ range (2nd–98th percentiles) of the distribution of the models obtained from the MCMC chains.

Figure 2

Average, inferred electron temperature profile of CMASS galaxies halos weighted by density obtained from the joint $\mathrm{kSZ}+\mathrm{tSZ}$ fit to the OBB model using the MCMC chains. The black line is the median profile and the blue band indicates the $2\sigma$ range of the models obtained from the MCMC chains. For comparison, the grey dashed line indicates the expected virial temperature for an isothermal sphere of mass equal to the mean mass of our CMASS sample ($M_{200}=3.3\times {10}^{13}{M}_{\odot }$), $T_{\mathrm{vir}}=1.7\times {10}^7\mathrm{K}$. The $x$ axis is converted to arcmins to ease the comparison to the density and pressure profiles. The average temperatures of the CMASS galaxies are closer to ${10}^7\mathrm{K}$ than they are to ${10}^6\mathrm{K}$.

Figure 3

Constraints on the log-amplitude of the gas density profile, ${\log }_{10}{\rho }_0$, the core radius, $x_{c,k}$, the outer slope, ${\beta }_k$, and the amplitude of the two-halo term, $A_{\mathrm{k}2\mathrm{h}}$, obtained by fitting the GNFW density model to kSZ measurements by [18]. The radial measurements have large correlations (see Fig. 7 in [18]) that we take into account in our analysis. The corner plot shows one and two dimensional projections of the posterior probability distributions of the free parameters. We assume uniform priors on the parameters within: $1<{\log }_{10}{\rho }_0<5$, $0.1<x_{c,k}<1$, $1<{\beta }_k<5$, $0<A_{\mathrm{k}2\mathrm{h}}<5$. The top right panel shows the measured kSZ profile at f090 and f150 (circles) with the median (50th percentile, dashed curves) and the $2\sigma$ (2nd–98th percentiles, bands) range of the models obtained from the MCMC chains. The solid lines indicate the best-fit model with ${\chi }^2=20.2$ and $\mathrm{PTE}=0.32$.

Figure 4

Constraints on the amplitude of the thermal pressure profile, $P_0$, the intermediate slope, ${\alpha }_t$, the outer slope, ${\beta }_t$, and the amplitude of the two-halo term, $A_{\mathrm{t}2\mathrm{h}}$, obtained by fitting the GNFW pressure model to tSZ measurements by [18]. The radial data have large correlations (see Figs. 7 and 8 in [18]) that are accounted for in the analysis. The blue contours and lines show the fit of the GNFW thermal $\mathrm{pressure}+\mathrm{dust}$ model to ACT and Herschel temperature measurements (see Fig. 11 for the simultaneous constraints on the dust model), while in red is the fit of the GNFW thermal pressure model to Compton-$y$ measurements obtained with CIB-deprojected maps. The corner plot shows one and two dimensional projections of the posterior probability distributions of the free parameters. We assume uniform priors within the following: $0.1<P_0<30$, $0.1<{\alpha }_t<2$, $1<{\beta }_t<10$, $0<A_{\mathrm{t}2\mathrm{h}}<5$. The top right panel shows best-fit (solid lines), the median (50th percentile, dashed lines), and the $2\sigma$ (2nd–98th percentiles, bands) of the distribution of the models obtained from the MCMC chains.

Figure 5

CMASS galaxy-galaxy lensing signal. Data from [26] (green circles) are compared to HOD model predictions from [96] (MDR1, red line) and our model that includes a baryons correction (blue line) to the MDR1. This correction uses the best-fit density profile from kSZ measurements (Sec. 3b and Fig. 3). The gold band illustrates the uncertainty in the model from the stellar component and the vertical grey lines show the radial range in which we have kSZ observations; outside this radial range we are extrapolating. The baryon correction that we estimated to the MDR1 model reduces the difference between the galaxy-galaxy measurements and HOD model predictions by half (50%), but does not reconcile it. The dashed red line illustrates the maximum correction to the MDR1 model, which is to remove all baryons without altering the dark matter profile. This extreme model still does not reconcile this model and observations below $500\mathrm{kpc}/h$.

Figure 6

Top: comparison of our best-fit gas density (left) and thermal pressure (right) profiles (blue curves and $2\sigma$ bands) with the related profiles from two cosmological simulations: [46] (magenta) and Illustris/TNG [28] (orange and green), and a NFW profile [20] (black). For the pressure profile, we also show the Planck 2013 [88] best fit (maroon dotted line). We show average profiles, where each halo contribution is weighted by its mass according to the mass probability density function of the CMASS catalog used in this work, and at the same redshift ($z=0.55$). We select red galaxies from TNG and show both stellar mass- (orange) and halo mass-weighted average profiles. The vertical grey lines enclose the range where we measure the kSZ and the tSZ. Middle: projected density and pressure profiles, for comparison purposes. Bottom: comparison of the profiles projected into the kSZ (left) and tSZ (right) observable space with the measurements by [18] in the ACT f150 band (blue points and $1\sigma$ error bars). The projections of the simulated and the NFW profiles account for the convolution with the ACT beam and the aperture photometry filtering, as described in Sec. 2. The black dashed curve shows the NFW profile truncated at the virial radius. The tSZ simulated profiles also include the dust correction from our $\mathrm{ACT}+\mathrm{Herschel}$ measurements ($2\sigma$).

Figure 7

One- and two-halo terms contributing to the density (left) and pressure (right) profiles of a halo of $3\times {10}^{13}{M}_{\odot }$ at $z=0.55$. The contribution of the two-halo term is not negligible above $\sim 2R_{200c}$.

Figure 8

Survey footprints, in equatorial coordinates, for the $\mathrm{ACT}+\mathrm{CMASS}$ (blue) and overlapping Herschel (magenta) regions: three H-ATLAS/GAMA fields (circles), HerS (triangle), and HeLMS (star). We use the H-ATLAS/GAMA data only to estimate the dust emission (see text).

Figure 9

CMASS stacked profiles from H-ATLAS/GAMA. For each of the three SPIRE frequency bands, we show the profiles in intensity units $[\mathrm{kJy}/\mathrm{sr}]$ (left) and cumulative temperature $[\mu \mathrm{K}·\mathrm{arcmi}]$ to match the units of the stacked SZ profiles. The small number density, $0.02\mathrm{sources}/{\mathrm{arcmin}}^2$ may explain the small covariance among the apertures. We have also tested that the covariance effectively increases at even larger apertures.

Figure 10

Null tests from stacking on random positions on the maps, for the same number of galaxies in the overlapping area. The ${\chi }^2$ computed accounting for the covariance in each band is consistent with an average zero signal.

Figure 11

Top: Constraints on the dust model (b1). Results obtained with the simultaneous fit to the GNFW pressure model using ACT and Herschel temperature measurements are shown in blue. Results from the fit of the dust model to Herschel data only are shown in orange. All parameters match within $1\sigma$. Middle: Profiles measured in the three Herschel/SPIRE frequency bands (black) in intensity units [kJy/sr]. The blue and orange curves show the best-fit models to $\mathrm{Herschel}+\mathrm{ACT}$ and Hershel only data, respectively, and the corresponding bands show the $2\sigma$ (2nd–98th percentiles) of the distribution of the models obtained from the MCMC chains. Bottom: Profiles measured in the two ACT frequency bands (black) in cumulative temperature units of $[\mu \mathrm{K}·{\mathrm{arcmin}}^2]$. The blue curves and $2\sigma$ bands show results obtained with the simultaneous fit of the dust and the GNFW pressure models using $\mathrm{Herschel}+\mathrm{ACT}$ data. We separate the dust contribution (dot-dashed curves) from the thermal pressure (dashed curves). The best-fit model is the sum of the two contributions.