A comparative test of different pressure profile models in clusters of galaxies using recent ACT data

Abstract: Context. The electron pressure profile is a convenient tool to characterize the thermodynamical state of a galaxy cluster, with several studies adopting a "universal" functional form. Aims. This study aims at using Sunyaev-Zel'dovich (SZ) data to test four different functional forms for the cluster pressure profile: generalized Navarro-Frenk-White (gNFW), $β$-model, polytropic, and exponential. The goal is to assess to what level they are universal over a population-level cluster sample. Methods. A set of 3496 ACT-DR4 galaxy clusters, spanning the mass range $[10^{14},10^{15.1}]\,\text{M}_{\odot}$ and the redshift range $[0,2]$, is stacked on the ACT-DR6 Compton parameter $y$ map over $\sim13,000\,\text{deg}^2$. An angular Compton profile is then extracted and modeled using the theoretical pressure recipes, whose free parameters are constrained against the measurement via a multi-stage MCMC approach. The analysis is repeated over cluster subsamples spanning smaller mass and redshift ranges. Results. All functional forms are effective in reproducing the measured $y$ profiles within their error bars, without a clearly favored model. While best-fit estimates are in broad agreement with previous findings, hints of residual subsample dependency are detected favoring higher amplitudes and steeper profiles in high-mass, low-redshift clusters. Conclusions. Population-level cluster studies based on SZ data alone are likely unable to accurately constrain different pressure profile models. Residual trends at population level and scatter at individual cluster level undermine the universal pressure model assumption whenever high precision is required. Finally, functional forms different from the gNFW prove equally effective while being more physically motivated.