The electron pressure profile is a convenient tool to characterize the thermodynamic state of a galaxy cluster, with several studies adopting a ``universal'' functional form. 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. A set of 3496 ACT--DR4 galaxy clusters, spanning the mass range 10^, 10^ 14 15. 1, _⊙ and the redshift range M 0, 2, is stacked on the ACT--DR6 Compton parameter y map over sim13, 000, 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 multistage Markov chain Monte Carlo approach. The analysis is repeated over cluster subsamples spanning narrower mass and redshift ranges. deg 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. Population-level cluster studies based on SZ data alone are likely unable to accurately constrain different pressure profile models. Residual trends at the population level as well as scatter at the individual cluster level undermine the universal pressure model assumption whenever high precision is required. Finally, functional forms that differ from the gNFW prove equally effective while being more physically motivated.
D. Tramonte (2026) studied this question.