  The relation between the mass and integrated electron pressure of galaxy
group and cluster halos can be probed by stacking maps of the thermal
Sunyaev-Zel'dovich (tSZ) effect. Perhaps surprisingly, recent observational
results have indicated that the scaling relation between integrated pressure
and mass follows the prediction of simple, self-similar models down to halo
masses as low as $10^{12.5} \, M_{\odot}$. Hydrodynamical simulations that
incorporate energetic feedback processes suggest that gas should be depleted
from such low-mass halos, thus decreasing their tSZ signal relative to
self-similar predictions. Here, we build on the modeling of Vikram, Lidz, and
Jain (2017) to evaluate the bias in the interpretation of stacked tSZ
measurements due to the signal from correlated halos (the "two-halo" term),
which has generally been neglected in the literature. We fit theoretical models
to a measurement of the tSZ -- galaxy group cross-correlation function,
accounting explicitly for the one- and two- halo contributions. We find
moderate evidence of a deviation from self-similarity in the pressure -- mass
relation, even after marginalizing over conservative miscentering effects. We
explore pressure -- mass models with a break at $10^{14} \, M_{\odot}$, as well
as other variants. We discuss and test for sources of uncertainty in our
analysis, in particular a possible bias in the halo mass estimates and the
coarse resolution of the Planck beam. We compare our findings with earlier
analyses by exploring the extent to which halo isolation criteria can reduce
the two-halo contribution. Finally, we show that ongoing third-generation CMB
experiments will explicitly resolve the one-halo term in low-mass groups; our
methodology can be applied to these upcoming data sets to obtain a clear answer
to the question of self-similarity and an improved understanding of hot gas in
low-mass halos.
