  Galaxies undergo processes throughout their lifetimes that ultimately lead to
the expulsion of the gas and the cessation of the star-forming activity. This
phenomenon commonly known as quenching, can be caused by environmental
processes. For this we use the results of Romero-G\'omez et al. (2024), who
analyzed galaxies from the SAMI-Fornax and ATLAS$^{3D}$ survey. Using t$_{90}$
as an approximation for the quenching time and comparing it with the infall
time derived from phase-space models, we determine the probability of the
quenching being produced by the local environment of galaxies. Our results
reveal a relation between galaxy mass and quenching probability. Down to
M$_{\star}$ $\sim$10$^{10}$ M$_{\odot}$, galaxies exhibit almost zero
probability of quenching, suggesting their independence from environmental
effects. As we move into the mass regime of dwarf galaxies, the probability
increases with decreasing mass, highlighting their sensitivity to environmental
quenching. For the dwarfs, 10$^{7}$ - 10$^{9}$ M$_{\odot}$, 36$\pm$9% of our
observational data are consistent with this hypothesis, challenging the idea
that the present-day cluster, Fornax, is the primary driver of quenching in the
low mass galaxies. We compare these results with cosmological simulations,
selecting galaxies under similar conditions to our observational sample. The
simulated sample shows lower quenching probabilities as we move down in mass,
only 5$\pm$1% of galaxies meet the quenching criteria. This discrepancy between
observations and simulations underlines that modelling quenching is still in
its infancy. In general, the number of observed galaxies quenched by their
environment is lower than expected, which suggests that pre-processing plays a
larger role in galaxy evolution. Ultimately, our results highlight the need for
higher-quality simulations and refinement of galaxy formation and evolution
models.
