  The presence of a central baryonic potential can have a significant impact on
the gravothermal evolution of self-interacting dark matter (SIDM) haloes. We
extend a semi-analytical fluid model to incorporate the influence of a static
baryonic potential and calibrate it using controlled N-body simulations. We
construct benchmark scenarios with varying baryon concentrations and different
SIDM models, including constant and velocity-dependent self-interacting cross
sections. The presence of the baryonic potential induces changes in SIDM halo
properties, including central density, core size, and velocity dispersion, and
it accelerates the halo's evolution in both expansion and collapse phases.
Furthermore, we observe a quasi-universality in the gravothermal evolution of
SIDM haloes with the baryonic potential, resembling a previously known feature
in the absence of the baryons. By appropriately rescaling the physical
quantities that characterize the SIDM haloes, the evolution of all our
benchmark cases exhibits remarkable similarity. Our findings offer a framework
for testing SIDM predictions using observations of galactic systems where
baryons play a significant dynamical role.
