  Self-interaction of particulate dark matter may help thermalising the central
region of the galactic halo and driving core formation. The core radius is
expectedly sensitive to the self-interaction strength of dark matter (DM). In
this paper we study the feasibility of constraining dark matter
self-interaction from the distribution of the core radius in isolated haloes.
We perform systematic DM only $N$-body simulations of spherically symmetric
isolated galactic haloes in the mass range of $10^{10} $-$10^{15}M_{\odot}$,
incorporating the impact of isotropic DM self-interaction. Comparing the
simulated profiles with the observational data, we provide a conservative upper
limit on the self-interaction cross-section, $ \sigma/m < $ $ 9.8 $ $\ \rm cm^2
/\rm gm $ at $ 95 \% $ confidence level. We report significant dependence of
the derived bounds on the galactic density distribution models assumed for the
analysis.
