Core Formation in Dwarf Halos with Self Interacting Dark Matter: No Fine-Tuning Necessary

We investigate the effect of self-interacting dark matter (SIDM) on the density profiles of $V_{\mathrm{m}\mathrm{a}\mathrm{x}}\simeq 40km{s}^{-1}$ isolated dwarf dark matter halos – the scale of relevance for the too big to fail problem (TBTF) – using very high-resolution cosmological zoom simulations. Each halo has millions of particles within its virial radius. We find that SIDM models with cross sections per unit mass spanning the range \sigma/m = $0.5-50$ $c{m}^2{g}^{-1}$ alleviate TBTF and produce constant density cores of size 300-1000 pc, comparable to the half-light radii of $M_{\star }$ ~ ${10}^{5-7}$ $M_{\odot }$ dwarfs. The largest, lowest density cores develop for cross sections in the middle of this range, \sigma/m ~ $5-10c{m}^2{g}^{-1}$. Our largest SIDM cross section run (\sigma/m = $50c{m}^2{g}^{-1}$) develops a slightly denser core owing to mild core-collapse behavior, but it remains less dense than the CDM case and retains a constant density core profile. Our work suggests that SIDM cross sections as large or larger than $50c{m}^2{g}^{-1}$ remain viable on velocity scales of dwarf galaxies ($v_{\mathrm{r}\mathrm{m}\mathrm{s}}$ ~ $40km{s}^{-1}$). The range of SIDM cross sections that alleviate TBTF and the cusp/core problem spans at least two orders of magnitude and therefore need not be particularly fine-tuned.