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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 $V_{\rm max} \simeq 40~km~s^{-1}$ 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 σ/m = $0.5 - 50$ $cm^2~g^{-1}$ 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, σ/m ~ $5-10~cm^2~g^{-1}$. Our largest SIDM cross section run (σ/m = $50~cm^2~g^{-1}$) 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 $50~cm^2~g^{-1}$ remain viable on velocity scales of dwarf galaxies ($v_{\rm rms}$ ~ $40~km~s^{-1}$). 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.