Core formation in dwarf haloes 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-max similar or equal to 40km s(-1) isolated dwarf dark matter haloes - 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 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 similar to 10(5-7)M(circle dot) dwarfs. The largest, lowest density cores develop for cross-sections in the middle of this range, sigma/m similar to 5-10 cm(2) g(-1). Our largest SIDM cross-section run (sigma/m = 50 cm(2) g(-1)) develops a slightly denser core owing to mild core-collapse behaviour, but it remains less dense than the cold dark matter 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(rms) similar to 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.