Gravothermal collapse of isolated self-interacting dark matter haloes: N-body simulation versus the fluid model

Self-interacting dark matter (SIDM) is a collisional form of cold dark matter (CDM), originally proposed to solve problems that arose when the collisionless CDM theory of structure formation was compared with observations of galaxies on small scales. The quantitative impact of the proposed elastic collisions on structure formation has been estimated previously by Monte Carlo N-body simulations and by a conducting fluid model, with apparently diverging results. To improve this situation, we make direct comparisons between new Monte Carlo N-body simulations and solutions of the conducting fluid model, for isolated SIDM haloes of fixed mass. This allows us to separate cleanly the effects of gravothermal relaxation from those of continuous mass accretion in an expanding background universe. When these two methods were previously applied to halo formation with cosmological boundary conditions, they disagreed by an order of magnitude about the size of the scattering cross-section required to solve the so-called 'cusp-core problem'. We show here, however, that the methods agree with each other within 20 per cent for isolated haloes. This suggests that the two methods are consistent and that their disagreement for cosmological haloes is not caused by a breakdown of their validity. The isolated haloes studied here undergo gravothermal collapse. We compare the solutions calculated by these two methods for gravothermal collapse starting from several initial conditions, including the self-similar solution by Balberg, Shapiro & Inagaki, and the Plummer, Navarro-Frenk-White and Hernquist profiles. We compare for the case in which the collisional mean free path is comparable to, or greater than, the size of the halo core. This allows us to calibrate the heat conduction which accounts for the effect of elastic hard-sphere scattering in the fluid model. The amount of tuning of the thermal conductivity parameters required to bring the two methods into such close agreement for isolated haloes, however, is too small to explain the discrepancy found previously in the cosmological context. We will discuss the origin of that discrepancy in a separate paper.