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Abstract When dark matter has a large cross section for self scattering, halos can undergo a process known as gravothermal core collapse, where the inner core rapidly increases in density and temperature.To date, several methods have been used to implement Self-Interacting Dark Matter (SIDM) in N-body codes, but there has been no systematic study of these different methods or their accuracy in the core-collapse phase. In this paper, we compare three different numerical implementations of SIDM, including the standard methods from the GIZMO and Arepo codes, by simulating idealized dwarf halos undergoing significant dark matter self interactions (σ/m= 50 cm²/g).When simulating these halos, we also vary the massresolution, time-stepping criteria, and gravitational force-softening scheme. The various SIDM methods lead to distinct differences in a halo's evolution during the core-collapse phase, as each results in spurious scattering rate differences and energy gains/losses.The use of adaptive force softening for gravity can lead to numerical heating that artificially accelerates core collapse, while an insufficiently small simulation time step can cause core evolution to stall or completely reverse. Additionally, particle numbers must be large enough to ensure that the simulated halos are not sensitive to noise in the initial conditions. Even for the highest-resolution simulations tested in this study (10⁶particles per halo), we find that variations of order 10% in collapse time are still present.The results of this work underscore the sensitivity of SIDM modeling on the choice of numerical implementation and motivate a careful study of how these results generalize to halos in a cosmological context. 

Abstract Rocky planets orbiting M-dwarf stars are among the most promising and abundant astronomical targets for detecting habitable climates. Planets in the M-dwarf habitable zone are likely synchronously rotating, such that we expect significant day–night temperature differences and potentially limited fractional habitability. Previous studies have focused on scenarios where fractional habitability is confined to the substellar or “eye” region, but in this paper we explore the possibility of planets with terminator habitability, defined by the existence of a habitable band at the transition between a scorching dayside and a glacial nightside. Using a global climate model, we show that for water-limited planets it is possible to have scorching temperatures in the “eye” and freezing temperatures on the nightside, while maintaining a temperate climate in the terminator region, due to reduced atmospheric energy transport. On water-rich planets, however, increasing the stellar flux leads to increased atmospheric energy transport and a reduction in day–night temperature differences, such that the terminator does not remain habitable once the dayside temperatures approach runaway or moist greenhouse limits. We also show that while water-abundant simulations may result in larger fractional habitability, they are vulnerable to water loss through cold trapping on the nightside surface or atmospheric water vapor escape, suggesting that even if planets were formed with abundant water, their climates could become water-limited and subject to terminator habitability.