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Precise tcool/tdyn fragmentation threshold in collapsar disks

Determine the precise critical order-unity threshold of the ratio of radiative cooling time to dynamical/orbital time (tcool/tdyn) required for gravitational fragmentation in neutrino-cooled, self-gravitating collapsar accretion disks, accounting for the disk equation of state and the electron/positron capture cooling function, by means of hydrodynamical simulations.

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Background

The viability of fragmentation in gravitationally unstable collapsar disks depends on the cooling condition tcool/tdyn being below a critical order-unity threshold, as suggested by Gammie (2001). In the context of neutrino-cooled, electron-degenerate disks with pair-capture cooling, the authors emphasize that the exact value of this threshold is not established and depends on the detailed microphysics.

Clarifying this threshold is essential for assessing whether proto-clumps in collapsar disks can cool and collapse fast enough to form self-bound objects that may continue to contract to neutron stars.

References

The precise order-unity threshold on the right side of (10) is uncertain in the present context, as it depends on the equation of state and cooling function of the disk and must be ascertained with hydrodynamical simulations (e.g., Rice et al. 2005; Chen et al. 2023).

— Fragmentation in Gravitationally-Unstable Collapsar Disks and Sub-Solar Neutron Star Mergers (2407.07955 - Metzger et al., 10 Jul 2024) in Section 2.2, following Eq. (10)