Disentangling effective cooling-time versus cooling-physics dependencies

Determine, by a systematic comparison of constant-β cooling and full radiative-cooling simulations of gravitational instability in protostellar disks, which quantitative outcomes depend solely on the effective cooling time β and which depend on the detailed cooling physics (e.g., optically thin versus optically thick radiative transport).

Background

Many previous simulations of gravitational instability in disks adopt a prescribed constant cooling time (constant β) for simplicity, while real disks cool radiatively with behavior differing in optically thin and optically thick regimes. Without a controlled, side-by-side comparison, it is difficult to know whether reported findings are governed by the overall cooling rate or by the specific cooling mechanism.

This paper highlights the need for a systematic comparison to clarify which results stem from the effective β alone and which intrinsically require the physics of radiative transport.

References

The existing works, however, do not include a systematic comparison between constant-β simulations and radiative simulations, so it is often unclear which results depend only on the overall cooling rate (effective β) and which results depend on the cooling type.

— Global Simulations of Gravitational Instability in Protostellar Disks with Full Radiation Transport. I. Stochastic Fragmentation with Optical-depth-dependent Rate and Universal Fragment Mass  (2410.12042 - Xu et al., 2024) in Section 1.2

Nevertheless, it remains uncertain whether the shock strengths and thermodynamic structures produced in β-cooling simulations quantitatively reproduce those obtained in radiation hydrodynamic models.

— Cooling-regulated gas accretion onto gap-opening planets  (2608.28019 - Kuwahara et al., 28 Aug 2026) in Section 4.4, β cooling approximation

Several fundamental questions remain open. From a thermodynamic perspective, the self-regulation mechanism in infall-driven discs has so far been characterised only in the isothermal limit (); understanding how a more realistic treatment of disc thermodynamics modifies the self-regulated state is a critical next step.

— Gravitational instability in planet-forming discs  (2609.05080 - Longarini et al., 4 Sep 2026) in Section 5.1.1, Theoretical perspective, p. 20