Testing the accuracy of radiative cooling approximations in SPH simulations

Abstract

Hydrodynamical simulations of star formation have stimulated a need to develop fast and robust algorithms for evaluating radiative cooling. Here we undertake a critical evaluation of what is currently a popular method for prescribing cooling in SPH simulations, i.e. the polytropic cooling due originally to Stamatellos et al. This method uses the local density and potential to estimate the column density and optical depth to each particle and then uses these quantities to evaluate an approximate expression for the net radiative cooling. We evaluate the algorithm by considering both spherical and disc-like systems with analytic density and temperature structures. In spherical systems, the total cooling rate computed by the method is within around 20 for the astrophysically relevant case of opacity dominated by ice grains and is correct to within a factor of order unity for a range of opacity laws. In disc geometry, however, the method systematically under-estimates the cooling by a large factor at all heights in the disc. For the self-gravitating disc studied, we find that the method under-estimates the total cooling rate by a factor of 200. This discrepancy may be readily traced to the method's systematic over-estimate of the disc column density and optical depth, since (being based only on the local density and potential) it does not take into account the low column density route for photon escape normal to the disc plane. These results raise an obvious caution about the method's use in disc geometry whenever an accurate cooling rate is required, although we note that there are situations where the discrepancies highlighted above may not significantly affect the global outcome of simulations. Finally, we draw attention to our introduction of an analytic self-gravitating disc structure that may be of use in the calibration of future cooling algorithms.

10 pages, 8 figures. Accepted for publication in MNRAS

References in corpus (8)

• The Importance of Radiative Feedback for the Stellar Initial Mass Function
• Fragmentation of gravitationally unstable gaseous protoplanetary disks with radiative transfer
• Radiative transfer and the energy equation in SPH simulations of star formation
• Can giant planets form by gravitational fragmentation of discs?
• Introducing a Hybrid Method of Radiative Transfer for Smoothed Particle Hydrodynamics
• The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks. IV. Simulations with Envelope Irradiation
• 3D Radiative Hydrodynamics for Disk Stability Simulations: A Proposed Testing Standard and New Results
• Flux-Limited Diffusion Approximation Models of Giant Planet Formation by Disk Instability

Cited by in corpus (10)

• Episodic accretion, protostellar radiative feedback, and their role in low-mass star formation
• Identifying and Analysing Protostellar Disc Fragments in Smoothed Particle Hydrodynamics Simulations
• Radiative cooling implementations in simulations of primordial star formation
• An N-body population synthesis framework for the formation of moons around Jupiter-like planets
• The diverse lives of massive protoplanets in self-gravitating discs
• Misaligned accretion on to supermassive black hole binaries
• An Efficient Radiative Cooling Approximation for Use in Hydrodynamic Simulations
• Efficient radiative transfer techniques in hydrodynamic simulations
• Reliable estimation of the column density in Smoothed Particle Hydrodynamic simulations
• Radiatively Cooled Binary Mass Transfer: Flow Structure, Luminosities, and L2 Outflows Across Mass Transfer Rates