Radiative transfer and the energy equation in SPH simulations of star formation

Abstract

Aims. We introduce and test a new and highly e
\nfficient method for treating the thermal and radiative e
\nffects influencing the energy equation in
\nSPH simulations of star formation.
\nMethods. The method uses the density, temperature and gravitational potential of each particle to estimate a mean optical depth, which
\nthen regulates the particle’s heating and cooling. The method captures – at minimal computational cost – the e
\nffects of (i) the rotational and
\nvibrational degrees of freedom of H
\n2; (ii) H
\n2
\ndissociation and H
\no
\nionisation; (iii) opacity changes due to ice mantle melting, sublimation of
\ndust, molecular lines, H
\n−
\n, bound-free and free-free processes and electron scattering; (iv) external irradiation; and (v) thermal inertia.
\nResults. We use the new method to simulate the collapse of a 1 M
\n⊙ cloud of initially uniform density and temperature. At first, the collapse
\nproceeds almost isothermally (
\nT
\n∝
\nρ
\n0
\n.08; cf. Larson 2005). The cloud starts heating fast when the optical depth to the cloud centre reaches
\nunity (ρ
\nC
\n∼
\n7
\n× 10
\n−13 g cm
\n−
\n3
\n). The first core forms at
\nρ
\nC
\n∼
\n4
\n× 10
\n−
\n9 g cm
\n−
\n3
\nand steadily increases in mass. When the temperature at the
\ncentre reaches
\nTC
\n∼ 2000 K, molecular hydrogen starts to dissociate and the second collapse begins, leading to the formation of the second
\n(protostellar) core. The results mimic closely the detailed calculations of Masunaga & Inutsuka (2000). We also simulate (i) the collapse
\nof a 1
\n.2 M
\n⊙ cloud, which initially has uniform density and temperature, (ii) the collapse of a 1
\n.2 M
\n⊙ rotating cloud, with an
\nm
\n= 2 density
\nperturbation and uniform initial temperature, and (iii) the smoothing of temperature fluctuations in a static, uniform density sphere. In all these
\ntests the new algorithm reproduces the results of previous authors and/or known analytic solutions. The computational cost is comparable to
\na standard SPH simulation with a simple barotropic equation of state. The method is easy to implement, can be applied to both particle- and
\ngrid-based codes, and handles optical depths 0 < τ
\n<∼ 1011
\n.