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

Aims:We introduce and test a new and highly efficient method for treating the thermal and radiative effects influencing the energy equation in SPH simulations of star formation. Methods: The method uses the density, temperature and gravitational potential of each particle to estimate a mean optical depth, which then regulates the particle's heating and cooling. The method captures - at minimal computational cost - the effects of (i) the rotational and vibrational degrees of freedom of H2; (ii) H{_2} dissociation and Ho ionisation; (iii) opacity changes due to ice mantle melting, sublimation of dust, molecular lines, H^-, bound-free and free-free processes and electron scattering; (iv) external irradiation; and (v) thermal inertia. Results: We use the new method to simulate the collapse of a 1 {M}_sun cloud of initially uniform density and temperature. At first, the collapse proceeds almost isothermally (T∝oρ0.08; cf. Larson 2005, MNRAS, 359, 211). The cloud starts heating fast when the optical depth to the cloud centre reaches unity (ρ_C˜ 7×10-13 {g cm-3}). The first core forms at ρ_C˜ 4×10-9 {g cm-3} and steadily increases in mass. When the temperature at the centre reaches T_C˜ 2000 K, molecular hydrogen starts to dissociate and the second collapse begins, leading to the formation of the second (protostellar) core. The results mimic closely the detailed calculations of Masunaga & Inutsuka (2000, ApJ, 531, 350). We also simulate (i) the collapse of a 1.2 {M}_sun cloud, which initially has uniform density and temperature, (ii) the collapse of a 1.2 {M}_sun rotating cloud, with an m=2 density perturbation and uniform initial temperature, and (iii) the smoothing of temperature fluctuations in a static, uniform density sphere. In all these tests the new algorithm reproduces the results of previous authors and/or known analytic solutions. The computational cost is comparable to a standard SPH simulation with a simple barotropic equation of state. The method is easy to implement, can be applied to both particle- and grid-based codes, and handles optical depths 0< τ⪉ 1011