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

By D. Stamatellos, A. Whitworth, T. Bisbas, S. University. 2007

143 citations recorded by the source corpus.

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) H2 dissociation and H$^{\rm o}$ 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 $1\,{M}_\odot$ cloud of initially uniform density and temperature. At first, the collapse proceeds almost isothermally ( $T\propto\rho^{0.08}$; cf. Larson 2005, MNRAS, 359, 211). The cloud starts heating fast when the optical depth to the cloud centre reaches unity ( $\rho_{_{\rm C}}\sim 7\times10^{-13}~{\rm g\ cm^{-3}}$). The first core forms at $\rho_{_{\rm C}}\sim 4\times10^{-9}~{\rm g\ cm^{-3}}$ and steadily increases in mass. When the temperature at the centre reaches $T_{_{\rm C}}\sim 2000\,{\rm K}$, 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 $1.2\,{M}_\odot$ cloud, which initially has uniform density and temperature, (ii) the collapse of a $1.2\,{M}_\odot$ 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 $0< \tau\la 10^{11}$.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/957a6ed9526970904d1de4fa55f33e6058ddfe7c

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Citations in the corpus

The stellar and sub-stellar IMF of simple and composite populations (2011, background): “…formation is via the fragmentation of massive circum-stellar disks (FMCSDs) beyond about 100 AU and subsequent dynamical separation of the resulting weekly bound BD companion (Goodwin & Whitworth 2007; Stamatellos et al. 2007a; Stamatellos & Whitworth 2009; Thies et al. 2010; Basu & Vorobyov 2012).”
The properties of brown dwarfs and low-mass hydrogen-burning stars formed by disc fragmentation (2008, methodology): “…the radiation transfer equation (which is unfeasible in hydrodynamic simulations with the current computing resources), but it is an appoximate method that performs well, in the optically-thin, intermediate and optically-thick regimes, and has been extensively tested (Stamatellos et al. 2007a).”
THE EFFECTS OF RADIATIVE TRANSFER ON LOW-MASS STAR FORMATION (2009, methodology): “…physics and computational expense, a few hybrid methods include heating by solving explicit diffusion approximations, estimating the instantaneous radiative cooling, or extrapolating from previously tabulated temperatures (Stamatellos et al. 2007; Banerjee & Pudritz 2007; Bonnell & Rice 2008).”
High- and Low-Velocity Magnetized Outflows in the Star Formation Process in a Gravitationally Collapsing Cloud (2008, background): “…bymany authors, including the detailed radiative process under spherical symmetry (e.g., Larson 1969; Tohline 1982;Winkler & Newman 1980a, 1980b; Masunaga et al. 1998; Masunaga & Inutsuka 2000), and in recent three-dimensional calculations (e.g., Whitehouse & Bate 2006; Stamatellos et al. 2007).”
A census of dense cores in the Aquila cloud complex: SPIRE/PACS observations from the Herschel Gould Belt survey (2015, background): “In reality, starless dense cores, which are externally heated objects, are known from both radiative transfer calculations (e.g., Evans et al. 2001; Stamatellos et al. 2007) and, e.g., Herschel observations (e.g., Nielbock et al. 2012; Roy et al. 2014) to have a stratified temperature structure…”