Ionizing radiation in smoothed particle hydrodynamics

A new method for the inclusion of ionizing radiation from uniform radiation fields into 3D smoothed particle hydrodynamics (SPHI) simulations is presented. We calculate the optical depth for the Lyman continuum radiation from the source towards the SPHI particles by ray-tracing integration. The time-dependent ionization rate equation is then solved locally for the particles within the ionizing radiation field. Using test calculations, we explore the numerical behaviour of the code with respect to the implementation of the time-dependent ionization rate equation. We also test the coupling of the heating caused by the ionization to the hydrodynamical part of the SPHI code.     

The Jeans instability in smoothed particle hydrodynamics

We derive analytically the Jeans criterion for a gas simulated using an SPH code in which the number of neighbours N _neighb is held constant (approximately) and the gravity-softening length, ε, equals the smoothing length, h (approximately). We show that the Jeans criterion is reproduced accurately for resolved structures, i.e. those represented by >  N _neighb particles. Unresolved structures are stabilized, as long as (i) the smoothing kernel W ( u ) is sufficiently centrally peaked, and (ii) the Jeans mass is resolved. Provided that these conditions are satisfied, then, in simulations of the formation of stars and galaxies, any fragmentation that occurs should be both physical and resolved. In particular there should be no creation of sub-Jeans condensations owing to numerical instability.     

Relaxation of protostellar accretion shocks using the smoothed particle hydrodynamics

It is believed that protostellar accretion disks are formed from nearly ballistic infall of molecular matter in rotating core collapse. Collisions of this infalling matter leads to formation of strong supersonic shocks, which if they cool rapidly, result in accumulation of that material in a thin structure in the equatorial plane. Here, we investigate the relaxation time of the protostellar accretion post‐shock gas using the smoothed particle hydrodynamics (SPH). For this purpose, a one‐dimensional head‐on collision of two molecular sheets is considered, and the time evolution of the temperature and density of the post‐shock region simulated. The results show that in strong supersonic shocks, the temperature of the post‐shock gas quickly increases proportional to square of the Mach number, and then gradually decreases according to the cooling processes. Using a suitable cooling function shows that in appropriate time‐scale, the center of the collision, which is at the equatorial plane of the core, is converted to a thin dense molecular disk, together with atomic and ionized gases around it. This structure for accretion disks may justify the suitable conditions for grain growth and formation of proto‐planetary entities (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Star formation and chemical evolution in smoothed particle hydrodynamics simulations: a statistical approach

In smoothed particle hydrodynamics (SPH) codes with a large number of particles, star formation as well as gas and metal restitution from dying stars can be treated statistically. This approach allows one to include detailed chemical evolution and gas re-ejection with minor computational effort. Here we report on a new statistical algorithm for star formation and chemical evolution, especially conceived for SPH simulations with large numbers of particles, and for parallel SPH codes.
For the sake of illustration, we also present two astrophysical simulations obtained with this algorithm, implemented into the Tree-SPH code by Lia & Carraro .
In the first simulation, we follow the formation of an individual disc-like galaxy, predict the final structure and metallicity evolution, and test resolution effects. In the second simulation we simulate the formation and evolution of a cluster of galaxies, to demonstrate the capabilities of the algorithm in investigating the chemo-dynamical evolution of galaxies and of the intergalactic medium in a cosmological context.     

Three-dimensional smoothed particle hydrodynamics simulations of radiation-driven warped accretion discs

We present three-dimensional smoothed particle hydrodynamics calculations of warped accretion discs in X-ray binary systems. Geometrically thin, optically thick accretion discs are illuminated by a central radiation source. This illumination exerts a non-axisymmetric radiation pressure on the surface of the disc, resulting in a torque that acts on the disc to induce a twist or warp. Initially planar discs are unstable to warping driven by the radiation torque and, in general, the warps also precess in a retrograde direction relative to the orbital flow. We simulate a number of X-ray binary systems which have different mass ratios, using a number of different luminosities for each. Radiation-driven warping occurs for all systems simulated. For mass ratios   q ∼ 0.1  a moderate warp occurs in the inner disc while the outer disc remains in the orbital plane (cf. X 1916−053). For less extreme mass ratios, the entire disc tilts out of the orbital plane (cf. Her X–1). For discs that are tilted out of the orbital plane in which the outer edge material of the disc is precessing in a prograde direction, we obtain both positive and negative superhumps simultaneously in the dissipation light curve (cf. V603 Aql).     

Mass transfer in eccentric binaries: the new oil-on-water smoothed particle hydrodynamics technique

To measure the onset of mass transfer in eccentric binaries, we have developed a two-phase smoothed particle hydrodynamics (SPH) technique. Mass transfer is important in the evolution of close binaries, and a key issue is to determine the separation at which mass transfer begins. The circular case is well understood and can be treated through the use of the Roche formalism. To treat the eccentric case, we use a newly developed two-phase system. The body of the donor star is made up from high-mass water particles, whilst the atmosphere is modelled with low-mass oil particles. Both sets of particles take part fully in SPH interactions. To test the technique, we model circular mass-transfer binaries containing a  0.6 M_⊙  donor star and a  1 M_⊙  white dwarf; such binaries are thought to form cataclysmic variable (CV) systems. We find that we can reproduce a reasonable CV mass-transfer rate, and that our extended atmosphere gives a separation that is too large by approximately 16 per cent, although its pressure scale height is considerably exaggerated. We use the technique to measure the semimajor axis required for the onset of mass transfer in binaries with a mass ratio of   q = 0.6  and a range of eccentricities. Comparing to the value obtained by considering the instantaneous Roche lobe at pericentre, we find that the radius of the star required for mass transfer to begin decreases systematically with increasing eccentricity.     

Equations of general relativistic radiation hydrodynamics from a tensor formalism

Radiation interacts with matter via exchange of energy and momentum. When matter is moving with a relativistic velocity or when the background space–time is strongly curved, rigorous relativistic treatment of hydrodynamics and radiative transfer is required. Here, we derive fully general relativistic radiation hydrodynamic equations from a covariant tensor formalism. The equations can be applied to any three-dimensional problems and are rather straightforward to understand compared to the comoving frame-based equations. The current approach is applicable to any space–time or coordinates, but in this work we specifically choose the Schwarzschild space–time to show explicitly how the hydrodynamic and the radiation moment equations are derived. Some important aspects of relativistic radiation hydrodynamics and the difficulty with the radiation moment formalism are discussed as well.     

A new exact method for line radiative transfer

We present a new method, the coupled escape probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations , and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as they are in the 'effectively thin' regime. In a comparative study of a number of standard problems, the CEP method outperformed the leading line transfer methods by substantial margins.
The algebraic equations employed by our new method are already incorporated in numerous codes based on the escape probability approximation. All that is required for an exact solution with these existing codes is to augment the expression for the escape probability with simple zone-coupling terms. As an application, we find that standard escape probability calculations generally produce the correct cooling emission by the C  ii 158-μm line but not by the ³P lines of O  i .