SPH History and Basics

The basic Smoothed Particle Hydrodynamics (SPH) method was created by Lucy (1977) and Gingold & Monaghan (1977) in order to study fission in rotating stars. It has since been used to study, among other astrophysical topics, large scale structure in the universe, galaxy formation, star formation, supernovae, solar system formation, tidal disruption of stars by massive black holes, and stellar collisions; see Rasio & Shapiro (1992), Monaghan (1992), and Rasio & Lombardi (1999) for a more complete list of references. Our particular code has been used primarily in the study of stellar collisions and mergers, including merging compact object binaries (Rasio & Shapiro, 1992; Rasio & Shapiro, 1994; Rasio & Shapiro, 1995), collisions involving main sequence stars (Rasio & Shapiro, 1991; Lai et al., 1993a; Sills et al., 2001; Sills et al., 1997), blue-straggler formation (Lombardi et al., 2002; Lombardi et al., 1996; Lombardi et al., 1995), and most recently post-Newtonian (PN) and relativistic studies of binary neutron star (NS) systems (Faber & Rasio, 2000; Faber et al., 2001; Faber & Rasio, 2002). A post-Newtonian code is in preparation for public release, and will form the core of version 2.0 of this code.

Because of its Lagrangian nature, SPH presents some clear advantages over more traditional grid-based methods for calculations of stellar interactions. Most importantly, fluid advection, even for stars with a sharply defined surface such as NS, is accomplished without difficulty in SPH, since the particles simply follow their trajectories in the flow. In contrast, to track accurately the orbital motion of two stars across a large 3D grid can be quite tricky, and the stellar surfaces then require a special treatment (to avoid ``bleeding''). SPH is also very computationally efficient, since it concentrates the numerical elements (particles) where the fluid is at all times, not wasting any resources on emty regions of space. For this reason, with given computational resources, SPH provides higher averaged spatial resolution than grid-based calculations, although Godunov-type schemes such as PPM typically provide better resolution of shock fronts (this is certainly not a decisive advantage for binary coalescence calculations, where no strong shocks ever develop). SPH also makes it easy to track the hydrodynamic ejection of matter to large distances from the central dense regions. Sophisticated nested-grid algorithms are necessary to accomplish the same with grid-based methods.