Consistent SPH Simulations of Protostellar Collapse and Fragmentation

Abstract

We study the consistency and convergence of smoothed particle hydrodynamics (SPH) as a function of the interpolation parameters, namely the number of particles N, the number of neighbors n, and the smoothing length h, using simulations of the collapse and fragmentation of protostellar rotating cores. The calculations are made using a modified version of the GADGET-2 code that employs an improved scheme for the artificial viscosity and power-law dependences of n and h on N, as was recently proposed by Zhu et al., which comply with the combined limit  ¥ N ,  h 0, and  ¥ n with  n N 0 for full SPH consistency as the domain resolution is increased. We apply this realization to the "standard isothermal test case" in the variant calculated by Burkert & Bodenheimer and the Gaussian cloud model of Boss to investigate the response of the method to adaptive smoothing lengths in the presence of large density and pressure gradients. The degree of consistency is measured by tracking how well the estimates of the consistency integral relations reproduce their continuous counterparts. In particular, C 0 and C 1 particle consistency is demonstrated, meaning that the calculations are close to second-order accuracy. As long as n is increased with N, mass resolution also improves as the minimum resolvable mass~-M n min 1 . This aspect allows proper calculation of small-scale structures in the flow associated with the formation and instability of protostellar disks around the growing fragments, which are seen to develop a spiral structure and fragment into close binary/multiple systems as supported by recent observations.

Strongly Misaligned Triple System in SR 24 Revealed by ALMA

“…The location of the molecular bridge between the two disks ( Figure 6) is slightly east of the HST bifurcated bridge, but both seem to join the two disks of the system. The nature of this bridge is unknown, although it is well known from numerical simulations that multiple systems have bridges of material like the one observed here (e.g., Gabbasov et al 2017). We have also noticed that the optical bridge between the disks of the system has a curvature and joins the west side of SR24S with the east side of SR24N.…”

Relativistic dust accretion onto a scale-dependent polytropic black hole

“…In order to describe the accretion process we must be able to obtain the radial velocity profile u(r) and the density ρ from Eqs. (7) and (9). Of course, depending on the nature of the matter content, the pressure can be obtained as a function of ρ from the equation of the state of the accreted matter.…”

The Mathematics of Smoothed Particle Hydrodynamics (SPH) Consistency

“…For example, in contrast to most conventional kernels, Wendland functions do not allow particle motions on a sub-resolution scale (i.e., within the kernel support) and therefore they maintain quasi-ordered particle distributions even in highly dynamical test problems [56]. A Wendland function that has been adopted in many recent tests and simulations [13,30] is the Wendland C 4 kernel function given by W q, h 495 32πh 3 1 − q…”

“…A formal derivation of the error carried by the SPH interpolation by Sigalotti et al [29] has shown that the inconsistency is removed by increasing the number of neighbors. This was thereafter tested in the astrophysical context with reasonably good results [30,31]. In this approach no corrections to the SPH discretization are required and full particle consistency is restored in the asymptotic limit N → ∞, h → 0, and n neigh → ∞ with n neigh /N → 0, where N is the total number of particles, h is the smoothing length, and n neigh is the number of neighbors within the kernel support.…”