We present 0.55 × 10⁶ particle simulations of the accretion of high-density dwarf galaxies by low-density giant galaxies, using models that contain both power-law central density cusps and point masses representing supermassive black holes. The cusp of the dwarf galaxy is disrupted during the merger, producing a remnant with a central density that is only slightly higher than that of the giant galaxy initially. Removing the black hole from the giant galaxy allows the dwarf galaxy to remain intact and leads to a remnant with a high central density, contrary to what is observed. Our results support the hypothesis that the persistence of low-density cores in giant galaxies is a consequence of supermassive black holes.

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 , , and with 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 . 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.

Recent observations of young stellar systems with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array are helping to cement the idea that close companion stars form via fragmentation of a gravitationally unstable disk around a protostar early in the star formation process. As the disk grows in mass, it eventually becomes gravitationally unstable and fragments, forming one or more new protostars in orbit with the first at mean separations of 100 au or even less. Here, we report direct numerical calculations down to scales as small as ∼0.1 au, using a consistent Smoothed Particle Hydrodynamics code, that show the large-scale fragmentation of a cloud core into two protostars accompanied by small-scale fragmentation of their circumstellar disks. Our results demonstrate the two dominant mechanisms of star formation, where the disk forming around a protostar (which in turn results from the large-scale fragmentation of the cloud core) undergoes eccentric (m = 1) fragmentation to produce a close binary. We generate two-dimensional emission maps and simulated ALMA 1.3 mm continuum images of the structure and fragmentation of the disks that can help explain the dynamical processes occurring within collapsing cloud cores.