The discovery of two neutron stars with gravitational masses $approx 2~M_odot$ has placed a strong lower limit on the maximum mass of nonrotating neutron stars, and with it a strong constraint on the properties of cold matter beyond nuclear density.
Current upper mass limits are much looser. Here we note that, if most short gamma-ray bursts are produced by the coalescence of two neutron stars, and if the merger remnant collapses quickly, then the upper mass limit is constrained tightly. If the rotation of the merger remnant is limited only by mass-shedding (which seems probable based on numerical studies), then the maximum gravitational mass of a nonrotating neutron star is $approx 2-2.2~M_odot$ if the masses of neutron stars that coalesce to produce gamma-ray bursts are in the range seen in Galactic double neutron star systems. These limits would be increased by $sim 4$% in the probably unrealistic case that the remnants rotate at $sim 30$% below mass-shedding, and by $sim 15$% in the extreme case that the remnants do not rotate at all. Future coincident detection of short gamma-ray bursts with gravitational waves will strengthen these arguments because they will produce tight bounds on the masses of the components for individual events. If these limits are accurate then a reasonable fraction of double neutron star mergers might not produce gamma-ray bursts. In that case, or in the case that many short bursts are produced instead by the mergers of neutron stars with black holes, the implied rate of gravitational wave detections will be increased.
Among the many intriguing aspects of optically discovered tidal disruption events (TDEs) is that their temperatures are lower than expected and that the temperature does not evolve as rapidly with decreasing fallback rate as would be expected in stan
dard disk theory. We show that this can be explained qualitatively using an idea proposed by Laor & Davis in the context of normal active galactic nuclei: that larger accretion rates imply stronger winds and thus that the accretion rate through the inner disk only depends weakly on the inflow rate at the outer edge of the disk. We also show that reasonable quantitative agreement with data requires that, as has been suggested in recent papers, the circularization radius of the tidal stream is approximately equal to the semimajor axis of the most bound orbit of the debris rather than twice the pericenter distance as would be expected without rapid angular momentum redistribution. If this explanation is correct, it suggests that the evolution of TDEs may test both non-standard disk theory and the details of the interactions of the tidal stream.
Electromagnetic observations over the last 15 years have yielded a growing appreciation for the importance of supermassive black holes (SMBH) to the evolution of galaxies, and for the intricacies of dynamical interactions in our own Galactic center.
Here we show that future low-frequency gravitational wave observations, alone or in combination with electromagnetic data, will open up unique windows to these processes. In particular, gravitational wave detections in the 10^{-5}-10^{-1} Hz range will yield SMBH masses and spins to unprecedented precision and will provide clues to the properties of the otherwise undetectable stellar remnants expected to populate the centers of galaxies. Such observations are therefore keys to understanding the interplay between SMBHs and their environments.
