ASTR 498 Problem Set 5 Due Thursday, April 17 1. [4 points] In accretion onto nonrelativistic and weakly magnetic nonrotating stars, half of the accretion energy is released in the inspiral to just above the surface, and half is released in the boundary layer formed when the matter slows down to a stop on the surface. What about for a neutron star? Assuming that matter (a) spirals in nearly-circular orbits to the ISCO, (b) drops to the surface without releasing further energy, then (c) releases any additional energy in a boundary layer so that it comes to rest on the surface, calculate in full general relativity the fraction of the total energy released in the boundary layer for neutron star radii of R = 6M, R = 5M, and R = 4M. Assume the star is nonrotating. These fractions suggest that high-amplitude timing phenomena in the accretion-powered X-rays (such as quasiperiodic oscillations) may have their clock set in the disk, but the energy release must primarily be on the stellar surface. 2. [4 po...