Starbursts near supermassive black holes: young stars in the Galactic Center, and gravitational waves in LISA band

We propose a scenario in which massive stars form in a self-gravitating gaseous disc around a supermassive black hole. We find that once the surface density of the disc exceeds a critical value, the disc fragments into dense clumps. The clumps accrete material from the remaining disc and merge into larger clumps; the upper mass of a merged clump is a few tens to a few hundreds of solar mass. This picture fits well with the observed young stellar discs near the SgrA* black hole in the Galactic Center. In particular, we show how the masses and spatial distribution of the young stars, and the total mass in the Galactic Center discs can be explained. However, explaining the origin of the several young stars closest to the black hole (the S-stars) is more problematic: their orbits are compact, eccentric, and have random orientation. We propose that the S-stars were born in a previous starburst(s), and then migrated through their parent disc via type I or runaway migration. Their orbits were then randomized by the Rauch-Tremaine resonant relaxation. We then explore the consequences of the star-formation scenario for AGN discs, which are continuously resupplied with gas. We argue that some compact remnants generated by the starburst will get embedded in the disc. The disc-born stellar-mass black holes will interact gravitationally with the massive accretion disc and be dragged towards the central black hole. Merger of a disc-born black hole with the central black hole will produce a burst of gravitational waves. If the central black hole is accreting at a rate comparable to the Eddington limit, the gas drag from the accretion disc will not alter significantly the dynamics of the final year of merger, and the gravitational waves should be observable by LISA.Comment: 11 pages. Submitted to MNRAS in December, this version addresses referee's remark

Why charges go to the surface: a generalized Thomson problem

We study a generalization of a Thomson problem of n particles confined to a sphere and interacting by a 1/r^g potential. It is found that for g \le 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for g>1 and n>n_c(g) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes

Nonlinear r-modes in a spherical shell: issues of principle

We use a simple physical model to study the nonlinear behaviour of the r-mode instability. We assume that r-modes (Rossby waves) are excited in a thin spherical shell of rotating incompressible fluid. For this case, exact Rossby wave solutions of arbitrary amplitude are known. We find that: (a) These nonlinear Rossby waves carry ZERO physical angular momentum and positive physical energy, which is contrary to the folklore belief that the r-mode angular momentum and energy are negative. (b) Within our model, we confirm the differential drift reported by Rezzolla, Lamb and Shapiro (1999). Radiation reaction is introduced into the model by assuming that the fluid is electrically charged; r-modes are coupled to electromagnetic radiation through current (magnetic) multipole moments. We find that: (c) To linear order in the mode amplitude, r-modes are subject to the CFS instability, as expected. (d) Radiation reaction decreases the angular velocity of the shell and causes differential rotation (which is distinct from but similar in magnitude to the differential drift reported by Rezzolla et al.) prior to saturation of the r-mode growth. This is contrary to the phenomenological treatments to date, which assume that the loss of stellar angular momentum is accounted for by the r-mode growth. We demonstrate, for the first time, that r-mode radiation reaction leads to differential rotation. (e) We show that for l=2 r-mode electromagnetic radiation reaction is equivalent to gravitational radiation reaction in the lowest post-Newtonian order.Comment: 8 pages, no figures, uses MNRAS style, abstract abridged to fit into 24 line