19,373 research outputs found
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
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