Influence of self-gravity on the runaway instability of black hole-torus systems

Results from the first fully general relativistic numerical simulations in axisymmetry of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium are presented, aiming to assess the influence of the torus self-gravity on the onset of the runaway instability. We consider several models with varying torus-to-black hole mass ratio and angular momentum distribution orbiting in equilibrium around a non-rotating black hole. The tori are perturbed to induce the mass transfer towards the black hole. Our numerical simulations show that all models exhibit a persistent phase of axisymmetric oscillations around their equilibria for several dynamical timescales without the appearance of the runaway instability, indicating that the self-gravity of the torus does not play a critical role favoring the onset of the instability, at least during the first few dynamical timescales.Comment: To appear on Phys.Rev.Let

Assessment of Distributed Energy Adoption in Commercial Buildings:Part 1: An Analysis of Policy, Building Loads, Tariff Design, andTechnology Development

Rapidly growing electricity demand brings into question theability of traditional grids to expand correspondingly while providingreliable service. An alternative path is the wider application ofdistributed energy resource (DER) that apply combined heat and power(CHP). It can potentially shave peak loads and satiate its growing thirstfor electricity demand, improve overall energy efficiency, and lowercarbon and other pollutant emissions. This research investigates a methodof choosing economically optimal DER, expanding on prior studies at theBerkeley Lab using the DER design optimization program, the DistributedEnergy Resources Customer Adoption Model (DER-CAM). DER-CAM finds theoptimal combination of installed equipment from available DERtechnologies, given prevailing utility tariffs, site electrical andthermal loads, and a menu of available equipment. It provides a globaloptimization, albeit idealized, that shows how the site energy loads canbe served at minimum cost by selection and operation of on-sitegeneration, heat recovery, and cooling. Utility electricity and gastariffs are key factors determining the economic benefit of a CHPinstallation, however often be neglected. This paper describespreliminary analysis on CHP investment climate in the U.S. and Japan. DERtechnologies, energy prices, and incentive measures has beeninvestigated

Collapse of a Rotating Supermassive Star to a Supermassive Black Hole: Analytic Determination of the Black Hole Mass and Spin

The collapse of a uniformaly rotating, supermassive star (SMS) to a supermassive black hole (SMBH) has been followed recently by means of hydrodynamic simulations in full general relativity. The initial SMS of arbitrary mass M in these simulations rotates uniformly at the mass--shedding limit and is marginally unstable to radial collapse. The final black hole has mass M_h/M = 0.9 and and spin J_h/M_h^2 = 0.75, approximately. The remaining mass goes into a disk of mass M_disk/M = 0.1, also approximately. Here we show that these black hole and disk parameters can be calculated analytically from the initial stellar density and angular momentum distribution. The analytic calculation thereby corroborates and provides a simple physical explanation for the computational discovery that SMS collapse inevitably terminates in the simultaneous formation of a SMBH and a rather substantial ambient disk. This disk arises even though the total spin of the progenitor star, J/M^2 = 0.97, is safely below the Kerr limit. The calculation performed here applies to any marginally unstable n = 3 polytrope uniformly rotating at the break--up speed, independent of stellar mass or the source of internal pressure. It illustrates how the black hole and disk parameters can be determined for the collapse of other types of stars with different initial density and rotation profiles.Comment: 5 pages, 1 figure, to appear in The Astrophysical Journal, October 1, 200