Low-speed impacts between rubble piles modeled as collections of polyhedra

We present results of modeling rubble piles as collections of polyhedra. The use of polyhedra allows more realistic (irregular) shapes and interactions (e.g. collisions), particularly for objects of different sizes. Rotational degrees of freedom are included in the modeling, which may be important components of the motion. We solved the equations of rigid-body dynamics, including frictional/inelastic collisions, for collections of up to several hundred elements. As a demonstration of the methods and to compare with previous work by other researchers, we simulated low-speed collisions between km-scale bodies with the same general parameters as those simulated by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151]. High-speed collisions appropriate to present-day asteroid encounters require additional treatment of shock effects and fragmentation and are the subject of future work; here we study regimes appropriate to planetesimal accretion and re-accretion in the aftermath of catastrophic events. Collisions between equal-mass objects at low speeds () were simulated for both head-on and off-center collisions between rubble piles made of a power-law mass spectrum of sub-elements. Very low-speed head-on collisions produce single objects from the coalescence of the impactors. For slightly higher speeds, extensive disruption occurs, but re-accretion produces a single object with most of the total mass. For increasingly higher speeds, the re-accreted object has smaller mass, finally resulting in complete catastrophic disruption with all sub-elements on escape trajectories and only small amounts of mass in re-accreted bodies. Off-center collisions at moderately low speeds produce two re-accreted objects of approximately equal mass, separating at greater than escape speed. At high speed, complete disruption occurs as with the high-speed head-on collisions. Head-on collisions at low to moderate speeds result in objects of mostly oblate shape, while higher speed collisions produce mostly prolate objects, as do off-center collisions at moderate and high speeds. Collisions carried out with the same dissipative coefficients (coefficient of restitution ?n=0.8, zero friction) as used by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151] result in a value for specific energy for disruption , somewhat lower than the value of 2 J/kg found by them, while collisions with a lower coefficient of restitution and friction [?n=0.5, ?t=0, μ=0.5, similar to those used by Michel, et al. [Michel, P., Benz, W., Richardson, D.C., 2004. Planet. Space Sci. 52, 1109-1117] for SPH + N-body calculations] yield .     

Energy-dependent variability from accretion flows

We develop a formalism to calculate energy-dependent fractional variability (rms) in accretion flows. We consider rms spectra resulting from radial dependences of the level of local variability (as expected from the propagation of disturbances in accretion flows) assuming the constant shape of the spectrum emitted at a given radius. We consider the cases when the variability of the flow is either coherent or incoherent between different radial zones. As an example of local emission, we consider blackbody, Wien and thermal Comptonization spectra. In addition to numerical results, we present a number of analytical formulae for the resulting rms. We also find an analytical formula for the disc Wien spectrum, which we find to be a very good approximation to the disc blackbody. We compare our results to the rms spectrum observed in an ultrasoft state of GRS 1915+105.     

Particle accretion and dissipation simulator: Collisional aggregation of icy particles

As a part of a project to study the cometary particle environment, a self-consistent ballistic rigid body particle colliding simulator, capable of producing fractal aggregates of icy particles modelled by hard or soft (metaball) spheres has been developed, to be used for creating test particles in future statistical studies of the cometary coma-particle interaction. Instead of a predefined sticking probability, actual surface interactions are modelled and a method for calculating internal stresses and fragmentation of an aggregate during the accretion phase is described. Simulations suggest that taking fragmentation into account has two major consequences, increase in the fractal dimension of resulting particles and a noticeable change in the mass spectrum of an ensemble.     

Non-axisymmetric instabilities in shocked adiabatic accretion flows

We investigate the linear stability of a shocked accretion flow on to a black hole in the adiabatic limit. Our linear analyses and numerical calculations show that, despite the post-shock deceleration, the shock is generally unstable to non-axisymmetric perturbations. The simulation results of Molteni, Tóth & Kuznetsov can be well explained by our linear eigenmodes. The mechanism of this instability is confirmed to be based on the cycle of acoustic waves between the corotation radius and the shock. We obtain an analytical formula to calculate the oscillation period from the physical parameters of the flow. We argue that the quasi-periodic oscillation should be a common phenomenon in accretion flows with angular momentum.     

Laser Interferometer Space Antenna double black holes: dynamics in gaseous nuclear discs

We study the inspiral of double black holes, with masses in the Laser Interferometer Space Antenna ( LISA ) window of detectability, orbiting inside a massive circumnuclear, rotationally supported gaseous disc. Using high-resolution smoothed particle hydrodynamics simulations, we follow the black hole dynamics in the early phase when gas-dynamical friction acts on the black holes individually, and continue our simulation until they form a close binary. We find that in the early sinking the black holes lose memory of their initial orbital eccentricity if they corotate with the gaseous disc. As a consequence, the massive black holes bind forming a binary with a low eccentricity, consistent with zero within our numerical resolution limit. The cause of circularization resides in the rotation present in the gaseous background where dynamical friction operates. Circularization may hinder gravitational waves from taking over and leading the binary to coalescence. In the case of counter-rotating orbits, the initial eccentricity (if present) does not decrease, and the black holes may bind forming an eccentric binary. When dynamical friction has subsided, for equal mass black holes and regardless their initial eccentricity, angular momentum loss, driven by the gravitational torque exerted on the binary by surrounding gas, is nevertheless observable down to the smallest scale probed (≃1 pc). In the case of unequal masses, dynamical friction remains efficient down to our resolution limit, and there is no sign of formation of any ellipsoidal gas distribution that may further harden the binary. During inspiral, gravitational capture of gas by the black holes occurs mainly along circular orbits; eccentric orbits imply high relative velocities and weak gravitational focusing. Thus, the active galactic nucleus activity may be excited during the black hole pairing process and double active nuclei may form when circularization is completed, on distance scales of tens of parsecs.     

An ultraluminous X-ray microquasar in NGC 5408?

We studied the radio source associated with the ultraluminous X-ray source in NGC 5408  ( L _X≈ 10⁴⁰ erg s⁻¹)  . The radio spectrum is steep (index  ≈−1  ), consistent with optically thin synchrotron emission, not with flat-spectrum core emission. Its flux density (≈0.28 mJy at 4.8 GHz, at a distance of 4.8 Mpc) was the same in the March 2000 and December 2004 observations, suggesting steady emission rather than a transient outburst. However, it is orders of magnitude higher than expected from steady jets in stellar-mass microquasar. Based on its radio flux and spectral index, we suggest that the radio source is either an unusually bright supernova remnant, or, more likely, a radio lobe powered by a jet from the black hole (BH). Moreover, there is speculative evidence that the source is marginally resolved with a radius ∼30 pc. A faint H  ii region of similar size appears to coincide with the radio and X-ray sources, but its ionization mechanism remains unclear. Using a self-similar solution for the expansion of a jet-powered electron–positron plasma bubble, in the minimum-energy approximation, we show that the observed flux and (speculative) size are consistent with an average jet power  ≈ 7 × 10³⁸ erg s⁻¹∼ 0.1 L _X∼ 0.1 L _Edd  , an age ≈10⁵ yr, a current velocity of expansion ≈80 km s⁻¹. We briefly discuss the importance of this source as a key to understand the balance between luminosity and jet power in accreting BHs.     

Radiation pressure supported stars in Einstein gravity: eternally collapsing objects

Even when we consider Newtonian stars, that is, stars with surface gravitational redshift   z ≪ 1  , it is well known that, theoretically, it is possible to have stars supported against self-gravity almost entirely by radiation pressure. However, such Newtonian stars must necessarily be supermassive. We point out that this requirement for excessively large M in the Newtonian case is a consequence of the occurrence of low   z ≪ 1  . However, if we remove such restrictions, and allow for the possible occurrence of a highly general relativistic regime,   z ≫ 1  , we show that it is possible to have radiation pressure supported stars (RPSSs) at an arbitrary value of M . Since RPSSs necessarily radiate at the Eddington limit, in Einstein gravity, they are never in strict hydrodynamical equilibrium. Further, it is believed that sufficiently massive or dense objects undergo continued gravitational collapse to the black hole (BH) stage characterized by   z =∞  . Thus, late stages of BH formation, by definition, would have   z ≫ 1  , and hence would be examples of quasi-stable general relativistic RPSSs. It is shown that the observed duration of such Eddington limited radiation pressure dominated states is   t ≈ 5 × 10⁸ (1 + z ) yr  . Thus,   t →∞  as BH formation  ( z →∞)  takes place. Consequently, such radiation pressure dominated extreme general relativistic stars become eternally collapsing objects (ECOs) and the BH state is preceded by such an ECO phase. This result is also supported by our previous finding that trapped surfaces are not formed in gravitational collapse and the value of the integration constant in the vacuum Schwarzschild solution is zero. Hence the supposed observed BHs are actually ECOs.