Energy and Momentum Transfer via Coulomb Frictions in Relativistic Two Fluids

We numerically calculate the energy and momentum transfer rates due to Coulomb scattering between two fluids moving with a relative velocity. The results are fitted by simple functions. The fitting formulae are useful to simulate outflows from active galactic nuclei and compact high energy sources.Comment: 29 pages, 11 figures. accepted for publication in ApJ

Formal Specification and Testing of a Management Architecture

The importance of network and distributed systems management to supply and maintain services required by users has led to a demand for management facilities. Open network management is assisted by representing the system resources to be managed as objects, and providing standard services and protocols for interrogating and manipulating these objects. This paper examines the application of formal description techniques to the specification of managed objects by presenting a case study in the specification and testing of a management architecture. We describe a formal specification of a management architecture suitable for scheduling and distributing services across nodes in a distributed system. In addition, we show how formal specifications can be used to generate conformance tests for the management architecture

Are Particles in Advection-Dominated Accretion Flows Thermal?

We investigate the form of the momentum distribution function for protons and electrons in an advection-dominated accretion flow (ADAF). We show that for all accretion rates, Coulomb collisions are too inefficient to thermalize the protons. The proton distribution function is therefore determined by the viscous heating mechanism, which is unknown. The electrons, however, can exchange energy quite efficiently through Coulomb collisions and the emission and absorption of synchrotron photons. We find that for accretion rates greater than \sim 10^{-3} of the Eddington accretion rate, the electrons have a thermal distribution throughout the accretion flow. For lower accretion rates, the electron distribution function is determined by the electron's source of heating, which is primarily adiabatic compression. Using the principle of adiabatic invariance, we show that an adiabatically compressed collisionless gas maintains a thermal distribution until the particle energies become relativistic. We derive a new, non-thermal, distribution function which arises for relativistic energies and provide analytic formulae for the synchrotron radiation from this distribution. Finally, we discuss its implications for the emission spectra from ADAFs.Comment: 29 pages (Latex), 3 Figures. Submitted to Ap

Scaling Laws for Advection Dominated Flows: Applications to Low Luminosity Galactic Nuclei

We present analytical scaling laws for self-similar advection dominated flows. The spectra from these systems range from 10$^{8}$ - 10$^{20}$ Hz, and are determined by considering cooling of electrons through synchrotron, bremsstrahlung, and Compton processes. We show that the spectra can be quite accurately reproduced without detailed numerical calculations, and that there is a strong testable correlation between the radio and X-ray fluxes from these systems. We describe how different regions of the spectrum scale with the mass of the accreting black hole, $M$, the accretion rate of the gas, $\dot{M}$, and the equilibrium temperature of the electrons, $T_e$. We show that the universal radio spectral index of 1/3 observed in most elliptical galaxies (Slee et al. 1994) is a natural consequence of self-absorbed synchrotron radiation from these flows. We also give expressions for the total luminosity of these flows, and the critical accretion rate, $\dot{M}_{crit}$, above which the advection solutions cease to exist. We find that for most cases of interest the equilibrium electron temperature is fairly insensitive to $M$, $\dot{M}$, and parameters in the model. We apply these results to low luminosity black holes in galactic nuclei. We show that the problem posed by Fabian & Canizares (1988) of whether bright elliptical galaxies host dead quasars is resolved, as pointed out recently by Fabian & Rees (1995), by considering advection-dominated flows.Comment: 30 pages, 5 postscript files. Accepted to ApJ. Also available http://cfa-www.harvard.edu/~rohan/publications.htm

Pair plasma relaxation time scales

By numerically solving the relativistic Boltzmann equations, we compute the time scale for relaxation to thermal equilibrium for an optically thick electron-positron plasma with baryon loading. We focus on the time scales of electromagnetic interactions. The collisional integrals are obtained directly from the corresponding QED matrix elements. Thermalization time scales are computed for a wide range of values of both the total energy density (over 10 orders of magnitude) and of the baryonic loading parameter (over 6 orders of magnitude). This also allows us to study such interesting limiting cases as the almost purely electron-positron plasma or electron-proton plasma as well as intermediate cases. These results appear to be important both for laboratory experiments aimed at generating optically thick pair plasmas as well as for astrophysical models in which electron-positron pair plasmas play a relevant role.Comment: Phys. Rev. E, in pres

Mapping Antarctic crevasses and their evolution with deep learning applied to satellite radar imagery

The fracturing of glaciers and ice shelves in Antarctica influences their dynamics and stability. Hence, data on the evolving distribution of crevasses are required to better understand the evolution of the ice sheet, though such data have traditionally been difficult and time-consuming to generate. Here, we present an automated method of mapping crevasses on grounded and floating ice with the application of convolutional neural networks to Sentinel-1 synthetic aperture radar backscatter data. We apply this method across Antarctica to images acquired between 2015 and 2022, producing a 7.5-year record of composite fracture maps at monthly intervals and 50 m spatial resolution and showing the distribution of crevasses around the majority of the ice sheet margin. We develop a method of quantifying changes to the density of ice shelf fractures using a time series of crevasse maps and show increases in crevassing on Thwaites and Pine Island ice shelves over the observational period, with observed changes elsewhere in the Amundsen Sea dominated by the advection of existing crevasses. Using stress fields computed using the BISICLES ice sheet model, we show that much of this structural change has occurred in buttressing regions of these ice shelves, indicating a recent and ongoing link between fracturing and the developing dynamics of the Amundsen Sea sector.</p

Distinguishing Solar Flare Types by Differences in Reconnection Regions

Observations show that magnetic reconnection and its slow shocks occur in solar flares. The basic magnetic structures are similar for long duration event (LDE) flares and faster compact impulsive (CI) flares, but the former require less non-thermal electrons than the latter. Slow shocks can produce the required non-thermal electron spectrum for CI flares by Fermi acceleration if electrons are injected with large enough energies to resonate with scattering waves. The dissipation region may provide the injection electrons, so the overall number of non-thermal electrons reaching the footpoints would depend on the size of the dissipation region and its distance from the chromosphere. In this picture, the LDE flares have converging inflows toward a dissipation region that spans a smaller overall length fraction than for CI flares. Bright loop-top X-ray spots in some CI flares can be attributed to particle trapping at fast shocks in the downstream flow, the presence of which is determined by the angle of the inflow field and velocity to the slow shocks.Comment: 15 pages TeX and 2 .eps figures, accepted to Ap.J.Let

X-Ray spectra from protons illuminating a neutron star

We consider the interaction of a slowly rotating unmagnetized neutron star with a hot (ion supported, ADAF) accretion flow. The virialized protons of the ADAF penetrate into the neutron star atmosphere, heating a surface layer. Detailed calculations are presented of the equilibrium between heating by the protons, electron thermal conduction, bremsstrahlung and multiple Compton scattering in this layer. Its temperature is of the order 40-70 keV. Its optical depth increases with the incident proton energy flux, and is of the order unity for accretion at $10^{-2}$--$10^{-1}$ of the Eddington rate. At these rates, the X-ray spectrum produced by the layer has a hard tail extending to 100 keV, and is similar to the observed spectra of accreting neutron stars in their hard states. The steep gradient at the base of the heated layer gives rise to an excess of photons at the soft end of the spectrum (compared to a blackbody) through an `inverse photosphere effect'. The differences with respect to previous studies of similar problems are discussed, they are due mostly to a more accurate treatment of the proton penetration process and the vertical structure of the heated layer.Comment: Accepted for publication in A&

The X-ray spectrum of a disk illuminated by ions

The X-ray spectrum from a cool disk embedded in an ion supported torus is computed. The interaction of the hot ions with the disk increases the hard X-ray luminosity of the system}. A surface layer of the disk is heated by the protons from the torus. The Comptonized spectrum produced by this layer has a shape that depends only weakly on the incident energy flux and the distance from the accreting compact object. It consists of a `blue bump' of unComptonized soft photons and a flat high energy tail, reminiscent of the observed spectra. The hard tail becomes flatter as the thermalization depth in the cool disk is increased. Further evidence for ion illumination are the Li abundance in the secondaries of low mass X-ray binaries and the 450 keV lines sometimes seen in black-hole transient spectra.Comment: 7p, to appear in Monthly Notice

Testing refinements by refining tests

One of the potential benefits of formal methods is that they offer the possibility of reducing the costs of testing. A specification acts as both the benchmark against which any implementation is tested, and also as the means by which tests are generated. There has therefore been interest in developing test generation techniques from formal specifications, and a number of different methods have been derived for state based languages such as Z, B and VDM. However, in addition to deriving tests from a formal specification, we might wish to refine the specification further before its implementation. The purpose of this paper is to explore the relationship between testing and refinement. As our model for test generation we use a DNF partition analysis for operations written in Z, which produces a number of disjoint test cases for each operation. In this paper we discuss how the partition analysis of an operation alters upon refinement, and we develop techniques that allow us to refine abstract tests in order to generate test cases for a refinement. To do so we use (and extend existing) methods for calculating the weakest data refinement of a specification