On the Energetics of Advection-Dominated Accretion Flows

Using mean field MHD, we discuss the energetics of optically thin, two temperature, advection-dominated accretion flows (ADAFs). If the magnetic field is tangled and roughly isotropic, flux freezing is insufficient to maintain the field in equipartition with the gas. In this case, we expect a fraction of the energy generated by shear in the flow to be used to build up the magnetic field strength as the gas flows in; the remaining energy heats the particles. We argue that strictly equipartition magnetic fields are incompatible with a priori reasonable levels of particle heating; instead, the plasma $\beta$ in ADAFs (defined to be the gas pressure divided by magnetic/turbulent pressure) is likely to be \gsim 5; correspondingly, the viscosity parameter $\alpha$ is likely to be \lsim 0.2Comment: 24 pages, ApJ submitte

Parsimonious modelling of winter season rainfall incorporating reanalysis climatological data

Several Markov Modulated Poisson Process (MMPP) models are developed to describe winter season rainfall with parsimonious parameter use. We propose a methodology for determining the best form of seasonal model for fine-scale rainfall within a MMPP framework. Of those proposed here, a model with a fixed transition rate is shown to be superior over the other MMPP models considered. The model is expanded to include covariate data for sea-level air pressure, relative humidity, and temperature using reanalysis data over 14 years from the coordinates covering the Bracknell rainfall collection site in England. Results are compared using the likelihood ratio test and the second-order properties of aggregated rainfall

Stochastic point process model for fine-scale rainfall time series

A stochastic point process model, which is constructed from a class of doubly stochastic Poisson processes, is proposed to analyse point rainfall time series observed in fine sub-hourly time scales. Under the framework of this stochastic model rain cells arrive according to a Poisson process whose arrival rate is governed by a finite-state Markov chain. Each cell of the point process has a random lifetime during which instantaneous random depths (pulses) of rainfall bursts occur as another Poisson process. The structure of this model enables us to study the variability of rainfall characteristics at small time intervals. The covariance structure of the pulse occurrence process is studied. Second-order properties of the time series of cumulative rainfall in discrete intervals are derived to model 5-minute rainfall data, over a period of 48 years, from Germany. The results show that the proposed model is capable of reproducing rainfall properties well at various sub-hourly resolutions

Semi-parametric modelling of trend in extremes

Assessment of trend has been a topic of major interest in extreme value analysis in recent years. Much of the previous work has focused on using parametric techniques to model trend in extremes. The parametric approach, however, is often not flexible enough for exploratory modelling. In this paper, we discuss and illustrate a semi-parametric method which can be used as an exploratory tool to draw more information about the extremes and to model trend in extremes. Our approach is based on local likelihood fitting of generalized extreme value distribution and related models. It aims to capture the pattern of trend by fitting locally weighted polynomials to the model parameters. We illustrate the application of this methodology in a study investigating changes in extreme temperatures in central England. Bootstrap methods are used to provide a measure of the variability of the fitted quantities

Precipitation modelling using doubly stochastic point process models at fine time-scale

This paper explores the use of a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall using tipping-bucket raingauge tip times. These models are used to analyse data from a single and multiple sites to study the temporal and spatial variability of precipitation at fine time-scales. The arrival pattern of raingauge bucket tip times is viewed as a Poisson process whose rate of occurrence varies according to an unobserved finite state irreducible Markov chain. Since the likelihood function can be expressed in a tractable form, the models are fitted with maximum likelihood methods, thus enabling a more straightforward estimation of parameter uncertainty than for Poisson-cluster models. One of the advantages of this modelling approach is that it allows us to fit various sub-models of interest for the data, and also to test hypotheses on model parameters. As the tip-times from raingauges are modelled directly, this approach overcomes the usual need to convert tip-times into rainfall depths. We study precipitation patterns at a network of gauges in the South-West of England (HYREX data) using univariate models and the extension of these models to a multivariate framework is examined. The multivariate version of our proposed model can provide the basis for a proper spatial-temporal model for which the parameters are well identified using maximum likelihood estimation. Results on fitting 3-state and 4-state models are presented. A small scale simulation study is carried out to compare some of the rainfall characteristics of accumulated rainfall

Bypass to Turbulence in Hydrodynamic Accretion: Lagrangian Analysis of Energy Growth

Despite observational evidence for cold neutral astrophysical accretion disks, the viscous process which may drive the accretion in such systems is not yet understood. While molecular viscosity is too small to explain the observed accretion efficiencies by more than ten orders of magnitude, the absence of any linear instability in Keplerian accretion flows is often used to rule out the possibility of turbulent viscosity. Recently, the fact that some fine tuned disturbances of any inviscid shear flow can reach arbitrarily large transient growth has been proposed as an alternative route to turbulence in these systems. We present an analytic study of this process for 3D plane wave disturbances of a general rotating shear flow in Lagrangian coordinates, and demonstrate that large transient growth is the generic feature of non-axisymmetric disturbances with near radial leading wave vectors. The maximum energy growth is slower than quadratic, but faster than linear in time. The fastest growth occurs for two dimensional perturbations, and is only limited by viscosity, and ultimately by the disk vertical thickness. After including viscosity and vertical structure, we find that, as a function of the Reynolds number, R, the maximum energy growth is approximately 0.4 (R/log R)^{2/3}, and put forth a heuristic argument for why R > 10^4 is required to sustain turbulence in Keplerian disks. Therefore, assuming that there exists a non-linear feedback process to replenish the seeds for transient growth, astrophysical accretion disks must be well within the turbulent regime. However, large 3D numerical simulations running for many orbital times, and/or with fine tuned initial conditions, are required to confirm Keplerian hydrodynamic turbulence on the computer.Comment: 25 preprint pages, 2 figures, some modifications mainly to the Discussions section, Accepted for publication in Ap

The Cooling Flow to Accretion Flow Transition

Cooling flows in galaxy clusters and isolated elliptical galaxies are a source of mass for fueling accretion onto a central supermassive black hole. We calculate the dynamics of accreting matter in the combined gravitational potential of a host galaxy and a central black hole assuming a steady state, spherically symmetric flow (i.e., no angular momentum). The global dynamics depends primarily on the accretion rate. For large accretion rates, no simple, smooth transition between a cooling flow and an accretion flow is possible; the gas cools towards zero temperature just inside its sonic radius, which lies well outside the region where the gravitational influence of the central black hole is important. For accretion rates below a critical value, however, the accreting gas evolves smoothly from a radiatively driven cooling flow at large radii to a nearly adiabatic (Bondi) flow at small radii. We argue that this is the relevant parameter regime for most observed cooling flows. The transition from the cooling flow to the accretion flow should be observable in M87 with the {\it Chandra X-ray Observatory}.Comment: emulateapj.sty, 10 pages incl. 5 figures, to appear in Ap

Gamma-ray Emission From Advection-Dominated Accretion Flows Around Black Holes: Application to the Galactic Center

We calculate the flux and spectrum of \gamma-rays emitted by a two-temperature advection-dominated accretion flow (ADAF) around a black hole. The \gamma-rays are from the decay of neutral pions produced through proton-proton collisions. We discuss both thermal and power-law distributions of proton energies and show that the \gamma-ray spectra in the two cases are very different. We apply the calculations to the \gamma-ray source, 2EG J1746-2852, detected by EGRET from the direction of the Galactic Center. We show that the flux and spectrum of this source are consistent with emission from an ADAF around the supermassive accreting black hole Sgr A^* if the proton distribution is a power-law. The model uses accretion parameters within the range made likely by other considerations. If this model is correct, it provides evidence for the presence of a two temperature plasma in Sgr A^*, and predicts \gamma-ray fluxes from other accreting black holes which could be observed with more sensitive detectors.Comment: 19 pages (Latex), 4 Figures. ApJ 486. Revised Tables and Figure

Possible Evidence for Truncated Thin Disks in the Low-Luminosity Active Galactic Nuclei M81 and NGC 4579

M81 and NGC 4579 are two of the few low-luminosity active galactic nuclei which have an estimated mass for the central black hole, detected hard X-ray emission, and detected optical/UV emission. In contrast to the canonical ``big blue bump,'' both have optical/UV spectra which decrease with increasing frequency in a $\nu L_\nu$ plot. Barring significant reddening by dust and/or large errors in the black hole mass estimates, the optical/UV spectra of these systems require that the inner edge of a geometrically thin, optically thick, accretion disk lies at roughly 100 Schwarzschild radii. The observed X-ray radiation can be explained by an optically thin, two temperature, advection-dominated accretion flow at smaller radii.Comment: emulateapj.sty, to appear in ApJ Letter

The Giant X-Ray Flare of NGC 5905: Tidal Disruption of a Star, a Brown Dwarf, or a Planet?

We model the 1990 giant X-ray flare of the quiescent galaxy NGC 5905 as the tidal disruption of a star by a supermassive black hole. From the observed rapid decline of the luminosity, over a timescale of a few years, we argue that the flare was powered by the fallback of debris rather than subsequent accretion via a thin disk. The fallback model allows constraints to be set on the black hole mass and the mass of debris. The latter must be very much less than a solar mass to explain the very low luminosity of the flare. The observations can be explained either as the partial stripping of the outer layers of a low-mass main sequence star or as the disruption of a brown dwarf or a giant planet. We find that the X-ray emission in the flare must have originated within a small patch rather than over the entire torus of circularized material surrounding the black hole. We suggest that the patch corresponds to the ``bright spot'' where the stream of returning debris impacts the torus. Interestingly, although the peak luminosity of the flare was highly sub-Eddington, the peak flux from the bright spot was close to the Eddington limit. We speculate on the implications of this result for observations of other flare events.Comment: 25 pages, including 5 figure