Long time-scale variability in GRS1915+105

We present very high resolution hydrodynamical simulations of accretion discs in black hole X-ray binaries accreting near the Eddington limit. The results show that mass loss, irradiation and tidal interactions all have a profound effect on the observed behaviour of long period X-ray transients. In particular, the interplay of all of these effects in the outer regions of the accretion disc is able to drive long time-scale (weeks to years) variability is these objects, and is a possible origin for some of the extreme variability of GRS1915+105.Comment: 7 pages, 9 figures (2 in colour), accepted for publication in MNRA

The steady-state structure of accretion discs in central magnetic fields

We develop a new analytic solution for the steady-state structure of a thin accretion disc under the influence of a magnetic field that is anchored to the central star. The solution takes a form similar to that of Shakura and Sunyaev and tends to their solution as the magnetic moment of the star tends to zero. As well as the Kramer's law case, we obtain a solution for a general opacity. The effects of varying the mass transfer rate, spin period and magnetic field of the star as well as the opacity model applied to the disc are explored for a range of objects. The solution depends on the position of the magnetic truncation radius. We propose a new approach for the identification of the truncation radius and present an analytic expression for its position.Comment: 11 pages, 7 figures, accepted by MNRA

Hydrodynamic modelling of accretion flows

In the proceedings of this, and of several recent close binary conferences, there have been several contributions describing smoothed particle hydrodynamics simulations of accretion disks. It is apposite therefore to review the numerical scheme itself with emphasis on its advantages for disk modelling, and the methods used for modelling viscous processes.Comment: 3 pages, to appear in proceedings of IAU Colloquium 194: Compact binaries in the galaxy and beyon

Accretion disc dynamics in extreme mass ratio compact binaries

An analysis is presented of a numerical investigation of the dynamics and geometry of accretion discs in binary systems with mass ratios q < 0.1, applicable to ultra-compact X-ray binaries, AM CVn stars and very short period cataclysmic variables. The steady-state geometry of the disc in the binary reference frame is found to be quite different from that expected at higher mass ratios. For q ~ 0.1, the disc takes on the usual elliptical shape, with the major axis aligned perpendicular to the line of centres of the two stars. However, at smaller mass ratios the elliptical gaseous orbits in the outer regions of the disc are rotated in the binary plane. The angle of rotation increases with gas temperature, but is found to vary inversely with q. At q = 0.01, the major axis of these orbits is aligned almost parallel to the line of centres of the two stars. These effects may be responsible for the similar disc structure inferred from Doppler tomography of the AM CVn star GP Com (Morales-Rueda et al. 2003), which has q = 0.02. The steady-state geometry at low mass ratios is not predicted by an inviscid, restricted three-body model of gaseous orbits; it is related to the effects of tidal-viscous truncation of the disc near the Roche lobe boundary. Since the disc geometry can be inferred observationally for some systems, it is proposed that this may offer a useful diagnostic for the determination of mass ratios in ultra-compact binaries.Comment: 17 pages, 9 figures, 7 in colour. Accepted for publication in MNRAS. Plain article formatting to get round arXiv problems with mn2e.st

Propeller-activated resonances and the fate of short-period cataclysmic variables

We show that the combination of a weak magnetic propeller and accretion disc resonances can effectively halt accretion in short-period cataclysmic variables (CVs) for large fractions of their lifetimes. This may help to explain the discrepancy between the observed and predicted orbital period distributions of CVs at short periods. Orbital resonances cause the disc to become eccentric, allowing material to fall back on to the donor star or out of the system. A weak magnetic field on a rapidly spinning primary star propels disc material outwards, allowing it to access these resonances. Numerical and analytic calculations show that this state can be long lived (∼1011 yr). This is because the magnetic propeller is required only to maintain access to the resonances, and not to push matter out of the Roche lobe, so that the spin-down time-scale is much longer than that for a classical propeller mode

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure

Mass transfer in tidally unstable compact binaries

The 2001 outburst of WZ Sagittae has shown the most compelling evidence yet for an enhancement of the mass transfer rate from the donor star during a dwarf nova outburst in the form of hot-spot brightening. I show that even in this extreme case, the brightening can be attributed to tidal heating near the interaction point of an accretion stream with the expanding edge of an eccentric accretion disc, with no need at all for an increase in the mass transfer rate. Furthermore, I confirm previous suggestions that an increase in mass transfer rate through the stream damps any eccentricity in an accretion disc and suppresses the appearance of superhumps, in contradiction to observations. Tidal heating is expected to be most significant in systems with small mass ratios. It follows that systems like WZ Sagittae - which has a tiny mass ratio - are those most likely to show a brightening in the hot-spot region.Comment: 6 pages, 5 figures (eps/ps). Accepted for publication in MNRA

The statistical significance of the superhump signal in U Gem

Although its well determined mass ratio of q=\Msec/\Mwd=0.357\pm0.007 should avoid superoutbursts according to the thermal tidal instability model, the prototypical dwarf nova U Gem experienced in 1985 an extraordinary long outburst resembling very much superoutbursts observed in SU UMa systems. Recently, the situation for the model became even worse as superhump detections have been reported for the 1985 outburst of U Gem. The superhump signal is noisy and the evidence provided by simple periodograms seems to be weak. Therefore and because of the importance for our understanding of superoutbursts and superhumps, we determine the statistical significance of the recently published detection of superhumps in the AAVSO light curve of the famous long 1985 outburst of U Gem. Using Lomb-Scargle periodograms, analysis of variance (AoV), and Monte-Carlo methods we analyse the 160 visual magnitudes obtained by the AAVSO during the outburst and relate our analyse to previous superhump detections. The 160 data points of the outburst alone do not contain a statistically significant period. However, using additionally the characteristics of superhumps detected previously in other SU UMa systems and searching only for signals that are consistent with these, we derive a $2\sigma$ significance for the superhump signal. The alleged appearance of an additional superhump at the end of the outbursts appears to be statistically insignificant. Although of weak statistical significance, the superhump signal of the long 1985 outburst of U Gem can be interpreted as further indication for the SU UMa nature of this outburst. This further contradicts the tidal instability model as the explanation for the superhump phenomenon.Comment: 7 pages, 7 figures, accepted for publication in A&