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

Comprehensive simulations of superhumps

(Abridged) We use 3D SPH calculations with higher resolution, as well as with more realistic viscosity and sound-speed prescriptions than previous work to examine the eccentric instability which underlies the superhump phenomenon in semi-detached binaries. We illustrate the importance of the two-armed spiral mode in the generation of superhumps. Differential motions in the fluid disc cause converging flows which lead to strong spiral shocks once each superhump cycle. The dissipation associated with these shocks powers the superhump. We compare 2D and 3D results, and conclude that 3D simulations are necessary to faithfully simulate the disc dynamics. We ran our simulations for unprecedented durations, so that an eccentric equilibrium is established except at high mass ratios where the growth rate of the instability is very low. Our improved simulations give a closer match to the observed relationship between superhump period excess and binary mass ratio than previous numerical work. The observed black hole X-ray transient superhumpers appear to have systematically lower disc precession rates than the cataclysmic variables. This could be due to higher disc temperatures and thicknesses. The modulation in total viscous dissipation on the superhump period is overwhelmingly from the region of the disc within the 3:1 resonance radius. As the eccentric instability develops, the viscous torques are enhanced, and the disc consequently adjusts to a new equilibrium state, as suggested in the thermal-tidal instability model. We quantify this enhancement in the viscosity, which is ~10 per cent for q=0.08. We characterise the eccentricity distributions in our accretion discs, and show that the entire body of the disc partakes in the eccentricity.Comment: 18 pages (mn2e LaTeX), 14 figures, 5 tables, Accepted for publication in MNRA

Going weighted: Parameterized algorithms for cluster editing

AbstractThe goal of the Cluster Editing problem is to make the fewest changes to the edge set of an input graph such that the resulting graph is a disjoint union of cliques. This problem is NP-complete but recently, several parameterized algorithms have been proposed. In this paper, we present a number of surprisingly simple search tree algorithms for Weighted Cluster Editing assuming that edge insertion and deletion costs are positive integers. We show that the smallest search tree has size O(1.82k) for edit cost k, resulting in the currently fastest parameterized algorithm, both for this problem and its unweighted counterpart. We have implemented and compared our algorithms, and achieved promising results.11This is an extended version of two articles published in: Proc. of the 6th Asia Pacific Bioinformatics Conference, APBC 2008, in: Series on Advances in Bioinformatics and Computational Biology, vol. 5, Imperial College Press, pp. 211–220; and in: Proc. of the 2nd Conference on Combinatorial Optimization and Applications, COCOA 2008, in: LNCS, vol. 5038, Springer, pp. 289–302

The outburst duration and duty-cycle of GRS 1915+105

The extraordinarily long outburst of GRS 1915+105 makes it one of the most remarkable low-mass X-ray binaries (LMXBs). It has been in a state of constant outburst since its discovery in 1992, an eruption which has persisted ~100 times longer than those of more typical LXMBs. The long orbital period of GRS 1915+105 implies that it contains large and massive accretion disc which is able to fuel its extreme outburst. In this paper, we address the longevity of the outburst and quiescence phases of GRS 1915+105 using Smooth Particle Hydrodynamics (SPH) simulations of its accretion disc through many outburst cycles. Our model is set in the two-alpha framework and includes the effects of the thermo-viscous instability, tidal torques, irradiation by central X-rays and wind mass loss. We explore the model parameter space and the examine the impact of the various ingredients. We predict that the outburst of GRS 1915+105 should last a minimum of 20 years and possibly up to ~100 years if X-ray irradiation is very significant. The predicted recurrence times are of the order of 10^4 years, making the X-ray duty cycle a few 0.1%. Such a low duty cycle may mean that GRS 1915+105 is not an anomaly among the more standard LMXBs and that many similar, but quiescent, systems could be present in the Galaxy.Comment: 10 pages, 9 figures, accepted for publication by MNRA

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