Prof Steven Balbus FRS, FInstP

Abstract:

We comprehensively model the X-ray luminosity emergent from time-dependent relativistic accretion discs, developing analytical models of the X-ray luminosity of thermal disc systems as a function of black hole mass M, disc mass Md, and disc α-parameter. The X-ray properties of these solutions will be directly relevant for understanding tidal disruption event (TDE) observations. We demonstrate an extremely strong suppression of thermal X-ray luminosity from large mass black holes, LX ∼ exp (− m7/6), where m is a dimensionless mass, roughly the black hole mass in unity of 106M⊙. This strong suppression results in upper observable black hole mass limits, which we demonstrate to be of order Mlim ≃ 3 × 107M⊙, above which thermal X-ray emission will not be observable. This upper observable black hole mass limit is a function of the remaining disc parameters, and the full dependence can be described analytically (equation 82). We demonstrate that the current population of observed X-ray TDEs is indeed consistent with an upper black hole mass limit of order M ∼ 107M⊙, consistent with our analysis.

Abstract:

We extend the relativistic time-dependent thin-disc TDE model to describe non-thermal (2-10 keV) X-ray emission produced by the Compton up-scattering of thermal disc photons by a compact electron corona, developing analytical and numerical models of the evolving non-thermal X-ray light curves. In the simplest cases, these X-ray light curves follow power-law profiles in time. We suggest that TDE discs act in many respects as scaled-up versions of XRB discs, and that such discs should undergo state transitions into harder accretion states. XRB state transitions typically occur when the disc luminosity becomes roughly one per cent of its Eddington value. We show that if the same is true for TDE discs then this, in turn, implies that TDEs with non-thermal X-ray spectra should come preferentially from large-mass black holes. The characteristic hard-state transition mass is MHS ≃ 2 × 107M⊙. Hence, subpopulations of thermal and non-thermal X-ray TDEs should come from systematically different black hole masses. We demonstrate that the known populations of thermal and non-thermal X-ray TDEs do indeed come from different distributions of black hole masses. The null-hypothesis of identical black hole mass distributions is rejected by a two-sample Anderson-Darling test with a p-value <0.01. Finally, we present a model for the X-ray rebrightening of TDEs at late times as they transition into the hard state. These models of evolving TDE light curves are the first to join both thermal and non-thermal X-ray components in a unified scenario.

Abstract:

[This corrects the article DOI: 10.1098/rspa.2020.0355.].

Abstract:

The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of ‘magnetoelastic waves’, the isotropic analogue of Alfvén waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.