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Abstract:

The probability density function of accretion disc luminosity fluctuations at high observed energies (i.e. energies larger than the peak temperature scale of the disc) is derived, under the assumption that the temperature fluctuations are lognormally distributed. Thin disc theory is used throughout. While lognormal temperature fluctuations would imply that the disc’s bolometric luminosity is also lognormal, the observed Wien-like luminosity behaves very differently. For example, in contrast to a lognormal distribution, the standard deviation of the derived distribution is not linearly proportional to its mean. This means that these systems do not follow a linear rms-flux relationship. Instead they exhibit very high intrinsic variance, and undergo what amounts to a phase transition, in which the mode of the distribution (in the statistical sense) ceases to exist, even for physically reasonable values of the underlying temperature variance. The moments of this distribution are derived using asymptotic expansion techniques. A result that is important for interpreting observations is that the theory predicts that the fractional variability of these disc systems should increase as the observed frequency is increased. The derived distribution will be of practical utility in quantitatively understanding the variability of disc systems observed at energies above their peak temperature scale, including X-ray observations of tidal disruption events.

Abstract:

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfvénic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. The partition of energy between these fluctuations determines the nature of dissipation, which, in many astrophysical systems, happens on scales where plasma is collisionless. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on collisional MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that, in such a case, the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In our reduced MHD model, the Alfvénic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfvénic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. In the decoupling scales, the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfvénic fluctuations. Finally, we discuss the application of this result to prescriptions of ion-to-electron heating ratio in hot accretion flows.

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.