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Abstract:

The observations of high-redshifts quasars at z ≳ 6 have revealed that supermassive black holes (SMBHs) of mass ∼109M⊙∼109M⊙ were already in place within the first ∼Gyr after the big bang. Supermassive stars (SMSs) with masses 103−5M⊙103−5M⊙ are potential seeds for these observed SMBHs. A possible formation channel of these SMSs is the interplay of gas accretion and runaway stellar collisions inside dense nuclear star clusters (NSCs). However, mass-loss due to stellar winds could be an important limitation for the formation of the SMSs and affect the final mass. In this paper, we study the effect of mass-loss driven by stellar winds on the formation and evolution of SMSs in dense NSCs using idealized N-body simulations. Considering different accretion scenarios, we have studied the effect of the mass-loss rates over a wide range of metallicities Z* = [.001–1]Z⊙ and Eddington factors fEdd=L∗/LEdd=0.5,0.7,and0.9fEdd=L∗/LEdd=0.5,0.7,and0.9⁠. For a high accretion rate of 10−4M⊙yr−110−4M⊙yr−1⁠, SMSs with masses ≳103M⊙yr−1≳103M⊙yr−1 could be formed even in a high metallicity environment. For a lower accretion rate of 10−5M⊙yr−110−5M⊙yr−1⁠, SMSs of masses ∼103−4M⊙∼103−4M⊙ can be formed for all adopted values of Z* and fEdd, except for Z* = Z⊙ and fEdd = 0.7 or 0.9. For Eddington accretion, SMSs of masses ∼103M⊙∼103M⊙ can be formed in low metallicity environments with Z* ≲ 0.01 Z⊙. The most massive SMSs of masses ∼105M⊙∼105M⊙ can be formed for Bondi–Hoyle accretion in environments with Z* ≲ 0.5 Z⊙. An intermediate regime is likely to exist where the mass-loss from the winds might no longer be relevant, while the kinetic energy deposition from the wind could still inhibit the formation of a very massive object.

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:

A new algorithm for toroidal flow shear in a linearly implicit, local δf gyrokinetic code is described. Unlike the current approach followed by a number of codes, it treats flow shear continuously in time. In the linear gyrokinetic equation, time-dependences arising from the presence of flow shear are decomposed in such a way that they can be treated explicitly in time with no stringent constraint on the time step. Flow shear related time dependences in the nonlinear term are taken into account exactly, and time dependences in the quasineutrality equation are interpolated. Test cases validating the continuous-in-time implementation in the code GS2 are presented. Lastly, nonlinear gyrokinetic simulations of a JET discharge illustrate the differences observed in turbulent transport compared with the usual, discrete-in-time approach. The continuous-in-time approach is shown, in some cases, to produce fluxes that converge to a different value than with the discrete approach. The new approach can also lead to substantial computational savings by requiring radially narrower boxes. At fixed box size, the continuous implementation is only modestly slower than the previous, discrete approach.