Simulations with the resistive general-relativistic magnetohydrodynamic (GR-MHD) code rHARM showed that a geometrically thin accretion disk threaded by a large-scale poloidal magnetic field around a Kerr black hole launches disk winds whose mass loading and ejection efficiency depend non-monotonically on the prescribed scalar magnetic diffusivity, with winds driven mainly by toroidal magnetic-field pressure gradients rather than by magneto-centrifugal acceleration, and with a dense infalling corona that can invert the sign of the net Blandford–Znajek electromagnetic flux at low black-hole spin. Later work in the same program enlarged the computational domains, raised the resolution, introduced a mean-field disk dynamo, and reproduced the critical-diffusivity peak in mass and Poynting flux — attributing it to the interplay of reconnection and diffusion/ohmic heating — but did not separate these mechanisms, did not establish magneto-centrifugal driving or asymptotic relativistic acceleration of the wind, did not apply turbulence-driven anisotropic diffusivity prescriptions, and did not quantify the contamination of the net Blandford–Znajek flux by coronal mass advection. The problem — how the magnitude and physical prescription of the disk magnetic diffusivity control the accretion–ejection interrelation, the dominant wind-driving mechanism, and the disk-wind/Blandford–Znajek energy partition — remains open.

Background

Relativistic jets in active galactic nuclei and black-hole X-ray binaries are believed to be powered by two canonical magnetic mechanisms operating side by side. In the Blandford–Znajek (BZ) mechanism, poloidal magnetic flux (the flux of the field component lying in the radius–latitude meridional planes) threading the event horizon of a rotating (Kerr) black hole, described by the dimensionless spin parameter aa, extracts the hole's rotational energy as an electromagnetic (Poynting) flux. In the Blandford–Payne (BP) mechanism, gas is flung centrifugally outward along poloidal field lines that are sufficiently inclined from the disk rotation axis, launching a magneto-centrifugal wind from the disk surface. Simulating both components together requires general relativistic magnetohydrodynamics (GR-MHD), the evolution of magnetized fluid flow in curved spacetime. Most GR-MHD codes assume ideal MHD, in which the magnetic field is frozen into the plasma; however, real accretion disks are turbulent, and the turbulence (commonly attributed to the magnetorotational instability, MRI — the destabilization of weakly magnetized Keplerian shear flow, which is not resolved in the simulations discussed here) provides an effective magnetic diffusivity η\eta that decouples matter and field, enables reconnection, and — as established in two decades of non-relativistic resistive-MHD simulations, e.g. Sheikhnezami et al. (2012) — is essential for loading matter onto wind-driving field lines. A central diagnostic of this accretion–ejection interrelation is the ejection efficiency ξ\xi, the ratio of the mass ejection rate to the mass accretion rate. Qian, Fendt & Vourellis (2018) extended this resistive treatment to GR-MHD with the code rHARM, a resistive extension of HARM, studying a thin disk threaded by inclined open poloidal field lines around black holes with spins from a=0a=0 to a=0.9375a=0.9375, using a prescribed scalar Gaussian diffusivity profile (peak value η0\eta_0 at the disk mid-plane, vertical scale parameter χ\chi). They found robust disk winds driven predominantly by the pressure gradient of the toroidal (azimuthal) magnetic field component — so-called tower jets — reaching only mildly relativistic speeds, which the authors attributed to the limited computational domain. The ejection efficiency does not grow monotonically with diffusivity: for their setup it peaks near η0≃5×10−4\eta_0 \simeq 5\times10^{-4}, and the competing candidate mechanisms (field-line tangling at low diffusivity, which lowers the efficiency of magnetic driving, versus enhanced mass loading at higher diffusivity, possibly through ohmic heating (resistive, Joule-type dissipation of the electric currents) raising the sound speed at the disk surface) could not be separated. Accretion and ejection rates are suppressed at high diffusivity and, curiously, at high black-hole spin. Comparing energy channels, the total matter energy flux of the disk wind exceeded the total electromagnetic energy flux by a factor of about 20, and for spins a≲0.5a \lesssim 0.5 the net electromagnetic flux measured near the horizon was negative: the dense, freely falling corona (the tenuous atmosphere initialized above and below the disk surface) advects Poynting flux into the black hole faster than the BZ mechanism extracts it, so the measured BZ output depends sensitively — and unquantifiably with the setups used — on the coronal initialization and on the numerical density floors (minimum-density prescriptions that keep the scheme stable in the low-density funnel and corona). The numerical diffusivity of the 128×128128\times128 grid, ηnum≲10−4\eta_{\rm num} \lesssim 10^{-4}, further limited the accessible diffusivity range, although a follow-up with the parallel code rHARM3D (Vourellis et al. 2019) reached larger domains, higher resolution, and longer evolution times, confirming the qualitative picture and finding a critical resistivity η0≃10−3\eta_0 \simeq 10^{-3} at which both mass flux and Poynting flux peak, interpreted — but not demonstrated by controlled experiments — as the interplay between reconnection (decreasing the flux available for launching) and diffusion plus ohmic heating (increasing mass loading). The physical origin of the non-monotonic efficiency, the possibility of a transition to BP-type magneto-centrifugal driving at larger scales or with physically motivated (turbulence-driven, anisotropic, dynamo-consistent) diffusivity prescriptions, and the decontamination of the net BZ flux from coronal advection remain unresolved.

Problem Statement

In resistive GR-MHD simulations of a geometrically thin accretion disk threaded by a large-scale poloidal magnetic field around a Kerr black hole, determine how the magnitude and the physical prescription of the disk magnetic diffusivity govern the accretion–ejection interrelation. This single objective comprises three linked questions left open by Qian, Fendt & Vourellis (2018) and only partially advanced by Vourellis et al. (2019) and Vourellis & Fendt (2021): (i) identify and separate the physical mechanisms that produce the non-monotonic dependence of the ejection efficiency ξ\xi (ratio of ejection rate to accretion rate) on the diffusivity level η0\eta_0 — specifically the competition between field-line tangling/reconnection, which depletes the magnetic flux driving the wind, and diffusivity-enhanced mass loading, potentially via ohmic heating and smoother field structure; (ii) establish how physically motivated diffusivity prescriptions (turbulence-driven or anisotropic resistivity, mean-field-dynamo-consistent profiles, as opposed to the prescribed scalar Gaussian profile) modify mass loading, ξ\xi, and the torque balance of the disk, and whether, on larger computational domains and longer evolutionary times, the observed toroidal-pressure-driven (tower-jet) winds give way to quasi-steady magneto-centrifugally (Blandford–Payne) driven winds with full asymptotic acceleration and collimation; and (iii) quantify the resulting partition of energy output between the disk wind and the Blandford–Znajek jet as a function of diffusivity and black-hole spin, including how coronal mass advection, coronal initialization, and numerical density floors alter the sign and magnitude of the net ergospheric electromagnetic flux, particularly at low spins where current simulations find it inverted. These linked questions and the components they enumerate jointly define the single objective; a resolution must address all of them, and no single component in isolation constitutes a resolution.

References

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