On the dynamics of magnetoviscous warped discs around compact objects

TL;DR

The paper investigates magnetoviscous warped discs around compact objects, incorporating general-relativistic epicyclic frequencies and external stellar magnetic torques to reassess warp dynamics. Using a hybrid analytic–numerical local-fluid framework, it derives how the perpendicular viscosity $\alpha_{\perp}$ relates to the standard viscosity $\alpha$ under Newtonian, GR, and magnetized conditions, revealing GR and magnetic fields can significantly modify warp eigenmodes and destabilize the disc. Key findings include GR-driven resonance suppression of radial warp response, GR/field-induced mode avoided crossings, and a magnetically enhanced propensity for tearing at sub-Eddington accretion, particularly in neutron-star X-ray binaries. The results offer a pathway to connect disc tearing to observed outbursts and variability in LMXBs and provide guidance for interpreting magnetized disc dynamics in ULXs and related systems, with implications for future X-ray polarimetry and timing observations.

Abstract

Accretion discs that are tilted with respect to their compact hosts can warp out-of-plane through general relativistic frame-dragging. Warp influences disc dynamics in ways that have been studied extensively, especially as regards instabilities that might lead to rapid angular-momentum cancellation between neighbouring rings of fluid and mass infall. We provide a review of warped-disc phenomena here, revisiting key hydrodynamical assumptions that impact calculations of the shear viscosity controlling instability thresholds. Relativistic effects at the level of gas-parcel orbits are included, as are external Lorentz forces applied by the compact primary's magnetic field. Semi-analytic analysis reveals that intense magnetic fields can bring about new branches of warp modes and avoided crossings that significantly reduce the perpendicular viscosity at sub-Eddington accretion rates. Critical strengths required for misaligned torques to tear a thin disc may thus relax for systems like neutron star X-ray binaries or radio-loud active galactic nuclei.

Figures (10)

• Figure 1: Schematic of a tilted accretion disc around a compact object. If sufficiently magnetised, truncation of the disc occurs at the Alfvén radius, $R_{\rm A}$, where magnetic pressure balances the ram pressure of circulating material (left; see Sec. \ref{['sec:maglocal']} for a definition). In cases of dynamical capture, young systems, or where the BP effect is not at work, there is no further expectation of any existing disc-object symmetry: the inner region(s) may be angled ($\beta$) with respect to the mid-plane of the compact primary as rotation and Lense-Thirring torques $(\Omega_{\rm LT})$ are 'switched on' (right). A differential precession is thus exerted on radially-neighbouring parcels of fluid which drives a warp ($|\psi|$) which depends on the amplitude of disturbances ($z_{0}$; see Sec. \ref{['sec:local']}). Pressure gradients between neighbouring 'rings', which vary as a function of polar angles, result from this warp. This effect is illustrated in the red-box inset. Balancing the energy-dissipation rates between shear motions in two orthogonal directions leads to estimations of the vertical and radial dissipation timescales (see also section 4.1 in lp07, from which parts of this figure are adapted).
• Figure 2: Ratio of the perpendicular viscosity coefficient, determined using the amplitude \ref{['eq:hydroamp']} and expression \ref{['perpviscnewt']}, to the Newtonian prediction \ref{['alphaperpN']} as a function of $\alpha$ for $q=0.2$ and $x=1/6$ (blue) or $x=1/20$ (red). The horizontal line marks equality, reached after $\alpha \approx 0.1$ for the less compact case. Solutions asymptote to this value for large $\alpha$.
• Figure 3: Stability diagram, as a function of viscosity and warp amplitude, for a highly-relativistic case with $x=1/6$ and $q=0.2$ (blue) and the Newtonian case ($x \to 0$; red). For comparison, we also show the prediction obtained when using $\alpha_{\perp} = 1/\alpha$ (pink) from lp07. Shaded regions correspond to unstable cases with $\text{Re}(s) > 0$ from Eq. \ref{['eq:det']}.
• Figure 4: Dimensionless magnetic parameter $\gamma (r_{0}/H)^2$ from expression \ref{['gammaprofile']} as a function of radius for $H/r_{0} = 10^{-2}$, $\alpha = 0.1$, $R = 10$ km, $M = 1.4 M_{\odot}$, $B_{0} = 2 \times 10^{8}$ G, and $\dot{M} = 10^{-6} \dot{M}_{\rm edd}$ (solid blue curve). The solid, vertical lines depict the limiting values associated with total disc truncation ($\gamma = 1$; left) and equality in \ref{['gammaalt']} (right) for $\alpha_{\perp} = 1$. The dotted, vertical lines mark the critical transition radius associated with the emergence of magnetic modes from condition \ref{['eq:gammaeqn1']} for either $\alpha_{\perp} \sim 1$ (with '$\gg$' interpreted as five in this case; blue shaded region) or $\alpha_{\perp} \sim 10$ (red shaded region). The dashed, horizontal line marks $\gamma (r_{0}/H)^2 = 1$.
• Figure 5: Stability diagram for $\alpha_{\perp} = 10 \alpha$, $H/r = 10^{-2}$, and $\dot{M} = 10^{-4} \dot{M}_{\rm Edd}$ at a radius of $r = 5 R$ in the $B_{0}$-$\alpha$ plane for unwarped ($\psi_{0} = 0$; blue) or highly-warped ($\psi_{0} = 1$; purple) cases. We fix $\epsilon_{i} = 1$ for all $i$. Shaded regions correspond to unstable cases with $\text{Im}(\sigma) < 0$. A visually-indistinguishable diagram is obtained for any choice $0.1 \lesssim \alpha_{\perp} / \alpha \lesssim 10$. The region shaded in black corresponds to $\gamma > 1$, where the scheme breaks down.