Disk warping and black hole X-ray binaries I. Tentative unification of low-frequency quasi-periodic oscillations

TL;DR

The paper proposes that Lense-Thirring–induced disk warping at a break radius $r_{ m b}$, driven by a spin–orbit misalignment $\theta$ and disk parameters $\alpha$ and $\epsilon$, occurs as the transition radius $r_{ m t}$ evolves during outbursts. This warp alters the inner hot flow geometry, changing QPO properties: type C QPOs (with strong BBN) arise when $r_{ m t} > r_{ m b}$, while type B QPOs and damped BBN emerge when $r_{ m t} < r_{ m b}$, thereby unifying the LFQPO phenomenology. The framework also accounts for the disappearance of BBN, shifts in lag patterns, and modifications to QPO frequency evolution, and offers a potential explanation for Cyg X-1’s peculiar behavior and for hysteresis in BHXRB outbursts. While this warp-based unification is compelling, it relies on several assumptions about warp morphology, torques, and alternative QPO mechanisms, and it highlights the need for numerical validation and consideration of additional torques and system geometries.

Abstract

X-ray binaries exhibit complex variability patterns studied in the power-spectrum. These include the broad-band noise (BBN) components and various types of narrow components called quasi-periodic oscillations (QPOs). There is currently no consensus about either what determines the presence/absence of the BBN or what generates the QPOs. Many believe the latter is due to frame-dragging effects caused by Lense-Thirring torques. We wish to investigate the potential impact of those frame-dragging effects on the accretion disk itself. In particular, we focus on its impact on the observed variability and the presence (and types) of QPOs associated. We make analytical estimates to assess the potential presence of a geometric warp in the inner accretion disk during state transitions. We show that the presence of a warp can modify the spectral-timing properties in a way that matches the observed transition between QPO types during outbursts. We also discuss the peculiar case of Cyg X-1, as well as how the hard-to-soft transition could be driven by the warp itself. The (expected) emergence of a warp provides a consistent explanation for the evolution of both the BBN and the QPO properties during state transitions. This offers a first path toward unifying the variability of black hole X-ray binary.

Figures (7)

• Figure 1: Schematic illustration of the cold disk -- hot flow system envisioned in this section. The black hole is depicted as a black circle, with its spin axis $\hat{k}$ shown by the black arrow, and the oblique dotted line indicating its normal. The horizontal dotted-line represents the orbital plane of the binary, normal to $\hat{I}$. The disk (light blue) and the hot flow (orange) are separated at the transition radius $R_{\mathrm{t}}$. The disk and the hot flow are both aligned with the binary plane, forming an angle $\theta$ relative to the black hole spin axis.
• Figure 2: Break radius evolution as function of the misalignment angle for different values of black hole spin (indicated in colors), assuming $\alpha \epsilon = 10^{-3}$. The break radius is here shown in units of $R_g= GM/c^2$, shown in dashed-lines when $r_{\mathrm{b}} < r_{\mathrm{isco}}$. Note that the vertical axis is scaled logarithmically.
• Figure 3: Schematic illustration of the system configuration envisioned in this paper, similar to Fig. \ref{['fig:LTconfig1']}: black hole in black, its spin axis in black arrow. The cold disk is in light blue, and the hot flow in orange; separated at the transition radius $R_{\mathrm{t}}$. The cold disk is warped outside of $R_{\mathrm{t}}$ at a radius $R_{\mathrm{b}}$, and its inner region are tilted to an angle $\theta_t < \theta$ with respect to the black hole spin axis.
• Figure 4: Schematic representation of the proposed evolution from the type C to the type B QPO during the rise and hard-to-soft transition of a typical X-ray binary outburst. This figure is similar to Fig. \ref{['fig:LTconfig2']}. The warp radius $r_{\mathrm{b}}$ is shown in red '+', the transition radius $r_{\mathrm{t}}$ in blue 'x'. A purple line illustrates the case $r_{\mathrm{b}} = r_{\mathrm{t}}$. In the type C configurations (right of the line), the outer disk is aligned at all radii with its outer region $\theta (r) = \theta$ because $r_{\mathrm{t}} > r_{\mathrm{b}}$. In the type B configurations (left of the line), the outer disk is now warped in $r_{\mathrm{b}}$, forcing a warp in the cold accretion disk and changing the alignment angle of the hot flow to $\theta_t < \theta$. See text for the associated discussion.
• Figure 5: Power spectrum from GRO J1655$-$40 during the observation reported in Motta12. The dotted lines show the different individual Lorentzian components used in the fitting procedure to fit the broad-band noise. The solid lines show the Lorentzian associated to the two peaked components $\nu_L$ (red) and $\nu_H$ (blue). This figure is adapted from 2023MNRAS.525..221R.