Flip-Flop Shocks and Tori in Bondi-Hoyle-Lyttleton Accretion onto Rotating Kerr-Weyl Black Holes and Their Quasi-Periodic Variability

Abstract

We present GRHD simulations of Bondi-Hoyle-Lyttleton accretion onto a rotating black hole in Weyl conformal gravity, described by the Kerr-Weyl metric. The equatorial flow is evolved for spins a=0.9M and a=0.5M and several Weyl coefficients, which enter through an effective curvature parameter k, and is compared with Kerr runs sharing the same setup. For the k considered, the horizon, ISCO and test-particle frequencies differ from Kerr by at most ~2%. However, the curvature term grows as kr^2 and acts at the accretion radius R_acc. The flow is controlled by one quantity, eta=|k|R_acc^3/M, the ratio of curvature-induced to Newtonian acceleration at R_acc. For eta<~0.03 a stable shock cone forms, indistinguishable from Kerr. For eta~0.2-0.3 the anti-de Sitter-like term traps shocked gas behind the black hole and drives persistent flip-flop oscillations. For eta>~1.6 the cone is destroyed and an oscillating torus forms. Spin modifies only the inner few gravitational radii and does not change the regime. In strongly deviating models the mean accretion rate is 1.7-3 times the Kerr value and varies by 20-60% rms, versus 0.1-1% in Kerr-like flows. The power spectra show global QPOs with fundamentals at 2.9-4.8 Hz for a 10 Msun black hole, with harmonic ladders whose 3:2 and 2:1 ratios come from one non-sinusoidal oscillation, not resonances. These lie in the low-frequency QPO band and are unrelated to test-particle frequencies (~70-200 Hz). They scale as f_0=xi f_K(R_acc), with xi~0.7-1.1 for stable cones and xi~0.23-0.38 for flip-flop and torus regimes. Strong oscillations would be detectable within seconds for a bright Galactic source. The required |k| exceeds galactic-rotation-curve values by 18-36 orders of magnitude, so a detected shock-driven QPO would measure a local deviation from Kerr, and its absence would constrain |k|.