VHFQPOs: Probing Extreme Accretion Physics

• VHFQPOs are rapid, high-frequency X-ray flux modulations observed in accreting compact objects, serving as direct probes of strong-field gravity and disk microphysics.
• They emerge from orbital motions near the innermost disk regions where modified spacetime metrics allow frequencies up to tens of kilohertz, discriminating between black holes and horizonless models.
• Detection strategies rely on high-sensitivity timing instruments and advanced spectral analysis to refine our understanding of accretion dynamics and strong gravitational fields.

Very-high-frequency quasi-periodic oscillations (VHFQPOs) are a class of rapid, periodic or quasi-periodic modulations observed or hypothesized in the X-ray flux from accreting compact objects, particularly black holes, neutron stars, and in some models, even horizonless, non-singular objects. Defined by their high centroid frequencies—often exceeding the canonical high-frequency QPO (HFQPO) domain of a few hundred Hz and extending into the kilohertz regime—VHFQPOs serve as direct probes of the most extreme strong-field gravity and disk microphysics near the innermost regions of accretion flows. Recent theoretical models and select observational campaigns have placed VHFQPOs at the forefront of research into the structure of compact objects and the processes governing accretion in the strong-gravity limit.

1. Theoretical Foundations and Metric Dependence

The theoretical landscape of VHFQPOs is shaped by the underlying spacetime metric that determines the effective potential for matter orbiting compact objects. In standard black holes described by the Kerr metric, orbital dynamics near the innermost stable circular orbit (ISCO) yield characteristic frequencies (orbital $\Omega_\phi$, radial epicyclic %%%%1%%%%, and vertical epicyclic $\Omega_\theta$) that set the natural scale for QPO phenomena. For a test particle, these are given by

$$\Omega_r^2 = -\frac{1}{2g_{rr}\dot{t}^2}\frac{\partial^2 V_{\rm eff}}{\partial r^2}, \qquad \Omega_\theta^2 = -\frac{1}{2g_{\theta\theta}\dot{t}^2}\frac{\partial^2 V_{\rm eff}}{\partial \theta^2}, \qquad \Omega_\phi = \frac{d\phi}{dt}$$

where $V_{\rm eff}$ is the effective potential determined by the metric $g_{\mu\nu}$.

Recent models of compact, non-singular, horizonless objects (Boos et al., 1 Oct 2025) introduce a regulator length scale $L$ that removes the event horizon, modifying the metric function $f(r)$ near the origin and resulting in a new family of stable circular orbits for $r \ll r_{\rm ISCO}$,

$$ds^2 = -f(r) dt^2 + \frac{dr^2}{f(r)} + R^2(r) (d\theta^2 + \sin^2\theta d\phi^2)$$

with $f(r)$ expanded for small $r$ as

$$f(r) = 1 - f_0 - f_2 \left(\frac{r}{\ell}\right)^2 + f_n \left(\frac{r}{\ell}\right)^n + O\left[\left(\frac{r}{\ell}\right)^{n+1}\right]$$

where $\ell = L^\lambda (2GM)^{1-\lambda}$, and the inner stable circular orbit $r_{L-\text{ISCO}}$ is supported entirely by the regularization scale $L$.

The central implication is that, in horizonless models, VHFQPOs can arise due to orbital motions at $r_{L-\text{ISCO}} \ll r_{\text{ISCO}}$, leading to much higher frequencies than possible in standard black holes.

2. Frequency Domain, Scaling Relations, and Observational Outlook

Canonical HFQPOs in black holes and neutron stars typically span $30$–$300$ Hz and up to $1$ kHz, depending on mass and spin. In non-singular, horizonless models the allowed quasi-periodic oscillation frequencies are far higher,

$$\nu_{\rm VHFQPO} \sim 1~\mathrm{kHz} \quad (M \sim 10\,M_\odot)$$

extending up to

$$\nu_{\rm VHFQPO} \sim 25~\mathrm{kHz} \quad (M \sim 2\,M_\odot)$$

(Boos et al., 1 Oct 2025). The scaling is essentially $\nu \propto 1/M$, with the regulator $L$ setting the location and stability of the inner orbit. Unlike Kerr black holes—where orbits inside the ISCO are causally disconnected—the absence of a horizon in non-singular models allows oscillatory modes generated at $r_{L-\text{ISCO}}$ to propagate to infinity and, in principle, be detected as VHFQPOs.

No confirmed detections of QPO features in the $1$–$25$ kHz band from accreting stellar-mass systems currently exist, but their observation—or lack thereof—serves as a test for the presence or absence of an event horizon. The absence of VHFQPOs in current spectra is consistent with standard black hole models.

3. Physical Mechanisms and Disk Microphysics

Multiple mechanisms have been advanced to explain both HFQPOs and the hypothetical extension to VHFQPOs:

• GRMHD Alfvén Wave Models: In black hole accretion disks dominated by toroidal magnetic fields, linearized GRMHD equations yield two stable Alfvén wave modes in the transition region between the inner advection-dominated accretion flow and the outer thin disk (Shi et al., 2010). The dispersion relation,

$$[ω - α c (k·β)]^2 (γ^2ψ_0 + B_0^2) - (2α γ^2ψ_0 v_0 k)[ω - α c (k·β)] + α^2γ^2ψ_0 (k^2 v_0^2) - α^2c^2 k^2B_0^2 = 0$$

supports two oscillation frequencies; their ratio is very close to $3:2$, and both scale $\propto 1/M$. These Alfvén modes could, in principle, extend to very high frequencies if excited closer to the central object.

• Epicyclic Resonance and Relativistic Precession Models: Rapid orbital and epicyclic motions modulate X-ray flux at the characteristic frequencies dictated by the metric. The resonance condition

$\frac{\Omega_\theta}{\Omega_r} \approx \frac{3}{2}$

may shift to higher order in VHFQPO regimes and is sensitive to the local spacetime curvature, providing a strong probe for deviations from Kerr (Shahzadi et al., 2023).

• Rossby Wave Instability (RWI): Instabilities triggered at extrema of $$\mathcal{L} = (\Sigma \Omega / 2\kappa^2)(p/\Sigma^\gamma)$$ produce density waves and vortices, which, via ray-traced light curve modeling, yield mode mixtures (evolving $m$) and power spectra with multiple peaks below the ISCO frequency (Vincent et al., 2013). VHFQPOs may arise in extreme disk conditions.
• Disk-Corona Radiative Feedback: Coupled delays between stochastic accretion rate variation (disc) and corona response produce self-consistent feedback loops, generating QPO peaks at $f \approx 1/(\tau_\mathrm{A}+\tau_\mathrm{B})$ and harmonics (Garg et al., 16 Jul 2025): $$\delta\dot{\mathcal{M}}_T(\omega) = \frac{\delta\dot{\mathcal{M}}_I(\omega)}{1 - AB e^{-i\omega(\tau_A+\tau_B)} e^{-\omega^2(\sigma_A+\sigma_B)^2/2}}$$ Short delays in this framework can naturally drive VHFQPOs.
• Dissipation Physics and Spin Effects: Spatial distribution of vertical dissipation and black hole spin plays a pivotal role in power spectral density and QPO quality factors. High spin promotes sharp QPOs (Q up to $6$) and, via enhanced vertical epicyclic frequencies, could permit even higher (VHFQPO) frequencies (Dezen et al., 19 Aug 2025).

4. Constraints and Discriminants: Horizons versus Horizonless Objects

VHFQPOs have emerged as critical discriminants in the compact object taxonomy. In standard Kerr black holes, oscillatory modes inside the ISCO (and thus potential VHFQPOs) are concealed by the horizon. Non-singular horizonless metrics with $L \gtrsim GM$ produce observable VHFQPOs due to causal connectivity of $r_{L-\text{ISCO}}$ to infinity (Boos et al., 1 Oct 2025). Absence of VHFQPOs in observational data is taken as indirect evidence for an event horizon. Discovery of VHFQPO features at $1$–$25$ kHz in the power spectrum would strongly favor horizonless models.

5. Impact on Black Hole Accretion Physics and Observational Strategies

VHFQPOs probe dynamical regimes at radii where the gravitational field is strongest and thus provide a window into:

• The microphysics of the innermost accretion disk, including vertical structure, magnetohydrodynamic turbulence, and radiative transfer.
• The spacetime geometry and possible deviations from the Kerr solution, impacting the predictions for epicyclic and orbital frequencies (Shahzadi et al., 2023).
• Resonant and feedback processes that couple the disk and corona (Garg et al., 16 Jul 2025), potentially providing a unified view of both low and high-frequency QPO classes.

From an observational perspective, the requirements for VHFQPO detection include

• Large effective area instruments (e.g., LOFT-class X-ray telescopes) for adequate count rate to resolve kilohertz QPOs.
• Advanced power spectral fitting techniques that account for QPO harmonics and underlying broadband noise.
• Timely targeting of states with inner disk dominance and extreme variability, as seen in “heartbeat” systems (Wang et al., 18 Jan 2024).

Future detection (or null results) of VHFQPOs will directly constrain the compact object’s causal structure, the physical nature of the inner disk, and possibly even enforce or rule out the existence of horizons.

6. Synthesis and Future Directions

VHFQPOs, whether currently observed or primarily theorized, represent a potent probe of fundamental physics at the interface of strong-field gravity, accretion microphysics, and spacetime topology. Their existence, properties, and detectability hinge on the detailed spacetime metric near the compact object, the action of instabilities and feedback in the accretion flow, and the causal structure set by the presence or absence of an event horizon. Ongoing and future X-ray timing campaigns, coupled with advances in theoretical modeling—GRMHD simulations, non-singular metric construction, and detailed disk-corona microphysics—are expected to clarify the physical mechanism behind VHFQPOs and their role as potential discriminants between black holes and exotic horizonless compact objects. Careful cross-comparison of predictions for frequency scaling, quality factor, coherence, and spectral state dependence will be crucial in this endeavor.