[Paper Review] Rethinking the 67 Hz QPO in GRS 1915+105: type-C QPOs at the innermost stable circular orbit

S. Motta, T. Belloni|arXiv (Cornell University)|Jul 3, 2023

Astrophysical Phenomena and Observations5 citations

TL;DR

This paper reclassifies the 67 Hz quasi-periodic oscillation (QPO) in GRS 1915+105 as a type-C QPO driven by nodal precession at the innermost stable circular orbit (ISCO), using the Relativistic Precession Model (RPM) to derive a black hole spin of $ a_* = 0.706 \pm 0.034 $. This interpretation reconciles the QPO with relativistic dynamics and explains higher-frequency features as orbital and periastron precession frequencies at larger radii.

ABSTRACT

Context. The study of Quasi-Periodic Oscillations (QPO) at low and high frequency in the variability of the high-energy emission from black-hole binaries and their physical interpretation in terms of signatures of General Relativity in the strong-field regime. Aims. To understand the nature of the 67 Hz QPOs observed in the X-ray emission of the peculiar black-hole binary GRS 1915+105 within the general classification of QPO and to determine the spin of the black hole in the system by applying the Relativistic Precession Model (RPM). Methods. Within the RPM, the only relativistic frequency that is stable in time over a large range of accretion rates and can be as low as 67 Hz (for a black-hole mass as measured dynamically) is the Lense-Thirring frequency at the Innermost Stable Circular Orbit (ISCO). In the application of the model, this corresponds to type-C QPOs. Under this assumption, it is possible to measure the spin of the black hole. We re-analysed a large number of RossiXTE observations to check whether other timing features confirm this hypothesis. Results. The identification of the 67 Hz QPO as the Lense-Thirring frequency at ISCO yields a value of 0.706 +/- 0.034 for the black hole spin. With this spin, the only two QPO detections at higher frequencies available in the literature are consistent with being orbital frequencies at a radius outside ISCO. The high-frequency bumps often observed at frequencies between 10 and 200 Hz follow the correlation expected for orbital and periastron-precession frequencies at even larger radii.

Motivation & Objective

• To re-evaluate the physical origin of the 67 Hz QPO in GRS 1915+105, historically classified as a high-frequency QPO (HFQPO), within the framework of general relativity.
• To test whether the 67 Hz QPO can be interpreted as the nodal precession frequency at the innermost stable circular orbit (ISCO), a stable relativistic frequency in the strong-field regime.
• To determine the black hole spin in GRS 1915+105 using the RPM, leveraging the dynamically measured black hole mass and the 67 Hz QPO as a frequency anchor.
• To assess the consistency of higher-frequency timing features (10–200 Hz) with relativistic precession frequencies predicted by the RPM for the derived spin and mass.
• To evaluate whether timing-based spin measurements from the RPM align with gravitational wave and electromagnetic spin distributions, particularly in the context of black hole population synthesis.

Proposed method

• Applies the Relativistic Precession Model (RPM), which links QPO frequencies to orbital, nodal, and periastron precession frequencies in a Kerr spacetime.
• Uses the 67 Hz QPO as the nodal precession frequency at ISCO, assuming it corresponds to the precession of plasma orbiting at the innermost stable circular orbit.
• Employs the dynamically measured black hole mass ($ M = 12.4^{+2.0}_{-1.8} \, M_\odot $) from Reid et al. (2014) as a fixed input to the RPM to derive the spin parameter $ a_* $.
• Performs a re-analysis of a large sample of RossiXTE observations to confirm the stability and consistency of the 67 Hz QPO across different flux states.
• Compares predicted frequencies from the RPM (nodal, orbital, periastron precession) with observed PDS features across 10–200 Hz, identifying correlations with broad noise components and harmonic structures.
• Uses the derived spin to predict the locations of orbital and periastron precession frequencies, validating consistency with observed high-frequency features.

Experimental results

Research questions

• RQ1 Is the 67 Hz QPO in GRS 1915+105 better explained as a nodal precession frequency at the ISCO rather than a high-frequency QPO?
• RQ2 Can the Relativistic Precession Model (RPM) consistently explain the 67 Hz QPO and other high-frequency features in the power density spectrum of GRS 1915+105?
• RQ3 What is the implied black hole spin of GRS 1915+105 if the 67 Hz QPO is interpreted as the nodal frequency at ISCO?
• RQ4 Do the higher-frequency features (10–200 Hz) in the PDS align with orbital or periastron precession frequencies predicted by the RPM for the derived spin?
• RQ5 How do timing-based spin estimates from the RPM compare with those from other electromagnetic and gravitational wave methods?

Key findings

• The 67 Hz QPO in GRS 1915+105 is interpreted as the nodal precession frequency at the ISCO, consistent with the RPM and implying a moderately high black hole spin.
• The derived spin parameter is $ a_* = 0.706 \pm 0.034 $, based on the 67 Hz QPO and the dynamically measured black hole mass of $ 12.4^{+2.0}_{-1.8} \, M_\odot $.
• The two higher-frequency QPO detections in the literature are consistent with being orbital frequencies at radii outside the ISCO, given the derived spin.
• The broad high-frequency features between 10 and 200 Hz follow the expected correlation for orbital and periastron precession frequencies at larger radii, supporting the RPM interpretation.
• The timing-based spin estimate from the RPM is consistent with the spin distribution inferred from the LIGO/Virgo/KAGRA GWTC-3 catalog, suggesting similar spin populations in X-ray binaries and binary black holes.
• The identification of the 67 Hz QPO as a type-C QPO at ISCO resolves long-standing inconsistencies in classifying this feature and strengthens the RPM as a diagnostic tool for strong-field gravity.