Which methods are used to estimate a black hole's spin?

• A. Modeling the continuum spectrum of the accretion disk, iron K-alpha line profiles, and QPOs.
• B. Measuring the galaxy's rotation curve.
• C. Observing the color of the host galaxy.
• D. Tracking the orbit of a single star at large radius.

Answer: (A)

Spin shows up in the innermost region around a black hole, where the accretion disk emits X-rays. The continuum spectrum from the disk depends on how close the disk can extend toward the hole, which is set by the innermost stable circular orbit (ISCO). The ISCO moves inward for higher spin, changing the disk’s temperature distribution and the shape of the thermal spectrum. By fitting the observed continuum with disk models, we can infer how close the inner edge sits and thus estimate the spin.

The iron K-alpha line also carries a clear signature. Emitted from the inner disk, this fluorescence line is broadened and skewed by rapid orbital motion and strong gravity near the black hole. The exact broadening pattern acts as a fingerprint of how deep the disk reaches toward the event horizon, giving another route to the spin.

Quasi-periodic oscillations offer a timing handle on the same inner-disk physics. Their frequencies relate to orbital and precession motions near the black hole, which depend on spin. When these timing signals are combined with spectral features, they provide a more robust spin estimate within the assumptions of the underlying models.

In contrast, measuring the galaxy’s rotation curve maps mass on large scales around the galaxy and tells you nothing definitive about the black hole’s spin. The host galaxy’s color reflects stellar populations, not the spin. Tracking a star far from the black hole probes the overall gravitational potential at large radii, where the hole’s spin has only a tiny influence. So those methods don’t yield meaningful spin measurements.