Another look at Black Hole Spins

TL;DR

This paper discusses the fundamental question of whether black holes rotate and how fast, highlighting observational challenges and future prospects for precise spin measurements.

Contribution

It provides a comprehensive review of current challenges and future opportunities in measuring black hole spins.

Findings

Current observational methods face significant challenges.

Future facilities may enable more precise spin measurements.

Understanding black hole spins has broad astrophysical implications.

Abstract

Do black holes rotate, and if yes, how fast? This question is fundamental and has broad implications, but still remains open. There are significant observational challenges in current spin determinations, and future facilities offer prospects for precision measurements.

Full text

The spin of a black hole (BH) is interesting not only ”because it is there‫”‬ (G. Mallory, on why climb Mt. Everest), but also because it tells us about the history of the angular momentum distribution of the material from which the BH formed and grew, and the efficiency at which this material was converted to energy, and thus the potential impact on the surrounding medium. Recent developments and future prospects on observing BH spin are comprehensively reviewed by Reynolds1. The purpose of this comment is to mention some pitfalls in the current techniques, and point out ways to get higher precision. The comment concerns mostly massive BHs in Active Galactic Nuclei (AGNs), where $>99.99$% of currently known BHs reside.

How can one measure the BH spin? The BH spin sets the radius of the innermost marginally stable orbit, $r_{\rm in}$, inwards of which matter cannot remain on a stable circular orbit, and falls freely to the BH. For a non spinning BH $r_{\rm in}=6r_{g}$ ($r_{g}=GM/c^{2}$), and for a maximally spinning BH $r_{\rm in}=1.23r_{g}$ [2]. So, measuring $r_{\rm in}$ will tell us the spin.

How do we measure $r_{\rm in}$? Material spinning near the BH may produces both continuum and line emission. The Fe K$\alpha$ fluorescence line at 6.4 keV, inevitably produced when X-rays illuminates gas at $T<10^{7}$ K, is potentially a particularly powerful diagnostic. The line profile is a sensitive measure of both the gas kinematics and the gravitational potential. Figure 1 [3] presents the disk line profile from the inner disk region at $r<6r_{g}$, required to measure the value of the spin. For a nearly face on view ($\mu=0.99$, where $\mu=\cos\theta$, and $\theta=0$ for a face on view), this emission produces just a low energy tail for the K$\alpha$ line at $\sim 3.5-5$ keV with a peak flux of only $\sim 15$% of the peak of the outer disk line flux. At an intermediate inclination ($\mu=0.5$), gravitational redshift and Doppler boosting conspire to produce emission line profiles from the inner and outer disk ($r>6r_{g}$) which are nearly identical. Only for a close to edge-on view ($\mu=0.1$, $\theta=84\deg$) the difference becomes dramatic. The inner disk line is highly Doppler boosted, peaks at 9 keV, and drops sharply to zero at 9.5 keV. The catch is that AGNs observed at $\mu<0.5$ are likely obscured by the famous obscuring torus. Such highly boosted lines have indeed never been observed4. In most objects with disk line detections, the profile fits give $\mu>0.5$ [4], as expected from the AGN obscuration scheme.

On top of this theoretically implied detection challenge, there are a host of observational challenges. The expected line equivalent width of $\sim 150eV$ [5], together with a typical width of $\sim 1keV$ [3], implies that the line flux rises on average by only $\sim 15$% above the continuum, and the inner disk flux will rise by only $\sim 2-3$% for a close to face on view. One therefore needs a rather high S/N spectrum, which is not commonly available in AGN X-ray spectroscopy. In addition, the exact shape of the underlying x-ray continuum is not really known. The power-law description is just a phenomenological local approximation, which breaks below 1-2 keV, and above 10-20 keV [6], and a local spectral curvature can be mistaken as a broad line feature. In addition, the X-ray spectral region is often rich in absorption and emission features6, which may also make it hard to constrain the net line emission. Line broadening may also occur due to scattering of the photons by hot and cold electrons as the photons propagate out, producing blue and red line wings7.

Despite all the above difficulties and systematic effects, what saves the day is that an accretion disk line profile has a robust signature. A very sharp and steep blue wing, and a shallow and extended red wing (Figure 1 [3]). This signature, is indeed clearly observed in a few high quality spectra (Figure 1 [8]), that likely prove beyond reasonable doubt that disk lines are indeed observed.

X-ray binaries (XRBs), which host stellar mass BHs, are typically $10^{4}$ times brighter in the X-rays than the brightest AGN. This provides an X-ray spectrum with effectively unlimited S/N (e.g. $\sim 10^{6}$ counts at 6-7 keV [9]). Can we measure the BH spin accurately in these object? Formally, yes, but the complex spectral shape and the multitude of additional free parameters required to obtain a fit (26 free parameters9), makes one worry about the solution degeneracy. What is more worrying is that the broad K$\alpha$ profile looks like a very broad base at 5-9 keV, and does not really show the disk line profile signature, observed in AGNs. This raises the suspicion that other line broadening mechanisms may be involved, such as electron scattering, given the hot inner disk in XRBs ($10^{7}$K) compared to the cooler disks in AGNs ($10^{5}$K).

Although disk line profiles can probe the BH spin, an accurate value requires a close to edge on system, showing a highly blue shifted profile. Such a system remains to be discovered. Can the disk continuum emission can be used instead as a more accurate probe of the BH spin?

An accretion disk extending below $6r_{g}$ inevitably produces significant continuum emission at $r<6r_{g}$. In fact, if the BH is maximally spinning (i.e. $r_{\rm in}=1.23r_{g}$) then $\sim 80$% of the radiation is produced at the inner disk. The five fold increase in the radiative efficiency (from $\sim 6$% to $\sim 30$%), moving from a non spinning to a maximally spinning BH, should have a dramatic effect on the spectral energy distribution (SED). However, this assumes we know what radiation is exactly produced there. The standard thin accretion disk model indeed provides such a prediction10, which formally allows an accurate determination of $r_{\rm in}$ from the SED, and thus the BH spin (once the BH mass and the disk inclination are known). The model works well in the optical emitting region, and likely also in the near IR and near UV, but it generally fails completely in the far UV bluewards of 1000 Å. The hot inner thin disk emitting regions at $T>30,000$K, required to measure $r_{\rm in}$, are just not there11. A possible physical mechanism leading to the observed breakdown of the thin accretion disk solution, is the inevitable sharp rise in the gas opacity at $T>30,000$K. The opacity rise puffs up the disk, and may lead to a radiation pressure driven wind, as observed in O stars11, or to a thick configuration where the emission may be far from just a simple local blackbody radiation.

Is there any way to avoid the opacity effect? If the accretion disk surface area is large enough (i.e around more massive BHs), and the accretion rate is low enough, the flux per unit area may be low enough to produce $T<30,000$K throughout, and the UV opacity rise is avoided. Indeed, one such case appears to be observed12,13. Since the SED solution is degenerate with the BH spin and disk inclination, the spin can only be constrained to have low values. Clearly, followup of similar objects is worthwhile, as this may be a particularly simple and potentially robust way to measure the spin, in particular for the most massive BHs.

In stellar mass BH systems the accretion disk is predicted to be $\sim 100$ times hotter, with peak emission at a couple of keV. Indeed, the SED of X-ray binaries in the soft-high-state is well fit by simple thermal thin disk models (up to electron scattering effects), which allow to constrain the BH spin14. The surface temperature is hot enough to eliminate almost all of the bound electrons, which reduces the opacity to the minimal possible value of electron scattering only. The accretion disk likely remains thin all the way to $r_{\rm in}$. For that reason, the classical $\alpha$-disk model was initially constructed for such systems10, rather than for massive BHs (R. Sunyaev, private communication).

The BH spin in X-ray binaries does not teach us about the spins of massive BHs, as these are formed by entirely different mechanisms (instantaneous core collapse, versus accretion over 10-100 million years). An accurate spin value can be derived if the other system parameters, in particular the absolute luminosity, the BH mass and the disk inclination can be constrained well by other means. This is a challenge for X-ray binaries, but is likely much simpler in AGNs, using the Hubble expansion law, the broad line region, and potentially the continuum polarisation.

Any other means to measure the spin? At $r>6r_{g}$ the metric is effectively independent of the spin2, so whatever process is probed, it has to take place at $r<6r_{g}$ (or $r<9r_{g}$ for a negative spin). Numerous various other probes were suggested, but the associated uncertainties appear too high to derive well constrained spin values.

There are two important exceptions. The nearest massive BH at the Galactic centre, where GRAVITY15, and potentially also the Event Horizon Telescoe16, may be able to image this region directly, and eventually measure the BH spin. If these extremely powerful new technologies will be further improved, they may allow precision spin measurements of some of the nearest massive BHs.

The other important exception is the LIGO/Virgo experiment, which is already providing spin result in merging stellar mass binary BH systems. Extension to space with LISA will allow to measure the spins of merging massive BHs. The only caveat to this on-going revolution is that these results may not apply for isolated massive BHs.

It is interesting to note that the words, black hole and spin, appear together in the abstracts of 3200 refereed papers on ADS, of which 240 appeared in 2018. This rate of about one new paper (mostly theoretical) per work day, stresses the relevance of BH spins to a wide range of subjects, and the importance of measuring the BH spins as precisely as possible. To do that we first need to understand well the innermost structure of AGNs. The fruits we pick on the way on our journey towards the BH spin, may eventually turn out to be the real feast.

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