Black Hole Spin Measurements Research Articles

Black hole spin estimation of XTE J2012+381 using simultaneous observations of Swift/XRT and NuSTAR

ABSTRACT A sufficiently precise measurement of black hole spin is required to carry out quantitative tests of the Kerr metric and to understand several phenomena related to astrophysical black holes. After 24 yr, XTE J2012+381 again underwent an outburst in 2022 December. In this work, we focused on the measurement of the spin and mass of the black hole candidate XTE J2012+381 using broad-band spectral analysis of X-ray data from Swift/XRT and NuSTAR. Using the relxillCp model, the spin and inclination of the source were found to be $0.883_{-0.061}^{+0.033}$ and $46.2_{-2.0}^{+3.7}$ deg, respectively, for high disc density ($i.e.\,\,10^{20}\,\,\mathrm{cm}^{-3}$). We further test our results for lamp-post geometry using the relxilllpCp model. The spin and inclination of the source were found to be $0.892_{-0.044}^{+0.020}$ and $43.1_{-1.2}^{+1.4}$ deg, respectively. Then ‘continuum-fitting’ method was used for the soft state to estimate the mass of BH and found to be $7.95_{-3.25}^{+7.65}\,\,\mathrm{M}_{\odot }$ and $7.48_{-2.75}^{+5.80}\,\,\mathrm{M}_{\odot }$ for the spin and inclination estimated from the relxillCp and relxilllpCp model, respectively. We used a distance of 5.4 kpc as measured by Gaia using the parallax method. This study also addresses the issue of supersolar iron abundance in XTE J2012+381 using reflionx-based reflection model and found high disc density for the source.

Systematically Revisiting All NuSTAR Spins of Black Holes in X-Ray Binaries

We extend our recent work on black hole spin in X-ray binary systems to include an analysis of 189 archival NuSTAR observations from 24 sources. Using self-consistent data reduction pipelines, spectral models, and statistical techniques, we report an unprecedented and uniform sample of 36 stellar-mass black hole spin measurements based on relativistic reflection. This treatment suggests that prior reports of low spins in a small number of sources were generally erroneous: our comprehensive treatment finds that those sources tend to harbor black holes with high spin values. Overall, within 1σ uncertainty, ∼86% of the sample are consistent with a ≥ 0.95, ∼94% of the sample are consistent with a ≥ 0.9, and 100% are consistent with a ≥ 0.7 (the theoretical maximum for neutron stars; a = cJ/GM 2). We also find that the high-mass X-ray binaries (those with A-, B-, or O-type companions) are consistent with a ≥ 0.9 within the 1σ errors; this is in agreement with the low-mass X-ray binary population and may be especially important for comparisons to black holes discovered in gravitational wave events. In some cases, different spectra from the same source yield similar spin measurements but conflicting values for the inclination of the inner disk; we suggest that this is due to variable disk winds obscuring the blue wing of the relativistic Fe K emission line. We discuss the implications of our measurements, the unique view of systematic uncertainties enabled by our treatment, and future efforts to characterize black hole spins with new missions.

Black Hole Spin Measurements in LMC X-1 and Cyg X-1 Are Highly Model Dependent

The black hole spin parameter, a *, was measured to be close to its maximum value of 1 in many accreting X-ray binaries. In particular, a * ≳ 0.9 was found in a number of studies of LMC X-1. These measurements were claimed to take into account both statistical and systematic uncertainties. We perform new measurements using a recent simultaneous observation by NICER and NuSTAR, providing a data set of high quality. We use the disk continuum method together with improved models for coronal Comptonization. With the standard relativistic disk model and optically thin Comptonization, we obtain values of a * similar to those obtained before. We then consider modifications to the standard model. Using a color correction of 2, we find a * ≈ 0.64–0.84. We then consider disks with dissipation in surface layers. To account for that, we assume the standard disk is covered by a warm and optically thick Comptonizing layer. Our model with the lowest χ 2 then yields a*≈0.40−0.32+0.41 . In order to test the presence of such effects in other sources, we also study an X-ray observation of Cyg X-1 by Suzaku in the soft state. We confirm the previous findings of a * > 0.99 using the standard model, but then we find a weakly constrained a*≈0.82−0.74+0.16 when including an optically thick Comptonizing layer. We conclude that determinations of the spin using the continuum method can be highly sensitive to the assumptions about the disk structure.

The High Energy X-ray Probe (HEX-P): probing accretion onto stellar mass black holes

Accretion is a universal astrophysical process that plays a key role in cosmic history, from the epoch of reionization to galaxy and stellar formation and evolution. Accreting stellar-mass black holes in X-ray binaries are one of the best laboratories to study the accretion process and probe strong gravity—and most importantly, to measure the angular momentum, or spin, of black holes, and its role as a powering mechanism for relativistic astrophysical phenomena. Comprehensive characterization of the disk-corona system of accreting black holes, and their co-evolution, is fundamental to measurements of black hole spin. Here, we use simulated data to demonstrate how key unanswered questions in the study of accreting stellar-mass black holes will be addressed by the High Energy X-ray Probe (HEX-P). HEX-P is a probe-class mission concept that will combine high spatial resolution X-ray imaging and broad spectral coverage (0.2–80 keV) with a sensitivity superior to current facilities (including XMM-Newton and NuSTAR) to enable revolutionary new insights into a variety of important astrophysical problems. We illustrate the capability of HEX-P to: 1) measure the evolving structures of black hole binary accretion flows down to low (≲ 0.1%) Eddington-scaled luminosities via detailed X-ray reflection spectroscopy; 2) provide unprecedented spectral observations of the coronal plasma, probing its elusive geometry and energetics; 3) perform detailed broadband studies of stellar mass black holes in nearby galaxies, thus expanding the repertoire of sources we can use to study accretion physics and determine the fundamental nature of black holes; and 4) act as a complementary observatory to a range of future ground and space-based astronomical observatories, thus providing key spectral measurements of the multi-component emission from the inner accretion flows of black hole X-ray binaries.

Research on the uncertainties of black hole spin measurement

Black hole is an important object and research object in astronomy and spin is one of the three physical quantities used to describe them. Its vital to get the spin parameter of a black hole as accurate as possible. Recently, researchers have used many methods to measure the spin parameter and two of them are most commonly used, the continuum-fitting method and the reflection-fitting method. Its difficult to avoid errors in the measurement of the two methods, but we can use various methods to minimize the error in the measurement. In this paper, we try to figure out using the two methods in measuring what kind of black holes spin can we reduce errors. We consider both the systematic error caused by model assumptions and the accidental error caused by dynamical parameter. Finally, we conclude that both the two methods can only measure black holes with certain accretion rate between 0.01 - 0.3. The continuum-fitting method can reduce errors in measuring high-spin black hole with small viscosity of the accretion disk. The reflection-fitting method can reduce errors in measuring high-spin/ low corona-height black hole.

Impact of the Accretion Disk Thickness on the Polarization of the Thermal Emission from Stellar Mass Black Holes

The Imaging X-ray Polarimetry Explorer, launched in 2021 December, enables precision measurements of the energy-dependent polarization of the X-ray emission from stellar mass and supermassive black holes. In this paper, we study the impact of the accretion disk geometry on the polarization of the thermal emission of mass-accreting stellar-mass black holes. We present a ray-tracing code that allows us to predict how the X-ray polarization energy spectra change as we dial up the thickness of the accretion disk from a geometrically thin accretion disk to a torus-shaped geometrically thick accretion disk. The results show that thicker disks can produce higher polarization degrees as the thick disk geometries lead to a larger fraction of X-rays reflecting off portions of the disk. We study the observational degeneracies between the disk shape on the one hand and the black hole spin and disk inclination on the other hand. We conclude with a discussion of the implications of our studies for black hole spin measurements.

Testing relativistic accretion disk models with GRO J1655‐40

AbstractBlack hole X‐ray binaries are ideal environments to test the accretion phenomena in the presence of strong gravitational potentials. KERRBB held an important place in the X‐ray spectral continuum method for measuring the black hole spin modeling the emission from the innermost regions of the accretion disk. In this work, we present the results of X‐ray spectral analysis using publicly available RXTE data of GRO J1655‐40 obtained during the 2005 outburst with the two relativistic accretion disk models, KERRBB and KYNBB. Our analysis showed that both models provide identical results with black hole spin measurements, disk temperature, and disk luminosity when the inner edge of the accretion disk is set at the innermost stable circular orbit (ISCO) for the same accretion rates. We could not obtain reasonable fits for ∼89% of the observations with a fixed black hole spin value at a* = 0.7 using both models. Allowing the spin parameter to vary improved the fit statistic significantly with reduced χ2 values being reduced from ∼10 to 100 to below 2. Both models revealed black hole spin values varying between 0.52 < a* < 0.94, which can be interpreted as a variable inner edge of the disk throughout different accretion states.

X-ray polarimetry as a tool to measure the black hole spin in microquasars: simulations of IXPE capabilities

ABSTRACT Measurements of the angular momentum (spin) of astrophysical black holes are extremely important, as they provide information on the black hole formation and evolution. We present simulated observations of an X-ray binary system with the Imaging X-ray Polarimetry Explorer (IXPE), with the aim to study the robustness of black hole spin and geometry measurements using X-ray polarimetry. As a representative example, we used the parameters of GRS 1915+105 in its former unobscured, soft state. In order to simulate the polarization properties, we modelled the source emission with a multicolour blackbody accounting for thermal radiation from the accretion disc, including returning radiation. Our analysis shows that the polarimetric observations in the X-ray waveband will be able to estimate both spin and inclination of the system with a good precision [without returning radiation we obtained for the lowest spin Δa ≤ 0.4 (0.4/0.998 ∼ 40 per cent) for spin and Δi ≤ 30° (30°/70$^\circ \, \sim$ 43 per cent) for inclination, while for the higher spin values we obtained Δa ≤ 0.12 (∼12 per cent) for spin and Δi ≤ 20° (∼29 per cent) for inclination, within 1σ errors]. When focusing on the case of returning radiation and treating inclination as a known parameter, we were able to successfully reconstruct spin and disc albedo in Δa ≤ 0.15 (∼15 per cent) interval and Δ albedo ≤0.45 (45 per cent) intervals within 1σ errors. We conclude that X-ray polarimetry will be a useful tool to constrain black hole spins, in addition to timing and spectral-fitting methods.

Population properties of spinning black holes using the gravitational-wave transient catalog 3

Binary black holes formed via different pathways are predicted to have distinct spin properties. Measuring these properties with gravitational waves provides an opportunity to unveil the origins of binary black holes. Recent work draws conflicting conclusions regarding the spin distribution observed by LIGO-Virgo-KAGRA (LVK). Some analyses suggest that a fraction of the observed black-hole spin vectors are significantly misaligned (by $>90\ifmmode^\circ\else\textdegree\fi{}$) relative to the orbital angular momentum. This has been interpreted to mean that some binaries in the LVK dataset are assembled dynamically in dense stellar environments. Other analyses find support for a subpopulation of binaries with negligible spin and no evidence for significantly misaligned spin---a result consistent with the field formation scenario. In this work, we study the spin properties of binary black holes in the third LVK gravitational-wave transient catalog. We find that there is insufficient data to resolve the existence of a subpopulation of binaries with negligible black-hole spin (the presence of this subpopulation is supported by a modest Bayes factor of 1.7). We find modest support for the existence of mergers with extreme spin tilt angles $>90\ifmmode^\circ\else\textdegree\fi{}$ (the presence of extreme-tilt binaries is favored by a Bayes factor of 10.1). Only one thing is clear based on gravitational-wave measurements of black hole spin: at least some of the LVK binaries formed in the field. At most 89% of binaries are assembled dynamically (99% credibility), though, the true branching fraction could be much lower, even negligible.

Black hole mass and spin measurements through the relativistic precession model: XTE J1859+226

ABSTRACT The X-ray light curves of accreting black holes and neutron stars in binary systems show various types of quasi-periodic oscillations (QPOs), the origin of which is still debated. The relativistic precession model identifies the QPO frequencies with fundamental time-scales from General Relativity, and has been proposed as a possible explanation of certain types of such oscillations. Under specific conditions (i.e. the detection of a particular QPOs triplet) such a model can be used to obtain self-consistent measurements of the mass and spin of the compact object. So far this has been possible only in the black hole binary GRO J1655-40. In the RXTE/PCA data from the 1999–2000 outburst of the black hole transient XTE J1859+226 we found a QPO triplet, and used the relativistic precession model to obtain high-precision measurements of the black hole mass and spin – M = (7.85 ± 0.46) M⊙, a* = 0.149 ± 0.005 – the former being consistent with the most recent dynamical mass determination from optical measurements. Similarly to what has been already observed in other black hole systems, the frequencies of the QPOs and broad-band noise components match the general relativistic frequencies of particle motion close to the compact object predicted by the model. Our findings confirm previous results and further support the validity of the relativistic precession model, which is the only electromagnetic-measurement-based method that so far has consistently yielded spins close to those from the gravitational waves produced by merging binary black holes.

Black hole spin measurements based on a thin disc model with finite thickness – I. An example study of MCG−06-30-15

ABSTRACT We present a re-analysis of the XMM–Newton and NuSTAR observing campaigns for the well-studied, X-ray-bright AGN MCG−06-30-15. In particular, we consider a disc model with finite thickness. By fitting the disc reflection spectra in the data, we obtain a black hole spin of 0.87–0.99 (90 per cent confidence range) after taking the thickness of the disc into consideration. Spectral models with a grid of mass accretion rate from 0 to $30{{\,\rm per\,cent}}\,\dot{M}_{\rm Edd}$ are calculated for MCG−06-30-15. This result is obtained by considering a free disc reflection fraction parameter frefl and is consistent with previous measurements based on razor-thin disc models. Besides, an isotropic, point-like geometry, i.e. the ‘lamppost’ geometry, is assumed for the corona in our model. We find that such a geometry overestimates frefl in the data. Therefore, thin disc models with consistent ‘lamppost’ values of frefl provide a worse fit than ones with a free frefl parameter. We discuss possible reasons for the discrepancy between the observed and theoretical values of frefl at the end of the paper. Modifications for the over-simplified lamppost model might be needed when the thickness of the thin disc is considered in future work.

XMM–Newton observations of the narrow-line Seyfert 1 galaxy IRAS 13224−3809: X-ray spectral analysis II

ABSTRACT Previously, we modelled the X-ray spectra of the narrow-line Seyfert 1 galaxy IRAS 13224−3809 using a disc reflection model with a fixed electron density of 1015 cm−3. An additional blackbody component was required to fit the soft X-ray excess below 2 keV. In this work, we analyse simultaneously five flux-resolved XMM–Newton spectra of this source comprising data collected over 2 Ms. A disc reflection model with an electron density of ne ≈ 1020 cm−3 and an iron abundance of $Z_{\rm Fe}=3.2\pm 0.5\, \mathrm{Z}_{\odot }$ is used to fit the broad-band spectra of this source. No additional component is required to fit the soft excess. Our best-fitting model provides consistent measurements of black hole spin and disc inclination angle as previous models where a low disc density was assumed. In the end, we calculate the average illumination distance between the corona and the reflection region in the disc of IRAS 13224−3809 based on best-fitting density and ionization parameters, which changes from 0.43$\sqrt{f_{\rm AD}/f_{\rm INF}}$ rg in the lowest flux state to 1.71$\sqrt{f_{\rm AD}/f_{\rm INF}}$ rg in the highest flux state assuming a black hole mass of $2\times 10^{6}\, \mathrm{M}_{\odot }$. fAD/fINF is the ratio between the flux of the coronal emission that reaches the accretion disc and infinity. This ratio depends on the geometry of the coronal region in IRAS 13224−3809. So we only discuss its value based on the simple ‘lamppost’ model, although detailed modelling of the disc emissivity profile of IRAS 13224−3809 is required in future to reveal the exact geometry of the corona.

Black hole spin-orbit misalignment in the x-ray binary MAXIJ1820+070.

The observational signatures of black holes in x-ray binary systems depend on their masses, spins, accretion rate, and the misalignment angle between the black hole spin and the orbital angular momentum. We present optical polarimetric observations of the black hole x-ray binary MAXIJ1820+070, from which we constrain the position angle of the binary orbital. Combining this with previous determinations of the relativistic jet orientation, which traces the black hole spin, and the inclination of the orbit, we determine a lower limit of 40° on the spin-orbit misalignment angle. The misalignment must originate from either the binary evolution or black hole formation stages. If other x-ray binaries have similarly large misalignments, these would bias measurements of black hole masses and spins from x-ray observations.

The spins of compact objects born from helium stars in binary systems

ABSTRACT The angular momentum (AM) content of massive stellar cores helps us to determine the natal spin rates of neutron stars and black holes. Asteroseismic measurements of low-mass stars have proven that stellar cores rotate slower than predicted by most prior work, so revised models are necessary. In this work, we apply an updated AM transport model based on the Tayler instability to massive helium stars in close binaries, in which tidal spin-up can greatly increase the star’s AM. Consistent with prior work, these stars can produce highly spinning black holes upon core-collapse if the orbital period is less than $P_{\rm orb} \lesssim \! 1 \, {\rm d}$. For neutron stars, we predict a strong correlation between the pre-explosion mass and the neutron star rotation rate, with millisecond periods ($P_{\rm NS} \lesssim 5 \, {\rm ms}$) only achievable for massive ($M \gtrsim 10 \, M_\odot$) helium stars in tight ($P_{\rm orb} \lesssim 1 \, {\rm d}$) binaries. Finally, we discuss our models in relation to type Ib/c supernovae, superluminous supernove, gamma-ray bursts, and LIGO/Virgo measurements of black hole spins. Our models are roughly consistent with the rates and energetics of these phenomena, with the exception of broad-lined Ic supernovae, whose high rates and ejecta energies are difficult to explain.

Hints of Spin-Orbit Resonances in the Binary Black Hole Population.

Binary black hole spin measurements from gravitational wave observations can reveal the binary's evolutionary history. In particular, the spin orientations of the component black holes within the orbital plane, ϕ_{1} and ϕ_{2}, can be used to identify binaries caught in the so-called spin-orbit resonances. In a companion paper, we demonstrate that ϕ_{1} and ϕ_{2} are best measured near the merger of the two black holes. In this work, we use these spin measurements to provide the first constraints on the full six-dimensional spin distribution of merging binary black holes. In particular, we find that there is a preference for Δϕ=ϕ_{1}-ϕ_{2}∼±π in the population, which can be a signature of spin-orbit resonances. We also find a preference for ϕ_{1}∼-π/4 with respect to the line of separation near merger, which has not been predicted for any astrophysical formation channel. However, the strength of these preferences depends on our prior choices, and we are unable to constrain the widths of the ϕ_{1} and Δϕ distributions. Therefore, more observations are necessary to confirm the features we find. Finally, we derive constraints on the distribution of recoil kicks in the population and use this to estimate the fraction of merger remnants retained by globular and nuclear star clusters. We make our spin and kick population constraints publicly available.

The Spin and Orientation of the Black Hole in XTE J1908+094

Abstract NuSTAR observed the black hole candidate XTE J1908+094 during its 2013 and 2019 outbursts. We use relativistic reflection to measure the spin of the black hole through 19 different assumptions of relxill flavors and parameter combinations. The most favored model in terms of the Deviance Information Criterion (DIC) measures the spin of the black hole to be a = 0.55 − 0.45 + 0.29 , and the inclination to be θ = 27 − 3 + 2 degrees (1σ statistical errors). We look at the effects of coronal geometry assumptions and the density of the accretion disk on the spin prediction. All 19 tested models provide consistent spin estimates. We discuss the evolution of spin measurement techniques using relativistic reflection in X-ray binaries and discuss the implications of this spin measurement in reconciling the distributions of stellar-mass black hole spin measurements made through X-ray and gravitational wave observations.

Stellar-mass Black Hole Spin Measurements and its Implementation

The spin of the black hole is one of the deterministic qualities for itself, providing us with the knowledge of its birth and evolution. In this review, I described two kinds of the spin measurements, respectively based upon electromagnetic waves and gravitational waves, and discuss the meaning for the black hole spin evolution indicated by the spin results measured by these methods. We find that for X-ray binaries, the spin results are much bigger than those results for natal spin, and for binary black holes the spin result are much smaller than those in X-ray binaries, which may be resulted from their different evolutions. For binary black holes detected through gravitational waves, formation channels of the binary systems are essential for interpreting spin results in these binary systems.

Disc tearing and Bardeen–Petterson alignment in GRMHD simulations of highly tilted thin accretion discs

ABSTRACT Luminous active galactic nuclei and X-ray binaries often contain geometrically thin, radiatively cooled accretion discs. According to theory, these are – in many cases – initially highly misaligned with the black hole equator. In this work, we present the first general relativistic magnetohydrodynamic simulations of very thin (h/r ∼ 0.015–0.05) accretion discs around rapidly spinning (a ∼ 0.9) black holes and tilted by 45°–65°. We show that the inner regions of the discs with h/r ≲ 0.03 align with the black hole equator, though out to smaller radii than predicted by analytic work. The inner aligned and outer misaligned disc regions are separated by a sharp break in tilt angle accompanied by a sharp drop in density. We find that frame dragging by the spinning black hole overpowers the disc viscosity, which is self-consistently produced by magnetized turbulence, tearing the disc apart and forming a rapidly precessing inner sub-disc surrounded by a slowly precessing outer sub-disc. We find that the system produces a pair of relativistic jets for all initial tilt values. At small distances, the black hole launched jets precess rapidly together with the inner sub-disc, whereas at large distances they partially align with the outer sub-disc and precess more slowly. If the tearing radius can be modeled accurately in future work, emission model independent measurements of black hole spin based on precession-driven quasi-periodic oscillations may become possible.

Testing the magnetic flux paradigm for AGN radio loudness with a radio-intermediate quasar

For understanding the diversity of jetted active galactic nuclei (AGN) and especially the puzzling wide range in their radio loudness, it is important to understand what role the magnetic fields play in setting the power of relativistic jets in AGN. We have performed VLBA phase-referencing observations of the radio-intermediate quasar IIIZw 2 to estimate jet magnetic flux by measuring the core-shift effect. Multi-frequency observations at 4 GHz, 8 GHz, 15 GHz, and 24 GHz were made using three nearby calibrators as reference sources. By combining the self-referencing core shift of each calibrator with the phase-referencing core shifts, we obtained an upper limit of 0.16 mas for the core shift between 4 and 24 GHz in IIIZw 2. By assuming equipartition between magnetic and particle energy densities and adopting the flux-freezing approximation, we further estimated the upper limit for both the magnetic field strength and poloidal magnetic flux threading the black hole. We find that the upper limit to the measured magnetic flux is smaller by at least a factor of five compared to the value predicted by the magnetically arrested disk (MAD) model. An alternative way to derive the jet magnetic field strength from the turnover of the synchrotron spectrum leads to an even smaller upper limit. Hence, the central engine of IIIZw 2 has not reached the MAD state, which could explain why it has failed to develop a powerful jet even though the source harbours a fast-spinning black hole. However, it generates an intermittent jet, which is possibly triggered by small-scale magnetic field fluctuations, as predicted by the magnetic flux paradigm. We propose here that combining black hole spin measurements with magnetic field measurements from the very-long-baseline-interferometry core-shift observations of AGN over a range of jet powers could provide a strong test for the dominant factor that sets the jet power relative to the available accretion power.

Towards Precision Measurements of Accreting Black Holes Using X-Ray Reflection Spectroscopy

Relativistic reflection features are commonly observed in the X-ray spectra of accreting black holes. In the presence of high quality data and with the correct astrophysical model, X-ray reflection spectroscopy can be quite a powerful tool to probe the strong gravity region, study the morphology of the accreting matter, measure black hole spins, and possibly test Einstein's theory of general relativity in the strong field regime. In the last decade, there has been significant progress in the development of the analysis of these features, thanks to more sophisticated astrophysical models and new observational facilities. Here we review the state-of-the-art in relativistic reflection modeling, listing assumptions and simplifications that may affect, at some level, the final measurements and may be investigated better in the future. We review black hole spin measurements and the most recent efforts to use X-ray reflection spectroscopy for testing fundamental physics.