Selected publications

Comparison between the new measurements obtained in this paper and the old values reported in the literature for spin (top left) and inclination (top right). The bottom-left panel shows a comparison between 1 − anew and 1 − aold in logarithmic scale, to better highlight the differences in measurements where both the initial and final spin are nearly maximal.

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

A Systematic View of Ten New Black Hole SpinsThe launch of NuSTAR and the increasing number of binary black hole (BBH) mergers detected through gravitational wave observations have exponentially advanced our understanding of BHs. Despite the simplicity owed to being fully described by their mass and angular momentum, BHs have remained mysterious laboratories that probe the most extreme environments in the universe. While significant progress has been made in the recent decade, the distribution of spin in BHs has not yet been understood. In this work, we provide a systematic analysis of all known BHs in X-ray binary systems (XBs) that have previously been observed by NuSTAR, but have not yet had a spin measurement made using the "relativistic reflection" method obtained from those data. By looking at all the available archival NuSTAR data of these sources, we measure 10 new BH spins: IGR J17454-2919 - $a={0.97}_{-0.17}^{+0.03};$ GRS 1758-258 - $a={0.991}_{-0.019}^{+0.007};$ MAXI J1727-203 - $a={0.986}_{-0.159}^{+0.012};$ MAXI J0637-430 - a = 0.97 ± 0.02; Swift J1753.5-0127 - $a={0.997}_{-0.003}^{+0.001};$ V4641 Sgr - $a={0.86}_{-0.06}^{+0.04};$ 4U 1543-47 - $a={0.98}_{-0.02}^{+0.01};$ 4U 1957+11 - $a={0.95}_{-0.04}^{+0.02};$ H 1743-322 - $a={0.98}_{-0.02}^{+0.01};$ and MAXI J1820+070 - $a={0.988}_{-0.028}^{+0.006}$ (all uncertainties are at the 1σ confidence level). We discuss the implications of our measurements on the entire distribution of stellar-mass BH spins in XBs, and we compare them with the spin distribution in BBHs, finding that the two distributions are clearly in disagreement. Additionally, we discuss the implications of this work on our understanding of how the "relativistic reflection" spin measurement technique works, and discuss possible sources of systematic uncertainty that can bias our measurements.

All current measurements of BH spins in XBs, obtained through continuum fitting (orange) or relativistic reflection. Spin measurements obtained through relativistic reflection using measurements from NuSTAR are indicated in blue, while reflection measurements using data from other instruments are shown in yellow. The new measurements of this paper are shown in green. The sources are ordered in increasing R.A., and the values and references for all measurements are presented in Table 6. The arrows indicate upper or lower limits.

Left: the MAXI light curve in the 2–20 keV band of the 2022–2023 outburst of XTE J2012+381 (top). The following five panels show the evolution of the measured Galactic column density NH, the inner disk temperature and normalization of the diskbb component, the power-law index Γ, and the normalization of the powerlaw component, obtained when fitting the NICER spectra of the source with the model TBabs*(diskbb+powerlaw). The seventh panel shows the exposure of the NICER observations analyzed, and the eighth panel shows the reduced χ2 returned by the fits to the NICER spectra. Right: the evolution of the measured disk temperature of the source (top) and of the 1–10 keV flux (bottom) vs. the hardness defined as the ratio of the 5–10 keV flux to the 2–5 keV flux. In the top panel, we omitted the measurements with an uncertainty larger than 0.5 keV. The colors of the points are the same as in the left panels and represent the time evolution of the source.

An Extreme Black Hole in the Recurrent X-Ray Transient XTE J2012+381The black hole (BH) candidate XTE J2012+381 underwent an outburst at the end of 2022. We analyzed 105 NICER observations and two NuSTAR observations of the source during the outburst. The NuSTAR observations of the M ~ 10 M ⊙ BH indicate clear signs of relativistic disk reflection, which we modeled to measure a BH spin of $a={0.988}_{-0.030}^{+0.008}$ and an inclination of $\theta ={68}_{-11}^{+6}$ deg (1σ statistical errors). In our analysis, we test an array of models and examine the effect of fitting NuSTAR spectra alone versus fitting simultaneously with NICER. We find that when the underlying continuum emission is properly accounted for, the reflected emission is similarly characterized by multiple models. We combined 52 NICER spectra to obtain a spectrum with an effective exposure of 190 ks in order to probe the presence of absorption lines that would be suggestive of disk winds, but the resulting features were not statistically significant. We discuss the implications of this measurement in relation to the overall BH spin distribution in X-ray binary systems.

The Spin of a Newborn Black Hole: Swift J1728.9-3613The origin and distribution of stellar-mass black hole spins are a rare window into the progenitor stars and supernova events that create them. Swift J1728.9-3613 is an X-ray binary, likely associated with the supernova remnant (SNR) G351.9-0.9. An NuSTAR X-ray spectrum of this source during its 2019 outburst reveals reflection from an accretion disk extending to the innermost stable circular orbit. Modeling of the relativistic Doppler shifts and gravitational redshifts imprinted on the spectrum measures a dimensionless spin parameter of a = 0.86 ± 0.02 (1σ confidence), a small inclination angle of the inner accretion disk θ < 10°, and a subsolar iron abundance in the disk A Fe < 0.84. This high spin value rules out a neutron star primary at the 5σ level of confidence. If the black hole is located in a still visible SNR, it must be young. Therefore, we place a lower limit on the natal black hole spin of a > 0.82, concluding that the black hole must have formed with a high spin. This demonstrates that black hole formation channels that leave an SNR, and those that do not (e.g., Cyg X-1), can both lead to high natal spin with no requirement for subsequent accretion within the binary system. Emerging disparities between the population of high-spin black holes in X-ray binaries and the low-spin black holes that merge in gravitational wave events may therefore be explained in terms of different stellar conditions prior to collapse, rather than different environmental factors after formation.

Panel (a) shows the unfolded spectrum of Swift J1728.9–3613. The blue points represent the spectrum from the NuSTAR FPMA detector, while the red points show the spectrum obtained from the FPMB sensor. The solid blue and red lines show the total model to the FPMA and FPMB spectra, while the dashed and dotted lines show the contribution to the model by the diskbb and relxill components, respectively. Panel (b) shows the residuals in terms of σ for the constant∗TBabs∗(diskbb+powerlaw) model. The residuals show clear indication of relativistic reflection. Panel (c) shows the residuals of the best-fit model, constant∗TBabs∗(diskbb+relxill).

Top: Stacked 1.28 GHz MeerKAT image of G351.9−0.9, with white contours at 25 μJy × (−3, 3, 6, 9, 12, 15) σ. The radio color bar indicates the flux density scale in janskys. The Chandra position of Swift J1728.9–3613 is indicated with a filled blue circle.

Bottom: Finder chart showing the IR emission from ESO-VISTA of Swift J1728. The red circle represents a region of radius equal to 1farcs3, centered at the known position of the source. The image was composed by displaying the Ks band in red, the H band in green, and the J band in blue.

The Black Hole Candidate Swift J1728.9-3613 and the Supernova Remnant G351.9-0.9A number of neutron stars have been observed within the remnants of the core-collapse supernova explosions that created them. In contrast, black holes are not yet clearly associated with supernova remnants (SNRs). Indeed, some observations suggest that black holes are "born in the dark," i.e., without a supernova explosion. Herein, we present a multiwavelength analysis of the X-ray transient Swift J1728.9-3613, based on observations made with Chandra, ESO-VISTA, MeerKAT, NICER, NuSTAR, Swift, and XMM-Newton. Three independent diagnostics indicate that the system likely harbors a black hole primary. Infrared imaging signals a massive companion star that is broadly consistent with an A or B spectral type. Most importantly, the X-ray binary lies within the central region of the cataloged SNR G351.9-0.9. Our deep MeerKAT image at 1.28 GHz signals that the remnant is in the Sedov phase; this fact and the nondetection of the soft X-ray emission expected from such a remnant argue that it lies at a distance that could coincide with the black hole. Utilizing a formal measurement of the distance to Swift J1728.9-3613 (d = 8.4 ± 0.8 kpc), a lower limit on the distance to G351.9-0.9 (d ≥ 7.5 kpc), and the number and distribution of black holes and SNRs within the Milky Way, extensive simulations suggest that the probability of a chance superposition is <1.7% (99.7% credible interval). The discovery of a black hole within an SNR would support numerical simulations that produce black holes and remnants, and thus provide clear observational evidence of distinct black hole formation channels. We discuss the robustness of our analysis and some challenges to this interpretation.

A New Spin on an Old Black Hole: NuSTAR Spectroscopy of EXO 1846-031The black hole candidate EXO 1846-031 underwent an outburst in 2019, after at least 25 yr in quiescence. We observed the system using NuSTAR on 2019 August 3. The 3-79 keV spectrum shows strong relativistic reflection features. Our baseline model gives a nearly maximal black hole spin value of $a={0.997}_{-0.002}^{+0.001}$ (1σ statistical errors). This high value nominally excludes the possibility of the central engine harboring a neutron star. Using several models, we test the robustness of our measurement to assumptions about the density of the accretion disk, the nature of the corona, the choice of disk continuum model, and the addition of reflection from the outer regions of the accretion disk. All tested models agree on a very high black hole spin value and a high value for the inclination of the inner accretion disk of $\theta \approx 73^\circ $ . We discuss the implications of this spin measurement in the population of stellar mass black holes with known spins, including LIGO and Virgo events.

Histogram of the spin-inclination parameter space for the mtable{nuMLIv1.mod}∗constant∗TBabs∗(diskbb+relxill+Gaussian) model. In the lower left panel, the red, blue, and green contours represent lines of 1σ, 2σ, and 3σ. The top left and lower right panels show the 1D histogram of the parameters. The yellow line represents the median of the distribution and the red lines represent the ±1σ confidence limits of the median. The top right panel represents the spin-inclination parameter space for the models presented in Table 1. The black dashed line shows the maximum theoretical prediction for the spin of a black hole with a thin disk of 0.998 (Thorne 1974).

Top: Panel (a) shows the unfolded spectrum of XTE J1908+094 when fit with model 6, requiring an inclination >79°. The colors of the spectra match those described in Figure 3. The dashed line shows the contribution of the diskbb component of the model, while the dotted line shows the contribution of the relxilllp component. Panels (b) and (c) show the residuals in terms of σ of the fits using the high inclination and free inclination models, respectively. The χ2 of the model requiring a high inclination is ∼85 worse than the model that allows a free inclination. Note the increased residuals at ∼7.4 keV (indicated by the vertical gray line) in panel (b) when compared to panel (c), suggesting that the high inclination model overpredicts the shape of the blue wing of the Fe K line. Panel (c) is a copy of panel (d) in Figure 3.

Right: The hardness ratio throughout the two observations computed as the ratio of the 8–20 keV count rate to the 3–8 keV count rate, as a function of the total 3–20 keV count rate. The blue points represent the 2013 observation, while the yellow points represent the 2019 one. The horizontal dashed lines show the hardness cuts placed on the two observations to divide them into the "high hardness" and "low hardness" spectra. The light curves were binned so that each point represents 200 s.

The Spin and Orientation of the Black Hole in XTE J1908+094NuSTAR 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 $\theta ={27}_{-3}^{+2}$ 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.

Multiband Optical Light Curves of Black-widow PulsarsWe collect new and archival optical observations of nine “black-widow” millisecond pulsar binaries. New measurements include direct imaging with the Keck, Gemini-S, MDM, and Las Cumbres Observatory 2 m telescopes. This is supplemented by synthesized colors from Keck long-slit spectra. Four black-widow optical companions are presented here for the first time. Together these data provide multicolor photometry covering a large fraction of the orbital phase. We fit these light curves with a direct (photon) heating model using a version of the ICARUS light-curve modeling code. The fits provide distance and fill-factor estimates, inclinations, and heating powers. We compare the heating powers with the observed GeV luminosities, noting that the ratio is sensitive to pulsar distance and to the gamma-ray beaming. We make a specific correction for “outer gap” model beams, but even then some sources are substantially discrepant, suggesting imperfect beaming corrections and/or errors in the fit distance. The fits prefer large metal abundance for half of the targets, a reasonable result for these wind-stripped secondaries. The companion radii indicate substantial Roche-lobe filling, f c ≈ 0.7-1 except for PSR J0952-0607, which with f c < 0.5 has a companion density ρ ≈ 10 g cm-3, suggesting unusual evolution. We note that the direct-heating fits imply large heating powers and rather small inclinations, and we speculate that unmodeled effects can introduce such bias.

Four BW light curves. Two periods are plotted; ϕB = 0 is at pulsar TASC (time of the pulsar ascending node). For J0952, photometry points during the "flare" at ϕB = 0.4–0.5 are not used in the fit. These are marked with open symbols. During the second cycle the error flags are omitted and the Isaac Newton Telescope (INT) r photometry is shown, for comparison.

Top: GMOS-N/NIRI/NIRC2 light curves. The data are phased to the ephemeris of Stovall et al. (2014), with ϕ = 0 at the pulsar ascending node; two periods are plotted for clarity. For the second period, the infrared points are the medians of the magnitudes during individual dither pointings. The model is an ICARUS direct heating fit to the data. Note the appreciable data fluctuations about the light curves, suggesting variability or finer substructure.

Right: Upper left panel: NIRC2 Ks image of PSR J0636+5128 (median of frames). Lower left panel: GMOS r image at maximum. Upper right panel: GMOS g image at maximum. Lower right panel: GMOS g image at minimum.

PSR J0636+5128: A Heated Companion in a Tight OrbitWe present an analysis of archival Gemini g‧, r‧, K and Keck H, K s imaging of this nearby short-period binary (P B = 95.8 minutes) 2.87 ms pulsar. The heated companion is clearly detected. Direct pulsar heating provides an acceptable model at the revised >700 pc parallax distance. The relatively shallow light curve modulation prefers an inclination i < 40° this high-latitude view provides a likely explanation for the lack of radio signatures of wind dispersion or eclipse. It also explains the low minimum companion mass and, possibly, the faintness of the source in X-rays and γ-rays.

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

Ratio of data to model produced when using models that do not account for relativistic reflection to fit the FPMA spectra from the 6 existing NuSTAR observations of EXO 1846-031 (blue) and similar simulated HEX-P LET (orange) and HET (red) spectra. The NuSTAR observations were taken during the 2019 outburst of EXO 1846-031. The HEX-P spectra were simulated to have an exposure equal to the existing NuSTAR observations, using the best-fit parameters determined when fitting the NuSTAR spectra with models that do account for relativistic reflection. The increased energy coverage of HEX-P paired with its increased sensitivity at high energies enables stronger constraints on the underlying continuum emission, reducing the degeneracy with the reflected radiation, enabling placing stronger constraints on the physical properties of the system.

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