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The black hole X-ray binary H1743-322 lies in a region of the Galaxy with high extinction, and therefore it has not been possible to make a dynamical mass measurement. In this paper we make use of a recent model which uses the X-ray reflection spectrum to constrain the ratio of the black hole mass to the source distance. By folding in a reported distance measurement, we are able to estimate the mass of the black hole to be $12\pm2~\text{M}_\odot$ ($1\sigma$ credible interval). We are then able to revise a previous disc continuum fitting estimate of black hole spin $a_*$ (previously relying on a population mass distribution) using our new mass constraint, finding $a_*=0.47\pm0.10$. This work is a proof of principle demonstration of the method, showing it can be used to find the mass of black holes in X-ray binaries., Comment: 13 pages, 7 figures. Accepted for publication in MNRAS

We present the first X-ray spectropolarimetric results for Cygnus X-1 in its soft state from a campaign of five IXPE observations conducted during 2023 May-June. Companion multiwavelength data during the campaign are likewise shown. The 2-8 keV X-rays exhibit a net polarization degree PD=1.99%+/-0.13% (68% confidence). The polarization signal is found to increase with energy across IXPE's 2-8 keV bandpass. The polarized X-rays exhibit an energy-independent polarization angle of PA=-25.7+/-1.8 deg. East of North (68% confidence). This is consistent with being aligned to Cyg X-1's AU-scale compact radio jet and its pc-scale radio lobes. In comparison to earlier hard-state observations, the soft state exhibits a factor of 2 lower polarization degree, but a similar trend with energy and a similar (also energy-independent) position angle. When scaling by the natural unit of the disk temperature, we find the appearance of a consistent trendline in the polarization degree between soft and hard states. Our favored polarimetric model indicates Cyg X-1's spin is likely high (a* above ~0.96). The substantial X-ray polarization in Cyg X-1's soft state is most readily explained as resulting from a large portion of X-rays emitted from the disk returning and reflecting off the disk surface, generating a high polarization degree and a polarization direction parallel to the black hole spin axis and radio jet. In IXPE's bandpass, the polarization signal is dominated by the returning reflection emission. This constitutes polarimetric evidence for strong gravitational lensing of X-rays close to the black hole., Comment: 20 pages, accepted for publication in ApJL

Recent observations of X-ray pulsars (XRPs) performed by the Imaging X-ray Polarimetry Explorer (IXPE) have made it possible to investigate the intricate details of these objects in a new way, thanks to the added value of X-ray polarimetry. Here we present the results of the IXPE observations of SMC X-1, a member of the small group of XRPs displaying super-orbital variability. SMC X-1 was observed by IXPE three separate times during the high state of its super-orbital period. The observed luminosity in the 2-8 keV energy band of $L=2\times10^{38}$ erg/s makes SMC X-1 the brightest XRP ever observed by IXPE. We detect significant polarization in all three observations, with values of the phase-averaged polarization degree (PD) and polarization angle (PA) of $3.2\pm0.8$% and $97\deg\pm8\deg$ for Observation 1, $3.0\pm0.9$% and $90\deg\pm8\deg$ for Observation 2, and $5.5\pm1.1$% and $80\deg\pm6\deg$ for Observation 3, for the spectro-polarimetric analysis. The observed PD shows an increase over time with decreasing luminosity, while the PA decreases in decrements of 10\deg. The phase-resolved spectro-polarimetric analysis reveals significant detection of polarization in three out of seven phase bins, with the PD ranging between 2% and 10%, and a corresponding range in the PA from $\sim$70\deg\ to $\sim$100\deg. The pulse-phase resolved PD displays an apparent anti-correlation with the flux. Using the rotating vector model, we obtain constraints on the pulsar's geometrical properties for the individual observations. The position angle of the pulsar displays an evolution over time supporting the idea that we observe changes related to different super-orbital phases. Scattering in the wind of the precessing accretion disk may be responsible for the behavior of the polarimetric properties observed during the high-state of SMC X-1's super-orbital period., Comment: 11 pages, 11 figures, submitted to A&A

The Neutron Star Interior Composition Explorer (NICER) monitoring campaign of Cyg X-1 allows us to study its spectral-timing behavior at energies ${<}1$ keV across all states. The hard state power spectrum can be decomposed into two main broad Lorentzians with a transition at around 1 Hz. The lower-frequency Lorentzian is the dominant component at low energies. The higher-frequency Lorentzian begins to contribute significantly to the variability above 1.5 keV and dominates at high energies. We show that the low- and high-frequency Lorentzians likely represent individual physical processes. The lower-frequency Lorentzian can be associated with a (possibly Comptonized) disk component, while the higher-frequency Lorentzian is clearly associated with the Comptonizing plasma. At the transition of these components, we discover a low-energy timing phenomenon characterized by an abrupt lag change of hard (${\gtrsim}2$ keV) with respect to soft (${\lesssim}1.5$ keV) photons, accompanied by a drop in coherence, and a reduction in amplitude of the second broad Lorentzian. The frequency of the phenomenon increases with the frequencies of the Lorentzians as the source softens and cannot be seen when the power spectrum is single-humped. A comparison to transient low-mass X-ray binaries shows that this feature does not only appear in Cyg X-1, but that it is a general property of accreting black hole binaries. In Cyg X-1, we find that the variability at low and high energies is overall highly coherent in the hard and intermediate states. The high coherence shows that there is a process at work which links the variability, suggesting a physical connection between the accretion disk and Comptonizing plasma. This process fundamentally changes in the soft state, where strong red noise at high energies is incoherent to the variability at low energies., Comment: 18+29 pages, 17+54 figures, accepted for publication in Astronomy & Astrophysics

Black-hole X-ray binaries exhibit different spectral and timing properties in different accretion states. The X-ray outburst of a recently discovered and extraordinarily bright source, Swift$~$J1727.8$-$1613, has enabled the first investigation of how the X-ray polarization properties of a source evolve with spectral state. The 2$-$8 keV polarization degree was previously measured by the Imaging X-ray Polarimetry Explorer (IXPE) to be $\approx$ 4% in the hard and hard intermediate states. Here we present new IXPE results taken in the soft state, with the X-ray flux dominated by the thermal accretion-disk emission. We find that the polarization degree has dropped dramatically to $\lesssim$ 1%. This result indicates that the measured X-ray polarization is largely sensitive to the accretion state and the polarization fraction is significantly higher in the hard state when the X-ray emission is dominated by up-scattered radiation in the X-ray corona. The combined polarization measurements in the soft and hard states disfavor a very high or low inclination of the system., Comment: 9 pages, 7 figures

Accretion around black holes is very often characterized by distinctive X-ray reflection features (mostly, iron inner-shell transitions), which arise due to the primary radiation being reprocessed by a dense and relatively colder medium, such as an accretion disk. Most reflection modeling assume that emission stops at the inner-most stable circular orbit (ISCO), and that for smaller radii - in the plunging region - the density drops and the accretion flow is far too ionized for efficient line production. We investigate the spectral features of the reflection in the plunging regions of optically-thick and geometrically-thin accretion disks around black holes. We show that for cases in which the density profile is considered constant (as expected in highly magnetized flows), or in cases in which the disk density is high enough such that the ionization still allows line formation within the ISCO, there is a significant modification of the observed reflected spectrum. Consistent with previous studies, we found that the impact of the radiation reprocessed in the plunging region is stronger the lower the black hole spin, when the plunging region subtends a larger area. Likewise, as for the case of standard reflection modeling, the relativistic broadening of the iron line is more pronounced at low inclination, whereas the blueshift and relativistic beaming effect is dominant at high inclination. We also tested the effects of various prescriptions of the stress at the ISCO radius on the reflection spectrum, and found that several of these cases appear to show line profiles distinct enough to be distinguishable with reasonably good quality observational data., Comment: 16 pages, 8 figures, in preparation for submission - comments welcome

The Imaging X-ray Polarimetry Explorer (IXPE) measured with high significance the X-ray polarization of the brightest Z-source Scorpius X-1, resulting in the nominal 2-8 keV energy band in a polarization degree of 1.0(0.2)% and a polarization angle of 8(6){\deg} at 90% of confidence level. This observation was strictly simultaneous with observations performed by NICER, NuSTAR, and Insight-HXMT, which allowed for a precise characterization of its broad-band spectrum from soft to hard X-rays. The source has been observed mainly in its soft state, with short periods of flaring. We also observed low-frequency quasi-periodic oscillations. From a spectro-polarimetric analysis, we associate a polarization to the accretion disk at <3.2% at 90% of confidence level, compatible with expectations for an electron-scattering dominated optically thick atmosphere at the Sco X-1 inclination of 44{\deg}; for the higher-energy Comptonized component, we obtain a polarization of 1.3(0.4)%, in agreement with expectations for a slab of Thomson optical depth of ~7 and an electron temperature of ~3 keV. A polarization rotation with respect to previous observations by OSO-8 and PolarLight, and also with respect to the radio-jet position angle, is observed. This result may indicate a variation of the polarization with the source state that can be related to relativistic precession or to a change in the corona geometry with the accretion flow.

We report on an observational campaign on the bright black hole X-ray binary Swift J1727.8$-$1613 centered around five observations by the Imaging X-ray Polarimetry Explorer (IXPE). These observations track for the first time the evolution of the X-ray polarization of a black hole X-ray binary across a hard to soft state transition. The 2--8 keV polarization degree decreased from $\sim$4\% to $\sim$3\% across the five observations, but the polarization angle remained oriented in the North-South direction throughout. Based on observations with the Australia Telescope Compact Array (ATCA), we find that the intrinsic 7.25 GHz radio polarization aligns with the X-ray polarization. Assuming the radio polarization aligns with the jet direction (which can be tested in the future with higher spatial resolution images of the jet), our results imply that the X-ray corona is extended in the disk plane, rather than along the jet axis, for the entire hard intermediate state. This in turn implies that the long ($\gtrsim$10 ms) soft lags that we measure with the Neutron star Interior Composition ExploreR (NICER) are dominated by processes other than pure light-crossing delays. Moreover, we find that the evolution of the soft lag amplitude with spectral state does not follow the trend seen for other sources, implying that Swift J1727.8$-$1613 is a member of a hitherto under-sampled sub-population., Comment: Accepted for publication in ApJ. 21 pages, 8 figures

During the outbursts of black hole X-ray binaries (BHXRBs), their accretion flows transition through several states. The source luminosity rises in the hard state, dominated by non-thermal emission, before transitioning to the blackbody-dominated soft state. As the luminosity decreases, the source transitions back into the hard state and fades to quiescence. This picture does not always hold, as $\approx$ 40$\%$ of the outbursts never leave the hard state. Identifying the physics that govern state transitions remains one of the outstanding open questions in black hole astrophysics. In this paper we present an analysis of archival RXTE data of multiple outbursts of GX 339-4. We compare the properties of the X-ray variability and time-averaged energy spectrum and demonstrate that the variability (quantified by the power spectral hue) systematically evolves $\approx$ 10-40 days ahead of the canonical state transition (quantified by a change in spectral hardness); no such evolution is found in hard state only outbursts. This indicates that the X-ray variability can be used to predict if and when the hard-to-soft state transition will occur. Finally, we find a similar behavior in ten outbursts of four additional BHXRBs with more sparse observational coverage. Based on these findings, we suggest that state transitions in BHXRBs might be driven by a change in the turbulence in the outer regions of the disk, leading to a dramatic change in variability. This change is only seen in the spectrum days to weeks later, as the fluctuations propagate inwards towards the corona., Comment: Accepted for publication in ApJ

We report the first detection of the X-ray polarization of the bright transient Swift J1727.8-1613 with the Imaging X-ray Polarimetry Explorer. The observation was performed at the beginning of the 2023 discovery outburst, when the source resided in the bright hard state. We find a time- and energy-averaged polarization degree of 4.1%+/-0.2% and a polarization angle of 2.2+/-1.3 degrees (errors at 68% confidence level; this translates to about 20-sigma significance of the polarization detection). This finding suggests that the hot corona emitting the bulk of the detected X-rays is elongated, rather than spherical. The X-ray polarization angle is consistent with that found in sub-mm wavelengths. Since the sub-mm polarization was found to be aligned with the jet direction in other X-ray binaries, this indicates that the corona is elongated orthogonal to the jet., Comment: 10 pages, 3 figures, submitted

X-ray polarization is a powerful tool to investigate the geometry of accreting material around black holes, allowing independent measurements of the black hole spin and orientation of the innermost parts of the accretion disk. We perform the X-ray spectro-polarimetric analysis of an X-ray binary system in the Large Magellanic Cloud, LMC X-3, that hosts a stellar-mass black hole, known to be persistently accreting since its discovery. We report the first detection of the X-ray polarization in LMC X-3 with the Imaging X-ray Polarimetry Explorer, and find the average polarization degree of 3.2% +- 0.6% and a constant polarization angle -42 deg +- 6 deg over the 2-8 keV range. Using accompanying spectroscopic observations by NICER, NuSTAR, and the Neil Gehrels Swift observatories, we confirm previous measurements of the black hole spin via the X-ray continuum method, a ~ 0.2. From polarization analysis only, we found consistent results with low black-hole spin, with an upper limit of a < 0.7 at a 90% confidence level. A slight increase of the polarization degree with energy, similar to other black-hole X-ray binaries in the soft state, is suggested from the data but with a low statistical significance., Comment: 14 pages, 8 figures, submitted to ApJ

This paper reports the first detection of polarization in the X-rays for atoll-source 4U 1820-303, obtained with the Imaging X-ray Polarimetry Explorer (IXPE) at 99.999% confidence level (CL). Simultaneous polarimetric measurements were also performed in the radio with the Australia Telescope Compact Array (ATCA). The IXPE observations of 4U 1820-303 were coordinated with Swift-XRT, NICER, and NuSTAR aiming to obtain an accurate X-ray spectral model covering a broad energy interval. The source shows a significant polarization above 4 keV, with a polarization degree of 2.0(0.5)% and a polarization angle of -55(7) deg in the 4-7 keV energy range, and a polarization degree of 10(2)% and a polarization angle of -67(7) deg in the 7-8 keV energy bin. This polarization also shows a clear energy trend with polarization degree increasing with energy and a hint for a position-angle change of about 90 deg at 96% CL around 4 keV. The spectro-polarimetric fit indicates that the accretion disk is polarized orthogonally to the hard spectral component, which is presumably produced in the boundary/spreading layer. We do not detect linear polarization from the radio counterpart, with a 99.97% upper limit of 50% at 7.25 GHz.

Accreting black holes commonly exhibit hard X-ray emission, originating from a region of hot plasma near the central engine referred to as the corona. The origin and geometry of the corona are poorly understood, and models invoking either inflowing or outflowing material (or both) can successfully explain only parts of the observed phenomenology. In particular, recent works indicate that the time-averaged and variability property might originate in different regions of the corona. In this paper we present a model designed to move beyond the lamp post paradigm, with the goal of accounting for the vertical extent of the corona. In particular, we highlight the impact of including self consistently a second lamp post, mimicking for example an extended jet base. We fully include the effect that the second source has on the time-dependent disk ionization, reflection spectrum, and reverberation lags. We also present an application of this new model to NICER observations of the X-ray binary MAXI J1820+070 near its hard-to-soft state transition. We demonstrate that in these observations, a vertically extended corona can capture both spectral and timing properties, while a single lamp post model can not. In this scenario, the illumination responsible for the time-averaged spectrum originates close to the black hole, while the variability is likely associated with the ballistic jet., Comment: 17 pages, 12 figures, accepted for publication on ApJ

The transient black hole X-ray binary MAXI J1803-298 was discovered on 2021 May 1, as it went into outburst from a quiescent state. As the source rose in flux it showed periodic absorption dips and fit the timing and spectral characteristics of a hard state accreting black hole. We report on the results of a Target-of-Opportunity observation with NuSTAR obtained near the peak outburst flux beginning on 2021 May 13, after the source had transitioned into an intermediate state. MAXI J1803-298 is variable across the observation, which we investigate by extracting spectral and timing products separately for different levels of flux throughout the observation. Our timing analysis reveals two distinct potential QPOs which are not harmonically related at 5.4+/-0.2 Hz and 9.4+/-0.3 Hz, present only during periods of lower flux. With clear relativistic reflection signatures detected in the source spectrum, we applied several different reflection models to the spectra of MAXI J1803-298. Here we report our results, utilizing high density reflection models to constrain the disk geometry, and assess changes in the spectrum dependent on the source flux. With a standard broken power-law emissivity, we find a near-maximal spin for the black hole, and we are able to constrain the inclination of the accretion disk at 75+/-2 degrees, which is expected for a source that has shown periodic absorption dips. We also significantly detect a narrow absorption feature at 6.91+/-0.06 keV with an equivalent width between 4 and 9 eV, which we interpret as the signature of a disk wind., Comment: 14 pages, 8 figures, accepted for publication (ApJ)

Ark 564 is an extreme high-Eddington Narrow-line Seyfert 1 galaxy, known for being one of the brightest, most rapidly variable soft X-ray AGN, and for having one of the lowest temperature coronae. Here we present a 410-ks NuSTAR observation and two 115-ks XMM-Newton observations of this unique source, which reveal a very strong, relativistically broadened iron line. We compute the Fourier-resolved time lags by first using Gaussian processes to interpolate the NuSTAR gaps, implementing the first employment of multi-task learning for application in AGN timing. By fitting simultaneously the time lags and the flux spectra with the relativistic reverberation model RELTRANS, we constrain the mass at $2.3^{+2.6}_{-1.3} \times 10^6M_\odot$, although additional components are required to describe the prominent soft excess in this source. These results motivate future combinations of machine learning, Fourier-resolved timing, and the development of reverberation models., Comment: 19 pages, 9 figures. Accepted for publication in The Astrophysical Journal

The degree to which the thin accretion disks of black hole X-ray binaries are truncated during hard spectral states remains a contentious open question in black hole astrophysics. During its singular observed outburst in $2009\mbox{--}2010$, the black hole X-ray binary XTE J1752-223 spent $\sim1$~month in a long-stable hard spectral state at a luminosity of $\sim0.02\mbox{--}0.1~L_{\rm Edd}$. It was observed with 56 RXTE pointings during this period, with simultaneous Swift-XRT daily coverage during the first 10 days of the RXTE observations. Whilst reflection modeling has been extensively explored in the analysis of these data, there is a disagreement surrounding the geometry of the accretion disk and corona implied by the reflection features. We re-examine the combined, high signal-to-noise, simultaneous Swift and RXTE observations, and perform extensive reflection modeling with the latest relxill suite of reflection models, including newer high disk density models. We show that reflection modeling requires that the disk be within $\sim5~R_{\rm ISCO}$ during the hard spectral state, whilst weaker constraints from the thermal disk emission imply higher truncation ($R_{\rm in}=6\mbox{--}80~R_{\rm ISCO}$). We also explore more complex coronal continuum models, allowing for two Comptonization components instead of one, and show that the reflection features still require only a mildly truncated disk. Finally we present a full comparison of our results to previous constraints found from analyses of the same dataset., Comment: 18 pages, 9 figures, accepted by ApJ

We perform the first systematic search of all NICER archival observations of black hole (and candidate) low-mass X-ray binaries for signatures of reverberation. Reverberation lags result from the light travel time difference between the direct coronal emission and the reflected disk component, and therefore their properties are a useful probe of the disk-corona geometry. We detect new signatures of reverberation lags in 8 sources, increasing the total sample from 3 to 11, and study the evolution of reverberation lag properties as the sources evolve in outbursts. We find that in all of the 9 sources with more than 1 reverberation lag detection, the reverberation lags become longer and dominate at lower Fourier frequencies during the hard-to-soft state transition. This result shows that the evolution in reverberation lags is a global property of the state transitions of black hole low-mass X-ray binaries, which is valuable in constraining models of such state transitions. The reverberation lag evolution suggests that the corona is the base of a jet which vertically expands and/or gets ejected during state transition. We also discover that in the hard state, the reverberation lags get shorter, just as the QPOs move to higher frequencies, but then in the state transition, while the QPOs continue to higher frequencies, the lags get longer. We discuss implications for the coronal geometry and physical models of QPOs in light of this new finding., Comment: 29 pages, 21 figures

We present the results of MAXI monitoring and two NuSTAR observations of the recently discovered faint X-ray transient MAXI J1848-015. Analysis of the MAXI light-curve shows that the source underwent a rapid flux increase beginning on 2020 December 20, followed by a rapid decrease in flux after only $\sim5$ days. NuSTAR observations reveal that the source transitioned from a bright soft state with unabsorbed, bolometric ($0.1$-$100$ keV) flux $F=6.9 \pm 0.1 \times 10^{-10}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$, to a low hard state with flux $F=2.85 \pm 0.04 \times 10^{-10}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$. Given a distance of $3.3$ kpc, inferred via association of the source with the GLIMPSE-C01 cluster, these fluxes correspond to an Eddington fraction of order $10^{-3}$ for an accreting neutron star of mass $M=1.4M_\odot$, or even lower for a more massive accretor. However, the source spectra exhibit strong relativistic reflection features, indicating the presence of an accretion disk which extends close to the accretor, for which we measure a high spin, $a=0.967\pm0.013$. In addition to a change in flux and spectral shape, we find evidence for other changes between the soft and hard states, including moderate disk truncation with the inner disk radius increasing from $R_\mathrm{in}\approx3\,R_\mathrm{g}$ to $R_\mathrm{in}\approx8\,R_\mathrm{g}$, narrow Fe emission whose centroid decreases from $6.8\pm0.1$ keV to $6.3 \pm 0.1$ keV, and an increase in low-frequency ($10^{-3}$-$10^{-1}$ Hz) variability. Due to the high spin we conclude that the source is likely to be a black hole rather than a neutron star, and we discuss physical interpretations of the low apparent luminosity as well as the narrow Fe emission., Comment: 19 pages, 9 figures, 3 tables. Accepted for publication in ApJ

We show that X-ray reverberation mapping can be used to measure the distance to type 1 active galactic nuclei (AGNs). This is because X-ray photons originally emitted from the `corona' close to the black hole irradiate the accretion disc and are re-emitted with a characteristic `reflection' spectrum that includes a prominent $\sim 6.4$ keV iron emission line. The shape of the reflection spectrum depends on the irradiating flux, and the light-crossing delay between continuum photons observed directly from the corona and the reflected photons constrains the size of the disc. Simultaneously modelling the X-ray spectrum and the time delays between photons of different energies therefore constrains the intrinsic reflected luminosity, and the distance follows from the observed reflected flux. Alternatively, the distance can be measured from the X-ray spectrum alone if the black hole mass is known. We develop a new model of our RELTRANS X-ray reverberation mapping package, called RTDIST, that has distance as a model parameter. We simulate a synthetic observation that we fit with our new model, and find that this technique applied to a sample of $\sim 25$ AGNs can be used to measure the Hubble constant with a $3 \sigma$ statistical uncertainty of $\sim 6~{\rm km}~{\rm s}^{-1}{\rm Mpc}^{-1}$. Since the technique is completely independent of the traditional distance ladder and the cosmic microwave background radiation, it has the potential to address the current tension between them. We discuss sources of modelling uncertainty, and how they can be addressed in the near future., Comment: Accepted for publication in MNRAS

We present a new release of the RELTRANS model to fit the complex cross-spectrum of accreting black holes as a function of energy. The model accounts for continuum lags and reverberation lags self-consistently in order to consider the widest possible range of X-ray variability timescales. We introduce a more self-consistent treatment of the reverberation lags, accounting for how the time variations of the illuminating flux change the ionisation level of the accretion disc. This process varies the shape of the reflection spectrum in time causing an additional source of lags besides the light crossing delay. We also consider electron densities in the accretion disc up to $10^{20}$ cm$^{-3}$, which are found in most of the stellar mass black holes and in some AGN. These high densities increase the amplitude of the reverberation lags below $1$ keV since the reflection flux enhances in the same energy range. In addition, we investigate the properties of hard lags produced by variations in the power-law index of the continuum spectrum, which can be interpreted as due to roughly $3\%$ variability in the corona's optical depth and temperature. As a test case, we simultaneously fit the lag energy spectra in a wide range of Fourier frequency for the black hole candidate MAXI J1820+070 observed with NICER. The best fit shows how the reverberation lags contribute even at the longer timescales where the hard lags are important. This proves the importance of modelling these two lags together and self-consistently in order to constrain the parameters of the system., Comment: Accepted for publication in MNRAS

We analyze 5 epochs of NICER data of the black hole X-ray binary MAXI J1820+070 during the bright hard-to-soft state transition in its 2018 outburst with both reflection spectroscopy and Fourier-resolved timing analysis. We confirm the previous discovery of reverberation lags in the hard state, and find that the frequency range where the (soft) reverberation lag dominates decreases with the reverberation lag amplitude increasing during the transition, suggesting an increasing X-ray emitting region, possibly due to an expanding corona. By jointly fitting the lag-energy spectra in a number of broad frequency ranges with the reverberation model reltrans, we find the increase in reverberation lag is best described by an increase in the X-ray coronal height. This result, along with the finding that the corona contracts in the hard state, suggests a close relationship between spatial extent of the X-ray corona and the radio jet. We find the corona expansion (as probed by reverberation) precedes a radio flare by ~5 days, which may suggest that the hard-to-soft transition is marked by the corona expanding vertically and launching a jet knot that propagates along the jet stream at relativistic velocities., Comment: 16 pages, 10 figures, accepted to be published in ApJL

We present the analysis of X-ray observations of the black hole binary 4U~1630$-$47 using relativistic reflection spectroscopy. We use archival data from the RXTE, Swift, and NuSTAR observatories, taken during different outbursts of the source between $1998$ and $2015$. Our modeling includes two relatively new advances in modern reflection codes: high-density disks, and returning thermal disk radiation. Accretion disks around stellar-mass black holes are expected to have densities well above the standard value assumed in traditional reflection models (i.e., $n_{\rm e}\sim10^{15}~{\rm cm^{-3}}$). New high-density reflection models have important implications in the determination of disk truncation (i.e., the disk inner radius). This is because one must retain self-consistency in the irradiating flux and corresponding disk ionization state, which is a function of disk density and system geometry. We find the disk density is $n_{\rm e}\ge10^{20}~{\rm cm^{-3}}$ across all spectral states. This density, combined with our constraints on the ionization state of the material, implies an irradiating flux impinging on the disk that is consistent with the expected theoretical estimates. Returning thermal disk radiation -- the fraction of disk photons which bend back to the disk producing additional reflection components -- is expected predominantly in the soft state. We show that returning radiation models indeed provide a better fit to the soft state data, reinforcing previous results which show that in the soft state the irradiating continuum may be blackbody emission from the disk itself., Comment: 20 pages, 6 figures, 6 tables, Accepted by ApJ

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., Comment: 64 pages, 23 figures. Prepared within the ISSI International Team project "Can We Use X-Ray Reflection Spectroscopy For Precision Measurements Of Accreting Black Holes?". v3: refereed version

Time lags due to X-ray reverberation have been detected in several Seyfert galaxies. The different travel time between reflected and directly observed rays naturally causes this type of lag, which depends directly on the light-crossing timescale of the system and hence scales with the mass of the central black hole. Featureless `hard lags' not associated with reverberation, and often interpreted as propagating mass accretion rate fluctuations, dominate the longer timescale variability. Here we fit our reltrans model simultaneously to the time-averaged energy spectrum and the lag-energy spectra of the Seyfert galaxy Mrk 335 over two timescales (Fourier frequency ranges). We model the hard lags as fluctuations in the slope and strength of the illuminating spectrum, and self-consistently account for the effects that these fluctuations have on the reverberation lags. The resulting mass estimate is $1.1^{+2.0}_{-0.7} \times 10^6~M_\odot$, which is significantly lower than the mass measured with the optical reverberation mapping technique (14 - 26 million $M_\odot$). When we add the correlated variability amplitudes to the time lags by fitting the full complex cross-spectra, the model is unable to describe the characteristic reverberation Fe K$\alpha$ line and cannot constrain the black hole mass. This may be due to the assumption that the direct radiation is emitted by a point-like source., Comment: Accepted for publication in MNRAS

We present the publicly available model \textsc{reltrans} that calculates the light-crossing delays and energy shifts experienced by X-ray photons originally emitted close to the black hole when they reflect from the accretion disk and are scattered into our line-of-sight, accounting for all general relativistic effects. Our model is fast and flexible enough to be simultaneously fit to the observed energy-dependent cross-spectrum for a large range of Fourier frequencies, as well as to the time-averaged spectrum. This not only enables better geometric constraints than only modelling the relativistically broadened reflection features in the time-averaged spectrum, but additionally enables constraints on the mass of supermassive black holes in active galactic nuclei and stellar-mass black holes in X-ray binaries. We include a self-consistently calculated radial profile of the disk ionization parameter and properly account for the effect that the telescope response has on the predicted time lags. We find that a number of previous spectral analyses have measured artificially low source heights due to not accounting for the former effect and that timing analyses have been affected by the latter. In particular, the magnitude of the soft lags in active galactic nuclei may have been under-estimated, and the magnitude of lags attributed to thermal reverberation in X-ray binaries may have been over-estimated. We fit \textsc{reltrans} to the lag-energy spectrum of the Seyfert galaxy Mrk 335, resulting in a best fitting black hole mass that is smaller than previous optical reverberation measurements ($\sim 7$ million compared with $\sim14-26$ million $M_\odot$)., Comment: Accepted for publication in MNRAS. 24 pages, 17 figures. Model available to download from https://adingram.bitbucket.io/reltrans.html

We present the first X-ray reverberation mass measurement of a stellar-mass black hole. Accreting stellar-mass and supermassive black holes display characteristic spectral features resulting from reprocessing of hard X-rays by the accretion disc, such as an Fe K$\alpha$ line and a Compton hump. This emission probes of the innermost region of the accretion disc through general relativistic distortions to the line profile. However, these spectral distortions are insensitive to black hole mass, since they depend on disc geometry in units of gravitational radii. Measuring the reverberation lag resulting from the difference in path length between direct and reflected emission calibrates the absolute length of the gravitational radius. We use a relativistic model able to reproduce the behaviour of the lags as a function of energy for a wide range of variability timescales, addressing both the reverberation lags on short timescales and the intrinsic hard lags on longer timescales. We jointly fit the time-averaged spectrum and the real and imaginary parts of the cross-spectrum as a function of energy for a range of Fourier frequencies to Rossi X-ray Timing Exporer data from the X-ray binary Cygnus X-1. We also show that introducing a self-consistently calculated radial ionisation profile in the disc improves the fit, but requires us to impose an upper limit on ionisation profile peak to allow a plausible value of the accretion disc density. This limit leads to a mass value more consistent with the existing dynamical measurement., Comment: 14 pages, accepted for publication in MNRAS

Accreting black holes show characteristic reflection features in their X-ray spectrum, including an iron K$\alpha$ line, resulting from hard X-ray continuum photons illuminating the accretion disk. The reverberation lag resulting from the path length difference between direct and reflected emission provides a powerful tool to probe the innermost regions around both stellar-mass and supermassive black holes. Here, we present for the first time a reverberation mapping formalism that enables modeling of energy dependent time lags and variability amplitude for a wide range of variability timescales, taking the complete information of the cross-spectrum into account. We use a pivoting power-law model to account for the spectral variability of the continuum that dominates over the reverberation lags for longer time scale variability. We use an analytic approximation to self-consistently account for the non-linear effects caused by this continuum spectral variability, which have been ignored by all previous reverberation studies. We find that ignoring these non-linear effects can bias measurements of the reverberation lags, particularly at low frequencies. Since our model is analytic, we are able to fit simultaneously for a wide range of Fourier frequencies without prohibitive computational expense. We also introduce a formalism of fitting to real and imaginary parts of our cross-spectrum statistic, which naturally avoids some mistakes/inaccuracies previously common in the literature. We perform proof-of-principle fits to Rossi X-ray Timing Explorer data of Cygnus X-1., Comment: Accepted for publication in MNRAS