Coronal Geometry Research Articles

Large and complex X-ray time lags from black hole accretion disks with compact inner coronae

Abstract Black hole X-ray binaries in their hard and hard-intermediate states display hard and soft time lags between broadband noise variations (high-energy emission lagging low-energy and vice versa), which could be used to constrain the geometry of the disk and Comptonising corona in these systems. Comptonisation and reverberation lag models, which are based on light-travel delays, can imply coronae which are very large (hundreds to thousands of gravitational radii, Rg) and in conflict with constraints from X-ray spectral modelling and polarimetry. Here we show that the observed large and complex X-ray time lags can be explained by a model where fluctuations are generated in and propagate through the blackbody-emitting disk to a relatively compact (∼10 Rg) inner corona. The model naturally explains why the disk variations lead coronal variations with a Fourier-frequency dependent lag at frequencies <1 Hz, since longer variability time-scales originate from larger disk radii. The propagating fluctuations also modulate successively the coronal seed photons from the disk, heating of the corona via viscous dissipation and the resulting reverberation signal. The interplay of these different effects leads to the observed complex pattern of lag behaviour between disk and power-law emission and different power-law energy bands, the energy-dependence of power-spectral shape, and a strong dependence of spectral-timing properties on coronal geometry. The observed spectral-timing complexity is thus a natural consequence of the response of the disk-corona system to mass-accretion fluctuations propagating through the disk.

A Comparison of the X-Ray Polarimetric Properties of Stellar and Supermassive Black Holes

X-ray polarization provides a new way to probe accretion geometry in black hole systems. If the accretion geometry of black holes is similar regardless of mass, we should expect the same to be true of their polarization properties. We compare the polarimetric properties of all nonblazar black holes observed with the Imaging X-ray Polarimetry Explorer. We find that their polarization properties are very similar, particularly in the hard state, where the corona dominates. This tentatively supports the idea that stellar and supermassive black holes share a common coronal geometry.

The 2018 Outburst of MAXI J1820+070 as Seen by Insight-HXMT

We present an analysis of the whole 2018 outburst of the black hole X-ray binary MAXI J1820+070 with Insight-HXMT data. We focus our study on the temporal evolution of the parameters of the source. We employ two different models to fit the disk’s thermal spectrum: the Newtonian model diskbb and the relativistic model nkbb. These two models provide different pictures of the source in the soft state. With diskbb, we find that the inner edge of the disk is close to the innermost stable circular orbit of a fast-rotating black hole and the corona changes geometry from the hard to the soft state. With nkbb, we find that the disk is truncated in the soft state and that the coronal geometry does not change significantly during the whole outburst. However, the model with nkbb can predict an untruncated disk around a fast-rotating black hole if we assume that the disk inclination angle is around 30° (instead of ∼60°, which is the inclination angle of the jet and is usually adopted as the disk inclination angle in the literature) and we employ a high-density reflection model. In such a case, we measure a high value of the black hole spin parameter with observations in the soft state, in agreement with the high spin value found from the analysis of the reflection features and in disagreement with the low spin value found by previous continuum-fitting method measurements with the disk inclination angle set to the value of the jet inclination angle.

Spectral Fittings of Warm Coronal Radiation with High Seed Photon Temperature: Apparent Low-temperature and Flat Soft Excess in AGNs

A warm corona has been widely proposed to explain the soft excess (SE) in X-ray above the 2–10 keV power law extrapolation in Active Galactic Nuclei (AGNs). In actual spectral fittings, the warm coronal seed photon temperature (T s) is usually assumed to be far away from the soft X-ray, but kT s can reach close to 0.1 keV in the standard accretion disk model. In this study, we used Monte Carlo simulations to obtain radiation spectra from a slab-like warm corona and fitted the spectra using the spherical-geometry-based routine thcomp or a thermal component. Our findings reveal that high T s can influence the fitting results. A moderately high kT s (around 0.03 keV) can result in an apparent low-temperature and flat SE, while an extremely high kT s (around 0.07 keV) can even produce an unobserved blackbody-like SE. Our conclusions indicate that, for spectral fittings of the warm coronal radiation (SE in AGNs), kT s should be treated as a free parameter with an upper limit, and an accurate coronal geometry is necessary when kT s > 0.01 keV.

Impact of Offset and Leg Length on Functional Outcomes Post-Total Hip Arthroplasty: How Accurate Should Coronal Reconstruction Be?

BackgroundAccurate hip reconstruction is associated with improved biomechanical behavior following total hip arthroplasty (THA). However, whether this is associated with improved patient-reported outcomes (PROs) is unknown. Hypothesis/PurposeThis study aimed to: 1) describe the ability to reconstruct coronal geometry during THA without advanced technology; 2) assess whether restoration of global offset (GO) and leg length (LL) is associated with improved PROs; and 3) investigate whether increased femoral offset (FO) to compensate for reduced acetabular offset (AO) influences PROs. MethodThis was a prospective, multicenter, consecutive cohort study of 500 patients treated with primary THA without robotics or navigation. The Oxford Hip score (OHS) was obtained preoperatively and at 1-year follow-up. Supine anteroposterior pelvic radiographs were analyzed to determine AO, FO, GO, and LL relative to the native contralateral side. Contour plots for ΔOHS based on ΔLL and ΔGO were created, and ΔOHS was calculated within and outside various ranges (±2.5, ±5, or ±10 mm). ResultsIn the operated hip, mean FO increased by 3 ± 6 mm (range, −16 to 27), while AO decreased by 2 ± 4 mm (range, −17 to 10). The contour graph for ±2.5 mm zones showed the best outcomes (ΔOHS >25) with GO and LL centered on 0 ± 2.5 mm (P < .01). However, only 10% achieved such reconstruction. When GO and LL differences were within ±10 mm, ΔOHS was superior when both AO and FO were within ±5 mm (mean: 24 ± 10; range, −5 to 40) compared with when FO was above 5 mm to compensate for a reduction in AO (mean: 22 ± 11; range, −10 to 46; P = .040). ConclusionsThe PROs were associated with biomechanical reconstruction, and the best clinical improvement can be expected when GO and LL differences are both within 2.5 mm. Maintenance of AO is important, as compensation by increasing FO is associated with inferior OHS.

Unveiling the X-ray polarimetric properties of LMC X−3 with IXPE, NICER, and Swift/XRT

ABSTRACT The incoming Imaging X-ray Polarimetry Explorer (IXPE) observations of X-ray binaries provide a new tool to investigate the underlying accretion geometry. Here, we report the first measurements of X-ray polarization of the extragalactic black-hole X-ray binary LMC X−3. We find a polarization fraction of $\sim 3~{{\ \rm per\ cent}}$ at a polarization angle of ∼135° in the 2–8 keV energy band with statistical significance at the 7σ level. This polarization measurement significantly exceeds the minimum detectable polarization threshold of 1.2 per cent for the source, ascertained at a 99 per cent confidence level within the 2–8 keV energy band. The simultaneous spectro-polarimetric fitting of Neutron Star Interior Composition Explorer, Swift/X-Ray Telescope (XRT), and IXPE revealed the presence of a disc with a temperature of ∼1 keV and a Comptonized component with a power-law index of ∼2.4, confirming the soft nature of the source. The polarization degree increases with energy from ∼3 per cent in the 2–5.7 keV band to ∼9 per cent in the 5.7–8 keV band, while the polarization angle is energy independent. The observed energy dependence and the sudden jump of polarization fraction above 5 keV supports the idea of a static slab coronal geometry for the Comptonizing medium of LMC X−3.

Toward More Accurate Synthetic Reflection Spectra: Improving the Calculations of Returning Radiation

We present a new model to calculate reflection spectra of thin accretion disks in Kerr spacetimes. Our model includes the effect of returning radiation, which is the radiation that is emitted by the disk and returns to the disk because of the strong light bending near a black hole. The major improvement with respect to the existing models is that it calculates the reflection spectrum at every point on the disk by using the actual spectrum of the incident radiation. Assuming a lamppost coronal geometry, we simulate simultaneous observations of NICER and NuSTAR of bright Galactic black holes and we fit the simulated data with the latest version of relxill (modified to read the table of reflionx, which is the nonrelativistic reflection model used in our calculations). We find that relxill with returning radiation cannot fit well the simulated data when the black hole spin parameter is very high and the coronal height and disk’s ionization parameter are low, and some parameters can be significantly overestimated or underestimated. We can find better fits and recover the correct input parameters as the value of the black hole spin parameter decreases and the value of the coronal height increases.

Rms–Flux Slope in MAXI J1820+070: A Measure of Disk–Corona Coupling

The linear rms–flux relation has been well established in different spectral states of all accreting systems. In this work, we study the evolution of the frequency-dependent rms–flux relation of MAXI J1820+070 during the initial decaying phase of its 2018 outburst with Insight-HXMT over a broad energy range of 1–150 keV. As the flux decreases, we first observe a linear rms–flux relation at frequencies from 2 mHz to 10 Hz, while such a relation breaks at varying times for different energies, leading to a substantial reduction in the slope. Moreover, we find that the low-frequency variability exhibits the highest sensitivity to the break, which occurs prior to the hard-to-hard state transition time determined through time-averaged spectroscopy, and the time deviation increases with energy. The overall evolution of the rms–flux slope and intercept suggests the presence of a two-component Comptonization system. One component is radially extended, explaining the strong disk–corona coupling before the break, while the other component extends vertically, contributing to a reduction of disk–corona coupling after the break. A further vertical expansion of the latter component is required to accommodate the dynamic evolution observed in the rms–flux slope. In conclusion, we suggest that the rms–flux slope in the 1–150 keV band can be employed as an indicator of disk–corona coupling, and the hard-to-hard state transition in MAXI J1820+070 could be partially driven by changes in the coronal geometry.

The high energy X-ray probe (HEX-P): probing the physics of the X-ray corona in active galactic nuclei

The hard X-ray emission in active galactic nuclei (AGN) and black hole X-ray binaries is thought to be produced by a hot cloud of electrons referred to as the corona. This emission, commonly described by a power law with a high-energy cutoff, is suggestive of Comptonization by thermal electrons. While several hypotheses have been proposed to explain the origin, geometry, and composition of the corona, we still lack a clear understanding of this fundamental component. NuSTAR has been playing a key role improving our knowledge of X-ray coronæ thanks to its unprecedented sensitivity above 10 keV. However, these constraints are limited to bright, nearby sources. The High Energy X-ray Probe (HEX-P) is a probe-class mission concept combining high spatial resolution X-ray imaging and broad spectral coverage (0.2–80 keV) with a sensitivity superior to current facilities. In this paper, we highlight the major role that HEX-P will play in further advancing our insights of X-ray coronæ notably in AGN. We demonstrate how HEX-P will measure key properties and track the temporal evolution of coronæ in unobscured AGN. This will allow us to determine their electron distribution and test the dominant emission mechanisms. Furthermore, we show how HEX-P will accurately estimate the coronal properties of obscured AGN in the local Universe, helping address fundamental questions about AGN unification. In addition, HEX-P will characterize coronæ in a large sample of luminous quasars at cosmological redshifts for the first time and track the evolution of coronæ in transient systems in real time. We also demonstrate how HEX-P will enable estimating the coronal geometry using spectral-timing techniques. HEX-P will thus be essential to understand the evolution and growth of black holes over a broad range of mass, distance, and luminosity, and will help uncover the black holes’ role in shaping the Universe.

X-ray polarization changes with the state transition in Cygnus X–1

ABSTRACT We studied the polarization properties of Cygnus X–1 in both hard and soft spectral states with imaging X-ray polarimetry explorer (IXPE) observations. The polarization degree is $\sim 4~{{\ \rm per\ cent}}$, and $\sim 2.6-2.8~{{\ \rm per\ cent}}$ in the hard and soft states, respectively. The polarization angle is observed along the jet axis and remains the same in both states. Energy-dependent analysis revealed an increasing polarization with the energy. The observed polarization rules out the lamp-post corona and prefers a conical corona if the coronal geometry remains the same in the hard and soft states. The disc is not detected in the hard state but is found in the soft state in the IXPE spectra. The spectral analysis revealed that the disc emission contributes $\sim 20~{{\ \rm per\ cent}}$ of the total emission in the soft state. The scattering of the seed photons inside the corona is likely to reduce the polarization. This could explain the different polarization in different spectral states. Additionally, if the disc polarization is perpendicular to that of the corona, it could also reduce the polarization in the soft state.

The X-ray polarization of the Seyfert 1 galaxy IC 4329A

ABSTRACT We present an X-ray spectro-polarimetric analysis of the bright Seyfert galaxy IC 4329A. The Imaging X-ray Polarimetry Explorer (IXPE) observed the source for ∼500 ks, supported by XMM–Newton (∼60 ks) and NuSTAR (∼80 ks) exposures. We detect polarization in the 2–8 keV band with 2.97σ confidence. We report a polarization degree of 3.3 ± 1.1 per cent and a polarization angle of 78° ± 10° (errors are 1σ confidence). The X-ray polarization is consistent with being aligned with the radio jet, albeit partially due to large uncertainties on the radio position angle. We jointly fit the spectra from the three observatories to constrain the presence of a relativistic reflection component. From this, we obtain constraints on the inclination angle to the inner disc (&amp;lt;39° at 99 per cent confidence) and the disc inner radius (&amp;lt;11 gravitational radii at 99 per cent confidence), although we note that modelling systematics in practice add to the quoted statistical error. Our spectropolarimetric modelling indicates that the 2–8 keV polarization is consistent with being dominated by emission directly observed from the X-ray corona, but the polarization of the reflection component is completely unconstrained. Our constraints on viewer inclination and polarization degree tentatively favour more asymmetric, possibly out-flowing, coronal geometries that produce more highly polarized emission, but the coronal geometry is unconstrained at the 3σ level.

The geometry of the hot corona in MCG-05-23-16 constrained by X-ray polarimetry

ABSTRACT We report on the second observation of the radio-quiet active galactic nucleus MCG-05-23-16 performed with the Imaging X-ray Polarimetry Explorer (IXPE). The observation started on 2022 November 6 for a net observing time of 640 ks, and was partly simultaneous with NuSTAR (86 ks). After combining these data with those obtained in the first IXPE pointing on 2022 May (simultaneous with XMM–Newton and NuSTAR) we find a 2–8 keV polarization degree Π = 1.6 ± 0.7 (at 68 per cent confidence level), which corresponds to an upper limit Π = 3.2 per cent (at 99 per cent confidence level). We then compare the polarization results with Monte Carlo simulations obtained with the monk code, with which different coronal geometries have been explored (spherical lamppost, conical, slab, and wedge). Furthermore, the allowed range of inclination angles is found for each geometry. If the best-fitting inclination value from a spectroscopic analysis is considered, a cone-shaped corona along the disc axis is disfavoured.

Detection of significant X-ray polarization from transient NS-LMXB XTE J1701−462 with IXPE and its implication on the coronal geometry

ABSTRACT In this paper, we performed a spectro-polarimetric analysis of the transient NS-LMXB XTE J1701−462 using IXPE, NICER, and NuSTAR data during its 2022 outburst. We report significant detection of energy-dependent polarization in the X-ray signal from the source on 2022 September 29 in the 2–4, 4–8, and 2–8 keV energy bands with a polarization degree of 3.9 ± 0.3, 5.5 ± 0.6, and 4.5 ± 0.4 per cent, respectively. The polarization angle in the overall 2–8 keV band was ∼143° ± 2°. The spectra were modelled using a combination of thermal emission from an accretion disc, Comptonized emission from a hot electron plasma (or corona) and a Gaussian line. From spectro-polarimetric analysis, the polarization degree due to the disc emission had an upper limit of ∼11.5 per cent, and that of the Comptonized emission was constrained at 7.7 ± 2.5 per cent (at the 3σ level). The results suggest that the Comptonized component probably originates from a spreading-layer/boundary-layer above the neutron star surface. IXPE observation of the source on 2022 October 8 does not show significant polarization which can be attributed to a weakening of the coronal Comptonized emission. The implication of these results are discussed.

NuSTAR View of the R − Γ Correlation in the Hard State of Black Hole Low-mass X-Ray Binaries

The power law and reflection emission have been observed in the X-ray spectra of both black hole X-ray binaries (BHXRBs) and active galactic nuclei (AGNs), indicating a common physical origin of the X-ray emission from these two types of sources. The relevant parameters describing the shape of both components and the potential correlation between these parameters can provide important clues on the geometric and physical properties of the disk and the corona in these sources. In this work, we present a positive correlation between the photon index Γ and the reflection strength R for the low-mass BHXRBs in the hard state by modeling NuSTAR data, which is qualitatively consistent with the previous studies. We compare our results with the predictions from different theoretical disk-corona models. We show that the R − Γ correlation found in this work seems to favor the moving corona model proposed by Beloborodov. Our results indicate that the coronal geometry varies significantly among BHXRBs. We further compare our results with that of AGNs. We find that the reflection strength R is smaller than unity in the hard state of BHXRBs, while it can be as large as ∼5 in AGNs, which implies that the variations of the disk-coronal geometry of AGNs are more vigorous than that of the BHXRBs in the hard state.

The NuSTAR view of the changing-look AGN ESO 323-G77

The presence of an obscuring torus at parsec-scale distances from the central black hole is the main ingredient for the Unified Model of active galactic nuclei (AGN), as obscured sources are thought to be seen through this structure. However, the Unified Model fails to describe a class of sources that undergo dramatic spectral changes, transitioning from obscured to unobscured and vice versa through time. The variability in these sources, which are known as changing-look AGN (CLAGN), is thought to be produced by a clumpy medium at much smaller distances than the conventional obscuring torus. ESO 323-G77 is a CLAGN that was observed in various states through the years with Chandra, Suzaku, Swift-XRT, and XMM-Newton, from unobscured (NH &lt; 3 × 1022 cm−2) to Compton-thin (NH ∼ 1 − 6 × 1023 cm−2) and even Compton-thick (NH &gt; 1 × 1024 cm−2), on timescales as short as one month. We present an analysis of the first NuSTAR monitoring of ESO 323-G77, consisting of five observations taken at different timescales (1, 2, 4, and 8 weeks from the first one) in 2016–2017, in which the AGN was caught in a persistent Compton-thin obscured state (NH ∼ 2 − 4 × 1023 cm−2). We find that a Compton-thick reflector is present (NH, refl = 5 × 1024 cm−2), most likely associated with the presence of the putative torus. Two ionized absorbers are unequivocally present, located within maximum radii of rmax, 1 = 1.5 pc and rmax, 2 = 0.01 pc. In one of the observations, the inner ionized absorber is blueshifted, indicating the presence of a possible faster (vout = 0.2c) ionized absorber, marginally detected at 3σ. Finally, we are able to constrain the coronal temperature and the optical depth of ESO 323-G77, obtaining kTe = 38 keV or kTe = 36 keV, and τ = 1.4 or τ = 2.8, depending on the coronal geometry assumed.

Evolution of Accretion Modes between Spectral States Inferred from Spectral and Timing Analysis of Cygnus X-1 with Insight-HXMT Observations

We execute a detailed spectral-timing study of Cygnus X-1 in the low/hard, intermediate, and high/soft states with observations from the Hard X-ray Modulation Telescope. The broadband energy spectra fit well with the “truncated disk model”: the inner boundary of the accretion disk stays within ∼10 R g and moves inward as the source softens. Through studying the power density spectrum, rms, and Fourier frequency component resolved spectroscopy, we find that the X-ray variations are generated in two different regions for each state. We discover that the major contribution to the X-ray variation is from the hot corona rather than the accretion disk. We suggest a scenario with different coronal geometry for each state based on the truncated disk geometry in which the corona envelops the disk to form a sandwich geometry in the low/hard state, and then gradually moves away from the disk in a direction perpendicular to the disk until it forms a jet-like geometry in the high/soft state.

Polarization properties of weakly magnetized neutron stars in low-mass X-ray binaries

ABSTRACT X-ray polarimetry missions like Imaging X-ray Polarimetry Explorer will be able to measure for the first time the polarization properties of accreting, weakly magnetized neutron stars in low-mass X-ray binaries. In this work, we present simulations of the expected X-ray polarized signal, including the coronal emission for different geometries of the corona itself, i.e. a slab above the accretion disc and a spherical shell around the neutron star. The simulations are performed with the fully relativistic Monte Carlo code monk capable of computing the X-ray polarization degree and angle for various physical input parameters of the neutron star, disc, and corona. Different coronal geometries result in significantly different X-ray polarization properties, which can therefore be used to constrain the geometry of the systems.

The NICER “Reverberation Machine”: A Systematic Study of Time Lags in Black Hole X-Ray Binaries

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 eight sources, increasing the total sample from three to 11, and study the evolution of reverberation lag properties as the sources evolve in outbursts. We find that in all of the nine sources with more than one 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 that 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 quasiperiodic oscillations (QPOs) move to higher frequencies, but then in the state transition, while the QPOs continue to higher frequencies, the lags get longer. We discuss the implications of the coronal geometry and physical models of QPOs in light of this new finding.

The X-Ray Coronae in NuSTAR Bright Active Galactic Nuclei

We present a systematic and uniform analysis of NuSTAR data of a sample of 60 SWIFT BAT-selected AGNs with 10–78 keV signal-to-noise ratio (S/N) > 50, 10 of which are radio loud. We measure their high-energy cutoff E cut or coronal temperature T e using three different spectral models to fit their NuSTAR spectra and show that a threshold in NuSTAR spectral S/N is essential for such measurements. High-energy spectral breaks are detected in the majority of the sample, and for the rest, strong constraints on E cut or T e are obtained. Strikingly, we find extraordinarily large E cut lower limits (>400 keV, up to >800 keV) in 10 radio-quiet sources, whereas we find none in the radio-loud sample. Consequently and surprisingly, we find a significantly larger mean E cut/T e of radio-quiet sources compared with radio-loud ones. The reliability of these measurements is carefully inspected and verified with simulations. We find a strong positive correlation between E cut and photon index Γ, which cannot be attributed to the parameter degeneracy. The strong dependence of E cut on Γ, which could fully account for the discrepancy of the E cut distribution between radio-loud and radio-quiet sources, indicates that the X-ray coronae in AGNs with steeper hard X-ray spectra have on average higher temperature and thus smaller opacity. However, no prominent correlation is found between E cut and λ edd. In the l–Θ diagram, we find a considerable fraction of sources lie beyond the boundaries of forbidden regions due to runaway pair production, posing (stronger) challenges to various (flat) coronal geometries.

Reflection Spectra of Accretion Disks Illuminated by Disk-like Coronae

Abstract Relativistic reflection features in the X-ray spectra of black hole binaries and active galactic nuclei are thought to be produced through illumination of a cold accretion disk by a hot corona. In this work, we assume that the corona has the shape of an infinitesimally thin disk with its central axis the same as the rotational axis of the black hole. The corona can either be static or corotate with the accretion disk. We calculate the disk’s emissivity profiles and iron line shapes for a set of coronal radii and heights. We incorporate these emissivity profiles into relxill_nk and we simulate some observations of a black hole binary with the Nuclear Spectroscopic Telescope Array to study the impact of a disk-like coronal geometry on the measurement of the properties of the system, and in particular, on the possibility of testing the Kerr nature of the source. We find that, in general, the astrophysical properties of the accretion disk are recovered well even if we fit the data with a model employing a broken power law or a lamppost emissivity profile, while it is more challenging to constrain the geometric properties of the black hole spacetime.