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Jiachen Jiang

Jiachen Jiang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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astro-ph.HEgr-qcastro-ph.SRArtificial Intelligenceastro-ph.COastro-ph.GAastro-ph.IMMachine LearningMultiagent Systems

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Published work

22 published item(s)

preprint2026arXiv

Decoding Cygnus X-2: The Critical Role of Reflection in IXPE Data

We present a spectro-polarimetric re-analysis of the first IXPE observation of Cygnus X-2 which we determine to be mainly in the normal branch, from quasi-simultaneous observations with NuSTAR, NICER, and INTEGRAL. We measure the hard X-ray polarization angle and find it to be consistent with the previously measured position angle of the radio jet. Leveraging NuSTAR's detection of both the relativistic Fe K emission line and the Compton hump, we constrain the flux contribution of the reflected emission from the inner accretion disk to be 10% of the total X-ray flux in the IXPE energy band. Unlike previous studies that modeled only the Fe K emission line, we fit the full-band reflection spectrum using a fully relativistic disk model. There is strong degeneracy between the Comptonized and reflection components. Given that the Comptonized component is not expected to be highly polarized, a polarization degree of approximately 20% for the reflection component could explain the X-ray polarization data from IXPE. We also discuss the disk inclination angle inferred from our spectro-polarimetric modeling, as well as other possible explanations for the data.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

SMCEvolve: Principled Scientific Discovery via Sequential Monte Carlo Evolution

LLM-driven program evolution has emerged as a powerful tool for automated scientific discovery, yet existing frameworks offer no principled guide for designing their individual components and provide no guarantee that the search converges. We introduce SMCEvolve, which recasts program search as sampling from a reward-tilted target distribution and approximates it with a Sequential Monte Carlo (SMC) sampler. From this view, three core mechanisms emerge as principled components: adaptive parent resampling, mixture of mutation with acceptance, and automatic convergence control. We further provide a finite-sample complexity analysis that bounds the LLM-call budget required to reach a target approximation error. Across math, algorithm efficiency, symbolic regression, and end-to-end ML research benchmarks, SMCEvolve surpasses state-of-the-art evolving systems while using fewer LLM calls under self-determined termination. The code is available at https://github.com/kongwanbianjinyu/SMCEvolve.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

The Advanced X-ray Imaging Satellite (AXIS) Community Science Book

The AXIS Community Science Book represents the collective effort of 592 scientists worldwide to define the transformative science enabled by the Advanced X-ray Imaging Satellite (AXIS), a next-generation X-ray mission selected by NASA's Astrophysics Probe Program for Phase A study. AXIS will advance the legacy of high-angular-resolution X-ray astronomy with ~1.5'' imaging over a wide 24' field of view and an order of magnitude greater collecting area than Chandra in the 0.3-12 keV band. Combining sharp imaging, high throughput, and rapid response capabilities, AXIS will open new windows on virtually every aspect of modern astrophysics, exploring the birth and growth of supermassive black holes, the feedback processes that shape galaxies, the life cycles of stars and exoplanet environments, and the nature of compact stellar remnants, supernova remnants, and explosive transients. This book compiles 138 community-contributed science cases developed by five Science Working Groups focused on AGN and supermassive black holes, galaxy evolution and feedback, compact objects and supernova remnants, stellar physics and exoplanets, and time-domain and multi-messenger astrophysics. Together, these studies establish the scientific foundation for next-generation X-ray exploration in the 2030s and highlight strong synergies with facilities of the 2030s, such as JWST, Roman, Rubin/LSST, SKA, ALMA, ngVLA, and next-generation gravitational-wave and neutrino networks.

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preprint2024arXiv

The Origin of the X-ray Emission from the Non-Starburst Gas-Rich Luminous Infrared Galaxies Arp 302

We present an analysis of the XMM-Newton observation of luminous infrared merging galaxies Arp 302 and a joint re-analysis of its Chandra observation. In particular, we focus on the more significant X-ray emitter of the pair, Arp 302N. Chandra detects significant soft X-ray emission from the hot gas in the star-forming region of Arp 302N spreading up to 12 kpc. We estimate the star-formation rate of Arp 302N to be around 1-2 $M_{\odot}$ yr$^{-1}$ based on the X-ray luminosity of the star-forming region, similar to previous measurements at longer wavelengths. Chandra and XMM-Newton observations show evidence of a Si XIII emission line with 86% confidence. Our best-fit model infers a super-solar silicon abundance in the star-forming region, likely related to the past core-collapse supernovae in this galaxy. Similar silicon overabundance was reported in the circumstellar medium of core-collapse supernova remnants in our Galaxy. We also detect narrow Fe K$α$ and Fe K$β$ (98.6% confidence) emission lines as part of the AGN emission. Our best-fit spectral model using Mytorus indicates the evidence of a heavily obscured power-law emission with $N_{\rm H}>3\times10^{24}$ cm$^{-2}$ in addition to a weak, unobscured power-law emission. The scattering fraction of the unobscured power-law emission from Compton-thin materials is 0.7%. All these spectral features suggest evidence of a Seyfert 2-like AGN in Arp 302N. The X-ray measurement of its AGN activity is consistent with the previous Spitzer measurement of the same object.

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preprint2022arXiv

A Disc Reflection Model for Ultra-Soft Narrow-Line Seyfert 1 Galaxies

We present a detailed analysis of the XMM-Newton observations of five narrow-line Seyfert 1 galaxies (NLS1s). They all show very soft continuum emission in the X-ray band with a photon index of $Γ\gtrsim 2.5$. Therefore, they are referred to as `ultra-soft' NLS1s in this paper. By modeling their optical/UV-X-ray spectral energy distribution (SED) with a reflection-based model, we find indications that the disc surface in these ultra-soft NLS1s is in a higher ionisation state than other typical Seyfert 1 AGN. Our best-fit SED models suggest that these five ultra-soft NLS1s have an Eddington ratio of $λ_{\rm Edd}=1-20$ assuming available black hole mass measurements. In addition, our models infer that a significant fraction of the disc energy in these ultra-soft NLS1s is radiated away in the form of non-thermal emission instead of the thermal emission from the disc. Due to their extreme properties, X-ray observations of these sources in the iron band are particularly challenging. Future observations, e.g. from Athena, will enable us to have a clearer view of the spectral shape in the iron band and thus distinguish the reflection model from other interpretations of their broadband spectra.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A multi-wavelength study of GRS 1716-249 in outburst : constraints on its system parameters

We present a detailed study of the evolution of the Galactic black hole transient GRS 1716-249 during its 2016-2017 outburst at optical (Las Cumbres Observatory), mid-infrared (Very Large Telescope), near-infrared (Rapid Eye Mount telescope), and ultraviolet (the Neil Gehrels Swift Observatory Ultraviolet/Optical Telescope) wavelengths, along with archival radio and X-ray data. We show that the optical/near-infrared and UV emission of the source mainly originates from a multi-temperature accretion disk, while the mid-infrared and radio emission are dominated by synchrotron emission from a compact jet. The optical/UV flux density is correlated with the X-ray emission when the source is in the hard state, consistent with an X-ray irradiated accretion disk with an additional contribution from the viscous disk during the outburst fade. We also report the long-term optical light curve of the source and find that the quiescent i-band magnitude is 21.39$\pm$0.15 mag. Furthermore, we discuss how previous estimates of the system parameters of the source are based on various incorrect assumptions, and so are likely to be inaccurate. By comparing our GRS 1716-249 dataset to those of other outbursting black hole X-ray binaries, we find that while GRS 1716-249 shows similar X-ray behaviour, it is noticeably optically fainter, if the literature distance of 2.4 kpc is adopted. Using several lines of reasoning, we argue that the source distance is further than previously assumed in the literature, likely within 4-17 kpc, with a most likely range of $\sim$4-8 kpc.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A NuSTAR and Swift View of the Hard State of MAXI J1813-095

We present an analysis of the NuSTAR and Swift spectra of the black hole candidate MAXI J1813-095 in a failed-transition outburst in 2018. The NuSTAR observations show evidence of reflected emission from the inner region of the accretion disc. By modelling the reflection component in the spectra, we find a disc inner radius of $R_{\rm in}<7$ $r_{\rm g}$. This result suggests that either a slightly truncated disc or a non-truncated disc forms at a few percent of the Eddington limit in MAXI J1813-095. Our best-fit reflection models indicate that the geometry of the innermost accretion remains consistent during the period of NuSTAR observations. The spectral variability of MAXI J1813-095 from multi-epoch observations is dominated by the variable photon index of the Comptonisation emission.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Black Hole Spin Measurements Based on a Thin Disc Model with Finite Thickness I. An example study of MCG-06-30-15

We present a re-analysis of the XMM-Newton and NuSTAR observing campaign 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\% confidence range) after taking the thickness of the disc into consideration. Spectral models with a grid of mass accretion rate from 0 to $30\%\dot{M}_{\rm Edd}$ are calculated for MCG-06-30-15. This result is obtained by considering a free disc reflection fraction parameter $f_{\rm refl}$ 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 $f_{\rm refl}$ in the data. Therefore, thin disc models with consistent `lamppost' values of $f_{\rm refl}$ provide a worse fit than ones with a free $f_{\rm refl}$ parameter. We discuss possible reasons for the discrepancy between the observed and theoretical values of $f_{\rm refl}$ 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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mapping the X-ray corona evolution of IRAS 13224-3809 with the power spectral density

We develop the power spectral density (PSD) model to explain the nature of the X-ray variability in IRAS 13224-3809, including the full effects of the X-ray reverberation due to the lamp-post source. We utilize 16 XMM-Newton observations individually as well as group them into three different luminosity bins: low, medium and high. The soft (0.3-1 keV) and hard (1.2-5 keV) PSD spectra are extracted and simultaneously fitted with the model. We find that the corona height changes from h ~ 3 $\ r_{\rm g}$ during the lowest luminosity state to ~ $25 \ r_{\rm g}$ during the highest luminosity state. This provides further evidence that the source height from the reverberation data is significantly larger than what constrained by the spectral analysis. Furthermore, as the corona height increases, the energy spectrum tends to be softer while the observed fractional excess variance, $F_{\rm var}$, reduces. We find that the PSD normalization is strongly correlated with $F_{\rm var}$, and moderately correlated with the PSD bending index. Therefore, the normalization is dependent on accretion rate that controls the intrinsic shape of the PSD. While the intrinsic variability of the disk is manifested by the reverberation signals, the disk and corona may evolve independently. Our results suggest that, during the source height increases, the disk itself generates less overall variability power but more high-frequency variability resulting in the PSD spectrum that flattens out (i.e. the inner disk becomes more active). Using the luminosity-bin data, the hint of Lorentzian component is seen, with the peak appearing at lower frequencies with increasing luminosity.

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preprint2022arXiv

Rapidly alternating flux states of GX 339-4 during its 2021 outburst captured by Insight-HXMT

The low mass X-ray binary GX 339-4 went into a new outburst in 2021. At the end of the hard to soft transition of this outburst, Insight-HXMT found that the source rapidly alternated between low flux and high flux states on a timescale of hours. Two high flux states lasted only for a period comparable to the orbital period of the observatory. Time-resolved spectral analysis shows that the sudden changes of flux are confined in the hard X-ray band (>4 keV). The variable non-thermal emission, including the power-law continuum from the corona and the reflected emission from the inner accretion disk, is responsible for the observed variability. The strength of disk thermal emission and the inner radius of the accretion disk are consistent between the two flux states. Assuming the lamppost geometry, our best-fit disk reflection models suggest a very low corona height (within 3 $R_{\rm g}$) and there is no evidence of significant variation in the corona geometry either. The observed rapidly alternating flux states suggest that the intrinsic power of the corona must change during the state transition. We discuss possible mechanisms for the observed sudden changes in the coronal power of GX 339-4.

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preprint2022arXiv

The disk wind in GRS 1915+105 as seen by Insight-HXMT

We analyze three observations of GRS 1915+105 in 2017 by Insight-HXMT when the source was in a spectrally soft state. We find strong absorption lines from highly ionized iron, which are due to absorption by disk wind outflowing at a velocity of $\sim$ 1000 km s$^{-1}$ along our line of sight. Two of the three observations show large amplitude oscillation in their light curves and the variation pattern corresponds to state $κ$ of GRS 1915+105. From time-averaged and flux-resolved analysis, we find that the variation of the ionization state of the disk wind follows the X-ray continuum on timescales from hundreds seconds to months. The radial location of the disk wind is consistent with thermal driving. The mass-loss rate due to the outflowing wind is comparable to the mass accretion rate in the inner disk, which demonstrates the important role of the disk wind in the disk accretion system.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

The long-stable hard state of XTE J1752-223 and the disk truncation dilemma

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

XMM-Newton Observations of the Narrow-Line Seyfert 1 Galaxy IRAS 13224$-$3809 : X-ray Spectral Analysis II

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 $10^{15}$ 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 $n_{\rm e}\approx10^{20}$ cm$^{-3}$ and an iron abundance of $Z_{\rm Fe}=3.2\pm0.5Z_{\odot}$ is used to fit the broad-band spectra of this source. No additional component is required to fit the soft excess. Our best-fit model provides consistent measurements of black hole spin and disc inclination angle as in 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$-$3809 based on best-fit density and ionisation parameters, which changes from 0.43$\sqrt{f_{\rm AD}/f_{\rm INF}}$ $r_{\rm g}$ in the lowest flux state to 1.71$\sqrt{f_{\rm AD}/f_{\rm INF}}$ $r_{\rm g}$ in the highest flux state assuming a black hole mass of $2\times10^{6}M_{\odot}$. $f_{\rm AD}/f_{\rm INF}$ 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$-$3809. So we only discuss its value based on the simple `lamp-post' model, although detailed modelling of the disc emissivity profile of IRAS 13224$-$3809 is required in future to reveal the exact geometry of the corona.

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preprint2021arXiv

A significant detection of X-ray Polarization in Sco X-1 with PolarLight and constraints on the corona geometry

We report the detection of X-ray polarization in the neutron star low mass X-ray binary Scorpius (Sco) X-1 with PolarLight. The result is energy dependent, with a non-detection in 3-4 keV but a 4$σ$ detection in 4-8 keV; it is also flux dependent in the 4-8 keV band, with a non-detection when the source displays low fluxes but a 5$σ$ detection during high fluxes, in which case we obtain a polarization fraction of $0.043 \pm 0.008$ and a polarization angle of $52.6^\circ \pm 5.4^\circ$. This confirms a previous marginal detection with OSO-8 in the 1970s, and marks Sco X-1 the second astrophysical source with a significant polarization measurement in the keV band. The measured polarization angle is in line with the jet orientation of the source on the sky plane ($54^\circ$), which is supposedly the symmetric axis of the system. Combining previous spectral analysis, our measurements suggest that an optically thin corona is located in the transition layer under the highest accretion rates, and disfavor the extended accretion disk corona model.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A NuSTAR View of GRS 1716$-$249 in the Hard and Intermediate States

We present a detailed analysis of the spectral properties of the black hole transient GRS 1716-249, based on the archival Swift and NuSTAR observations taken during the outburst of this source in 2016-2017. The first six NuSTAR observations show that the source is in a canonical hard state, where the spectrum is dominated by a power-law continuum. The seventh NuSTAR observation is taken during the intermediate state where both a disc thermal component and a power-law continuum are shown. All of our observations show a broad emission line feature in the iron band and a Compton hump above 10 keV. We model the broad band spectra using a high density disc reflection model, where the soft X-ray emission in the hard state is interpreted as part of the disc reflection component. This model enables us to constrain the disc density parameter of GRS 1716-249 in the range of $10^{19}$-$10^{20}$ cm$^{-3}$. We only obtain an upper limit of the inner disc radius using high density disc reflection spectroscopy and the results indicate either a non-truncated disc or a slightly truncated disc with $R_{\rm in}<20r_{\rm g}$.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A study for testing the Kerr metric with AGN iron line eclipses

Recently, two of us have studied iron line reverberation mapping to test black hole candidates, showing that the time information in reverberation mapping can better constrain the Kerr metric than the time-integrated approach. Motivated by this finding, here we explore the constraining power of another time-dependent measurement: an AGN iron line eclipse. An obscuring cloud passes between the AGN and the distant observer, covering different parts of the accretion disk at different times. Similar to the reverberation measurement, an eclipse might help to better identify the relativistic effects affecting the X-ray photons. However, this is not what we find. In our study, we employ the Johannsen-Psaltis parametrisation, but we argue that our conclusions hold in a large class of non-Kerr metrics. We explain our results pointing out an important difference between reverberation and eclipse measurements.

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preprint2016arXiv

Testing the Kerr black hole hypothesis: comparison between the gravitational wave and the iron line approaches

The recent announcement of the detection of gravitational waves by the LIGO/Virgo collaboration has opened a new window to test the nature of astrophysical black holes. Konoplya & Zhidenko have shown how the LIGO data of GW 150914 can constrain possible deviations from the Kerr metric. In this letter, we compare their constraints with those that can be obtained from accreting black holes by fitting their reflected X-ray spectrum, the so-called iron line method. We simulate observations with eXTP, a next generation X-ray mission, finding constraints much stronger than those obtained by Konoplya & Zhidenko. Our results can at least show that, contrary to what is quite commonly believed, it is not obvious that gravitational waves are the most powerful approach to test strong gravity. In the presence of high quality data and with the systematics under control, the iron line method may provide competitive constraints.

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preprint2016arXiv

Testing the Kerr metric with the iron line and the KRZ parametrization

The spacetime geometry around astrophysical black holes is supposed to be well approximated by the Kerr metric, but deviations from the Kerr solution are predicted in a number of scenarios involving new physics. Broad iron K$α$ lines are commonly observed in the X-ray spectrum of black holes and originate by X-ray fluorescence of the inner accretion disk. The profile of the iron line is sensitively affected by the spacetime geometry in the strong gravity region and can be used to test the Kerr black hole hypothesis. In this paper, we extend previous work in the literature. In particular: i) as test-metric, we employ the parametrization recently proposed by Konoplya, Rezzolla, and Zhidenko, which has a number of subtle advantages with respect to the existing approaches; ii) we perform simulations with specific X-ray missions, and we consider NuSTAR as a prototype of current observational facilities and eXTP as an example of the next generation of X-ray observatories. We find a significant difference between the constraining power of NuSTAR and eXTP. With NuSTAR, it is difficult or impossible to constrain deviations from the Kerr metric. With eXTP, in most cases we can obtain quite stringent constraints (modulo we have the correct astrophysical model).

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preprint2016arXiv

Testing the Kerr nature of black hole candidates using iron line reverberation mapping in the CPR framework

The iron K$α$ line commonly observed in the X-ray spectrum of black hole candidates is produced by X-ray fluorescence of the inner accretion disk. This line can potentially be quite a powerful tool to probe the spacetime geometry around these objects and test the Kerr black hole hypothesis. In a previous paper, we studied the ability to constrain possible deviations from the Kerr solution from the standard time-integrated iron line spectrum within the Cardoso-Pani-Rico framework. In the present work, we expand on that study and consider iron line reverberation mapping in the CPR framework. That is, we consider the time-evolution of the iron line profile in response to fluctuations in the X-ray primary source. Our simulations clearly show that the time information in reverberation mapping can better constrain the background metric than the time-integrated approach, and this is true, notably, for the deformation parameter $ε^r_3$, which is only weakly informed by a time-integrated observation.

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preprint2016arXiv

Testing the no-hair theorem with the continuum-fitting and the iron line methods: a short review

The continuum-fitting and the iron line methods are leading techniques capable of probing the spacetime geometry around astrophysical black hole candidates and testing the no-hair theorem. In the present paper, we review the two approaches, from the astrophysical models and their assumptions, to the constraining power with present and future facilities.

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preprint2015arXiv

Testing the Kerr Nature of Black Hole Candidates using Iron Line Spectra in the CPR Framework

The iron K$α$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates originates from X-ray fluorescence of the inner accretion disk. Accordingly, it can be used to map the spacetime geometry around these objects. In this paper, we extend previous work using the iron K$α$ line to test the Kerr black hole hypothesis. We adopt the Cardoso-Pani-Rico parametrization and we test the possibility of constraining possible deviations from the Kerr solution that can be obtained from observations across the range of black hole spins and inclination angles. We confirm previous claims that the iron K$α$ line is potentially a quite powerful probe for testing the Kerr metric given sufficiently high quality data and with systematics under control, especially in the case of fast-rotating black holes and high inclination angles since both conditions serve to maximize relativistic effects. We find that some geometric perturbations from Kerr geometry manifest more strongly in the iron line profile than others. While the perturbation parameter $ε^t_3$ can be well constrained by the iron line profile, an orthogonal data set is necessary to constrain departures from Kerr geometry in $ε^r_3$.

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preprint2015arXiv

Using iron line reverberation and spectroscopy to distinguish Kerr and non-Kerr black holes

The iron K$α$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates is produced by the illumination of a cold accretion disk by a hot corona. In this framework, the activation of a new flaring region in the hot corona imprints a time variation on the iron line spectrum. Future X-ray facilities with high time resolution and large effective areas may be able to measure the so-called 2-dimensional transfer function; that is, the iron line profile detected by a distant observer as a function of time in response to an instantaneous flare from the X-ray primary source. This work is a preliminary study to determine if and how such a technique can provide more information about the spacetime geometry around the compact object than the already possible measurements of the time-integrated iron line profile. Within our simplified model, we find that a measurement of iron line reverberation can improve constraints appreciably given a sufficiently strong signal, though that most of the information is present in the time-integrated spectrum. Our aim is to test the Kerr metric. We find that current X-ray facilities and data are unable to provide strong tests of the Kerr nature of supermassive black hole candidates. We consider an optimistic case of $10^5$ iron line photons from a next-generation data set. With such data, the reverberation model improves upon the spectral constraint by an order of magnitude.

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