The reflection spectroscopic model RELXILL is commonly implemented in studying relativistic X-ray reflection from accretion disks around black holes. We present a systematic study of the model's capability to constrain the dimensionless spin and ionization parameters from $\sim$6,000 NuSTAR simulations of a bright X-ray source employing the lamppost geometry. We employ high count spectra to show the limitations in the model without being confused with limitations in signal-to-noise. We find that both parameters are well-recovered at 90% confidence with improving constraints at higher reflection fraction, high spin, and low source height. We test spectra across a broad range - first at 10$^6-$10$^7$ and then $\sim$10$^5$ total source counts across the effective 3-79 keV band of NuSTAR, and discover a strong dependence of the results on how fits are performed around the starting parameters, owing to the complexity of the model itself. A blind fit chosen over an approach that carries some estimates of the actual parameter values can lead to significantly worse recovery of model parameters. We further stress on the importance to span the space of nonlinear-behaving parameters like $log~ξ$ carefully and thoroughly for the model to avoid misleading results. In light of selecting fitting procedures, we recall the necessity to pay attention to the choice of data binning and fit statistics used to test the goodness of fit by demonstrating the effect on the photon index $Γ$. We re-emphasize and implore the need to account for the detector resolution while binning X-ray data and using Poisson fit statistics instead while analyzing Poissonian data.
We present the public release version of relxill_nk, an X-ray reflection model for testing the Kerr hypothesis and general relativity. This model extends the relxill model that assumes the black hole spacetime is described by the Kerr metric. We also present relxilllp_nk, the first non-Kerr X-ray reflection model with a lamppost corona configuration, as well as all other models available in the full relxill_nk package. In all models the relevant relativistic effects are calculated through a general relativistic ray-tracing code that can be applied to any well-behaved, stationary, axisymmetric,…
In this paper, we briefly present RELXILL_NK, the first and currently only readily available model of the relativistic reflection spectrum of black hole accretion disks that includes non-Kerr solutions for the black hole spacetime, thus allowing for tests of the Kerr hypothesis and GR. RELXILL_NK makes use of a general relativistic ray-tracing code to calculate the relativistic effects of any well-behaved, stationary, axisymmetric, and asymptotically flat black hole spacetime, while the disk physics is handled through the non-relativistic X-ray reflection code XILLVER. A number of different fl…
The models currently used for the analysis of the reflection spectra of black holes usually assume a disk with constant ionization and electron density. However, there is some debate on the impact of these assumptions on the estimate of the properties of the sources, in particular when the fits suggest very steep emissivity profiles in the inner part of the accretion disk. In this work, we re-analyze a selected set of high-quality NuSTAR and Suzaku data of Galactic black holes and we fit the reflection component with three different models: RELXILL_NK, in which the ionization parameter and the…
Einstein's theory of general relativity was proposed over 100 years ago and has successfully passed a large number of observational tests in the weak field regime. However, the strong field regime is largely unexplored, and there are many modified and alternative theories that have the same predictions as Einstein's gravity for weak fields and present deviations when gravity becomes strong. RELXILL_NK is the first relativistic reflection model for probing the spacetime metric in the vicinity of astrophysical black holes and testing Einstein's gravity in the strong field regime. Here we present…
We present a detailed spectral analysis of the black hole candidate MAXI J1836-194. The source was caught in the intermediate state during its 2011 outburst by Suzaku and RXTE. We jointly fit the X-ray data from these two missions using the relxill model to study the reflection component, and a steep inner emissivity profile indicating a compact corona as the primary source is required in order to achieve a good fit. In addition, a reflection model with a lamp-post configuration (relxilllp), which is normally invoked to explain the steep emissivity profile, gives a worse fit and is excluded at…
We present new reflection models specifically tailored to model the X-ray radiation reprocessed in accretion disks around neutron stars, in which the primary continuum is characterized by a single temperature blackbody spectrum, emitted either at the surface of the star, or at the boundary layer. These models differ significantly from those with a standard power-law continuum, typically observed in most accreting black holes. We show comparisons with earlier reflection models, and test their performance in the NuSTAR observation of the neutron star 4U 1705-44. Simulations of upcoming missions …
Very steep reflection emissivity profiles in the inner part of accretion disks are commonly found in the analysis of X-ray observations of black hole binaries and AGN, but there is some debate about their exact origin. While steep reflection emissivity profiles can be naturally produced by compact coronae close to black holes, the measured radial emissivity parameter can be further increased by the radial disk ionization profile when the theoretical model assumes a disk with constant ionization. In this paper, we implement the possibility of a radial disk ionization profile in the reflection m…
The profile of the fluorescent iron line from black hole accretion disks is a powerful diagnostic of black hole properties, such as spin and inclination. The state-of-the-art, however, considers an accretion disk whose angular momentum is aligned with that of the black hole; this is a very constraining assumption which is unlikely to apply to many or even most astrophysical systems. Here, we present the first simulation of the reflection spectrum from warped accretion disks using a realistic model of the reflected emission based on the xillver code. We present the effects that the radial locat…
In a previous paper, we tried to test the Kerr nature of the stellar-mass black hole in GRS 1915+105 by analyzing NuSTAR data of 2012 with our reflection model RELXILL_NK. We found that the choice of the intensity profile of the reflection component is crucial and eventually we were not able to get any constraint on the spacetime metric around the black hole in GRS 1915+105. In the present paper, we study the same source with Suzaku data of 2007. We confirm that the intensity profile plays an important role, but now we find quite stringent constraints consistent with the Kerr hypothesis. The k…
Relativistic reflection within an extended hot plasma geometry
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Dr. Karl Remeis-Sternwarte & ECAP（卡尔·雷梅斯天文台与极端条件天体物理中心）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；California Institute of Technology（加州理工学院）；University of Hertfordshire（赫特福德大学）；Universität Würzburg（维尔茨堡大学）；Goethe Universität（歌德大学）；Max-Planck-Institut für Radioastronomie（马克斯·普朗克射电天文研究所）；H. H. Wills Physics Laboratory（H.H.威尔斯物理实验室）；Center for Astrophysics | Harvard & Smithsonian（哈佛-史密森尼天体物理中心）
Type I X-ray bursts are the result of an unstable thermonuclear burning of accreting matter on the neutron star (NS) surface. The quick release of energetic X-ray photons during such bursts interacts with the surrounding accretion disk, which raises the accretion rate due to Poynting-Robertson drag and, thus, a fraction of the burst emission is reflected. We analyzed two photospheric radius expansion bursts in the NS low-mass X-ray binary 4U 1636--536 that took place in 2017, using data from Neutron star Interior Composition Explorer. The time-resolved burst spectra showed clear deviations fro…
Measuring relativistic reflection is an important tool to study the innermost regions of the an accreting black hole system. In the following we present a brief review on the different aspects contributing to the relativistic reflection. The combined approach is for the first time incorporated in the new relxill model. The advantages of this more self-consistent approach are briefly summarized. A special focus is put on the new definition of the intrinsic reflection fraction in the lamp post geometry, which allows to draw conclusions about the primary source of radiation in these system. Addit…
We present a spectral analysis of NuSTAR and NICER observations of the luminous, persistently accreting neutron star (NS) low-mass X-ray binary Cygnus X-2. The data were divided into different branches that the source traces out on the Z-track of the X-ray color-color diagram; namely the horizontal branch, normal branch, and the vertex between the two. The X-ray continuum spectrum was modeled in two different ways that produced a comparable quality fit. The spectra showed clear evidence of a reflection component in the form of a broadened Fe K line, as well as a lower energy emission feature n…
We report the results from \textit{AstroSat} observations of the transient Galactic black hole X-ray binary MAXI J1535-571 during its hard-intermediate state of the 2017 outburst. We systematically study the individual and joint spectra from two simultaneously observing \textit{AstroSat} X-ray instruments, and probe and measure a number of parameter values of accretion disc, corona and reflection from the disc in the system using models with generally increasing complexities. Using our broadband ($1.3-70$ keV) X-ray spectrum, we clearly show that a soft X-ray instrument, which works below $\si…
Recently, we have extended the X-ray reflection model relxill to test the spacetime metric in the strong gravitational field of astrophysical black holes. In the present Letter, we employ this extended model to analyze XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495 and test deviations from a Kerr metric parametrized by the Johannsen deformation parameter $α_{13}$. Our results are consistent with the hypothesis that the spacetime metric around the black hole in 1H0707-495 is described by the Kerr solution.
The primary X-ray emission from AGN, described by a power law, irradiates the accretion disc producing reflection features in the spectrum. The reflection features arising from the inner regions of the disc can be significantly modified by the relativistic effects near the black hole. We investigate the relationship between the relativistic reflection fraction $R_f$, defined as the ratio of the coronal intensity that illuminates the accretion disc to the coronal intensity observed directly, and the hard X-ray photon index $Γ$ of a NuSTAR sample of Seyfert 1 galaxies. The X-ray spectra are mode…
We report the spectral analysis of accretion powered millisecond X-ray pulsar SAX J1748.9-2021 from the NuSTAR observation made during its 2015 outburst. The spectra displayed a broad emission line at $\sim 6.5$ keV with line width of $\sim 0.5$ keV and excess above $\sim 20$ keV due to Compton hump. The persistent emission of SAX J1748.9-2021 is described by a combination of soft thermal component with $kT =0.62^{+0.03}_{-0.05}$ keV and thermally Comptonized component with $kT_e=2.50^{+0.06}_{-0.03}$ keV reflected from the disc with reflection fraction of $0.30^{+0.08}_{-0.04}$. We have model…
We analyze simultaneous observations with NuSTAR and Swift of the black hole binary GX 339-4 in which we clearly detect both a strong thermal component and prominent relativistic reflection features. We employ NKBB and RELXILL_NK, which are the state of the art of, respectively, the thermal and reflection models to test the Kerr black hole hypothesis. We obtain unprecedented precise measurements of the Johannsen deformation parameter $α_{13}$: $α_{13} = -0.012_{-0.039}^{+0.011}$ (lamppost coronal geometry) and $α_{13} = -0.010_{-0.018}^{+0.024}$ (broken power-law emissivity profile) at a 90% c…
Modeling X-ray reflection spectra from disk returning radiation: Application to 4U 1630-47
Eberhard-Karls Universität Tübingen（蒂宾根大学）；Fudan University（复旦大学）；Ulugh Beg Astronomical Institute of the Uzbekistan Academy of Sciences（乌兹别克斯坦科学院乌卢格别克天文研究所）；New Uzbekistan University（新乌兹别克斯坦大学）；University of Warwick（华威大学）
Einstein's gravity has been extensively tested in the weak field regime, primarily with experiments in the Solar System and observations of binary pulsars, and current data agree well with theoretical predictions. On the other hand, strong gravity is largely unexplored and there are a number of theories beyond Einstein's gravity that make the same predictions for weak fields and present deviations only when gravity becomes strong. The best laboratory for testing strong gravity is the spacetime around astrophysical black holes. X-ray reflection spectroscopy can be a powerful tool to probe the s…
We report on the first simultaneous $NICER$ and $NuSTAR$ observations of the neutron star (NS) low-mass X-ray binary 4U 1735$-$44, obtained in 2018 August. The source was at a luminosity of $\sim1.8~(D/5.6\ \mathrm{kpc})^{2}\times10^{37}$ ergs s$^{-1}$ in the $0.4-30$ keV band. We account for the continuum emission with two different continuum descriptions that have been used to model the source previously. Despite the choice in continuum model, the combined passband reveals a broad Fe K line indicative of reflection in the spectrum. In order to account for the reflection spectrum we utilize a…
Irradiation of the accretion disc causes reflection signatures in the observed X-ray spectrum, encoding important information about the disc structure and density. A Type I X-ray burst will strongly irradiate the accretion disc and alter its properties. Previous numerical simulations predicted the evolution of the accretion disc due to an X-ray burst. Here, we process time-averaged simulation data of six time intervals to track changes in the reflection spectrum from the burst onset to just past its peak. We divide the reflecting region of the disc within $r\lesssim50$ km into 6-7 radial zones…
X-ray reflection spectroscopy is a powerful tool for probing the strong gravity region of black holes and can be used for testing general relativity in the strong field regime. Simplifications of the available relativistic reflection models limit the capability of performing accurate measurements of the properties of black holes. In this paper, we present an extension of the model RELXILL_NK in which the accretion disk has a finite thickness rather than being infinitesimally thin. We employ the accretion disk geometry proposed by Taylor & Reynolds (2018) and we construct relativistic reflectio…
We present a high density disc reflection spectral analysis of a sample of 17 Seyfert 1 galaxies to study the inner disc densities at different black hole mass scales and accretion rates. All the available XMM-Newton observations in the archive are used. OM observations in the optical/UV band are used to estimate their accretion rates. We find that 65% of sources in our sample show a disc density significantly higher than 1e15 cm^{-3}, which was assumed in previous reflection-based spectral analyses. The best-fit disc densities show an anti-correlation with black hole mass and mass accretion r…
NuSTAR observed the black hole candidate XTE J1908$+$094 during its 2013 and 2019 outbursts. We use relativistic reflection to measure the spin of the black hole through 19 different assumptions of relxill flavors and parameter combinations. The most favored model in terms of Deviance Information Criterion (DIC) measures the spin of the black hole to be $a = 0.55^{+0.29}_{-0.45}$, and an inclination of $θ=27^{+2}_{-3}$ degrees ($1σ$ statistical errors). We look at the effects of coronal geometry assumptions and density of the accretion disk on the spin prediction. All 19 tested models provide …
A multi-epoch X-ray spectral and variability analysis is conducted for the narrow-line Seyfert 1 (NLS1) active galactic nucleus (AGN) Mrk 478. All available X-ray data from XMM-Newton and Suzaku satellites, spanning from 2001 to 2017, are modelled with a variety of physical models including partial covering, soft-Comptonisation, and blurred reflection, to explain the observed spectral shape and variability over the 16 years. All models are a similar statistical fit to the data sets, though the analysis of the variability between data sets favours the blurred reflection model. In particular, th…
We present the study of a sample of seven "bare" active galactic nuclei (AGN) observed with Suzaku. We interpret the spectrum of these sources with a relativistic reflection component and we employ our model RELXILL_NK to test the Kerr nature of their supermassive black holes. We constrain the Johannsen deformation parameters $α_{13}$ and $α_{22}$, in which the Kerr metric is recovered when $α_{13} = α_{22} = 0$. All our measurements are consistent with the hypothesis that the spacetime geometry around these supermassive objects is described by the Kerr solution. For some sources, we obtain qu…
X-ray reflection in oxygen-rich accretion discs of ultra-compact X-ray binaries
我们给出了两个候选超致密X射线双星4U~0614+091和4U~1543 $-$ 624的光谱X射线数据。我们使用2012年和2013年获得的{ \it XMM-牛顿}和{ \it钱德拉}观测结果确认了宽O VIII Ly $α$反射线（在$\approx18\ Å$）的存在。这些来源中的施主星是碳-氧或氧-氖-镁白矮星。因此，吸积盘富含氧，这使得O VIII Ly $α$线特别强。我们还证实了一个强大的吸收边在$\approx14$的存在，到目前为止，在文献中解释为由于中性氖在拱星和星际介质的吸收。然而，要获得一个很好的拟合到这个边缘所需的丰度是$\approx3-4$倍太阳，提出了一个问题，这种解释。此外，用假设太阳成分的模型对富含碳和氧、氢和氦贫乏的盘的X射线反射进行建模可能会使几个最佳拟合参数偏置。为了自洽地描述X射线反射谱，我们修改了现有的{ \sc xillver}反射模型。我们提出了初始网格，可以用来模拟X射线反射光谱的UCXB与富碳氧吸积盘。结果表明，与假设太阳丰度的反射模型相比，新的反射模型能更好地描述4U~0614+091和4U~1543 $-$ 624的反射谱.除了强O VIII Ly $α$线外，新的反射模型还显示出强O VIII K边缘（在$14.23$线处）。我们发现，在$\approx 14$的吸收边的数据中存在的O VIII K-边缘形成由于在吸积盘…
Accretion disk signatures in Type I X-ray Bursts: prospects for future missions
来自吸积中子星的I型X射线爆发和超爆发照亮了吸积盘，并产生了反射信号，随着爆发的减弱而演变。研究光谱中反射特征的演变将使我们深入了解爆发-吸积盘相互作用，这是吸积盘物理学的一个潜在的强有力的探测器。目前，仅在两次异常持续时间的爆发期间观察到反射。我们调查的反射签名的可探测性与四个最新的研究X射线天文台的概念：瞳，NICER，雅典娜，和LOFT。突发光谱建模为不同的值的通量，温度和磁盘电离参数，这是最已知的爆发和源的代表。Hitomi类望远镜的有效面积和吞吐量不足以表征爆发反射特征。NICER和Athena将检测具有峰值通量$\ge 10^{-7.5}$ erg cm $^{-2}$ s $^{-1}$的I型爆发中的反射特征，并且还有效地约束在几秒钟的曝光中具有$10^{-7}$ erg cm $^{-2}$ s $^{-1}$的通量的明亮爆发的反射参数。因此，这些天文台将为吸积流和X射线爆发的相互作用提供至关重要的新见解。对于具有低视线吸收的源，这些仪器的宽带通允许检测软X射线反射特征，其对盘金属丰度和密度敏感。作为LOFT设计一部分的大收集区域将通过在整个短爆发中详细追踪吸积几何形状的演变来彻底改变该领域。
The black hole candidate MAXI J1348-630 was discovered on January 26th, 2019, with the Gas Slit Camera (GSC) on-board \textit{MAXI}. We report a detailed spectral analysis of this source by using the archived data of \textit{NuSTAR}. A total of 9 observations covered the complete outburst evolution of MAXI J1348-630 from the hard state to the soft state and finally back to the hard state. Additionally, the intermediate state is found in the transition from the hard state to the soft state. We use the state-of-art reflection model \verb'relxill' family to fit all the 9 spectra, and the spectra …
We study the effect of returning radiation on the shape of the X-ray reflection spectrum in the case of thin accretion disks. We show that the returning radiation mainly influences the observed reflection spectrum for a large black hole spin (a > 0.9) and a compact primary source of radiation close to the black hole at height h < 5 $r_\mathrm{g}$, and that it dominates the reflected flux for extreme values of spin and compactness. The main effect of the returning radiation is to increase the irradiating flux on to the outer parts of the accretion disk, leading to stronger reflection and a flat…
X-ray reflection spectroscopy is a promising technique for testing general relativity in the strong field regime, as it can be used to test the Kerr black hole hypothesis. In this context, the parametrically deformed black hole metrics proposed by Konoplya, Rezzolla \& Zhidenko (Phys. Rev. D93, 064015, 2016) form an important class of non-Kerr black holes. We implement this class of black hole metrics in \textsc{relxill\_nk}, which is a framework we have developed for testing for non-Kerr black holes using X-ray reflection spectroscopy. We perform a qualitative analysis of the effect of the le…
The Novikov-Thorne model is the standard framework for the description of geometrically thin and optically thick accretion disks around black holes and is widely used to study the electromagnetic spectra of accreting black holes. One of the assumptions of the model is that the particles of the gas move on nearly-geodesic circular orbits on the equatorial plane. In this work, we propose to test the Keplerian velocity of the particles in the accretion disk using X-ray reflection spectroscopy. We present a modified version of RELXILL in which we introduce a phenomenological parameter, $α$, to qua…
