arXiv subjects

Jun-Xian Wang

Publications and source records attributed to Jun-Xian Wang.

At least 37 records · Page 2Linked to original sources

arXiv2024

On joint analysing XMM-NuSTAR spectra of active galactic nuclei

A recently released XMM-Newton technical note has revealed a significant calibration issue between NuSTAR and XMM-Newton EPIC, and provided an empirical correction to EPIC effective area. To quantify the bias caused by the calibration issue to joint analysis of XMM-NuSTAR spectra and verify the effectiveness of the correction, in this work we perform joint-fitting of NuSTAR and EPIC-pn spectra for a large sample of 104 observation pairs of 44 X-ray bright AGN. The spectra were extracted after requiring perfect simultaneity between XMM-Newton and NuSTAR exposures (merging GTIs from two missions) to avoid bias due to rapid spectral variability of AGN. Before the correction, the EPIC-pn spectra are systematically harder than corresponding NuSTAR spectra by $ΔΓ\sim 0.1$, subsequently yielding significantly underestimated cutoff energy $E_{\rm cut} $ and the strength of reflection component R when performing joint-fitting. We confirm the correction is highly effective and can commendably erase the discrepancy in best-fit $Γ$, $E_{\rm cut} $ and R, and thus we urge the community to apply the correction when joint-fitting XMM-NuSTAR spectra. Besides, we show that as merging GTIs from two missions would cause severe loss of NuSTAR net exposure time, in many cases joint-fitting yields no advantage compared with utilizing NuSTAR data alone. We finally present a technical note on filtering periods of high background flares for XMM-Newton EPIC-pn exposures in the Small Window mode.

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arXiv2024

Could the inter-band lag of active galactic nucleus vary randomly?

The inter-band lags among the optical broad-band continua of active galactic nuclei (AGNs) have been intensively explored over the past decade. However, the nature of the lags remains under debate. Here utilizing two distinct scenarios for AGN variability, i.e., the thermal fluctuation of accretion disk and the reprocessing of both the accretion disk and clouds in the broad line region, we show that, owing to the random nature of AGN variability, the inter-band lags of an individual AGN would vary from one campaign with a finite baseline to another. Specifically, the thermal fluctuation scenario implies larger variations in the lags than the reprocessing scenario. Moreover, the former predicts a positive correlation between the lag and variation amplitude, while the latter does not result in such a correlation. For both scenarios, averaging the lags of an individual AGN measured with repeated and non-overlapping campaigns would give rise to a stable lag, which is larger for a longer baseline and gets saturation for a sufficiently long baseline. However, obtaining the stable lag for an individual AGN is very time-consuming. Alternatively, it can be equivalently inferred by averaging the lags of a sample of AGNs with similar physical properties, thus can be properly compared with predictions of AGN models. In addition, discussed are several new observational tests suggested by our simulations as well as the role of the deep high-cadence surveys of the Wide Field Survey Telescope in enriching our knowledge of the lags.

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arXiv2024

Varstrometry Selected Radio-Loud Candidates of Dual and Off-Nucleus Quasars at Sub-kpc Scales

Dual super massive black holes at sub-kpc to kpc scales, the product of galaxy mergers, are progenitors of eventually coalescing binary SMBHs. If both or one of the dual SMBHs are accreting, they may appear as dual AGNs or off-nucleus AGNs. Studying such systems is essential to learn the dynamical evolution of binary SMBHs as well as the process of galaxy merging. Recently a novel astrometry-based method named varstrometry has been put forward to search for dual SMBHs at high redshift, as the unsynchronized flux variability of dual AGNs (or off-nucleus AGNs) will cause astrometric jitters detectable by Gaia without spatially resolving them. Based on Gaia varstrometry we select a rare sample of 5 radio loud quasars with clear Gaia astrometric jitters. With e-MERLIN observations we have revealed a single compact radio source for each of them. Remarkably all but one exhibit clear Gaia-radio offsets of ~ 7 -- 40 mas. The observed Gaia jitters appear consistent with the expected values. These detected Gaia-radio offsets suggest these candidate dual SMBHs may have projected separations as small as ~ 0.01 -- 0.1'' (~ 0.1 kpc, depending on the optical flux ratio of two SMBHs). Meanwhile, this work highlights the remarkably high efficiency of Gaia varstrometry selection of jittering sources.

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arXiv2024

Intermediate-Mass Black Holes in Green Pea Galaxies (IMBH-GP) I: a Candidate Sample from LAMOST and SDSS

The scaling relation of central massive black holes (MBHs) and their host galaxies is well-studied for supermassive BHs (SMBHs, $M_{\rm BH}\ \ge 10^6\, M_{\rm \odot}$). However, this relation has large uncertainties in the mass range of the intermediate-mass BHs (IMBHs, $M_{\rm BH}\ \sim10^3-10^{6}\, M_{\rm \odot}$). Since Green Pea (GP) galaxies are luminous compact dwarf galaxies, which may be likely to host less massive SMBHs or even IMBHs, we systematically search for MBHs in a large sample of 2190 GP galaxies at $z < 0.4$, selected from LAMOST and SDSS spectroscopic surveys. Here, we report a newly discovered sample of 59 MBH candidates with broad H$α$ lines. This sample has a median stellar mass of $10^{8.83\pm0.11}\, M_{\rm \odot}$ and hosts MBHs with single-epoch virial masses ranging from $M_{\rm BH}\ \sim 10^{4.7}$ to $10^{8.5}\, M_{\rm \odot}$ (median $10^{5.85\pm0.64}\, M_{\rm \odot}$). Among the 59 MBH candidates, 36 have black hole masses $M_{\rm BH} \le 10^{6}\, M_{\rm \odot}$ (IMBH candidates), one of which even has $M_{\rm BH} \ \lesssim 10^{5}\, M_{\rm \odot}$. We find that the $M_{\rm BH}-M_{\rm *}$ relation of our MBH sample is consistent with the $M_{\rm BH}-M_{\rm bulge}$ relation for SMBHs, while is above the $M_{\rm BH}-M_{\rm *}$ relation for MBHs in dwarf galaxies in the same mass range. Furthermore, we show that 25 MBH candidates, including 4 IMBH candidates, have additional evidence of black hole activities, assessed through various methods such as the broad-line width, BPT diagram, mid-infrared color, X-ray luminosity, and radio emission. Our studies show that it is very promising to find IMBHs in GP galaxies, and the BH sample so obtained enables us to probe the connection between the MBHs and compact dwarf galaxies in the low-redshift Universe.

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arXiv2024

Is quasar variability regulated by the close environment of accretion?

UV/optical variability in quasars is a well-observed phenomenon, yet its primeval origins remain unclear. This study investigates whether the accretion disk turbulence, which is responsible for UV/optical variability, is influenced by the close environment of the accretion by analyzing the correlation between variability and infrared emission for two luminous SDSS quasar samples. The first sample includes light curves from SDSS, Pan-STARRS, and ZTF $g$ band photometry, while the second sample utilizes SDSS Stripe 82 $g$ band light curves. We explore the correlation between the $g$ band excess variance ($σ_{rms}$) and the wavelength-dependent infrared covering factor ($L_{\rm IR}(λ)/L_{\rm bol}$), controlling for the effects of redshift, luminosity, and black hole mass. An anti-correlation between two variables is observed in both samples, which is strongest at wavelengths of 2-3$μ$m but gradually weakens towards longer wavelength. This suggests the equatorial dusty torus (which dominates near-infrared emission) plays a significant role in influencing the UV/optical variability, while the cooler polar dust (which contributes significantly to mid-infrared emission) does not. The findings indicate that quasar variability may be connected to the physical conditions within the dusty torus which feeds the accretion, and support the notion that the close environment of the accretion plays an important role in regulating the accretion disk turbulence.

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arXiv2024

Integrated Study of X-ray Spectrum and Time Lags for HBL Mrk 421 within the Framework of the Multiple-Zone Leptonic Model

We present the timing analysis of 10 archived \XMM observations with an exposure of $>40$ ks of Markarian 421. Mrk 421 is the brightest high-frequency-peaked BL Lac object (HBL) emitting in X-rays produced by electrons accelerated in the innermost regions of a relativistic jet pointing toward us. For each observation, we construct averaged X-ray spectra in 0.5--10 keV band, as well as 100 s binned light curves (LCs) in various subbands. During these observations, the source exhibited various intensity states differing by close to an order of magnitude in flux, with the fractional variability amplitude increasing with energy through the X-ray band. Bayesian power spectral density analysis reveals that the X-ray variability can be characterized by a colored noise, with an index ranging from $\sim-1.9$ to $-3.0$. Moreover, both the standard cross-correlation function and cross-spectral methods indicate that the amount of time lags increases with the energy difference between two compared LCs. A time-dependent two-zone jet model is developed to extract physical information from the X-ray emission of Mrk 421. In the model, we assume that the jet emission mostly comprises a quasi-stationary component and a highly variable one. Our results show that the two-zone model can simultaneously provide a satisfactory description for both the X-ray spectra and time lags observed in different epochs, with the model parameters constrained in a fully acceptable interval. We suggest that shocks within the jets may be the primary energy dissipation process responsible for triggering the rapid variability, although magnetic reconnection cannot be excluded.

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arXiv2024

A surprising excess of radio emission in extremely stable quasars: a unique clue to jet launching?

Quasars are generally divided into jetted radio-loud and non-jetted radio-quiet ones, but why only 10% quasars are radio loud has been puzzling for decades. Other than jet-induced-phenomena, black hole mass, or Eddington ratio, prominent difference between jetted and non-jetted quasars has scarcely been detected. Here we show a unique distinction between them and the mystery of jet launching could be disclosed by a prominent excess of radio emission in extremely stable quasars (ESQs, i.e., type 1 quasars with extremely weak variability in UV/optical over 10 years). Specifically, we find that $>$ 25% of the ESQs are detected by the FIRST/VLASS radio survey, while only $\sim$ 6-8% of the control sample, matched in redshift, luminosity, and Eddington ratio, are radio-detected. The excess of radio detection in ESQs has a significance of 4.4 $σ$ (99.9995%), and dominantly occurs at intermediate radio loudness with R $\sim$ 10 - 60. The radio detection fraction of ESQs also tends to increase in the ESQ samples selected with more stringent thresholds. Our results are in contrast to the common view that RL quasars are likely more variable in UV/optical due to jet contribution. New clues/challenge posed by our findings highlight the importance of extensive follow-up observations to probe the nature of jets in ESQs, and theoretical studies on the link between jet launching and ESQs. Moreover, our results makes ESQs, an essential population which has never been explored, unique targets in the burgeoning era of time domain astronomy, like their opposite counterparts of quasars exhibiting extreme variability or changing-look features.

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arXiv2024

A new timescale-mass scaling for the optical variation of active galactic nuclei across the intermediate-mass to supermassive scales

Variability of active galactic nuclei (AGNs) has long been servicing as an essential avenue of exploring the accretion physics of black hole (BH). There are two commonly used methods for analyzing AGN variability. First, the AGN variability, characterized by the structure function (SF) of a single band, can be well described by a damped random walk (DRW) process on timescales longer than ~weeks, shorter than which departures have been reported. Second, the color variation (CV) between two bands behaves timescale-dependent, raising challenges to the widely accepted reprocessing scenario. However, both the departure from the DRW process and the timescale-dependent CV are hitherto limited to AGNs, mainly quasars, at the supermassive scale. Here, utilizing the high-cadence multi-wavelength monitoring on NGC 4395 harboring an intermediate-mass BH, we unveil at the intermediate-mass scale for the first time, prominent departures from the DRW process at timescales shorter than ~hours in all three nights and bands, and plausible timescale-dependent CVs in the two longest nights of observation. Furthermore, comparing SFs of NGC 4395 to four AGNs at the supermassive scale, we suggest a new scaling relation between the timescale (\uptau; across nearly three orders of magnitude) and the BH mass (M_BH): \uptau \propto M^γ_BH where the exponent γis likely ~ 0.6 - 0.8. This exponent differs from most previous measurements, but confirms a few and is consistent with a recent theoretical prediction, suggesting a similar accretion process in AGNs across different mass scales.

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arXiv2024

Sizes of active galactic nuclei inhomogeneous disks -- large in microlensing, small in reverberation mapping

Magnetohydrodynamics (MHD) turbulence can drive significant temperature fluctuations in the accretion disk of an active galactic nucleus (AGN). As a result, the disk can be highly inhomogeneous and has a half-light radius larger than the static Shakura \& Sunyaev Disk (SSD), in agreement with quasar microlensing observations. Meanwhile, the accretion-disk sizes can also be determined using continuum reverberation mappings which measure interband cross correlations and time lags. The interband time lags are often understood in the X-ray reprocessing scenario. Here we show that the interband continuum time lags of the X-ray reprocessing of an inhomogeneous disk are similar to or even smaller than those of a static SSD. Consequently, the X-ray reprocessing of an inhomogeneous disk cannot account for the recent continuum reverberation mappings of some Seyfert 1 AGNs, whose measured time lags are larger than those of a static SSD. In contrast to the tight correlation between UV/optical variations, the cross correlation between X-ray and disk emission is rather weak in this model; this behavior is consistent with recent continuum reverberation mappings. Moreover, the time lags in this model are anti-correlated with the amplitude of disk temperature fluctuations. Our results suggest that the temperature fluctuations should be properly considered when modeling interband continuum time lags.

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arXiv2024

Stellar black holes can "stretch'' supermassive black hole accretion disks

Stellar black holes (sBHs) are widely believed to exist in the accretion disks of active galactic nuclei (AGNs). Previous studies often focus on the transient emission produced by embedded sBHs. Here, we explore the possible observational consequences of an AGN accretion disk that contains a population of accreting sBHs. Embedded accreting sBHs change the effective temperature distribution of the AGN accretion disk by heating gas in the outer regions. Two possible observational consequences are presented. First, the spectral energy distribution has a turnover feature at $\sim 4700\ \textrmÅ$ when the supermassive black hole (SMBH) mass is $\sim 10^8\ M_{\odot}$, which can help explain the observed shallow spectral shape at wavelengths $>5000\ \textrmÅ$ for the Sloan Digital Sky Survey quasar composite spectrum. Second, the half-light radius of a given relatively long wavelength is significantly larger than for an AGN disk without sBHs, which can be tested by microlensing observations. With appropriate sBH distributions, the model can be reconciled with quasar microlensing disk sizes. We propose that the half-light radius-wavelength relation can be utilized to investigate the distributions of embedded sBHs in AGN accretion disks.

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arXiv2024

How long will the quasar UV/optical flickering be damped?

The UV/optical light curves of Active Galactic Nuclei (AGNs) are commonly described by the Damped Random Walk (DRW) model. However, the physical interpretation of the damping timescale, a key parameter in the DRW model, remains unclear. Particularly, recent observations indicate a weak dependence of the damping timescale upon both wavelength and accretion rate, clearly being inconsistent with the accretion-disk theory. In this study, we investigate the damping timescale in the framework of the Corona Heated Accretion disk Reprocessing (CHAR) model, a physical model that describes AGN variability. We find that while the CHAR model can reproduce the observed power spectral densities of the 20-year light curves for 190 sources from \cite{Stone2022}, the observed damping timescale, as well as its weak dependence on wavelength, can also be well recovered through fitting the mock light curves with DRW. We further demonstrate that such weak dependence is artificial due to the effect of inadequate durations of light curves, which leads to best-fitting damping timescales lower than the intrinsic ones. After eliminating this effect, the CHAR model indeed yields a strong dependence of the intrinsic damping timescale on the bolometric luminosity and rest-frame wavelength. Our results highlight the demand for sufficiently long light curves in AGN variability studies and important applications of the CHAR model in such studies.

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arXiv2023

How can the optical variation properties of active galactic nuclei be unbiasedly measured?

The variability of active galactic nuclei (AGNs) is ubiquitous but has not yet been understood. Measuring the optical variation properties of AGNs, such as variation timescale and amplitude, and then correlating them with their fundamental physical parameters, have long served as a critical way of exploring the origin of AGN variability and the associated physics of the accretion process in AGNs. Obtaining accurate variation properties of AGNs is thus essential. It has been found that the damped random walk (DRW) process can well describe the AGN optical variation, however, there is a controversy over how long a minimal monitoring baseline is required to obtain unbiased variation properties. In this work, we settle the controversy by exhaustively scrutinizing the complex combination of assumed priors, adopted best-fit values, ensemble averaging methods, and fitting methods. Then, the newly proposed is an optimized solution where unbiased variation properties of an AGN sample possessing the same variation timescale can be obtained with a minimal baseline of about 10 times their variation timescale. Finally, the new optimized solution is used to demonstrate the positive role of time domain surveys to be conducted by the Wide Field Survey Telescope in improving constraints on AGN variation properties.

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arXiv2023

A universal average spectral energy distribution for quasars from optical to extreme ultraviolet

The well-known anti-correlation between the optical/ultraviolet (UV) emission line equivalent widths of active galactic nuclei and the continuum luminosity (the so-called Baldwin effect) is a long-standing puzzle. One common hypothesis is that more luminous sources have softer spectral energy distribution (SED) in the extreme UV (EUV), as revealed by some observational studies. In this work we revisit this issue through cross-matching SDSS quasars with GALEX far-UV/near-UV catalogs and correcting the effect of a severe observational bias of significant UV detection incompleteness, i.e., the more luminous in observed-frame optical, the more likely detected in observed-frame UV. We find that, for GALEX detected quasars at 1.8 < z < 2.2, the rest-frame mean UV SED (~ 500 -- 3000 Angstrom) bewilderingly shows no luminosity dependence at log(νL_ν(2200 Angstrom)) > 45 (up to 47.3), contrary to the standard thin disc model predictions and the observed Baldwin effect in this luminosity range. Probably, the universal mean UV SED is the result of a local atomic-originated process, and in fainter quasars stronger disk turbulence launching more clouds is the main origin of the Baldwin effect. After correcting for the absorption of the intergalactic medium, a rest-frame intrinsic mean EUV SED is derived from a sub-sample of bright quasars and is found to be much redder in the EUV than all previous quasar composite spectra, highlighting the significance of properly accounting for the sample incompleteness. Interestingly, the global consistence between our extremely red mean EUV SED and the line-driven wind model again supports an origin of a local physical process.

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arXiv2023

What can be learnt from a highly informative X-ray occultation event in NGC 6814? A marvellous absorber

A unique X-ray occultation event in NGC 6814 during an XMM-Newton observation in 2016 has been reported, providing useful information of the absorber and the corona. We revisit the event with the aid of the hardness ratio (HR) - count rate (CR) plot and comparison with two other absorption-free XMM exposures in 2009 and 2021. NGC 6814 exhibits a clear "softer-when-brighter" variation pattern during the exposures, but the 2016 exposure significantly deviates from the other two in the HR - CR plot. While spectral fitting does yield transient Compton-thin absorption corresponding to the eclipse event in 2016, rather than easing the tension between exposures in the HR - CR plot, correcting the transient Compton-thin absorption results in new and severe deviation within the 2016 exposure. We show that the eclipsing absorber shall be clumpy (instead of a single Compton-thin cloud), with an inner denser region composed of both Compton-thin and Compton-thick clouds responsible for the previously identified occultation event, and an outer sparser region with Compton-thin clouds which eclipses the whole 2016 exposure. With this model, all the tension in the HR - CR plots could be naturally erased, with the observed spectral variability during the 2016 exposure dominated by the variation of absorption. Furthermore, the two warm absorbers (with different ionization and column densities but similar outflowing velocities) detected in the 2016 exposure shall also associate with the transient absorber, likely due to ablated or tidal stretched/disrupted fragments. This work highlights the unique usefulness of the HR - CR plot while analysing rare occultation events.

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arXiv2023

Discovery of Five Green Pea Galaxies with Double-peaked Narrow [OIII] Lines

Although double-peaked narrow emission-line galaxies have been studied extensively in the past years, only a few are reported with the green pea galaxies (GPs). Here we present our discovery of five GPs with double-peaked narrow [OIII] emission lines, referred to as DPGPs, selected from the LAMOST and SDSS spectroscopic surveys. We find that these five DPGPs have blueshifted narrow components more prominent than the redshifted components, with velocity offsets of [OIII]$λ$5007 lines ranging from 306 to 518 $\rm km\, s^{-1}$ and full widths at half maximums (FWHMs) of individual components ranging from 263 to 441 $\rm km\, s^{-1}$. By analyzing the spectra and the spectral energy distributions (SEDs), we find that they have larger metallicities and stellar masses compared with other GPs. The H$α$ line width, emission-line diagnostic, mid-infrared color, radio emission, and SED fitting provide evidence of the AGN activities in these DPGPs. They have the same spectral properties of Type 2 quasars. Furthermore, we discuss the possible nature of the double-peaked narrow emission-line profiles of these DPGPs and find that they are more likely to be dual AGN. These DPGP galaxies are ideal laboratories for exploring the growth mode of AGN in the extremely luminous emission-line galaxies, the co-evolution between AGN and host galaxies, and the evolution of high-redshift galaxies in the early Universe.

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arXiv2023

Ensemble Mapping the Inner Structure of Luminous Quasars

A simple prediction of the well-known unification model of active galactic nuclei is that a sample of sources should exhibit an anti-correlation between the solid angle of the dusty torus and of the ionization cone (as the sum of them shall equal 4$π$), which however has never been detected. In this work, we analyze the correlation between [OIII] 5007 narrow emission line equivalent width and $L_{\rm IR}(λ)/L_{\rm bol}$ for a large sample of luminous quasars. For the first time, we detect a clear intrinsic anti-correlation between them, which immediately verifies the torus/ionization-cone geometry in luminous quasars. More interestingly, the anti-correlation significantly weakens with increasing wavelength from $\sim$ 2 to 12 $μ$m, and disappears at $\sim$ 12 $μ$m. Simulations show a cool dust component (in addition to equatorial torus) with its strength positively correlating with the solid angle of the ionization cone is required to explain the observations. This shows that the polar dust seen in nearby active galaxies also exists in luminous quasars, with its contribution to total dust emission increasing with $λ$ (from $\sim$ 2 to 12 $μ$m) and reaching between 39%-62% (model dependent) at rest frame 12 $μ$m. Our findings provide a unique approach to map the otherwise spatially unresolvable inner structure of quasars.

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arXiv2023

X-ray Unveiling Events in a z~1.6 Active Galactic Nucleus in the 7 Ms Chandra Deep Field-South

We investigate the extreme X-ray variability of a z = 1.608 active galactic nucleus in the 7 Ms Chandra Deep Field-South (XID 403), which showed two significant X-ray brightening events. In the first event, XID 403 brightened by a factor of $>2.5$ in $\lesssim6.1$ rest-frame days in the observed-frame 0.5-5 keV band. The event lasted for $\approx5.0\textrm{-}7.3$ days, and then XID 403 dimmed by a factor of $>6.0$ in $\lesssim6.1$ days. After $\approx1.1\textrm{-}2.5$ years in the rest frame (including long observational gaps), it brightened again with the 0.5-5 keV flux increasing by a factor of $>12.6$. The second event lasted over 251 days and the source remained bright until the end of the 7 Ms exposure. The spectrum is a steep power law (photon index $Γ=2.8\pm0.3$) without obscuration during the second outburst, and the rest-frame 2-10 keV luminosity reaches $1.5^{+0.8}_{-0.5}\times10^{43}$ erg s$^{-1}$; there is no significant spectral evolution within this epoch. The infrared-to-UV spectral energy distribution of XID 403 is dominated by the host galaxy. There is no significant optical/UV variability and $R$-band (rest-frame $\approx2500$ $\unicode{xC5}$) brightening contemporaneous with the X-ray brightening. The extreme X-ray variability is likely due to two X-ray unveiling events, where the line of sight to the corona is no longer shielded by high-density gas clumps in a small-scale dust-free absorber. XID 403 is probably a high-redshift analog of local narrow-line Seyfert 1 galaxies, and the X-ray absorber is a powerful accretion-disk wind. On the other hand, we cannot exclude the possibility that XID 403 is an unusual candidate for tidal disruption events.

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arXiv2023

Hidden biases in flux-resolved X-ray spectroscopy

Flux-resolved X-ray spectroscopy is widely adopted to investigate the spectral variation of a target between various flux levels. In many cases it is done through horizontally splitting a single light curve into multiple flux levels with certain count rate threshold(s). In this work we point out there are two hidden biases in this approach which could affect the spectral analyses under particular circumstances. The first is that, when Poisson fluctuations of the source counts in light curve bins are non-negligible compared with the intrinsic variation, this approach would over-estimate (under-estimate) the intrinsic average flux level of the high (low) state. The second bias is that, when the Poisson fluctuations of the background count rate is non-negligible, the background spectrum of the high (low) state would be under-estimated (over-estimated), thus yielding biased spectral fitting parameters. We take NuSTAR spectra for example to illustrate the effects of the biases, and particularly, how the measurements of the coronal temperature in AGNs would be biased. We present a toy method to assess the significance of such biases, and approaches to correct for them when necessary.

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