arXiv subjects

K. R. W. Tristram

Publications and source records attributed to K. R. W. Tristram.

At least 19 recordsLinked to original sources

arXiv2024

VLTI/GRAVITY Interferometric Measurements of Innermost Dust Structure Sizes around AGNs

We present new VLTI/GRAVITY near-infrared interferometric measurements of the angular size of the innermost hot dust continuum for 14 type 1 AGNs. The angular sizes are resolved on scales of ~0.7 mas and the inferred ring radii range from 0.028 to 1.33 pc, comparable to those reported previously and a factor 10-20 smaller than the mid-infrared sizes in the literature. Combining our new data with previously published values, we compile a sample of 25 AGN with bolometric luminosity ranging from $10^{42}$ to $10^{47} \rm erg~s^{-1}$, with which we study the radius-luminosity (R-L) relation for the hot dust structure. Our interferometric measurements of radius are offset by a factor 2 from the equivalent relation derived through reverberation mapping. Using a simple model to explore the dust structure's geometry, we conclude that this offset can be explained if the 2 um emitting surface has a concave shape. Our data show that the slope of the relation is in line with the canonical $R \propto L^{0.5}$ when using an appropriately non-linear correction for bolometric luminosity. In contrast, using optical luminosity or applying a constant bolometric correction to it results in a significant deviation in the slope, suggesting a potential luminosity dependence on the spectral energy distribution. Over four orders of magnitude in luminosity, the intrinsic scatter around the R-L relation is 0.2 dex, suggesting a tight correlation between innermost hot dust structure size and the AGN luminosity.

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arXiv2024

The size-luminosity relation of local active galactic nuclei from interferometric observations of the broad-line region

By using the GRAVITY instrument with the near-infrared (NIR) Very Large Telescope Interferometer (VLTI), the structure of the broad (emission-)line region (BLR) in active galactic nuclei (AGNs) can be spatially resolved, allowing the central black hole (BH) mass to be determined. This work reports new NIR VLTI/GRAVITY interferometric spectra for four type 1 AGNs (Mrk 509, PDS 456, Mrk 1239, and IC 4329A) with resolved broad-line emission. Dynamical modelling of interferometric data constrains the BLR radius and central BH mass measurements for our targets and reveals outflow-dominated BLRs for Mrk 509 and PDS 456. We present an updated radius-luminosity (R-L) relation independent of that derived with reverberation mapping (RM) measurements using all the GRAVITY-observed AGNs. We find our R-L relation to be largely consistent with that derived from RM measurements except at high luminosity, where BLR radii seem to be smaller than predicted. This is consistent with RM-based claims that high Eddington ratio AGNs show consistently smaller BLR sizes. The BH masses of our targets are also consistent with the standard $M_\mathrm{BH}$-$σ_*$ relation. Model-independent photocentre fitting shows spatial offsets between the hot dust continuum and the BLR photocentres (ranging from $\sim$17 $μ$as to 140 $μ$as) that are generally perpendicular to the alignment of the red- and blueshifted BLR photocentres. These offsets are found to be related to the AGN luminosity and could be caused by asymmetric K-band emission of the hot dust, shifting the dust photocentre. We discuss various possible scenarios that can explain this phenomenon.

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arXiv2022

Towards measuring supermassive black hole masses with interferometric observations of the dust continuum

This work focuses on active galactic nuclei (AGNs), and the relation between the sizes of the hot dust continuum and the broad-line region (BLR). We find that the continuum size measured using optical/near-infrared interferometry (OI) is roughly twice that measured by reverberation mapping (RM). Both OI and RM continuum sizes show a tight relation with the H$β$ BLR size with only an intrinsic scatter of 0.25 dex. The masses of supermassive black holes (BHs) can hence be simply derived from a dust size in combination with a broad line width and virial factor. Since the primary uncertainty of these BH masses comes from the virial factor, the accuracy of the continuum-based BH masses is close to those based on the RM measurement of the broad emission line. Moreover, the necessary continuum measurements can be obtained on a much shorter timescale than those required monitoring for RM, and are also more time efficient than those needed to resolve the BLR with OI. The primary goal of this work is to demonstrate measuring the BH mass based on the dust continuum size with our first calibration of the $R_\mathrm{BLR}$-$R_\mathrm{d}$ relation. The current limitation and caveats are discussed in detail. Future GRAVITY observations are expected to improve the continuum-based method and have the potential to measure BH masses for a large sample of AGNs in the low-redshift Universe.

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arXiv2021

Deep Images of the Galactic Center with GRAVITY

Stellar orbits at the Galactic Center provide a very clean probe of the gravitational potential of the supermassive black hole. They can be studied with unique precision, beyond the confusion limit of a single telescope, with the near-infrared interferometer GRAVITY. Imaging is essential to search the field for faint, unknown stars on short orbits which potentially could constrain the black hole spin. Furthermore, it provides the starting point for astrometric fitting to derive highly accurate stellar positions. Here, we present $\mathrm{G^R}$, a new imaging tool specifically designed for Galactic Center observations with GRAVITY. The algorithm is based on a Bayesian interpretation of the imaging problem, formulated in the framework of information field theory and building upon existing works in radio-interferometric imaging. Its application to GRAVITY observations from 2021 yields the deepest images to date of the Galactic Center on scales of a few milliarcseconds. The images reveal the complicated source structure within the central $100\,\mathrm{mas}$ around Sgr A*, where we detected the stars S29 and S55 and confirm S62 on its trajectory, slowly approaching Sgr A*. Furthermore, we were able to detect S38, S42, S60, and S63 in a series of exposures for which we offset the fiber from Sgr A*. We provide an update on the orbits of all aforementioned stars. In addition to these known sources, the images also reveal a faint star moving to the west at a high angular velocity. We cannot find any coincidence with any known source and, thus, we refer to the new star as S300. From the flux ratio with S29, we estimate its K-band magnitude as $m_\mathrm{K}\left(\mathrm{S300}\right)\simeq 19.0 - 19.3$. Images obtained with CLEAN confirm the detection.

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arXiv2021

The mass distribution in the Galactic Centre from interferometric astrometry of multiple stellar orbits

The stars orbiting the compact radio source Sgr A* in the Galactic Centre are precision probes of the gravitational field around the closest massive black hole. In addition to adaptive optics assisted astrometry (with NACO / VLT) and spectroscopy (with SINFONI / VLT, NIRC2 / Keck and GNIRS / Gemini) over three decades, since 2016/2017 we have obtained 30-100 mu-as astrometry with the four-telescope interferometric beam combiner GRAVITY / VLTI reaching a sensitivity of mK = 20 when combining data from one night. We present the simultaneous detection of several stars within the diffraction limit of a single telescope, illustrating the power of interferometry. The new data for the stars S2, S29, S38 and S55 yield significant accelerations between March and July 2021, as these stars pass the pericenters of their orbits between 2018 and 2023. This allows for a high-precision determination of the gravitational potential around Sgr A*. Our data are in excellent agreement with general relativity orbits around a single central point mass, M = 4.30 x 10^6 M_sun with a precision of about +-0.25%. We improve the significance of our detection of the Schwarzschild precession in the S2 orbit to 7 sigma. Assuming plausible density profiles, an extended mass component inside S2's apocentre (= 0.23" or 2.4 x 10^4 R_S) must be 3000 M_sun (1 sigma), or 0.1% of M. Adding the enclosed mass determinations from 13 stars orbiting Sgr A* at larger radii, the innermost radius at which the excess mass beyond Sgr A* tentatively is seen is r = 2.5" >= 10x the apocentre of S2. This is in full harmony with the stellar mass distribution (including stellar-mass black holes) obtained from the spatially resolved luminosity function.

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arXiv2021

A geometric distance to the supermassive black Hole of NGC 3783

The angular size of the broad line region (BLR) of the nearby active galactic nucleus (AGN) NGC 3783 has been spatially resolved by recent observations with VLTI/GRAVITY. A reverberation mapping (RM) campaign has also recently obtained high quality light curves and measured the linear size of the BLR in a way that is complementary to the GRAVITY measurement. The size and kinematics of the BLR can be better constrained by a joint analysis that combines both GRAVITY and RM data. This, in turn, allows us to obtain the mass of the supermassive black hole in NGC3783 with an accuracy that is about a factor of two better than that inferred from GRAVITY data alone. We derive $M_\mathrm{BH}=2.54_{-0.72}^{+0.90}\times 10^7\,M_\odot$. Finally, and perhaps most notably, we are able to measure a geometric distance to NGC 3783 of $39.9^{+14.5}_{-11.9}$ Mpc. We are able to test the robustness of the BLR-based geometric distance with measurements based on the Tully-Fisher relation and other indirect methods. We find the geometric distance is consistent with other methods within their scatter. We explore the potential of BLR-based geometric distances to directly constrain the Hubble constant, $H_0$, and identify differential phase uncertainties as the current dominant limitation to the $H_0$ measurement precision for individual sources.

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arXiv2021

The central parsec of NGC 3783: a rotating broad emission line region, asymmetric hot dust structure, and compact coronal line region

Using VLTI/GRAVITY and SINFONI data, we investigate the sub-pc gas and dust structure around the nearby type 1 AGN hosted by NGC 3783. The K-band coverage of GRAVITY uniquely allows a simultaneous analysis of the size and kinematics of the broad line region (BLR), the size and structure of the near-IR continuum emitting hot dust, and the size of the coronal line region (CLR). We find the BLR probed through broad Br$γ$ emission is well described by a rotating, thick disk with a radial distribution of clouds peaking in the inner region. In our BLR model the physical mean radius of 16 light days is nearly twice the 10 day time lag that would be measured, which matches very well the 10 day time lag that has been measured by reverberation mapping. We measure a hot dust FWHM size of 0.74 mas (0.14 pc) and further reconstruct an image of the hot dust which reveals a faint (5% of the total flux) offset cloud which we interpret as an accreting cloud heated by the central AGN. Finally, we directly measure the FWHM size of the nuclear CLR as traced by the [CaVIII] and narrow Br$γ$ line. We find a FWHM size of 2.2 mas (0.4 pc), fully in line with the expectation of the CLR located between the BLR and narrow line region. Combining all of these measurements together with larger scale near-IR integral field unit and mid-IR interferometry data, we are able to comprehensively map the structure and dynamics of gas and dust from 0.01--100 pc.

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arXiv2020

The spatially resolved broad line region of IRAS 09149-6206

We present new near-infrared VLTI/GRAVITY interferometric spectra that spatially resolve the broad Br$γ$ emission line in the nucleus of the active galaxy IRAS 09149-6206. We use these data to measure the size of the broad line region (BLR) and estimate the mass of the central black hole. Using an improved phase calibration method that reduces the differential phase uncertainty to 0.05 degree per baseline across the spectrum, we detect a differential phase signal that reaches a maximum of ~0.5 degree between the line and continuum. This represents an offset of ~120 $μ$as (0.14 pc) between the BLR and the centroid of the hot dust distribution traced by the 2.3 $μ$m continuum. The offset is well within the dust sublimation region, which matches the measured ~0.6 mas (0.7 pc) diameter of the continuum. A clear velocity gradient, almost perpendicular to the offset, is traced by the reconstructed photocentres of the spectral channels of the Br$γ$ line. We infer the radius of the BLR to be ~65 $μ$as (0.075 pc), which is consistent with the radius-luminosity relation of nearby active galactic nuclei derived based on the time lag of the H$β$ line from reverberation mapping campaigns. Our dynamical modelling indicates the black hole mass is $\sim 1\times10^8\,M_\odot$, which is a little below, but consistent with, the standard $M_{\rm BH}$-$σ_*$ relation.

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arXiv2020

The Flux Distribution of Sgr A*

The Galactic Center black hole Sagittarius A* is a variable NIR source that exhibits bright flux excursions called flares. The low-flux density turnover of the flux distribution is below the sensitivity of current single-aperture telescopes. We use the unprecedented resolution of the GRAVITY instrument at the VLTI. Our light curves are unconfused, overcoming the confusion limit of previous photometric studies. We analyze the light curves using standard statistical methods and obtain the flux distribution. We find that the flux distribution of SgrA* turns over at a median flux density of (1.1\pm0.3)mJy. We measure the percentiles of the flux distribution and use them to constrain the NIR K-band SED. Furthermore, we find that the flux distribution is intrinsically right-skewed to higher flux density in log space. Flux densities below 0.1mJy are hardly ever observed. In consequence, a single powerlaw or lognormal distribution does not suffice to describe the observed flux distribution in its entirety. However, if one takes into account a power law component at high flux densities, a lognormal distribution can describe the lower end of the observed flux distribution. We confirm the RMS-flux relation for Sgr~A* and find it to be linear for all flux densities in our observation. We conclude that Sgr~A* has two states: the bulk of the emission is generated in a lognormal process with a well-defined median flux density and this quiescent emission is supplemented by sporadic flares that create the observed power law extension of the flux distribution.

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arXiv2019

An image of the dust sublimation region in the nucleus of NGC 1068

We present near-infrared interferometric data on the Seyfert 2 galaxy NGC 1068, obtained with the GRAVITY instrument on the European Southern Observatory Very Large Telescope Interferometer. The extensive baseline coverage from 5 to 60 Mλallowed us to reconstruct a continuum image of the nucleus with an unrivaled 0.2 pc resolution in the K-band. We find a thin ring-like structure of emission with a radius r = 0.24+/-0.03 pc, inclination i = 70+/-5 deg, position angle PA = -50+/-4 deg, and h/r < 0.14, which we associate with the dust sublimation region. The observed morphology is inconsistent with the expected signatures of a geometrically and optically thick torus. Instead, the infrared emission shows a striking resemblance to the 22 GHz maser disc, which suggests they share a common region of origin. The near-infrared spectral energy distribution indicates a bolometric luminosity of (0.4-4.7) x 10^45 erg/s, behind a large A_K ~ 5.5 (A_V ~ 90) screen of extinction that also appears to contribute significantly to obscuring the broad line region.

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arXiv2019

A Compact Jet at the Infrared Heart of the Prototypical Low-Luminosity AGN in NGC 1052

The feeble radiative efficiency characteristic of Low-Luminosity Active Galactic Nuclei (LLAGN) is ascribed to a sub-Eddington accretion rate, typically at $\log(L_{\rm bol}/L_{\rm edd}) \lesssim -3$. At the finest angular resolutions that are attainable nowadays using mid-infrared (mid-IR) interferometry, the prototypical LLAGN in NGC 1052 remains unresolved down to $< 5\, \rm{mas}$ ($0.5\, \rm{pc}$). This is in line with non-thermal emission from a compact jet, a scenario further supported by a number of evidences: the broken power-law shape of the continuum distribution in the radio-to-UV range; the $\sim 4\%$ degree of polarisation measured in the nuclear mid-IR continuum, together with the mild optical extinction ($A_V \sim 1\, \rm{mag}$); and the "harder when brighter" behaviour of the X-ray spectrum, indicative of self-Compton synchrotron radiation. A remarkable feature is the steepness of the IR-to-UV core continuum, characterised by a power-law index of $\sim 2.6$, as compared to the canonical value of $0.7$. Alternatively, to explain the interferometric data by thermal emission would require an exceptionally compact dust distribution when compared to those observed in nearby AGN, with $A_V \gtrsim 2.8\, \rm{mag}$ to account for the IR polarisation. This is in contrast with several observational evidences against a high extinction along the line of sight, including the detection of the nucleus in the UV range and the well defined shape of the power-law continuum. The case of NGC 1052 shows that compact jets can dominate the nuclear emission in LLAGN across the whole electromagnetic spectrum, a scenario that might be common among this class of active nuclei.

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arXiv2018

Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole

The highly elliptical, 16-year-period orbit of the star S2 around the massive black hole candidate Sgr A* is a sensitive probe of the gravitational field in the Galactic centre. Near pericentre at 120 AU, ~1400 Schwarzschild radii, the star has an orbital speed of ~7650 km/s, such that the first-order effects of Special and General Relativity have now become detectable with current capabilities. Over the past 26 years, we have monitored the radial velocity and motion on the sky of S2, mainly with the SINFONI and NACO adaptive optics instruments on the ESO Very Large Telescope, and since 2016 and leading up to the pericentre approach in May 2018, with the four-telescope interferometric beam-combiner instrument GRAVITY. From data up to and including pericentre, we robustly detect the combined gravitational redshift and relativistic transverse Doppler effect for S2 of z ~ 200 km/s / c with different statistical analysis methods. When parameterising the post-Newtonian contribution from these effects by a factor f, with f = 0 and f = 1 corresponding to the Newtonian and general relativistic limits, respectively, we find from posterior fitting with different weighting schemes f = 0.90 +/- 0.09 (stat) +\- 0.15 (sys). The S2 data are inconsistent with pure Newtonian dynamics.

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arXiv2018

Hi-5: a potential high-contrast thermal near-infrared imager for the VLTI

Hi-5 is a high-contrast (or high dynamic range) infrared imager project for the VLTI. Its main goal is to characterize young extra-solar planetary systems and exozodiacal dust around southern main-sequence stars. In this paper, we present an update of the project and key technology pathways to improve the contrast achieved by the VLTI. In particular, we discuss the possibility to use integrated optics, proven in the near-infrared, in the thermal near-infrared (L and M bands, 3-5~$μ$m) and advanced fringe tracking strategies. We also address the strong exoplanet science case (young exoplanets, planet formation, and exozodiacal disks) offered by this wavelength regime as well as other possible science cases such as stellar physics (fundamental parameters and multiplicity) and extragalactic astrophysics (active galactic nuclei and fundamental constants). Synergies and scientific preparation for other potential future instruments such as the Planet Formation Imager are also briefly discussed.

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arXiv2018

The path towards high-contrast imaging with the VLTI: the Hi-5 project

The development of high-contrast capabilities has long been recognized as one of the top priorities for the VLTI. As of today, the VLTI routinely achieves contrasts of a few 10$^{-3}$ in the near-infrared with PIONIER (H band) and GRAVITY (K band). Nulling interferometers in the northern hemisphere and non-redundant aperture masking experiments have, however, demonstrated that contrasts of at least a few 10$^{-4}$ are within reach using specific beam combination and data acquisition techniques. In this paper, we explore the possibility to reach similar or higher contrasts on the VLTI. After reviewing the state-of-the-art in high-contrast infrared interferometry, we discuss key features that made the success of other high-contrast interferometric instruments (e.g., integrated optics, nulling, closure phase, and statistical data reduction) and address possible avenues to improve the contrast of the VLTI by at least one order of magnitude. In particular, we discuss the possibility to use integrated optics, proven in the near-infrared, in the thermal near-infrared (L and M bands, 3-5 $μ$m), a sweet spot to image and characterize young extra-solar planetary systems. Finally, we address the science cases of a high-contrast VLTI imaging instrument and focus particularly on exoplanet science (young exoplanets, planet formation, and exozodiacal disks), stellar physics (fundamental parameters and multiplicity), and extragalactic astrophysics (active galactic nuclei and fundamental constants). Synergies and scientific preparation for other potential future instruments such as the Planet Formation Imager are also briefly discussed.

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arXiv2017

Embedded AGN and star formation in the central 80 pc of IC 3639

[Abridged] Methods: We use interferometric observations in the $N$-band with VLTI/MIDI to resolve the mid-IR nucleus of IC 3639. The origin of the nuclear infrared emission is determined from: 1) the comparison of the correlated fluxes from VLTI/MIDI with the fluxes measured at subarcsec resolution (VLT/VISIR, VLT/ISAAC); 2) diagnostics based on IR fine-structure line ratios, the IR continuum emission, IR bands produced by polycyclic aromatic hydrocarbons (PAH) and silicates; and 3) the high-angular resolution spectral energy distribution. Results: The unresolved flux of IC 3639 is $90 \pm 20\, \rm{mJy}$ at $10.5\, \rm{μm}$, measured with three different baselines in VLTI (UT1-UT2, UT3-UT4, and UT2-UT3; $46$-$58\, \rm{m}$), making this the faintest measurement so far achieved with mid-IR interferometry. The correlated flux is a factor of $3$-$4$ times fainter than the VLT/VISIR total flux measurement. The observations suggest that most of the mid-IR emission has its origin on spatial scales between $10$ and $80\, \rm{pc}$ ($40$-$340\, \rm{mas}$). A composite scenario where the star formation component dominates over the AGN is favoured by the diagnostics based on ratios of IR fine-structure emission lines, the shape of the IR continuum, and the PAH and silicate bands. Conclusions: A composite AGN-starburst scenario is able to explain both the mid-IR brightness distribution and the IR spectral properties observed in the nucleus of IC 3639. The nuclear starburst would dominate the mid-IR emission and the ionisation of low-excitation lines (e.g. [NeII]$_{12.8 \rm{μm}}$) with a net contribution of $\sim 70\%$. The AGN accounts for the remaining $\sim 30\%$ of the mid-IR flux, ascribed to the unresolved component in the MIDI observations, and the ionisation of high-excitation lines (e.g. [NeV]$_{14.3 \rm{μm}}$ and [OIV]$_{25.9 \rm{μm}}$).

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arXiv2017

PAH features within few hundred parsecs of active galactic nuclei

Spectral features from PAH molecules observed in the mid-IR range are typically used to infer the amount of recent and ongoing star formation (SF) on kpc scales around AGN where more traditional methods fail. This assumes that the observed PAH features are excited predominantly by SF. With current ground-based telescopes and the upcoming JWST, much smaller spatial scales can be probed and we aim at testing this assumption in the range of few tens to few hundreds of pc. For that, we spatially map the emitted 11.3μm PAH surface flux as a function of distance from 0.4-4 arcsec from the centre in 28 nearby AGN using ground-based high-angular resolution mid-IR spectroscopy. We detect and extract the 11.3μm PAH feature in 13 AGN. The fluxes within each aperture are scaled to a luminosity-normalised distance from the nucleus to be able to compare intrinsic spatial scales of AGN radiation spanning about 2 orders of magnitude in luminosity. For this, we establish an empirical relation between the absorption-corrected X-ray luminosity and the sublimation radius in these sources. Once normalised, the radial profiles of the emitted PAH surface flux show similar radial slopes, with a power-law index of approximately -1.1, and similar absolute values, consistent within a factor of a few of each other as expected from the uncertainty in the intrinsic scale estimate. We interpret this as evidence that the profiles are caused by a common compact central physical process, either the AGN itself or circumnuclear SF linked in strength to the AGN power. A photoionisation-based model of an AGN exciting dense clouds in its environment can reproduce the observed radial slope and confirms that the AGN radiation field is strong enough to explain the observed PAH surface fluxes within ~10-500 pc of the nucleus. Our results advice caution in the use of PAH emission as a SF tracer within a kpc around AGN.

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arXiv2016

Radiative transfer modelling of parsec-scale dusty warped discs

Warped discs have been found on (sub-)parsec scale in some nearby Seyfert nuclei, identified by their maser emission. Using dust radiative transfer simulations we explore their observational signatures in the infrared in order to find out whether they can partly replace the molecular torus. Strong variations of the brightness distributions are found, depending on the orientation of the warp with respect to the line of sight. Whereas images at short wavelengths typically show a disc-like and a point source component, the warp itself only becomes visible at far-infrared wavelengths. A similar variety is visible in the shapes of the spectral energy distributions. Especially for close to edge-on views, the models show silicate feature strengths ranging from deep absorption to strong emission for variations of the lines of sight towards the warp. To test the applicability of our model, we use the case of the Circinus galaxy, where infrared interferometry has revealed a highly elongated emission component matching a warped maser disc in orientation and size. Our model is for the first time able to present a physical explanation for the observed dust morphology as coming from the AGN heated dust. As opposed to available torus models, a warped disc morphology produces a variety of silicate feature shapes for grazing lines of sight, close to an edge-on view. This could be an attractive alternative to a claimed change of the dust composition for the case of the nearby Seyfert 2 galaxy NGC 1068, which harbours a warped maser disc as well.

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arXiv2016

NGC 1068: No change in the mid-IR torus structure despite X-ray variability

Context. Recent NuSTAR observations revealed a somewhat unexpected increase in the X-ray flux of the nucleus of NGC 1068. We expect the infrared emission of the dusty torus to react on the intrinsic changes of the accretion disk. Aims. We aim to investigate the origin of the X-ray variation by investigating the response of the mid-infrared environment. Methods. We obtained single-aperture and interferometric mid-infrared measurements and directly compared the measurements observed before and immediately after the X-ray variations. The average correlated and single-aperture fluxes as well as the differential phases were directly compared to detect a possible change in the structure of the nuclear emission on scales of $\sim$ 2 pc. Results. The flux densities and differential phases of the observations before and during the X-ray variation show no significant change over a period of ten years. Possible minor variations in the infrared emission are $\lesssim$ 8 %. Conclusions. Our results suggest that the mid-infrared environment of NGC 1068 has remained unchanged for a decade. The recent transient change in the X-rays did not cause a significant variation in the infrared emission. This independent study supports previous conclusions that stated that the X-ray variation detected by NuSTAR observations is due to X-ray emission piercing through a patchy section of the dusty region.

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