arXiv subjects

P. Chainakun

Publications and source records attributed to P. Chainakun.

18 recordsLinked to original sources

arXiv2025

Hybrid corona and transient soft X-ray lags in Fairall 9

Fairall 9 is among the most massive Seyfert galaxies exhibiting a strong soft X-ray excess, but it is challenging to probe soft X-ray reverberation lags (if any) due to the long intrinsic timescales expected from its large black hole mass of $\sim 2.55 \times 10^8 M_\odot$. We fit five XMM-Newton spectra of Fairall 9 using the hybrid reXcor model taking into account both hot and warm corona. The soft excess is explained by a combination of a physically motivated warm corona and the disc reflection. Then, we perform a wavelet coherence analysis of the light curves between 0.3 - 1 and 1 - 4 keV bands. The spectral fits are consistent with a rapidly spinning black hole ($a = 0.99$), a warm corona with optical depth $\sim$10 - 30, and a hot lamp-post corona located at either 5 or $20~r_{\rm g}$. This configuration supports a coexisting hot and warm corona scenario, allowing the disc to extend almost to the event horizon. Our wavelet analysis on combined observations reveals signatures of transient soft X-ray lags, confined to specific time-frequency intervals. The earlier observations exhibit more variable and transient lag behavior. In contrast, the later observations display more persistent soft X-ray lags at the frequencies of $\sim 9\times 10^{-6}$ - $2.5 \times 10^{-5}$ Hz, with amplitudes reaching $\sim$1000 s. The results indicate a progressively stable disc-corona configuration in later observations. Given the mass and geometry of Fairall 9, the observed soft lags appears plausibly consistent in both size and timescales with expectations from X-ray reverberation.

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arXiv2025

Revealing Hidden Repeaters in the CHIME/FRB Catalog: Semi-Supervised Insights into the Fast Radio Burst Population

Fast radio bursts (FRBs) are millisecond-duration extragalactic transients, observationally classified as repeaters or nonrepeaters. This classification may be biased, as some apparently non-repeating sources could simply have undetected subsequent bursts. To address this, we develop a semi-supervised learning framework to identify distinguishing features of repeaters using primary observational parameters from the Blinkverse database, which draws from the CHIME/FRB Catalogs. The framework combines labeled data (known repeaters and confidently classified non-repeaters) with unlabeled sources previously flagged as non-repeaters but exhibiting repeater-like characteristics. We employ uniform manifold approximation and projection with a nearest-neighbor scheme to select potential candidates, followed by semi-supervised classification using five base estimators, including random forest, support vector machine, logistic regression, AdaBoost, and Gradient boost. Each model is fine-tuned through cross-validation, and a voting strategy among the five models is employed to enhance robustness. All models achieve consistently high performance, identifying dispersion measure, peak frequency, and fluence as the most discriminative features. Repeaters tend to show lower dispersion measures, higher peak frequencies, and higher fluences than non-repeaters. We also identify a set of candidate repeaters, several of which are consistent with prior independent studies. Our approach can identify 36 additional repeater candidates that conventional methods may have missed. Finally, the results highlight dispersion measure as a key discriminator between repeaters and non-repeaters, revealing a tension between physical and instrumental origins-either environmental effects, if the two populations arise from distinct progenitors, or detection bias, as nearby sources are more easily observed.

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arXiv2024

Tracing the evolving X-ray reverberation lags within an individual AGN light curve

We present the Granger causality (GC) test for the X-ray reverberation analysis of Active Galactic Nuclei (AGN). If the light curves in the continuum-dominated band help predict (Granger cause) those dominated by reflection, the Granger lags that associate to the intrinsic reverberation lags can be inferred. We focus on six AGN observed by XMM-Newton, including the sources well-known to exhibit clear X-ray reverberation lags (IRAS 13224-3809 and 1H 0707-495) and those in which reverberation signatures are not well confirmed (MCG-6-30-15, IZW1, Mrk 704 and Mrk 1040). We employ the sliding-window algorithm and estimate the Granger (intrinsic) Fe-L lags along the light curve as the window moves through. This reveals the evolving lags towards the end of some individual observations, suggesting that the corona varies progressively. Occasionally, we observe two clearly separate lags that suggest an extended corona consisting of two zones while producing competing reverberation of two lags. While the GC test is purely hypothetical and might not explain true causality, our conclusion is that the lags are present and could be understood as reverberation lags. Assuming the lags changing solely with the corona, we find that the IRAS 13224-3809 corona varies between $\sim 10$-$25$ $r_{\rm g}$ and sometimes move to $\gtrsim 50$ $r_{\rm g}$. The corona of 1H 0707-495 and MCG-6-30-15 may be analogous to that of IRAS 13224-3809, while in IZw1, Mrk 704 and Mrk 1040 a more compact corona is expected.

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arXiv2024

Parameter dependency on the public X-ray reverberation models kynxilrev and kynrefrev

We present a comparative study of the constrained parameters of active galactic nuclei (AGN) made by the public X-ray reverberation model kynxilrev and kynrefrev that make use of the reflection code xillver and reflionx, respectively. By varying the central mass ($M_{\rm BH}$), coronal height ($h$), inclination ($i$), photon index of the continuum emission ($\Gamma$) and source luminosity ($L$), the corresponding lag-frequency spectra can be produced. We select only the simulated AGN where their lag amplitude ($\tau$) and $M_{\rm BH}$ follow the known mass-scaling law. In these mock samples, we show that $\tau$ and $h$ are correlated and can possibly be used as an independent scaling law. Furthermore, $h$ (in gravitational units) is also found to be positively scaled with $M_{\rm BH}$, suggesting a more compact corona in lower-mass AGN. Both models reveal that the coronal height mostly varies between $\sim 5$-$15~r_{\rm g}$, with the average height at $\sim 10~r_{\rm g}$ and can potentially be found from low- to high-mass AGN. Nevertheless, the kynxilrev seems to suggest a lower $M_{\rm BH}$ and $h$ than the kynrefrev. This inconsistency is more prominent in lower-spin AGN. The significant correlation between the source height and luminosity is revealed only by kynrefrev, suggesting the $h$-$L$ relation is probably model dependent. Our findings emphasize the differences between these reverberation models that raises the question of biases in parameter estimates and inferred correlations.

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arXiv2023

Investigating scaling relations in X-ray reverberating AGN using symbolic regression

Symbolic regression (SR) is a regression analysis based on genetic algorithms to search for mathematical expressions that best fit a given data set, by allowing the expressions themselves to mutate. We use the SR to analyze the parameter relations of the X-ray reverberating Active Galactic Nuclei (AGN) where the soft Fe-L lags were observed by XMM-Newton. Firstly, we revisit the lag-mass scaling relations by using the SR to derive all possible mathematical expressions and test them in terms of accuracy, simplicity and robustness. We find that the correlation between the lags, $\tau$, and the black hole mass, $M_{\rm BH}$, is certain, but the relation should be written in the form of $\log ({\tau}) = \alpha + \beta (\log{(M_{\rm BH}/M_{\odot})})^{\gamma}$, where $1 \lesssim \gamma \lesssim 2$. Moreover, incorporating more parameters such as the reflection fraction ($RF$) and the Eddington ratio ($\lambda_{\rm Edd}$) to the lag-mass scaling relation is made possible by the SR. It reveals that $\alpha$, rather than being a constant, can be $-2.15 + 0.02RF$ or $0.03(RF + \lambda_{\rm Edd})$, with the fine-tuned different $\beta$ and $\gamma$. These further support the relativistic disc-reflection framework in which such functional dependencies can be straightforwardly explained. Furthermore, we derive their host-galaxy mass, $M_{\ast}$, by fitting the spectral energy distribution (SED). We find that the SR model supports a non-linear $M_{\rm BH}$--$M_{\ast}$ relationship, while $\log (M_{\rm BH}/M_{\ast})$ varies between $-5.4$ and $-1.5$, with an average value of $\sim -3.7$. No significant correlation between $M_{\ast}$ and $\lambda_{\rm Edd}$ is confirmed in these samples.

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arXiv2023

Coronal height constraint in IRAS 13224-3809 and 1H 0707-495 by the random forest regressor

We develop a random forest regressor (RFR) machine learning model to trace the coronal evolution in two highly variable active galactic nuclei (AGNs) IRAS 13224-3809 and 1H 0707-495 observed with XMM-Newton, by probing the X-ray reverberation features imprinted on their power spectral density (PSD) profiles. Simulated PSDs in the form of a power-law, with similar frequency range and bins to the observed data, are produced. Then, they are convolved with relativistic disc-response functions from a lamp-post source before being used to train and test the model to predict the coronal height. We remove some bins that are dominated by Poisson noise and find that the model can tolerate the frequency-bin removal up to $\sim 10$ bins to maintain a prediction accuracy of $R^{2} > 0.9$. The black hole mass and inclination should be fixed so that the accuracy in predicting the source height is still $> 0.9$. The accuracy also increases with the reflection fraction. The corona heights for both AGN are then predicted using the RFR model developed from the simulated PSDs whose frequency range and bins are specifically adjusted to match those from each individual observation. The model suggests that their corona varies between $\sim~5 - 18~r_{\rm g}$, with $R^{2} > 0.9$ for all observations. Such high accuracy can still be obtained if the difference between the true mass and the trained value is $\lesssim 10\%$. Finally, the model supports the height-changing corona under the light-bending scenario where the height is correlated to source luminosity in both IRAS 13224-3809 and 1H 0707-495.

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arXiv2023

Revealing the intrinsic X-ray reverberation lags in IRAS 13224-3809 through the Granger causality test

The Granger causality is an econometric test for determining whether one time series is useful for forecasting another one with a certain Granger lag. Here, the light curves in the 0.3-1 keV (reflection dominated, soft) and 1.2-5 keV (continuum dominated, hard) bands of Active Galactic Nuclei (AGNs) are produced, and the Granger lags are estimated and compared to the traditional lag-frequency spectra. We find that the light curves in the hard band Granger-cause (lead) those in the soft band, whereas the obtained Granger lags could be interpreted as the intrinsic reverberation lags. Then, we extract the Granger-lag profiles from 14 XMM-Newton observations of IRAS 13224-3809, and find that the lags are significant in 12 observations. The majority of the obtained Granger (intrinsic) lags are ~ 200-500 s. With the IRAS 13224-3809 mass of 2 $\times 10^6$ $M_{\odot}$, these lags correspond to the true light-travel distance of ~ 20-50 $r_g$. Hence, by assuming a lamp-post geometry and a face-on disc, this places the corona at ~ 10-25 $r_{g}$ above the central black hole. Moreover, multiple Granger lags consisting of the small and large lags of < 500 s and > 1000 s are detected in 4 observations. This means that the corona height can significantly evolve from ~ 10-25 $r_{g}$ to ~ 55 $r_{g}$, or vice versa, towards the end of the observation. Granger lags are a promising way to measure the intrinsic lags, and provide evidence of coronal height variability within each individual observation.

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arXiv2023

Extended Corona Models of X-ray Reverberation in the AGN 1H~0707-495 and IRAS 13224-3809

We fit a new vertically extended corona model to previously measured reverberation time lags observed by \emph{XMM-Newton} in two extremely variable Narrow Line Seyfert 1 Active Galactic Nuclei (AGN), 1H~0707-495 and IRAS~13224-3809, in a variety of similarly observed flux groups and explore the model in all observations over a 16 year period. The model employs two X-ray sources located along the black hole rotational axis at height, $h_1$ and $h_2$ respectively. These sources have their associated photon indices $\Gamma_1$ and $\Gamma_2$ which respond to fluctuations in the disc with a maximum response duration of $t_\text{max}$ and a propagation delay between the response of the two of $t_\text{shift}$. We find that for 1H 0707-495, $h_2$ is significantly correlated with $\Gamma_1$ and anti-correlated with ionisation $\xi$. Whilst the 1H 0707-495 corona extends upwards, the emission appears softer and the disc is less ionised. We find similarities in IRAS 13224-3809, but significant anti-correlation between $\Gamma_2$ and both $t_\text{max}$ and $t_\text{shift}$. This suggests that when the IRAS 13224-3809 corona becomes softer while extending vertically upwards, the overall corona response occurs faster. This may also suggest that the inner disc also becomes more active. In addition, $\Gamma_1$ and $\Gamma_2$ are extreme, relatively less variable, but more separate in IRAS 13224-3809 than in 1H 0707-495. This suggests that the IRAS 13224-3809 corona may be more patchy in the sense that it has two more clear distinct spectral zones of $\Gamma_1$ and $\Gamma_2$ (possibly relating to two distinct zones of coronal temperature) when compared to 1H 0707-495.

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arXiv2022

Predicting the black hole mass and correlations in X-ray reverberating AGN using neural networks

We develop neural network models to predict the black hole mass using 22 reverberating AGN samples in the XMM-Newton archive. The model features include the fractional excess variance ($F_{\rm var}$) in 2-10 keV band, Fe-K lag amplitude, 2-10 keV photon counts and redshift. We find that the prediction accuracy of the neural network model is significantly higher than what is obtained from the traditional linear regression method. Our predicted mass can be confined within $\pm (2$-5) per cent of the true value, suggesting that the neural network technique is a promising and independent way to constrain the black hole mass. We also apply the model to 21 non-reverberating AGN to rule out their possibility to exhibit the lags (some have too small mass and $F_{\rm var}$, while some have too large mass and $F_{\rm var}$ that contradict the $F_{\rm var}$-lag-mass relation in reverberating AGN). We also simulate 3200 reverberating AGN samples using the multi-feature parameter space from the neural network model to investigate the global relations if the number of reverberating AGN increases. We find that the $F_{\rm var}$-mass anti-correlation is likely stronger with increasing number of newly-discovered reverberating AGN. Contrarily, to maintain the lag-mass scaling relation, the tight anti-correlation between the lag and $F_{\rm var}$ must preserve. In an extreme case, the lag-mass correlation coefficient can significantly decrease and, if observed, may suggest the extended corona framework where their observed lags are more driven by the coronal property rather than geometry.

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arXiv2022

Effects of the refractive index of the X-ray corona on the emission lines in AGN

X-ray reflection from an accretion disc produces characteristic emission lines allowing us to probe the innermost regions in AGN. We investigate these emission lines under a framework of Riemannian geometrical optics where the corona has a refractive index of $n \neq 1$. The empty space outside is a vacuum with $n = 1$. The Kerr metric is modified to trace the light rays that are bent due to not only the gravity of the black hole, but also the effects of coronal plasma dependent on $n$. The choice of $n$ alters the null geodesics, producing the effect which is analogous to the light deflection. For the corona with $n > 1$, the disc on the far side within the corona covers a larger area on the observer' sky, enhancing the blue wing of the line and producing more flux difference between the blue peak and extended red tail. The inverse effects are seen when $n < 1$. Moreover, the corona with $n > 1$ and $n < 1$ could induce extra shifts in the blue wing ($\Delta g_{max}$) to higher and lower energy, respectively. These effects are more prominent when the inclination angle is $\gtrsim 60^\circ$ and the corona extends to $\gtrsim 5r_g$. To obtain the deviation of the line shift of $\Delta g_{\rm max} \gtrsim 0.01$, the difference between the refractive index of the corona and that of the empty space must be $\Delta n \gtrsim 0.5%$. Finally, the lensing corona can influence the arrival time of photons that may affect the observed variability of these emission lines

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arXiv2021

X-ray reverberation models of the disc wind in ultraluminous X-ray source NGC 5408 X-1

Majority of ultraluminous X-ray sources (ULXs) are believed to be super-Eddington objects, providing a nearby prototype for studying an accretion in super-critical regime. In this work, we present the study of time-lag spectra of the ULX NGC 5408 X-1 using a reverberation mapping technique. The time-lag data were binned using two different methods: time averaged-based and luminosity-based spectral bins. These spectra were fitted using two proposed geometric models: single and multiple photon scattering models. While both models similarly assume that a fraction of hard photons emitted from inner accretion disc could be down-scattered with the super-Eddington outflowing wind becoming lagged, soft photons, they are different by the number that the hard photons scattering with the wind: i.e. single vs multiple times. In case of averaged spectrum, both models consistently constrained the mass of ULX in the range of $\sim$80-500 M$_{\rm \odot}$. However, for the modelling results from the luminosity based spectra, the confidence interval of the BH mass is significantly improved and is constrained to the range of $\sim$75-90 M$_{\rm \odot}$. In addition, the models suggest that the wind geometry is extended in which the photons could down-scatter with the wind at the distance of $\sim$10$^{4}$ - 10$^{6}$ $r_{\rm g}$. The results also suggest the variability of the lag spectra as a function of ULX luminosity, but the clear trend of changing accretion disc geometry with the spectral variability is not observed.

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arXiv2021

The nature of the extreme X-ray variability in the NLS1 1H 0707-495

We examine archival XMM-Newton data on the extremely variable narrow-line Seyfert 1 (NLS1) active galactic nucleus (AGN) 1H 0707-495. We construct fractional excess variance (Fvar) spectra for each epoch, including the recent 2019 observation taken simultaneously with eROSITA. We explore both intrinsic and environmental absorption origins for the variability in different epochs, and examine the effect of the photoionised emission lines from outflowing gas. In particular, we show that the unusual soft variability first detected by eROSITA in 2019 is due to a combination of an obscuration event and strong suppression of the variance at 1 keV by photoionised emission, which makes the variance below 1 keV appear more extreme. We also examine the variability on long timescales, between observations, and find that it is well described by a combination of intrinsic variability and absorption variability. We suggest that the typical extreme high frequency variability which 1H 0707-495 is known for is intrinsic to the source, but the large amplitude, low frequency variability that causes prolonged low-flux intervals is likely dominated by variable low-ionisation, low velocity absorption.

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arXiv2021

Machine learning application to detect light echoes around black holes

X-ray reverberation has become a powerful tool to probe the disc-corona geometry near black holes. Here, we develop Machine Learning (ML) models to extract the X-ray reverberation features imprinted in the Power Spectral Density (PSD) of AGN. The machine is trained using simulated PSDs in the form of a simple power-law encoded with the relativistic echo features. Dictionary Learning and sparse coding algorithms are used for the PSD reconstruction, by transforming the noisy PSD to a representative sparse version. Then, the Support Vector Machine is employed to extract the interpretable reverberation features from the reconstructed PSD that holds the information of the source height. The results show that the accuracy of predicting the source height, $h$, is genuinely high and the misclassification is only found when $h$ > 15$r_g$. When the test PSD has a bending power-law shape, which is completely new to the machine, the accuracy is still high. Therefore, the ML model does not require the intrinsic shape of the PSD to be determined in advance. By focusing on the PSD parameter space observed in real AGN data, classification for $h \leq$ 10$r_g$ can be determined with 100% accuracy, even using a PSD in an energy band that contains a reflection flux as low as 10% of the total flux. For $h$ > 10$r_g$, the data, if misclassified, will have small uncertainties of $\Delta h$ ~ 2-4$r_g$. This work shows, as a proof of concept, that the ML technique could shape new methodological directions in the X-ray reverberation analysis.

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arXiv2020

Evolution of the truncated disc and inner hot-flow of GX 339-4

Aims. We study the changes in geometry of the truncated disc and the inner hot-flow of GX 339-4 by analyzing the Power SpectralDensity (PSD) extracted from six XMM-Newton observations taken at the very end of an outburst. Methods. A theoretical model of the PSD of GX 339-4 in the 0.3-0.7 keV (thermal reverberation dominated) and 0.7-1.5 keV (disc continuum dominated) energy bands is developed. The model assumes the standard accretion disc to be truncated at a specific radius, inside of which are two distinct hot-flow zones: one spectrally soft and the other spectrally hard. The effects of disc-fluctuations and thermal reverberation are taken into account. Results. This model successfully produces the traditional bumpy PSD profiles and provides good fits to the GX 339-4 data. The truncation radius is found to increase from $r_{\rm trc}$ $\sim$ 10 to 55 $r_{\rm g}$ as the source luminosity decreases, strongly confirming that the truncation radius can be characterized as a function of luminosity. Keeping in mind the large uncertainty in previous measurements of the truncation radius, our values are larger than some obtained from spectroscopic analysis, but smaller than those implied from reverberation lag analysis. Furthermore, the size of two inner hot-flow zones which are spectrally hard and spectrally soft are also growing from $\sim$ 5 to 27 $r_{\rm g}$ and from $\sim$ 3 to 26 $r_{\rm g}$, respectively, as the flux decreases. We find that the radial range of inner hard zone is always larger than the range of the soft hot-flow zone, but by a comparatively small factor of $\sim$ 1.1-2.2

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arXiv2019

X-ray time lags in AGN: inverse-Compton scattering and spherical corona model

We develop a physically motivated, spherical corona model to investigate the frequency-dependent time lags in AGN. The model includes the effects of Compton up-scattering between the disc UV photons and coronal electrons, and the subsequent X-ray reverberation from the disc. The time lags are associated with the time required for multiple scatterings to boost UV photons up to soft and hard X-ray energies, and the light crossing time the photons take to reach the observer. This model can reproduce not only low-frequency hard and high-frequency soft lags, but also the clear bumps and wiggles in reverberation profiles which should explain the wavy-residuals currently observed in some AGN. Our model supports an anti-correlation between the optical depth and coronal temperatures. In case of an optically thin corona, time delays due to propagating fluctuations may be required to reproduce observed time lags. We fit the model to the lag-frequency data of 1H0707-495, Ark 564, NGC 4051 and IRAS 13224-3809 estimated using the minimal bias technique so that the observed lags here are highest-possible quality. We find their corona size is ~7-15 r_g having the constrained optical depth ~2-10. The coronal temperature is ~150-300 keV. Finally, we note that the reverberation wiggles may be signatures of repeating scatters inside the corona that control the distribution of X-ray sources.

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arXiv2016

Investigating the X-ray time-lags in PG 1244+026 using an extended corona model

We present an extended corona model based on ray-tracing simulations to investigate X-ray time lags in Active Galactic Nuclei (AGN). This model consists of two axial point sources illuminating an accretion disc that produce the reverberation lags. These lags are due to the time delays between the directly observed and reflection photons and are associated with the light-travel time between the source and the disc, so they allow us to probe the disc-corona geometry. We assume the variations of two X-ray sources are triggered by the same primary variations, but allow the two sources to respond in different ways (i.e. having different source responses). The variations of each source induce a delayed accretion disc response and the total lags consist of a combination of both source and disc responses. We show that the extended corona model can reproduce both the low-frequency hard and high-frequency soft (reverberation) lags. Fitting the model to the timing data of PG~1244+026 reveals the hard and soft X-ray sources at $\sim6r_{\text{g}}$ and $\sim11r_{\text{g}}$, respectively. The upper source produces small amounts of reflection and can be interpreted as a relativistic jet, or outflowing blob, whose emission is beamed away from the disc. This explains the observed lag-energy in which there is no soft lag at energies $<1$~keV as they are diluted by the soft continuum of the upper source. Finally, our models suggest that the fluctuations propagating between the two sources of PG~1244+026 are possible but only at near the speed of light.

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arXiv2016

Relativistic X-ray reverberation modelling of the combined time-averaged and lag-energy spectra in AGN

General relativistic ray tracing simulations of the time-averaged spectrum and energy-dependent time delays in AGN are presented. We model the lamp-post geometry in which the accreting gas is illuminated by an X-ray source located on the rotation axis of the black hole. The spectroscopic features imprinted in the reflection component are modelled using REFLIONX. The associated time delays after the direct continuum, known as reverberation lags, are computed including the full effects of dilution and ionization gradients on the disc. We perform, for the first time, simultaneous fitting of the time-averaged and lag-energy spectra in three AGN: Mrk 335, IRAS 13224-3809 and Ark 564 observed with XMM-Newton. The best fitting source height and central mass of each AGN partly agree with those previously reported. We find that including the ionization gradient in the model naturally explains lag-energy observations in which the 3 keV and 7-10 keV bands precede other bands. To obtain the clear 3 keV and 7-10 keV dips in the lag-energy profile, the model requires either a source height > 5$r_g$, or a disc that is highly ionized at small radii and is colder further out. We also show that fitting the lag or the mean spectra alone can lead to different results and interpretations. This is therefore important to combine the spectral and timing data in order to find the plausible but self-consistent fits which is achievable with our model.

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arXiv2015

Simultaneous spectral and reverberation modelling of relativistic reflection in Mrk 335

We present an X-ray spectral and timing model to investigate the broad and variable iron line seen in the high flux state of Mrk 335. The model consists of a variable X-ray source positioned along the rotation axis of the black hole that illuminates the accretion disc producing a back-scattered, ionized reflection spectrum. We compute time lags including full dilution effects and perform simultaneous fitting of the 2-10 keV spectrum and the frequency-dependent time lags of 2.5-4 vs. 4-6.5 keV bands. The best-fitting parameters are consistent with a black hole mass of approximately 1.3 x 10^7 M_sun, disc inclination of 45 degrees and the photon index of the direct continuum of 2.4. The iron abundance is 0.5 and the ionization parameter is 10^3 erg cm / s at the innermost part of the disc and decreases further out. The X-ray source height is very small, approximately 2 r_g. Furthermore, we fit the Fe L lags simultaneously with the 0.3-10 keV spectrum. The key parameters are comparable to those previously obtained. We also report the differences below 2 keV using the xillver and reflionx models which could affect the interpretation of the soft excess. While simultaneously fitting spectroscopic and timing data can break the degeneracy between the source height and the black hole mass, we find that the measurements of the source height and the central mass significantly depend on the ionization state of the disc and are possibly model-dependent.

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