Discovery of soft and hard X-ray time lags in low-mass AGNs
Labani Mallick, Daniel R. Wilkins, William N. Alston, Alex Markowitz, Barbara De Marco, Michael L. Parker, Anne M. Lohfink, C. S. Stalin
aa r X i v : . [ a s t r o - ph . H E ] J a n MNRAS , 1–7 (0000) Preprint 26 January 2021 Compiled using MNRAS L A TEX style file v3.0
Discovery of soft and hard X-ray time lags in low-mass AGN
L. Mallick , , ⋆ D. R. Wilkins , W. N. Alston , , A. Markowitz , , B. De Marco , ,M. L. Parker , , A. M. Lohfink , and C. S. Stalin Indian Institute of Astrophysics, Block II, Koramangala, Bangalore 560034, India Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305, USA Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK European Space Agency (ESA), European Space Astronomy Centre (ESAC), E-28691 Villanueva de la Ca˜nada, Madrid, Spain Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716, Warsaw, Poland University of California, San Diego, Center for Astrophysics and Space Sciences, 9500 Gilman Dr, La Jolla, CA 92093, USA Departament de F´ısica, EEBE, Universitat Polit´ecnica de Catalunya, Av. Eduard Maristany 16, E-08019, Barcelona, Spain eXtreme Gravity Institute, Department of Physics, Montana State University, Bozeman, MT 59717, USA
26 January 2021
ABSTRACT
The scaling relations between the black hole (BH) mass and soft lag propertiesfor both active galactic nuclei (AGN) and BH X-ray binaries (BHXRBs) suggest thesame underlying physical mechanism at work in accreting BH systems spanning abroad range of mass. However, the low-mass end of AGN has never been explored indetail. In this work, we extend the existing scaling relations to lower-mass AGN, whichserve as anchors between the normal-mass AGN and BHXRBs. For this purpose, weconstruct a sample of low-mass AGN ( M BH < × M ⊙ ) from the XMM-Newton archive and measure frequency-resolved time delays between the soft (0.3 − − ∼ [1 . − . × − Hz, which is interpreted as a signof reverberation from the inner accretion disc in response to the direct coronal emission.At low frequencies ( ∼ [3 − × − Hz), the hard band lags behind the soft bandvariations, which we explain in the context of the inward propagation of luminosityfluctuations through the corona. We find that the X-ray source for the sample extendsat an average radius of around 8 r g and a median height of around 15 r g above thedisc plane, assuming a lamppost geometry for the corona. Our results confirm thatthe scaling relations between the BH mass and soft lag amplitude/frequency derivedfor higher-mass AGN can safely extrapolate to lower-mass AGN, and the accretionprocess is indeed independent of the BH mass. Key words: black hole physics — accretion, accretion discs — relativistic processes—galaxies: active— galaxies: Seyfert
Active galactic nuclei (AGN) emit radiation across the en-tire electromagnetic spectrum, and they are highly vari-able in the X-ray waveband. The observed fast variabil-ity indicates that the X-ray emitting region is compactand located in the vicinity of the central supermassiveblack hole (SMBH). The measurement of time delays be-tween different X-ray energy bands as a function of Fourierfrequency can shed light not only on the physical pro-cesses at work in the strong gravitational field of the BH ⋆ Email: [email protected] (LM) but also on the geometry of the accretion disc-corona sys-tem (e.g., Wilkins & Fabian 2013; Emmanoulopoulos et al.2014; Wilkins & Gallo 2015; Alston et al. 2020). When thehard band (1 − − c Hardy et al. 2004). The origin of hard lags hasbeen attributed to the standard Comptonization processwithin the X-ray corona (Nowak et al. 1999) or mass ac-cretion rate fluctuations propagating inwards through theaccretion disc (Kotov et al. 2001; Ar´evalo & Uttley 2006; © L. Mallick et al.
Hogg & Reynolds 2016). On the other hand, we observe asoft or negative lag when the variations in the reflection-dominated soft band lag behind the variations in the pri-mary emission-dominated hard band. These have now beenobserved in many AGN (Fabian et al. 2009; De Marco et al.2013; Kara et al. 2016; Wilkins et al. 2017; Mallick et al.2018) as well as in stellar-mass BH binaries (Uttley et al.2011; De Marco et al. 2015). The soft lag can be explainedas a signature of reverberation of X-ray photons from theaccretion disc (e.g., Zoghbi et al. 2010; Cackett et al. 2013;De Marco et al. 2015) and/or as thermally reprocessed emis-sion from the warm corona (Gardner & Done 2014). An al-ternative interpretation of the soft lag is scattering of X-rays from a distant (10 −
100 gravitational radii), partially-covering absorbing medium (Miller et al. 2010). However,this model is unable to explain the fundamental proper-ties of the observed variability process: the linear root meansquared (rms)–flux relation and the log-normal flux distri-bution (Uttley & M c Hardy 2001; Uttley et al. 2005; Alston2019).The unification theory of BH accretion suggests that theaccretion process is independent of the BH mass, and we ex-pect to observe similar timing properties in sources spanninga wide range of BH mass (e.g., M c Hardy et al. 2006). Thediscovery of scaling relations between the BH mass and softlag properties for both supermassive (De Marco et al. 2013;hereafter DM13) and stellar-mass BHs (De Marco et al.2015) is a breakthrough in this context. However, it is stillunknown how the lower-mass SMBHs fit into these scalingrelations. The lower-mass AGN are intriguing sources thatdemand our attention for several reasons. They have greatpotential to provide crucial constraints on the nature of pri-mordial SMBHs for models of cosmological BH growth. Theycan serve as anchors to test if the scaling relations derivedfor higher-mass AGN can safely extrapolate to stellar-massBH binaries and validate the existence of prevalent accre-tion properties at all mass scales. For a given radius, the in-ner disc temperature of lower-mass AGN is higher comparedto higher-mass AGN discs, which could potentially impactcoronal geometry and/or reflection emission properties oflower-mass SMBHs. We thus aim to extend the existing BHmass vs. soft lag scaling relations of DM13 to lower-massSMBHs (log M BH ∼ −
6) and obtain a complete assess-ment of the lag-mass correlations for a broader mass range(log M BH ∼ − We selected a sample of very low-mass AGN ( M BH < × M ⊙ ) from the Sloan Digital Sky Survey (SDSS) that werecataloged by Greene & Ho (2007) (hereafter GH07) and oneAGN (POX 52) discovered in the POX objective-prism sur-vey (Kunth et al. 1981). A thorough search of the XMM-Newton (Jansen et al. 2001) archive resulted in a sample of 26 objects having one or multiple observations. The
XMM-Newton /European Photon Imaging Camera (EPIC) data forthe 26 objects were reduced with the Scientific Analysis Sys-tem (
SAS v.18.0.0) and the updated (as of 2020 May 12)calibration files. We processed the data obtained from bothEPIC pn and MOS with the
SAS tasks epproc and emproc ,respectively. We rejected the bad pixel events by setting
FLAG ==0, and filtered the processed pn and MOS events us-ing
PATTERN PATTERN
12, respectively. To search forthe flare-corrected good time intervals (
GTI ), we adopted a3 σ clipping method which can effectively eliminate the high-count-rate tail of the flare histogram while retaining usefulevents (Chen et al. 2018). We first created single-pixel eventlight curves for the 10 −
12 keV band with time bins of 100 sand rejected those time intervals whose 10 −
12 keV countrates exceeded 3 σ above the mean. We then applied the 3 σ clipped GTI to the 0.3 −
10 keV light curves and obtained theflare-filtered cleaned event files. This criterion excluded threesources massively dominated by background flares and led toa sample consisting of 23 AGN. The source and backgroundarea for each observation were selected from a circular regionof radius 20 arcsec centered on the point source and nearbysource-free zone, respectively. We extracted the deadtime-corrected, background-subtracted source light curves withtime bin size of 100 s using the
SAS task epiclccorr . TheEPIC-pn and MOS light curves were then added using the lcmath tool to increase the signal-to-noise. The resultinglight curves contain periods when both the detectors werefunctioning. A small number of data gaps were replaced bythe method of linear interpolation implemented in the X-raytiming analysis package
PYLAG . We excluded Seyfert 2 AGNfrom further analysis to concentrate only on sources with un-obscured views of their central engines. To probe variabilitypower above the Poisson noise level of 20 Hz − , we applieda stringent total filtered exposure threshold of 30 ks and en-sure that the background-subtracted average source countsin the 0.3 −
10 keV band is at least 3 × . These criterialead to a final sample of 8 AGN which are Seyfert 1 galaxies.The characteristics and observational details of the final 8sources are listed in Table 1 and Table A1, respectively. Forthe GH07 sample, the central BH masses were estimated(see equation A1 of GH07) using the L – L α relationfrom Greene & Ho (2005) in combination with the revised R BLR - L α relation from Bentz et al. (2006), where L ˚A isthe nonstellar continuum luminosity at 5100˚A, R BLR is thebroad line region (BLR) size and L α is the H α line luminos-ity. We adopted a typical BH mass uncertainty of 0.3 dex(Greene & Ho 2006) incurred by the BLR geometrical fac-tor in the R BLR - L α relation. The BH mass of POX 52 wasderived from R BLR and the H β linewidth (equation 2 ofBarth et al. 2004) where R BLR was inferred using the cali-brated L versus R BLR relation from Kaspi et al. (2000).The BH mass uncertaity for POX 52 was obtained from thefitting of updated M BH − σ ⋆ relation (Tremaine et al. 2002)where both the measurement error on the host galaxy ve-locity dispersion ( σ ⋆ ) for POX 52 and the error in the fittedparameters of the M BH − σ ⋆ relation contribute to the BHmass uncertainty. http://github.com/wilkinsdr/pylag MNRAS000
10 keV band is at least 3 × . These criterialead to a final sample of 8 AGN which are Seyfert 1 galaxies.The characteristics and observational details of the final 8sources are listed in Table 1 and Table A1, respectively. Forthe GH07 sample, the central BH masses were estimated(see equation A1 of GH07) using the L – L α relationfrom Greene & Ho (2005) in combination with the revised R BLR - L α relation from Bentz et al. (2006), where L ˚A isthe nonstellar continuum luminosity at 5100˚A, R BLR is thebroad line region (BLR) size and L α is the H α line luminos-ity. We adopted a typical BH mass uncertainty of 0.3 dex(Greene & Ho 2006) incurred by the BLR geometrical fac-tor in the R BLR - L α relation. The BH mass of POX 52 wasderived from R BLR and the H β linewidth (equation 2 ofBarth et al. 2004) where R BLR was inferred using the cali-brated L versus R BLR relation from Kaspi et al. (2000).The BH mass uncertaity for POX 52 was obtained from thefitting of updated M BH − σ ⋆ relation (Tremaine et al. 2002)where both the measurement error on the host galaxy ve-locity dispersion ( σ ⋆ ) for POX 52 and the error in the fittedparameters of the M BH − σ ⋆ relation contribute to the BHmass uncertainty. http://github.com/wilkinsdr/pylag MNRAS000 , 1–7 (0000) -ray lags in low-mass AGN Table 1.
Source sample employed in this work. Columns (1) and (2) show the source name and total filtered exposure length in ks,respectively. Columns (3), (4) and (5) show the background-subtracted EPIC pn+MOS counts in the full (0.3 −
10 keV), soft (0.3 − − ∼ . Name Total filtered exp. (ks) Total counts Soft counts Hard counts Type Redshift L bol /L E M BH (10 M ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9)J0107 34.8 1 . × . × . × NLSy 1 0.0767 0.40 15.8 +15 . − . J0942 55.0 7 . × . × . × Sy 1 0.197 0.63 15.8 +15 . − . J1023 219.4 3 . × . × . × NLSy 1 0.0989 0.50 5.0 +4 . − . J1140 150.7 1 . × . × . × NLSy 1 0.081 0.63 12.6 +12 . − . J1347 30.8 2 . × . × × NLSy 1 0.0643 0.50 10.0 +9 . − . J1434 47.9 8 . × . × . × NLSy 1 0.0283 0.10 6.3 +6 . − . J1559 208.6 7 . × . × . × NLSy 1 0.031 0.63 15.8 +15 . − . POX52 85.3 7 . × . × . × Sy 1.8 0.021 0.75 1.6 +1 . − . Table 2.
Columns (2) and (3) show detected soft ( ν s ) and hard ( ν h ) lag frequencies in mHz, respectively. Columns (4) and (5) showthe measured soft and hard lag amplitudes in seconds, respectively. The 1 σ uncertainty in lags was obtained through Monte Carlosimulations. The direct-to-reflected flux fraction ( δ soft ) in the soft band and reflected-to-direct flux fraction ( δ hard ) in the hard band arequoted in columns (6) and (7), respectively. Columns (8) and (9) show the coronal height ( h c ) and radius ( r c ) in units of r g , respectively.Both the height and radius of the corona for each source were corrected for dilution effects and source redshift. Columns (10) and (11)show the confidence intervals of detected soft and hard lags, respectively. Source ν s (mHz) ν h (mHz) | τ soft | (s) τ hard (s) δ soft δ hard h c ( r g ) r c ( r g ) C.I.-soft C.I.-hard(%) (%)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)J0107 1.55 ± .
49 0.57 ± .
49 65.2 ± . ± . ± . ± . ± .
41 0.45 ± . < . ± . < . ± . ± .
47 0.78 ± .
47 74.5 ± . < . ± . < . ± .
35 0.39 ± .
35 35.2 ± . ± . ± . ± . ± .
49 0.57 ± .
49 74.0 ± . ± . ± . ± . ± .
48 0.64 ± .
48 51.6 ± . < . ± . < . ± .
31 0.35 ± .
31 22.1 ± . ± . ± . ± . ± . − ± . − ± . − − We measured the time lag as a function of temporal fre-quency between the soft and hard X-ray light curves follow-ing the Fourier method presented in Nowak et al. (1999) andUttley et al. (2014). The soft and hard X-ray light curvesrepresent the variations of the 0.3 − − S ( ν ), H ( ν ) of two evenly sampledlight curves, s ( t ) and h ( t ). Then we estimate the cross spec-trum by multiplying the Fourier transform of one light curvewith the complex conjugate of the Fourier transform of theother light curve. The cross spectrum is defined as C ( ν ) = S ∗ ( ν ) H ( ν ) = | S ( ν ) || H ( ν ) | e i [ φ h ( ν ) − φ s ( ν )] . The time lag be-tween the soft and hard X-ray light curves is derived from the formula, τ ( ν ) = φ ( ν ) / πν , where φ ( ν ) = arg( h C ( ν ) i ) isthe phase of the average cross spectrum which is estimatedby first taking the average of the cross spectral values C ( ν )over multiple, non-overlapping segments and then binned inlogarithmically spaced frequency bins. The number of binsis decided by the data quality and exposure time of the ob-servations. The lower frequency bound is set by the inverseof the segment length, and the upper frequency bound isequal to 1/2∆ t , where ∆ t = 100 s is the time bin size used.The errors on the lag were estimated using the formula givenin Nowak et al. (1999). In Figure A1, we show the Poissonnoise corrected intrinsic variability power of each source as afunction of frequency both in the soft and hard X-ray bands.The Poisson noise generally dominated > × − Hz, whichis well above the frequencies where the soft and hard lagswere detected. We verified the significance of lags following
MNRAS , 1–7 (0000)
L. Mallick et al.
Figure 1.
Lag-frequency spectra for the sample. The time lag was estimated between the 0.3 − − σ error bars were calculated using the formula given in Nowak et al. (1999). Thesimulated 1 σ contour plots are shown by solid green lines. The black arrow refers to the frequency at which the soft lag was observed.C.I. on each panel represents the confidence interval of negative soft lag as determined from Monte Carlo simulations. 6 out of 8 AGNshow soft lags with >
90% confidence. the approach of Zoghbi et al. (2010). The basic idea of thisapproach is to generate a pair of artificial light curves, thenimpose the observed lag between the light curve pair, andcheck how well the lag can be recovered. We simulated 1000pairs of soft and hard X-ray Monte Carlo light curves us-ing the method of Emmanoulopoulos et al. (2013) after im-posing the observed frequency-dependent phase lag betweeneach light curve pair. The resulting simulated light curveshave the same statistical and variability properties as theobserved pairs. We then derived the lag-frequency spectrumfor each pair of the simulated light curves. The confidenceinterval was estimated from the distribution of the resultinglag values in each frequency bin. The observed lag-frequencyspectra and simulated 1 σ confidence contours for the sam-ple are shown in Figure 1. The simulations suggest that theobserved 1 σ error bars were underestimated for a few AGNdue to the data having low counts. The negative soft lags are detected in 6/8 AGN at the >
90% confidence level, while5 out of 8 AGN show positive hard lags with >
94% con-fidence. From a statistical point of view, the measurementof soft lags in low-mass sources is more challenging as thecharacteristic time scales are shorter, and thus the numberof collected photons is lower. Therefore, the detection sig-nificance of soft lags is expected to be lower in the case oflower-mass AGN. One possible way to raise the detectionsignificance is to obtain longer monitoring of these AGN.The frequencies, amplitudes, and significance levels of nega-tive soft and positive hard lags are reported in Table 2. Thesoft lag amplitude refers to the largest amplitude negativelag and the corresponding frequency is identified as the softlag frequency. To check the reality of the soft lag dip, wefit the lag-frequency spectra with a monotonically declininghard lag model, τ h = kν − α . The model resulted in poor fitswith χ /d.o.f > MNRAS000
94% con-fidence. From a statistical point of view, the measurementof soft lags in low-mass sources is more challenging as thecharacteristic time scales are shorter, and thus the numberof collected photons is lower. Therefore, the detection sig-nificance of soft lags is expected to be lower in the case oflower-mass AGN. One possible way to raise the detectionsignificance is to obtain longer monitoring of these AGN.The frequencies, amplitudes, and significance levels of nega-tive soft and positive hard lags are reported in Table 2. Thesoft lag amplitude refers to the largest amplitude negativelag and the corresponding frequency is identified as the softlag frequency. To check the reality of the soft lag dip, wefit the lag-frequency spectra with a monotonically declininghard lag model, τ h = kν − α . The model resulted in poor fitswith χ /d.o.f > MNRAS000 , 1–7 (0000) -ray lags in low-mass AGN Figure 2.
Soft lag frequency vs. BH mass (left), soft lag amplitude vs. BH mass (middle), and soft lag amplitude vs. frequency (right).The 1 σ error bars were determined from Monte Carlo simulations. Sources with a soft lag detected at >
90% confidence are includedand marked as diamonds. Sources obtained from DM13 are marked as squares. The dashed lines represent the DM13 best-fit relations.The black solid lines and red shaded regions represent the best-fit linear regression models and corresponding confidence area for thecombined sample consisting of the 6 Seyfert 1 galaxies from this work and 15 Seyfert 1 galaxies from DM13. The dotted line representsthe light-crossing time at 10 r g as a function of mass. The lag amplitudes and frequencies are only corrected for redshift in order to becompared with the DM13 lag data. lag model alone cannot describe the lag profile, and there-fore, there is a need for an additional soft lag component(see Fig. A2). We also ensured that the soft lag was not pro-duced due to the phase wrapping of the low-frequency hardlag. The phase-wrapping is a type of aliasing that wrapsaround from π to − π , and the hard lag can become negativeat an interval of ν = n τ h (Uttley et al. 2014), where n isan odd integer and τ h is the hard lag amplitude. We veri-fied that the detected soft lag frequencies are well below thephase-wrapping frequencies for all sources in the sample. The nature of the lag-frequency spectra is similar to whatwe usually observe in higher-mass AGN, as reported byDM13. They show a transition from a positive lag at lowfrequencies to a negative lag, predicted from reverberationat high frequencies. The lag spectra are typically mod-eled as a combination of ‘transfer functions’ for the re-processed reflection component (including all general rela-tivistic effects) and a power-law like frequency response forthe intrinsic component (e.g., Emmanoulopoulos et al. 2014;Alston et al. 2020). A detailed transfer function modellingof these data will be shown in a follow up paper.At higher frequencies, the soft band variations are de-layed relative to the hard band. The soft lag amplitude andfrequency correspond to the maximum, negative point in thelag-frequency profile. We detected soft lags with >
90% con-fidence in 6 out of 8 AGN. In order to test the dependenceof BH mass ( M BH ) on the soft lag frequency ( ν soft ) and am-plitude ( | τ soft | ), we examined the correlations between ν soft and M BH as well as the correlations between | τ soft | and M BH for the combined sample consisting of the 6 Seyfert 1 galax-ies from this work and 15 Seyfert 1 galaxies from DM13.We also investigated whether there is a correlation between | τ soft | and ν soft . We considered the combined sample andapplied a Bayesian approach to linear regression with er-ror both in X and Y coordinates (Kelly 2007). The best-fit relations are:log h ν soft Hz i = − . ± . h M BH M ⊙ i − . ± . . (1)log h | τ soft | sec i = 0 . ± . h M BH M ⊙ i + 2 . ± . . (2)log h | τ soft | sec i = − . ± . h ν soft Hz i − . ± . . (3)where M BH is the BH mass in units of M ⊙ , ν soft and | τ soft | are the soft lag frequency and amplitude in Hz and second,respectively. The soft lag frequency vs. BH mass, soft lagamplitude vs. BH mass, and soft lag amplitude vs. frequencyplots and their corresponding best-fit linear models in log-log space are shown in Figure 2. The results are consistentwith the mass-lag scaling relations of DM13. The spread inthe lag amplitude may be the result of dilution effects. Forsome AGN, the scatter could be due to the changes in thecoronal geometry (e.g., Alston et al. 2020).We also performed a Spearman’s rank correlation teston the combined sample to evaluate the correlations betweenthese three parameters. The Spearman coefficient values forthe ν soft − M BH , | τ soft |− M BH and | τ soft |− ν soft correlations are − .
87, 0 .
73, and − .
71 with null-hypothesis probabilities of2 . × − , 1 . × − , and 3 . × − , respectively, suggestingthat the inverse correlation between lag frequency and BHmass is more significant and secured.If we assume a lamppost model with a stationary coronaabove the disc and the coronal height is significantly largerthan the innermost stable circular orbit (ISCO), then thesoft lag amplitude can be approximated as the light-crossingtime delay between the corona and the face-on disc, τ soft ≈ (cid:18) h c r g (cid:19) (cid:18) M BH M ⊙ (cid:19) (4)where h c is the height or vertical extent of the corona in MNRAS , 1–7 (0000)
L. Mallick et al. units of r g = GM BH /c , M BH is the BH mass in unitsof M ⊙ . The light-crossing time over 1 r g for a BH of mass10 M ⊙ is 50 s. However, the measured lags get diluted asthe reflection-dominated soft band (0.3 − − −
10 keV spec-tral data with the model, [ tbabs × (relxill+zpowerlw) ],we estimated the direct and reflected photon flux both in thesoft and hard X-ray bands. We then calculated the direct-to-reflected flux fraction ( δ soft ) in the soft band and thereflected-to-direct flux fraction ( δ hard ) in the hard band foreach source (see Table 2). The observed soft and hard lagsget diluted by a factor of δ soft and δ hard , respectively(Uttley et al. 2014). We corrected the observed soft lags fordilution effects and source redshift, and then measured thevertical extent of the corona using equation (4). The inferredmedian value of the coronal height is h c ∼ r g , which pos-sibly indicates that the lower-mass AGN have a relativelyextended corona than their higher-mass counterparts (e.g.,Emmanoulopoulos et al. 2014).The hard band lags behind the soft band variationsat the lowest observed frequencies of ∼ [3 − × − Hz.We explain the hard lag in the context of viscous propaga-tion of mass accretion rate fluctuations propagating inwardsthrough the accretion disc to create variations in the corona(Kotov et al. 2001; Hogg & Reynolds 2016). Therefore, thehard lag ( τ hard ) can correspond to the viscous timescale( τ vis ) of the variations that originate at the edge of thecorona and propagate inwards, τ hard = τ vis = 500 (cid:18) r c h c (cid:19) (cid:18) M BH M ⊙ (cid:19) (cid:18) r c r g (cid:19) / . (5)where the viscosity parameter, α ≈ . M BH is the BHmass in units of M ⊙ . r c and h c represent the radial and ver-tical extents of the corona in units of r g , respectively. Fromthe measured hard lag and source height, we estimated theradial extent of the corona in the context of propagatingfluctuation models using equation (5) after correcting fordilution effects and source redshift. The vertical and radialextents of corona for each source in the sample are shownin Table 2. We find that the corona extends at an averageradius of r c ∼ r g over the surface of the accretion disc onan average timescale of ∼
30 minutes. The radial extent ofthe corona is in agreement with the disc break radius mea-sured from the emissivity profile modeling (Wilkins & Gallo2015) of higher-mass AGN discs. We note that the mea-sured hard lags are not well sampled in these data setsbecause of the limited frequency window. They might ex-tend to much lower frequencies and larger amplitudes (seePapadakis et al. 2019).
We report the first results on the measurement and anal-ysis of time lags between the soft (0.3 − − M BH < × M ⊙ ) active galaxies. Wesummarize our conclusions as follows:(i) The shape of the lag-frequency spectra resembles thelag-frequency profile of higher-mass AGN with a transitionfrom a hard lag at low frequencies to a soft lag at highfrequencies.(ii) The origin of soft lags can be explained in the contextof disc reflection, which reverberates in response to the directcoronal emission. The median value of the coronal heightinferred from soft reverberation lags is around 15 r g , whichindicates that the corona of lower-mass AGN is relativelyextended compared to the higher-mass AGN corona.(iii) The origin of hard lags is most likely the viscouspropagation of fluctuations that originate at the edge of thecorona and propagate inwards through it. On an averagetimescale of around 30 minutes, the inferred average radialextent of the corona on the disc surface is around 8 r g . Thisvalue matches well with the break radius obtained from thedisc emissivity profile fitting of higher-mass AGN.(iv) The inverse correlation between the soft lag ampli-tude and frequency implies that shorter timescale variationshave been generated in a more compact X-ray emitting re-gion that radiates at the smaller disc radii and hence closerto the central BH.(v) The correlations between the BH mass and the soft-lag amplitude/frequency for a broad mass range (log M BH ∼ −
8) follow the DM13 scaling relations suggesting the pres-ence of a BH mass-independent universal accretion processin accreting black hole systems.(vi) This work will pave the way for more comprehensiveinvestigations into the low-mass end of AGN, which is cru-cial to understand the nature of cosmological ‘seed’ blackholes. The overall conclusion is that the existence of timelags between various X-ray energy bands is inevitable unlesssome strange accretion physics is at work in this low-massrange. We aim to further explore this kind of accreting blackhole systems in great detail with future long-duration, multi-wavelength observations.
We thank the anonymous reviewer for their time and con-structive feedback that improved this work. LM acknowl-edges support from the Department of Science of Technology(DST), India, fellowship agreement No. PDF/2020/3226.BDM acknowledges support from the European Union’sHorizon 2020 research and innovation programme underthe Marie Sk lodowska-Curie grant agreement No. 798726and via Ram´on y Cajal Fellowship RYC2018-025950-I. AGM acknowledges partial support from NarodowymCentrum Nauki (NCN) grants 2016/23/B/ST9/03123 and2018/31/G/ST9/03224, and also from NASA via NASA-ADAP Award NNX15AE64G. We dedicate this paper tohealthcare workers fighting the COVID-19 global pandemic.
MNRAS000
MNRAS000 , 1–7 (0000) -ray lags in low-mass AGN This research has made use of the NASA/IPAC Ex-tragalactic Database (NED), which is operated by the JetPropulsion Laboratory, California Institute of Technology,under contract with the NASA.This research has made use of data, software and/orweb tools obtained from the High Energy Astrophysics Sci-ence Archive Research Center (HEASARC), a service of theAstrophysics Science Division at NASA/GSFC and of theSmithsonian Astrophysical Observatory’s High Energy As-trophysics Division.This research has made use of ISIS functions (ISISs-cripts) provided by ECAP/Remeis observatory and MIT( ). All data used in this work are publicly avail-able from the
XMM-Newton science archive( http://nxsa.esac.esa.int/ ). REFERENCES
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APPENDIX A: ADDITIONAL TABLE AND PLOTS
This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS , 1–7 (0000)
L. Mallick et al.
Table A1.
Observation log of the used sample. The columns are (1) name of the source, (2) right ascension, (3) declination, (4)
XMM-Newton observation Id, (5) observation start date, (6) exposure time in ks after excluding the intervals of background flares.
Source Name [Short] RA DEC Obs. Id Date Filtered(Deg) (Deg) (yyyy-mm-dd) duration (ks)(1) (2) (3) (4) (5) (6)SDSS J010712.03+140844.9 [J0107] 16.800 14.146 0305920101 2005-07-22 34.8SDSS J094240.92+480017.3 [J0942] 145.6705 48.005 0201470101 2004-10-14 42.00201470301 2004-11-13 13.0SDSS J102348.44+040553.7 [J1023] 155.952 4.098 0108670101 2000-12-05 51.10605540201 2009-12-13 111.60605540301 2009-05-08 56.7SDSS J114008.71+030711.4 [J1140] 175.036 3.120 0305920201 2005-12-03 39.60724840101 2013-12-18 38.10724840301 2014-01-01 73.0SDSS J134738.23+474301.9 [J1347] 206.909 47.717 0744220701 2014-11-22 30.8SDSS J143450.62+033842.5 [J1434] 218.711 3.645 0305920401 2005-08-18 36.30674810501 2011-08-16 11.6SDSS J155909.62+350147.4 [J1559] 239.790 35.030 0112600801 2003-01-16 14.60744290101 2015-03-02 98.70744290201 2015-02-24 95.3POX52 180.737 − MNRAS000
Source Name [Short] RA DEC Obs. Id Date Filtered(Deg) (Deg) (yyyy-mm-dd) duration (ks)(1) (2) (3) (4) (5) (6)SDSS J010712.03+140844.9 [J0107] 16.800 14.146 0305920101 2005-07-22 34.8SDSS J094240.92+480017.3 [J0942] 145.6705 48.005 0201470101 2004-10-14 42.00201470301 2004-11-13 13.0SDSS J102348.44+040553.7 [J1023] 155.952 4.098 0108670101 2000-12-05 51.10605540201 2009-12-13 111.60605540301 2009-05-08 56.7SDSS J114008.71+030711.4 [J1140] 175.036 3.120 0305920201 2005-12-03 39.60724840101 2013-12-18 38.10724840301 2014-01-01 73.0SDSS J134738.23+474301.9 [J1347] 206.909 47.717 0744220701 2014-11-22 30.8SDSS J143450.62+033842.5 [J1434] 218.711 3.645 0305920401 2005-08-18 36.30674810501 2011-08-16 11.6SDSS J155909.62+350147.4 [J1559] 239.790 35.030 0112600801 2003-01-16 14.60744290101 2015-03-02 98.70744290201 2015-02-24 95.3POX52 180.737 − MNRAS000 , 1–7 (0000) -ray lags in low-mass AGN Figure A1.
Poisson-noise subtracted power spectral density in the soft (red circles) and hard (blue squares) X-ray bands, demonstratingvariability power intrinsic to the source as a function of frequency. The vertical dashed lines indicate the range of frequencies where softlags were detected.MNRAS , 1–7 (0000) L. Mallick et al.
Figure A2.
Lag-frequency spectra fitted by a monotonically declining hard lag model ( τ h = kν − α ). The red, solid line shows the fittedhard lag model. The residuals shown in the lower panels demonstrate the existence of negative soft lags in the spectra.MNRAS000