Caught in the act: Measuring the changes in the corona that cause the extreme variability of 1H 0707-495
aa r X i v : . [ a s t r o - ph . H E ] J un Mon. Not. R. Astron. Soc. , 1–12 (2014) Printed 5 February 2018 (MN L A TEX style file v2.2)
Caught in the act: Measuring the changes in the coronathat cause the extreme variability of 1H 0707 − D. R. Wilkins , ⋆ † , E. Kara , A. C. Fabian and L. C. Gallo Department of Astronomy & Physics, Saint Mary’s University, Halifax, NS. B3H 3C3 Canada Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge. CB3 0HA UK
Accepted 2014 June 24. Received 2014 June 22; in original form 2014 February 19
ABSTRACT
The X-ray spectra of the narrow line Seyfert 1 galaxy, 1H 0707 − XMM-Newton , from time periods of varying X-ray luminosity are analysed in thecontext of understanding the changes to the X-ray emitting corona that lead to theextreme variability seen in the X-ray emission from active galactic nuclei (AGN). Theemissivity profile of the accretion disc, illuminated by the X-ray emitting corona, alongwith previous measurements of reverberation time lags are used to infer the spatialextent of the X-ray source. By fitting a twice-broken power law emissivity profile tothe relativistically-broadened iron K α fluorescence line, it is inferred that the X-rayemitting corona expands radially, over the plane of the accretion disc, by 25 to 30 percent as the luminosity increases, contracting again as the luminosity decreases, whileincreases in the measured reverberation lag as the luminosity increases would requirealso variation in the vertical extent of the source above the disc. The spectrum ofthe X-ray continuum is found to soften as the total X-ray luminosity increases and weexplore the variation in reflected flux as a function of directly-observed continuum flux.These three observations combined with simple, first-principles models constructedfrom ray tracing simulations of extended coronæ self-consistently portray an expandingcorona whose average energy density decreases, but with a greater number of scatteringparticles as the luminosity of this extreme object increases. Key words: accretion, accretion discs – black hole physics – galaxies: active – X-rays:galaxies.
The X-ray emission from the accreting black holes in ac-tive galactic nuclei (AGN) is highly variable, particularly innarrow line Seyfert 1 (NLS1) galaxies (Leighly 1999; Turneret al. 1999). For instance, the X-ray count rate observed fromthe NLS1 galaxy 1H 0707 −
495 is seen to vary by factors oftwo to three on timescales of just a few hours (Fabian et al.2009) while Fabian et al. (2013) find that the X-ray emissionfrom the NLS1 galaxy IRAS 13224 − × erg s − and even decrease by 50 per cent in onlya few hundred seconds; a rate approaching 10 erg s − .Detailed studies of this X-ray emission and, particularly,its variability have recently added a further dimension tothe study of accreting black holes. X-rays are emitted froma corona of energetic particles surrounding the central blackhole. These particles are thought to be accelerated and con- ⋆ E-mail: [email protected] † CITA National Fellow fined by magnetic fields arising from the ionised accretiondisc (Galeev et al. 1979; Haardt & Maraschi 1991; Merloni& Fabian 2001) and they inverse-Compton scatter thermalseed photons from the accretion disc to the X-ray energiesthat are observed with a power law spectrum (Sunyaev &Tr¨umper 1979).In addition to being observed directly, this coronal X-ray continuum is seen to be reflected from the optically thick,geometrically thin accretion disc (George & Fabian 1991).X-rays incident on the accretion disc are backscattered, andfluorescent lines as well as secondary emission caused byheating of the gas are produced (Fabian & Ross 2010). Themost prominent of these lines is the K α fluorescence lineof iron at 6.4 keV for neutral iron (Matt et al. 1997). Thisemission line is seen clearly in the X-ray spectra of manyaccreting black holes and is broadened by relativistic effectsbetween the emitting material in the accretion disc and theobserver (Fabian et al. 1989); the combination of Dopplershifts and relativistic beaming from the orbital motion ofthe material and the redshift from the strong gravitational c (cid:13) D. R. Wilkins et al. field close to the black hole give the line a characteristic blueshifted ‘horn’ and extended redshifted ‘wing’ to low energies.Wilkins & Fabian (2011) find that the profile of this rel-ativistically broadened emission line reveals the emissivityprofile , that is the radial illumination pattern of the accre-tion disc by the coronal X-ray source. This emissivity pro-file is, in turn, sensitive to the spatial extent of the X-rayemission allowing the location and geometry of the X-rayemitting corona to be constrained by observational data. In1H 0707 − r g (Wilkins &Fabian 2012), where a gravitational radius, 1 r g = GM/c ,is the characteristic scale-length in the gravitational fieldaround a point mass such as the black hole while extendingjust a couple of gravitational radii above the plane of theaccretion disc (Wilkins & Fabian 2013).It is through the reflection of X-rays from the accretiondisc that the variability of the emission can be exploitedas a probe of the innermost regions. Due to the additionalpath the light must travel between the corona and accretiondisc, variability in the X-rays reflected from the disc is seento lag behind the corresponding variability in the directlyobserved continuum emission that is illuminating it. Fabianet al. (2009) and Zoghbi et al. (2010) first measured theseso-called reverberation time lags in 1H 0707 −
495 and foundthem to correspond to the light travel time over around twogravitational radii, indicating that the reflected componentof the X-ray spectrum really is being emitted from the inner-most regions of the accretion flow around the black hole andallowing the structure of the corona and accretion flow tobe probed using these measurements. Analogous reverbera-tion time lags have since been measured in a multitude offurther AGN ( e.g.
Emmanoulopoulos et al. 2011; de Marcoet al. 2011; Zoghbi & Fabian 2011; Zoghbi et al. 2012; deMarco et al. 2012). Measuring the reverberation time lag asa function of energy reveals the redshifted wing of the broadiron K α emission line emitted from the innermost part of theaccretion disc (and hence closer to the coronal emission) re-sponding to changes in the continuum before emission fromthe outer disc (Zoghbi et al. 2012; Kara et al. 2012).Variations in luminosity are widely attributed to fluc-tuations in the mass accretion rate onto the black hole, withover- and under-densities in the accretion flow that diffuseinwards on viscous timescales in the disc ( e.g. Kotov et al.2001; Ar´evalo & Uttley 2006). The gravitational binding en-ergy liberated by the accretion process is therefore modu-lated by the fluctuations in the density of the accretion disc,causing the luminosity we observe to fluctuate.In order to understand the exact cause of this variabilityand also the underlying process by which energy is liberatedfrom the accretion flow to power the X-ray emission that isobserved, the X-ray spectra of accreting black holes havebeen studied, in detail, at both high and low flux levels.Fabian & Vaughan (2003) compare the X-ray spectrum ofanother NLS1 galaxy, MCG–6-30-15 in states of high andlow flux, finding that the flux reflected from the accretiondisc remains almost constant while it is the flux in the con-tinuum emission that varies. This apparent constancy of thereflected flux while the illuminating continuum varies can beunderstood in terms of a compact coronal X-ray source mov-ing closer to and further from the black hole (Miniutti et al.2003). As the X-ray source moves closer to the black hole, more photons are focussed towards the black hole and onto the inner parts of the accretion disc, which means fewerphotons are able to escape to be observed in the contin-uum, while the reduction in continuum flux is compensatedby more photons being focussed on to the disc, causing thereflected flux to appear constant.We here discuss detailed analysis of the X-ray spectraof the NLS1 galaxy 1H 0707 −
495 from periods of varying lu-minosity. Combining the profile of the relativistically broad-ened iron K α emission line, the spectrum of the continuumemission and the variation in reflected and directly observedfluxes, along with simple models, we trace the underlyingchanges to corona that are driving the extreme variabilitywe observe in the X-ray emission. Kara et al. (2013) obtain the lag spectrum of the 0.3-1.0 keVband, dominated by reflection from the accretion disc, rel-ative to the 1.0-4.0 keV band, dominated by the directlyobserved continuum emitted from corona during periods inwhich the total observed flux from a different NLS1 galaxy,IRAS 13224 − . × − Hz to 1 . × − Hz.Interpreted in the context of X-rays emitted from acorona around the central black hole and reflecting off theaccretion disc, such a result is due to the average light traveltime between the source and the reflector increasing. Look-ing at theoretical lag spectra obtained in ray tracing sim-ulations (see, e.g. , Wilkins & Fabian 2013), it can be seenthat while increasing the radial extent of the coronal X-raysource decreases the observed lag time, increasing the ver-tical extent of the X-ray source increases the measured lag.This is not to say that the radial extent of the X-ray sourceis not also increasing, merely that the dominant effect is dueto the increasing vertical extent of the source. It should benoted that like-for-like, the extra lag time due to increasingthe vertical extent of the source is, in itself, a greater effectthan that of increasing the radial extent of the source sincethe vertical extent of the source acts to extend the light pathto the disc, while increasing the radial extent of the sourcedecreases the impact of the Shapiro delay close to the blackhole as more rays are now travelling further from the blackhole to reach the accretion disc.Analysis of reverberation lags through lag spectra re-quires continuous light curves. It is therefore only possibleto compare the lag spectra during low and high flux stateswhen there are extended, continuous periods during whichthe source can be found in such a state.
While there may not be prolonged periods of high and lowflux from which lag spectra can be extracted in all sources,it is possible to extract X-ray spectra from the different c (cid:13) , 1–12 he changing corona of 1H 0707 − C oun t R a t e / c t s − C oun t R a t e / c t s − Time / 10 s C oun t R a t e / c t s − Figure 1.
Background-subtracted, corrected X-ray lightcurves of the of the NLS1 galaxy 1H 0707 −
495 recorded with the pn detector onboard
XMM-Newton and produced by the SAS task epiclccorr , illustrating the extreme X-ray variability exhibited by this accretingblack hole. Vertical lines separate observations (orbits) taking place at different times. Details of the observations can be found in Table 1.These light curves were used to construct GTI filters to select cumulative times of varying X-ray flux. Grid lines on the axes are in unitsof 10 s and the solid horizontal lines show the the primary set of independent. non-overlapping flux cuts used in the analysis. flux states. Spectra are extracted across varying flux statesof the NLS1 galaxy 1H 0707 − α emission lineto constrain the geometry of the corona. The 2011 XMM-Newton observation during the period in which 1H 0707-495dropped into an extremely low flux state is not included dueto the substantially different behaviour of the X-ray spec-trum, with little or no directly observed continuum emissiondetected, though this observation is considered thoroughlyby Fabian et al. (2011).
X-ray spectra in different flux limits were extracted fromobservations of 1H 0707 −
495 using the EPIC pn detector(Str¨uder et al. 2001) on board
XMM-Newton (Jansen et al.2001). Data collected during individual orbits were reducedseparately using the
XMM-Newton Science Analysis System (SAS) version 12.0.1 using the most recent calibration datafor the observations in question.After initial reduction of the event lists and removalof background flares, the light curves recording the totalcount rate from the source were extracted (and are shownin Fig. 1) and used to create a good time interval (GTI) filterthat selects the periods during the orbit in which specifiedcriteria are met. Time intervals were selected in which thetotal count rate from the source was within specified ranges,shown in Table 2 (the rapidity of the variability and how longis spent at each flux level in the X-ray emission can be seen c (cid:13) , 1–12 D. R. Wilkins et al.
Table 1.
XMM-Newton observations from which periods of vary-ing flux were extracted.
Obs ID Start Exposure Reference in Fig. 1 showing the light curves from the observations).Relatively broad cuts in flux across all times were selectedrather than continuous time periods at different flux levelsin order to maximise the number of photon counts withineach to enhance spectral analysis.When studying the variation in parameters between theflux segments and particularly when searching for correla-tions of these parameters with flux, only non-overlappingsegments can be compared such that the different flux cutspectra are composed of independent sets of photons and aretherefore statistically independent. The flux segments in Ta-ble 2 are grouped into two sets, within which each of the seg-ments are independent and non-overlapping. These groupsare treated separately throughout the following analysis.These GTI filters ere then used to extract the spectracounting only the photons that arrived during the periodsin which the count rate was within the required range. Thesource spectra were extracted from a circular region of thedetector centred on the co-ordinates of the point source,35 arcsec in diameter. Thus, we obtain the average spec-trum of the source over all times when the count rate is asrequired. Corresponding background spectra were extractedfrom a region of the same size, on the same chip as thesource using photons from the same time periods. The spec-tra were binned using the grppha tool such that there wereat least 25 counts in each spectral bin. The photon redis-tribution matrices (RMF) and ancillary response matrices(ARF) were computed for each spectrum, then the spectrafrom all orbits in a given flux state were summed under av-erage response matrices.Above 1.1 keV, the X-ray spectrum of 1H 0707 −
495 iswell described as the combination of the continuum emissionfrom the coronal X-ray source (taking the form of a powerlaw) and reflection from the accretion disc. The emissivityprofile of this reflection (the reflected flux as a function ofposition on the disc) takes the form of a twice broken powerlaw (Wilkins & Fabian 2011; Miniutti et al. 2003) and inthe case of an X-ray emitting region extending radially overthe disc, the outer break point of this function between theflattened middle region and the outer power law r − corre-sponds to the radial extent of the source over the accretiondisc (Wilkins & Fabian 2012). Fig. 2 shows the spectrum in −4 −3 no r m a li ze d c oun t s s − k e V − r a ti o Energy (keV) + Spectrum, 5-10 ct s -1 + Spectrum, 0-3 ct s -1 Total Model Continuum Reflection
Figure 2.
The EPIC pn X-ray spectrum across the band 1.1-10.0 keV of 1H 0707 −
495 in the lowest (0-3 ct s − ) and secondhighest (5-10 ct s − ) flux cuts extracted from the total 1.3 Msdataset. The spectrum between 1.1 and 10.0 keV is well describedby simply the power law continuum emission from the corona andits relativistically blurred reflection from the accretion disc. Thebest fitting model components are shown. high and low flux states with the best fitting model consist-ing of the continuum emission and its relativistically blurredreflection from the accretion disc. It is immediately appar-ent that the majority of the variability is due to changes inthe continuum with only small changes seen in the reflectionspectrum.In this simultaneous fit to the two flux segments, χ /N DoF = 1 .
15, indicating an acceptable, though not per-fect fit. The majority of the residuals to the model hereadopted lie below 1.5 keV and above 7 keV (indeed, ignor-ing the data points below 1.5 keV reduces χ /N DoF to 1.03).Blustin & Fabian (2009) find a complex series of emissionand absorption features in high resolution spectra below2.5 keV attributed to the narrow cores of atomic featuresarising from the outer parts of the accretion disc. Dauseret al. (2012) conduct a detailed analysis of the most re-cent
XMM-Newton observations of 1H 0707 −
495 and findthat the absorption structure seen above 7 keV is explainedby a complex ionisation structure to the disc, representedin their models by two cospatial reflection components withdifferent ionisation parameters, indicative of a complex ioni-sation structure to the accretion disc, while small structuresbetween 2 and 5 keV can be attributed to a fast outflowfrom the accretion disc. These features, however, representonly small corrections to the overall shape of the continuumspectrum and the profile of the relativistically broadenediron K α line which are used here to probe the behaviour ofthe variable X-ray emitting corona, so will not be discussedfurther in this work in the interests of adopting a simplermodel of the X-ray emission and its reflection from whichthe variations in the corona can be understood more easily. The best way to determine the change in the extent of the X-ray source as the flux received from the source varies wouldbe to determine the emissivity profile of the reflection com- c (cid:13) , 1–12 he changing corona of 1H 0707 − Table 2.
Flux cut segments for which spectra were extractedfrom the observations of 1H 0707 − Segment Mean Count Rate Exposure Counts − . ± .
75 ct s − . × s 1 . × − . ± .
26 ct s − . × s 8 . × − . ± .
53 ct s − . × s 1 . × − . ± .
84 ct s − . × s 5 . × − . ± .
97 ct s − . × s 2 . × − . ± .
25 ct s − . × s 7 . × − . ± .
98 ct s − . × s 1 . × ponent from each flux cut by decomposing the detected ironK α emission line into the contributions from successive radiifollowing the procedure of Wilkins & Fabian (2011). The ef-fective exposures, however, of the spectra in each of the fluxcuts are only around 100 ks. This means that, particularlyin the lower flux states, there were not a sufficient numberof photons detected in the reflection component to prop-erly constrain the emissivity profile in this way, with a largenumber of degrees of freedom.Rather than fitting directly for the emissivity profileof the accretion disc, we are guided by the emissivity pro-files obtained from the total observations of 1H 0707 − − kdblur convolution kernel used in the radialdecomposition of the reflection spectrum) to five. The reflec-tion spectrum as measured in the rest frame of the materialin the accretion disc was computed by the reflionx modelof Ross & Fabian (2005) and was convolved with the profileof a single emission line broadened by the relativistic effectsfrom an orbiting accretion disc in the Kerr spacetime us-ing a twice-broken power law form of the emissivity profile,computed using the kdblur3 model of Wilkins & Fabian(2011) constructed as an analytic approximation to the ob-served emissivity profile that was determined directly andfound therein to best reproduce the observe profile of thebroad iron K α line. The directly observed continuum emis-sion from the corona was modelled as a power law, givingthe total model spectrumpowerlaw + kdblur3 ⊗ reflionx (1)The inclination of the accretion disc and the iron abundancewere fixed at the previously found best-fit values of Zoghbiet al. (2010) as these certainly do not change during theobservations. In the interests of limiting the number of freeparameters while obtaining the accretion disc emissivity pro-file, the ionisation parameter in the reflionx model was Table 3.
Values of frozen parameters in the model that was fitto the spectra of 1H 0707 −
495 in varying flux states.
Component Parameter Value kdblur3
Inclination, i .
96 deg reflionx
Incident photon index, Γ = powerlaw:
ΓIron abundance, A Fe ξ − Redshift, z . × − also assumed to remain constant between the high and lowflux periods within the observations. While in reality, vari-ation in the incident X-ray flux will likely change the ioni-sation state of the reflecting material, the value obtained infitting to the whole observation will be the average ionisationparameter during this period. The frozen model parametersare detailed in Table 3.It can readily be shown in this model that the assumedvalue of the ionisation parameter does not influence themeasured location of the outer break radius in the emis-sivity profiles long as ξ <
150 erg cm s − . In this ‘low ion-isation’ regime, the spectrum is dominated by the lesser-ionised species which produce the prominent iron K α line at6.4 keV. Once convolved with the relativistic blurring ker-nel, it is this emission line that provides the strongest mea-sure of the emissivity profile. It is only once the ionisationparameter exceeds 150 erg cm s − that the measurement ofthe emissivity profile is affected. Initially, the greater abun-dance of more ionised species with a vacancy in the L shellcauses the iron K α photons to be reabsorbed, weakeningthe emission line and hence the statistical constraint on theemissivity profile. Finally, once helium-like and hydrogeniciron become prevalent when ξ >
500 erg cm s − , the K α lineis shifted from 6.4 keV to 6.67 keV and 6.97 keV, respectivelyand the correct emissivity profile will not be measured whenassuming too low an ionisation parameter. As such, accuratedetermination of the ionisation state of the accretion disconly starts to become important when ξ >
150 erg cm s − and becomes critical when ξ >
500 erg cm s − .In the case of 1H 0707 − − in the high-est flux segment (when fitting to the full 0.3-10 keV energyrange to include the structure in the reflection spectrumbelow 1 keV), thus the assumption of a constant ionisationparameter does not influence the measured emissivity profileof the accretion disc.The slope of the power law continuum and the nor-malisations of the continuum and reflection are fit as freeparameters to the spectrum and the slopes and break radiiof the emissivity profile are fit, but constrained to be withinreasonable ranges to give the expected shape of the emissiv-ity profile ( i.e. a steep decline, followed by a flatter regionbefore a slope close to r − over the outer parts of the disc)as shown in Table 4.Fitting the emissivity profile to the observed spectrum(namely the profile of the relativistically broadened iron K α emission line) as a twice-broken power law, the location ofthe outermost break radius (between the flat part of theemissivity profile and the approximate inverse-cube profileover the outer part of the disc) as a function of count rate c (cid:13) , 1–12 D. R. Wilkins et al.
Table 4.
Allowed ranges for the parameters of the twice-brokenpower law emissivity profile when fitting to find the extent of theX-ray source.
Parameter Fit Range
Index 1 5 – 10Break radius 1 3 – 5 r g Index 2 0 – 2Break radius 2 5 – 35 r g Index 3 2 – 4 for 1H 0707 −
495 for the first set of four statistically inde-pendent, non-overlapping lux segments is shown in Fig. 3(a).The same increase is seen through the second set, with thebreak radius increasing from 24 . +3 . − . r g in the lowest of theflux segments to lower and upper limits of > . r g and < . r g respectively, in the greater flux segments.In each of the spectra, the innermost power law index ofthe emissivity profile was found to be steep (between 7 and8 in each case), the power law index of the middle section isclose to zero in each case, and over the outer part of the disc,the emissivity profile falls off with a power law index around3.3, consistent with previous findings from spectra averagedover the whole of the observations (Wilkins & Fabian 2011).These parameters were, however, still allowed to be free inthe fitting procedure as any slight variation here that is notaccounted for can lead to errors in the determined breakradii to compensate for the real shape of the emissivity pro-file. In each case, the model was found to provide a goodfit to the spectrum, yielding values of the reduced χ fitstatistic between 1.0 and 1.1, except in the case of the lowestcount rate segments where the value increased to between1.20 and 1.25. We find, however, that it is the structure inthe spectrum below 2.5 keV that largely contributes to thisas it is not thoroughly accounted for in the simple modelwe employ here as discussed above. This does not, however,affect our conclusions based upon the profile of the iron K α emission line and slope of the continuum spectrum.Wilkins & Fabian (2012) demonstrate that in order toreproduce both the steep inner part of the emissivity profile and the outer break radii that are found, an X-ray emit-ting corona extending radially at a low height (but with afinite vertical extent that may be allowed to vary, althoughthe emissivity profile is not sensitive to the vertical extentof such a source) above the accretion disc is required, thusalternative models such as a ‘lamppost’ point source or col-limated vertical source along the rotation axis of the blackhole will not be considered further.Identifying the outer break radius of the emissivity pro-file with the outermost radial extent of the X-ray sourcein a plane parallel to the accretion disc, following Wilkins& Fabian (2012), we see evidence that the X-ray emittingcorona expands as the luminosity increases then contractsas the luminosity decreases again (note we are finding theaverage extent of the source between all times of a givencount rate rather than following the evolution of the sourcein time as the count rate varies). The Spearman rank cor-relation co-efficient for the first set of independent flux seg-ments is ρ = 0 .
84, indicating p < .
01 that the appearanceof a correlation is merely due to random chance. A linear relation can be fit to the best-fitting outer break radius forthe first set of four flux segments data with gradient 2 . ± . χ /N DoF = 0 . σ variation between points atlow and high count rates. Turning to the photon index of the directly observed con-tinuum emission from the corona, Γ (where the continuumspectrum takes the form I E ( E ) ∝ E − α in terms of the spec-tral energy density or N E ( E ) ∝ E − Γ in terms of photoncount rates, with Γ = 1 + α ), the best-fit value for thephoton index of the continuum spectrum for each flux cutis shown in Fig. 3(b). Experimenting with various energybands reveals that the best-fit power law index is driven bythe continuum-dominated 2-3 keV energy band rather thanbeing an artefact of variability in the reflection component oreven the thermal emission from the disc just encroaching onthe region of the spectrum immediately above 1.1 keV andconsistent results are obtained if the lower energy bound isincreased to either 1.5 or 2.0 keV.It is clear to see that as the luminosity of the X-raysource increases, the coronal emission becomes softer, witha more steeply falling spectrum such that fewer hard X-raysare emitted compared to the softer photons. In this case,the Spearman rank correlation co-efficient for the first setof flux segments is ρ = 0 .
95, indicating p < .
001 that theappearance of a correlation is merely due to random chance.In this case, the best-fit linear relation is better constrainedwith gradient 0 . ± .
002 ( χ /N DoF = 0 . . +0 . − . to2 . +0 . − . and 3 . +0 . − . as the flux increases.This trend is well-known in the X-ray emission in AGN.As the luminosity increases, the X-ray continuum spectrumbecomes softer ( e.g. , Markowitz et al. 2003). A key prediction of models in which the increase in luminos-ity of an X-ray emitting corona corresponds to the spatialexpansion of that corona is that a collapse of the coronainto a more confined region around the central black holenot only leads to reduced overall luminosity but also mustresult in an increase in the number of photons hitting thedisc to be reflected relative to the number that are able toescape to be observed in the continuum ( e.g.
Miniutti &Fabian 2004; Fukumura & Kazanas 2007). This increase inthe reflection fraction is due to emission from closer to theblack hole being bent towards the black hole and thus fo-cussed onto the accretion disc and was invoked to explainthe simultaneous steepening of the iron line emissivity pro-file and disappearance of the continuum when 1H 0707 − c (cid:13) , 1–12 he changing corona of 1H 0707 − (a) Emissivity profile outer break radius (b) Photon index of X-ray continuum Figure 3. (a) The outer break radius of the emissivity profile (taken to be a twice-broken power law) of the X-ray reflection from theaccretion disc and (b) the photon index of the continuum emission from the corona in 1H 0707 −
495 as a function of the total countrate from the source for the first set of four non-overlapping, statistically independent flux segments. Error bars correspond to 1 σ on thebreak radius and spectral index and to the standard deviation of the count rate within the filter segments. dropped into an extremely low flux state in January 2011(Fabian et al. 2011).The fraction of the photons that are reflected and ob-served directly from a spatially expanding corona can be ex-plored through general relativistic ray tracing simulations.Ray tracing simulations will predict the number of photonsemitted from the corona that hit the disc compared to thenumber that escape to infinity. They will not, however, di-rectly predict the number of photons that will be observed in the reflection component of the observed spectrum with-out inputting a detailed model of the (spatially resolved)properties of the disc material and the ‘reflection’ processesthat take place when photons are incident upon it (Comptonscattering, photoelectric absorption, fluorescent line emis-sion, bremsstrahlung, etc. ). As such, the number of photonsthat are seen in the reflection spectrum is not directly indica-tive of the number of photons that hit the disc and cannotbe directly compared to the number of photons detected inthe continuum.It is, however, possible to probe the variation in re-flection fraction by measuring the photon flux seen in thereflection component of the spectrum as a function of thephoton flux directly detected in continuum emission fromthe corona. This is achieved by fitting the model consistingof a power law continuum and reflection from the accretiondisc described by the reflionx code as detailed above andthen computing the flux (which can be found as both thephoton flux and energy flux) that would be detected by thetelescope in each of these spectral model components byfolding the fitted model through the instrument responses.When considering reflection from the accretion disc, signif-icant flux emerges in the ‘Compton hump’ around 30 keVand in emission lines at soft X-ray energies, around 0.1 keV.It is therefore necessary to compute fluxes integrating pho-tons over a wide energy range, here taken to be 0.1-100 keVand the instrument response is extrapolated from its limit at 12 keV up to 100 keV for the purposes of computing theflux represented by the model components.The continuum and reflected fluxes are determined byfitting a model spectrum to the data over the 0.3-10 keVenergy band (the full energy range of the pn detector). Pho-toelectric absorption by Galactic material is accounted forin the model fit over the 0.3-10 keV energy band, using the phabs model in xspec , so too is the thermal emission de-tected from the accretion disc, modelled by a black bodyspectrum whose temperature is around 0.05 keV, consistentwith the model of Zoghbi et al. (2010) for this source. Theionisation parameter is allowed to vary as a free parameterin this instance as changes in the ionisation state of the disccould affect the overall flux as changes in ionisation alterthe large number of emission lines below 1 keV in which asignificant part of the reflected flux emerges ( e.g. Ross &Fabian 2005), though, as already discussed, does not affectthe measurement of the accretion disc emissivity profile fromthe 6.4 keV iron K α line. It is therefore necessary to includethe 0.3-1.1 keV energy range to ensure that the ionisationparameter is properly determined and find that excludingthe 0.3-1.1 keV part of the spectrum causes the ionisationparameter to be systematically underestimated, being mea-sured as low as half the value obtained using the full 0.3-10 keV energy band. When fitting our model assuming asingle ionisation parameter over the whole disc, the ioni-sation parameter is found to increase systematically from59 erg cm s − in the lowest flux segment to 65 erg cm s − inthe highest flux segment, thus the earlier assumption thatthe disc remains in the ‘low ionisation’ state and, as such,the measured emissivity profile is not altered by the ionisa-tion state of the disc is justified.Results are shown in Fig. 4 and we approximate therelationship between the, the reflected flux, R , and the con-tinuum flux, C , as a power law with R ∝ C β . Consid-ering just the first set of four independent flux segments,we find for 1H 0707 −
495 that the index of this power law, c (cid:13) , 1–12 D. R. Wilkins et al.
Figure 4.
The relationship between the photon counts in the X-ray reflection from the accretion disc and the directly observedcontinuum emission in 1H 0707 −
495 obtained by fitting a modelconsisting of a power law continuum and reflection from the ac-cretion disc described by the reflionx model of Ross & Fabian(2005) as well as Galactic absorption and black body emissionfrom the accretion disc to the energy band 0.3-10 keV, along withthe best fitting power laws. The upper panel shows the first set ofindependent, non-overlapping, flux segments and the lower panel,the second set. The best fit relation is found separately for eachset. β = 0 . +0 . − . which is consistent with that found when con-sidering the second set of independent flux segments, forwhich β = 0 . +0 . − . . Critically, we find that β <
1, as weshall discuss in the forthcoming section.
If the reflection fraction remained constant ( i.e. the sourcegeometry remained constant or reflection took place fromdistant material and experienced no gravitational lightbending that enhances reflection as the X-ray sourcechanges) and the reflected flux changed only due to the vari-ations in the illuminating luminosity (the intrinsic variabil-ity in the source), one would expect the reflected photonflux to rise linearly with the continuum flux detected di-rectly from the corona. This linear relation would hold nomatter how the intrinsic luminosity of the source varies intime. At the other extreme, if the total photon count rateemitted from the source remains constant but its locationor geometry changes, changing the fraction of the emittedphotons that are reflected, the reflected photon flux wouldfall linearly as the continuum flux increases ( i.e. the shape y = 1 − x where y and x correspond respectively to the re-flected and continuum flux). The total number of photons isconserved, they are just moved from one component to theother, except when the source is close to the black hole, whenboth the reflected and continuum fluxes would fall as a sig- nificant proportion of the photons emitted from the coronaare lost through the event horizon.If the luminosity of the source is allowed to vary whileit expands, the relationship between the continuum and re-flected fluxes cannot be simply interpreted in terms of theextent or position of the corona. Instead, a simplified modelis constructed to test if the data we obtain are consistentwith the picture of an expanding corona giving rise to in-creased X-ray luminosity. While we do not know how the in-trinsic luminosity of the X-ray source changes, we are guidedby the observation that the radial extent of the source, r in-creases as the source becomes brighter, to approximate thetotal luminosity as a power law in the radius of the emittingregion, L ∝ r β . The vertical extent of the source, ∆ z mustalso increase if the reverberation lag time between the con-tinuum emission and its reflection from the accretion disc isto lengthen in the high flux state, though this variation isnot a necessity to describe these data.Ray tracing simulations are used to compute the frac-tion of the emitted photons that hit the accretion disc, areable to escape to be observed as the continuum and thatare lost into the black hole event horizon as a function ofthe source radius. The vertical extent of the source is eitherheld constant or defined to increase linearly with the ra-dius within the limits of the coronal geometry inferred fromemissivity and reverberation lag measurements (though itturns out that the functional form of reflection fraction isnot greatly altered by how the vertical extent of the sourcevaries with radius). The general relativistic ray tracing al-gorithm of Wilkins & Fabian (2012) is employed. The X-rayemission from the corona is sampled using a Monte Carlotechnique, starting rays in random directions at random lo-cations within the defined region of the corona. They aretraced by numerical integration of the null geodesic equa-tions until they either reach the equatorial plane (defined tobe the accretion disc), are lost within the black hole eventhorizon or the innermost stable circular orbit (the inneredge of the accretion disc) or escape to a limiting radiusof 10,000 r g , at which point they are said to be able to bedetected as part of the X-ray continuum.These simulations are similar in their aim to those ofMiniutti & Fabian (2004) and Fukumura & Kazanas (2007)who calculate the reflection fractions from an accretion discilluminated by an isotropic point source of radiation lo-cated on the rotation axis of the black hole. Fukumura &Kazanas (2007) compute the radiative transfer analytically,however here we numerically integrate the geodesic equa-tions describing each ray and extend the calculation to ageneralised, spatially extended X-ray source by starting raystravelling in random directions at random locations withinthe defined bounds of the corona (thus simulating an opti-cally thin corona). Full details of the ray tracing algorithmcan be found in Wilkins & Fabian (2012).It is assumed that the reflected flux varies proportionalto the number of photons incident upon the accretion disc( i.e. regardless of the scattering, absorption and re-emissionprocesses that give rise to the X-ray reflection spectrum,doubling the flux incident upon the disc doubles the reflectedflux). The fractions of photons incident upon the disc andable to escape to become part of the continuum are multi-plied by the total luminosity of the source using the aboveparametrisation, L ∝ r β . Note that here, L represents the c (cid:13) , 1–12 he changing corona of 1H 0707 − integrated luminosity of the corona and its dependence onthe radial extent of the corona, r , rather than a luminosityprofile as a function of radius within the corona.Fig. 5 shows the predicted relationship between the ob-served continuum, C , and reflected flux, R , for three simplecases. First is the case of a corona whose total luminos-ity remains constant but which expands spatially, shown inFig. 5(a). When the corona is smaller (and less luminous),more of the photons emitted are focussed towards the blackhole and hence on to the accretion disc as more of the coronais confined in the stronger gravitational field close to theblack hole. This increase in the fraction of the radiation thatis reflected compared to that able to escape to be observeddirectly in the X-ray continuum leads to the y = 1 − x rela-tionship as discussed above. This is except for the smallestcoronæ where the reflected fraction drops owing to a signif-icant number of the emitted photons being lost through theevent horizon or within the innermost stable orbit, missingthe disc. This particular case is an extension of the modelof Miniutti & Fabian (2004) who compute the reflected vs. continuum flux for a constant-luminosity point source that ismoved vertically above the black hole and accretion disc andshows the same trend at large heights but a more extremedrop in reflected flux at the low continuum fluxes when thesource is at a low height and photons are lost into the blackhole.When the total luminosity of the corona simply increaseproportional to its volume, Fig. 5(b), the reflected flux isseen to rise linearly with the directly observed continuumflux. In this case, the increase in total luminosity overcomesthe decrease in the fraction that is reflected as the coronaexpands.We find that in order to produce the observed flux-flux relation for 1H 0707 − R ∝ C . , the total countrate emitted from the entire volume of the corona obeys L ∝ r . (Fig. 5) in this simple model, shown in Fig. 5(c).We find that this is insensitive to how the vertical extentof the source varies with radius, so long as it does not risemore rapidly than linearly with the source radius. Identifying the outer break radius of the emissivity pro-file with the outermost radial extent of the X-ray sourcein a plane parallel to the accretion disc, following Wilkins& Fabian (2012), we see evidence that the X-ray emittingcorona expands as the luminosity increases then contractsas the luminosity decreases again. Wilkins & Fabian (2012)show that the emissivity profile of the accretion disc is sen-sitive to the radial extent of the X-ray emitting region overthe plane of the accretion disc, while being relatively insen-sitive to its vertical extent perpendicular to the disc plane inthe case of a radially extended source at low height, as is re-quired to match the observed form of the emissivity profile.The emissivity profile only becomes sensitive to the verti-cal extent of the corona once this becomes greater than theradial extent, though such a geometry is not able to simul-taneously reproduce the location of the outer break radiusand the steep inner part of the emissivity profile (Dauseret al. 2013; Wilkins & Fabian 2012). Wilkins & Fabian (2013) show that varying the ra-dial extent of the X-ray emitting region above the accre-tion disc has only a slight effect on the measured reverber-ation lag seen in the reflection from the accretion disc. Infact, increasing the radial extent of the source decreasedthe reverberation lag since the X-rays emitted further fromthe central black hole do not experience such an extremeShapiro delay which slows down their passage from the in-ner parts of the corona. Therefore, if the increasing lag timewith increasing count rate observed by Kara et al. (2013)in IRAS 13224 − − i.e. perpendicular to the plane of the accretiondisc), though the vertical extent of the corona is not wellconstrained by the emissivity profile. That said, it is notphysically unreasonable to picture a corona of acceleratedparticles expanding in all directions (either through moreparticles being accelerated or the accelerated particles beingless confined) as more energy is injected into it to increasethe luminosity. Comptonisation of thermal seed photons emitted from theaccretion disc by high energy electrons in the corona hasbeen widely explored as the means of producing the X-raycontinuum seen from accreting black holes (see, e.g. , Galeevet al. 1979; Titarchuk 1994). Following Sunyaev & Tr¨umper(1979) and modelling the corona as a spherical plasma attemperature T , with optical depth τ , at photon energies ≪ E/k B T , the continuum spectrum produced from this coronaby the Comptonisation of thermal seed photons is a powerlaw, with specific flux J ν ∝ ν − α , where the spectral indexis given by α = −
32 + (cid:18)
94 + γ (cid:19) (2)Where, for a spherical geometry, γ = − π m e c k B T (cid:0) τ + (cid:1) And the photon index, Γ = 1 + α . At photon energies ≫ E/k B T , Comptonisation produces an exponentially de-caying spectrum (a ‘Wein tail’), with the cut-off in the powerlaw occurring at E cut ∼ k B T .A softer continuum spectrum (with a greater photonindex) is produced if the average energy of each individ-ual electron in the corona is reduced (that is to say thetemperature, T is lower), or if the number density of scat-tering electrons and hence the optical depth through whichthe seed photons scatter before they can escape the coronais reduced. Given that we do detect relativistically blurredline emission from the inner parts of the accretion disc thatwould be beneath the corona we infer from the observedemissivity profile, the optical depth of the corona due toCompton scattering cannot be much above unity as an op-tically thick corona should scatter the emission we detectfrom the inner parts of the disc.In order for the spectrum to soften, the average en-ergy per electron decreases, or the optical depth through thecorona is reduced. However, more electrons are accelerated c (cid:13) , 1–12 D. R. Wilkins et al. −0.6 −0.5 −0.4 −0.25 −0.23 −0.21 −0.19 −0.17 −0.15 Escaping Photons (Continuum) P ho t on s on D i sc ( R e f l e c t i on ) (a) Constant photon count Escaping Photons (Continuum) P ho t on s on D i sc ( R e f l e c t i on ) (b) L ∝ r ∆ z −0.2 −0.1 R ∝ C Escaping Photons (Continuum) P ho t on s on D i sc ( R e f l e c t i on ) (c) L ∝ r . Figure 5.
The relationship between the photon counts in the X-ray reflection from the accretion disc and the directly observedcontinuum emission computed from ray tracing simulations counting the rays that hit the disc and that are able to escape to infinity.The coronæ extend radially from 2 to 50 r g and vertical extents vary linearly with the radial extent from 0.5 r g to 5 r g with the baseof the corona fixed at 1 r g , for (a) constant source luminosity where the total photon count is constant and photons are just shiftedbetween the two groups giving a y = 1 − x relationship, except for the most confined sources where a substantial fraction of the photonsis lost into the black hole. In (b), the source luminosity varies proportional to its volume, r ∆ z . In this case the significant intrinsicvariability outweighs the change in reflection fraction resulting in the reflected flux rising linearly with the continuum flux. Finally, in(c), the intrinsic, total luminosity of the source is taken to vary as r . to reproduce the R ∝ C . relationship seen in 1H 0707 − r g . The total luminosity of the corona is increasing as it expands through at an arbitrary rate, notdirectly in proportion to its volume. At larger source radii, the reflection fraction becomes approximately constant and the reflectedflux starts to rise linearly with the continuum flux. The absolute scaling on each axis is arbitrary; the power law relationship betweenthe two is the relevant quantity. into a corona filling a larger volume. This would provide alarger cross section for scattering seed photons emitted fromthe accretion disc, explaining the increase in count rate ofX-ray photons emitted from the corona.If the optical depth experienced by the seed photonsthrough the corona is assumed to remain constant, we cancalculate the variation in coronal temperature required toproduce the observed variation in the photon index of theX-ray continuum using Equation 2. The photon index wasfound to vary between 2.95 and 3.075. Computing the exacttemperature of the corona would require either the energyof the cut-off to the power law continuum spectrum to bemeasured or the optical depth to be known. However, select-ing any value for the optical depth between 0.5 and 5 yieldsfrom Equation 2 the consistent result that the temperatureof the corona is varying by approximately 8 per cent. For in-stance, taking τ = 1 as an upper limit to the optically thinregime in order to give a lower limit to the temperature, wefind that T varies between 58 and 63 keV to produce theobserved range in spectral indices, or for τ = 0 . T rangesfrom 118 keV to 128 keV. It should be noted that Equation 2is derived from the Kompaneets equation (see, e.g. Lightman& Zdziarski 1987) which is derived via a diffusion approx-imation, so is formally valid in the limit τ >
1. Here, weconsider the limiting case as a vastly simplified model, toestimate the magnitude of the changes occurring within thecorona, though a more thorough treatment is beyond thescope of this work, though the results of Titarchuk (1994)for Comptonisation in an optically thin plasma give broadlyconsistent results for the cases considered here.Such high coronal temperatures and, indeed, low opti-cal depths are plausible in AGN. For instance, Burlon et al.(2011) find that stacking the spectra of all 199 non-blazarAGN from the
Swift BAT AGN Survey , covering the en-ergy range 15-195 keV, constrains the cut-off energy to be greater than 80 keV and in many cases the data are bestmodelled fixing the cut-off energy at 300 keV. While mea-suring the exact energy of the cut-off is out of the reach ofpresent instrumentation, the measurement of both the cut-off energy and any variation therein due to changes in thecoronal temperature may be achievable in bright AGN withthe
Soft Gamma-Ray Detector on board the forthcoming
Astro-H
X-ray observatory offering spectral coverage up to600 keV (Tajima et al. 2010). vs.
Continuum Flux
Na¨ıvely, if the average energy density of the corona remainedconstant and it simply grew, the luminosity of an axisym-metric corona will follow L ∝ r ∆ z or L ∝ r if the heightwere to increase linearly with the radial extent. This rela-tion remains valid for a corona that produces X-ray emis-sion through the inverse-Compton scattering of seed photonsfrom the accretion disc below, so long as the corona remainsoptically thin to both the X-rays it produces (which it mustbe for us to see the characteristic reflection signatures fromthe inner parts of the accretion disc) and to the seed pho-tons. The scattering cross section for the corona in this casesimply increases proportional to its volume, increasing thenumber of scattered photons accordingly.Finding such a low power law index relating the lu-minosity to the radial extent of the source implies that thenumber of seed photons scattered to form the continuum perunit volume decreases as it expands. In the context of Comp-tonisation by an optically thin corona, this means the av-erage number density of scattering particles (and hence thecross-section per unit volume for interaction with seed pho-tons from the accretion disc below) is reduced. Coupled withthe observed softening of the continuum spectrum as thecorona is inferred to expand, this portrays a corona whose c (cid:13) , 1–12 he changing corona of 1H 0707 − average temperature and density throughout its extent isdecreasing. This reduction in photons scattered per unit volume andspectral softening can be explained not only by a whole-sale reduction of the energy per particle or number densitythroughout the entire volume, but also if the corona wasthe most dense and energetic in its central regions and theexpanding and contracting outer parts of the corona wereeither made up of less energetic particles or were less dense.This is in line with the two component corona model ofTaylor et al. (2003) who were able to explain the broadbandspectral variability of MCG–6-30-15 by a harder power lawcontinuum component that remained constant with a vari-able soft power law component driving much of the variabil-ity. If the outer part of the corona were less dense, the op-tical depth to photons just scattering through these outerparts is less meaning that (disregarding any variation in thetemperature of these regions), the spectrum produced wouldbe softer. This can, again, be illustrated using Equation 2.If the coronal temperature is fixed to be T = 100 keV, theaverage optical depth to electron scattering of the corona tothe seed photons, τ reduces by around 7 per cent from 0.65to 0.59 to explain the observed softening in the spectrumfrom Γ = 2 .
95 to Γ = 3 .
08. The result is similar when thetemperature is fixed to be 50 keV.The transient nature of the outer parts of the coronaas it expands and contracts mean it is the softer part of thecoronal emission that is more variable.This is most likely an overestimate to the variation inthe optical depth, as, of course, changes to both the coro-nal temperature and optical depth are likely to contributeto the change in spectral slope. We do also approximatethe corona to being a spherical cloud with the seed photonsource embedded at the centre. Measurements of the coro-nal extent via the accretion disc emissivity profile suggestan extended structure covering part of the accretion disc(though more of the seed photons will be emitted from themore central parts of the disc, e.g.
Novikov & Thorne 1973).Many models too suggest that the X-ray continuum emis-sion arises from ephemeral ‘flares’ of accelerated particlesrather than a static corona ( e.g.
Beloborodov 1999; Merloni& Fabian 2001). In these cases, the values we derive here forthe temperature and optical depth represent averages acrossthe corona that would apply to a spherical corona producingthe same spectrum and the ‘corona’ represents the volumesurrounding the black hole and accretion disc in which theseflares take place. The model of Beloborodov (1999) suggeststhat the reflection of the radiation produced by the flaresfrom the accretion disc causes the particles in the flare tobe rapidly accelerated to relativistic velocities away from thedisc, through the radiation pressure exerted upon them. Thecontinuum radiation is therefore beamed away from the disc,resulting in a reduced reflection fraction and, in this model,the slope of the continuum spectrum is determined almostentirely by the Lorentz factor of the scattering particles pro-ducing the continuum. This model is, however, inconsistentwith the typically large reflection fractions,
R/C >
1, seen and, as it is presented, is unable to reproduce the steep con-tinuum spectra, Γ >
2, characteristic of NLS1 galaxies.
By analysing spectra obtained for the NLS1 galaxy1H 0707 −
495 in states of high and low flux, evidence hasbeen found for the expansion of the X-ray emitting corona asthe coronal luminosity increases and contraction to a moreconfined region around the black hole as the luminosity de-creases again. The emissivity profile of the accretion disc,obtained by fitting a twice-broken power law emissivity pro-file to the relativistically broadened iron K α emission lineimplies that the radial extent of the corona in 1H 0707 − − −
495 discussed in Fabian et al.(2011), a picture is emerging of X-ray emitting coronæ thatexpand and contract both radially and vertically above theplane of the accretion disc as more or less energy is injectedfrom the accretion flow.It is observed that as the flux received from the sourceincreases, the continuum spectrum becomes softer, while inorder to reproduce the observed relationship between theprimary continuum and reflected fluxes by simply follow-ing the changing reflection fraction as the corona expandsand contracts it is required that the total luminosity of thecorona expands only as a weak function of its radius ratherthan scaling with its volume. These observations suggestthat as the corona expands, the energy per scattering parti-cle (the coronal temperature) decreases and so too does thenumber density and hence the average optical depth experi-enced by the seed photons through the corona. There beingmore scattering particles spread through a larger corona in-creases the total scattering cross section and explains theincrease in luminosity if the corona is said to arise from theinverse-Compton scattering of thermal seed photons emittedfrom the accretion disc.This analysis demonstrates the understanding that canbe gained of the processes at work in the X-ray emittingcorona around a black hole through detailed analysis of theobserved data combined with insight gained from theoreti-cal predictions. These conclusions are, however, limited to1H 0707 −
495 due to the much longer total exposure timeavailable on this source. It will be possible to draw firmerconclusions from longer observations of other objects suchthat high quality spectra can be obtained in many differentstates of the systems under consideration.Measurements of changes to the X-ray emitting corona,causing the variability we see in the luminosity, shed lighton the underlying mechanisms driving the variability andultimately the means by which energy is liberated from theaccretion flow into the corona. Deriving the fundamentalbehaviours of the corona seen in observational data placeimportant constraints on the theoretical models and simu-lations of material accreting onto supermassive black holes. c (cid:13) , 1–12 D. R. Wilkins et al.
ACKNOWLEDGEMENTS
DRW is supported by a CITA National Fellowship. ACFthanks the Royal Society for support. This work is basedupon observations obtained with
XMM-Newton , an ESAscience mission with instruments and contributions directlyfunded by ESA Member States and NASA. We thank theanonymous referee for their useful feedback on the originalmanuscript.
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