KYNREFREV - implementation of an X-ray reverberation model in XSPEC

0.17 MB·

by  M. D. Caballero-Garcia

KYNREFREV - implementation of an X-ray
reverberation model in XSPEC
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n
a
J M. D.Caballero-Garciaa∗,M. Dovcˇiaka,I. Papadakisbc,A. Epitropakisb, J.Svobodaa,

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E. Karad,V.Karasa
1

a AstronomicalInstituteoftheAcademyofSciences,BocˇníII1401,CZ-14100Praha4,
]
E
CzechRepublic,E-mail:[email protected]
H b DepartmentofPhysicsandInstituteofTheoreticalandComputationalPhysics,
.
h UniversityofCrete,GR-71003Heraklion,Greece
p cFoundationforResearchandTechnology-Hellas,IESL,Voutes,GR-7110Heraklion,
-
o Greece
r d DepartmentofAstronomy,UniversityofMaryland,CollegePark,MD20742-2421,USA
t
s
a
[

WepresentbrieflythefirstresultsobtainedbytheapplicationoftheKYNREFREV-reverberation
1
v model,whichisreadyforitsuseinXSPEC.Thismodelcomputesthetimedependentreflection
5
spectra of the disc as a response to a flash of primary power-law radiation from a point source
0
9 coronalocated on the axis of the black-holeaccretion disc. The assumptionsof the modelare:
3
central Kerr black hole, surroundedby a Keplerian, geometrically thin, optically thick, ionised
0
. discwiththepossibilityofdefiningtheradialdensityprofileandastationaryhotpoint-likepatch
1
0 ofplasmalocatedonthesystemrotationaxisandemittingisotropicpower-lawradiation(lamp-
7
post geometry). Full relativistic ray-tracing code in vacuum is used for photon paths from the
1
: corona to the disc and to the observer and from the disc to the observer. The ionisation of the
v
i discissetforeachradiusaccordingtotheamountoftheincidentprimaryfluxandthedensityof
X
the accretiondisc. Inthispaperwe commentonsome preliminaryresultsobtainedthroughthe
r
a analysisofX-rayreverberationtime-lagsfrom1H0707-495andIRAS13224-3809.
AccretionProcessesinCosmicSources-APCS2016-
5-10September2016,
SaintPetersburg,Russia
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommons
Attribution-NonCommercial-NoDerivatives4.0InternationalLicense(CCBY-NC-ND4.0). http://pos.sissa.it/
X-rayreverberation M.D.Caballero-Garciaa
1. Introduction
TheX-ray emission from accreting black holes (BHs), in particular the narrow line Seyfert 1
(NLS1) Active Galactic Nuclei (AGN) reported in this work, is believed to come from the inner-
mostpartoftheaccretiondisc. Thishasbeenseentobehighlyvariable[1,2,3]. Theaccretiondisc
reprocesses and “reflects” the inner radiation, so part of the X-ray photons emitted by the corona
are reflected and vary in luminosity partially according to variations in the flux received from the
latter. Theemission atthe energy bands predominantly composed ofreflection from the accretion
disc (i.e. the soft-excess at 0.3-1keV and the broadened Fe Ka line at ≈3-8keV) is expected to
lag behind correlated variations in energy bands dominated by the directly observed continuum
emission(1-4keV).Thetimedelaycorresponds totheadditionallighttraveltimefromthecoronal
sourcetothereflectingaccretiondisc[4]. Someofthesesourcesshowareflection-dominatedspec-
trumandpotentially havemaximallyspinning BHs. Thisfactcanbeunderstood iflightbending is
an important effect for them [5]. Their high-energy source (i.e. the jet or corona) is very close to
the BHand theobserved direct continuum (i.e. power-law) isverylow. Thiswouldcorrespond to
RegimeIof[5],corresponding toalowheightoftheprimarysource(h≤2−4r ,dependingonthe
g
observer inclination), where strong light-bending suffered by the primary radiation dramatically
reduces theobservedpower-lawemissioncomponent atinfinityandthetotalluminosity atinfinity
staysrelativelyconstant. DuringRegimeIItheheightoftheprimarysourceishigher(h≈4−13r ,
g
depending ontheobserverinclination) andthetotalluminosityatinfinityvariesbyafactoroffour
andmostlyduetovariations oftheprimarysource.
The recent detection of time delays, as afunction of the Fourier frequency, between the soft-
band and the hard-band photons in Active Galactic Nuclei (AGN), can shed light on the X-ray
emission mechanism and the geometry of these BH systems. Currently, the observed negative
X-ray time-lags (i.e. soft-band variations lagging the hard band variations observed at high fre-
quencies) have triggered a great deal of scientific interest on interpreting their nature. The first
tentative detection was in the AGN Ark 564 [6], where an origin in reflection from the accretion
disc was proposed. The first statistically significant detection came from the AGN 1H 0707-495
[7]. More recent works [8, 9] then found that such X-ray time-delays are much more common
than itwas initially thought by the analysis of the X-ray data from several tens of AGN[10]. The
opposite time-delayed behaviour, i.e. positive X-raytime-delays (hard-band variations lagthesoft
band variations observed at low frequencies), has been known for quite some time in both AGN
(e.g. [11,12,13])andX-raybinaries (e.g. [14,15,16]). Although positive time-lags areexpected
inthestandardComptonizationprocesswithintheX-raysource[16],theycanalsobeproducedby
diffusivepropagation ofperturbations intheaccretion flow[17].
Inthispaperwebrieflydescribe ageneralized schemeandacodewhichcanbeusedwiththe
standard X-ray spectral fitting package, XSPEC [18]. This model takes into account a treatment
ofallthegeneralrelativistic effectsforaccretion discsandlightbending effectsinthedisc-corona
geometry. Time-lags versus frequency and energy can be produced and fitted by the user, either
in XSPEC or using another suitable tool. Sec. 1.1 shows a brief description of the model, Sec. 2
provides some preliminary results obtained using the model, and in Sec. 3 we briefly discuss and
comparethemwithotherresultsobtained intheliterature.
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X-rayreverberation M.D.Caballero-Garciaa
1.1 Themodel
This model (KYNREFREV;[19]) computes the X-ray emission from an accretion disc that is
illuminated from the primary power-law source located on the axis above the central BH with a
“flash” (hereafter referred to as “flare”). All relativistic effects are taken into account for photon
paths invacuum from thecorona tothediscand totheobserver andfrom thedisc totheobserver.
The transfer functions (see [20]) for these effects have been precalculated and stored in the FITS
filesthatareusedbythemodeltospeeduptheexecution ofthecode. Thereflectionistakenfrom
theREFLIONX1FITStablefiles[21],whichareintegrated overthedisc.
✄❜☛✞☎✎✞☎
❛
❝✄☎✄✆✝
❤
❜☞✝❝✌✍✄☞✞ ✦✐ ✦❡
▼ ★✏
r✐(cid:0)
✧
r♦✁✂ ✝❝❝☎✞✟✠✄✆✡✠☛❝
Figure1: Thesketchofthelamp-postgeometry.
Thelamp-post geometry used inthe KYNREFREVmodel (see Fig. 1) consists ofa BH,sur-
rounded by an equatorial accretion disc, that is illuminated by an X-ray source located on the
symmetry axis of the disc. Some of the main physical parameters of the model are the mass (in
unitsof108M⊙)andtheangularmomentum(−1≤a/M≤1),i.e. thespinoftheBHingeometrized
units, the height (h) of the X-ray source (in units of r =GM/c2), and the viewing angle (q ) of a
g
distant observerwithrespect totheaxisofthedisc.
The disc is assumed to be ionized, geometrically thin, Keplerian and co-rotating with the
BH, with a radial extent ranging from the inner edge of the disc (in units of the innermost stable
circular orbit, r ) up to the outer radius (r =103r ). The spin of the BH uniquely defines
ISCO out g
r . Whenmeasured ingeometrized units, thespin canattain anyvalue between zeroandunity,
ISCO
with a=0 (r =6r ) and a=1 (r =1r ) indicating a non-spinning (i.e. Schwarzschild)
ISCO g ISCO g
and a maximally spinning (i.e. “extreme” Kerr) BH, respectively. The primary X-ray source (i.e.
corona) is assumed to be a hot cloudlet of plasma on the rotation axis at height h and emitting a
power-law spectrum of X-ray radiation, Fp(cid:181) E−G eE/Ec, with a sharp low-energy cut-off at 0.1keV
andhigh-energy exponential cut-offatE =300keV.
c
In the new model the REFLIONX [21] tables for constant density slab illuminated by the
power-lawincidentradiationareusedtocomputethelocalreprocessingoftheincidentradiationin
theionizedaccretiondisc. Theionizationofthedisc,x ,issetbytheamountoftheincidentprimary
flux (dependent on the luminosity and height of the primary source and the mass of the BH) and
1https://heasarc.gsfc.nasa.gov/xanadu/xspec/newmodels.html
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X-rayreverberation M.D.Caballero-Garciaa
by the density of the accretion disc as x (r)(cid:181) F(r)/n(r). We used a constant-density disc in our
analysis. Thissimplificationiswellsatisfiedbecausetheradialdependence ofanyrealisticdensity
profile is much less significant than the radial decrease of the disc illumination by the lamp-post
corona (see,e.g.,Fig.3in[22]).
We may consider several limb brightening/darkening prescriptions for the directionality of
there-processed emission: isotropic emission(flux∼1),Laor’slimbdarkening (flux∼(1+2.06m );
[23])andHaardt’slimbbrightening (flux∼ln(1+1/m );[24,25]),withm beingcosineofemission
angle.
1.1.1 Transferfunctionandtime-lags
We refer as reverberation to the variable signal that we get (i.e. hereafter called “response
function”)correspondingtothevariationsofthedrivingprimarysourceofradiation[4]. Weassume
that the emission which wesee in each band isrelated to theunderlying driving signal byalinear
impulse response, which represents the response of the emission in that band to an instantaneous
“flash” (i.e. a delta-function impulse) in the underlying primary signal. Therefore, the observed
lightcurveistheconvolutionoftheunderlyingdrivingsignaltime-serieswiththeimpulseresponse
forthatenergy band.
Inthisworkwereferas“transferfunction”therelativeresponseofthedisctotheillumination:
F
y (E,t)= r,
r
F
p
where F (E,t)isthe timedependent observed reflected fluxfrom thedisc asaresponse toaflare2
r
thatwouldbeobserved asF d (t)(F istotalobserved primaryfluxatenergyE).
p p
TheFouriertransform ofthetransferfunction iscalculated as:
fˆ(E,f)=A (E,f)efr(E,f)
r r
withamplitudeA (E,f)andphasef (E,f)(whichissometimesreferredtoastransferfunctionin
r r
otherworks).
And the total phase of the Fourier transform of the total flux (i.e. both the primary and the
reflection continuum aretakenintoaccount) is:
A (E,f)sinf (E,f)
f (E,f)=arctan r r .
tot 1+A (E,f)cosf (E,f)
r r
One can calculate the time-lag of the signal, computed from the total phase at energy bin E with
respect tothetotalphaseatsomereference energybin:
D f (E,f)
t (E,f)= tot ,
2p f
where D f (E,f) is defined as the phase difference at any energy value E with respect to the
tot
reference energy rangeE ,i.e. D f (E,f)=f (E,f)−f (E ,f).
ref tot ref
2Implicitlyreferredtoa“Box”flareinpracticebecauseofnumerical/computationreasons.
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X-rayreverberation M.D.Caballero-Garciaa
To determine the response function of the disc, we assume that the primary X-ray source
isotropically emits a flare of duration equal to 1t (t =GM/c3). However, after computing the
g g
response, the Fourier transform is corrected for the “box” shape of the primary flare so that it
corresponds to the delta function impulse. Upon being illuminated, each area element of the disc
“responds” tothisflarebyisotropically andinstantaneously emittinga“reflection spectrum” inits
rest-frame. We assume that the reprocessed flux is proportional to the incident flux, and that the
discmaterialisionized.
2. Analysisandresults
2.1 1H0707-495
1H 0707-495 (z=0.0411) is a narrow-line Seyfert 1 galaxy with a BH mass estimate of M=
2×106M [26]. ItisoneofthemosthighlyvariableSeyfertgalaxies,commonlyknowntoincrease
⊙
byanorderofmagnitudeinfluxontimescalesasshortasonehour. Thereforethismakesthissource
an ideal target for extensive spectral-timing analysis as previous studies based on the X-ray data
from the XMM-Newton satellite have shown so far. [7] and [27] showed that the high-frequency
variations in thesoft excess from 0.3-1keV lag behind those inthe 1-4keV band by∼30s. They
interpreted this short timescale lag as the reverberation time delay between the primary-emitting
corona and the inner accretion disc. This short time delay would put the corona at a height of
<10r fromtheaccretion disc(usingtheaforementioned valuefortheBHmass).
g
2.2 IRAS13224-3809
IRAS13224-3809 (z=0.066) isalso one of the mostX-ray variable Seyfert 1galaxies known
[28],andthereforeitisausefulsourceforwhichtoprobetheenvironmentsoftheinnermostregions
around the BH. It was first observed with XMM-Newton in 2002 for 64ks [29, 30, 31], and later
for 500 ks, which led to a significant detection of the soft time-lag [32]. Later [33] followed the
source and reported ontheanalysis ofthesoft time-lags ofIRAS13224-3809 inthe lowand high
flux states. Together with 1H 0707-495 it is one of the very few sources for which XMM-Newton
hasdevoted long-exposure (&500ks)observational campaigns.
2.3 Time-lagversusfrequencyspectralfitting
We fitted the (0.3-1 versus 2-4keV) time-lag versus frequency global spectrum of 1H 0707-
495 with the model KYNREFREVand obtained a very good fit (c 2/n =28/30; with n being the
number ofd.o.f.) asshowninFig.2. Theprimaryisotropic fluxwassettoslightly sub-Eddington
(i.e. L/Ledd=0.1) according to previous studies [7]. The value for the density of the accretion
disc obtained was N =(30±10)×1015cm−3 (adopting a constant radial density profile) and the
H
valuesoftherestoftheparameters ofthefit(spin,massandheightofthelamp-post) areshownin
Tab.1. Themassisinverygoodagreement withprevious findingsbuttheheight ofthelamp-post
is higher (5.8±0.5r ) than previously found (2.4±0.5r ; [34]) and the value for the BH spin is
g g
lower than usually obtained from X-ray spectroscopy (>0.98, e.g. [7]) but in agreement with the
previousvalueobtainedfromtime-lagfittingby[34]usingasimilarmodel. AsshowninFig.3the
difference between the obtained slow-rotation (model A) and high-spinning BH (model B)is that
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X-rayreverberation M.D.Caballero-Garciaa
inthelatterweobtainphasewrappingathighfrequencies(stillnotdetectedwithcurrentdetectors).
Theextrapolationofthemodelwithhighspintothelower(observed)frequenciesisnotcompatible
withthedata,hencethereasonofgettingalowervalueforthespinoftheBH.
When fitting the two datasets from IRAS 13224-3809 (the same as previously analyzed by
[33]) we obtained also a good fit (c 2/n =10/6) as shown in Fig. 4. We tested the “pure” lamp-
post geometry, in which the change of the state (i.e. luminosity) is due to the variable height of
the corona. According to the expectation of a (near) Eddington accreting BH for the given mass
[35]wesettheprimaryisotropicfluxtoaslightlysub-Eddington value(L/Ledd=0.1). Thevalue
for the density of the accretion disc obtained was N =(26±5)×1015cm−3 (adopting a constant
H
radial densityprofile)andthevalues oftherestoftheparameters ofthefit(spin,massandheights
of the lamp-post during both states) are shown in Tab. 2. Weobtain a moderate value for the spin
(0.74±0.02)thatislowerthanpreviously obtained (a=0.99;[36])
Thereason forsuchadisagreement forthespinisthefactthatforsuchahigh value(&0.95)
phase-wrapping occurs (and it is more pronounced for high values of the intrinsic primary lumi-
nosity, after performing some testing). This can be seen in Fig. 5 where the current fitted model
(model C) and a high-spinning BH (model D) are shown. If the spin is changed to a lower value
(e.g. ≤0.5)phase-wrapping totallydisappears.
Aspointedpreviously[33]thechangeintheshapeoftheobservedtime-lagscanbeinterpreted
asachangeinthepropertiesofthecorona. Inthetermsofthemodelandparametrization usedthis
is shown in the form of a change in the height of the lamp-post (from 4.9±0.2r to 9.0±1.0r ).
g g
Both values are higher to what has been previously reported in the framework of the lamp-post
model (2.9±0.8r ; [34]), alike in the case of 1H 0707-495, which might be due to the slightly
g
different modelused. Nevertheless, thevaluesobtained fortheEddington ratioandcoronal height
areconsistent withwhatisobtained andshowninFig.7byrecentwork[10].
1H0707-495
200
ds) 100
n
o
ec
g (s
a
L
0
-100
1.0e-03
Frequency (Hz)
Figure2: The(0.3-1versus2-4keV)X-raysofttime-lagversusfrequencyspectrumof1H0707-495fitted
withtheKYNREVREFmodelinXSPEC(redline). Thetwocomponentsofthebest-fittingtime-lagmodel
aretherelativisticreflectedcomponent(black-dottedline)andthepower-law(black-dashedline).
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X-rayreverberation M.D.Caballero-Garciaa
Model A Model B
200 200
100 100
Lag (seconds) 0 Lag (seconds) 0
−100 −100
−20010−4 10−3 Frequency (seconds) 0.01 −20010−4 10−3 Frequency (Hz) 0.01
Figure 3: Extrapolated to higher frequencies fitted models for 1H 0707-495 with the obtained value for
spin giventhe data(0.52±0.09; modelA) andfora highlyspinningBH (0.95, modelB) atleftand right,
respectively.
Mass Spin View. angle Height PLnorm. PLindex c 2/d.o.f.
M a/M q h A(s) s
o
(×106M⊙) (GM/c) (GM/c2)
2.6±0.2 0.52±0.09 77±3 5.8±0.5 (2.2±0.3)×10−6 2.23±0.02 28/30
Table 1: Valuesofthemain parametersobtainedfromthe best-fitusingthe KYNREFREVMODELof the
time-lagsof1H0707-495showninFig.2. Errorsare68%confidenceerrors.
IRAS13224−3809
0
0
2
0
econds) −200
g (s
a
L
0
0
4
−
5×10−4 10−3 2×10−3
Frequency (Hz)
Figure 4: The (0.3-1 versus 1.2-5keV) X-ray soft time-lag versus frequency spectrum of IRAS 13224-
3809fittedwiththeKYNREVREFmodelinXSPEC(blackandredline,forthelowandthehigh-fluxstates,
respectively).
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X-rayreverberation M.D.Caballero-Garciaa
Model C Model D
500 500
Lag (seconds) 0 Lag (seconds) 0
−500 −500
10−4 10−3 0.01 10−4 10−3 0.01
Frequency (Hz) Frequency (Hz)
Figure 5: Extrapolatedto higherfrequenciesfitted modelsfor IRAS 13224-3809with the obtainedvalue
forspingiventhedata(0.74±0.02;modelC)andforahighlyspinningBH(0.95,modelD)atleftandright,
respectively.
Mass Spin View. angle Height(1) Height(2) c 2/d.o.f.
M(×106M⊙) a/M(GM/c) q o h1 (GM/c2) h2 (GM/c2)
7.1±0.2 0.74±0.02 66±5 4.9±0.2 9.0±1.0 10/6
Table 2: Valuesofthemain parametersobtainedfromthe best-fitusingthe KYNREFREVMODELof the
time-lagsofIRAS13224-3809showninFig.4. Errorsare68%confidenceerrors.
3. Discussionand conclusions
In this paper we briefly presented a model (KYNREFREV)which deals with X-ray reverber-
ation effects in AGN and can be used in and/or outside XSPEC. This model takes into account
all the relativistic effects acting on light in the vicinity of the BH and a realistic prescription of
the accretion disc surrounding it under the lamp-post primary source geometry. A more detailed
description ofthemodelwillbepresented inaforthcoming publication [19].
Wepresent somepreliminary interesting results obtained through theanalysis ofX-rayrever-
beration time-lags from 1H 0707-495 and IRAS 13224-3809 using this model. The global (0.3-1
versus ≈2−4keV) X-ray soft time-lag spectrum is well fitted with this model, confirming previ-
ous statements on the X-ray reverberation origin of the negative X-ray soft time-lags [7]. Wefind
that the BH is low and moderately-spinning for the case of 1H 0707-495 and IRAS 13224-3809,
respectively. This is in contrast with previous results obtained from X-ray spectroscopy which
suggest a maximally-spinning BH for both sources. We chose a near to Eddington value for the
primary isotropic flux in the 2–10keV energy range of L/L =0.1, which is reasonable given
EDD
the masses of both BHs. We notice that these results are sensitive to the chosen L/L value,
EDD
mostly in the case of IRAS 13224-3809, with a higher BH mass and hence with (observable with
currentinstrumentation) phase-wrapping. Wenoticethat,althoughourresultsarepreliminarythey
areinagreementwithprevious claimsofalow-spinning BHforthecaseof1H0707-495 [37].
In the case of IRAS 13224-3809 we point out that the (0.3-1 vs 1.2-5keV) spectral time-
lag transition related with the flux state of the source reported previously [33] might be due to a
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X-rayreverberation M.D.Caballero-Garciaa
change intheheight ofthecorona(from4.9±0.2to9.0±1.0r inthelowandthehigh-fluxstates,
g
respectively). These results are consistent withthe light-bending scenario proposed by [5], where
inlow-fluxstatesthecoronaisclosertotheBHandgeneralrelativistic effectsaremoreimportant.
If confirmed (with higher time-resolution observations), these results would indicate the power of
analyzing X-rayreverberation time-lags inorder toset further constraints oftheinner disc-corona
geometry forthesesystems.
Acknowledgments
MCG and MD acknowledge support provided by the European Seventh Frame-work Programme
(FP7/2007-2013) under grant agreement n◦ 312789. JS acknowledges financial support from the
GrantAgencyoftheCzechRepublicwithintheproject n◦14-20970P.
References
[1] Leighly,K.M.ApJS,125,297,(1999)
[2] Turner,T.J.,George,I.M.,Nandra,K.&Turcan,D.ApJ,524,667,(1999)
[3] Ponti,G.,Papadakis,I.,Bianchi,S.,etal.A&A,542,83,(2012)
[4] Uttley,P.,Cackett,E.M.,Fabian,A.C.,etal.A&ARv,22,72,(2014)
[5] Miniutti,G.&Fabian,A.C.MNRAS,349,1435,(2004)
[6] McHardy,I.M.,Arévalo,P.,Uttley,P.,etal.MNRAS,382,985,(2007)
[7] Fabian,A.C.,Zoghbi,A.,Ross,R.R.,etal.Nature,459,540,(2009)
[8] Emmanoulopoulos,D.,McHardy,I.M.&Papadakis,I.E.MNRAS,416,94,(2011)
[9] DeMarco,B.,Ponti,G.,Cappi,M.,etal.MNRAS,431,2441,(2013)
[10] Kara,E.,Alston,W.N.,Fabian,A.C.,etal.MNRAS,462,511,(2016)
[11] Papadakis,I.E.,Nandra,K.&Kazanas,D.ApJL,554,133,(2001)
[12] McHardy,I.M.,Papadakis,I.E.,Uttley,P.,etal.MNRAS,348,783,(2004)
[13] Arévalo,P.,Papadakis,I.E.,Uttley,P.etal.MNRAS,372,401,(2006)
[14] Miyamoto,S.&Kitamoto,S.Nature,342,773,(1989)
[15] Nowak,S.&Vaughan,S.MNRAS,280,227,(1996)
[16] Nowak,M.A.,Wilms,J.&Dove,J.B.MNRAS,517,355,(1999)
[17] Kotov,O.,Churazov,E.&Gilfanov,M.MNRAS,327,799,(2001)
[18] Arnaud,K.A.AstronomicalSocietyofthePacificConferenceSeries,101,17,(1996)
[19] Dovcˇiak,M.,Caballero-García,M.D.,Papadakis,I.E.,etal.Inpreparation,,,(2017)
[20] Dovcˇiak,M.,Karas,V.&Yaqoob,T.ApJS,153,205,(2004)
[21] Ross,R.R.&Fabian,A.C.,MNRAS,358,211,(2005)
[22] Svoboda,J.,Dovcˇiak,M.,Goosmann,R.W.,etal.A&A,545,106,(2012)
8
X-rayreverberation M.D.Caballero-Garciaa
[23] Laor,A.ApJ,376,90,(1991)
[24] Haardt,F.&Matt,G.MNRAS,261,346,(1993)
[25] Czerny,B.,Róz˙an´ska,A.,Dovcˇiak,M.,etal.A&A,420,1,(2004)
[26] Bian,W.&Zhao,Y.MNRAS,343,164,(2003)
[27] Zoghbi,A.,Fabian,A.C.,Uttley,P.,etal.MNRAS,401,2419,(2010)
[28] Boller,T.,Brandt,W.N.&Fink,H.A&A,305,53,(1996)
[29] Boller,T.,Tanaka,Y.,Fabian,A.,etal.MNRAS,343,L89,(2003)
[30] Gallo,L.C.,Boller,T.,Tanaka,Y.,etal.MNRAS,347,269,(2004)
[31] Ponti,G.,Gallo,L.C.,Fabian,A.C.,etal.MNRAS,406,2591,(2010)
[32] Fabian,A.C.,Zoghbi,A.,Wilkins,D.,etal.MNRAS,419,116,(2012)
[33] Kara,E.,Fabian,A.C.,Cackett,E.M.,etal.MNRAS,430,1408,(2013)
[34] Emmanoulopoulos,D.,Papadakis,I.E.,Dovcˇiak,M.&McHardy,I.M.MNRAS,439,3931,(2014)
[35] Boller,T.,Brandt,W.N.,Fabian,A.C.&Fink,H.H.MNRAS,289,393,(1997)
[36] Fabian,A.C.,Kara,E.,Walton,D.J.,etal.MNRAS,429,2917,(2012)
[37] Done,C.&Jin,C.MNRAS,460,1716,(2016)
9