Line shifts in accretion disks - the case of Fe K$\alpha$

0.64 MB·

by  P. Jovanović

Line shifts in accretion disks - the case of Fe Kα
P. Jovanovi´c • V. Borka Jovanovi´c • D. Borka •
L. Cˇ. Popovi´c
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Abstract Here we present a short overview and main 1 Introduction
]
A resultsofourinvestigationsofseveraleffects whichcan
G induce shifts in the broad Fe Kα line emitted from rel- It is now widely accepted that most galaxies harbor
ativistic accretion disks around single and binary su- a supermassive black hole (SMBH) in their centers
.
h permassive black holes. We used numerical simula- and that the formation and evolution of galaxies is
p
tions based on ray-tracing method in the Kerr metric fundamentally influenced by properties of their cen-
-
o to study the roleofclassicalDoppler shift, specialrela- tral SMBHs (see e.g. Kormendy & Ho 2013, and ref-
tr tivistic transverse Doppler shift and Doppler beaming, erences therein). Active galaxies most likely represent
as general relativistic gravitational redshift, and pertur- one phase in galactic evolution, and they derive their
[ bations of the disk emissivity in the formation of the extraordinaryluminosities from energyrelease by mat-

observed Fe Kα line profiles. Besides, we also investi- teraccretingtowards,andfallinginto,acentralSMBH
1
gatedwhethertheobservedlineprofilesfromthebinary
v through a relativistic accretion disk which represents
9 systems of supermassive black holes could be affected an efficient mechanism for extracting the gravitational
8 by the Dopplershifts due to dynamics ofsuchsystems.
potential energy and converting it into the electro-
3 Thepresentedresultsdemonstratethatalltheseeffects
magneticradiation(seee.g.Jovanovi´c & Popovi´c2009;
2
could have a significant influence on the observed pro-
0 Jovanovi´c2012, and references therein)
files of the broad Fe Kα line emitted from relativistic
. Since its discoveryin Seyfert 1 galaxyMCG-6-30-15
1
accretion disks around single and binary supermassive
0 by Tanaka et al.(1995), the broadFe Kα emission line
black holes.
6 at6.4keVwasobservedinanumberofActiveGalactic
1
Nuclei (AGNs) (see e.g. Nandra et al. 2007, and ref-
: Keywords black holes: black-hole binaries; galaxies:
v erence therein). Based on the observations with the
active; accretion and accretion disks; spectral lines; X-
Xi ray emission spectra X-raysatellites like Ginga,ASCA, RXTE, BeppoSAX,
XMM-Newton, Suzaku and Chandra, the fact that X-
r
a ray irradiation of the accretion disk surface in a class
P.Jovanovi´c
of AGNs known as Seyfert 1 galaxies gives rise to the
Astronomical Observatory, Volgina 7, P.O. Box 74 11060 Bel-
fluorescent Fe Kα line emission via the X-ray reflec-
grade,Serbia
tionisnowwellestablished(seee.g.Fabian et al.2000).
V.BorkaJovanovi´c
Thebroadandasymmetricprofileofthisline withnar-
D.Borka
row bright ”blue” and wide faint ”red” peak is most
AtomicPhysicsLaboratory(040),VinˇcaInstituteofNuclearSci-
commonlyattributed to the relativisticeffects due to a
ences,UniversityofBelgrade,P.O.Box522,11001Belgrade,Ser-
bia veryfastrotationofthe emitting materialinthe inner-
L.Cˇ.Popovi´c mostregionsoftheaccretiondisk(seee.g.Fabian et al.
Astronomical Observatory, Volgina 7, P.O. Box 74 11060 Bel- 2000, and references therein), although there are some
grade,Serbia alternative attempts to explain such profile by scatter-
ing/reflection/absorptionby the disk wind and/or ion-
izedoutflowswhichcouldmimic relativisticeffects (see
Turner & Miller 2009, and references therein). Since
2
thislineisemittedfromaverycompactregionintheac-
cretiondisknearthecentralSMBH,itrepresentsapow-
erful diagnostic tool for studying the effects of strong
gravitationalfield (see e.g.Jovanovi´c& Popovi´c2008),
accretionphysicsandspace-timegeometryinthevicin-
ityofSMBHs(seeJovanovi´c(2012)foranoverviewand
Jovanovi´c et al. (2011) for a case study).
So far, the extensive theoretical studies of the line
profilesemittedfromrelativisticaccretiondisksaround
SMBHs have been carried out, in which the line pro-
files have been modeled using different approaches(see
e.g. Reynolds & Nowak 2003, for a review). In the
weak field limit such line profiles can be evaluated
analytically (Chen & Halpern 1989; Chen et al. 1989).
Fabian et al. (1989) were the first who calculated the
Fe Kα profiles emitted by the accretion disk in the
Schwarzschild metric. A full general relativistic ap-
proachbasedon”thetransfer-function”whichcontains Fig. 1 Simulated image of a highly inclined (i = 80◦)
allrelativisticeffectsisalsousedformodelingrelativis- relativistic accretion disk in Kerr metric around a SMBH
ticallybroadenedlines(Laor1991). Theexactlinepro- with spin a=0.5, colored according toenergy shift g (top)
files can be also computed by the direct integration of and observed flux (bottom). Inner and outer radii of the
thephotontrajectoriesintheKerrmetric(Karas et al. disk are Rin =Rms and Rout=20 Rg, respectively and its
power law emissivity indexis q=−2.5
1992;Bromley et al.1997)whichenabledstudiesofthe
complex disk models, such as geometrically thick or
warpedaccretiondisks (Hartnoll & Blackman2000) or some angular momentum (spin) a. Due to several ef-
disks with non-axisymmetric structures in form of spi- fects which will be discussed below, photons emitted
ralarms(Karas et al.2001). ThestandardX-rayspec- from a disk at energy E (or wavelength λ ) will
em em
tral fitting code, XSPEC (Arnaud 1996) is often used be observed at energy E (or wavelength λ ) by
obs obs
for evaluating the general relativistic models of accre- an observer at infinity, causing the energy shift g or,
tiondisksandsimulatingthecorrespondinglineprofiles equivalently, the usual redshift in wavelength z:
(see e.g. Dovˇciak et al. 2004).
E λ 1
Here we study several phenomena which can induce g = obs = em = . (1)
E λ 1+z
line shifts, and thus cause the variability of the profile em obs
of the Fe Kα line emitted from a relativistic accretion
In the ray-tracing method one takes into account only
diskaroundaSMBH,usingacodebasedonray-tracing
those photon trajectories reaching the observer’s sky
method in the Kerr metric (see e.g. Cˇadeˇz et al. 1998;
plane. An observer’s sky plane is divided into a num-
Jovanovi´c 2012, and references therein). This paper is
ber of small elements (pixels), and for each pixel the
organized as follows: in Section 2 we briefly describe
photon trajectories are traced backward from the ob-
the method used to obtain the simulated line profiles,
server by following the geodesics in a Kerr space-time,
in Section 3 we describe severaltypes of line shifts and
until their intersection with the disk. We assumed an
study different effects which can induce them, and fi-
optically thick and geometrically thin disk for which
nally in Section 4 we point out our conclusions.
thespectrumofemittedradiationdependsonitsstruc-
ture,andthereforeonthedistancetothecentralSMBH
(Shakura & Sunyaev 1973). Thus, assuming that disk
2 Simulated line shapes
radiates according to an emissivity law ε(r), for each
pixel at observer’s sky plane it is possible to calculate
We studied the radiation from relativistic accretion
the flux density and the energy shift g of the photons
disks around SMBHs using numerical simulations
emitted by the disk (see Jovanovi´c 2012, for more de-
based on ray-tracing method in the Kerr metric (see
tails). Usually, a power law for disk emissivity is as-
Fanton et al.1997;Cˇadeˇz et al.1998,formoredetails), sumed: ε(r) ∝ r−q, where q is an emissivity index.
in which we used the pseudo-analytical integration of
In that way, one can obtain a simulated image of a
the geodesic equations describing the photon trajec-
relativisticaccretiondiskaswouldbe seenbyadistant
tories in the general case of a rotating SMBH with
observerusingapowerfulhighresolutiontelescope. An
3
Table 1 Parameters of the simulated accretion disks, and the intervals of energy shift (gmin <g <gmax) over which the
corresponding simulated line profiles presented in the Figs. 2-3 have nonzero intensity, as well as the widths of each line
bin ∆g. In all cases it is assumed that thedisk emissivity follows a power law with emissivity index q=2.5.
◦
R (R ) R (R ) i ( ) a g g ∆g
in g out g min max
7000 8000 10 0.99 0.9985 1.0012 0.0001
1000 2000 10 0.99 0.9935 1.0045 0.0001
10 20 35 0.01 0.72 1.10 0.01
6 20 35 0.01 0.60 1.10 0.01
10 20 35 1 0.73 1.10 0.01
1 20 35 1 0.02 1.10 0.01
exampleofsuchsimulatedimageofarelativisticaccre- tral SMBH, is practically Keplerian since the relativis-
tion disk is presented in Fig. 1, where R = GM/c2 tic effects are negligibleat suchlargedistances. There-
g
is the gravitational radius of the central SMBH with fore,thelinesemittedfromtheseregionsarebroadened
massM (Gbeing gravitationalconstantandcspeedof depending on Keplerian rotational velocity and have
light), and R representsthe radius ofthe marginally two symmetric peaks (see the solid line profile in Fig.
ms
stable orbit which depends on spin a of the SMBH. 2): the ”blue” one emitted by the material located on
Thecorrespondingsimulatedprofileofthelineemit- the side of the disk which is approaching towards an
tedfromthesimulatedaccretiondiskcanbecalculated observer (denoted by blue shades in the simulated ac-
by taking into account the total observed flux and ob- cretion disk image presented in the top panel of Fig.
servedphotonenergiesofallpixelsoverthediskimage: 1), and the ”red” one, emitted by the material on the
receding side of the disk with respect to the observer
(denoted by red shades in the top panel of Fig. 1).
Fobs(Eobs)= ε(r)g4δ(Eobs−gE0)dΞ, (2)
imZage R =7000 R , R =8000 R
in g out g
where dΞ is the solid angle subtended by the disk in s) R =1000 R , R =2000 R
it in g out g
the observer’s sky and E0 is the rest energy. Several n 1
u
examples for the simulated line profiles emitted from y
r
different regions of the relativistic accretion disks with a
tr 0.8
different parameters are given in Figs. 2-3. bi
r
a
(
x 0.6
u
3 Results: Fe Kα line shifts ed fl 0.4
v
r
Inthissectionwewilldiscussseveralphenomenawhich e
s
can induce shifts in the lines emitted from relativis- Ob 0.2
tic accretion disks around SMBHs. For that purpose
wesimulatedthe lineprofilesemittedfromdifferentre- 0
gions of accretion disks, which parameters are given in 0.99 0.995 1 1.005 1.01
Table 1. In the following paragraphs we describe the g=E /E
obs em
obtained results in more details. However, one should
take into account that some other phenomena, such as Fig. 2 Two shapes of the lines emitted from the outer
gravitational microlensing could also induce line shifts regions of a slightly inclined (i=10◦) relativistic accretion
(see e.g. Popovi´c et al. 2003a,b, 2006; Jovanovi´cet al. disk around a maximally rotating Kerr SMBH, extending
2008; Jovanovi´c & Popovi´c 2009), but they will not be between 7000 and 8000 Rg (solid line) and 1000 and 2000
discussed here. Rg (dashed line)
3.1 Classical Doppler shift due to Keplerian rotation 3.2 Transverse Doppler shift and Doppler beaming
in accretion disk due to special relativistic effects
Rotation of emitting material in the outermost regions However, in the regions which are located less than a
ofanaccretiondisk,locatedthousandsR fromthecen- few thousand R from the SMBH, the rotational ve-
g g
4
1
locities are much higher (on the order of several thou-
R =10 R
−1 in g
sand km s ) inducing, not only the wider line shapes,
s) R =R =6 R
but also the special relativistic effects which produce nit 0.8 in ms g
u
an asymmetry in the line shapes by shifting the emis- y
r
sionfromthe innerregionsofthe disktothe ”red”and bitra 0.6
beaming its radiation in the direction of motion (see r
a
(
e.g. Fabian 1999), and thus enhancing the ”blue” peak x
with respect to the ”red” one (see the dashed line pro- flu 0.4
d
file in Fig. 2). These two special relativistic effects are ve
r
known as transverse Doppler shift and Doppler beam- se 0.2
b
ing, respectively. O
ThetransverseDopplershiftoriginateswhentheob- 0
server is displaced in a direction perpendicular to the 0 0.5 1 1.5 2
directionofthemotionofemittersintheaccretiondisk, g=E /E
obs em
and is a consequence of the relativistic Doppler effect 1
R =10 R
which includes the time dilation. Namely, if in the ob- in g
s) R =R =1 R
server’s frame the angle between the direction of the nit 0.8 in ms g
u
emitter at the time of emissionandthe observeddirec- y
r
tπi/o2n,othfethreelalitgihvtistaitctDhoeptpilmereeofffecotbsreerdvuacteisontoistheequtraalntso- rbitra 0.6
a
verseDopplershift,duetowhichtheobservedradiation x (
from a rapidly rotating accretion disk is redshifted by flu 0.4
d
the Lorentz factor, as it is the case with the dashed e
v
r
simulated line profile in Fig. 2. se 0.2
b
Doppler beaming (boosting) modifies the apparent O
brightnessoftherapidlymovingemittingmatterinthe
0
sense that, if it is moving towards the observer then it 0 0.5 1 1.5 2
will appearbrighterthan ifit is at rest,andvice versa, g=E /E
obs em
if it is moving away from the observer it will appear
fainter than if it is at rest. When this is applied to Fig. 3 Top: the shape of the Fe Kα line emitted from
the rapidly rotating emitters in the accretion disk, it theinnermostregionsofarelativisticaccretiondiskaround
◦
a Schwarzschild SMBH with inclination of i = 35 , outer
willenhancetheapparentbrightnessoftheapproaching
sideofthediskwithrespecttoitsrecedingside(seethe radiusof20Rg andinnerradiusofRin =10Rg (solidline),
as well as Rin = Rms = 6 Rg (dashed line). Bottom: the
bottom panel in Fig. 1), and thus it will also enhance
same as above, but in the case of an accretion disk around
the ”blue” peak of the line with respect to its ”red” a maximally rotating KerrSMBH for which Rms =1 Rg
peak, as it can be seen from the dashed simulated line
profile in Fig. 2.
−1
thousands of km s ). Therefore, the previously men-
Sincethevelocitiesofmaterial,aswellastheradiiof
tioned classical and special relativistic effects are even
the emitting regionof the dashed simulatedline profile
moresignificantin the case of Fe Kα line (see the both
inFig. 2,correspondtothepartsofthediskfromwhich
panels in Fig. 3, as well as the corresponding rows in
theopticalspectrallineslikeHαandHβ areobserved,
Table1). AsitcanbeseenfromFig. 3,whencompared
one can conclude that the transverseDoppler shift and
to the simulated profile of an optical line (dashed pro-
Doppler beaming significantly affect even the optical
file from Fig. 2), the Fe Kα line profile is much wider
lineswhichoriginatefromouterregionsoftheaccretion
(due to the larger classical Doppler shift), more asym-
disk. In the case of such lines, as it can be seen from
Table1,themaximumredshiftofthephotons(1/g − metric (due to the larger Doppler beaming) and more
min
redshifted (due to the larger transverse Doppler shift,
1) is significantly larger by absolute value than their
maximum blueshift (1/g −1), which quantitatively aswellasdue tothe gravitationalredshiftwhichisdis-
max
cussed in more details in the following paragraph).
represents the influence of transverse Doppler shift in
this case.
However,sincetheFeKαlineoriginatesintheinner-
most regions of an accretiondisk, its emitting material
rotateswiththefastestvelocities(ontheorderoftensof
5
3.3 Gravitational redshift due to general relativistic 2008) and, as it canbe seenfrom both panels in Fig. 3
effects and the corresponding rows of Table 1, it significantly
affectstheprofileofthe FeKαline,especiallyits”red”
According to the general relativity, the observed fre- wing by extending it towardsthe lowerenergies forthe
quencyofelectromagneticradiationemittedbyasource higher values of a (see also Jovanovi´cet al. (2011) for
in a strong gravitational field in vicinity of a SMBH a case study and Jovanovi´c(2012) for more details).
will be reduced with respect to the emitted frequency,
due to gravitational time dilation. This effect is called 3.4 Line shifts due to perturbed disk emissivity
the gravitational redshift (Misner et al. 1973), and in
the Newtonian limit it is approximately proportional Beside the previously mentioned classical, special and
to the mass of a SMBH and inversely proportional to general relativistic effects, several observational/theo-
thedistancebetweenitandapointinthediskatwhich retical studies indicated that the line shapes and shifts
a photon is emitted. couldbeaffectedbytheperturbationsofthediskemis-
In order to study the influence of the gravitational sivityintheformofflaresororbitingbrightspots,espe-
redshiftontheFeKαlineprofile,wesimulatedtheline ciallyin the caseofhighaccretionrate objects,suchas
profiles originating from two emitting regions in accre- Seyfert galaxies and QSOs (see e.g. Czerny et al. 2004;
tion disk around a non-rotating Schwarzschild SMBH Czerny & Goosmann 2004; Jovanovi´cet al. 2010). For
(top panel in Fig. 3) and a maximally rotating Kerr instance, appearance of the redshifted Fe Kα emis-
SMBH (bottom panel in Fig. 3), having two different sion feature due to co-rotating flare above the accre-
inner radii: R = 10 R (denoted by solid lines) and tion disk which irradiates a spot on its surface was re-
in g
R =R (denoted by dashed lines). The outer radii ported in the case of the Seyfert galaxies NGC 3516
in ms
in both casesareR =20 R . As it canbe seenfrom (Iwasawa et al. 2004) and NGC 3783 (Tombesi et al.
out g
Fig. 3, in the case of both metrics the profiles origi- 2007), based on their observations by XMM-Newton.
nating from emitting regions with smaller inner radii However,sincethesensitivityofXMM-Newtonwasnot
are redshifted with respect to the profiles from emit- sufficient to clearly resolve sub-orbital features in the
ting regions with larger inner radii, due to the gravita- observedX-rayspectra,theazimuthalirradiationstruc-
tional redshift. This is even more obvious if one com- ture of the inner accretion disk is modeled and sim-
parethecorrespondingmaximumredshifts(1/g −1) ulated by Czerny et al. (2004); Czerny & Goosmann
min
and blueshifts (1/g −1) presented in Table 1, from (2004); Goosmann et al. (2007a,b) in order to investi-
max
which it can be seen that the maximum redshifts are gatethedetectabilityoforbitingspotsinnearbySeyfert
much bigger in the cases with the smaller inner radii, galaxies with current and future X-ray observatories,
while the blueshifts are the same in both cases. There- suchasX-rayEvolvingUniverseSpectroscopy(XEUS),
fore,the gravitationalredshiftcausesthefurtherdefor- a planned successor to XMM-Newton which evolved
mationsoftheFeKαlineprofilebysmearingits”blue” to Advanced Telescope for High Energy Astrophysics
emission into the ”red” one. (ATHENA+)thatiscurrentlyunderdevelopment,aim-
This effect is strongerin the case ofa maximally ro- ingtohaveseveralhundredtimeslargersensitivitythan
tating Kerr SMBH than in the case of a non-rotating Chandra X-ray Observatory and XMM-Newton. For
SchwarzschildSMBH due to the fact that the radius of that purpose, Goosmann et al. (2007a,b) developed a
the innermost stable circular orbit (also known as ra- method to compute the local spectra of the hot spot
dius of marginally stable orbit, R ) strongly depends emissionfrom the surface of an accretiondisk underly-
ms
on SMBH spin a, so that in the case of a non-rotating ingastrongco-rotatingflareabovethedisk,andusedit
SchwarzschildSMBH(i.e. fora=0)itis equalto 6R to model the X-ray reprocessing from a persisting flare
g
(top panel in Fig. 3), and in the case of an extremely lastingforasignificantfractionofoneorbitalperiodat
rotating Kerr SMBH (i.e. for a = 1) it is equal to the given disk radius in some AGNs such as MCG-6-
1 R (bottom panel in Fig. 3). Thus, in the case of an 30-15 and NGC 5548, as well as the short-term flares
g
extremelyrotatingSMBHitispossibletodetectthera- with durations of a few hundreds of seconds. These
diationwhichoriginatescloserto the SMBHitself, and studies showed that the future high precision observa-
which is therefore more subjected to the gravitational tions will allow to disentangle the effects of the flares
redshift (see the last row in Table 1), than in the case in the accretion disks of Seyfert galaxies from the in-
of a non-rotating SchwarzschildSMBH. trinsic variability of the local emission, even at dis-
In that way the SMBH spin a affects the radiation tanceswhicharelessthan5R fromthecentralSMBHs
g
originatingfromtheinnermostregionsofthediskwhich (Goosmann et al. 2007b). Also, the spectral variations
are closestto the SMBH (see e.g. Jovanovi´c& Popovi´c induced by such flares depend on the viewing direction
6
andarestrongerforintermediate(edge-on)viewingan- where q is power law emissivity index, ε is emissiv-
p
gles,assupposedforSeyfert-2galaxies,thanforaface- ity of perturbing region, and (x ,y ) and σ are its
p p p
on viewing direction, as assumed in Seyfert-1 galax- positionandwidth(bothinR ),respectively. Anillus-
g
ies, and thus, they could be used to put observational tration of the perturbed disk emissivity is presented in
constraints on the disk inclination (Czerny et al. 2004; the top panel of Fig. 4, and the perturbed and unper-
Czerny & Goosmann 2004). However, indications for turbed Fe Kα line profiles for three different positions
the flares in the accretion disks were found not only in and widths of perturbing region are given in the bot-
the X-ray band, but alsoin the opticalspectra of some tom panel of the same figure. As one can see from
AGNs. Forexample,thevariabilityoftheobservedHβ Fig. 4, a perturbing region on the receding side of ac-
line profiles of quasar 3C 390.3 was recently success- cretion disk, affects only the ”red wing” of the Fe Kα
fully explainedby a perturbationofthe powerlaw disk line, while the ”blue” one and the line core stay nearly
emissivity, revealing the appearance of two successive unaffected. Moreover, the position of perturbing re-
bright spots on the approaching side of the disk which gionis ina directrelationwiththe positionofthe ”red
were interpreted as the fragments of spiral arms in the peak” of the line. Recently, a model of accretion disk
accretion disk of 3C 390.3 (Jovanovi´c et al. 2010). withperturbingregionwasusedforfittingtheobserved
spectra of some AGNs, resulting with a non-random
distribution of bright spot positions along the receding
side ofthe disk. This indicatedthatthe mostplausible
physical mechanism which can explain such behaviour
is a fragmented spiral arm of the accretion disk (see
e.g. Jovanovi´c et al. 2010; Lewis et al. 2010, and refer-
ences therein). Perturbing regions could be then ex-
plainedbytheemissivitylumpscausedbyfragmentsin
spiral arms, such as isolated clumps which could pass
through the arm and dominate in its emissivity. The
fragments naturally travel with the arm as it precesses
1.0
Unperturbed line through the disk, but since the outer parts of an ac-
y units) 0.8 xxpp==1106 RRgg,, σσpp==25 RRgg carremtisoncoduilsdkbaereaslseolf-lgaruanvcihtaetdinfgro,mthethfreagomuteenrtrseogfiosnpsiroafl
arbitrar 0.6 xp=26 Rg, σp=10 Rg tshideesd,isiknatnhdepinronperagraetgeioinnwsaorfdth(Leedwiissk,etthael.d2i0s1k0)w.inBdes-
x ( and highly ionized fast outflows could play an impor-
d flu 0.4 tantroleandcouldalsocausethe outwardpropagation
e
v of such clumps (see e.g. Popovi´c et al. 2011; Sim et al.
bser 0.2 2010). Since the flux variabilitycaused by a spiralarm
O
isontimescalesofayeartoseveralyearswhileitsfrag-
0.0
ments cause shorter variations on timescales of several
0.4 0.6 0.8 1.0 1.2 1.4
months,thismodelisabletoexplaintheobservedvari-
g=E /E
obs em
ability of some AGNs on the timescales ranging from
Fig. 4 Top: illustration of perturbed emissivity of an severalmonths to severalyears (Lewis et al. 2010). As
accretion disk in Schwarzschild metric with inclination of itcanbeseenfromFigure4,whenaperturbationwhich
◦
i = 35 , extending from Rms up to 30 Rg for a perturb- originates in the inner regions of the disk and, due to
ing region located at thereceding side of thedisk. Bottom:
some wind or outflow, spirals away along the receding
the unperturbed (solid line) and perturbed (dashed lines)
side of the disk further from the central SMBH and
shapes of the Fe Kα line for a perturbing region located at
toward the outer parts of the disk, it will cause the
three different positions along x-axis and with three differ-
ent widths: a) xp = 10 Rg, σp = 2 Rg, b) xp = 16 Rg, blueward shift of the ”red peak” which will therefore
σp =5 Rg and c) xp =26 Rg, σp =10 Rg move towards the line core. This demonstrates that in
some cases, the deformations of the line profiles could
Such perturbations of the power law disk emissivity arisedue to shifts of some of their parts, causedby the
can be modeled as (Jovanovi´c et al. 2010): variability of the disk emissivity (for more details see
Jovanovi´cet al. 2010).
ε(x,y)∝r(x,y)−q· 1+εp·e−(x−xp)2σ+p2(y−yp)2 , (3)
!
7
3.5 Line shifts in the binary systems of SMBHs twoconstituentunshiftedlineprofilesF1(g)andF2(g)
according to (Jovanovi´c et al. 2014):
Binary systems of supermassiveblack holes are formed
−1 −1
in galactic mergers, and at some stage when two 1 Vrad 1 Vrad
SMBHs become gravitationally bound and start to or- F(g)=F1 g − 1c +F2 g − 2c .
(cid:20) (cid:21) ! (cid:20) (cid:21) !
bit around their center of mass, accretion of the sur-
(4)
rounding matter on both SMBHs could be expected
and as a result, a strong line emission could arise (see
Three such simulated composite Fe Kα line profiles
Popovi´c (2012) for theoretical aspects and Bon et al. emitted during three different phases along the Keple-
(2012); Yan et al. (2015) for observational evidences). rianorbitofaSMBHbinarywithsub-parsecseparation
In such a case, the Fe Kα line might be also observed, between the components are presented in Fig. 5. As
and it would most likely arise from both accretion it can be seen from Fig. 5, Doppler shifts due to the
disks around primary and secondary SMBHs, located orbital motion of the components in the binary have
in a central low density cavity of a circumbinary disk significant influence on the observed composite Fe Kα
(Jovanovi´c et al. 2014). Therefore, the Fe Kα line pro- lineprofilesandinducetheirripplevariability,aswellas
filesemittedfrombothaccretiondisksmightbeaffected the shifts of their parts, especially of the line coresand
by the Doppler shifts due to the orbital motion of the their”blue”wings(formoredetailsseeJovanovi´cet al.
SMBH binary, and in that case the corresponding sig- 2014). Suchshifts andripple variabilityofthe complex
natures would be imprinted in the observed composite FeKαlineprofilesstronglydependontheorbitalphase
line profile (Jovanovi´c et al. 2014). of the binary system, and therefore if observed in the
spectra of some AGNs, they could represent the ob-
1.4
servationalsignaturesofthe existence ofSMBH binary
Phase=0.2
systems in the cores of these AGNs.
s) 1.2 Phase=0.5
nit
u Phase=0.8
y 1
ar 4 Conclusions
r
bit 0.8
r
(a HerewediscusseddifferenttypesoftheFeKαlineshifts
ux 0.6 in AGNs, as well as several phenomena that can in-
fl
d duce them. For that purpose, we performed numerical
e 0.4
v
r simulations of the X-ray radiation from the relativis-
e
s
Ob 0.2 tic accretion disks around single and binary SMBHs,
based on ray-tracing method in the Kerr metric. The
0 obtained results showed that the following effects have
0.4 0.6 0.8 1 1.2 1.4 1.6
a significant influence on the line profiles:
g=E /E
obs em • classical Doppler shift which causes double-peaked
Fig. 5 Composite profiles of the Fe Kα line emitted from profiles of the lines emitted over a whole relativistic
the accretion disks around two SMBHs in a binary system accretion disk, from its innermost regions where X-
duringthreedifferentphasesofitsKeplerianorbit. Thepa- rayradiationoriginates,toitsoutermostpartswhich
rametersoftheSMBHbinarysystemare: massratioq=1, emit in the optical band;
separation between thecomponentsofa=0.01 pc,inclina- • special relativistic transverse Doppler shift and rela-
◦
tion i = 60 , eccentricity e = 0.75, longitude of pericenter
tivistic beaming which cause the redshift of the line
◦
ω =90 and systemic velocity γ =0. Both accretion disks
profile, as well as the relative enhancement of its
surround the slowly rotating Kerr primary and secondary
”blue” peak with respect to the ”red” one, not only
SMBHs with the same spins J/(Mc) = 0.1 (M being the
mass of a SMBH), and both of them extend from Rms to in the case of the broad Fe Kα line which originates
30 Rg, have the same inclinations of 60◦, as well as power from the innermost regions of the disk, but also in
law emissivity indices of p=2 the case of the optical lines which originate from its
outer parts;
Assuming that the radial velocities of the primary • generalrelativisticgravitationalredshiftwhichcauses
and secondary components are V1r,a2d ≪ c so that the the further deformations of the Fe Kα line profile by
corresponding Doppler shifts due to their orbital mo- smearing its ”blue” emission into the ”red” one, as
tion are ≈ V1r,a2d/c, a composite profile F (g) of the Fe wellastheSMBHspinawhichaffectsthe”red”wing
Kα line emitted from both accretion disks of a SMBH ofthe lineby extendingittowardsthe lowerenergies
binary at some orbital phase can be calculated from for the higher values of a;
8
• perturbations of the disk emissivity in form of flares Fabian, A. C.: Emission lines: signatures of relativistic ro-
orbrightspots movingalongthe recedingside ofthe tation, chapterin book ”Theory of Black Hole Accretion
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J. E. Pringle, ISBN: 0521623626. Cambridge University
peak” not only of the Fe Kα line, but also of the
Press, Cambridge, UK,123 (1999)
lines in other spectral bands;
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• DopplershiftsduetotheorbitalmotionintheSMBH
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Acknowledgements This research is part of the Goosmann, R. W., Dovˇciak, M., Karas, V.: Probing the
projects 176003”Gravitationandthe largescale struc- irradiation pattern of AGN accretion disks with future
satellitemissions.SF2A-2007: ProceedingsoftheAnnual
ture of the Universe” and 176001”AstrophysicalSpec-
meeting of the French Society of Astronomy and Astro-
troscopy of Extragalactic Objects”, supported by the
physics, 186 (2007)
Ministry of Education, Science and Technological De-
Hartnoll, S. A., Blackman, E. G.: Reprocessed emission
velopment of the Republic of Serbia. This research is
from warped accretion discs with application to X-ray
also partially supportedby the SEENET-MTP- ICTP iron line profiles. Mon. Not. R. Astron. Soc. 317, 880
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