Line shifts and sub-pc super-massive binary black holes

0.58 MB·

by  Sasa Simic

Line shifts and sub-pc super-massive binary black holes
Saˇsa Simi´c1 • Luka Cˇ. Popovi´c2
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] Abstract Here we discuss the possibility of super- broadand narrow emission lines. Due to the dynamics
A
massive binary black hole (SMBBH) detection, using and composition of the two line emitting regions, how-
G the shifts of the broad lines emitted from a binary sys- ever, the line profiles and shifts are expected to show
. tem. Weperformanumberofsimulationsofshapesand some specific characteristics (see Popovi´c 2012).
h
p shifts of Hβ lines emitted from SMBBHs, taking into Based on the analysis of Very Large Telescope in-
- accountthe emissionfromtwodifferentregionslocated tegral field spectroscopy and Hubble Space Telescope
o
aroundboth black holes, and kinematical effects which (HST) imaging SMBBHs are detected on a kpc scale
r
t should be present in a SMBBH. In the model we con- (see e.g. Woo et al. 2013, 2014), but there is a prob-
s
a nect the parametersof the lines with the mass of black lem to detect the sub-pc scale SMBBHs. It seems that
[ holes andfind that the peak shift depends, not only on sub-pc SMBBHs may be detected only using the spec-
1 kinematical effects of system rotation and black hole tralcharacteristicsofabinarysystem(forareview,see
v mass ratio, but it is also a function of the individual
Popovi´c 2012; Bogdanovi´c 2015).
7 masses of the two black holes (BHs).
The broad lines emitted from an AGN are used
0
0 to probe of the geometry of the broad line region
Keywords line shifts; binary black holes
2 (BLR). The BLR seems to be close to the cen-
0 tral SMBH, since the reverberation technique gives
.
1 1 Introduction the sizes of the BLR as an order of several light
0 days to several light weeks (see Kaspi et al. 2005)).
6
It is widely accepted that mergers play an important There is a group of AGNs that emit very broad and
1
: role in the galaxy formation and evolution, and merg- complex line profiles, which could be interpreted as
v ers of supermassive black holes (SMBHs) are expected two displaced peaks, one blueshifted and one red-
i
X to be present at the centers of a number of galaxies shifted from the systemic velocity defined by the
r (Begelman et al. 1980). In the case that a super- narrow lines, or a single peak shifted line. It has
a massive binary black hole (SMBBH) system is sur- been proposed that such line shapes could indicate a
rounded by gas, one can expect that observational ef- SMBBHsystem (see e.g.Gaskell 1983; Popovi´cet al.
fects may be present as a combination of the accretion
2000; Shen & Loeb 2010; Tsalmantza et al. 2011;
ontooneorbothoftheSMBHsandthedynamicsofthe
Eracleous et al. 2012;Popovi´c 2012;Bon et al. 2012;
binary system (see Popovi´c 2012). In some cases, this
Liu et al.2014;Bogdanovi´c 2015;Runnoe et al. 2015,
couldresultinabinaryActiveGalacticNucleus(AGN)
etc.).
system, that is similar to a single AGN, i.e. the sys-
HerewediscusshowthepresenceofaSMBBHwould
tememitsabroadbandelectromagneticspectrumwith
affecttheshiftofbroadlinesandwhatmightbetheob-
servational consequences. First we describe our model
SaˇsaSimi´c of a SMBBH, and after that we analyze a number of
LukaCˇ.Popovi´c simulations (combining different masses ofcomponents
AstronomicalObservatory,Volgina7,Belgrade and different dynamical effects). The simulations have
1FacultyofScience,RadojaDomanovica12,Kragujevac,Serbia. beenperformedtoinvestigateline shifteffects inbroad
2AstronomicalObservatory, Volgina7,Belgrade,Serbia. lines due to emission from SMBBH. We specifically in-
2
corporatesomeempiricalrelationshipsbetweenthesize lines and they have high red asymmetry (Robinson
of the gas, line intensity and BH masses in the model. 2010; Shapovalova et al. 2015). Recent monitoring
of the same source (performed over an interval of 20
1.1 SMBBH and broad line shift years), however, showed that there is no high vari-
ability in the line profile shapes and shifts, which do
The idea that AGN activity is triggered by mergers is not agree with the predicted long-term variability (see
not new (see Komberg 1968a,b), however it is hard Shapovalova et al. 2015). In spite of observational
to spatially resolve (i.e. direct imaging) a binary sys- facts, one can expect that the line profiles in a long
tem at sub-pc scale at the center of an AGN. There- termperiodshouldvary(seeBon et al. 2012;Popovi´c
fore, spectroscopy is a tool to study some effects of a 2012).
SMBBH in the centers of AGNs. Spectroscopic stud- We should mention here that the highly shifted
ies may provide a method for identifying binary AGNs broad emission lines may indicate two possible sce-
at sub-pc scale, through the search of velocity shifts narios of a SMBBH: i) the case where in a SMBBH
in the complex broad line profile that is caused by system only one component has a BLR, and ii) emis-
orbiting the two BHs around common center of mass sion of the BLR bound to a recoiling SMBH, i.e.,
(see e.g. Gaskell 1983; Boroson& Lauer 2009). How- in the stage following coalescence. There are sev-
ever, it is interesting that of those AGNs, which have eral AGNs with a relatively large shift of the broad
been detected as SMBBH candidates by spectroscopic line components (see e.g. Tsalmantza et al. 2011;
methods, seem to be controversial because the line Eracleous et al. 2012; Runnoe et al. 2015). Among
shifts and shapes may be explained by other phenom- them SDSS J092712.65+294344.0 was the first candi-
ena in the BLR (as e.g. double-peaked lines with dateforarecoilingSMBH(Komossa et al. 2008),with
disc emission, or strong shift and asymmetry due to abroadcomponentblueshiftof2650kms−1 relativeto
inflows/outflows Eracleous et al. 1997; Gaskell 2010) the narrow emission lines. One can expect that both
and/or there are some disagreementswith other obser- SMBH have emitting region. In this case there can be
vational facts (e.g. long-term variability does not show broad lines with specific shapes (see Bon et al. 2012),
expectedthelineprofilevariabilityDecarli et al.2010a; or lines with two peaks. Here we will discuss only the
Shapovalova et al. 2015). case where we have a binary system which has one or
First Gaskell (1983) discussed the shifted emission two broad line emitting regions. We will not consider
lines in light of the SMBBH hypothesis and reported recoiling black holes. Here we perform a number of
about two quasars (see Fig. 1 and 2 in the paper modelstakinginto accountthe dynamicalandphysical
of Gaskell 1983). The broad lines in the quasars effects connected with the masses of black holes and
0945+076and1404+285wereoff-centered(shiftedwith their separations.
respect to the systemic velocity) to -2100 km s−1
and +2700 km s−1, respectively. The idea about
SMBBHs in the center of AGNs has come into focus 2 Model
again nearly three decades later. There is a num-
ber of AGNs that show shifts in their broad emis- In order to explore the shift of the total broad line
sion lines and are good candidates for the SMBBH emission, which is the composite of the emission from
scenario(seeTsalmantza et al. 2011;Eracleous et al. two BLRs located around the SMBH members of a
2012; Runnoe et al. 2015). In the framework of a binary system, we propose a relatively simple model,
SMBBH system there are some expected long term which takes into account the dynamics of the SMBBH
effects that apparently are not confirmed by observa- similarly to Popovi´c et al. (2000) and Shen & Loeb
tions. Let us mention here two interesting cases with (2010). Moreover, our model incorporates the proper-
large shift which may indicates SMBBH system. The ties of the BLRs aroundBHs in more detail; the broad
first case is the AGN 4C+22.25 where Decarli et al. emissionlineparametersarecorrelatedwiththemasses
(2010a) found that the Hβ and Hα lines show very of the central BHs, as revealed by studies involving re-
broad line profiles (FWHM 12,000 km s−1), faint verberation techniques (Wu et al. 2004; Kaspi et al.
∼
fluxes,andextremeoffsets(duetotheredshift)(8700 2005; Peterson 2014).
±
1300kms−1)withrespecttothenarrowemissionlines,
but the line profiles do not vary in a period of 3.1 2.1 Dynamics of SMBBH
years (Decarli et al. 2010a). The second example is
the quasar E1821+643 where the broad Balmer lines Basic theory of motion of binary systems is very well
are redshifted by 1000kms−1 relative to the narrow established. Here we consider the general case where
∼
3
two components with masses m and m and eccen- few tens of light days in diameter (Kaspi et al. 2005).
1 2
tricity e and e revolve around common the center of ThekinematicsoftheBLRcanbeverycomplex,butit
1 2
mass located at a common focus of the elliptical orbit is clear that the properties of the BLR depend on the
of BHs. In such case the major axes of the ellipses are: parameters of the central black hole (Peterson 2014).
Here we use some results obtained from reverberation
R
a = to constrain the BLR parameters, taking into account
1
(1+q)(1+e )
1 the BHs masses in the binary system. We will con-
sider the Hβ line, since the line has been widely used
and
inblackholedeterminationandinthemonitoringcam-
qR
a = , paigns. We also suppose, that other optical lines, such
2
(1+q)(1+e )
2 areFeII or MgII,if they are generatedby same BLR
where R presents the maximum separation between cloud, mimic the behaviour of the Hβ line, although
components and q denotes the component mass ratio similaranalyseoftheir behaviourcouldgiveadditional
m1/m2. At any particular moment during the orbital resultsforourcomputations. Forthereasonofsimplic-
periodonecanfindthepositionofthecomponentswith ity we will suppose the Gaussian line profile instead of
respecttothebarycenterusingthebasicequationofthe Lorentzian, since we are particulary interested in ana-
ellipse: lyzing the line shifts which does not depends much on
a (1 e2) the line profile itself.
ri(t)= i − i . We should note here that the BLRs of two interact-
1 e cos(ωt)
i
− ing BHs (within the small separation (< 1pc)) may be
The period of rotation of such system Porb and significantlyaffectedby the dynamicalinteraction,and
the orbital velocities of components vi(t) are (see itmaycausethattheBLRkinematicsineachBLRcan
Paczynski 1971; Yu & Lu 2001): be different that one observed in the case of the single
centralBH.To avoidit, wetakethatthe BLRsaresig-
RS 3/2 2 108M⊙ 1/2 nificantly smaller than the distance between two BHs,
P =210 × yr (1)
orb
(cid:18)0.1pc(cid:19) (cid:18) m1+m2 (cid:19) andassumethatthe gravitationofablackholeisdom-
inant for the local BLR. In that case we can apply the
empirical relationships obtained from the case of sin-
0.1pc m +m 2m m gle BH. However, there may be some gas around the
v (t)=1.5 103 1 2 1 2 µ
i × s r(t) r2×108M⊙ (cid:20)mi(m1+m2)(cid:21)· i SnMegBleBctHedthinattchaisnmcoondterilb,ustinecteootnhleylianedpetraoifileled,tmhaagtnwee-
(2)
tohydrodynamical study can give the gas distribution
around such complex system, that is out of scope of
withidenotingthetwocomponents(i=1,2),R mean
S
this work. Moreover, such a component probably will
component distance, r (t) represents the i th compo-
i − contribute to the center of line (expected smaller dis-
nent position relative to the common focus as a func-
persion velocity since the emitting gas in this region is
tion of time t. The parameter µ replace expression
i not too close to BHs as the local BLRs), and will have
µ = sin(θ)cos(ωt + (i 1)π), where θ is the angle
i − negligible influence on the total line shift.
between the normal to the orbital plane and the line-
of-sight of an observer (inclination of the orbit) and ω
2.2.1 Estimation of the BLR sizes
angular velocity of the system.
We assume that each component has its own accre-
We estimate the BLR size by using the empirical for-
tion disc that represents a source of emission able to
mulas (Kaspi et al. 2005):
produce broad lines in the BLR.
R λL (5100˚A) 0.69±0.05
BLR λ
2.2 Physical properties of BLRs and broad line =(2.21 0.21) ,
10 lt-days ± 1044 ergs s−1
parameters (cid:20) (cid:21)
(3)
Inthe standardAGNmodelalargeregionofmoderate where λL (5100˚A) is the total disc luminosity at
density (ne ∼ 109cm−3) surrounds the accretion disc, 5100˚A; forλdifferent wavelengths different BLR dimen-
also known as the Broad Line Region – BLR (see e.g.
sions can be computed, e.g., utilizing formulas given
Sulentic et al.2000). WesupposethatmostoftheBLR
by Kong et al. (2006). Here we calculate the con-
isdistributedinsameplaneasaccretiondiscitself,with tinuum emission at 5100 ˚A for each of the two ac-
inner parts overlapping the accretion disc and spans a
cretion discs. Given empirical dependence Eq. 3 is
4
derived for the case of the low and intermediate lumi- We define λL(H ) IHβ, the luminosity of the H
β ≡ λ0 β
nosity quasars, and we will restrict our simulations for line, and substitute the R with its coresponding
BLR
this case. Further computations could be conducted expression from Eq. 4. This allow us to identify the
in the same way on the high-luminosity/high redshift individual contributions of the two components to the
quasars using the empirical relations presented in the total line emission in the binary system.
Kaspi et al. (2007).
2.2.3 The width and shift of Hβ
The disc has the inner radius ρ several R and
in g
∼
outer radius ρ R (R is gravitationalradius for
out ∼ RL g TheHβ linewidthissupposedtobeproportionaltothe
each black hole separately given by Ri = Gmi). The
g c blackholemass,sincemoremassiveBHsinduce higher
outerradiuscanbeestimatedastheradiusoftheRoche
velocities in the BLR (see Peterson 2014).
lobe of two bodies (see Eggleton 1983)
The velocity distribution in the BLR can be esti-
mated based on the viral theorem as:
0.49R x2/3
s
R (x)= ,
RL 0.6x2/3+Log[1+x1/3]) Gm
i
v (m )= ,
BLR i
R
wherex isdefined bythe massratioofthe components r BLR
asfollows: x=q forthe moremassiveBHandx=1/q giving the spectral line width dispersion as σi =
for the less massive one. The inner radius of the disc λHβvBLRc(mi). Note here that the velocity of gas in the
is not exactly equal to the one R since the radiation BLRisadirectfunctionoftheassociatedBHmassand
g
pressure is huge within one R , producing impossible itisnotdirectlytiedintothemassratioq. Thiswillbe
g
conditions for any material to condensate and undergo very important in computing line shifts, since different
laminar motion. This effect is known as Advection- mass combinations can produce the same mass ratio,
DominatedAccretionFlow(ADAF)anditispresentin but different orbital velocities of binary components,
consequently different line shifts and velocity disper-
the case of the spinning black holes described with the
sion.
Kerrmetric(seeNarayan & Yi 1994;Manmoto 2010).
For this reason we adopted that ρi = 3.5Ri as inner The line shift caused by gravitational effects in the
in g close vicinity of the BH can be computed by ∆λi =
radius of the disc. On the other hand the outer disc g
radius is just a half of the corresponding Roche radius Gmi . FortheBLRsizesadoptedinourcomputation,
cRBLR
since the disc can not entirely fill the space defined by however,theproducedline-shift∆λi issmallcompared
g
R (see Yan et al. 2014). to the shifts producedbythe radialvelocities ofbinary
RL
The distribution of temperature over the radius of components. Consequently, one can neglect the effect
the disc follows the power law which in simplified ofgravitationalline shift from the line shape computa-
form is given as T (ρ) ρ−3/4 (Shakura & Sunyaev tion. On the other hand, one should include the shift
eff
1973). The emission mo∼del is assumed to be thermal of lines emitted from different components taking into
in nature and the amount of radiation generated by accountthe dynamics of the system. We take that rest
other mechanisms (inverse Comptonor synchrotron)is wavelength of lines is shifted according to
thought to be negligible for optical and UV bands. In
λ=λ (1+zi ),
order to compute the total amount of radiation com- 0 dopp
ing from the surface of the disc one needs to integrate where zi represents the ratio vi/c, particulary for
dopp r
emission of the entire disc area. This allows the com- each component of the binary system.
putation of the specific luminosity L (5100˚A) that is
λ
usedinEq. 3. Consequently,weconnectthe sizeofthe 2.2.4 The line shapes
BLR with the individual masses of the two BHs and
We calculate line shapes of different configurations of
also with their mass ratio.
SMBBH system as:
2.2.2 The intensity of the Hβ line
I (λ)=I (λ)+I (λ)
tot 1 2
The Hβ line intensityisestimatedusingempiricalrela-
where we assume that each component emits Gaussian
tion given by Wu et al. (2004):
line profile:
λL(Hβ)
logR (lt-days)=1.381+0.684 log .
BLR · 1042ergs s−1 2
(cid:18) ((cid:19)4) Ii(λ)=Ii(λ0)exp λ−λ0·(1+zdiopp) cos(θ)
− √2σi ! 
 
5
(5)
Table 1 Computed values for duration of orbital phases
with i designating the components 1 and 2, λ wave- t[years]andcorrespondingcomponentseparationsrsepp for
0 different dynamical parameters q. The eccentricity of the
lengthofHβlineinlaboratoryframe,andzi Doppler
dopp orbits is taken as e1,2 =e1 =e2 =0.7.
corection for radial component velocities. We also as-
cribe a flat distribution to the BLR, coplanar with the
parameters P /4 P /2 3P /4 P
orbitalplanes ofthe SMBBHs andtherefore definedby orb orb orb orb
q = 1 14.2 28.6 42.8 57.1
the same inclination angle θ.
q = 0.5 11.6 23.3 35.1 46.6
2.2.5 Model constraints and measured line parameters q = 0.25 9.1 18.0 27.1 36.1
r (pc) 0.03 0.017 0.03 0.1
sepp
Firstofall,usingthismodel,onehastoadoptsomecon-
straints: a) since we derive the radius of the BLR from
1.0
the continuum luminosity, one should check if the size
of the BLR fit within the separation between the two
0.8
BH components. In order to avoid semi-detached sys-
temweconstrainourmodelthatR +R <R.
BLR1 BLR2
0.6
In first approximation, even if there are small interac-
IΛ
tions of BLRs,it shouldnothadmuchinfluence onthe
dynamics of binary system, as well as on the emitted 0.4
amount of radiation, since the interacting volumes are
expectedtobequitesmallincomparisonwiththewhole 0.2
region of BLRs. After severaltests, we obtain that the
limiting value of R in considered models is 0.05pc for
4000 4500 5000 5500
masses of the order of 108M⊙. b) As we investigate Λobs@AD
the role of BH mass on the line shapes and shifts, we
eBxHpslo.rce)tTheheraonrbgietaolfpmaarassmeest1e0rs8a−s1w0e9llMas⊙thfoermthaesstrwao- Fanigd.p1artHicβullainrecfoomrpaoBnBenHtsmysatsesmes,wofithmm1a=ssr4at·io10q8=a0n.d5
tio affect the total line shift (see Popovi´cet al. 2000; m2=8·108M⊙. SolidcurvedlineshowsatotalHβlinefrom
component 1 (dashed curved line) and component 2 (dot-
Shen & Loeb 2010). To explore individual mass effect
dashedcurvedline). Verticalstraightlinesdesignateunper-
weconsiderthecasesq=0.25,0.5and1,andweassume
turbed wavelength (dotted line), shift of the peak (dashed
eccentricities e1,2 =e1 =e2 =0.7. line) and centroid (solid line) of combined Hβ line. Note:
We would like to get time-scale estimates for an or- Centroid shift is intentionally slightly displaced from it’s
bital period, which can be used to predict the long- computed position for thereason of clarity.
termeffectsonline-shiftstocompareagainstlong-term
monitoring campaigns for SMBBH candidates. Thus,
δλ =λ λ
wecalculatethetimefordifferentphases(specificsnap- c 0− c
shots)andthecorrespondingseparationsbetweenBHs, The totalline shape ofthe Hβ line generatedby the
testing various mass ratios and maximum separations sub-pc binary system of SMBHs (with masses of m =
1
between the components. 4 108 and m2 = 8 108M⊙) and parameters q = 0.5
· ·
As one can see from Table 1, the changes in the line and R = 0.05 pc is presented in Fig. 1. As we can see
shift (caused by dynamical effects) can be present in in this example, the line shows a complex profile with
a time interval of the order of decades. The calcula- a high blue asymmetry, showing a blue shoulder and a
tion for periods and distances has been performed for redshifted peak. We present the line peak and shift of
a SMBBH system with mass of the smaller component the centroid with vertical lines. In this particular case
equalto 109M⊙ anda distance betweencomponents of the shiftofthe line peakis significantlylargerthanthe
R=0.1 pc. shift of the line centroid.
To explore the shift in SMBBHs and its usage for
detection of binary black holes we measure the shift
of the peak (the maximum of the line). Additionally, 3 Results and discussion
we compute the wavelength of the line centroid and
appropriate shift as: In previous sections we assume that both components
of binary system retain their accretion discs and sur-
I (λ)λdλ rounding BLRs. However,it is of particular interest to
tot
λ =
c I (λ)dλ investigate a system where just the smaller component
R tot
R
6
has BLR, since in that case there is no line combina- and R = 0.05pc. The lower/bottom panels show the
tion with the other component, and the resulting shift largermass casewith m1 =4 109M⊙, m2 =8 109M⊙
· ·
would be more clearly defined. For that reason we will and R = 0.1pc. In both considered cases with in-
discuss two cases in this section: i) both components creasingthe massesofthe BHs,the BLRdiameter also
have a BLR and ii) only the smaller component has a increase, so we intentionally increase separation R to
BLR. avoid mutual interaction of BLRs. As it is well known
(see Popovi´c et al. 2000; Shen & Loeb 2010) during
3.1 The case of both black holes with BLRs anorbitalcycle,thebroadlineprofilebeenchanges,the
asymmetry and shift acquiring different values. How-
In the case of bound BHs orbiting aroundthe common ever, the asymmetry and line profile changes are ex-
barycenter,their massesdetermine the dynamics ofor- pected to be more important in the case where the
bital motion and consequently the shifts of the compo- components have bigger masses ( 109M⊙). The most
nentsthatcontributingtothe shiftoftheobserved(to- interesting is that only in one case∼(panel e) for higher
tal) line profile. As we noted above, we have compute mass case) there is clearly seen a double-peak profile
the shape of the Hβ line for different combinations of that may indicate the emission of two BLRs. These
masses and mass ratios q. We first consider the case of simulationssuggestthattheasymmetricprofilesarefar
q = 1,0.5,0.25, with associated individual BH masses
more prevalent then the extreme double-peak ones.
of m1 =1 108M⊙ andm2 =1,2,4 108M⊙ (see Fig. 2 Note here that different geometries could be ap-
· ·
panels a), b), c)). We than change the individual BH
plied in order to explain the observed broad spectral
masses to m1 = 1 109M⊙ and m2 = 1,2,4 109M⊙ lines components. Double peaked lines could be a
· ·
while keeping the same q ratios as before (see Fig. 2
result of binary system dynamics, but it seems that
panels d), e), f)). In both cases computations here
double-peaked line shapes could be achieved when a
referstothequitespecificconfigurationwithlongitudi-
single AGN has two or more broad line emitting re-
nalalignmentbetweenline-of-sight(LOS)andtheaxes
gions, and if the emission of an accretion disc is domi-
of the elliptical paths of two BHs, for the reason that
nant(Eracleous et al. 1997;Popovi´c 2004;Bon et al.
in such case radial velocities over the LOS are highest
2009;Popovi´c et al. 2011). InthecasethataSMBBH
forthe orbitalphaseP /2andgiveninclinationangle
orb system is emitting double-peaked line profiles, the dis-
θ,withthecomponentsatclosestseparation(seeTable
tances between peaks has to be changed, and also,
1). Consequently a larger line shift during the orbit is
single peaked asymmetric profile can be observed in
expected.
a monitoring campaigns, while in the case of double-
As one can see in Fig.2, when increasing the mass
peaked profiles emitted by the disk one cannot expect
of the second component m , both the intensity and
2 abigchangesintheshiftofthepeaks(Eracleous et al.
the width of the associated line go up. Although the
1997). Additionally, double peaked profiles originated
mass ratio is the same (panels a-d, b-c,c-f), both the
by the disk-like regionusually have a boost in the blue
shift and asymmetry of the total/composite line be-
peak, and extended red wing (Eracleous et al. 1997;
come more prominent in the more massive binary sys-
Popovi´cet al. 2011), that is not a rule in the profiles
tem (panels d-e-f compared to a-b-c). It shows, that
of SMBBHs. The most important difference between
besidethedynamicalparameters(themassratio,phase
doublepeakedlines fromthe disk andSMBBHs is that
andseparations),themassesofcomponentshaveanim-
the line profiles of SMBBHs are changing dramatically
portantinfluenceontheline profilesanddeterminethe
during time (fromsingle to double peaked), that is not
detectability of the effect in SMBBH system. In Table
case for the lines emitted from the disk (see the case
2 we give measured values of the line shifts for compo-
3C390.3 in Popovi´cet al. 2011).
nents (Columns 2 and 3), the total shifts (Column 4)
We should note here that observed broad line pro-
and centroid shift (Column 5). As it can be seen, with
files in AGN can be complex and specific, as we men-
bigger mass of the components the shift stays larger,
tioned above, the double-peaked profiles can be ob-
and consequently the effect of a binary system is more
served in a group of AGN (around 10% of AGN,
pronounced.
see Strateva et al. 2003; Eracleous & Halpern 1994),
With increasing the orbital eccentricity of BHs line
which seems to be emitted from a disc-like geome-
shifts could be more defined in some particular phases
try. On the other side, it seems that we can di-
of the orbit with minimum separation between com-
vided the AGN using the width of their profiles
ponents. For that reason we compute the shape of the
(as e.q. FWHM>4000 km s−1, see Sulentic et al.
totalHβ spectrallinefordifferentphases,seeFig. 3. In
2009; Zamfir et al. 2010; Marziani et al. 2010) where
upper/toppanels wepresentthe caseoflow masscom-
broader lines show a red/blue asymmetry. Comparing
ponents with masses m1 =4 108M⊙, m2 =8 108M⊙
· ·
7
1.0
q=1 a) q=0.5 b) q=0.25 c)
m =10 8M m =2‰108 M m =4‰10 8M
0.8 2 s 2 s 2 s
0.6
Il
0.4
0.2
1.0
q=1 d) q=0.5 e) q=0.25 f)
m =10 9M m =2‰109 M m =4‰10 9M
0.8 2 s 2 s 2 s
0.6
Il
0.4
0.2
4000 4500 5000 5500 4000 4500 5000 5500 4000 4500 5000 5500
lobs@AD lobs@AD lobs@AD
Fig. 2 Hβ lineshiftsfordifferentmassratioq andmassofcomponents(givenon plots). Infirstrow(panelsa),b),c))the
maximumBHcomponentseparation isR=0.05pc, whileinthesecondraw(panelsd),e) andf))themaximumseparation
is R=0.1pc.
1.0
t[years] = 0 a) t[years] = 1 b) t[years] = 2 c) t[years] = 3 d)
0.8 ddllc==--142658 kkmm//ss ddllc==--130334 kkmm//ss ddllc==110701 kkmm//ss ddllc==219973 3k mkm/s/s
m m m m
0.6
Il
0.4
0.2
0.0
1.0
t[years] = 4.1 e) t[years] = 5.1 f) t[years] = 6.2 g) t[years] = 7.2 h)
0.8 ddllc==351682 4k mkm/s/s ddllc== 219973 3kmkm/s/s ddllc==110701 kkmm//ss ddllc==--130334k kmm/s/s
m m m m
0.6
Il
0.4
0.2
4000 4500 5000 5500 4000 4500 5000 5500 4000 4500 5000 5500 4000 4500 5000 5500
lobs@AD lobs@AD lobs@AD
1.0
a) t[years]= 0 b) t[years]= 0.9 c) t[years]=1.8 d) t[years]=2.7
0.8 dlc= -305 dlc= -241 dlc= 234 dlc= -21
dl = -2734 dl = -1961 dl = 343 dl = -8649
m m m m
0.6
Il
0.4
0.2
1.0
e) t[years]=3.7 f) t[years]=4.6 g) t[years] = 5.5 h) t[years]=6.4
0.8 ddllmc==--71133442 ddllcm== --281649 ddllcm== 233443 ddllcm== --2149161
0.6
Il
0.4
0.2
4000 4500 5000 5500 4000 4500 5000 5500 4000 4500 5000 5500 4000 4500 5000 5500
lobs@AD lobs@AD lobs@AD lobs@AD
Fig. 3 The total Hβ line profiles during full orbits for two SMBBH systems. Upper panels (from a) to h) are given for
the mass m1 =4·108M⊙ and R=0.05pc, and lower panels (from a) to h) for m1 =4·109M⊙ and R=0.1pc. For both
systems we fixed q = 0.5 and e1 = e2 = 0.7. Dashed and dot-dashed lines represents contributions of the components to
the total Hβ lines (solid lines). In the panels from a) to h) we indicate the corresponding phase t in years, line centroid
shift δλc and peak shift δλm in km/s on each plot.
8
Table 2 Numerical values of shifts presented in Fig. 2. First Column denotes the corresponding panel in Fig. 2, second
andthirdColumnstheshiftofpeaksforcomponents,respectively. Infourthandfifthcolumnsaregivenshiftsofpeakand
centroid of the total line profile, respectively.
panel δλ1 [km/s] δλ2 [km/s] δλ [km/s] δλ [km/s]
m m m c
a) -3450 3696 -110 32
b) -5711 3050 1266 278
c) -8915 2405 1935 451
d) -7828 8156 -6268 -110
e) -12881 6718 6482 333
f) -20042 5294 5282 630
our, modeled broad line profiles with observations we
found that (see Fig. 3) all type of line profiles in the
case of a SMBBH is expected. If there is a SMBBH
with smaller masses, we can expect relatively narrow
andsymmetric broadline profiles during 2/3 of the or-
biting period, in the case of a massive SMBBH, the
è line profiles are mostly asymmetric. Therefore, to find
è è
5000 more evidence about the structure of emitting system
(SMBBH vs. complex BLR), a long-term monitoring,
4000 è è
and analysis of the line profile (shift, width and inten-
-1Ds 3000 sity) variation is needed.
m The time evolution of the total line peak shift and
∆Λ@k 2000 è è line centroidshift forthe two casesshownin Fig. 3 are
presented in Fig. 4. It is obvious that the peak shift is
1000
more prominent than the centroid shift. However it is
0 è è èè èè è è è è è è è èè èè è è interesting that only in a relatively short time-window
è è è è
(several years, see Fig. 4), the line shift is significant
0 2 4 6 8
and could be easily measured, whereas, for about 3/4
t@yearsD
è of a period the shift has small values.
è è
We should note here, that some previous studies of
è è
a large number broad line AGN seem to suggest that
10000
è è blue-shifted peaks are more prevalent than redshifted
ones(seee.g.Zamfir et al. 2010;Marziani et al. 2013)
-∆Λ1@Dkms 5000 tahlsaotscuapnpnoorttsbetheexpfalactintehdatbythSeMloBnBgHtehrmypoobthseersvisa.tiTohniss,
whichcanindicatethechangesinthelineshift,maybe
0 è è èè èè è è è è è è è èè èè è è used for detection of a SMBBH system.
è è
è è 3.2 SMBBHs with one BLR
0 1 2 3 4 5 6 7
t@yearsD For a compact binary system there is a possibility that
Fig. 4 Thecorrespondingshifts (dotedline)andlinecen- justoneBHhastheBLR(seee.g.Armitage & Natarajan
troidshifts(dashedline)forthecasesgiveninFig. 3. Upper 2002;Hayasakiet al. 2007;Cuadra et al.2009;Lodato et al.
panelcorrespondstothecaseoflowermassesofcomponents 2009; Popovi´c 2012).
(upperpanels in Fig. 3). Good examples of subparsec BBH quasar are PG
1302-102 reported by Graham et al. (2015) and Mrk
231, see Yan et al. (2015), recently suggested via ei-
ther periodical variations or peculiar continuum spec-
trum. PG1302-102isdescribedasabinarySMBHpair
with a total virial mass of 108.5M⊙, with observed pe-
riod limiting the separation between the pair to 0.01
9
pc. This means that the system has evolved well into
Table3 CentroidshiftforsingleHβ linepresentedinFig.
the finalparsecscale,withtwocomponentsignificantly 5. The first three rows of data are for the case when m2 =
different in their mass, as it can be concluded from fit- 1,2,4·108M⊙, while last three rows are for m2 = 1,2,4·
tingthespectrallinesofHydrogenseries(seetheirFig. 109M⊙.
4). Also, Mrk 231 binary is high mass ratio system
(q 50), with unique features in the optical-to-UV q δλc[km/s]
∼ 1
spectrum and the intrinsic X-ray weakness. In both
1 -1844
cases the emissionfrom the smallBH component dom-
0.5 -3047
inates and the disk associatedwith the big BH compo-
0.25 -4745
nent emits little ionizing photons.
1 -4517
In such case the observedHβ line is a singlet, which
0.5 -7440
could be shifted around the rest wavelength. It is of
0.25 -11578
particular interest to analyze the case when a compo-
nent with bigger mass is without BLR. This is more
probable scenario since there is a bigger chance that Also, in this case, we obtain that shifts in the single
smaller mass component retain it’s accretion disc and componentdependsonthemass,asexpected. However,
BLR. if we have the same mass ratios, one can expect that
the shift will be larger in the higher mass system. As
a) one can see in Table 3, when the mass is increased by
1.0
an order of magnitude, the shift increases 2-3 times.
Line shifts in the single BLR case is caused by the
0.8
orbital motion of the smaller component. Our com-
putation in Fig. 5 is performed for the highest radial
Il 0.6
velocity. As we can see in Fig. 5, and Table 3, for
both considered cases (a) and b)), the shift is, approx-
0.4
imately, a linear function of the mass, i.e. δλc m .
1 ∼ 2
This is in accordance with expectations since with in-
0.2
crease of m , the center of mass of the system is closer
2
to bigger component, and smaller component will have
1.0 b) higher radial velocity, producing higher line shifts.
In Fig. 6 we show the time-evolution for the line
0.8 centroidandshiftoverafullorbitalperiodoftherather
peculiar system we simulate. We note that the line is
Il 0.6 very symmetric at all phases, so the line asymmetry as
showninthecaseoftwoemittingBLRs,cannotbeseen.
0.4 Asystemlikethiscannotaccountforhighlyasymmetric
lines that show complex profiles.
0.2
4000 4500 5000 5500 4 Conclusion
lobs@AD
In this paper we consider the possibility to detect the
Fig. 5 The Hβ line from a single BLR associated with
the lower mass BH component of binary system. Panel a) line shift of SMBBH systems. To investigate the shift
presentsthecomputationforparameterR=0.05pcandthe effectwe developa model, whichis taking into account
mass of the bigger component having values m2 = 1,2,4· the dynamical effects similar to Popovi´cet al. (2000)
108M⊙. Panel b) shows the case of R = 0.1pc and m2 = and Shen & Loeb (2010), but in contrast with models
1,2,4·109M⊙. Usedlinedesignationsare: dottedlineq=1, givenin these papers,we include physicalproperties of
dashed line q=0.5, and solid line q=0.25.
the emitting regions in both components of a SMBBH
system. We constrain the radius of the BLR taking
AswecanseeinFig. 5andTable3wherewepresent
into account the emission of the continuum at 5100 ˚A
the computations for the case of just a lower mass BH
(estimatedfromdiscemissionaroundcomponents),the
containing it’s BLR, the total shift of the Hβ line is
intensity of the Hβ line of each component considering
significantly greater than the shift in the case of the
empiricalrelationshipbetweentheHβlineintensityand
combined line produced by two BLRs.
10
01..80 tll[cmy==e a 25r90s2]63=2kk m0m//ss a) ltl[mcy==e a 24r66s8]58=7kk m1m//ss b) tll[cmy==e a 91r05sk]8m=km/ s2/s c) d) tll[cmy==e a --4r7s35]08=82 k3kmm//ss
Il0.6
0.4
0.2
01..80 e) tll[cmy==e a --6r1s51]05=91 k44mk.1m/s/s f) tll[cmy==e a --4r7s35]08=82 k5kmm.1//ss tll[cmy==e a 91r05sk]8m=km/ s6/.s2 g) tll[cmy==e a 24r66s8]58=7kk m7m./2/ss h)
Il0.6
0.4
0.2
4000 4500 5000 5500 4000 4500 5000 5500 4000 4500 5000 5500 4000 4500 5000 5500
lobs@AD lobs@AD lobs@AD lobs@AD
Fig. 6 The Hβ line for the case where only the lower mass BH in the binary system retains its emmiting BLR. Given
parameter are same as in Fig. 3, butfor single line.
the BLR radius, andfinally the line velocity dispersion andwidthoflinesarelargerinthecaseofmoremassive
using the virial theorem. This model allows to explore SMBBHcomponents(>109M⊙)andtheyareeasierto
timevariabilityofthelineparameters(shift,widthand detect. During a period of revolution of binaries, one
intensity)ofaSMBBHsystemduringanorbit,andcan can expect that shift is changing form blue to red or
be applied for modeling of long term spectroscopic ob- vice versa, therefore the systematic shift to the blue or
servations of the SMBBH candidates. We perform a red in a period can indicate presence of a SMBBH.
number of simulations, changing the masses of compo- Basedonthedynamicaltime-scaleofbinaryBHsys-
nents exploring how it’s (not only the mass ratio that tem we could say that the probability of detection of
isusuallyisconsidered)affectthelineprofiles. Herewe such an objects is rather moderate, since the the peri-
consideredtwocases: A)bothBHshaveaBLR,andB) odsofthe orbitingareinrangeoffewyearsto few tens
only the smaller BH has a BLRFromour investigation of the years. However, other parameters also has big
we can outline following conclusions: influence, such are individual masses, mass ratio, incli-
In the case A) nations, etc., which consequently lower the probability
(i) Beside the dynamical parameters and the mass of detection binary system.
ratioinaSMBBHsystem,the massofcomponentshas Asasummarywecanconcludethat,besidedynami-
animportantroleintheobservedlineprofiles. Itseems caleffects,thetotalmassofaSMBBHhasinfluenceon
that low mass components (with total mass smaller the line shift and profile shape. Consequently, the ob-
than108M⊙)willonlymoderatelyaffectthe broadline servationaleffects inthe broadlines seemtobepresent
profiles. Consequently,thedynamiceffectofbinarysys- in massive systems (> 109M⊙). However it is a ques-
tem can be dominated by kinematical effects in BLRs tioniftheeffectsofaclosebinarysystemcanbeseenin
and probably they are not good candidates for detec- lowmassBHs,i.e. alargenumberofSMBBHsmaygive
tion of SMBBHs using broadlines. The SMBBHs with ordinarybroadlineprofileswhicharetypicalforasingle
biggermasses (>109M⊙) seems verypromising for de- AGN.Therefore,spectralmonitoringofSMBBHcandi-
tection using SMBBHs broad lines. The line profiles datescanbeveryusefulforconfirmationoftheirbinary
show a complex shape, and line peak can be signifi- nature,i.e. thevariationinthebroadlineprofiles(shift,
cantly shifted. width and intensity) should be present, and this varia-
(ii) The line shapes are changing during an orbit of tionhas to have a periodicalor quasi-periodicalnature
SMBBHs showingthe double-peakedprofile(two sepa- following the orbiting period of a SMBBH.
rated peaks) only in a short period in the case of mas-
sive black holes. This indicates that the double-peaked Acknowledgements
profilesmaybenotcharacteristicprofilesobservedfrom This work is a part of the project (176001) ”Astro-
SMBBH,i.e. onecanexpecttoobservemorefrequently physical Spectroscopy of Extragalactic Objects,” sup-
the asymmetric profiles from SMBBHs, and also some ported by the Ministry of Science and Technological
shoulders in the line profiles. Development of Serbia.
In the case B)
(iii)Asitiswellknown,theemissionofasingleBLR
in SMBBHs gives single shifted line, however,the shift