Predicting the broad lines polarization emitted by supermassive binary black holes
mmanuscript no. SMBBH_pol_arx c (cid:13)
Predicting the broad lines polarization emitted by supermassivebinary black holes -D. Savi´c , , F. Marin , and L. ˇC. Popovi´c , Astronomical Observatory Belgrade, Volgina 7, 11060 Belgrade, Serbia Université de Strasbourg, CNRS, Observatoire Astronomique de Strasbourg, UMR 7550, 11 rue de l’Université, F-67000 Stras-bourg, France Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia e-mail: [email protected] Received October 16, 2018; accepted December 16, 2018
ABSTRACT
Context.
Some of Type-1 active galactic nuclei (AGNs) are showing extremely asymmetric Balmer lines with the broad peak red-shifted or blueshifted by thousands of km s − . These AGNs may be good candidates for supermassive binary black holes (SMBBHs).The complex line shapes can be very well due to the complex kinematics of the two broad line regions (BLRs). Therefore anothermethods should be applied to confirm the SMBBHs. One of them is spectropolarimetry. Aims.
We rely on numerical modeling of the polarimetry of binary black holes systems since polarimetry is highly sensitive togeometry, in order to find specific influence of supermassive binary black hole (SMBBH) geometry and dynamics on polarizedparameters across the broad line profiles. We apply our method to SMBBHs in which both components are assumed to be AGNs withdistances at the sub-pc scale.
Methods.
We use a Monte Carlo radiative transfer code that simulates the geometry, dynamics and emission pattern of a binarysystem where two black holes are getting increasingly closer. Each gravitational well is accompanied by its own BLR and the wholesystem is surrounded by an accretion flow from the distant torus. We examine the emission line deformation and predict the associatedpolarization which could be observed.
Results.
We model scattering induced broad line polarization for various BLR geometries with complex kinematics. We find thatthe presence of SMBBHs can produce complex polarization angle profiles ϕ and strongly a ff ect the polarized and unpolarized lineprofiles. Depending on the phase of the SMBBH, the resulting double-peaked emission lines either show red or blue peak dominance,or both the peak can have the same intensity. In some cases, the whole line profile appears as a single Gaussian line, hiding the truenature of the source. Conclusions.
Our results suggest that future observation with the high resolution spectropolarimetry of optical broad emission linescould play an important role in detecting sub-pc SMBBHs.
Key words.
Galaxies: active galactic nuclei – black holes – polarization – scattering
1. Introduction
According to the standard paradigm, every massive galaxy is ex-pected to host a supermassive black hole (SMBH) in its cen-ter (Kormendy & Richstone 1995). The typical mass range ofthose black holes is ranging between 10 and 10 , with few ex-amples of 10 solar masses cases (Shemmer et al. 2004; Walkeret al. 2014; Zuo et al. 2015). The mass of the SMBH slowlyevolves with time (Vika et al. 2009) and is tightly correlatedwith the properties of the host galaxy it resides in (e.g., bulgemass,velocity dispersion, see Kormendy & Ho 2013). It is thencrucial to better understand the evolution of SMBH in order toconstrain galaxy formation models. If accretion of matter fromthe surrounding environment is a natural way to increase themass of the SMBH, it is a slow process that has di ffi culties toexplain the most massive cases (Mayer et al. 2010). In addition,only 60% of the accreted mass is e ff ectively transferred into thepotential well, the rest being converted into high energy radia-tion (Dobbie et al. 2009). Another hypothesis for the evolutionof SMBH is via mergers with other SMBHs (Volonteri et al.2003a,b). On large scales, dynamical friction is the main pro-cess that brings the SMBHs closer (Begelman et al. 1980) but once the merging of the two host galaxies has been achieved,the final parsec problem onsets (Milosavljevi´c & Merritt 2003).Dynamical friction becomes ine ffi cient when the two SMBHsform a bound binary; the system has no options to release en-ergy and transfer angular momentum. One possible solution isthat the spinning black holes lose energy by emitting gravita-tional waves (GW, Begelman et al. 1980). The first discovery ofGWs with frequency ∼ Hz coming from stellar-mass binaryBHs (Abbott et al. 2016) is a huge advancement in general rel-ativity. The GW frequency for SMBBHs with mass range from10 – 10 M (cid:12) falls in the range from nanohertz to milihertz bandand so far, none have been detected. In this frequency regime,pulsar timing arrays (PTAs, Shannon et al. 2015) can be used fordetecting GW by monitoring pulses from millisecond pulsars,however we are still waiting for the detection of such signaturesthat should be numerous. The occurrence of long-lived binarySMBHs signals appears to be too rare. Hence, are there reallybinary SMBHs?Finding observational evidences of binary SMBHs is a dif-ficult task. First of all, it is hard to spatially resolve at pc-scalethe central part of the nearest galaxies with existing telescopes, Article number, page 1 of 20 a r X i v : . [ a s t r o - ph . GA ] D ec & A proofs: manuscript no. SMBBH_pol_arx therefore one has to find other methods to search for sub-pcSMBBHs. The emission of broad, double-peaked Balmer emis-sion lines observed in the spectra of several active galactic nuclei(AGN) may (not) be associated with binary systems (Eracleous& Halpern 2003; Eracleous et al. 2009). During the merging ef-fect of two galaxies, in a sub-pc phase of SMBBH system, thereis enough gas which may produce an activity similar to the oneobserved in AGNs (Popovi´c 2012). Since AGNs have some com-parable and well-known spectroscopic characteristics, one of thepromising methods of the SMBBH detection is broadband spec-troscopy, i.e. observations in a wide wavelength band includingthe emission lines (see Popovi´c 2012, for review) can give someindications for SMBBH presence in the center of some activegalaxies (see e.g. Bon et al. 2012; Graham et al. 2015; Li et al.2016).According to the standard theory, AGNs are powered by asupermassive black hole that releases tremendous amounts of en-ergy throught accretion processes. A thermal continuum is aris-ing from the accretion flow and line emission is dominated byemission from the so-called broad-line region (BLR) that sur-rounds the accretion disk. (Gaskell 2008, 2009). The BLR isa rotating, turbulent disc that is both optically and physicallythick, and probably composed of numerous cloudlets of ionizedgas. When this distribution of gas is seen face-on (i.e., fromthe AGN polar direction, which is free of opaque media) wesee centrally-peaked line profiles. When the BLR is seen at adi ff erent inclination, a characteristic double-humped “disk-like”profile appears (Eracleous & Halpern 2003). However a signif-icant fraction of AGNs show broad-line profiles that cannot beexplained by this axisymmetric BLR model (see, e.g., Capriottiet al. 1979; Meyers & Peterson 1985; Netzer 1990; Gaskell &Klimek 2003; Shapovalova et al. 2016, etc.). They show strongasymmetric displaced BLR peaks with the broad peak redshiftedor blueshifted by thousands of km.s − . According to Boroson &Lauer (2009) those signatures could be due to a binary SMBHsystem, resembling a spectroscopic binary. As it was discussedby Popovi´c (2012), the broad line profiles and their variabilitymay indicate the SMBBH presence, however an additional evi-dence is needed to check it, as e.g. γ -ray and X -ray emission orpolarization in the broad emission lines.To test this hypothesis polarimetry is a natural tool sincethe geometry of the emitting and scattering system is expectedto produce polarimetric features that are easily distinguishablefrom model to model (Goosmann & Gaskell 2007; Marin et al.2012; Goosmann et al. 2014). A single SMBH surrounded bycoplanar cylindrically-shaped scattering regions produces verylow amounts of polarization when seen from a close to pole-on inclination (Marin et al. 2012). The polarization in the lineshares similar values as the continuum and shows characteristic,wavelength-dependent variations across the line profile(Smithet al. 2002; Afanasiev et al. 2014). The polarization angle acrossthe line profile for a single SMBH can indicate Keplerian-likemotion, and consequently can be used for the black hole massmeasurements (Afanasiev & Popovi´c 2015; Savi´c et al. 2018).The case of extremely asymmetric Balmer lines with large red-shifted or blueshifted peaks could not be tested since the spec-tropolarimetric signal for binary SMBHs, each surrounded by itsown BLR, is not known.There is a number of publications which consider the broadline shapes of AGNs in the case of sub-pc SMBBHs (see e.g.Gaskell 1983; Popovic et al. 2000; Shen & Loeb 2010; Eracleouset al. 2012; Simi´c & Popovi´c 2016; Nguyen & Bogdanovi´c 2016,etc.), while the polarization e ff ects in the line profiles was neverconsidered in details. Exception is the observations (Robinson et al. 2010) and theoretical consideration (Piotrovich et al. 2017)of the shift of polarized broad lines for a kicked supermassiveblack hole. Robinson et al. (2010) gave an observational evi-dence that quasar E1821 + may be an example of gravita-tional recoil, i.e. they found that broad Balmer lines indicate thekick o ff velocity of ∼ − in polarized light. Piotrovichet al. (2017) also considered recoiling black hole, taking thatkick radius is similar to the BLR dimension and found that po-larization data in this case can give an estimation of the kick o ff velocity.The purpose of our study is to explore, for the first time, thepolarization parameters across the broad lines in the case of anemission by a sub-pc scale SMBBH system. By doing so, we aimto predict what should be the observational signature we expectfrom those yet-to-be-confirmed sources. We consider a model ofsub-pc supermassive binary black holes, where each of the BHcomponents has own accretion disk and BLR. We consider equa-torial scattering of such complex system on the inner part of thetorus, and we modeled the Stokes parameters which can be ob-served from the system. The paper is organized as followed: InSection 2 we describe the model and the basis parameters of themodel which we used to calculate the polarization parameters. InSection 3 we present and analyze obtained results of our simula-tions, where we take di ff erent parameters of SMBBHs. Finally,in Section 4 we discuss our results and in Section 5 we outlineour conclusion.
2. Model setup
We model SMBBH system as two black holes orbiting aroundthe common center of mass under the force of gravity. This is awell known problem for which it was shown that it is equivalentto the problem of a single body with reduced mass µ moving inan external gravitational field (Landau & Lifshitz 1969) which isdetermined by the total mass of the system: M = M + M , (1)where M is the total mass, and M and M are masses of eachcomponent. The reduced mass µ is µ = M M M . (2)In general, the body µ moves in elliptical trajectory with semi-major axis a and eccentricity e . The relationship between theorbital period P , orbital frequency Ω , M and a is given by theKepler’s third law: Ω = π P = (cid:114) GMa , (3)where G is gravitational constant. This relation is valid for anyeccentricity e . Each component is moving around the center ofmass in elliptical orbit with the same eccentricity e . Both ellipseslie in the same plane and have one common focus. The semi-major axes are inversely proportional to the masses: a a = M M , (4) The quasar has highly shifted Balmer lines around 1000 km s − anda red asymmetry (see Shapovalova et al. 2016)Article number, page 2 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes and they satisfy the equation: a = a + a . (5)Our goal is to create a simple, yet comprehensive model, withoutintroducing hydrodynamic simulations and three body problemsolving. A second model, based on hydrodynamic simulationsis presented in Section 3.4. In this work, we are considering thecase with e =
0, i.e. orbits are circular. and with both black holeshaving the same mass M = M = × M (cid:12) , i.e. the mass ratio q = M / M = ff ectively lowers the kick velocity (Dotti et al. 2010).The timescale of the angular momentum aligning with the indi-vidual spin of each component is few hundreds of times shorterthan the timescale for which the angular momentum of the bi-nary aligns with the angular momentum of the inspiraling cir-cumbinary gas, unless the mass ratio is extreme (Miller & Krolik2013). In case that the accretion occurs in the opposite directionof the binary rotation, there will be a misalignment of variousaxes on a timescale of the order of a fraction of the whole bi-nary evolution time. As was mentioned above, each black holehas an accretion disc surrounding it, from which the isotropiccontinuum radiation is emitted. We used point source approxi-mation for disc emission with emissivity given by a power law: F C ∝ ν − α where α is spectral index equal to 2. Both black holesare surrounded by the BLR. Depending on the distance betweenthe black holes, we treated four di ff erent SMBBH cases: distant , contact , mixed and spiral . We modeled BLR with flared-diskgeometry (Goosmann & Gaskell 2007) with half-opening angleof 25 ◦ which gives a covering factor of the order of 0.1 (Net-zer 2013). The size of the BLRs were set to few light days withBLR inner radius R BLRin = R BLRout = − (Peterson et al. 2004; Kaspi et al. 2005). This wasdone for all cases except for the spiral one. Distant:
Both BLRs are distinctive and each black holea ff ects only the dynamics of the BLR it is surrounded with.Each BLR cloud has two velocity components: Keplerian mo-tion around the black hole plus additional motion due to the bi-naries orbiting each other (see Fig. 1, top panel). Black holes areat the orbital distance a = . q = . q = . R BLR ∝ L . (Kaspi et al.2005). We used mass luminosity relation M BH ∝ L . (Woo &Urry 2002) in order to obtain the BLR size depending solely onmass of each component. An illustration for these two cases isshown in Fig. 2. Contact:
Black holes are separated by a = . Mixed:
For this model, black holes are much closer to eachother, at the orbital separation of 3 light days and with orbitalperiod of 1.2 years. On Fig. 1, third panel, clumps denoted inred are the ones with additional chaotic component, while forthe rest we calculated velocity as if in the center was a singleSMBH with mass equal to the sum of binary components.
Spiral:
Hydrodynamic simulations involving subparsecSMBBHs have shown that black holes are surrounded by a com-mon circumbinary (CB) disc. Accreting gas around the binariesforms a low density cavity inside the CB disc (MacFadyen &Milosavljevi´c 2008; Cuadra et al. 2009). It was found that the ac-cretion streams are in the form of spiral arms with higher densitythat is connecting mini accretion disk of each black hole with thesurrounding CB disk (Noble et al. 2012; Shi & Krolik 2015). Inthis scenario, the cavity is of the order of a , and the CB disk ex-tends from 1 . a to 3 a . Following the similar setup as Smailagi´c& Bon (2015), we built a SMBBH model with spiral arms andthe surrounding CB disk in order to investigate the polarizationsignatures coming from the SMBBH. We keep the same mass ofeach component to be 5 × M (cid:12) with the orbital separation thesame as in the case for contact model a = . R = a e b φ < R ( φ ) < R = a e B φ , Article number, page 3 of 20 & A proofs: manuscript no. SMBBH_pol_arx
Fig. 2: Distant model with mass ratio q = . q = . ff set from the xy plane.where b and B are parameters describing the wrapping of the spi-rals. We chose wrapping parameters to be B = .
55 and b = . b and B were chosen in order to havetwo distinct spirals with single winding and to avoid mixture orinteraction of the spirals. We chose the half-opening angle for thespirals and the CB disk to be 20 ◦ . An illustration of the modelis shown at Fig. 3. For kinematics of the spirals, we used therotation of absolute rigid body, i.e. the spirals are stationary inthe rotating reference frame of the SMBBH. The CB is underthe Keplerian motion around the common center of mass. Thesystem is again surrounded by the same scattering region as inprevious models, with the same radial optical depth in the equa-torial plane.The BLR is represented by thousands of clumps. The volumefilling factor of the BLR of 0.25, as constrained from simulationsand observations (Marin et al. 2015). Total number of clumps permodel as well as the other parameters used in the model are listedin Table 1 Optical continuum and line polarization properties typicallyfound in Type-1 objects can be produced by electron scatteringof a flattened distribution that is surrounding the accretion diskand the BLR (Antonucci 1984; Smith et al. 2005). The scatter-ing region is modeled with flared-disk geometry with inner andouter radius of 0.1 and 0.5 parsec. The half-opening angle is 30 ◦ with respect to the equatorial plane. Electron concentration ischosen in such a way that the total radial optical depth in theequatorial plane for Thomson scattering is 3, which is enough toproduce typical degree of polarization that is found in Type-1 ob-jects (Marin et al. 2012). An illustration of the scattering regionsurrounding the central engine is illustrated on Fig. 4 Fig. 3: SMBBHs (black circles) with spiral arms surrounded bya CB disk. Each spiral is modeled with 500 clumps. The CB ismodeled with 1000 clumps. Color bar is denoting the verticalo ff set from the xy plane. xy xz Fig. 4: Cartoon illustrating equatorial scattering region. Left fig-ure shows the face-on view, while on the right the same geome-try is shown when viewed edge-on. An example is shown for thecase with the two BLRs being separated. The BLRs are shownin yellow. Scattering region is denoted in grey.
Assuming that AGN polarization arises predominantly fromscattering in non-jetted systems, we apply full 3D radiative trans-fer with polarization using the publicly available code stokes (Goosmann & Gaskell 2007; Marin et al. 2012, 2015; Marin2018; Rojas Lobos et al. 2018). It is based on Monte Carlo al-gorithm, for which a vast literature already exist, and with 3Dkinematics fully implemented in spherical coordinates. The codefollows the trajectory of each photon through the model space,from their creation, until they are being registered by the webof virtual detectors positioned all over the sky. The net Stokesparameters I , Q , U and V are thus being determined and otherphysical quantities may be inferred, namely degree of linear po-larization (PO), polarized flux (PF) and polarization position an-gle ( ϕ ). Originally, the code was developed for studying opticaland UV scattering induced continuum polarization in the radio-quiet AGNs, but nowadays it is widely used for studying polar- Article number, page 4 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes
Table 1: Description of the 3 SMBBH model. V and V are orbital velocities and q is the mass ratio.Model Orbital separation a Orbital period P Number V V qlight days years of clouds km s − km s − Distant 47.65 75.0 2000 1639 1639 1.0Distant 47.65 75.0 2000 1093 2186 0.5Distant 47.65 75.0 2000 298 2980 0.1Contact 16.68 15.5 1600 2771 2771 1.0Mixed 2.978 1.2 1000 6558 6558 1.0ization of many astrophysical phenomena (Marin & Goosmann2014). We used the intermediate 2.04 version of the code stokes which is not yet publicly available . We adopt the same conven-tion as Goosmann & Gaskell (2007): we defined ϕ to be 0 ◦ whenthe polarization angle is perpendicular to the projected symme-try axis of the model. When ϕ is 90 ◦ , the polarization angle isparallel to the symmetry axis of the model.
3. Results
We simulated the di ff erent SMBBH scenarios presented in theprevious section with di ff erent kinematics of the BLR dependingon the model. In the following, we thoroughly investigate theresults for each case. For clarity and easy comparison, we presentthe results of a model with a single SMBH in the center withmass M bh = M (cid:12) , so the reader could have a clearer picturewhen comparing the results for a single SMBH scenario witha SMBBH. The result of the single SMBH model is given inFig. 5, the results for a SMBBH with the same center of mass inFig. 6 and the numerous results for all the SMBBH scenarios areshown in Appendix.For Type-1 objects, for a single case scenario i. e. a singleblack hole and a single BLR surrounded by a dusty torus, inthe case for equatorial scattering, the ϕ shows symmetric swingaround the line center (Smith et al. 2005; Afanasiev et al. 2014;Afanasiev & Popovi´c 2015; Savi´c et al. 2018). This feature wasvery well observed in few objects (e.g. Mrk 6, NGC 4051, NGC4151) and can be used for measuring masses of SMBHs us-ing polarization of broad line profiles (Afanasiev et al. 2014;Afanasiev & Popovi´c 2015; Savi´c et al. 2018). In Figs. 6 (panel a) and A.1 we show the simulated ϕ -profiles fortwo viewing inclinations i and for di ff erent azimuthal viewingangles φ . We can see that profiles of ϕ are complex and dif-fer much from the profiles for the single black hole scenario.For a fixed viewing φ the ϕ -profiles show similar profiles withthe peaks most prominent when viewed towards face-on inclina-tions. For di ff erent azimuthal viewing angles, ϕ -profiles are quitediverse. This diversity is the result of di ff erent velocity projec-tions towards the observer since the model is not azimuthallysymmetric. The ϕ -profiles are symmetric with respect to the linecenter which is not the case for a single case scenario where theswing occurs.Typical degree of polarization PO found for Type-1 objectsis around 1% or less. Our simulations show that PO is in therange between 1% and 4% (Fig. A.2). This unusually high PO isdue to the high radial optical depth of the scattering region. It isinclination dependent and it is increasing when observing fromface-on towards edge-on viewing inclinations as expected from http: // / Thomson law. For some φ (Fig. A.2, top left and bottom rightpanels), PO profile peaks in the line wings and has a minimumvalue in the line core. This is the same as in the case for a singleblack hole scenario and it was confirmed observationally (e.g.Mrk 6 Smith et al. 2002; Afanasiev et al. 2014). However, this isnot the case for all φ and we can see the opposite situation – POpeaks in the line core and has minimum in the line wings.The total flux shows variability in the line profiles A.3. Lineprofiles are sensitive both to viewing inclinations and view-ing azimuthal angles. In general, double-peaked profiles are ob-served, with line width being broader when observing from face-on towards edge-on inclinations. Line widths are di ff erent withrespect to φ with the broadest lines coming from the directionwhen φ = ◦ or φ = ◦ (Fig. A.3, middle upper and bot-tom panels). Some viewing angles are showing single-peak lines(Fig. A.3, top left and bottom right panels) and the correspond-ing PO profiles are as in the case for a single black hole scenario.This means that in the certain phase, we would not be able toobservationally distinguish between the SMBBHs and SMBHsfrom the unpolarized optical spectra. However for this case, ϕ is showing di ff erent profile than expected, which could providemore insight if the SMBBHs is situated in the center.For Distant model with mass ratio q = . ϕ , PO and TF (Figs. A.4, A.5, A.6). The ϕ is having similar profiles as for the case with mass ratio q = ff erent in-tensities. When compared with the previous case, the ϕ -profile issimilar except for azimuthal viewing angles φ = ◦ where theprofile is flat in the core (Fig. A.4, lower left panel), or an addi-tional swing can be noticed in the core for φ = ◦ (Fig. A.4,upper right panel).Degree of polarization is having profiles with the same shapeas for the previous case except that they are asymmetric and it isthe case for all viewing angles. We obtained the same order ofpolarization with the same inclination dependency (Fig. A.5).The unpolarized line is showing a displaced single peak pro-files when viewed almost face-on for most of the azimuthalviewing angles, except when φ = ◦ and 270 ◦ where a cleardouble-peaked profile can be observed (Fig. A.6, bottom left andmiddle panels). For intermediate inclinations, line profiles areasymmetric with double peaks and with di ff erent line shifts de-pending on the azimuthal viewing angles (Fig. A.6).For the same model with q = .
1, we obtained similar pro-files as before for ϕ , PO and TF (Figs. A.7, A.8, A.9), howeverthey are more asymmetric than for the case with q = .
5. The ϕ is having similar profiles as for the cases with q = q = . ff erent positions as the system is Article number, page 5 of 20 & A proofs: manuscript no. SMBBH_pol_arx i = 38 : / i = 32 : / x i = 25 : / z ? [ / ] i = 25 : / i = 32 : / i = 38 : / D e g r ee o f p o l a r i z a t i o n V [km s ! ] -1 -0.5 0 0.5 1 T o t a l . u x -4 Fig. 5: On the left panel, an illustration of the model with a single SMBH in the center surrounded by a BLR (yellow) and thescattering region (gray) is shown. Right panel: the profiles of polarization angle (top), the degree polarization (middle), total flux(bottom) when viewed from two intermediate inclinations. Polarization angle is given in degrees ( ◦ ). We point out that the degreeof polarization is given as fraction units and is lower than the ones we obtain in the following section due to the di ff erent size andoptical depth of the scattering region. The total flux is given in arbitrary units. Model parameters are the same as the ones given bySavi´c et al. (2018).viewed in di ff erent orbital phases (A.9). When q = .
1, the moremassive component is having smaller orbital velocity and it ismuch smaller compared to the Keplerian velocity of the BLRclouds surrounding it. For the less massive component, orbitalvelocity is of the same order in comparison with the Keplerianvelocity of the BLR clouds surrounding it, which contributes tohigher line shift. With these two e ff ects combined, we observehighly asymmetric line profiles which significantly vary with theorbital phase. This scenario is geometrically similar with the previous one withthe SMBBHs being closer and allowing additional chaotic veloc-ity component will a ff ect the line profile mostly around its core.Simulated ϕ is shown on Figs. 6 (panel b);A.10. The ϕ profilesare also similar as in the case for separated BLRs. Figures A.10(left panels; upper and middle right) clearly show two minimain the wings and a maximum in the line core; or minimum inthe line core and maximum in the line wings. The observed ϕ profile is the most sensitive to random velocity when the systemis viewed from φ = ◦ and φ = ◦ (Fig. A.10, middle upand bottom panels), for which we observe two minima and al-most flat profile in the core. For φ = ◦ (Fig. A.10, bottomright panel) we see one peak in the red wing for the near face-onviewing i , while the profile is almost constant for the intermedi-ate inclination. We expect that additional chaotic velocity com- ponent will a ff ect the profile mostly the core, which is exactlywhat we get from the models.In Fig. A.11 the resulting PO is shown. The degree of polar-ization is in the same range as it was for the previous case. Again,PO is increasing when viewing from face-on towards edge-on in-clinations.The total flux is largely a ff ected by the additional randommotion of the BLR clouds in the line core (Fig. A.12). We canclearly observe double-peaked lines for intermediate inclinations( i = ◦ and i = ◦ , Fig. A.12, upper panels and bottom leftand middle panels). For φ = ◦ , ◦ and 342 ◦ (Fig. A.12), weobserve single-peak profiles, and for intermediate inclinations,line cores are flattened. The highest line widths are for φ = ◦ and φ = ◦ . With the two BLRs being mixed and surrounding both blackholes, we can observe that the change of ϕ is small with the re-spect to the continuum level (Figs. 6 (panel c); A.13) and it isthe highest for nearly face-on inclinations. For intermediate in-clinations, the ϕ profiles could be considered as constant withadditional noise. This is expected since the largest fraction offlux is coming from the clouds with additional random velocitycomponents that are the close to the black holes.Figure A.14 shows the resulting PO for a set of viewing in-clinations and azimuthal angles. We can see that the broad line Article number, page 6 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes Fig. 6: On the left panels the illustration of each model with SMBBH in the center: Distant (a), Contact (b), Mixed (c), Spiral (d).On the right panels, from top to bottom are ϕ , PO and TF for two viewing inclination and for azimuthal viewing angle φ = ◦ .profiles are almost flat with very low characteristic features. Weobtain the same range for PO as in the previous models.The total flux is showing seemingly complex profiles (A.15)with multiple spikes. This is however due to the fact that we arevery much limited to the number of BLR clouds when runningthe simulations. Running the stokes code with more than 5000individual clouds would be impractical and extremely time con-suming. These results are in agreement as the ones obtained bySmith et al. (2005) i.e. we can see that an additional random ve-locity component besides the Keplerian applied to a large num-ber of BLR clouds, have the tendency to smooth and flatten theresulting spectra. We obtain flat profiles for ϕ and PO, and wecan expect a single peaked lines. In Figs. 6 (panel d); A.16 the results for ϕ for the spiral model areshown. The simulated ϕ is showing double peak profiles whetherwith minima or maxima occurring around V ≈ − forall i and φ . This velocity is close to the orbital velocity of eachbinary component for which V ≈ − . This result isdue to most of the emitted flux that is originating from the innerparts of the spiral arms closer to the black holes, and due to thevelocity of the rigid body scaling with the distance. The intensityof the peaks is inclination dependent and is decreasing when thesystem is viewed from face-on towards edge-on inclinations.In Fig. A.17 the results for the simulated PO are shown. Wecan see that PO is having similar profiles as ϕ – visible peaksin the line wings and minimum in the line core (Fig. A.17, leftupper and middle panels; right bottom and middle panels) thatis characteristic for a single black hole scenario, or the oppositeprofiles with maximum PO in the line core and minimum in thewings. The results for TF are shown in Fig. A.18. We can see vari-ous line profiles for di ff erent φ . For intermediate inclinations, weobserve double-peaked line profiles. For near face-on viewingangles and some φ , profiles with strong single peak (Fig. A.18,bottom right panel), or two peaks very close to each other(Fig. A.18, middle left and right panels) are observed.
4. Discussion
The presence of another BLR (as in the case of our model) hasa unique signature on the simulated ϕ -profiles for all the mod-els we tested. A double peaked feature can be observed, and the ϕ -profile is varying drastically depending on the observed or-bital phase of the system and it is di ff erent than in case of a sin-gle SMBH. This is always the case for PO and TF, which oftenshow complex profiles. However, in some cases, when viewedfrom certain azimuthal viewing angles, the simulated PO and TFprofiles are very similar for the case with a single SMBH in thecenter. AGN monitoring is therefore required for distinguishingbetween these two cases. We have seen that additional randommotion tends to smooth the profiles of TF in the line core, whilediluting ϕ -profiles. The total flux is also largely dependent on theobserved phase of the binary system. Lines show complex vary-ing profiles, and long-term monitoring spectroscopy, combinedwith spectropolarimetry could prove very useful in the search forSMBBH candidates. In order to see the variability in the line,we are limited only to close subparsec SMBBHs for which thehalf-period of revolution is of the order up to few tens of years.Less massive SMBBHs or the ones with greater orbital distancewould yield orbital periods of the order of few centuries, that theline profile change would be impractical to observe. Article number, page 7 of 20 & A proofs: manuscript no. SMBBH_pol_arx
In Savi´c et al. (2018), we simulated equatorial scattering withadditional complex (inflows / outflows) motion in the BLR withfor a single SMBH in the center. The ϕ -profiles are showingpoint (central) symmetry for all treated cases (e.g. a prominentminimum followed by a maximum of the same amplitude), whilethe TF remains axisymmetric with the respect to the line center.Smith et al. (2005) have included inflows and high-velocity ro-tation in the scattering region and it yielded complex, but againpoint symmetric ϕ -profiles. Depending on the model, our sim-ulations involving SMBBHs as a result have axisymmetric ϕ -profiles. This behavior of polarization angle may prove crucialas a distinct feature in the search for SMBBHs. Broad emission line profiles and line variability can be explainedby a wide variety of di ff erent kinematic models that would yieldsimilar results. Naturally, AGNs with variable double-peakedlines make good targets for spectropolarimetric observations andlong-term monitoring campaigns. We discuss our results withobservations of three well known double-peaked AGNs: NGC1097, 3C 390.3 and Arp 102B.Spectral optical monitoring of Arp 102B over the periodfrom 1987 to 2010 shows no significant change in the broaddouble-peaked H α and H β profiles (Shapovalova et al. 2013;Popovi´c et al. 2014). The H β line is broader than H α duringthe monitored period and both can be well reproduced by diskmodel. However, spectropolarimetric observations are partiallyinconsistent with the disc model (Corbett et al. 1998, 2000). TheH α polarization angle has almost the same value as the angleof the jet direction, which is in good agreement with equato-rial scattering. The observed single-peak profile of the polarizedline with respect to the unpolarized suggest that the BLR cloudsmight be undergoing biconical outflows (Antonucci et al. 1996;Corbett et al. 1998, 2000). The ϕ -profile is flat without any dis-tinctive feature.The active galaxy 3C 390.3 is a well known source with re-markably strong variability in the X-, UV and optical regime(see Afanasiev et al. 2015, and the references therein). The un-polarized and polarized flux are quite di ff erent. The unpolar-ized H α has a double-peaked profile with blue peak being moreprominent. The polarized H α is single-peaked shifted to bluefor 1200 km s − with the respect to narrow component and isstrongly depolarized in the center (Afanasiev et al. 2015). Amodel with biconical outflows (Corbett et al. 2000) for this ob-ject is not in agreement with the optical monitoring of the BLR.The CCF analysis by Afanasiev et al. (2015) for H α and H β shows no significant delay in the variation between the blue andthe red line wing relative to each other or with the respect to theline core. This is in favour of a model with the BLR originatingfrom an accretion disk with dominant Keplerian motion. A two-component BLR model with disc and an outflowing region canwell explain spectropolarimetric observations. In this model, anoutflowing region is located above the disk and it can depolarizethe radiation emitted from the disk.Optical monitoring of NGC 1097 between 1991 and 1996have shown a peculiar evolution of the H α line profile. Thebroad H α double peak showed a red-peak dominance (Storchi-Bergmann et al. 1993), followed by a nearly symmetrical profile(Storchi-Bergmann et al. 1995) and up to a blue-peak dominantprofile (Storchi-Bergmann et al. 1997). A model of a precess-ing elliptical ring around the SMBH (Eracleous et al. 1995) wasused to explain observed line profiles and to fit the data. In thismodel it was proposed that the origin of the elliptical disk is due to the tidal disruption of a star by a SMBH or it could be dueto the existence of a SMBBH. In both cases, broad line vari-ability that could be observed is of the order of few years whenthe total mass is smaller than 10 M (cid:12) . For SMBH with mass ofthe order of 10 M (cid:12) , which is the case for NGC 1097 , the pre-cession period is of the order of a few centuries and could notbe observed. However, in the scenario we studied, where eachcomponent is having a separate accretion disk surrounded by theBLR, the variability of the order of few years could be observedif the binary system is close enough. Line variability would showsystematic periodicity and it is attributed only to the viewed or-bital phase of the system. In order to fit the observational datawith our model, a large grid of models needs to be conducted.Besides the main parameters of the model such as total mass,orbital distance and mass ratio, the parameter space would alsoinclude luminosities and BLR sizes of each components alongwith the parameters describing the scattering region as well asthe optical depth. This is well beyond the scope of the presentwork and limits our investigation based on a simple model.When viewed in polarized light, NGC 1097 shows a weakcontinuum polarization ( p = . ± .
02 %) in optical domainover 5100–6100 Å (Barth et al. 1999). The H α line is also show-ing weak polarization and no characteristic feature for a singleor binary BH could be detected in the PO and PF profiles. Newhigh quality spectropolarimetric observations are thus requiredin order to confirm our results.AGNs with unpolarized double-peaked profiles with varyingred and blue peak with respect to each other are probably the bestcandidates in the search for SMBBHs. Although a single SMBHin the center of AGNs is the most probable case, SMBBH inthe central engine should have their distinctive signiture in thepolarized spectra due to the polarization sensitivity on geometryand kinematics.
5. Conclusions
We investigated the polarization signatures of SMBBHs inAGNs using a set of simple yet representative models. We as-sumed equatorial scattering as a main mechanism for optical po-larization and we used the Monte Carlo code stokes for solving3D polarized radiative transfer with kinematics. We used simplegeometry for polarization modeling of SMBBHs in AGNs andwe treated four di ff erent cases with di ff erent geometry of theBLRs: distant , contact , mixed and spiral . We outline the char-acteristic features of ϕ , PO and TF that are in common for allthe models we studied. Polarization position angle ϕ is showingdouble-peaked or even more complex profiles most of the time.The PO shows double-peak profiles with minimum in the linecore, which is common for the single SMBH scenario, but thereare opposite profiles with minima in the line wings and maximalPO in the line core which may be an indicator of a SMBBHs.The TF shows most of the time double-, or multi-peaked profileswhich are often associated with the disk profiles. The combinedresults of all of our simulations involving SMBBHs leads to thefollowing two conclusions: – The degree of polarization and total flux, along with theunique profiles characteristic for SMBBHs also show pro-files that are common for single SMBHs and alone mayprove inconclusive for disentangling the central engine ofAGNs. M bh = (1 . ± . × M (cid:12) (Lewis & Eracleous 2006); M bh = (1 . ± . × M (cid:12) (Onishi et al. 2015)Article number, page 8 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes – On the other hand, the polarization position angle ϕ showsquite unique profiles than the ones observed for singleSMBH scenario, and it’s inspection could be used as a firststep for finding the SMBBH candidates.We demonstrated that when a SMBBH is situated in thecenter of Type-1 AGNs, spectropolarimetry could be a power-ful tool for searching the SMBBH candidates amongst them. Inthis paper we assumed that the accretion disks of the two blackholes are coplanar and that they are coplanar with the torus,i.e. scattering region. Our assumption of coplanarity is very wellsupported by previous results from high-resolution hydrodynam-ical simulations. However, for a general picture of how signifi-cant is the orientation between the disks in the short-lived phasewith misaligned disks, a more detailed analysis with the ex-panded model space grid is required. With the results obtainedso far, in this case, we expect to have highly asymmetric pro-files of the total flux and the degree of polarization, while for thepolarization position angle, we expect to have lower amplitudeand more flat profiles. We intend to explore the cases of non-coplanarity in a follow-up paper that will investigate the whole(and large) phase space of free parameters. Acknowledgements.
This work was supported by the Ministry of Education andScience (Republic of Serbia) through the project Astrophysical Spectroscopy ofExtragalactic Objects (176001), the French PNHE and the grant ANR-11-JS56-013-01 “POLIOPTIX”. F. M. is grateful to the Centre national d’études spatiales(CNES) and its post-doctoral grant "Probing the geometry and physics of activegalactic nuclei with ultraviolet and X-ray polarized radiative transfer". D. Savi´cthanks the French Government and the French Embassy in Serbia for supportinghis research without which this work would not be possible.
Article number, page 9 of 20 & A proofs: manuscript no. SMBBH_pol_arx
Appendix A: Detailed results of modeling
Simulations for all models are presented in the figuresfrom A.1 to A.18. The simulated profiles for ϕ , PO andTF are given for two viewing inclinations: i ≈ ◦ and32 ◦ . Azimuthal viewing angles takes eight values: φ = ◦ , ◦ , ◦ , ◦ , ◦ , ◦ , ◦ and 342 ◦ . The results aregiven as a function of velocity defined as V = c ( λ − λ ) /λ , where λ is wavelength and λ is the central wavelength of a given spec-tral line. The broad line region for each model is shown in thecenter of every image. Arrows represent the velocity field of theBLR. For each model, we outline the main features for complete-ness. Distant : This case is shown in Figs. A.1-A.3 for mass ratio q =
1. In Fig. A.1 the polarisation angle ϕ is shown. We canobserve a double-peaked profiles of ϕ that drastically vary de-pending on the orbital phase of the system. For φ = ◦ and198 ◦ , ϕ reaches maximum values in the line wings and mini-mum in the core, while for φ = ◦ and φ = ◦ , it is theopposite way around. The PO is shown in Figs. A.2 shows sim-ilar profiles as ϕ , but they are not correlated. Profiles with mini-mum in the core and maxima in the wings, which is common forthe single SMBH scenario can be seen for φ = ◦ and 342 ◦ .The opposite profiles are for φ = ◦ , ◦ , ◦ and 234 ◦ . TheTF is shown in Fig. A.3. Double-peaked profiles can be seen for φ = ◦ , ◦ , ◦ and 234 ◦ and for all viewing inclinations.Single-peaked profiles are for φ = ◦ and φ = ◦ .The results of the same model for mass ratio q = . ϕ and PO are shown in Figs. A.4and A.5 respectively and both are following the same trend asit was for the case with mass ratio q = q = .
1, simulated profiles for ϕ , PO and TFare shown in Figs. A.7-A.9. The results are very similar as in theprevious case with remarkable asymmetry in the profiles. Contact : The results for this model are shown in Figs. A.10-A.12. The ϕ -profiles are shown in Fig. A.10 for di ff erent orbitalphase of the system. Profiles are very similar as the ones ob-tained for distant model, but with greater amplitude of max-ima / minima. The PO profiles are shown in Fig. A.11. For φ = ◦ , ◦ and 342 ◦ , the profiles are the same as for the singleSMBH scenario, while for all the other azimuthal viewing an-gles, the maximum PO is in the line core. The TF is shownin Fig. A.12. Lines are the broadest when viewed for φ = ◦ and 270 ◦ . The random velocity component in this model that ispresent in the BLR flattens the line profiles, making it di ffi cult todistinguish between sinle-peaked and double-peaked profiles. Mixed : Simulations for this model are shown in Figs. A.13-A.15. Polarization angle is shown in Fig. A.13. The ϕ -profilesare double-peaked for φ = ◦ , ◦ and 198 ◦ . A swing in the ϕ -profile in the line core, common for single SMBH, can is when φ = ◦ . The PO is overall flat with very mild features in theline core (Fig. A.14). As explained in the Results section, due tofinite number of clouds in the simulations we obtain spiky pro-files for TF (Fig. A.15). We could expect that unpolarized linesare single-peaked. Spiral : The results for this model are shown in Figs. A.16-A.18. The ϕ -profiles are shown in Fig. A.16. This model isunique for having double-peaked ϕ -profiles when viewed fromall azimuthal angles, similar to those found for distant and con-tact models, but with lower amplitude. The PO is shown inFig. A.17. It shows profile common for single SMBH scenario for φ = ◦ , ◦ , ◦ and 342 ◦ , but also those with maximumPO in the core when viewed for all the other azimuthal viewingangles. The TF is shown in Fig. A.18. For intermediate inclina-tion, it shows clear double-peaked profiles, while for nearly face-on viewing inclinations, a single-peaked profile or profiles withpeaks very close to each other, can be seen when φ = ◦ , ◦ and 342 ◦ . References
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Article number, page 11 of 20 & A proofs: manuscript no. SMBBH_pol_arx -0.03 -0.02 -0.01 0 0.01 0.02 0.03-0.015-0.01-0.00500.0050.010.015 Fig. A.2: Same as figure A.1, but for PO. -4 -0.03 -0.02 -0.01 0 0.01 0.02 0.03-0.015-0.01-0.00500.0050.010.015 -4 -4 -4 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 Fig. A.3: Same as figure A.1, but for TF.
Article number, page 12 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04-0.015-0.01-0.00500.0050.010.015 Fig. A.4: Same as figure A.1, but for q = . -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04-0.015-0.01-0.00500.0050.010.015 Fig. A.5: Same as figure A.2, but for q = . Article number, page 13 of 20 & A proofs: manuscript no. SMBBH_pol_arx -4 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04-0.015-0.01-0.00500.0050.010.015 -4 -4 -4 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 Fig. A.6: Same as figure A.3, but for q = . -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05-0.02-0.015-0.01-0.00500.0050.010.0150.02 Fig. A.7: Same as figure A.1, but for q = . Article number, page 14 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05-0.02-0.015-0.01-0.00500.0050.010.0150.02 Fig. A.8: Same as figure A.2, but for q = . -4 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05-0.02-0.015-0.01-0.00500.0050.010.0150.02 -4 -4 -4 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 Fig. A.9: Same as figure A.3, but for q = . Article number, page 15 of 20 & A proofs: manuscript no. SMBBH_pol_arx -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-0.01-0.00500.0050.01 Fig. A.10: Same as figure A.1, but for contact model. -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-0.01-0.00500.0050.01 Fig. A.11: Same as figure A.10, but for PO.
Article number, page 16 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes -4 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-0.01-0.00500.0050.01 -4 -4 -4 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 Fig. A.12: Same as figure A.10, but for TF. -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01-0.01-0.00500.0050.01 Fig. A.13: Same as figure A.1, but for mixed model.
Article number, page 17 of 20 & A proofs: manuscript no. SMBBH_pol_arx -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01-0.01-0.00500.0050.01 Fig. A.14: Same as figure A.13, but for PO. -4 -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01-0.01-0.00500.0050.01 -4 -4 -4 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 -1 -0.5 0 0.5 110 -4 Fig. A.15: Same as figure A.13, but for TF.
Article number, page 18 of 20D. Savi´c et al.: Predicting the broad lines polarization emitted by supermassive binary black holes -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05-0.0500.05 Fig. A.16: Profiles of ϕ across the line profile. -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05-0.0500.05 Fig. A.17: Profiles of PO across the line profile.