Photo-centric variability of quasars caused by variations in their inner structure: Consequences on Gaia measurements
Luka C. Popovic, Predrag Jovanovic, Marko Stalevski, Sonia Anton, Alexandre H. Andrei, Jelena Kovacevic, Maarten Baes
aa r X i v : . [ a s t r o - ph . GA ] O c t Astronomy&Astrophysicsmanuscript no. ms-rev c (cid:13)
ESO 2018November 7, 2018
Photocentric variability of quasars caused by variations in theirinner structure: Consequences for Gaia measurements
L. ˇC. Popovi´c , , P. Jovanovi´c , , M. Stalevski , , , S. Anton , , A. H. Andrei , , , J. Kovaˇcevi´c , , and M. Baes Group for Astrophysical Spectroscopy, Astronomical Observatory, Volgina 7, 11060 Belgrade 74, Serbia Isaac Newton Institute of Chile, Yugoslavia Branch, Serbia CICGE, Faculdade de Ciˆencias da Universidade do Porto, Portugal SIM, Faculdade de Ciˆencias da Universidade de Lisboa, Portugal Observat´orio Nacional / MCT, R. Gal. Jos´e Cristino 77, CEP 20921-400 Rio de Janeiro, Brazil Osservat´orio Astronomico di Torino / INAF, Strada Osservat´orio 20, 10025 Pino Torinese, Italy SYRTE / Observatoire de Paris, 61 Avenue de lObservatoire, 75014 Paris, France Obswervatrio do Valongo / UFRJ, Ladeira PedroAnt´onio 43, CEP 20080-090 Rio de Janeiro, Brazil Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281-S9, Gent, 9000, BelgiumReceived May 12, 2011; accepted — —, 2011
ABSTRACT
Context.
We study the photocenter position variability caused by variations in the quasar inner structure. We consider the variabilityin the accretion disk emissivity and torus structure variability caused by the di ff erent illumination by the central source. We discussthe possible detection of these e ff ects by Gaia. Observations of the photocenter variability in two AGNs, SDSS J121855 + + Aims.
For variations in the quasar inner structure, we explore how much this e ff ect can a ff ect the position determination and whetherit can (or not) be detected with the Gaia mission. Methods.
We use models of (a) a relativistic disk, including the perturbation that can increase the brightness of part of the disk, andconsequently o ff set the photocenter position, and (b) a dusty torus that absorbs and re-emits the incoming radiation from the accretiondisk (central continuum source). We estimate the value of the photocenter o ff set caused by these two e ff ects. Results.
We found that perturbations in the inner structure can cause a significant o ff set to the photocenter. This o ff set depends on thecharacteristics of both the perturbation and accretion disk and on the structure of the torus. In the case of the two considered QSOs,the observed photocenter o ff sets cannot be explained by variations in the accretion disk and other e ff ects should be considered. Wediscuss the possibility of exploding stars very close to the AGN source, and also that there are two variable sources at the center ofthese two AGNs that may indicate a binary supermassive black hole system on a kpc (pc) scale. Conclusions.
The Gaia mission seems to be very promising, not only for astrometry, but also for exploring the inner structure ofAGNs. We conclude that variations in the quasar inner structure can a ff ect the observed photocenter (by up to several mas). There isa chance to observe such an e ff ect in the case of bright and low-redshift QSOs. Key words. galaxies: active – galaxies: quasar – astrometry: reference systems
1. Introduction
Gaia is a global astrometric interferometer mission that aims todetermine high-precision astrometric parameters for one billionobjects with apparent magnitudes in the range 5.6 ≤ V ≤ ff erent physical processes occur that may cause Send o ff print requests to : L. ˇC. Popovi´c,e-mail: [email protected] a variation in the photometric center of the object. Accordingto the standard model of AGNs, the central region of a QSOconsists of a SMBH (10 − M ⊙ ) surrounded by an accre-tion disk (see Sulentic et al., 2000), and a broad emission-lineregion (BLR). That central region might be surrounded by dust,arranged in a toroidal-like distribution. All these components ra-diate, and its strength is a function of the geometry of the system,and its orientation relative to the observer. One of the most im-portant properties of AGNs is their flux variability, which mayhave multiple origins such as variation in the accretion rate, in-stabilities of the accretion disk around the central black hole,supernova bursts, jet instabilities, and gravitational microlensing(see e.g. Andrei et al., 2009; Shields et al., 2010; Popovi´c et al.,2011).Taris et al. (2011) reported on the possibility of a correlationbetween the flux variability and photocenter motion in QSOs,which is a very relevant subject for missions such as Gaia. Thereare di ff erent sources for photocenter variation. It is well-knownthat the main output of the di ff erent structures of an AGN (suchas accretion disk, jets, line-emitting regions, torus, etc.) di ff er in
1. ˇC. Popovi´c et al.: Photocentric variability of AGNs energy, consequently the sizes and position of the emitting re-gions are ”wavelength dependent”. Opacity e ff ects also explainthe frequency-dependent core-shifts in the radio synchrotronemission at the base of relativistic jets (Porcas, 2009), and coreshifts (between two radio wavelengths) of up to 1.4 mas havebeen reported by Kovalev et al. (2008).As we mentioned above, an AGN has a complex structure,and one can expect that the origin of this variation is caused bythe inner structure of this object, as for instance a torus that isilluminated by a varying central continuum may contribute tosome photocenter variation. However, variable processes occur-ring in the accretion disk, such as outburst, and perturbations(see e.g. Jovanovi´c et al., 2010; Popovi´c et al., 2011).In this paper, we investigate the spectro-photocentric vari-ability of quasars caused by changes in their inner structure. Weconsider: (a) a perturbation in a relativistic accretion disk arounda SMBH, and (b) changes in the pattern of radiation scattered bythe dust particles in the surrounding torus caused by the varia-tions in the accretion disk luminosity and dust sublimation ra-dius.The aims of the paper are: (a) to show how much these ef-fects may contribute to the variability of the photocenter, i.e. toquantify “noise“ and more accurately characterize any resultingerror in the position determination; (b) to estimate the possibilityof detecting this e ff ect with Gaia mission; and (c) to identify inwhich QSOs these e ff ects may be dominant.The paper is organized as follows: in § § § ff erent parame-ters of both the disk and torus and at di ff erent redshifts; in § §
6, we outline ourconclusions.In this paper, we use a flat cosmological model with the fol-lowing parameters: Ω m = Ω Λ = .
73, and H =
71 km s − Mpc − .
2. Disk model around SMBH
In the standard model of an AGN accretion disk, accretion oc-curs via an optically thick and geometrically thin disk. The e ff ec-tive optical depth in the disk is very high and photons are closeto thermal equilibrium with electrons (Jovanovi´c & Popovi´c,2009). The spectrum of thermal radiation emitted from the ac-cretion disk surface depends on its structure and temperature,hence on the distance to the black hole.An accretion disk around a supermassive black hole at thecenter of an AGN extends from the radius of a marginally stableorbit R ms to several thousands of gravitational radii. On the basisof radiation emitted in di ff erent spectral bands, it can be stratifiedin several parts (Jovanovi´c & Popovi´c, 2009): a) an innermostpart close to the central black hole that emits X-rays and extendsfrom the radius of marginally stable orbit R ms to several tensof gravitational radii; b) a central part ranging from ∼ R g to ∼ R g , which emits UV radiation; and c) an outer partextending from several hundreds to several thousands R g , fromwhich the optical emission orriginates (Eracleous & Halpern,1994, 2003).Here we consider an optical emission disk. The model isdescribed in our previous papers (see e.g. Popovi´c et al., 2003;Jovanovi´c & Popovi´c, 2009; Jovanovi´c et al., 2010), and herewill not be repeated in detail. We model the emission froman accretion disk using numerical simulations based on a ray-tracing method in a Kerr metric (see e.g. Jovanovi´c & Popovi´c, 2009, and references therein). In this method, one divides theimage of the disk on the observer’s sky into a number of smallelements (pixels), and for each pixel the photon trajectory istraced backward from the observer by following the geodesicsin a Kerr space-time. Although this method was developedfor studying the X-ray radiation originating from the inner-most parts of the disk close to the central black hole (see e.g.Jovanovi´c & Popovi´c, 2008), it can be also successfully appliedto the modeling of the UV / optical emission originating from theouter regions of the disk (see e.g. Jovanovi´c et al., 2010).However, some general relativistic and strong gravitationale ff ects (such as gravitational redshift) are significant only in theinnermost regions of the accretion disk, close to its marginallystable orbit. Since the inner radius of the disk is here taken tobe 100 R g , and it has a small inclination angle, these e ff ectswill have a negligible influence on the photocenter displacement.Therefore, we assumed a non-rotating central black hole, suchthat the Kerr metric reduces to its special Schwarzschild case. Inthis way, we also included in our simulations some Newtonianand special relativistic phenomena, such as the Doppler e ff ectand relativistic beaming (see Fig. 1 and top left panel of Fig.2), which cannot be neglected even at such relatively large dis-tances from the central black hole, hence could cause significantdisplacements of the photocenter from the position obtained bysimply averaging the assumed emissivity function of the disk.On the other hand, this method is very convenient for investigat-ing photocenter variability, because the relativistic ray-tracingenables us to calculate for instance the brightness of each pixelin the accretion disk image on the observer’s sky. This disk im-age can then be used to easily obtain the photocenter position, aswe show in the later text. To model a bright spot on the disk, we considered perturbationsin the surface emissivity on some region of the disk. Surfaceemissivity of the disk is usually assumed to vary with radius asa power law (e.g. Popovi´c et al., 2003) ε ( x , y ) = ε · r a ( x , y ) , where ε is an emissivity constant, a is emissivity index, and( x , y ) is a position along the disk. We introduce the perturba-tion in accretion disk emissivity (bright spot) in the form of atwo-dimensional circular Gaussian, by modifying its power-lawemissivity according to (Jovanovi´c & Popovi´c, 2009) ε ′ ( x , y ) = ε ( x , y ) · + ε p · e − (cid:18) x − xpwp (cid:19) + (cid:18) y − ypwp (cid:19) ! , (1)where ε ′ ( x , y ) is the modified disk emissivity, ε ( x , y ) is the ordi-nary power-law disk emissivity at the same position ( x , y ), ε p isthe emissivity of the perturbing region (i.e. the amplitude of thebright spot), ( x p , y p ) is the position of the perturbing region withrespect to the disk center (expressed in gravitational radii, here-after denoted by R g = GM / c , where M is the mass of the SMBH,and G and c are well known constants) and w p is its width (alsoin R g ). A three-dimensional (3D) plot of the above expressionfor the modified emissivity law is given in Fig. 1.Owing to relativistic e ff ects, photons emitted from the disk atfrequency ν em will reach observers at infinity at frequency ν obs ,and their ratio determines the shift caused by these e ff ects g = ν obs /ν em . The total observed flux at the observed energy E obs isthen given by F ( E obs ) = Z image ε ′ ( x , y ) g δ ( E obs − gE ) d Ξ , (2)
2. ˇC. Popovi´c et al.: Photocentric variability of AGNs
Fig. 1.
A 3D plot of modified disk emissivity given by Eq. (1)for 100 R g ≤ r ( x , y ) ≤ g , q = − ε p = x p = g , y p = g , and w p =
300 R g . Table 1.
The simulated o ff sets of photocenter (in mas) caused byperturbation to the accretion disk emissivity for di ff erent valuesof its redshift and mass of a central black hole. Other parameterscorrespond to the bottom left panel of Fig. 2. M BH z ( M ⊙ ) 0.01 0.05 0.10 0.15 0.2010 where ε ′ ( r ) is the modified disk emissivity given by Eq. (1), d Ξ is the solid angle subtended by the disk in the observer’s sky, and E is the rest energy.This simple model is suitable for our purpose because it al-lows us to change the amplitude, width, and location of brightspots with respect to the disk center. In this way, we are able tosimulate the displacement of a bright spot along the disk, and itswidening and amplitude variations with time. The observed photocenter ( X pc , Y pc ) of the accretion disk can bemodeled as a centroid of observed flux F ( E obs ) over the diskimage, i.e. as the mean of impact parameters ( x , y ) of all pixelsalong the disk image, weighted by FX pc = P Ni = P Nj = F ( i , j ) · x ( i , j ) P Ni = P Nj = F ( i , j ) , Y pc = P Ni = P Nj = F ( i , j ) · y ( i , j ) P Ni = P Nj = F ( i , j ) , (3)where ( i , j ) is a point on a N × N grid of the disk image pixels.We consider a perturbation (or bright spot) at a certain partof the disk, for di ff erent values of the spot brightness, and cal-culate the photocenter. In Fig. 2, we present simulations of thephotocenter variability. Fig. 2.
Simulations of the accretion disk without (top left) andwith perturbation for three di ff erent values of emissivity index: a = a = − a = − ff ects (i.e. ratio of the observed to emitted energy), while inthe other three panels it represents the observed flux (in arbitraryunits). The inner and outer radii of the disk, as well as the posi-tion and width of the perturbing region, are the same as in Fig. 1.The maximum emissivity of the perturbing region is taken to beten times greater than the emissivity of the disk at its inner ra-dius. Linear distances are converted to angular units along the x and y axes assuming an accretion disk located at cosmologi-cal redshift z = .
01 around the central black hole with mass of10 M ⊙ . In the model, we are able to change the parameters of the accre-tion disk (dimension, emissivity, inner and outer radius, inclina-tion) and the parameters of the perturbation (size, position, andbrightness). Taking into account the results of previous studies,one can expect the dimensions of the accretion disk to be severalthousands of gravitational radii (see e.g. Eracleous & Halpern,1994, 2003; Popovi´c et al., 2011), hence here we assume anaccretion disk with an inner and outer radius of R inn = g and R out = g , respectively. In our simulation, we con-sider a low-inclined ( i = ◦ ) or near face-on disk, because offrom investigations of the broad line shapes a near face-on diskis preferred (see e.g. Popovi´c et al., 2004; Bon et al., 2009a).Although the adopted inclination angle is small, it is su ffi cient toinduce Doppler and relativistic beaming e ff ects (see e.g. Fig. 9 inReynolds & Nowak, 2003, and the corresponding discussion be-low). As shown in Reynolds & Nowak (2003), even in the caseof a nearly face-on disk, these e ff ects can still produce ratherbroad emission lines, unlike the case of a face-on Newtoniandisk, which would display very narrow lines. In addition, for asteep disk emissivity where a < −
2, the line emission of thedisk is dominated by its inner regions R out < R g . However,
3. ˇC. Popovi´c et al.: Photocentric variability of AGNs for the disk emissivity where a > −
2, the bulk of the line emis-sion comes from the outer regions of the disk, thus both Dopplerand relativistic beaming e ff ects cannot be neglected even at suchrelatively large distances from the central black hole. Since themost realistic values for the emissivity of the disk are probablybetween 0 and − a = a = −
1, and a = − ff erent values for the brightness and positionalong the disk.
3. Dusty torus model
According to the AGN unification model, the central continuumsource is surrounded by the geometrically and optically thicktoroidal structure of dust and gas with an equatorial visual op-tical depth much larger than unity. To prevent the dust grainsfrom being destroyed by the hot surrounding gas, it has beensuggested (Krolik & Begelman, 1988) that the dust in the torusis organized into a large number of optically thick clumps. In anedge-on view, this dusty torus blocks the radiation coming fromthe accretion disk and BLR and object appears as type 2 activegalaxy. When the line of sight does not cross the dusty torus,both the accretion disk and BLR are exposed and the object isclassified as a type 1 active galaxy. This dusty torus absorbs theincoming radiation and re-emits it, mostly in the infrared do-main, but a part of the radiation is also scattered in the opticaldomain.The model of a torus that we used in this work is describedin detail in Stalevski et al. (2011); here we present only its mostimportant properties. Our approach allows us to model the torusas a 3D structure, composed of (a) isolated clumps, or (b) atwo-phase medium with high-density clumps and low densitymedium filling the space between the clumps. We employed a3D Monte Carlo radiative transfer code called SKIRT (for moredetails see Baes et al., 2003, 2011) to calculate spectral energydistributions (SED) and images of the torus at di ff erent wave-lengths.We approximate the obscuring toroidal dusty structure witha conical torus (i.e. a flared disk). Its characteristics are definedby (a) half opening angle θ , (b) inner and outer radius, R in and R out respectively, and (c) parameters describing the dust densitydistribution, p and q . The inner radius is calculated according tothe prescription given by Barvainis (1987) R in ≃ . · q L AGN · T − . [ pc ] , (4)where L AGN is the bolometric ultraviolet / optical luminosityemitted by the central source, expressed in units of 10 erg s − and T is the sublimation temperature of the dust grains givenin units of 1500 K.We describe the spatial distribution of the dust densitywith a law that allows a density gradient along the radial di-rection and with polar angle, similar to the one adopted byGranato & Danese (1994): ρ ( r , θ ) ∝ r − p e − q | cos ( θ ) | , (5)where r and θ are coordinates in the adopted coordinate system.The dust mixture consists of separate populations of graphiteand silicate dust grains with a classical MRN size distribution (Mathis et al., 1977). The total amount of dust is fixed based onthe equatorial optical depth at 9 . µ m ( τ . ).To generate a clumpy medium, we apply the algorithm de-scribed by Witt & Gordon (1996). The parameters that define theclumpiness of the dusty medium are the filling factor and con-trast. Filling factor sets the number of clumps; contrast is de-fined as the ratio of the dust density in the high- to low-densityphase. For example, setting the contrast to unity would result in acontinuous, smooth dust distribution. Setting an extremely highvalue of contrast ( > ff ectively puts all the dust into theclumps, without a low-density medium between them. The primary continuum source of dust heating is the intenseUV-optical continuum coming from the accretion disk. A verygood approximation of its emission is a central, point-likeenergy source, emitting isotropically. Its SED is very well-approximated by a composition of power laws with di ff erentspectral indices in di ff erent spectral ranges. The adopted valuesare: λ L ( λ ) ∝ λ . . < λ < .
01 [ µ m ] λ . < λ < . µ m ] λ − . . < λ < µ m ] λ − < λ <
50 [ µ m ] . (6)These values have been quite commonly adopted in the liter-ature, and come from both observational and theoretical argu-ments (see e.g., Schartmann et al., 2005). Variations in the primary continuum source-emission (not onlyperturbations, but also changes to the total luminosity of accre-tion disk) may also cause a photocenter o ff set due to another ef-fect. According to Eq. (4), the dust sublimation radius (i.e. innerradius of torus) depends on the total bolometric luminosity ofthe central source (accretion disk). Thus, with increasing centralsource luminosity, the inner radius of the torus also increases.This means that (a) the innermost structure of the torus changesand (b) the radiation from the central source is able to penetratefurther into the torus. These two e ff ects will change the illumina-tion of clumps and the pattern of the scattered radiation, whichmay lead to variations in the photocenter position. The photo-center of dusty torus is calculated in the same way as for theaccretion disk (see Eq. 3). The parameter that has a very prominent e ff ect on the shape ofSED is the inclination. The inclination i = ◦ corresponds to aface-on (type 1) AGN and i = ◦ an edge-on (type 2) AGN.Fig. 3 shows images of a torus model for a face-on and an edge-on view. In Fig. 4, we present the total SED and its thermal andscattered components, along with primary source SED, for thesetwo inclinations. As it can be seen from this figure, there is aclear distinction between the cases of a dust-free line of sight( i = ◦ ; left panel) and those that pass through the torus ( i = ◦ ,right panel). In the case of dust-free lines of sight, we can di-rectly see the radiation coming from the accretion disk, while in
4. ˇC. Popovi´c et al.: Photocentric variability of AGNs .i = 0° .i= 90°
Fig. 3.
Images of torus for face-on (left panel) and edge-on view (right panel), at 9 . µ m, in logarithmic scale. The values of torusparameters are: optical depth τ . =
5, dust distribution parameters p = q =
0, half opening angle θ = ◦ , inner radius R in = . R out =
15 pc; filling factor 0 .
25, contrast 10 , size of clumps 1 . L = L ⊙ . Fig. 4.
The total (solid line), thermal (dotted line), scattered (dashed line), and primary source (dash-dotted line) emission are plotted.The left panel is a type 1 inclination ( i = ◦ ), the right panel a type 2 inclination ( i = ◦ ). The two vertical lines indicate the centralwavelengths of the two dispersing prisms of the Gaia photometric instrument (integrated with the astrometric instrument), at 0 . . µ m. The values of torus parameters are the same as taken in Fig. 3. Fig. 5.
Images of the torus at di ff erent wavelengths. From left to right, panels represent model images at 0 .
83, 3 .
98, 9 .
31, and 17 . µ m. Images are in logarithmic scale. The visible squared structure is due to the clumps which in our model are in the form of cubes.The inclination is i = ◦ ; the values of other parameters are the same as taken in Fig. 3.
5. ˇC. Popovi´c et al.: Photocentric variability of AGNs the case of dust-intercepting paths most of the radiation is ab-sorbed and re-emitted at di ff erent wavelengths. From the figure,one can also see that the thermal component predominates themid- and far-infrared parts of a SED and its shape is similar forboth face-on and edge-on orientations. However, the shape andamount of the scattered component is quite di ff erent; in the edge-on view, it determines the total SED shortward of 1 µ m, while inthe face-on view it is negligible compared to the primary sourceemission. We illustrate this further in Fig. 5, where images ofthe torus at di ff erent wavelengths are presented. Shortward of 1 µ m (first panel), the thermal component is negligible and onlythe scattered component that arises randomly from the entiretorus is present. In the near- and mid-infrared domain (secondand third panel), the thermal radiation from the inner (and hot-ter) region predominates. At longer wavelengths (forth panel),emission arises from the dust placed further away.Since in the wavelength range relevant to this work ( < µ m), the scattered component of dust emission is dominant, theother parameters, (e.g. those defining geometry and dust distri-bution) have only a marginal influence on images of the torus.Therefore, we fix the following values of torus parameters: op-tical depth τ . =
5; dust distribution parameters (see Eq 5) p = q =
0; half opening angle θ = ◦ ; and outer ra-dius R out =
15 pc. For the parameters defining clumpiness, weadopt a filling factor of 0 .
25, which allows single clumps as wellas clusters of several merged clumps, and to define the contrastan extremely high value (10 ), which e ff ectively puts all the dustinto the clumps, without any dust being smoothly distributed be-tween the clumps. For the size of clumps, we adopt the value of1 . i = ◦ (dust-free line of sight) and i = ◦ (line of sight that passes throughthe torus). For the total bolometric luminosity of the central con-tinuum source, we adopt the values of L = , , , × L ⊙ .According to Eq. 4 (assuming the dust sublimation temperatureof 1200 K), the corresponding values of the inner radius of torusare R in = . , . , . , .
4. Modeled photocenter offset caused by changesto the inner quasar structure: Results anddiscussion
We performed simulations for di ff erent emissivities and di ff er-ent positions of the bright spot on the disk. As an example, wepresent in Fig. 2 three simulations of the photocenter o ff set dueto a perturbation in the disk for three di ff erent values of its emis-sivity index. In Fig. 2, we show the simulations of accretion diskwithout (top left panel) and with a perturbation (other three pan-els), i.e. the disk images (for a quasar with a SMBH of 10 M ⊙ at z = .
01) for three di ff erent values of emissivity index a = a = − a = − g , respec-tively. The emissivity of the bright spot is ε p = , the positionis X p = g , Y p = g , and the dimension of the brightspot is taken to be w p =
300 R g . As can be seen from the Figure, Note here that in the case of tidal disruptions of stars by a super-massive black hole the amplification in the total optical brightness canincrease around two times (see Komossa et al., 2008, and discussion be-low), therefore the small bright spot should have a significantly (aroundone order) higher emissivity than the disk the o ff set of the photocenter depends on the disk emissivity andit is the most prominent in a disk with flat emission ( q = ff sets are smaller for steeper emissivity laws andvice versa. We also note here that we take a very strong pertur-bation at the disk edge, and that the maximum emissivity of theperturbing region is taken to be ten times greater than emissivityof the disk disk center (hereafter we refer to this as the centralsource).Occurrences of perturbations in the accretion disk emissiv-ity could be caused by several physical mechanisms, such asdisk self-gravity, baroclinic vorticity, disk-star collisions, tidaldisruptions of stars by a central black hole, and fragmented spi-ral arms of the disk (see e.g. Jovanovi´c et al., 2010, and refer-ences therein). All these phenomena appear and last at di ff er-ent frequencies and timescales, and could cause perturbationsof di ff erent strengths, proportions and characteristics. In partic-ular, perturbations of accretion disk emissivity in the form offlares with high amplitudes are of great significance becausethey could provide information about accretion physics underextreme conditions. The flares with the highest amplitudes areusually interpreted in terms of tidal disruptions of stars by su-permassive black holes (see e.g. Komossa et al., 2008, and ref-erences therein). Stars approaching a SMBH will be tidally dis-rupted once the tidal forces of the SMBH exceed the star’s self-gravity, and part of the stellar debris will be accreted, producinga luminous flare of radiation that persists on a timescale of be-tween months and years. This flare is expected to occur in theouter part of the disk (similar to our simulations).Although, the frequency of these events in a typical ellipticalgalaxy is very low, between 10 − and 10 − per year (see e.g.Jovanovi´c et al., 2010, and references therein), Komossa et al.(2008) reported the discovery of an X-ray outburst of large am-plitude in the galaxy SDSS J095209.56 + ff set of thephotocenter will be negligible, especially if the bright spot ap-pears close to the center. In addition, when there is high emis-sivity in the bright spot close to the central source, the e ff ect issmall. Only a luminous bright spot located relatively far fromthe central source can be a good candidate to be observed withGaia. To estimate whether the o ff set of the photocenter can beobserved we give numerical values of the photocenter o ff sets (inmas) for di ff erent redshifts and black hole masses in Table 1.The parameters for the disk and perturbation are taken as givenabove, for the emissivity index of a = − ff sets( ∼ several mas) found at the lowest redshifts ( z ∼ .
01) andthe most massive black holes ( M BH ∼ M ⊙ ), where we canexpect to find the accretion disk with the larger dimensions. As explained in § § ff erent luminosities and corresponding innerradii (i.e. dust sublimation radii), i.e. L = , , , × L ⊙ and R in = . , . , . , . i = ◦ (dust-free line of sight) and i = ◦
6. ˇC. Popovi´c et al.: Photocentric variability of AGNs
Table 2.
The simulated o ff sets of photocenter (in mas) for dif-ferent values of redshift and accretion disk luminosity, calculatedfor the two photometric instruments with central wavelengths at0 . µ m and 0 . µ m. The values of torus parameters are thesame as in Fig. 5. L z (10 L ⊙ ) 0.01 0.05 0.100 . µ m3 1.579 0.208 0.0396 8.400 1.886 0.86010 8.170 1.353 0.6930 . µ m3 0.814 0.252 0.1356 7.120 1.422 0.99010 7.978 1.466 0.843 (line of sight that passes through the torus). For each model, wecalculated the photocenter position and its o ff set from the one inthe starting model ( L = L ⊙ ).We found that when the central source is unobscured ( i = ◦ ), the brightness of the source is dominant and the photo-center o ff set is negligible. In Table 2, we present values of thephotocenter o ff set in the case of i = ◦ and for di ff erent accre-tion disk luminosities and cosmological redshifts. As can be seenfrom the Table, the photocenter o ff set is larger for lower cosmo-logical redshifts and bigger luminosity outbursts. In Fig. 6, wepresent images of the torus in the case of the largest photocentero ff set (8 . z = .
01, for the central source luminositiesof 10 L ⊙ (left panel) and 6 × L ⊙ (right panel).As can be seen from Table 2, a large jump in the photocentero ff set between the luminosities of 3 and 6 × L ⊙ is present.This is caused by the change in the illumination of the torus. Asthe luminosity of the central source increases, the inner radiusof the torus increases as well (the inner structure changes), andthe group of clumps farther away from the center may be illu-minated (see Fig. 6, right panel). However, a further increase inthe central source luminosity does not change the illuminationpattern of the clumps significantly (depending on the actual dis-tribution of the clumps) hence the value of the photocenter o ff setremains nearly the same. In addition as the central source lumi-nosity continues to increas, the brightness of the central sourcebegins to dominate, and the photocenter gets closer to the centralsource. For one object Taris et al. (2011) found that a relationship be-tween the astrometric and photometric variability exists. We alsomodeled the expected flux variation with brightness of the per-turbed region, and found that the o ff set of the photocenter inprinciple can be a function of the flux variation only in specialcases where there is a perturbation located at the same place andthe brightness changes with time. In general, there are many pos-sible locations of the perturbations and possible values of theiremissivities with respect to the central source. The photocen-ter position varies in terms of both the central source brightness(that may show variability) and the emissivity of the bright spot,hence the relationship between the astrometric and photomet-ric variability cannot be assumed as the general rule, although itmay exist particularly in the µ as astrometric regime.On the other hand, in the case of the changes in the torusstructure, as can be seen from Table 2, there is a partial correla- tion between the photometric and astrometric variability, but itis not a rule, especially when illumination stays higher.
5. Observations vs. simulations
The amplitudes of the flux variations in quasars, at certain red-shifts, indicate that an enormous amount of energy is produced.The rapid flux variations often seen are convincing evidence ofthe compactness of the emitting region. Thus, in this case a cor-relation between astrometric and photometric variability will ei-ther not exist or be discerned only with an astrometric precisionfar higher than the mas level. At the same time, since longer,year-long, and large amplitude variations are also recorded, thesame logic would imply that the other quasars elements are notat a standstill, as discussed. The specific causes can be studiedwhen and if an observed long-term, large-amplitude optical vari-ability is related to the astrometric variability of the quasar pho-tocenter (Johnston et al., 2003). In addition, if this were verified,the relationship could indicate that a large photometric variationwould make a given quasar less apt to materialize a stable extra-galactic reference frame, such as the one from the Gaia mission.The long-term program required to monitor optical fluctuationsin long cycles can only be established by ground-based observa-tions. Therefore, the astrometric limit should be on the level offew mas, which, in turn, requires high quality seeing, telescopeimaging, and relative astrometry.We now present observations of the photocenter variabilityof two objects and discuss the possibility that it was caused bychanges to the inner structure of the AGNs.
To maximize the chances of the photocenter variability beingdetected on a mas scale, 20 quasars were selected based ontheir long variability timescales and large photo-variability. Mostobjects were collected from Teerikorpi et al. (2000), as wellas Maccacaro et al. (1987) and inspections of light curves inSmith et al. (1993). The observations were performed under theObservat´orio Nacional / MCT, Brasil, telescope time contractedto ESO at the Max Planck 2 . × . × . .
238 arcsec / px. For all the observations the same CCD wasused, keeping the quasar on a clean spot, at about one third of thediagonal starting from the optical axis. The same configurationwas repeated for all the observations of a same quasar, jitteringallowed. The observations as a rule were made within two hoursof hour angle. Red (Rc / . . / . .
7. ˇC. Popovi´c et al.: Photocentric variability of AGNs
Fig. 6.
Images of torus model at 0 . µ m for two di ff erent luminosities and corresponding inner radii, 10 L ⊙ and R in = . × L ⊙ and R in = .
16 pc (right) panel. Photocenter in both panels is denoted with a white cross; black hole in bothpanels is at the center of the images, denoted with ’x’ The photocenter o ff set between the images is 8 . -5 0 5 10 15 20 4500 4600 4700 4800 4900 5000 5100 5200 R e l a t i v e i n t en s i t y Wavelength (in A)-1 0 1 2 3 4 5 6 7 8 4650 4700 4750 4800 4850 4900 4950 5000 5050 5100 R e l a t i v e i n t en s i t y Wavelength (in A)
Fig. 7.
The best fit of the H β wavelength band (left), and broad lines (right) after subtracting the narrow components for SDSSJ121855.80 + +
8. ˇC. Popovi´c et al.: Photocentric variability of AGNs fluxes are obtained adjusting bi- dimensional Gaussians. The in-ner ring where the object counting is made and the outer ringwhere the sky background is counted are variable for each ob-ject and frame, but their ratio is kept constant. The plate scaleand frame orientation are derived by IRAF IMCOORDS frompositions of UCAC2 catalogue stars (though, since the astrome-try is totally relative, their values are of no great consequence todefine the correlation under study).Additional aspects of the method described above were pre-sented in Andrei et al. (2009), for the error analysis, and inAndrei et al. (2011), for relative astrometry to derive mas-levelvariations. A full analysis of the program itself will be presentedelsewhere (Andrei et al., 2011). Here we present the preliminaryresults regarding the R filter, where the WFI sensitivity is higher,for two selected sources (see Table 3), to exemplify the e ff ectsdiscussed in this paper. The relative astrometric and variabilityprocedure initially adjusts the frames one on top of the other, interms of coordinates and magnitudes, with respect to the quasarposition. Next, frame after frame, on the basis of the PHOT data,the objects common to all frames are stored, provided that the(X,Y) coordinates and the magnitudes do not vary above a cho-sen threshold. The common objects (X,Y) coordinates and mag-nitudes are then adjusted by a complete third degree polynomialto a mean frame, where C represents either for X, Y or M, givenby C mn − < C > n = DC + , X i , j , k A mi , j , k X i Y j M k (7)Finally, a further round of analysis discards the referenceobjects for which (X,Y) or magnitude variation are above thethreshold. The averages of (X,Y) and magnitude for the remain-ing objects (with reference to the quasar as a fixed origin) areobtained and correlated with both the time-line and each other.Table 3 presents the timeline variation in positionand magnitude for quasars J121855.80 + + + + . .
001 for both objects.From the six values of right ascension and declinationvariation for the two example sources in Table 3, we cancalculate the non-parametric correlations against the magni-tude variations. They were calculated by the Spearman rankcorrelation coe ffi cient, which permitted weighting by the in-verse squared sum of the position and magnitude uncertain-ties. For quasar J121855.80 + ∆ RA × ∆ MAG = ∆ DE × ∆ MAG = + ∆ RA × ∆ MAG = ∆ DE × ∆ MAG = >> − ). To explore whether the observed variations in SDSSJ121855.80 + z = . m .
1) and SDSS
Table 3. . The summary of the measurements of the o ff set ofphotocenter: Col. 1 - the mean epoch of observation; Col. 2 -the time interval in days between each measurement; Col. 3 -the X-direction (basically RA) astrometric variation in mas fromthe previous measurement ; Col. 4 - the Y-direction (basicallyDEC) astrometric variation in mas from the previous measure-ment; Col. 5 - the magnitude variation given in tenths of magni-tude from the previous measurement. In the first lines, the valuescorrespond to the o ff sets to the nominal CDS references. In thesubsequent lines, we present the o ff sets to the previous line val-ues. The combined corresponding errors ( σ ) are given. SDSS J121855.80 + = R = m .1DATE DAYs ∆ RA ± σ ∆ DE ± σ ∆ MAG R ± σ (mas) (mas) (10 − )2008.016 0.0 -11 ± ± ± + ± + ± + ± + ± ± ± ± + ± + ± ± + ± ± ± ± + ± + = R = m .2DATE DAYs ∆ RA ± σ ∆ DE ± σ ∆ MAG R ± σ (mas) (mas) (10 − )2007.277 0.0 -17 ± + ±
22 -0.136 ± + ± ± + ± + ± + ± + ± ± ± + ± + ± + ± + ± ±
18 -58 ±
22 -0.560 ± J162011.28 + z = . m . , we firstestimate the masses of the black holes ( M bh ) for these twoobjects. There are several estimators for M bh in AGN (see e.gMcGill et al., 2008, and reference therein), and to measurethem for these two objects we used spectra observed with HST(for SDSS J121855.80 + + β line in both objects has a red asymmetry,indicating a very complex geometry of the BLR. Also, twoseparated broad components may indicate the presence ofdisk emission. After measuring the full width at half max-imum (FWHM), we used the three estimators M S , M V and M N , given by Shields et al. (2003), Vestergaard & Peterson(2006), and Netzer & Trakhtenbrot (2007), respectively.The estimated masses for SDSS J121855.80 + Both observed objects have broad lines (type 1 AGN); in our sim-ulations, we found that the photocenter o ff set is significant only whenthe central source is partly obscured by the dust. Therefore, there is asmall chance that the observed variations are caused by changes in thetorus structure. 9. ˇC. Popovi´c et al.: Photocentric variability of AGNs −20 −15 −10 −5 0 5 10 15 20−20−15−10−505101520 X (in mas) Y ( i n m a s ) −100 −80 −60 −40 −20 0 20 40 60 80 100−100−80−60−40−20020406080100 X (in mas) Y ( i n m a s ) Fig. 8.
Observed astrometric variability of the photocenter,measured for SDSS J121855.80 + z = .
327 (up)and SDSS J162011.28 + z = . M S = . × M ⊙ , M V = . × M ⊙ , and M N = . × M ⊙ , or on average M bh = (1 . ± . × M ⊙ .In the same way, we estimated the black hole masses ofSDSS J162011.28 + M S = . × M ⊙ , M V = . × M ⊙ , M N = . × M ⊙ , or on average M bh = (4 . ± . × M ⊙ .To estimate the possibility that the photocenter variability iscaused by some perturbation in the disk (or in the BLR), we cal-culated dimensions of the BLR of these two objects, using therelation between the BLR radius and luminosity at 5100 Å (seee.g. Vestergaard & Peterson, 2006). We estimated the BLR sizesfor SDSS J121855.80 + ∼ .
02 mas) and for Mrk 877 10 light days ( ∼ . As we noted in § − − − arcsec (that translates intolight day to several hundred light day scale), which is inconsis-tent with the photocenter variations. We note that these compactregions cannot be resolved by Gaia, as its PSF will be ∼ ff set in the photocenter (at z = . − ,if the infrared luminosity is produced entirely by starbursts(Mannucci et al., 2003, see). In the extreme case of this kind ofobjects, a large supernova rate (SNr) may have influence on thestability of the photocenter. We estimate the SNr, consideringthe relation given in Mattila & Meikle (2001), and assumingthat the SNr and the star formation rate (SFR) are correlated(Mannucci et al., 2003), the latter calculated using the luminos-ity of the H α line (Calzetti et al., 2007). We could only calculatethe SNr for SDSS J121855.80 + α spectral data for Mrk 877. We obtained SFR ≈ − anda corresponding SNr ≈ − (i.e. one SN every ten years)for SDSS J121855.80 + R = F GHz / F Bband >
10, SDSSJ121855.80 + R ∼ . R ∼ .
41 (Sikora et al. , 2007), very farfrom the values shown by radio loud quasars, which tend to haverelativistic jets. Radio-quiet objects can have jet emission (e.g.Mrk 348, see Anton et al., 2002), though their radio-brightnesscan be significantly higher (Anton et al., 2002) than that of theobjects under study. There are VLA 1 . + ff set is almost aligned, especially in SDSSJ121855.80 + ff set may cor-respond to two variable sources close to each other, with the
10. ˇC. Popovi´c et al.: Photocentric variability of AGNs photocenter always shifting towards the brighter of the two. Aspeculative possibility is a binary supermassive black-hole sys-tem, of the type discussed in (see e.g. Lauer & Boroson, 2009;Bogdanovi´c et al., 2009; Shields et al., 2010; Barrows, 2011;Popovi´c, 2011, and references therein), and based on the obser-vations of double-peaked narrow and broad lines. We note thatthe broad-line shapes of the objects under study are complex(see Fig. 7) and can be properly fitted with two broad Gaussiansthat are shifted (toward either the blue or red) with respect tothe central narrow component (the vertical line in Fig. 7. InPopovi´c et al. (2000) and Shen & Leob (2010), a binary broademission-line region has been investigated, and the line profilesof this system have been discussed. To detect two peaks in thebroad line profile, it is necessary to be able to resolve the twoBLRs, and the plane of the orbit must be edge on with respect tothe line of observation. An asymmetric line profile might resultsolely from a system where the two BLRs have di ff erent dimen-sions and luminosities (see Figs. 4-8 in Popovi´c et al., 2000).Such a system might exist at the center of our quasars, and maybe the cause of their photocenter variability.We note that in addition to the binary black hole scenario,the superposition of two visually close and variable sources (seethe several examples presented in Popovi´c, 2011) can explain analigned variability. All of these scenarios should be consideredin future investigations.
6. Conclusions
We have simulated the perturbation in the inner structure ofquasars (accretion disk and dusty torus), to find how muchthese e ff ects can o ff set their photocenters, and try to determinewhether it will be observable with future Gaia mission. We haveconsidered two AGNs whose the photocenter variations havebeen observed, in order to compare them with our simulations.From our investigations, we draw the following conclusions:i) Perturbations (or bright spots) in an accretion disk maycause an o ff set of the photocenter, and this e ff ect has a goodchance of being detected by the Gaia mission. The most likelycandidates are low-redshifted AGNs with massive black holes(10 -10 ) that are in principle very bright objects. One can ex-pect a maximal o ff set of the center (in the case of a bright spotlocated at disk-edge) on the order of few mas.ii) A photocenter o ff set can be caused by changes to the torusstructure due to di ff erent illuminations of the torus when the cen-tral source is obscured by the dust. A maximal o ff set can be sev-eral mas, which also be detectable with Gaia.iii) A photocenter o ff set caused by both e ff ects is connectedto the photometric variation in the objects, but there is a smallprobability of a correlation between astrometric and photomet-ric variations. We note here that quasars with high photometricvariability are not good objects for constructing the optical ref-erence frame.iv) To exclude the possibility of the photocenter variationbeing caused by a perturbation in the accretion disk, or in theBLR, one may estimate the dimensions of the BLR and chooseobjects with a compact BLR. However, to avoid any variation inthe photocenter caused by filaments in the torus, it is preferableto choose quasars with face-on oriented tori.v) The observed photocenter variability of two quasars can-not be explained by the variation in their inner structure (ac-cretion disk and torus). It seems that the observed photocentervariation can be reproduced very well by a scenario with doublevariable sources at the center of these objects. It may indicate (as well as complex broad line shapes) that these objects are goodcandidates for binary black hole systems.At the end, we conclude that Gaia, in addition to provid-ing astrometrical measurements, may be very useful for an as-tronomical investigation of the inner quasar structure (physicalprocesses), especially in low redshift variable sources. Acknowledgements.
This research is part of the projects ”AstrophysicalSpectroscopy of Extragalactic Objects“ (176001) and ”Gravitation and the LargeScale Structure of the Universe“ (176003) supported by Ministry of Educationand Science of the Republic of Serbia. L. ˇC. P., A. S. and P. J. are grateful tothe COST action 0905 ”Black Hole in an Violent Universe” that helps themto meet each other and discuss the problem. M. S. acknowledges support ofthe European Commission (Erasmus Mundus Action 2 partnership between theEuropean Union and the Western Balkans, http: // / CTE / UI0190 / References
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11. ˇC. Popovi´c et al.: Photocentric variability of AGNs