Variability of GeV gamma-ray emission in QSO B0218+357 due to microlensing on intermediate size structures
aa r X i v : . [ a s t r o - ph . GA ] A p r Mon. Not. R. Astron. Soc. , 1– ?? (2010) Printed 27 August 2018 (MN L A TEX style file v2.2)
Variability of GeV gamma-ray emission in QSO B0218+357due to microlensing on intermediate size structures
J. Sitarek & W. Bednarek
Department of Astrophysics, University of L´od´z, PL-90236 L´od´z, Poland; [email protected], [email protected]
Accepted . Received ; in original form
ABSTRACT
Strong gravitational lensing leads to an occurrence of multiple images, with differentmagnifications, of a lensed source. Those magnifications can in turn be modified bymicrolensing on smaller mass scales within the lens. Recently, measurements of thechanges in the magnification ratio of the individual images have been proposed asa powerful tool for estimation of the size and velocity of the emission region in thelensed source. The changes of the magnification ratios in blazars PKS1830-211 andQSO B0218+357, if interpreted as caused by a microlensing on individual stars, putstrong constraints on those two variables. These constraints are difficult to accommo-date with the current models of gamma-ray emission in blazars. In this paper we studyif similar changes in the magnification ratio can be caused by microlensing on inter-mediate size structures in the lensing galaxy. We investigate in details three classesof possible lenses: globular clusters (GC), open clusters (OC) and giant molecularclouds (GMC). We apply this scenario to the case of QSO B0218+357. Our numer-ical simulations show that changes in magnifications with similar time scales can beobtained for relativistically moving emission regions with sizes up to 0.01 pc in thecase of microlensing on the cores of GCs or clumps in GMCs. From the density ofsuch structures in spiral galaxies we estimate however that lensing in giant molecularclouds would be more common.
Key words: gravitational lensing: micro — galaxies: active — globular clusters:general — open clusters and associations: general — ISM: clouds
If a large mass, such as a galaxy, is located between a sourceof radiation and observer, it will bend the trajectories of thephotons and distort the observed image. In particular it canlead to the occurrence of multiple images of the same source.In such cases, the radiation that is emitted at the same timefrom the source will travel along different paths. As a con-sequence, in the case of time variable sources, the observerwill record the same variability pattern from the various im-ages, but with a time delay dependent on the geometry ofthe source-lens-observer system. This effect due to the massdistribution of the whole galaxy, is referred to as macrolens-ing, and may be accompanied by additional effects due toindividual stars in the lensing galaxy, i.e. microlensing. Thelatter affects the images on much smaller angular scales, notobservable with imaging instruments.However, the deflection of the photon’s trajectories re-sults in changes of the magnification that can be observed(see e.g. Wambsganss 2006). The microlensing is sensi-tive to small changes in the size and the location of theemission region. Thus, it can be used to find and study the morphology of sources well beyond the reach of theangular resolution of even radio instruments. This tech-nique is suitable for search of e.g. dark matter clumps(see e.g. Paczynski 1986) and extrasolar planets (see e.g.Udalski et al. 2002). Recently, microlensing was used to ex-plain the time variability properties displayed in the hundredMeV-GeV band by the known gravitationally-lensed blazarsPKS1830-211 (Abdo et al. 2015; Neronov et al. 2015) andQSO B0218+357 (Vovk & Neronov 2015). These authorsshow that the changes in the magnification ratio of the lead-ing and trailing component are consistent with microlensingdue to individual stars in the lensing galaxy, as long as theemission region is relatively small, ∼ − cm, and therelative speed of the source and the microlens is of the or-der of 10 km/s. Those results are however at odds with thestandard paradigm of blazars, where the high-energy emis-sion is generated in compact regions moving with relativisticvelocities along the jet. Relativistic velocities are needed toexplain the observed properties of blazars, such as high lumi-nosity during flares, fast intrinsic variability, and indirectlyalso the lack of strong absorption of TeV gamma rays.In this paper we investigate whether the observed c (cid:13) J. Sitarek & W. Bednarek changes in the relative gamma-ray magnification of bothcomponents can be explained by microlensing on largerstructures than stars. The size of those objects would resultin much larger regions in the source plane being magnified bya single microlensing event, than for the case of microlensingon individual stars. Therefore, microlensing on such inter-mediate size objects, if plausible, can relax the strong con-straints on the size of the gamma-ray emission region andits velocity. We study the following classes of objects actingas possible lenses for such a process: OCs, GCs and GMCs.We focus on the interpretation of the changes in the magni-fication pattern of the 2012 high state of QSO B0218+357.In Section 2 we introduce the blazar QSO B0218+357. InSection 3 we estimate how probable the microlensing is onvarious intermediate scale structures. Using the inverted rayshooting method we compute the magnification maps fortypical parameters of such structures in Section 4. In Sec-tion 5 we discuss the plausibility of such a scenario to occurin QSO B0218+357 and how it would affect the future ob-servations of this source.
QSO B0218+357 is a blazar located at a redshift of0 .
944 (Linford et al. 2012). It is gravitationally lensedby [PBK93] B0218+357 G located at a redshift of 0 . H = 69 .
6, Ω M = 0 .
286 andΩ vac = 0 . D s = 1650 Mpc, to the lens D L =1480 Mpc and between the two: D LS = 370 Mpc. The ra-dio image shows two distinct components A and B withan angular separation of only 335 mas and an Einstein’sring of a similar size (O’Dea et al. 1992). The two radiocomponents are separated by a time delay of 10 . ± . µ A /µ B ≈ . . +1 . − . days and 11 . ± . ± ∼ Fermi
Large Area Telescope (LAT) in the MeV-GeV range(Cheung et al. 2014). Vovk & Neronov (2015) claimed to beable to decompose the emission into two separated com-ponents, delayed by ∼ . magnification ratio by a factor of a few. Interestingly, an-other flare of QSO B0218+357 in 2014 allowed the detec-tion of this source also in VHE gamma-rays (Mirzoyan 2014;Sitarek et al. 2015). In this section we consider lensing of QSO B0218+357 by dif-ferent types of intermediate size and mass structures (withmasses 10 − M ⊙ ). We investigate in details 3 objectclasses: GCs, OCs and GMCs. Such masses for the geom-etry of the observer-lens-source of QSO B0218+357 wouldstill result in microlensing effect as the separation of theindividual images is too small. Another possible target formicrolensing would be dark matter substructures (see e.g.Moore et al. 1999). However, as the details of the dark mat-ter distribution are not known and only estimated from thesimulations, we do not consider lensing on dark matter inthis work.The Einstein radius, which determines the angular scaleat which lensing can occur may be computed for a point likeobject with mass M as: θ E ( M ) = r GMc × D LS D L D S = 3 . × − (cid:18) M M ⊙ (cid:19) / [ ◦ ] . (1)Lensing can occur on the whole structure if, for the geometryof the QSO B0218+357 source-lens system, θ E is larger thanthe angular size of the lens. However, even if θ E is a factor ofa few smaller than the size of the lens, the lensing might stilloccur on substructures, or the inner part of the lens. Finally,for a coherent lensing of the whole emission region to occur, θ E must by larger than the size of the lensed source. GCs are spherical, tightly bound by gravity, collections ofstars. They are normally composed of a few times 10 late-type stars, within a typical half-mass radius of the order of afew pc. They are distributed in the spherical galactic halo. Inthe Milky Way galaxy so far over 150 GC have been detected(Harris 1996), but for example in the Andromeda galaxy ∼
500 are expected (Barmby & Huchra 2001). Giant ellipti-cal galaxies, such as M87, can have as much as 13000 GCs(McLaughlin et al. 1994). The density of the stars at the ra-dius R from the centre of the cluster can be described bythe following profile (see Michie 1963; Kuranov & Postnov2006): D ( R ) = , R < R c ( R c /R ) , R c < R < R h ( R c R h ) /R , R h < R < R t , (2)where R c , R t and R h = p R c R t / c (cid:13) , 1– ?? Distance from the center [kpc] −
10 1 10 G C k − − − Figure 1.
Enhancement of the probability of lensing on a GCas a function of the distance of the image from the centre of thelensing galaxy for QSO B0218+357. they mostly populate the galactic plane. In both, GC andOC, radiation pressure and supernova explosions drive thegas away from the cluster. Emission of sources with sizesup to ∼ θ E D S = 0 . p M/ M ⊙ pc can be magnified viamicrolensing on a GC or an OC.Let us now estimate how probable a lensing event isby computing the microlensing optical depth τ . It can beestimated as τ = Nkπ ( θ E ( M ) D L ) /S , where N is the totalnumber of GCs or OCs in the lensing galaxy and S is theprojected size of the region in which they are distributed. k , dependent on the distance from the centre of the lensinggalaxy, is the correction factor for the inhomogeneity of thesurface density of the clusters. In the case of GCs, we cantake S GC = πr halo , where r halo is the size of the halo inwhich they are distributed. We obtain: τ GC = 9 . × − k GC M GC M ⊙ N GC (cid:18) r halo (cid:19) − . (3)Note that this estimation does not depend on the orienta-tion of the lensing galaxy. As the special density of GCs isstrongly peaked towards the centre of a galaxy ( ∝ R − , seeHarris & Racine 1979) and the surface density is addition-ally enhanced by the projection effect, k GC can obtain highvalues. In order to estimate it we use the de Vaucouleurs(1977) relation on the surface density of GCs in the MilkyWay: log σ ( R ) = 3 . − . R/ kpc) / . In order to use theabove equation for [PBK93] B0218+357 G, one has to cor-rect the distance scale of R by a factor of 2 . k GC as the ratio of thesurface density at the distance R from the centre of thelensing galaxy, to a flat surface density up to a radius of r halo = 10kpc and plot it in Fig. 1. For the distances ofinterest in QSO B0218+357 we obtain k GC (0 .
47 kpc) ∼ k GC (1 . ∼ S OC = πr , where r disk is the ra-dius of the galactic disk where the OCs are present, τ OC,face =6 . × − k OC , face × M OC M ⊙ N OC (cid:18) r disk (cid:19) − . (4)However, if the same lens is seen edge-on the areacovered by OCs is much smaller. It can be computed as S OC = 4 r disk h disk , with h disk being the maximum height ofthe disk up to which the OCs are observed, τ OC,edge =8 . × − k OC , edge × M OC M ⊙ N OC (cid:18) r disk h disk (cid:19) − . (5)Due to the projection effect, the lensing on OCs would bemuch more probable if the lensing galaxy itself is seen edge-on. Note however, that in the case of QSO B0218+357, theoptical image with the individual spiral arms is visible face-on. The optical depth values are rather low making the lens-ing on GCs and OCs not very probable except for galaxieswith a greater abundance of star clusters. GMCs are large gas structures where intense star formationoccurs. They typically have masses of the order of 10 M ⊙ and radii ∼
20 pc (Blitz 1993). Nevertheless, there is a largespread in both of those parameters (see e.g. Murray 2011).GMC have complicated structures, with filaments, clumpsand cores (see Williams et al. 2000 and references within).There are over 10 GMCs in the Milky Way, with 10 ofthem having masses above 2 × M ⊙ (Murray 2011).Since GMCs are much more irregular than star clusters,microlensing can occur on smaller scales (clumps) withinthem. We can compute roughly the optical depth for a sourcebeing microlensed at a given moment by a clump in a GMC: τ clump = k GMC N GMC N clump ( θ E ( M clump ) D L ) /r = 2 × − k GMC M GMC M ⊙ N GMC (cid:18) r disk (cid:19) − , (6)where N clump and M clump are the number and mass ofclumps in a typical GMC and M GMC = N clump M clump .Based on the H distribution in the Galaxy, estimated withCO measurements (Sanders et al. 1984), and rescaling themfor the different sizes of [PBK93] B0218+357 G and theGalaxy, the inhomogeneity factor k GMC is expected to be ofthe order of 1 for the A image, and of the order of 10 for theB image. Moreover, as the projected position of the lensedsource traverses the GMC, it can cross multiple individualclumps on time scales of months. Therefore, the probabilityfor the image of a lensed source to cross a GMC, and thusbeing periodically magnified via microlensing on individualclumps, scales with the projected area of the GMCs. It is afactor ∼
60 larger then the value obtained in Eq. 6.In fact, there are reasons to believe that at least oneof the images of QSO B0218+357 crosses a GMC in thelensing galaxy. Falco et al. (1999) interpreted the differentreddening of the two images of QSO B0218+357 as an addi-tional absorption of the leading image with the differentialextinction ∆ E ( B − V ) = 0 . ± .
14. The absorption is sostrong, that it inverts the brightness ratio of the two images c (cid:13) , 1– ?? J. Sitarek & W. Bednarek in the optical range, making the trailing image brighter.Moreover, molecular absorption line has been detected inthe leading image, allowing the estimation of the H columndensity, which is a rather large value of 0 . − × cm − (Menten & Reid 1996). Interestingly, a similarly large col-umn of absorbing gas has been also detected in the otherknown gravitationally lensed gamma-ray quasar PKS1830-211 (Wiklind & Combes 1996), for which microlensing wassuggested (Neronov et al. 2015). In this section we use numerical simulations to compute themagnification maps caused by microlensing on intermediatescale structures. We use the inverse ray shooting method (seee.g. Schneider & Weiss 1986). We project a large number ofpoints homogeneously on the lens plane and compute theircorresponding position in the source plane. To compute thedeflection angles of individual rays we use the typical thinsheath approximation of the lens, i.e. we project the 3D dis-tribution of the mass on the XY plane of the lens. Then,we divide the source plane in a grid of cells and computethe magnification as the ratio of the number of rays hittinga given cell to the average number of rays emitted in thesolid angle of this cell. The maps presented in this work aredivided in 1000x1000 cells and 1 − × rays are simulatedper map. Therefore, the accuracy of the computed multipli-cations is ∼ − We simulate a GC with the total mass of 10 M ⊙ composedof individual stars with masses of 0 . M ⊙ . The stars are dis-tributed according to Eq. 2. Note that as the number of starsis large, and we are interested in the lensing on the wholestructure of GC rather than on the individual stars the pre-cise distribution of the star masses is not relevant for thisstudy. We select R c = 0 . R t = 30 pc (correspondingto R h = 3 pc) as a typical GC parameters. The shadowing ofindividual rays by the stars is negligible, therefore the starsare treated as point masses. In Fig. 2 we show the magni-fication map obtained from such a GC with the inverse rayshooting method. The caustics normally occurring in the mi-crolensing on a set of point-like masses are not visible in thisplot as they happen on size scales below the resolution ofthe plot. On the other hand, the combined effect of the starsin the core of the GC causes strong magnification. Values ofthe order of 10 occur if the projection of the emission regioncrosses the core. For a source with an emission region below0 .
01 pc, magnifications up to a factor of 100 are achieved atthe centre of the GC.
OCs are less abundant in stars than GCs. They also showhigher irregularities in their structure. This causes difficul- ties in modelling the distribution of the mass inside OC. Forthose simplified calculations we assume the same profile aswas used in the case of GCs (see Eq. 2). We selected pa-rameters describing the typical size of an OC following theKharchenko et al. (2005) catalog. We simulate the OC witha geometric size determined by R c = 1 . R t = 4 . M OC = 3 × M ⊙ . We assumed a power-law distribution of the mass of the stars with a standard in-dex of − .
3. The distribution spreads between 0 . M ⊙ and100 M ⊙ . Those mass ranges were selected such that the num-ber of massive OB stars agrees (after correction for the totalmass of the OC) with the number observed in the Cyg OB2cluster (Butt et al. 2003).The magnification obtained in such a case is presentedin Fig. 3. As OCs are on average much less massive than GCsand still spread over a relatively large size, there is nearlyno coherent lensing by the whole structure. Relatively smallregions, 0.01 pc (resolution of the simulations) – 0.05 pc witha magnification a factor of a few occur due to the microlens-ing on individual stars and crossing of caustics for the caseof a few nearby stars. GMCs can have a very complicated structure. For simplicitywe simulate a GMC as a spherical structure composed of in-dividual extended clumps. We use a typical mass and radiusof GMC of M GMC = 2 × M ⊙ , R GMC = 20 pc. We con-sider two different scenarios of the distribution of clumps,homogeneous (i.e. dN clump /dV ∝ const) and more peakedtowards the centre of the GMC (i.e. dN clump /dV ∝ r − ).We take the mass distribution function of the clumps fromStutzki & Guesten (1990). The masses of individual clumpsare drawn from a power law distribution with an index − .
7. The values of masses are spread between 0 . M ⊙ and3 × M ⊙ . The radius of the clump is estimated follow-ing the empirical correlation shown by Stutzki & Guesten(1990): R clump = 0 . × p M clump / M ⊙ . (7)We assume that the individual clumps have homogeneousmass density.In Fig. 4 we show the results of the calculations forthe case of homogeneously distributed clumps. For the as-sumed parameters, the Einstein radius computed accordingto Eq. 1 is a factor of a few smaller than the actual size ofa GMC. Then, most of the magnification happens on indi-vidual clumps. Magnifications by a factor of a few can beachieved and occur on distance scales of a fraction of pc.In Fig. 5 we present the magnification map for the caseof GMC with a dN clump /dV ∝ r − density of the clumps.In this case, due to more peaked mass distribution, the mi-crolensing is mostly pronounced in the inner pc. Also, it ismuch more common for a combination of multiple individualclumps to cause strong magnifications ( >
5) at the causticcrossings. Note however, that those strong magnificationsare possible for sources with the sizes up to ∼ .
01 pc. c (cid:13) , 1– ?? Magnification −
10 1 10 F r a c t i on o f m ap abo v e t he m agn i f i c a t i on − − − − − − [pc] lens X5 − − − − − [ p c ] l en s Y − − − − − ] D en s i t y [ M s un / p c Figure 2.
Microlensing by a GC with M GC = 10 M ⊙ , R c = 0 . R h = 3 pc. Top panels: magnification maps obtained for theresolution of 0.011 pc (right map is zoomed by a factor of 10) Fraction of a map with a magnifications above a given value is shown in thebottom left panel. The surface mass density of GC (in the reference frame of the lens), with individual stars marked with black pointsis shown in bottom right panel. [pc] lens X-5 -4 -3 -2 -1 0 1 2 3 4 5 [ p c ] l en s Y -5-4-3-2-1012345 ] D en s i t y [ M s un / p c Magnification0 1 2 3 4 5 6 7 8 9 10 F r a c t i on o f m ap abo v e t he m agn i f i c a t i on -5 -4 -3 -2 -1 Figure 3.
Microlensing by an OC with M OC = 3 × M ⊙ , R c = 0 . R t = 4 . (cid:13) , 1– ?? J. Sitarek & W. Bednarek [pc] lens
X20 − − − − [ p c ] l en s Y − − − − ] D en s i t y [ M s un / p c Magnification0 1 2 3 4 5 6 7 8 9 10 F r a c t i on o f m ap abo v e t he m agn i f i c a t i on − − − − − − [pc] lens X2 − − − − [ p c ] l en s Y − − − − ] D en s i t y [ M s un / p c Magnification0 1 2 3 4 5 6 7 8 9 10 F r a c t i on o f m ap abo v e t he m agn i f i c a t i on − − − − − Figure 4.
Microlensing by a GMC with M GMC = 2 × M ⊙ , R GMC = 20 pc composed of homogeneously distributed clumps. Surfacedensity (in the reference frame of the lens) of the mass of the lens, with individual clumps marked with black points (left panels).Magnification map in the reference frame of the source (middle panels). Fraction of the map with a magnification above a given value(right panels) Top panels show the case of the whole GMC (map resolution of 0.045 pc) Zoom to the inner part of the GMC with ahigher resolution of 0.0045 pc is shown in bottom panels. [pc] lens
X20 − − − − [ p c ] l en s Y − − − − ] D en s i t y [ M s un / p c Magnification0 1 2 3 4 5 6 7 8 9 10 F r a c t i on o f m ap abo v e t he m agn i f i c a t i on − − − − − − [pc] lens X2 − − − − [ p c ] l en s Y − − − − ] D en s i t y [ M s un / p c Magnification0 1 2 3 4 5 6 7 8 9 10 F r a c t i on o f m ap abo v e t he m agn i f i c a t i on − − − − − − Figure 5.
As in Fig. 4 but for a distribution of clumps in GMC following dN clump /dV ∝ r − c (cid:13) , 1– ?? time [days]-200 -150 -100 -50 0 50 100 150 200 M agn i f i c a t i on Figure 6.
Expected evolution of the magnification shown in themap on Fig. 4 for a source crossing with superluminal speed of5 c . The magnification is averaged over the size of the emissionregion of 0.01 pc. The blue, red and black curves show the case ofcrossing along the Y direction -0.5 pc, 0 pc and +0.5 pc from thecentre of the map If the gamma-ray emission of QSO B0218+357 is emittedaccording to the classical blob-in-jet models, it would belikely accompanied by a superluminal motion of the emis-sion region. Such movement is at odds with the interpre-tation of the change of the magnification ratio of the twoimages in terms of microlensing on individual stars in thegalaxy (Vovk & Neronov 2015). The change in the magni-fication factor can also be explained as microlensing on in-termediate scale structures. Vovk & Neronov (2015) claimedchanges in the magnification factors occurring in the
Fermi -LAT data on the time scales of 20 days. In order to accountfor these, with a typical 5 c superluminal motion, one re-quires features in the magnification map with a length of ∼ . ∼ . c . As ex-pected, crossing of the individual clumps in GMC causesmagnification by a factor of a few lasting between days andhundreds of days. The magnification pattern is complicatedas multiple clumps might influence the magnification at agiven moment.In order to study in detail the possible time scalesfor various magnifications, we simulated 10 random pathsthrough the central region of GMC. For each path wesearched for the time periods during which a magnificationwas above a given value. The results of the calculations, for aflat and a peaked distribution of clumps, are shown in Fig. 8.Due to the interplay between the influence of clumps withvarious sizes, the distribution of time scales for a flares of agiven magnification is rather broad. Also for some paths the time [days]-200 -150 -100 -50 0 50 100 150 200 M agn i f i c a t i on Figure 7.
Like in Fig. 6, but for the case of GMC with a peakedprofile (corresponding to the map in Fig. 5).
Min magnification1.5 2 2.5 3 3.5 4 4.5 5 l og ( D u r a t i on / da y ) Min magnification1.5 2 2.5 3 3.5 4 4.5 5 l og ( D u r a t i on / da y ) Figure 8.
Time scales of different magnifications for a sourcecrossing randomly selected paths in the inner 4 × region ofGMC. The source is moving with a superluminal speed of 5 c .The case of a flat distribution of clumps in GMC (using magnifi-cation map of 4) is shown in the top panel. The case of a peakeddistribution of clumps in GMC (using magnification map of 5) isshown in the bottom panel.c (cid:13) , 1– ?? J. Sitarek & W. Bednarek
MJD-5610040 60 80 100 120 140 160 180 200 T o t a l A / B m agn i f i c a t i on r a t i o Figure 9.
Changes of the total magnification ratio of the leadingto trailing component seen in
Fermi -LAT data during 2012 highstate of QSO B0218+357 (black circles, Vovk & Neronov 2015).The black solid line shows the changes of the magnification ra-tio obtained along one of simulated paths of the trailing imagethrough a GMC with mass of 2 × M ⊙ . Strong lensing withmagnification ratio of 3.6, apparent superluminal speed of thesource of 5 c and size of the gamma-ray emission region of 0.01 pcare assumed. emission might start in a region already magnified, thereforeshortening the time scale compared with crossing throughcomplete clump. The flares with a time scales of a few tens ofdays can be obtained for the peaked distribution of clumpsup to a magnification factor of a few.In order to explain the changes in the magnification ra-tio claimed by Vovk & Neronov (2015) in the framework ofthis model, we compute the total magnification ratio as theproduct of the strong lensing magnification and the magni-fication from microlensing on clumps in a GMC. Based onthe radio measurements we assume the value of the stronglensing magnification ratio of the leading to trailing image of ∼ . Fermi -LAT data.One may question how stable is the magnificationmap being considered in the case of microlensing on themedium-sized structures. In particular, it is curious whethersignificant changes of the magnification pattern can hap-pen during the 2012 and 2014 flaring period, assumingthat the location of the emission zone is the same inboth cases. The Keplerian velocity of GC or GMC orbit-ing around the lensing galaxy at the distance r is v =670( M/ M ⊙ ) / ( r/ − / [km / s], where M is thepart of the mass of the lensing galaxy contained within r . The relative velocity of the source galaxy, lens, and theMilky Way is also expected to be of the same order (see themeasurement of the Local Group with respect to the CosmicMicrowave Background, 627 ±
22 km s − , Kogut et al. 1993).These speeds are about an order of magnitude larger thanthe movement of individual clumps in the GMC (see e.g.Stutzki & Guesten 1990). Therefore, we can expect shifts ofthe magnification patterns by ∼ − pc per year, which is much smaller than the size of the individual clumps in aGMC.On the other hand, the location of the emission region inQSO B0218+357 might vary between different flaring states.Such possibility is further supported by clearly differentGeV gamma-ray spectral shape in both cases (Buson et al.2015) and by a different type of activity (multiple flares in2012 versus a single flare in 2014). In the case of flat spec-trum radio quasars, the gamma-ray emission can be easilygenerated up to R em , max = 0 . θ jet , this corre-sponds to a distance (measured in the frame of the lens)of 8 × − ( R em , max / . θ jet / ◦ )pc. Therefore, in thisscenario it is still expected that the microlensing magni-fication pattern does not change significantly for differentflaring periods. Note however that one to two order of mag-nitude larger distances from the base of the jet are possibleif the emission occurs as a comptonization of radiation ofthe dust torus rather than the broad line region. In thiscase the changes of the magnification pattern on the yearlyscale would be expected. Therefore, the comparison of theevolution of the relative magnification ratio between differ-ent flaring periods might be another discriminant in the longstanding problem of the location of the emission region in theFSRQs. Finally, Cheung et al. (2014) and Barnacka et al.(2015) interpreted the difference in the time delay of thetwo images in the radio and in gamma rays as a differencein the projected distance of the radio core and the high en-ergy emission region to be ∼
50 pc. If the location of thegamma-ray emission region can vary by a fraction of thisnumber (which might be difficult taking into account theavailable radiation fields which might serve as a target forgamma-ray production), the projected location of the emis-sion zone might move in and out of the region covered by aGMC.One may wonder whether the occurrence of medium sizestructures like a GMC or a GC in the line of sight of oneof the quasar images might affect the spectral shape of theobserved gamma rays from those sources. We note howeverthat the optical emission of stars in the GC is too weakto provide a strong absorption of the sub-TeV gamma-rays.On the other hand, the IR radiation from the GMCs wouldonly affect TeV photons which are normally not observablefrom distant sources (such as lensed blazars) due to strongabsorption by the extragalactic background light.
We investigated the microlensing of QSO B0218+357on medium-size structures in its lensing galaxy[PBK93] B0218+357 G. We studied the cases of GC,OC and GMC. We derived the probability of such an eventand expected magnification values as well as their timescales.We conclude that microlensing, occurring on clumps ofa GMC, is a tempting alternative to explain the variabil-ity of the magnification factor seen in the GeV gamma-rayobservations of QSO B0218+357. Such a scenario is consis-tent with the current models of high-energy emission fromblazars and, contrary to the microlensing on individual stars,is able to explain the high luminosity of a flare with simple c (cid:13) , 1– ?? relativistic boosting of the emission. The scenario is furthersupported by the measurements of large H column densi-ties in the direction of some of the images of the two lensedblazars in which short-term changes in the magnification dueto microlensing were observed. ACKNOWLEDGMENTS
We would like to thank Ievgen Vovk and the anonymousjournal reviewer for their comments on the manuscript. Wewould also like to thank John E. Ward for his English cor-rections of the manuscript text. This work is supported bythe Polish NCN No. 2014/15/B/ST9/04043 grant. JS is par-tially supported by Fundacja U L.
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