Is the rapid radio variability seen in PKS due to. BL Lacertae (BL Lac) Objects are a population of active galaxies that possess featureless

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1 Mon. Not. R. Astron. Soc. 000, 000{000 (1996) Printed 11 November 1996 (MN L A TEX style le v1.4) Is the rapid radio variability seen in PKS due to microlensing? 1;2 G. F. Lewis? and 2 L. L. R. Williams y 1 Astronomy Program, Dept. of Earth and Space Sciences, SUNY at Stony Brook, Stony Brook, NY , USA 2 Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA Final Draft ABSTRACT BL Lacertae (BL Lac) Objects are a population of active galaxies that possess featureless spectra, rapid variability from the X-ray to the radio, and strongly varying polarization. One explanation of these extreme properties invokes the action of gravitational microlensing due to stars in an intervening galaxy, amplifying the continuum of a background active galaxy to swamp the line emission. The BL Lac object PKS exhibits rapid variability at radio frequencies and it has been suggested that microlensing by sub-solar mass stars is a possible source of these uctuations. In this paper we demonstrate, when considering the physical scale of the optical through radio emission region in BL Lac object systems, that microlensing can not have a dominant inuence on the properties of this system, and therefore suggest that the observed variability is due to some other process. Key words: Gravitational Microlensing, BL Lacertae Objects 1 INTRODUCTION Within our own galaxy, microlensing by individual halo stars can amplify the light from stars in the Galactic bulge and the LMC (Paczynski 1986b; Alcock et al. 1995). Due to the low optical depth of microlensing stars in the Galactic halo, such events are rare and tend to be very simple in form. At cosmological distances, however, the action of stars in an intervening galaxy can induce violent uctuations in the observed light curve of a high redshift quasar, resulting in complex variability (Wambsganss 1990). Such variability was rst observed in Q , the Einstein Cross Lens (Irwin et al. 1989). Microlensing has also been cited as a source of the residuals seen between the light curves of the Double Quasar, Q (Schild and Thomson 1994), and as a mechanism to explain all of quasar variability (Hawkins 1993; Hawkins 1996). Recently, Romero et al. (1995) have analyzed the radio variability seen in the BL Lac object PKS They concluded, from time-scale arguments, that the variability seen in this system is consistent with microlensing by stars in a foreground galaxy. This subject is the focus of this paper. The paper begins with a review of the theory of microlensing, followed by its applicability to BL Lac systems.? gfl@brenda.ess.sunysb.edu y llrw@ast.cam.ac.uk The observational monitoring campaign of the BL Lac system, PKS , is presented in Section 2.3, with a discussion of the suggested eects of microlensing in this system, presented by Romero et al. (1995). These arguments are discussed in the latter sections of this paper, where we demonstrate that microlensing can not play a dominant role in the observed properties of this system. 2 BACKGROUND 2.1 Microlensing Considering an isolated, point-mass micro-lens of mass M, the Einstein radius, in the source plane, is dened to be (Schneider et al. 1992); o = r 4GM c 2 D osd ls D ol : (1) Here, D ij are the source (s), lens (l) and observer (o) angular diameter distances. A point-like source passing within this radius is amplied by a factor of at least 1:34. The light curve induced by the passing of an isolated microlens possess a very simple form, with a characteristic time-scale,, due to a star of mass M, dened to be o ; (2) V e c 1996 RAS

2 2 G. F. Lewis and L. L. R. Williams where V e is the eective velocity of the source across the source plane (Kayser et al. 1986). When there are many stars in the beam of a lensed object the source plane is covered with a intricate web of caustics, and the resulting light curves possess complex variability, with non-symmetric uctuations (Paczynski 1986a; Wambsganss 1990; Lewis et al. 1993). The surface mass density of microlensing objects,, is expressed in units of a critical surface density, c2 D os cr = : (3) 4 G D old ls The quantity is referred to as the microlensing optical depth. Although complex, the time averaged amplication is the theoretically expected mean z, th = (1? )?2 : (4) In a high optical depth regime, when the light from the distant source shines through the inner regions a foreground galaxy, the action of the individual lensing masses combine in a highly non-linear fashion, and the time-scale of individual \events", given by Equation 2, is no longer characteristic of the variability. With this can not be used to characterize the mass of the microlenses (Wambsganss 1992). Here, statistical analysis of the temporal properties of the variability seen in microlensing light curves can be used to constrain the form of the underlying mass-function of the microlenses (Lewis and Irwin 1996). Chang (1984) demonstrated that the degree of microlensing amplication of a source is strongly dependent on its scale size relative to the Einstein radius of the characteristic lensing masses. At caustic crossings a point source is amplied by an innite amount, but any physical extent leads to nite amplications. Sources whose scale size is only a fraction of an Einstein radius can be amplied by signicant factors, while sources whose scale is much greater than an Einstein radius are amplied by a negligible amount. The dependence on source scale size can be seen in the light curves presented by Wambsganss (1990), and can strongly aect the spectra of a microlensed source which possess emission regions of diering scale. This is case microlensed active galactic nuclei, the population including BL Lac objects, where infrared through X-ray continuum emission is thought to arise from a compact accretion disk around a central black hole, while radio and line emission is thought to arise from a larger region (Rees 1984). Such a dierential amplication eect has recently been observed in radio observations and in optical spectroscopy of the quadruply lensed quasar, Q (Lewis et al. 1996a; Lewis et al. 1996b; Falco et al. 1996) 2.2 Microlensing Models of BL Lac Objects Several authors have considered gravitational microlensing as a source of the extreme properties observed in BL Lac systems. Ostriker and Vietri (1985,1986,1990) suggested that z Note that strictly this equation should contain a term for the external shear,, due to the action of matter on large scales. The action of shear will not quantitatively change the conclusions presented in this paper and has, therefore, been not considered. BL Lac systems are in fact Optically Violently Variable (OVV) quasars whose central continuum source has been amplied by the action of microlensing. In this scenario, the more extended line emitting regions are too large to be signi- cantly enhanced and in the case of BL Lac systems it is assumed that the enhanced continuum completely swamps any line emission. It should be noted that, in the Ostriker and Vietri model, the observed variability arises in the source OVV and is not a consequence of microlensing. Several models exist to explain the observed spectral properties of BL Lac system. The variability seen in multiband monitoring of the BL Lac object system PKS (Edelson et al. 1995) appears to be most consistent with optical-infrared-radio emission arising from a shock in a relativistic jet (Ghisellini et al. 1985). The details of the shock acceleration and high frequency emission is a matter of debate, but it is thought that the radio emission arises in a region where the jet has opened to 1pc. As pointed out by Kayser (1988) and Gear (1991), for typical stellar masses at cosmological distances, such an emission region is too large to be signicantly microlensed. Gopal-Krishna and Subramanian (1991; Subramanian and Gopal-Krishna 1991) suggested that the observed variability could be due to microlensing of such a relativistic jet. In the case of a BL Lac object, where the source is a jet moving with a relativistic velocity V t, at an angle with respect to the observer (Rees 1966), the eective source velocity, Equation 2, is superluminal and is given by V e = c sin (1 + z s) (1? cos ) ; (5) where = V t c and z s is the redshift of the BL Lac object. If microlensing is the source of the properties in BL Lac systems, then it would be expected that these systems would be found to lie behind foreground galaxies. Observationally, this has proved to be the case in a number of cases (Stocke et al, 1995 and references therein). The high optical depth needed to grossly amplify the continuum, thus swamping the emission lines, requires the source to be well aligned with the central regions of a foreground galaxy. As this is a random projection (the eects of magnication bias are not very signicant), statistically it would be unlikely that the BL Lac object would appear directly aligned with the core of the foreground lensing galaxy. Also, fraction of BL Lac systems should be macrolensed into multiple components (Narayan and Schneider 1990). Observationally, BL Lac systems are seen to be highly aligned with the core of extended \host" emission, with no cases of multiple imaging (Abraham et al. 1991; Abraham et al. 1993). These arguments alone have led some authors to conclude that gravitational lensing can play a negligible role in BL Lac systems (Narayan and Schneider 1990; Merrield 1992). 2.3 PKS Observations of the BL Lac object PKS normally display a featureless spectrum. However, during minima, spectra have revealed the presence of two separate emission features. These were identied as being due to C III] 1909 and Mg II 2798, indicating that this system is at z = 0:894 (Peterson et al. 1976; Wilkes et al. 1983).

3 Imaging by Stickel et al. (1988) reveals that PKS appears superimposed within a system of low redshift galaxies. A spiral galaxy, at z = 0:186, is seen to lie in an approximately eastward direction of the BL Lac object, while PKS is itself seen to lie at the core of an extended system, with an exponential disk prole. Although the redshift for this system is unknown, the absence of Mg II and Ca II absorption indicates that it lies at 0:18 < z < 0:32 (Tytler et al. 1987). This BL Lac object has been the subject of several monitoring campaigns, in diering wave-bands (Maraschi et al. 1985; Luna 1990), and recently was observed in the radio, at 1.42GHz, at twenty minute intervals over several hours at seven epochs in a two week period (Romero et al. 1994). These observations revealed large variations, up to a factor of 1:7, on time-scales of 10 4 seconds. By considering the source of the radio emission being a shock in a jet moving superluminally ( app 10) Romero et al. (1995) interpreted these variations as being due to microlensing by stars in the foreground galaxy. Applying the formalism for independent microlenses, and considering amplications of > 1:34, three \events" were tted with a symmetric, isolated point mass lensing light curves. The asymmetric nature of a fourth event required the combination of two independent point mass light curves. The duration of the events < 1:2hours, implies that the lenses must consist of sub-solar mass stars in the range 10?4? 10?3 M. To circumvent the arguement presented by Gear (1991), that the emission region in BL Lac objects is to large to be signicantly enhanced by microlensing, Romero et al (1995) invoke the eects of \relativistic rotation" which can make the jet appear vanishingly thin (Eichler and Smith 1983), for certain combinations of jet orientation and velocity. In Section 3.2 we discuss this eect and demonstrate how this cannot induce the violent radio uctuations observed in PKS MICROLENSING IN PKS Microlensing Simulations To examine the possible eect of microlensing on the radio region, several examples of microlensing light curves were generated using the backwards ray-tracing technique (Kayser et al. 1986; Wambsganss 1990). Here, a regular grid of rays are shot into a star eld and suer a gravitational lensing deection. The rays are then traced into the source plane, where they are binned. The density of rays over the source plane is then a map of the amplication. The convolution of a source surface brightness prole with this map gives the brightness of composite microlensed image. A microlensing light curve is compiled by repeating this procedure at positions along a line in the source plane. The light curves for the simulations are presented in Figure 1. For each optical depth ( = 0:05; 0:1; 0:5), the ampli- cation map was convolved with three Gaussian sources. The details for each source employed is presented in Table 1. The x-axis is in units of the Einstein radius for a solar mass star ( o), and can be converted into observed temporal units using Equation 2. For a app 10 each unit corresponds to 2:510 5 secs. This is greater than the observed time-scale, Light Curve Microlensing in PKS Source Radius h? pc r s= o 1 10? ? ? Table 1. Details of the sources employed in the simulations presented in Figure 1. This values are for lens masses of 1M. The nal column presents the source radius in units of an Einstein radius of a Solar mass star. of secs observed for the radio variability in PKS (Romero et al. 1994), but noting that the lensing time-scale scales with the square root of the characteristic lensing mass it can be seen that the observed and simulation time-scales will agree if the lensing mass is 10?3 M. Scaling the mass in this way also scales the eective source scale-size in the simulation presented in Figure 1 by a factor of 0:03. With this, the dotted light curve in each frame represents a source of 1 10?2 pc. As can be seen, although the light curves for the very small sources do display variations, the dotted light curves show no variability and therefore we can expect that, for a reasonable model of the emission regions in relativistic jets in BL Lac objects, microlensing plays a negligible r^ole in the observed radio variability in PKS The eects of Relativistic Rotation As mentioned previously, for a source to be signicantly amplied during gravitational microlensing its scalesize must be smaller than the Einstein radius of the characteristic mass of the lensing objects. As the radio emission region in BL Lac objects is thought to be typically 1pc in extent, Romero et al. (1995) suggest that in PKS the jet may suer from a relativistic aberration, or rotation, such that it appears edge on and therefore innitely thin (Eichler and Smith 1983). With this, they claim, the radio emitting region can have a small enough scale size to be signicantly enhanced. In this section we examine this claim and the eect of microlensing on an innitely thin, linear source. Let us consider an innitely thin, circular shock traveling along a jet at a velocity c at an angle with respect to an observer, the apparent radius, r 0, of the shock region in the plane containing the source, observer and jet, is r 0 r = cos? 1? cos ; (6) where r is the actual radius of the shock region. The tangential radius is unchanged and therefore the apparent projected area of the shock front is given by rr 0. Equation 6 is plot-? ted as a function of = 1? 2? 1 2 in Figure 2, for several values of the jet orientation. For jets where cos = the projected radius of the jet is zero and, as the shock is considered to be innitely thin, the emission appears to come from a one-dimensional source. As an aside, it is interesting to note that, for a xed jet velocity,, as one moves to greater jet angles than the case where the jet's apparent

4 4 G. F. Lewis and L. L. R. Williams Figure 1. Example light curves for three dierent microlensing optical depths. From top to bottom, these are = 0:05, 0.10 and 0.50 respectively. The lines on each plot are for diering source size, with the solid line representing the smallest, dashed intermediate and dotted the largest. All the sources are Gaussian and the details of each source size is presented in Table 1. All the stars in the simulation were 0:386M [the simulation algorithm was designed to also implement a Scalo mass function (1986) between the limits of 63M and 0:087M, which has a mean mass of hmi = 0:386M (Williams and Saha 1995)], and the units on the abscissa are Einstein radii for a solar mass star, while the uctuations are in magnitudes, relative to the mean microlensing amplication (Equation 4). Figure 2. The apparent projected radius of a shock in a jet mov-? 2? ing with a Lorenz factor = 1? 1 2, at several angles,, with respect to an observer. The dashed line indicates where the source has a projected radius of zero. Note that a negative projected radius indicates that the source has appeared to rotate passed this zero width conguration, and an observer is seeing a reversed image of the source on the sky. thickness is zero, the projected jet radius is negative, appearing as though one can see the back of the shock front. The eect of gravitational microlensing on an extended, one-dimensional source has been studied by Witt (1993) and Lewis et al.(1993,1995). The inuence of a single microlensing object is presented in Figure 3. As well as kinking the shock front, the point mass adds an image loop (note that this loop is not attached to the microlensing object as the shock front is nite in extent) x. Typically, the additional length of image is < 2 o, and so the fractional increase of ux received during microlensing of an isolated point mass is < o=r. For a shock front 1pc in extend this is < few%. As with o, this value scales with the square root of the characteristic lensing mass. The eect of an ensemble of stars, which would be expected at a reasonable optical depth to microlensing, is presented in Figure 3 of Lewis and Irwin (1996). The linear source is deformed into a series of \wiggles", accompanied x The length of the image line is nite, even if the source line crosses caustics. This is illustrated graphically in the gures presented by Witt (1993). This implies that, unlike a point source, an innitely thin line does not suer innite amplication as it crosses a caustic network

5 Microlensing in PKS Shock Front source is a thin line, a result of a relativistic rotation of a thin planar shock front in the jet. For microlenses of 1M a source would have to have a length of 4:2 10?4 pc to possess the level of variability observed in the optical, with smaller microlenses requiring even smaller source size. Observational evidence indicates that the optical emission arises from a shocked region in a relativistic jet of at least 10?2 pc in extent (Edelson et al. 1995; Gear 1991). This is too large to be signicantly amplied, and we reiterate the conclusions of Kayser (1988) and Gear (1991), that the sources of optical through radio emission in BL Lac objects are too large to be microlensed. Figure 3. A schematic representation of microlensing of an innitely thin shock front. The zoom-box represents the image of the shock front in the vicinity of a point mass lens. by a number of image loops. As the source moves behind the lensing masses this image of the shock front changes, but the total apparent amount of image remains eectively constant. Fluctuations, again at 1% for solar mass stars, can be expected, but this value will decrease for any realistic jet due to its nite thickness. 4 MICROLENSING AT OTHER WAVELENGTHS? PKS is known to vary at frequencies higher than the radio. In particular, the uctuations in the optical have been observed to be larger than in the radio band. Historic optical light curves of PKS have recorded uctuations of over 4 magnitudes, with rapid changes of about 2 magnitudes occuring on several occasions in 1941, 1945 and 1972 (Liller 1974), and these variations have time-scales of several tens to hundreds of days. These rapid large amplitude variations have been interpreted as being due to microlensing by sub-solar mass stars in the intervening galaxy, at z l = 0:186 (Stickel 1988). Large amplitude variations require the lens to be much bigger than the source, i.e. r s= o 1. In principle, one can reproduce the observed optical uctuations. If one considers the synthetic light curves of Wambsganss (1990), an optical depth,, between 0.5 and 0.7, a r s= o 0:04 and a relativistic 10 at an orientation angle 10 results in uctuations similar to those observed. Considering the PKS system, the optical depth requirement is possibly satised, since is less than 1 as no multiple images are observed [see the discussion by Narayan and Schneider (1990) for the importance of this statement]. Note, however, that if is between 0.8 and 1, the light curves are characterized by smooth rather than violent uctuations, such that = th is small for all nite sources. However, as with the radio uctuations, the source size requirement is probably not satised, even if the projected 5 CONCLUSIONS In this paper we have considered the potential action of microlensing by sub-solar mass stars on the optical-throughradio emitting region of the BL Lac system PKS We have shown, considering realistic models where this emission arises from a shock in a relativistic jet, that microlensing has a negligible eect on the observed variability. This conclusion holds true even if the redshift of the `intervening' galaxy is actually dierent from the one assumed Romero et al (1995), namely z gal = 0:186. We have also demonstrated that even if the source suffers a relativistic rotation, appearing innitely thin to the microlensing caustics, it still cannot be signicantly ampli- ed by the eects of gravitational microlensing. In conclusion, we suggest the gravitational microlensing can play only a negligible role in the nature of the extraordinary properties seen in BL Lac systems. In closing, we would like to emphasis a nal point. Although applicable to microlensing in the halo of our galaxy, the simple, isolated point mass lens and point source formalism cannot be applied to BL Lac systems. In such cosmological microlensing cases it is expected that the optical depth to microlensing is approaching unity, and although one can derive a time-scale from a single microlensing event, its value is meaningless in the context of high optical depth microlensing variability (Wambsganss 1992; Lewis and Irwin 1996). ACKNOWLEDGMENTS GFL is pleased to thank Michael Merrield and Martin Rees for discussions on the state of the microlensing of BL Lac objects. Joachim Wambsganss and Hans Witt are thanked for discussions on microlensing simulations and their applicability to BL Lac systems. Hans Witt is also thanked for critically reading the manuscript. The anonymous referee is thanked for useful suggestions.

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