2. Data and method
2.1. The double quasar Q0957+561 and the data
The double quasar Q0957+561A,B was the first multiply imaged quasar discovered (Walsh, Carswell & Weymann 1979). It consists of two quasar images of mag and identical redshift , separated by . Image A is about 5 arcseconds away from the center of the lensing galaxy, image B is about 1 arcsecond off. Very briefly after its discovery, Chang & Refsdal (1979) suggested that stellar mass objects in the light path of one of the images can produce uncorrelated changes in its apparent brightness. The lensing galaxy at is the central galaxy of a rich cluster, whose weak lensing effects on background galaxies have been seen (Barkana et al. 1999). Q0957+561A,B is the best investigated gravitational lens with far more than 100 papers written about it. The time delay between the two images has been established to be around 417 days (e.g., Schild & Thomson 1997; Kundic et al. 1998). Earlier results on microlensing had shown that for a period of about 5 years, there was a monotonic change between the time-delay-corrected apparent brightnesses of images A and B (Schild 1996, Pelt et al. 1998, Refsdal et al. 2000). The time and amplitude of that fluctuation is consistent with microlensing due to low mass stars, which is expected to happen again for image B before too long.
In Fig. 1 we show the lightcurves of images A and B covering the epochs 1995-1997 for the leading image A (and epochs 1996-1998 for the trailing image B), based on data by CKT. The 1995/1996 data set has already been analysed with respect to microlensing by Schmidt & Wambsganss (1998, hereafter SW98). Analysing the complete data set which covers three full years instead of 160 days allows us here to extend the mass limits by one order of magnitude. The difference light curve in the lower panel of Fig. 1 has been calculated by interpolating the data points of image B and subtracting them from the corresponding data point of image A. We have only included data points in the difference lightcurve where an interpolation was possible. It is obvious from the lower part of Fig. 1 that there are no major effects in the difference lightcurve. There are some trends visible, but it is not clear whether they can be attributed to microlensing or whether they are due to some other systematic effects. The dip around day 1125, for example, is likely to be the effect of a lack of data points for quasar B to interpolate in between. In any case, including the 1- error bars, all the data points are consistent with the conservative assumption that no microlensing with an amplitude mag has been detected.
The method we use is described in detail in SW98 and in Schmidt (2000). The first step is to produce a "difference lightcurve" from the data of images A and B, by shifting one set by the appropriate time delay (we chose days, see Kundic et al. 1998) and by the difference in apparent brightness ( mag 1). The second step is to either identify significant fluctuations in the difference lightcurve which could be attributed to microlensing, or to find an upper limit on the possible action of microlenses.
In the third step we produce magnification patterns via numerical simulations for both images A and B with the appropriate values of surface mass density and external shear (cf. Schneider, Falco & Ehlers 1992). We investigated three different scenarios, assuming 100%, 50% or 25% of the matter density consists of Machos, respectively. We explore mass ranges from . In the fourth step, the resulting magnification patterns are convolved with a brightness profil of the quasar. We chose Gaussian profiles with sizes of (the smallest size we consider corresponds to a few Schwarzschild radii of a presumed central supermassive black hole with a mass of about ). Step 5 is the simulation of randomly oriented (straight) tracks through these magnification patterns that cover the same sampling intervals as the actual observations. In the final step 6 we determine the fraction of all lightcurves for a particular parameter pair that produced fluctuations larger than the ones observed.
For the ray shooting simulations (cf. Wambsganss 1999), we used values of and for convergence and shear of images A and B, as in SW98. For each of the masses , ,..., , 1, we used three independent magnification patterns with 20482 pixels each, and sidelengths of L = 16, 160, 1600 (where the Einstein radius in the source plane for a 1 -object is cm; , , are the angular diameter distances observer-lens, observer-source, lens-source, respectively, c is the velocity of light, and G is the gravitational constant). We assumed an effective transverse velocity of km/sec (cf. Paczynski 1986; Kayser, Refsdal, Stabell 1986). For each parameter pair , , we produced 100,000 simulated microlensing lightcurves each for image A and image B, sampled like the observed data set. We looked for the differences between the lowest and highest part in each lightcurve and binned those maximum differences. The fractions of those lightcurves that showed fluctuations larger than the observed difference of mag were labelled and , respectively. We assumed the fluctuations to be independent between images A and B, i.e. the combined exclusion probability is defined as 2. The method is illustrated in Fig. 2, where two panels with small parts of the magnification patterns are reproduced for objects of masses (left), and (right). The three white line segments show how the tracks were modelled after the time coverage of the real data in Fig. 1. The corresponding microlensed lightcurves are shown in the lower part of Fig. 2.
© European Southern Observatory (ESO) 2000
Online publication: October 30, 2000