Astron. Astrophys. 362, L37-L40 (2000)

3. Results, discussion and summary

The lightcurves of Q0957+561A, B as monitored between 1995 and 1998 do not show any significant differences beyond mag, when corrected for time delay and magnitude difference. In Fig. 3 we present the resulting "exclusion probabilities" for the two parameters "Macho mass" and quasar size (assuming 100% of the halo mass is in MACHOs), derived from four years of monitoring and comparison with numerical simulations. The numbers indicate the percentage of the 100,000 simulated lightcurves that showed fluctuations larger than the observed ones. In the diagram, we encircled and shaded the parts of parameter space that produced exclusion probabilities of 67% (1-, thin shading), 95% (2-, medium shading), and 99.7% (3-, cross shading). It is obvious that a mass range from can be excluded at the 3- level for all quasar sizes except for the largest one, for which is barely allowed. For objects of mass 0.1 , the exclusion probability is at the 70% to 85% level. We need a longer time coverage, in order to improve significantly on these limits. In Fig. 4 and Fig. 5 we present the resulting numbers and respective exclusion regions for the assumption of only 50% or 25% of the halo mass in MACHOs. The exclusion probabilities get slightly smaller in these cases, and the exclusion regions shrink a bit as well, but the general picture does not change much.

Fig. 3. Exclusion Probability (in percent) as a function of Macho mass and quasar size , for 100% of the halo mass in MACHOs. The shaded parts encircle regions of parameter space that can be excluded at the 67%, 95%, and 99.7% probability level (increasing line density; the latter two coincide).

Fig. 4. Same as Fig. 3 for 50% of the halo mass in MACHOs.

Fig. 5. Same as Fig. 3 for 25% of the halo mass in MACHOs.

Pelt et al. (1998) and Refsdal et al. (2000) investigated the double quasar lightcurve as well. Their main focus was microlensing on medium and long time scales (baseline 15 years), including a continuous change in the difference lightcurve of about 0.25 mag in the first five years. Whereas their data set covers a longer baseline than ours, we have many more and more accurate data on short time scales ( 100 days). Furthermore, we also take into account the gaps in the difference lightcurve, which means we treat the short term behaviour more realistically. Pelt el al. (1998)'s finding that the quasar size is about cm is consistent with our results (though we cannot put an upper limit on the size).

We extend the "exclusion" area by roughly one order of magnitude in mass, compared to the first results in SW98 and Wambsganss & Schmidt (1998). This is due to the fact that the coverage of the difference light curve increased by more than a factor of 4 (without showing any more variability), and the mass limits increase with the square of the length scale. But it also means that in order to increase the limits from short/medium term microlensing by another order of magnitude in mass - reaching the very interesting regime of solar mass objects - the frequent monitoring has to continue for another six or eight years.

The method and results described here, in particular the exclusion diagram (Fig. 3; see also Fig. 2 of Refsdal et al. 2000), are very similar to those of the groups investigating microlensing of the Milky Way halo (e.g., Alcock et al. 2000, Lasserre et al. 2000). Hence it is obvious that monitoring multiple quasars (Gott 1981) is as powerful a tool in constraining the abundance of MACHOs in galactic halos as is monitoring LMC stars (Paczynski 1986).

© European Southern Observatory (ESO) 2000

Online publication: October 30, 2000
helpdesk.link@springer.de