Astron. Astrophys. 360, 853-860 (2000)

5. Is microlensing detected in HE 1104-1805?

The possibility of microlensing can be judged from a comparison between the size of the Einstein ring and the size of a quasar continuum emitting region. The latter is thought to be produced by an accretion disk and is of the order of to cm (Wambsganss et al. 1990; Krolik 1999 and references therein). The former depends on the mass of the microlenses, M, and is  cm. In this calculation and those that follow, we have assumed that the lens is at , and we have assumed a cosmology where  km s^-1 Mpc^-1, and . Thus, given that there is a suitable alignment, microlensing of the continuum is possible. Furthermore, the spectrum of the A component is considerably harder than that of the B component. This chromatic effect supports the idea that the continuum is microlensed since higher energy photons come from the inner part of the accretion disk, and are hence more susceptible to high amplification microlensing than lower energy photons. In fact, with suitable modeling of the lens and additional spectroscopic data, it may be possible to place constraints on accretion disc models (e.g., Agol & Krolik, 1999).

The likelihood of microlensing then depends on the density of micro-lenses. If we model the mass distribution of the lensing galaxy as in Sect. 3.2, we can use the distance between the two macro images to determine the mass density at each image position. This gravitational convergence or optical depth, , is quite high for both components. For the A component, it is ; for the B component, it is 0.53. If this is made entirely of stars then microlensing of either component is highly likely. In detail, however, only the main lensing galaxy is contributing to microlensing. The actual microlensing optical depth at the two quasar image positions is then lower, but still high.

The typical time-scale between two consecutive microlensing events depends on the transverse velocity of the source and the velocity dispersion of the microlenses. The velocity dispersion for the lensing galaxy is high (using a single galaxy model one derives  km s^-1, or about 235 km s^-1 if a cluster is also involved) and it is probably larger than the transverse bulk velocity. Dividing this velocity directly by the diameter of the Einstein ring, one derives a time scale of 3 years. This is quite long; however, it has been shown that stellar proper motions produce a higher microlensing rate than the one produced by a bulk velocity of the same magnitude (Wambsganss and Kundic 1995, Wyithe et al. 2000). Furthermore, the typical duration of a microlensing event is the time for the continuum emitting region () to cross a caustic with velocity  km s^-1. This is of the order of a few months and much shorter than the time between consecutive microlensing events.

Thus, it is likely that microlensing affects the A component. As the stellar density of the lens near the B component is approximately half that of the A component, it is quite likely that microlensing affects the B component as well. We should expect that the continuum of the A component should be preferentially amplified relative to that of the B component for the majority of the time, but we should also expect that the B component should be preferentially amplified for a fraction of the time. HE 1104-1805 has now been monitored spectroscopically for six years (Wisotzki et al. 1998). During that time, the continuum of both components have been observed to vary; however, the continuum of the A component has always been harder (Wisotzki, private communication). As the time delay between the two components is of the order of 0.73 year (W98), the hardness of the continuum in the A component cannot be attributed to time delay effects. The most natural explanation is microlensing.

Additionally, the relative level of the continuum of the A component is more variable than that of the B component (see Fig. 2 in W98). This cannot be attributed to photometric errors, because the A component is a factor of 3 brighter than B, both components are well separated and the lensing galaxy is much fainter than either component.

Conversely, the BLR does not appear to be affected by microlensing. From 1993 to 1999, the ratio of the broad lines between the two components has varied little, with (W98 and this paper).

The lines of the BLR in the IR spectra presented here subtract very cleanly, better than 1% of the original line flux. Naively, one may then expect that any substructure in the BLR needs to be considerably larger than the microlensing caustics, i.e.,  cm. However, a more secure estimate requires better modeling of how microlensing in this particular lens can affect the profile of lines from the BLR (e.g., Schneider & Wambsganss, 1990).

© European Southern Observatory (ESO) 2000

Online publication: August 23, 2000
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