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Astron. Astrophys. 358, 793-811 (2000)

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7. Microlensing versus scintillation

We have seen many arguments in Sects. 3-5, for and/or against scintillation and microlensing as the cause of variability in compact flat-spectrum radio sources. Both can in principle explain the observed modulation-index and variability time scales in the VLA 8.5-GHz light curves in the individual lensed images of B1600+434, although it remains very difficult to explain the longer ([FORMULA]1 day) variations in the light curves or the difference in modulation-index between the two lensed images in terms of scattering. In the case of microlensing, one would expect to see scintillation at some level as well, possibly complicating a straightforward analysis. How can we then separate these mechanisms as the dominant cause of variability?

Scintillation and microlensing have different dependencies on frequency. Although microlensing is achromatic, the frequency dependence of the source structure predicts a clear dependence of the microlensing variability as a function of frequency. For flat-spectrum synchrotron self-absorbed source sources, the source size is inverse proportional to frequency (Eq. (24)). Thus the modulation-index decreases with decreasing frequency (Eq. (32)). In the case of weak and strong refractive scattering (i.e. flickering), however, the modulation-index usually increases with decreasing frequency (e.g. BNR86; Narayan 1992; Rickett et al. 1995). The key to testing whether the observed short-term variability in gravitationally lensed flat-spectrum radio sources is partly or fully dominated by microlensing or scintillation is therefore their strong opposite dependence on frequency.

In Fig. 11, we have plotted the dependence of the modulation index in the case of weak and strong refractive scintillation versus that of microlensing. We assume that the source or jet-component size scales as [FORMULA] and that scatter-broadening is negligible. All curves are normalized at [FORMULA]=3.7% at 6 cm, as measured with the WSRT in 1999 (Table 1). We determine the modulation-index from scintillation following Rickett et al. (1995) and that from microlensing using Eq. (32). In the case of microlensing, we use the maximum range of the turn-over scale [FORMULA]=0.9-4.5 µas and the jet-component size at 8.5 GHz [FORMULA]=2-5 µas, found from Tables 2 and 5. We furthermore assume that the short-term variability is dominated by image A, as observed in the VLA 8.5-GHz light curves. The resulting curves show a clear opposite trend as a function of wavelength and therefore act as a strong discriminator between microlensing and scintillation. The constraints on the microlensing curves were determined from the VLA 8.5-GHz light curves only and therefore independent from the WSRT 1.4 and 5-GHz modulation-indices.

[FIGURE] Fig. 11. Dependence of the modulation-index from scintillation and microlensing on wavelength. The solid line shows the modulation-index from scintillation. The dashed and dot-dashed lines show the modulation-indices from microlensing, using [FORMULA]=2 and 5 µas at 8.5 GHz, respectively, assuming [FORMULA]=0.9 µas. The dotted and dash-dot-dotted lines indicates the same for [FORMULA]=4.5 µas. All curves are normalized to the [FORMULA]=3.7% modulation at 6.0 cm observed with the WSRT in 1999 (Table 1). The open circle indicates the upper limit on the ratio [FORMULA] (Table 1).

From the WSRT modulation-indices ([FORMULA]) at 1.4 and 5 GHz (Table 1), one finds [FORMULA][FORMULA]0.31, as indicated by the open circle in Fig. 11. Although this result is based on two frequencies only, it clearly agrees much better with the predictions from microlensing and not that from scintillation! The latter would require a [FORMULA]8 times larger value for [FORMULA] (i.e about 9%). We do not plot the VLA 8.5-GHz modulation-index, because it was determined from a different epoch. The modulation-index from microlensing and scintillation might change as function of time, whereas the ratio of modulation-indices, measured simultaneously, is less likely to change.

Thus, if all short-term variability seen in the light curves of B1600+434 is external, it follows the predictions from microlensing. Moreover, if the short-term variability seen in the WSRT 1.4 and 5-GHz light curves is intrinsic, this would be very hard to reconcile with the fact that in 1998 almost all of the VLA 8.5-GHz short-term variability was shown (see Sect. 2) to be external. The most logical conclusion from all this is that the short-term variability at 1.4, 5 and 8.5 GHz is dominated by microlensing. This explains both the modulation-indices as function of frequency at 1.4 and 5 GHz and the longer variability time scale in the VLA 8.5-GHz light curves. In the case of scintillation, one would require either different sizes of the lensed images or a very different ionized ISM towards the images and also a different time scale and frequency-dependence of scattering from that expected from a Kolmogorov spectrum of inhomogeneities of the ionized ISM. All evidence thus far is therefore only consistent with microlensing as the dominant cause of the observed short-term variability.

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© European Southern Observatory (ESO) 2000

Online publication: June 20, 2000