Australia Telescope National Facility

Microlensing of Quasars
Joachim Wambsganss, PASA, 18 (2), in press.

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Introduction

The lensing effects on quasars by compact objects in the mass range

$10^{-6} \le m/M_{\odot} \le 10^6$ is usually called ``quasar microlensing". The microlenses can be ordinary stars, brown dwarfs, planets, black holes, molecular clouds, globular clusters or other compact mass concentrations. The relevant length scale for microlensing (in the quasar plane) is the Einstein radius of the lens:

$\begin{displaymath} r_E = \sqrt{ { {4 G M } \over {c^2} } { {D_S D_{LS} \over... ... } } \approx 4 \times 10^{16} \sqrt{M / M_\odot} \rm\, cm, \end{displaymath}$

where ``typical" lens and source redshifts of

$z_L \approx 0.5$

$z_S \approx 2.0$ are assumed for the expression on the right hand side (G, c and D_L, D_S, D_LS have their usual meaning). Quasar microlensing turns out to be an interesting phenomenon, because the size of the continuum emitting region of quasars is comparable to or smaller than the Einstein radius of stellar mass objects. The angular Einstein radius is

$\theta_E = r_E/D_S \approx 10^{-6} \sqrt {M /M_\odot} \ \ \rm arcsec,$ by far too small for direct observations. What makes microlensing observable anyway is the fact that observer, lens(es) and source move relative to each other. Due to this relative motion, the micro-image configuration changes with time, and so does the total magnification, i.e. the sum of the magnifications of all the micro-images. And this change in magnification over time can be measured: microlensing is a ``dynamical" phenomenon. The standard lensing time scale t_E is the time it takes the source to cross the Einstein radius of the lens, i.e.

$t_E = r_E/v_\perp \approx 15 \sqrt {M / M_\odot} v_{600}^{-1} \ \ \rm years,$ assuming a relative transverse velocity of 600 km/sec. However, in practice we can expect fluctations on much shorter time intervals: if a source crosses one of the sharp caustic lines that separate regions of low and high magnification, we can observe a large change in magnification during the time t_cross it takes the source to cross its own diameter R_source:

$t_{cross} = R_{source}/v_\perp \approx 4 R_{15} v_{600}^{-1} \ \ \rm months.$ Here the quasar size R₁₅ is parametrized in units of 10¹⁵cm.

Next Section: Theoretical work on quasar
Title/Abstract Page: Microlensing of Quasars
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