A small source in Q2237+0305?

Microlensing in Q2237+0305 between 1985 and 1995 has been interpreted in two different ways. First, the observed variations can be explained through microlensing by stellar mass objects of a continuum source with dimensions significantly smaller than the microlens Einstein Radius (η₀), but consistent with that expected for thermal accretion discs. However, other studies have shown that models having sources as large as 5η₀ can reproduce the observed variation. In this paper we present evidence in favour of a small source. Our approach uses the distribution of microlensed light-curve derivatives to place statistical limits (as a function of source size) on the number of microlens Einstein radii crossed by the source during the monitoring period. In contrast with previous analyses, our results are therefore not dependent on an assumed time-scale. Limits on the source size are obtained from two separate light-curve features. First, recently published monitoring data show large variations (∼0.8-1.5 mag) between image brightnesses over a period of ∼700 d or ∼15 per cent of the monitoring period. Secondly, the 1988 peak in the image A light curve had a duration that is a small fraction (≲0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large, rapid variation limits the source size to be <0.2η₀ (95 per cent confidence). The width of the light-curve peak provides a stronger constraint of <0.025η₀ (99 per cent confidence). The Einstein radius (projected into the source plane) of the average microlens mass 〈m〉 in Q2237+0305 is η₀ ∼ 10¹⁷ √〈m〉 cm. The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.