Statistics of Microlensing Caustic Crossings in Q 2237+0305: Peculiar Velocity of the Lens Galaxy and Accretion Disk Size

Original · EN

We use the statistics of caustic crossings induced by microlensing in the lens system Q 2237+0305 to study the lens galaxy peculiar velocity. We calculate the caustic crossing rates for a comprehensive family of stellar mass functions and find a dependence of the average number of caustic crossings with the effective transverse velocity and the average mass, n ∝ veff / √ m, equivalent to the theoretical prediction for the case of microlenses with identical masses. We explore the possibilities of the method to measure veff using the 12 years of OGLE monitoring of the four images of Q 2237+0305. To determine a lower limit for veff we count, conservatively, a single caustic crossing for each one of the 4 high magnification events identified in the literature (plus one additional proposed by us) obtaining veff 240√ m /0.17Mkm s⁻¹ at 68% of confidence. From this value and the average FWHM of 4 high magnification events we obtain a lower limit of rₛ 1.4 √ m /0.17M light-days for the radius of the source (rₛ=FWHM/2.35). Tentative identification of 3 additional caustic crossing events leads to estimates of veff≃ (493± 246)√ m /0.17Mkm s⁻¹ for the effective transverse velocity and of rₛ ≃ (2.7± 1.3)√ m /0.17M light-days for the source size. The estimated transverse peculiar velocity of the galaxy is vₜ ≃(429±246)√ m /0.17Mkm s⁻¹.