Further Evidence that Quasar X-Ray Emitting Regions Are Compact: X-Ray and Optical Microlensing in the Lensed Quasar Q J0158-4325

We present four new seasons of optical monitoring data and six epochs of X-ray photometry for the doubly-imaged lensed quasar Q J0158-4325. The high-amplitude, short-period microlensing variability for which this system is known has historically precluded a time delay measurement by conventional methods. We attempt to circumvent this limitation by application of a Monte Carlo microlensing analysis technique, but we are only able to prove that the delay must have the expected sign (image A leads image B). Despite our failure to robustly measure the time delay, we successfully model the microlensing at optical and X-ray wavelengths to find a half light radius for soft X-ray emission log(r_{1/2,X,soft}/cm) = 14.3^{+0.4}_{-0.5}, an upper limit on the half-light radius for hard X-ray emission log(r_{1/2,X,hard}/cm) <= 14.6 and a refined estimate of the inclination-corrected scale radius of the optical R-band (rest frame 3100 Angstrom) continuum emission region of log(r_s/cm) = 15.6+-0.3.