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We aim to reveal the sizes of the continuum and broad emission line (BEL)emitting regions in the gravitationally lensed quasar SDSS J1004+4112 byanalyzing the unique signatures of microlensing in this system. Through acomprehensive analysis of 20 spectroscopic observations acquired between 2003and 2018, we studied the striking deformations of various BEL profiles anddetermined the sizes of their respective emitting regions. Our approachinvolves a detailed analysis of the magnitude differences in the BEL wings andtheir adjacent continua, and the implementation of a statistical model toquantify the distribution and impact of microlensing magnifications. To ensurea reliable baseline for no microlensing, we used the emission line cores as areference. We then applied a Bayesian estimate to derive the size lower limitsof the Ly$\alpha$, Si IV, C IV, C III], and Mg II emitting regions, as well asthe sizes of the underlying continuum-emitting sources. We analyzed theoutstanding microlensing-induced distortions in the line profiles of variousBELs in the quasar image A, characterized by a prominent magnification of theblue part and a strong demagnification of the red part. From the statistics ofmicrolensing magnifications and using Bayesian methods, we estimate the lowerlimit to the overall size of the regions emitting the BELs to be a few lt-daysacross, which is significantly smaller than in typically lensed quasars. Theasymmetric deformations in the BELs indicate that the broad-line region isgenerally not spherically symmetric, and is likely confined to a plane andfollowing the motions of the accretion disk. Additionally, the inferredcontinuum-emitting region sizes are larger than predictions based on standardthin-disk theory by a factor of $\sim$3.6 on average. The size-wavelengthrelation is consistent with that of a geometrically thin and optically thickaccretion disk.

Probing the structure of the lensed quasar SDSS J1004+4112 through microlensing analysis of spectroscopic data