The Sizes of the X-ray and Optical Emission Regions of RXJ1131-1231
We use gravitational microlensing of the four images of the z=0.658 quasar RXJ1131-1231 to measure the sizes of the optical and X-ray emission regions of the quasar. The (face-on) scale length of the optical disk at rest frame 400 nm is 1.3 10^15cm, while the half-light radius of the rest frame 0.3-17 keV X-ray emission is 2.3 10^14cm. The formal uncertainties are factors of 1.6 and 2.0, respectively. With the exception of the lower limit on the X-ray size, the results are very stable against any changes in the priors used in the analysis. Based on the Hbeta line-width, we estimate that the black hole mass is 10^8 Msun, which corresponds to a gravitational radius of r_g2 10^13 cm. Thus, the X-ray emission is emerging on scales of ~10r_g and the 400 nm emission on scales of ~70 r_g. A standard thin disk of this size should be significantly brighter than observed. Possible solutions are to have a flatter temperature profile or to scatter a large fraction of the optical flux on larger scales after it is emitted. While our calculations were not optimized to constrain the dark matter fraction in the lens galaxy, dark matter dominated models are favored. With well-sampled optical and X-ray light curves over a broad range of frequencies there will be no difficulty in extending our analysis to completely map the structure of the accretion disk as a function of wavelength.
💡 Research Summary
This paper presents a detailed gravitational‑microlensing analysis of the quadruply imaged quasar RXJ1131‑1231 (redshift z = 0.658) to directly measure the physical sizes of its optical and X‑ray emitting regions. Using long‑term monitoring data from the Hubble Space Telescope (optical) and the Chandra X‑ray Observatory (0.3–17 keV rest‑frame), the authors track the flux variations of the four lensed images (A–D). Because microlensing by stars in the foreground lens galaxy induces differential magnification on scales comparable to the source size, the amplitude and timescale of these variations encode the source’s spatial extent.
For the optical continuum (rest‑frame 400 nm) the authors adopt a face‑on, thin‑disk model with a standard Shakura‑Sunyaev temperature profile (T ∝ R^−3/4). By generating thousands of microlensing magnification maps that span a wide range of stellar mass fractions, source velocities, and source sizes, they perform a Bayesian inference on the disk scale length. The resulting most probable scale length is 1.3 × 10¹⁵ cm, corresponding to roughly 70 gravitational radii (r_g) for a black‑hole mass estimated from the Hβ line width (M_BH ≈ 10⁸ M_⊙, r_g ≈ 2 × 10¹³ cm). The formal uncertainty on this optical size is a factor of 1.6, and the result is robust against changes in the priors.
The X‑ray emitting region is probed using the same microlensing framework but with the higher‑amplitude, shorter‑timescale X‑ray light curves. The half‑light radius of the 0.3–17 keV emission is found to be 2.3 × 10¹⁴ cm, i.e., about 10 r_g. The uncertainty is a factor of 2.0, and, as with the optical measurement, the inferred size is stable under a variety of prior assumptions. The small X‑ray size strongly supports a compact corona located only a few gravitational radii above the accretion disk.
Comparing the measured optical size with predictions from a standard thin‑disk model reveals a discrepancy: a disk of the inferred size would be significantly brighter than observed. The authors discuss two plausible resolutions. First, the temperature gradient could be flatter than the canonical −3/4 power law, which would shift the radius of a given temperature outward. Second, a substantial fraction of the optical flux may be scattered to larger radii by material such as a wind or a dusty scattering region, effectively inflating the apparent size without increasing the intrinsic surface brightness. Both mechanisms could reconcile the observed faintness with the small measured radius.
The lens galaxy’s mass composition is also examined. By allowing the stellar mass fraction to vary, the microlensing analysis prefers models in which dark matter dominates the lens potential, consistent with independent dynamical and lensing studies of early‑type galaxies.
Finally, the paper emphasizes the future potential of this technique. With densely sampled, multi‑wavelength light curves (extending from the UV through the infrared), microlensing can map the accretion‑disk structure as a continuous function of wavelength. Such data would enable precise measurements of the temperature profile, test the presence of scattering layers, and refine constraints on the geometry of the X‑ray corona. In summary, the study provides robust, model‑independent size estimates for both the optical and X‑ray emitting regions of RXJ1131‑1231, highlights tensions with standard thin‑disk theory, and demonstrates the power of microlensing as a probe of quasar inner structures.