The Einstein Cross offers a fresh measure of a quasar’s glowing disk

Four views of one quasar

The Einstein Cross is not four separate quasars. A foreground galaxy bends light from one background quasar, Q2237+0305, into four images, labeled A through D. Stars within that galaxy add smaller-scale gravitational lensing effects, changing how strongly different emitting regions are magnified.

This microlensing supplies an indirect probe of the quasar’s inner structure. Smaller emitting regions respond more strongly to the fine structure of the magnification pattern than larger ones. Because different wavelengths trace different parts of an accretion disk, comparing colors across the four images can reveal how the disk’s characteristic size changes with wavelength.

R. Jerez-Nicurcar and colleagues revisit this system using archival observations taken with the Very Large Telescope’s X-shooter instrument in June 2018. Their analyzed spectra span roughly 300 to 2,000 nanometers, extending from ultraviolet through visible light into the near-infrared.

Finding a reference within the spectrum

The researchers compare two ingredients: the relatively smooth continuum emitted by the disk and the central cores of emission lines produced by surrounding gas.

Their method assumes these line cores come from sufficiently extended regions to be much less affected by microlensing. The cores therefore provide a reference against which to measure additional magnification of the compact continuum. Subtracting the core-based brightness difference between two images from the continuum difference isolates an estimated microlensing signal.

Dust is another possible source of color differences. Light reaching us through different parts of the foreground galaxy may experience different amounts of extinction. Fitting a Milky Way-type extinction law to the line-core measurements, the team finds a small differential color excess of 0.04 magnitudes between images C and A, which they interpret as negligible differential extinction.

That concerns the difference between two sightlines; it does not establish that neither sightline contains dust. The result also differs from earlier estimates discussed in the paper.

Turning magnification into a disk measurement

The authors combine their spectroscopy with two earlier photometric datasets, giving three observing epochs. They compare the measured color-dependent magnification with simulated microlensing maps for the four images.

In the simulations, the emitting region has a Gaussian brightness profile. Its characteristic size follows a power law, rₛ ∝ λᵖ, where λ is wavelength and p controls how quickly the emitting region grows toward redder light. The standard thin-disk prediction is p = 4/3.

The Bayesian analysis gives an expected value of p = 0.77, with reported uncertainties of −0.28 and +0.47. This favors a weaker size increase with wavelength than the standard prediction. Under the temperature interpretation used in the paper, that corresponds to a steeper temperature decline with radius.

At a reference wavelength of 102.6 nanometers in the quasar’s rest frame, the inferred characteristic size is 4.9 light-days, with uncertainties of −2.6 and +2.3 light-days, assuming a mean lensing-star mass of 0.3 solar masses. A light-day is the distance light travels in one day. This size is a Gaussian scale, not a sharply defined outer edge; the corresponding half-light radius is about 5.8 light-days.

The physical size scales with the square root of the assumed mean microlens mass, so the mass assumption matters.

A preference, not a decisive rejection

Although the preferred power-law index falls below 4/3, the authors report that the standard value remains consistent within their two-sigma region. The findings therefore suggest tension with the standard wavelength dependence rather than ruling it out.

The inference also depends on the adopted galaxy lens model, the source brightness profile and the assumption that the relevant lensing matter consists entirely of compact objects. Combining epochs helps address the limitations of estimating disk properties from a single microlensing state, but does not eliminate modeling assumptions.

Clues in the surrounding gas

The spectra also reveal differences in the broad emission-line wings, especially the red wings of hydrogen lines in image C relative to A. These could indicate microlensing of portions of the surrounding gas.

However, weak signals, absorption, atmospheric corrections and overlapping iron emission complicate some comparisons. The authors call for more accurate near-infrared spectra to test that interpretation. The study provides another constraint on this well-studied quasar, not a final map of its disk or surrounding gas.