Physically motivated AGN emissivity profiles and their effects on quasar microlensing signatures. 1. Multi-epoch accretion disc size inference

Technical Summary: Physically motivated AGN emissivity profiles and their effects on quasar microlensing signatures

Problem Statement
Quasar microlensing serves as a primary probe for the physical size scales of accretion flows on micro-arcsecond scales. However, a persistent discrepancy exists between accretion disc sizes inferred from microlensing statistics and those predicted by standard Shakura-Sunyaev (1973) disc theory, often referred to as the "disc-size problem." This tension mirrors findings in continuum reverberation mapping campaigns. Current microlensing analyses typically model the source surface-brightness distribution using simplified prescriptions, such as circular Gaussian profiles or standard thin-disc models. These approaches often neglect the presence of extended continuum-emitting structures, specifically the diffuse free-bound continuum emission originating from the Broad-Line Region (BLR). The authors posit that interpreting a composite emission picture (compact disc + extended BLR) as a single compact disc introduces systematic biases in inferred source sizes.

Methodology
The authors construct a physically motivated framework to quantify the impact of large-scale diffuse emission on microlensing signatures. The methodology proceeds in three stages:

1. Intrinsic Disc Modeling: The authors adapt the agnsed framework (Kubota & Done 2018) to generate energetically self-consistent emissivity profiles. They model two fiducial accretion flow structures:

   • A standard Shakura-Sunyaev (1973) thermal disc.
   • A modified disc featuring a warm Comptonised region (warm corona) between the outer standard disc and an inner hot X-ray plasma.
     These models utilize a Novikov-Thorne (1973) temperature profile and account for X-ray irradiation heating the disc on both sides. The models produce full Spectral Energy Distributions (SEDs) and 2D emissivity maps for specific bandpasses.

2. BLR Diffuse Continuum Calculation: Using the cloudy photoionisation code (Ferland et al. 2017), the authors compute the diffuse free-bound continuum emission generated by the BLR. They assume a bi-conical geometry with a covering fraction of $f_c \approx 0.3$ and photo-ionised equilibrium. The BLR emission is calculated based on the ionizing SED from the agnsed models, assuming isotropic radiation from the illuminated BLR surface.

3. Microlensing Simulation and Size Recovery:

   • Magnification Maps: The authors generate source-plane magnification maps using the Fast Multipole Method–Inverse Polygon Mapping (FMM–IPM) technique for both positive-parity (minimum) and negative-parity (saddle) lens configurations.
   • Convolution: The 2D emissivity maps (incorporating both disc and BLR components) are convolved with the magnification maps to produce extended-source magnification distributions.
   • Mock Observations: They generate 100 mock microlensing light curves by drawing random trajectories across the magnification maps, simulating observational constraints (cadence, noise, gaps) based on the Cosmograil dataset.
   • Size Inference: Source sizes are recovered by comparing the variability statistics (standard deviation of microlensing magnification, $\sigma_{\Delta m}$) of the mock light curves against a grid of trial half-light radii. The recovery is performed under three different modeling assumptions: (1) standard Shakura-Sunyaev disc only, (2) warm Comptonised disc only, and (3) the full composite warm Compton + BLR model.

Key Contributions and Results

• Emissivity Profile Sensitivity: The study finds that the detailed shape of the compact disc emissivity profile (thermal vs. warm Comptonised) has only a higher-order effect on the microlensing profile. The microlensing signal is primarily sensitive to the effective half-light radius of the source.
• Impact of Diffuse BLR Emission: The inclusion of the diffuse BLR continuum significantly alters the microlensing signatures. Because the BLR emission originates from physically larger scales, it acts as a smoothing component that averages out the small-scale caustic network. This results in narrower magnification distributions and reduced variability amplitudes compared to compact-only models.
• Wavelength Dependence: The magnitude of the bias is strongly wavelength-dependent, dictated by the fractional contribution of the diffuse BLR emission to the total SED in the observed bandpass. In low-energy bands (e.g., $\lambda \approx 7500$ Å) where the BLR contribution is significant ($\sim 30\%$), the smoothing effect is pronounced. In high-energy bands (e.g., $\lambda \approx 1650$ Å) where the BLR contribution is minimal ($\sim 1.4\%$), the effect is negligible.
• Systematic Size Bias: When mock light curves generated from a composite (disc + BLR) model are analyzed using compact-only source prescriptions, the inferred half-light radius systematically overestimates the true compact disc size. The recovered size tends toward the effective half-light radius of the composite source.
• Mechanism of Bias: The authors clarify that this bias is not a simple flux-weighted average of the disc and BLR radii. Instead, in the optical/UV regime where the BLR flux fraction is less than 50%, the inferred size is determined by the radius required to enclose half of the total (disc + BLR) flux. Since the BLR adds flux without contributing significantly to the inner compact emission, the radius required to enclose 50% of the total flux shifts outward, leading to an apparent size increase.

Significance
The paper concludes that a portion of the "disc-size problem"—the systematic excess in microlensing-inferred accretion disc sizes—likely arises from interpreting composite disc+BLR emission as emission from a single compact accretion disc. By neglecting the extended diffuse continuum from the BLR, standard microlensing analyses effectively measure an "effective" size that is larger than the true compact disc size. This finding provides a physical explanation for the size tension observed in both microlensing and continuum reverberation mapping, suggesting that the discrepancy is not necessarily a failure of the standard disc theory but rather a consequence of incomplete source modeling that omits extended reprocessing regions. The authors emphasize that their results are modest in scope, demonstrating the bias through physically motivated models rather than claiming to resolve all observational tensions, but they establish that the fractional contribution of diffuse emission is a critical parameter in size inference.