Empirical estimation of asteroid diameters using photopolarimetric observables

Abstract

Asteroid diameters are physical parameters for understanding the size distribution, collisional evolution, and surface properties of minor planets. Existing polarimetric approaches estimate diameters indirectly through albedo determination, propagating uncertainties from intermediate calibrations. Here we derive direct empirical relationships between asteroid diameter (D), absolute magnitude (HV), and two polarimetric observables: the absolute minimum polarization (|Pmin|) and the polarimetric slope (h). Using a calibration sample of 98 asteroids with reliable diameters from thermal-infrared, occultation, and radar measurements, we derive two empirical relations using orthogonal distance regression (ODR), which accounts for uncertainties in both dependent and independent variables. The relations achieve coefficients of determination of R2 = 0.921 (N = 98) and R2 = 0.950 (N = 82) for |Pmin|- and h-based formulations. Leave-one-out cross-validation (LOOCV) yields cross-validated coefficients of $R^2_{\rm CV}=0.910$ and 0.947, with median fractional errors of 14.00% and 11.99%, demonstrating predictive capability for excluded asteroids. Validation against radar-, occultation-, and NEOWISE-derived diameters confirms consistency for most moderate- to low-albedo main-belt asteroids below ~523 km. The relations provide a convenient operational alternative for estimating asteroid diameters directly from polarimetric data and HV, avoiding the need to separately catalogue or re-derive albedo values whenever photometric compilations are updated. Comparison with reference geometric albedos shows larger scatter than the diameter comparison (RMS fractional residuals of 36–44 per cent), consistent with error amplification in the diameter-to-albedo conversion; nonetheless, a binary dark/bright classification test (pV = 0.12 boundary) achieves 96.9 and 93.9 per cent accuracy, demonstrating strong discriminating power for broad reflectance class despite noisier continuous albedo recovery.