Bayesian Doppler Imaging: Simultaneous Inference of Surface Maps and Geometric Parameters

We present a fully Bayesian, pixel-based Doppler imaging framework that enables the simultaneous inference of surface brightness maps and geometric parameters, including the inclination i and equatorial rotation velocity v rot, from high-resolution spectral time series. We treat the inference as a Bayesian linear inverse problem conditioned on nonlinear geometric parameters. The surface map is modeled as a Gaussian Process prior over pixel intensities, introducing a characteristic spatial scale that sets the map resolution. This allows analytical marginalization of the linear coefficients and efficient sampling of the nonlinear parameters with Hamiltonian Monte Carlo. Validation with synthetic data demonstrates that our method recovers the longitudes of large-scale surface inhomogeneities and constrains v rot and i under the adopted model assumptions, while also revealing the limited latitudinal sensitivity intrinsic to Doppler imaging. We applied this framework to high-resolution VLT/CRIRES observations of the brown dwarf Luhman 16B. Our analysis reveals a large-scale dark region at mid-latitudes, consistent with previous studies but now with spatially resolved uncertainty estimates. Furthermore, we successfully constrained the geometric parameters without fixing v rot i or i to literature values, deriving an inclination of i = 61.0-12.3+14.3 degrees and an equatorial rotation velocity of v rot = 31.2-3.1+5.3 km,s-1. These results indicate a radius broadly consistent with evolutionary models and suggest a possible spin-axis misalignment under the assumption of comparable equatorial rotation velocities for the two components. Our code is publicly available under the MIT license.