Direct Retrieval of Protoplanetary Disk Dust Properties Using Auto-differentiable Gaussian Processes and Their Application to the HD 169142 Disk

Retrieving dust properties in protoplanetary disks, including the surface density distribution, temperature, and grain size distribution, is a fundamental task in observational studies of planet formation. While multiwavelength analysis of the spectral energy distribution (SED) using interferometers such as the Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful diagnostic tool, traditional methods are often hindered by strong biases arising from a limited imaging beam size. In this paper, we present a new retrieval framework for dust disk properties designed to overcome this challenge. We assume that the underlying physical structures are expressed as sample paths from Gaussian processes, compute the radial intensity distributions at observed wavelengths, and produce one-dimensional visibility models. The models are compared with the observed data and the posterior distributions are sampled via the Markov Chain Monte Carlo method. The whole procedure is implemented in JAX, which enables end-to-end auto-differentiation and significantly accelerates the inference. We validate our methodology using mock datasets, and find that the results are not strongly biased and better reproduce the input profiles. We also demonstrate its capabilities through an application to ALMA Band 3, 6, and 9 observations of the HD 169142 disk, revealing a new complex structure. Our developed code is publicly available as a Python module, Flexible Radial Analysis of Protoplanetary Disks. This framework provides a next-generation infrastructure for disk SED modeling, enabling high-precision studies of the physical environments in which planets form.