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Abstract We use two different methods, Monte Carlo sampling and variational inference (VI), to perform a Bayesian calibration of the effective-range parameters in³He–⁴He elastic scattering. The parameters are calibrated to data from a recent set of³He–⁴He elastic scattering differential cross section measurements. Analysis of these data forE_lab≤ 4.3 MeV yields a unimodal posterior for which both methods obtain the same structure. However, the effective-range expansion amplitude does not account for the 7/2⁻state of⁷Be so, even after calibration, the description of data at the upper end of this energy range is poor. The data up toE_lab = 2.6 MeV can be well described, but calibration to this lower-energy subset of the data yields a bimodal posterior. After adapting VI to treat such a multi-modal posterior we find good agreement between the VI results and those obtained with parallel-tempered Monte Carlo sampling. 

ABSTRACT We report the discovery of a warm sub-Saturn, TOI-257b (HD 19916b), based on data from NASA’s Transiting Exoplanet Survey Satellite (TESS). The transit signal was detected by TESS and confirmed to be of planetary origin based on radial velocity observations. An analysis of the TESS photometry, the Minerva-Australis, FEROS, and HARPS radial velocities, and the asteroseismic data of the stellar oscillations reveals that TOI-257b has a mass of MP = 0.138 ± 0.023 $$\rm {M_J}$$ (43.9 ± 7.3 $$\, M_{\rm \oplus}$$), a radius of RP = 0.639 ± 0.013 $$\rm {R_J}$$ (7.16 ± 0.15 $$\, \mathrm{ R}_{\rm \oplus}$$), bulk density of $$0.65^{+0.12}_{-0.11}$$ (cgs), and period $$18.38818^{+0.00085}_{-0.00084}$$ $$\rm {days}$$. TOI-257b orbits a bright (V = 7.612 mag) somewhat evolved late F-type star with M* = 1.390 ± 0.046 $$\rm {M_{sun}}$$, R* = 1.888 ± 0.033 $$\rm {R_{sun}}$$, Teff = 6075 ± 90 $$\rm {K}$$, and vsin i = 11.3 ± 0.5 km s−1. Additionally, we find hints for a second non-transiting sub-Saturn mass planet on a ∼71 day orbit using the radial velocity data. This system joins the ranks of a small number of exoplanet host stars (∼100) that have been characterized with asteroseismology. Warm sub-Saturns are rare in the known sample of exoplanets, and thus the discovery of TOI-257b is important in the context of future work studying the formation and migration history of similar planetary systems.