Open clusters are fundamental benchmarks for calibrating stellar evolution models. However, the precise determination of cluster parameters is often hindered by the broadening of the main sequence due to unresolved binaries and stellar rotation, particularly near the main-sequence turnoff (MSTO). Ruprecht 147, as the oldest (∼ 2. 5 Gyr) and nearest (d ∼ 300 pc) open cluster, provides a unique opportunity to resolve these degeneracies. We aim to simultaneously constrain the fundamental parameters (age, metallicity, distance, and extinction) and the underlying population properties (binary fraction and rotational distribution) of Ruprecht 147 using a rigorous statistical framework that explicitly models the "Kraft break" in stellar rotation. We constructed a 4D differentiable emulator based on PARSEC v2. 0 stellar evolutionary tracks, utilizing for GPU-accelerated inference. This emulator continuously interpolates mass, age, metallicity, and rotation rate (ω). We performed a hierarchical Bayesian analysis on high-precision JAX data release 3 photometry using the No-U-Turn Sampler (NUTS) to sample the high-dimensional posterior distribution. Our analysis yields a precise distance modulus of (m-M) ₀ = 7. 416^ +0. 003 _ -0. 002 mag and an age of τ = 2. 340 ± 0. 002 Gyr. We derive a super-solar metallicity of mh = +0. 087^ +0. 001 _ -0. 003 dex. The inferred rotation distribution shape parameters (α_ ̊m rot ≈ 7. 9, β_ ̊m rot ≈ 5. 1) indicate a mean rotation rate of barω ≈ 0. 46 for turnoff stars. We find a photometric binary fraction of f_ ̊m bin ≈ 33. 9%. The application of differentiable programming enables the robust breaking of the age-metallicity-extinction degeneracy. The detection of rapid rotation at the MSTO confirms the inefficiency of magnetic braking for stars with thin convective envelopes (the Kraft break), even at an advanced age of 2 Gyr. Its high metallicity suggests that Ruprecht 147 likely originated in the inner Galactic disk and migrated to its current location.
Chi et al. (Thu,) studied this question.