A Sensitivity Interface between Dark-Matter Perturbations and Pycnonuclear Burning in Ultramassive White Dwarfs

Pycnonuclear burning in ultramassive white dwarfs is governed by quantum tunneling and is therefore unusually sensitive to small changes in the dense stellar environment. Rather than asking whether dark matter immediately explains a cooling anomaly, we address a more controlled question: how strongly does a known pycnonuclear rate respond when the ion density, temperature, or tunneling barrier is weakly perturbed? We develop a logarithmic framework that separates this nuclear response from the model-dependent origin of the perturbation. For the validated [Formula: see text] benchmark, the density sensitivity is [Formula: see text]–[Formula: see text] over [Formula: see text]–[Formula: see text], so percent-level ion-density changes can produce several-percent to roughly twenty-percent variations in the local rate. A published-parameter [Formula: see text] extension is more responsive, with [Formula: see text]–[Formula: see text] wherever its rate is non-negligible, although it is not treated as an independently benchmarked stellar-evolution input. A Yukawa-type barrier correction remains sub-percent for effective couplings [Formula: see text] and MeV-scale mediators. Finally, a capture-to-hydrostatic mapping shows that ordinary Galactic-halo conditions generate effects far too small to account for Gyr-scale cooling delays. The resulting interface is intended as a reusable nuclear-response layer for future white-dwarf structure, cooling, and population studies.