Diffusive Nuclear Burning of Helium on Neutron Stars

Diffusive nuclear burning of H by an underlying material capable of capturing protons can readily consume H from the surface of neutron stars (NSs) during their early cooling history. In the absence of subsequent accretion, it will be depleted from the photosphere. We now extend diffusive nuclear burning to He, motivated by the recent observation by Ho & Heinke of a carbon atmosphere on the NS in the Cassiopeia A supernova remnant. We calculate the equilibrium structure of He on an underlying $\alpha$ capturing material, accounting for thermal, mass defect, and Coulomb corrections on the stratification of material with the same zeroth order $\mu_e = A/Z$. We show that Coulomb corrections dominate over thermal and mass defect corrections in the highly degenerate part of the envelope. We also show that the bulk of the He sits deep in the envelope rather than near the surface. Thus, even if the photospheric He abundance is low, the total He column could be substantially larger than the photospheric column, which may have implications for rapid surface evolution ($\approx 1$ yr timescales) of neutron stars. When nuclear reactions are taken into account, we find that for base temperatures $\gtrsim 1.6 \times 10^8$ K, He is readily captured onto C. As these high temperatures are present during the early stages of NS evolution, we expect that the primordial He is completely depleted from the NS surface like the case for primordial H. We also find that magnetic fields $\lesssim 10^{12}$ G do not affect our conclusions. Armed with the results of this work and our prior efforts, we expect that primordial H and He are depleted, and so any observed H or He on the surfaces of these NS must be due to subsequent accretion (with or without spallation). If this subsequent accretion can be prevented, the underlying mid-Z material would be exposed.

💡 Research Summary

The paper extends the concept of diffusive nuclear burning (DNB), previously applied to hydrogen on neutron‑star (NS) surfaces, to helium. The authors first construct the equilibrium stratification of a helium layer that sits atop an α‑capturing substrate (e.g., carbon). In doing so they incorporate three corrections to the basic pressure‑density relation: thermal gradients, mass‑defect effects (binding‑energy differences), and Coulomb interactions among ions. Their calculations show that in the highly degenerate part of the envelope—where the electron gas is almost completely pressure‑supporting—the Coulomb correction dominates over the thermal and mass‑defect terms, because ion–ion electrostatic forces shape the density profile far more strongly than temperature‑induced pressure variations.

A key structural result is that most of the helium mass resides deep in the envelope (densities of 10⁶–10⁸ g cm⁻³, pressures of 10²⁴–10²⁶ dyn cm⁻²), rather than forming a thin surface veneer. Consequently, even if the photospheric helium abundance is tiny, the total helium column can be orders of magnitude larger than the column inferred from spectroscopy. This deep reservoir implies that surface composition can evolve on very short (≈ 1 yr) timescales if material is mixed upward or lost.

The nuclear physics is then addressed. The dominant reaction is ⁴He(α,γ)⁸Be → ¹²C, i.e., α‑capture onto carbon. Reaction rates rise steeply with temperature; for base temperatures T ≳ 1.6 × 10⁸ K the helium capture timescale becomes much shorter than the early cooling time of a NS (∼10³ yr). Since such temperatures are present in the envelope during the first few thousand years after birth, the authors conclude that primordial helium will be essentially exhausted, just as primordial hydrogen is in earlier work.

Magnetic fields up to B ≈ 10¹² G are examined and found not to alter the conclusions appreciably. In this regime the electron cyclotron radius remains much larger than the atomic scale, so the electron pressure and thus the stratification are unchanged. Stronger fields (≫10¹³ G) could modify the picture, but they lie outside the scope of the present study.

Putting the pieces together, the authors argue that any helium (or hydrogen) observed on the surface of an isolated NS must be supplied after the initial DNB phase, either by fallback accretion, interstellar capture, or spallation of heavier elements. If such post‑birth accretion can be prevented, the underlying mid‑Z material (carbon, oxygen, etc.) would be directly exposed, consistent with recent observations of a carbon atmosphere on the Cassiopeia A NS (Ho & Heinke). The work therefore provides a robust theoretical framework for predicting the chemical evolution of NS surfaces, emphasizing that early‑time high temperatures and Coulomb‑driven stratification efficiently erase primordial light elements, while magnetic fields below 10¹² G play a negligible role.