Superfluid effects on gauging core temperatures of neutron stars in low-mass X-ray binaries

Neutron stars accreting matter from low-mass binary companions are observed to undergo bursts of X-rays due to the thermonuclear explosion of material on the neutron star surface. We use recent results on superfluid and superconducting properties to show that the core temperature in these neutron stars may not be uniquely determined for a range of observed accretion rates. The degeneracy in inferred core temperatures could contribute to explaining the difference between neutron stars which have very short recurrence times between multiple bursts and those which have long recurrence times between bursts: short bursting sources have higher temperatures and normal neutrons in the stellar core, while long bursting sources have lower temperatures and superfluid neutrons. If correct, measurements of the lowest luminosity from among the short bursting sources and highest luminosity from among the long bursting sources can be used to constrain the critical temperature for the onset of neutron superfluidity.

💡 Research Summary

The paper investigates how superfluidity and superconductivity in the cores of neutron stars (NSs) that reside in low‑mass X‑ray binaries (LMXBs) affect the inference of their core temperatures from observed accretion‑driven heating. Accretion onto the NS surface releases gravitational energy, a small fraction (≈0.78 %) of which is deposited as heat in the core (L_heat = 0.0078 L_acc). The core cools primarily by neutrino emission. In a normal (non‑superfluid) core the dominant cooling channel is the modified Urca process, with a luminosity L_MUν ≈ 7.4 × 10³¹ (T/10⁸ K)⁸ erg s⁻¹.

When neutrons become superfluid and protons become superconducting, two major changes occur: (1) the modified Urca reactions involving these particles are strongly suppressed, and (2) a new cooling channel opens—Cooper‑pair breaking and formation (PBF). The authors model the neutron critical temperature T_cn(ρ) with simple parameterizations (quadratic and Gaussian profiles) characterized by a peak temperature T_cn,max, a peak density ρ_cn,peak, and a width. Proton pairing is assumed to have a fixed critical temperature T_cp = 3 × 10⁹ K, making proton PBF negligible and only suppressing the modified Urca process.

Balancing heating and cooling (L_heat = L_ν) yields two thermally stable solutions for a given accretion luminosity, provided T_cn,max is low enough (≈4–5 × 10⁸ K). The “high‑temperature branch” corresponds to T ≫ T_cn,max, where neutrons are normal, cooling is relatively inefficient, and the core temperature is roughly
T_MU ≈ 1.3 × 10⁸ K (L_acc/10³⁵ erg s⁻¹)¹⁄⁸.
The “low‑temperature branch” corresponds to T ≪ T_cn,max, where neutrons are strongly superfluid, PBF dominates cooling, and the core temperature is lower:
T_npSF ≈ 9 × 10⁷ K (L_acc/10³⁵ erg s⁻¹)¹⁄⁸.

The intermediate temperatures are thermally unstable because a slight cooling increase boosts neutrino emission, driving the star toward the low‑temperature branch. This temperature degeneracy provides a natural explanation for the observed dichotomy in burst recurrence times among LMXBs. Keek et al. (2010) identified fifteen LMXBs with short recurrence times (≤ 1 h) and a separate set with long recurrence times (≥ 1 h). The short‑recurrence sources have higher observed accretion‑driven luminosities (≈2 × 10³⁶ erg s⁻¹) and, according to the model, reside on the high‑temperature branch, implying normal neutrons in the core. The long‑recurrence sources have lower luminosities (≈8 × 10³⁷ erg s⁻¹) and sit on the low‑temperature branch, implying a superfluid neutron core.

Because surface temperature scales roughly as T_core^0.5 (Gudmundsson et al. 1982), the high‑temperature branch predicts surface fluxes about (3.5)⁴ ≈ 150 times larger than the low‑temperature branch. This should manifest as higher quiescent X‑ray luminosities (L_q) for short‑recurrence systems, a trend that is hinted at in existing data.

A key observational consequence is that the minimum accretion luminosity among short‑recurrence bursts and the maximum among long‑recurrence bursts can be used to constrain the neutron superfluid critical temperature. The authors argue that if T_cn,max lies in the range (4–5) × 10⁸ K, the observed luminosity ranges naturally produce the two stable temperature solutions. This range is compatible with, but slightly lower than, the values inferred from the rapid cooling of the Cassiopeia A NS (≈5–9 × 10⁸ K).

In summary, the paper demonstrates that superfluid effects introduce a non‑uniqueness in core‑temperature estimates for accreting neutron stars, and that this non‑uniqueness may be responsible for the observed split between short‑ and long‑recurrence X‑ray bursts. Precise measurements of the extremal burst luminosities in both classes could therefore provide a novel probe of neutron superfluidity in dense matter, complementing cooling observations of isolated neutron stars.