[Paper Review] On the PBF neutrino losses in superfluid cores of neutron stars

L. B. Leinson|arXiv (Cornell University)|Nov 10, 2016

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper re-evaluates neutrino energy losses via the pair-breaking and formation (PBF) process in superfluid neutron stars by including previously neglected axial anomalous contributions from triplet-paired neutrons. It finds that these contributions suppress the axial channel by a factor of four and eliminate the vector channel, significantly reducing neutrino emissivity and altering neutron star cooling rates compared to traditional models.

ABSTRACT

Axial anomalous contributions into neutrino PBF losses due to triplet pairing of neutrons are still ignored in modeling the evolution of neutron stars. In this paper, the influence of the anomalous axial contributions onto the rate of neutron stars cooling is estimated.

Motivation & Objective

• To assess the impact of axial anomalous weak interactions on neutrino emissivity in superfluid neutron stars.
• To correct the standard model of neutron star cooling by including neglected anomalous contributions in the PBF process.
• To improve the accuracy of thermal evolution simulations by accounting for triplet-pairing effects in the inner core.
• To re-evaluate the role of 3P2 pairing with m_j = 0 in determining neutrino energy loss rates.

Proposed method

• The study uses the NSCOOL code to simulate the thermal evolution of a spherically symmetric neutron star with a 1.4 M☉ mass and iron envelope.
• It modifies the reaction constant $ a_{nt} $ in the PBF emissivity formula to include axial anomalous contributions.
• The neutrino emissivity is calculated using the expression $ Q = \frac{2C_A^2}{15\pi^5\hbar^{10}c^6} \mathcal{N}_\nu G_F^2 p_F M_n^* (k_B T)^7 F_t(\Delta_\mathbf{n}/T) $, where $ F_t $ incorporates the anisotropic gap $ \Delta_\mathbf{n} = \Delta_0(T) \sqrt{1 + 3\cos^2\theta} $.
• The function $ F_t $ is evaluated via the integral $ \int \frac{d\mathbf{n}}{4\pi} y^2 \int_0^\infty dx \frac{z^4}{(1 + \exp z)^2} $ with $ z = \sqrt{x^2 + y^2} $ and $ y = \Delta_\mathbf{n}/T $.
• Cooling trajectories are compared with and without anomalous terms to isolate their effect on surface temperature evolution.
• The analysis uses the APR equation of state to determine critical temperatures for neutron and proton superfluidity as a function of density.

Experimental results

Research questions

• RQ1 How do axial anomalous weak interactions affect the PBF neutrino emissivity in superfluid neutron stars?
• RQ2 What is the quantitative impact of these anomalous contributions on the rate of neutrino energy losses?
• RQ3 How do the inclusion of anomalous terms alter the predicted cooling trajectories compared to the standard model?
• RQ4 To what extent do these contributions suppress the vector and axial channels in the PBF process?
• RQ5 Can a more accurate treatment of anomalous interactions improve the consistency between theoretical cooling models and observational data?

Key findings

• The inclusion of axial anomalous contributions suppresses the vector channel of neutrino emission entirely in the PBF process.
• The axial channel is reduced by a factor of four due to the anomalous contributions, significantly lowering the emissivity.
• The modified emissivity formula leads to a slower cooling rate, as shown by the comparison of cooling trajectories.
• The upper cooling trajectory (with anomalous terms) results in a higher surface temperature at a given age than the traditional model.
• The critical temperature for neutron superfluidity is calculated as a function of density using the APR equation of state.
• The results suggest that a more accurate treatment of anomalous interactions is necessary for consistent modeling of neutron star thermal evolution.