Constraints on axion-like particles and nucleon pairing in dense matter from the hot neutron star in HESS J1731-347

If the thermal evolution of the hot young neutron star in the supernova remnant HESS J1731-347 is driven by neutrino emission, it provides a stringent constraint on the coupling of light (mass $\ll 10\mathrm{keV}$) axion-like particles to neutrons. Using Markov-Chain Monte Carlo we find that for the values of axion-neutron coupling $g_{ann}^2>7.7\times {10}^{-20}$ (90% c.l.) the axion cooling from the bremsstrahlung reaction $n+n\to n+n+a$ is too rapid to account for the high observed surface temperature. This implies that the Pecci-Quinn scale or axion decay constant $f_a>6.7\times {10}^7\mathrm{GeV}$ for KSVZ axions and $f_a>1.7\times {10}^9\mathrm{GeV}$ for DFSZ axions. The high temperature of this neutron star also allows us to tighten constraints on the size of the nucleon pairing gaps.

Figure 1

Interior temperature $T_b$ of J1732, as a function of the amount of carbon in the envelope, parametrized by $\eta$ as in Eq. (4.1), for three effective temperatures. (From the envelope models of [40] and assuming a star of mass 1.4 ${\mathrm{M}}_{\odot }$with a radius of 11.8 km.)

Figure 2

Examples of proton ${}^1\mathrm{S}_0$ pairing gaps, lower panel, and the resulting neutrino and axion emissivities, middle panel for uniform gap and upper panel for the CCDK [48] gap. See text for details.

Figure 3

Cooling curves of effective temperature at infinity $T_{\mathrm{eff}}^{\infty }$ versus model age $t$ illustrating the effect of neutron ${}^1\mathrm{S}_0$ pairing (which is mostly located in the inner crust). The data point corresponds to J1732 with $1\sigma$ uncertainties. See text for details.

Figure 4

Same as Fig. 3 with four models illustrating the effect of the stellar mass, with masses as labeled. These models assume that the proton superconductivity critical temperature is density independent and very high. See text for details and Fig. 8 for the effect of density-dependent $T_{c,p}$.

Figure 5

Same as Fig. 3 with four models illustrating the basic effects of proton versus neutron pairing and envelope chemical composition. The two upper curves have protons ${}^1\mathrm{S}_0$, paired in the whole core with a density independent $T_c$ of $7.3\times {10}^9\mathrm{K}$ and normal neutrons while the two lower curves have normal protons and ${}^3\mathrm{P}\text{−}{\mathrm{F}}_2$, paired neutrons in the whole core with a density independent $T_c$ of ${10}^9\mathrm{K}$. For each pairing scenario the two curves correspond to two different thickness of carbon layer in the envelope, $\eta$ in Eq. (4.1), as labeled.

Figure 6

Corner plot of the ${log}_{10}{T}_{c,p}^{\max }$ and ${log}_{10}{T}_{c,n}^{\max }$ posterior probability distributions, in the diagonal panels, and their correlation, in the bottom left panel, from our MCMC run A. Dash-dotted and dotted lines show 90% and 99% quantiles respectively, and the grayscale density is proportional to the probability density. The high probability region marked as “a” corresponds to strong proton superconductivity, i.e., with high $T_c$, and weak neutron superfluidity, i.e., with small $T_c$, while the peak marked as “b” has the opposite, weak proton superconductivity and strong neutron superfluidity. Given the present core temperature of J1732, peak “a” implies normal neutrons and peak “b” normal protons in its core. See also Fig. 7 and text for details.

Figure 7

Density of cooling curves corresponding to Fig. 6. 10000 curves were used to generate this density plot, a representative sample of the MCMC run. The two different subpopulations, corresponding to the two separated probability peaks “a” and “b” seen in Fig. 6, clearly appear by their cooling behavior at late times. The data point corresponds to J1732 with $1\sigma$ uncertainties. See details in the text.

Figure 8

Same as Fig. 4 with four models illustrating the effect of the stellar mass, with masses as labeled, when a density-dependent proton ${}^1\mathrm{S}_0$ gap, model CCDK from Ref. [48], is used. See text for details.

Figure 9

Histograms of posterior probability distribution of $R_{\sigma }$, ${log}_{10}{R}_A$, ${log}_{10}\eta$, and ${log}_{10}{T}_{c,p}$ from our MCMC run B. Vertical lines are: dotted = 50%, dashed = 90%, and solid = 99% quantiles. See text for details.

Figure 10

Comparison of posterior $R_A$ probability distributions with variable, MCMC run B, and fixed, MCMC run C, $R_{\sigma }$. Vertical lines are the same quantiles, 50%, 90%, and 99%, as in Fig. 9. Distribution with variable $R_{\sigma }$ (gray line) is identical to one in Fig. 9. Black lines correspond to distribution of $R_A$ obtained with fixed $R_{\sigma }=0.25$. See details in the text.

Figure 11

Density of cooling curve to illustrate of the role of $R_{\sigma }$: left panel has $0.1\le R_{\sigma }\le 3$ and right panel has a fixed $R_{\sigma }=0.25$. 10000 curves were used to generate each density plot, a representative sample of the MCMC runs B and C. The data point corresponds to J1732 with $1\sigma$ uncertainties.

Figure 12

Corner plots of posterior probability distributions of $R_{\sigma }$ and $R_A$ for our four MCMC runs D1, D2, D3, and D4, assuming different ages for the remnant J1732, as indicated in the panels corners. See text for details.