Core Composition Effects on the QCD Axion Mass Limit from Neutron Star Cooling

The gist Neutron stars are very dense media in which axions may be produced, and this work studies how the limit on the mass of QCD axions, namely KSVZ and DFSZ invisible axions, is altered when different equations of state are used to allow for heavier particles to appear in the neutron star core<ref:2606.07742#pg14>

Construction of Neutron Star Equations of State

The construction of the equations of state was done through the MUSES Calculation Engine, which allows for the construction of NS EOSs with varying particle composition in the core<ref:2606.07742#pg5> The workflow schematically represents a factorization where Crust-DFT, χEFT, CMF are combined to build a complete EOS for NS<ref:2606.07742#pg6> This approach is computationally convenient and reflects the fact that the outer crust, the outer core and the inner core are controlled by different effective degrees of freedom and constraints<ref:2606.07742#pg9> The low density regions are described using Crust Density Functional Theory (Crust-DFT), which provides a free-energy density description of matter in thermodynamic space Around saturation density, a Chiral Effective Field theory (χEFT)-based module is employed to bridge the low and high density regions High density regions are performed by the Chiral Mean Field (CMF) module, which is a relativistic mean field realization of a non linear SU(3) sigma model

Core Compositions Studied

The study considers four scenarios for NS core compositions:

1. npeµ This case is the most commonly used, consisting of neutrons, protons, electrons, and muons The relevant neutrino emission processes include Direct URCA, Modified URCA, Bremsstrahlung and PBF in the singlet gaps

2. Spin 3/2 resonances This scenario allows for the presence of baryonic resonances with spin 3/2, such as Delta baryons These resonances show up only deep within the NS core, amounting to roughly 1% of the composition at large baryon densities

3. Hyperons This allows for the full baryonic octet and decuplet, including all hyperons The inclusion of hyperons implies a large variety of weak processes to be considered, such as DURCA processes and modified URCA processes involving hyperons

4. More Exotic Compositions This includes possibilities like on-shell pions and kaons, or QCD deconfinement leading to hybrid stars The study does not pursue the pion and kaon abundances due to current MUSES CE limitations, but hybrid stars are explored in a first approach

Axion Emission Models and Limits

Axions can be emitted through processes analogous to those involving neutrino pairs, namely bremsstrahlung processes like n + n → n + n + a, and the nucleon pair-breaking formation process of the form ↔ NN → N + N + a The axion is a neutral pseudoscalar particle that arises from an anomalous global symmetry, and its coupling to nucleons can be parametrized by gaNN The two benchmark invisible axion scenarios are the KSVZ and DFSZ models For KSVZ models, the axion does not couple to SM quarks at tree level but couples to gluons, leading to specific couplings like cKSV Z ap = −0.47 ± 0.03 DFSZ axions couple at tree-level to SM quarks and depend on the parameter tan β in their nucleon couplings

Results and Conclusions

The statistical analysis comparing observed NS ages and luminosities with dedicated cooling simulations shows that there is no strong dependence on the upper limit on the axion mass due to the particle content allowed to be present in the NS core, which reinforces the robustness of the limit offered by [36] For KSVZ axions, best-fit values for ma oscillate closely around zero, contrasting with previous results that were always negative For DFSZ axions, the same conclusion is drawn: allowing the presence of heavier SM particles in the NS core has a mild effect on the derived constraint on the axion mass The strongest limit found, given by MUSES CE EOS with neutron and proton singlet superfluidity in the npeµ case, is almost a factor of 2 stronger than that in previous work and goes right beyond IAXO sensitivity This suggests that an axion discovery in this region would allow testing the core composition within the NS

How it works

1. The study uses MUSES CE [43] to build EOSs for four scenarios: npeµ, Octet, Delta, and Oct+Dec

2. The cooling code NSCool [49] is upgraded with new processes depending on the composition considered

3. A statistical analysis follows the strategy introduced in [36], comparing observed data with cooling simulations to construct a likelihood test statistic

4. For KSVZ axions, the analysis is performed as a one-dimensional scan in the axion mass ma, fixing gaNN by Eq. (4.6)

5. For DFSZ axions, the analysis is performed on a two-parameter grid spanning ma and tan β

Conclusion

Overall, the result is very compatible with that from [36], with our weakest bound being just very slightly looser than the original one, which once again gives further soundness to the bound The strongest limit is enhanced by almost a factor of two and reaches now beyond IAXO sensitivity If IAXO were to discover an axion in this region, it may then help disentangle the composition within the NS The work shows the versatility of MUSES CE [43] and opens the door to exciting future analyses

Acknowledgements

The authors are deeply grateful to M. Giannotti, L. Merlo and E. Nardi for encouraging the development of this project from its early stages as well as for enlightening conversations The authors are also thankful for their hospitality during different moments in the past year, for welcoming us to their institutions, and for allowing us to discuss this matter with a broader audience about The authors kindly thank as well the MUSES Collaboration, for their openness, availability, and swiftness

References

[1] J. M. Lattimer and M. Prakash, The Ultimate energy density of observable cold matter, Phys. Rev. Lett. 94 (2005) 111101, [astro-ph/0411280]

[2] D. Page, Thermal evolution of isolated neutron stars, in NATO Advanced Study Institute: The Many Faces of Neutron Stars, 6, 1997. astro-ph/9706259

[3] D. G. Yakovlev, A. D. Kaminker, O. Y. Gnedin, and P. Haensel, Neutrino emission from neutron stars, Phys. Rept. 354 (2001) 1, [astro-ph/0012122]

[4] D. Page, U. Geppert, and F. Weber, The Cooling of compact stars, Nucl. Phys.

1. Improved AI system can perform robust constraint validation by checking if a proposed axion mass limit is compatible with all four core composition scenarios (npeµ, Octet, Delta, Oct+Dec) and both KSVZ and DFSZ models simultaneously against the derived 95% CL upper limits in Table 2 and Figure 9.

2. Improved AI system can precisely predict which particle content within a neutron star core will result in the strongest cooling limit for a given axion mass, specifically identifying that the strongest limit is enhanced by almost a factor of two when considering the npeµ case with neutron and proton singlet superfluidity.

3. Improved AI system can distinguish between results from different Equation of State families, noting that the inclusion of the baryon octet lowers the maximum value of the NS mass, whenever a NS lighter than roughly 1.7M⊙ is considered, no difference in its radius is observed.

4. Improved AI system can analyze the dependence of axion limits on superfluidity models and EOS families, concluding that allowing for hyperons and/or spin 3/2 resonances in the NS core does not seem to largely affect the limit derived on the axion mass, with EOS family and superfluidity having a stronger impact.

5. Improved AI system can identify regions where axion discovery might help resolve core composition by noting that this region is precisely sensitive to the particles within the core.