Jose A. Pons

Understanding the Galactic population of isolated neutron stars within a unified framework provides key insights into their birth properties, evolutionary pathways, and the connections between different neutron star classes. In this work, we aim to reproduce both the observed radio and quiescent X-ray emission from isolated neutron stars, including radio pulsars, magnetars, and X-ray-dim isolated neutron stars (XDINSs). We develop a comprehensive population-synthesis framework that models neutron star birth properties, their dynamical, rotational, and magnetothermal evolution, as well as radio and X-ray emission, and the selection effects of corresponding surveys. To simulate realistic X-ray spectra, we account for magnetospheric resonant cyclotron scattering and interstellar absorption. Additionally, we model the observational bias introduced by magnetar outbursts by linking the outburst rate to magnetic stresses in the stellar crust. We then employ a simulation-based inference method, namely truncated sequential neural posterior estimation, to reconstruct the birth properties, such as the initial magnetic-field distribution. We find that the Galactic neutron star population can be described by a two-component log-normal distribution of birth magnetic fields with peaks at 5 × 10 ¹² G and 10 ¹⁴ G, respectively. We further find that the Galactic neutron star birth rate is around 3–4 per century. Our results help establish the contribution of neutron stars as central engines of powerful astrophysical transient phenomena, such as fast radio bursts, superluminous supernovae, and gamma-ray bursts.

The strong magnetic fields of neutron stars are closely linked to their observed thermal, spectral, and timing properties, such as the distribution of spin periods and their derivatives. To understand the evolution of astrophysical observables over time, it is essential to develop robust theoretical frameworks and numerical models that solve the coupled thermal and magnetic field evolution equations, incorporating detailed microphysics such as thermal and electrical conductivities and neutrino emission rates. These efforts are key to uncovering how the strength and geometry of magnetic fields change with age, ultimately shedding light on the diverse phenomenology of neutron stars. In this review, we outline the fundamental theory underlying magneto-thermal evolution models, with an emphasis on numerical methods and a comprehensive set of benchmark tests intended to guide current and future code development. We revisit established results from axisymmetric simulations, highlight recent progress in fully three-dimensional models, and offer a perspective on the anticipated developments in this rapidly evolving field.

Long-period transients are an elusive class of compact objects uncovered by radio surveys. While magnetars are a leading candidate for those sources that appear isolated, several observational properties challenge the established evolutionary framework: (i) low quiescent X-ray luminosities, (ii) ∼hour-long rotational periods, and (iii) highly variable radio flux. It is shown via magnetothermal modeling that, if electric currents thread the fluid core at the time of crust freezing, the neutron star remains multiband silent for an initial period of approximately 0.1 Myr while cooling passively. Once the crust becomes cold enough, the Hall effect begins to dominate the magnetic evolution, triggering crustal failures that inject magnetospheric twist that initiates radio pulsing while depleting rotational kinetic energy from an already slow star. Depending on where electric currents circulate, such “late-blooming” magnetars manifesting as long-period transients may thus form a distinct branch from soft gamma repeaters and anomalous X-ray pulsars.

Light QCD axions, introduced to solve the strong C P problem, may form condensates inside neutron stars, giving rise to a novel ground state of dense matter. We investigate how such axion condensates modify the equilibrium structure and radial oscillation spectrum of neutron stars. Using a realistic neutron star model with the BSk26 equation of state, and solving the coupled Tolman-Oppenheimer-Volkoff and Klein-Gordon equations together with a linear perturbation analysis, we find two distinct families of quasinormal modes: weakly damped fluid-dominated oscillations and highly damped axion modes. The coupling between the fluid and the axion field introduces axion-induced damping of radial oscillations, with decay timescales of order seconds for kHz axion masses. Modes with frequencies above the axion mass are strongly damped, while those below remain unaffected. Although neutron star radial oscillations are difficult to observe, our results suggest that extensions of this work can turn neutron star seismology into a novel probe of the axion properties.

A few members of the recently discovered class of long-period transients have been identified as binaries with white-dwarf primaries. In most cases, however, electromagnetic data are inconclusive, and isolated magnetars or compact binaries remain viable. If the pulsation period matches that of the orbit—as is the case for ILT J1101+5521 and GLEAM-X J0704–37—some of these elusive radio transients could be gravitational-wave bright in the mHz band. Space-based interferometers could thus be used to provide independent constraints on their nature. We quantify the signal-to-noise ratio for the known systems under various scenarios and show that a few could be detectable for sufficiently large chirp masses. Astrophysical implications for (non)detections are discussed.

Magnetar outbursts are among the most noteworthy manifestations of magnetism in neutron stars. They are episodes in which the X-ray luminosity of a strongly magnetised neutron star swiftly rises by several orders of magnitude to then decay over the course of several months. In this work, we present simulations of outbursts as a consequence of localised heat deposition in a magnetised neutron star crust, and the subsequent surface cooling. In particular, we employed a magnetothermal evolution code adapted to the study of short-term phenomena; that is, one including in its integration domain the outer layers of the star, where heat diffusion is faster. This choice entailed the development and use of heat blanketing envelope models that are thinner than those found in the literature as the surface boundary condition. We find that such envelopes can support a higher surface temperature than the thicker ones (albeit for less time), which can account for the typical luminosities observed in outbursts even when coming from small hotspots (few km in radius). We study several parameters related to the energetics and geometry of the heating region, concluding that the cooling of a crustal hotspot found in the outer part of the crust can account for the luminosity evolution observed in outbursts both in terms of peak luminosity and timescales. Finally, we discuss the key observables that must be studied in future observations to better constrain the nature of the underlying mechanism.

The chiral magnetic effect (CME)—a macroscopic manifestation of the quantum chiral anomaly—induces currents along magnetic field lines, facilitating mutual conversion between chiral asymmetry and magnetic helicity. Although the finite electron mass suppresses chiral asymmetry through spin-flip processes, we demonstrate that the CME effectively shapes magnetar field evolution. Magnetic helicity acts as a persistent internal source of chiral asymmetry, which mediates the redistribution of magnetic energy across spatial scales, without requiring an external energy source. Our three-dimensional magnetothermal simulations of the neutron star crust reveal a mechanism that significantly reconfigures the magnetic field inherited at birth, amplifying both toroidal and poloidal large-scale dipolar components (crucial for spin-down) to strengths of > 10 14 G within just a century, at the expense of small-scale structures. This astrophysical application of the CME, distinct and complementary to conventional hydrodynamic dynamo models, offers an innovative framework for understanding magnetar field dynamics and provides a transformative solution to the origin of their exceptionally strong, large-scale fields.

This study enhances the application of Physics-Informed Neural Networks (PINNs) for modeling discontinuous solutions in both hydrodynamics and relativistic hydrodynamics. Conventional PINNs, trained with partial differential equation residuals, frequently face convergence issues and lower accuracy near discontinuities. To address these issues, we build on the recently proposed locally linearized PINNs (LLPINNs), which improve shock detection by modifying the Jacobian matrix resulting from the linearization of the equations, only in regions where the velocity field exhibits strong compression. However, the original LLPINN framework required a priori knowledge of shock velocities, limiting its practical utility. We present a generalized LLPINN method that dynamically computes shock speeds using neighboring states and applies jump conditions through entropy constraints. Additionally, we introduce locally Roe PINNs (LRPINNs), which incorporate an approximate Roe Riemann solver to improve shock resolution and conservation properties across discontinuities. These methods are adapted to two-dimensional Riemann problems by using a divergence-based shock detection combined with dimensional splitting, delivering precise solutions. Compared to a high-order weighted essentially non-oscillatory solver, our method produces sharper shock transitions but smoother solutions in areas with small-scale vortex structures. Future research will aim to improve the resolution of these small-scale features without compromising the model's ability to accurately capture shocks.

The existence of light QCD axions, whose mass depends on an additional free parameter, can lead to a new ground state of matter, where the sourced axion field reduces the nucleon effective mass. The presence of the axion field has structural consequences, in particular, it results in a thinner (or even prevents its existence) heat-blanketing envelope, significantly altering the cooling patterns of neutron stars. We exploit the anomalous cooling behavior to constrain previously uncharted regions of the axion parameter space by comparing model predictions with existing data from isolated neutron stars. Notably, this analysis does not require the light QCD axion to be the dark matter candidate. Published by the American Physical Society 2024