Magnetic, thermal and rotational evolution of isolated neutron stars

Abstract

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.

Figures (27)

• Figure 1: Structure and composition of a $1.4\,M_\odot$ NS, with SLy EoS. The plot shows, as a function of density from the outer crust to the core, the following quantities: mass fraction in the form of nuclei $X_h$ (blue dot-dashed line), the fraction of electrons per baryon $Y_e$ (black dashes), the fraction of free neutrons per baryon $Y_n$ (red dashes), the atomic number $Z$ (dark green triple dot-dashed), the mass number $A$ (cyan long dashes), radius normalized to $R$ (pink solid), and the corresponding enclosed mass normalized to the star mass (green solid). Note that the total neutron fraction (not shown here) varies continuously across the NS interior, unlike the fraction of free neutrons per baryon, $Y_n$.
• Figure 2: Contributions to the specific heat from neutrons (red dashes), protons (green dot-dashed), electrons (blue dots), and ions (black solid line) as a function of density, from the outer crust to the core, and for different temperatures in each panel (as indicated). The superfluid models employed here are the same as in Ho2012. The plots refer to the representative NS shown in Fig. \ref{['fig:ns_profile']}.
• Figure 3: Thermal conductivity in the directions parallel (solid lines) and perpendicular (dashes) to the magnetic field, including quantizing effects. We show the cases $T=10^9$ K, $B=10^{15}$ G (left panel) and $T=10^8$ K, $B=10^{14}$ G (right panel). For comparison, the $B=0$ values are shown with green lines in both figures. The plots refer to the representative NS shown in Fig. \ref{['fig:ns_profile']}.
• Figure 4: Evolution of neutrino and photon luminosities from the different emission processes throughout the NS history, computed with the SLy4 EoS for a mass of $M = 1.6 \, M_\odot$. Solid-colored lines represent different neutrino emission processes occurring in the core. Dashed lines represent different neutrino emission processes occurring in the crust. The same process (marked with a given color) may involve both the core and the crust. Black lines represent the total neutrino luminosity for processes involving the core (continuous line) and the crust (dashed line), respectively. The black-dots report the surface photon luminosity. This figure assumes the gap model of Ho2015. It is worth noticing that while the legend includes all the possible neutrino processes included in the simulation, some of them are not effectively active in this particular simulation, as such, they do not appear in the figure. Moreover, in case magnetic fields are present in the core, additional processes can become relevant Kantor2021. Image reproduced with permission from MATINS2, copyright by the author(s)
• Figure 5: Schematic illustration of the allocation of temperatures (cell centers) and fluxes (cell interfaces) in a typical grid in polar coordinates.