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ABSTRACT The thermal evolution of isolated neutron stars is a key element in unravelling their internal structure and composition and establishing evolutionary connections among different observational subclasses. Previous studies have predominantly focused on one-dimensional or axisymmetric two-dimensional models. In this study, we present the thermal evolution component of the novel three-dimensional magnetothermal code MATINS (MAgneto-Thermal evolution of Isolated Neutron Star). MATINS employs a finite volume scheme and integrates a realistic background structure, along with state-of-the-art microphysical calculations for the conductivities, neutrino emissivities, heat capacity, and superfluid gap models. This paper outlines the methodology employed to solve the thermal evolution equations in MATINS, along with the microphysical implementation that is essential for the thermal component. We test the accuracy of the code and present simulations with non-evolving magnetic fields of different configurations (all with electrical currents confined to the crust and a magnetic field that does not thread the core), to produce temperature maps of the neutron star surface. Additionally, for a specific magnetic field configuration, we show one fully coupled evolution of magnetic field and temperature. Subsequently, we use a ray-tracing code to link the neutron star surface temperature maps obtained by MATINS with the phase-resolved spectra and pulsed profiles that would be detected by distant observers. This study, together with our previous article focused on the magnetic formalism, presents in detail the most advanced evolutionary code for isolated neutron stars, with the aim of comparison with their timing properties, thermal luminosities and the associated X-ray light curves. 

Abstract The combined detection of a gravitational-wave signal, kilonova, and short gamma-ray burst (sGRB) from GW170817 marked a scientific breakthrough in the field of multimessenger astronomy. But even before GW170817, there have been a number of sGRBs with possible associated kilonova detections. In this work, we re-examine these ‘historical’ sGRB afterglows with a combination of state-of-the-art afterglow and kilonova models. This allows us to include optical/near-infrared synchrotron emission produced by the sGRB as well as ultraviolet/optical/near-infrared emission powered by the radioactive decay of r-process elements (i.e. the kilonova). Fitting the light curves, we derive the velocity and the mass distribution as well as the composition of the ejected material. The posteriors on kilonova parameters obtained from the fit were turned into distributions for the peak magnitude of the kilonova emission in different bands and the time at which this peak occurs. From the sGRB with an associated kilonova, we found that the peak magnitude in H bands falls in the range [−16.2, −13.1] ($$95{{\ \rm per\ cent}}$$ of confidence) and occurs within $$0.8\!-\!3.6\, \rm d$$ after the sGRB prompt emission. In g band instead we obtain a peak magnitude in range [−16.8, −12.3] occurring within the first 18 h after the sGRB prompt. From the luminosity distributions of GW170817/AT2017gfo, kilonova candidates GRB130603B, GRB050709, and GRB060614 (with the possible inclusion of GRB150101B, GRB050724A, GRB061201, GRB080905A, GRB150424A, and GRB160821B) and the upper limits from all the other sGRBs not associated with any kilonova detection we obtain for the first time a kilonova luminosity distribution in different bands.