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The discovery of several ultraluminous X-ray sources exhibiting fast and rapidly evolving X-ray pulsations unequivocally associates these sources with accreting neutron stars orbiting relatively massive companion stars (> 8M$��{\hspace{0.17em}}_{\odot }�$). Among these ULXs, the brightest pulsating ULX (PULX), NGC 5907 ULX-1, displays a peak luminosity (~2 × 10⁴¹ erg s⁻¹) that exceeds its Eddington limit by ~1000 times. These discoveries have raised several key questions, the most urgent of which include: what physical process (or processes) is driving the observed luminosities? What is the nature of compact objects in the still non-pulsating ULXs, and how can we unambiguously ascertain it? Why are PULXs so rare and elusive, and how can we identify more members of this class? In this contribution, a brief overview of the ULX class is provided focusing on PULXs, presenting the most recent results obtained for NGC 5907 ULX-1, NGC 7793 P13, M82 X-2 and M51 ULX-7. How current-generation X-ray missions are already providing (and can continue to do so in the next years) a wealth of information to address the aforementioned questions is also outlined.

This is a concise and non-technical review of topics related to neutron star (NS) cooling, for both young NSs and NSs in low-mass x-ray binaries. Neutrino emission from the NS core drives cooling rates, via different processes including Urca processes and pair breaking and formation at the neutron superfluid critical temperature. Key insights have been given by the temperatures of the coldest NSs, by the rapid (questioned) cooling of the Cas A NS, and by measuring the cooling of transient NS x-ray binaries after accretion episodes.

A0538-66 is a neutron star/Be x-ray binary located in the Large Magellanic Cloud and, since its discovery in the 70s, it showed a peculiar behavior that makes it a unique object in the high-mass x-ray binaries scene: the extremely eccentric orbit ($��e�=�0.72�$), the short spin period of the neutron star ($��P�=�69�$ ms), the episodes of super-Eddington accretion. These characteristics contribute to a remarkable bursting activity that lasts from minutes to hours and increases the flux by a factor $��{10}^3�-�{10}^4�$. In 2018, A0538-66 was observed by XMM-Newton in a particularly active state, characterized by a forest of short bursts lasting $��0.7�-�50�$ s each. In this contribution, we present a reanalysis of these observations. The timing analysis allowed us to distinguish between the epochs of direct accretion and propeller state that do not correlate with the orbital position of the neutron star. The spectral analysis revealed that during the accretion regime, three components (a soft one, a hard one, and a $��\sim �6.4�$-keV emission line) equally contribute to the overall emission, while the propeller regime is characterized by a single soft component. We discuss these findings in the context of spherical and disk accretion regimes, highlighting the similarities and differences with other x-ray binary systems.

The INTEGRAL satellite has collected a large amount of data on magnetars in our Galaxy, spanning more than 20 years starting from 2003. The large data set obtained with the IBIS/ISGRI instrument at energies above 20 keV allows us to study both the properties and long-term evolution of their persistent hard X-ray emission and the population characteristics of the short bursts emitted during active periods. We are carrying out a comprehensive analysis of the observed magnetars, exploiting the most recent calibrations and analysis software. Here we report on the long term evolution of the hard X-ray flux of the magnetars detected with ISGRI and the results of a sensitive search for short bursts in SGR J1935+2154.

The persistent BeXRBs are a class of high-mass X-ray binaries (HMXRBs), which are characterized by persistent low X-ray luminosities ($��L_X�~�{10}^{34}�$ erg s$��{\hspace{0.17em}}^{�-�1�}�$) and wide ($��P_{\mathrm{orb}}�>�$ 30 days), almost circular orbits. In these sources the NS is slowly rotating (with $��P_{\text{spin}}�$ well above 100 s) and accretes matter directly from the wind of the companion Be star, without the formation of an accretion disk. Since the '90s, when the first four members of this class were identified, several other sources of the same type have been discovered and investigated. Thanks to follow-up XMM-Newton observations, we have verified that most of them share common spectral and timing properties, such as a pulsed fraction that does not vary with the photon energy and a hot (kT = 1–2 keV) blackbody spectral component which contributes for 20%–40% to the total flux and has a size consistent with the NS polar cap. Here we provide an overview of how XMM-Newton contributed to constrain the observational properties and the current understanding of this type of sources. We also report about the first results obtained with a very recent XMM-Newton observation of the poorly known BeXRB 4U 0728-25.