We present a timing analysis of the 2015 outburst of the accreting millisecond Xray pulsar SAX J1808.4-3658, using non-simultaneous XMM-Newton and NuSTAR observations. We estimate the pulsar spin frequency and update the system orbital solution. Combining the average spin frequency from the previous observed, we confirm the long-term spin down at an average rateν SD = 1.5(2) × 10 −15 Hz s −1 . We also discuss possible corrections to the spin down rate accounting for mass accretion onto the compact object when the system is X-ray active. Finally, combining the updated ephemerides with those of the previous outbursts, we find a long-term orbital evolution compatible with a binary expansion at a mean rateṖ orb = 3.6(4) × 10 −12 s s −1 , in agreement with previously reported values. This fast evolution is incompatible with an evolution driven by angular momentum losses caused by gravitational radiation under the hypothesis of conservative mass transfer. We discuss the observed orbital expansion in terms of non-conservative mass transfer and gravitational quadrupole coupling mechanism. We find that the latter can explain, under certain conditions, small fluctuations (of the order of few seconds) of the orbital period around a global parabolic trend. At the same time, a non-conservative mass transfer is required to explain the observed fast orbital evolution, which likely reflects ejection of a large fraction of mass from the inner Lagrangian point caused by the irradiation of the donor by the magneto-dipole rotator during quiescence (radio-ejection model). This strong outflow may power tidal dissipation in the companion star and be responsible of the gravitational quadrupole change oscillations.

We report the discovery by the Nuclear Spectroscopic Telescope Array (NuSTAR) and the Neutron Star Interior Composition Explorer (NICER) of the accreting millisecond X-ray pulsar IGR J17591–2342. Coherent X-ray pulsations around 527.4 Hz (1.9 ms) with a clear Doppler modulation were detected. This implies an orbital period of ∼8.8 h and a projected semi-major axis of ∼1.23 lt-s. With the binary mass function, we estimate a minimum companion mass of 0.42 M⊙, obtained assuming a neutron star mass of 1.4 M⊙ and an inclination angle lower than 60°, as suggested by the absence of eclipses or dips in the light curve of the source. The broad-band energy spectrum, obtained by combining NuSTAR, swift and INTEGRAL observations, is dominated by Comptonisation of soft thermal seed photons with a temperature of ∼0.7 keV by electrons heated to 21 keV. We also detect black-body-like thermal direct emission that is compatible with an emission region of a few kilometers and a temperature compatible with the seed source of Comptonisation. A weak Gaussian line centred on the iron Kα complex can be interpreted as a signature of disc reflection. A similar spectrum characterises the NICER spectra, which was measured when the outburst faded.

In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s.

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