Dense matter with eXTP

eXTP offers unprecedented discovery space for the EOS of cold supranuclear density matter. eXTP’s large area will enable the most sensitive searches for accretion-powered pulsations and burst oscillations ever undertaken. Both yield the spin frequency of the NS; a single measurement of sub millisecond period spin would provide a clean and extremely robust constraint on the EOS. However, eXTP will also deliver high precision measurements of M and R. The combination of large effective area and polarimeter will enable us to deploy multiple independent techniques: pulse profile modelling of accretionpowered pulsations, burst oscillations, and rotation-powered pulsations; spectral modelling of bursts, and using phenomena related to the accretion disc such as kHz QPOs and the relativistic Fe line. Many sources show several of these phenomena, allowing us to make completely independent measurements for a single source, to reduce systematic errors. Examples of targets in this class include the accretionpowered millisecond pulsar SAX J1808.4–3658, which goes into regular outburst, and the persistently accreting burster 4U 1636–536. We anticipate that eXTP could delivery precision constraints on M and R, at the few percent level, for of order 10 sources for a reasonable observing plan and given the anticipated mission lifetime. This would be unprecedented in terms of mapping the EOS and expanding the frontiers of dense matter physics.