We report on the phase-coherent timing analysis of the accreting millisecond X-ray pulsar IGR J17591-2342, using Neutron Star Interior Composition Explorer (NICER) data taken during the outburst of the source between 2018 August 15 and 2018 October 17. We obtain an updated orbital solution of the binary system. We investigate the evolution of the neutron star spin frequency during the outburst, reporting a refined estimate of the spin frequency and the first estimate of the spin frequency derivative ($dot{ u} sim -7times 10^{-14}$ Hz s$^{-1}$), confirmed independently from the modelling of the fundamental frequency and its first harmonic. We further investigate the evolution of the X-ray pulse phases adopting a physical model that accounts for the accretion material torque as well as the magnetic threading of the accretion disc in regions where the Keplerian velocity is slower than the magnetosphere velocity. From this analysis we estimate the neutron star magnetic field $B_{eq} = 2.8(3)times10^{8}$ G. Finally, we investigate the pulse profile dependence on energy finding that the observed behaviour of the pulse fractional amplitude and lags as a function of energy are compatible with a thermal Comptonisation of the soft photons emitted from the neutron star caps.
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