tokens: of the X-ray flux (see e.g. Patruno, Wijnands van der Klis 2009b ), which can hinder the detection of relative weak spin derivatives (see e.g. Galloway et al. 2002 ; Burderi et al. 2006 ; Riggio et al. 2008 ; Bult et al. 2019 ). Here, we report on the phase-coherent timing analysis of the AMXP IGR J17591–2342 (Sanna et al. 2018d ), first detected by INTEGRAL on 2018 August 10 (Ducci et al. 2018 ) and extensively monitored by the NICER instrument during its outburst. Moreover, we investigated the evolution of the spin pulse delays within the framework of magnetically disc-threading theories in which the material torque (dependent on mass accretion rate) as well as the disc-threading torques exerted by the magnetic field are taken into account (see e.g. Rappaport et al. 2004 ; Kluźniak Rappaport 2007 ). For the first time in phase-coherent timing analysis of AMXPs, we modelled variations of the frequency spin derivative taking into account instantaneous values of the mass accretion rate by following the X-ray flux evolution. Recently, a similar approach has been successfully applied to the timing of the X-ray pulsar GRO J1744–28, a slowly spinning (∼2 Hz) NS accreting from a low-mass companion (Sanna et al. 2017b ). The obtained results show that, at least in this case, the standard theory of accretion on to NS works very well also for fast rotators and allowed an accurate determination of the magnetic field strength that is in the range of the values expected for this class of sources. Finally, we report on the updated source ephemerides and we discuss the properties of the X-ray pulsation as well as its temporal evolution. 2 OBSERVATIONS AND DATA ANALYSIS NICER (Gendreau, Arzoumanian Okajima 2012 ) started monitoring the X-ray transient IGR J17591–2342 on 2018 August 15 (MJD 58345) up to 2018 October 17 (MJD 58408.2) for a total of 37 dedicated observations. We processed the available NICER observation using the nicerdas pipeline (version V004a) retaining events in the 0.2–12 keV energy range, for which the pointing offset was 54 arcsec, the dark Earth limb angle was >30°, the bright Earth limb angle was >40°, and the ISS location was outside of the South Atlantic Anomaly (SAA). Moreover, we removed short intervals that showed background flaring in high geomagnetic latitude regions. As a result of the filtering process we retained a total exposure time of ∼101 ks. The spectral background was obtained from a blank-sky observation of the RXTE-6 region. We did not detect any Type-I thermonuclear bursts during the observations analysed in this work. For each observation we modelled the energy spectrum with an absorbed blackbody component plus a thermally comptonized continuum ( Tbabs(bbody+nthcomp) in Xspec) and we extracted the source unabsorbed flux in the energy range 0.5–10 keV (see Fig. 1 ). Finally, we barycentred the NICER photon arrival times with the barycorr tool using the JPL DE-405 Solar system ephemeris and adopting the
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