ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O B-Telescope O O O O O O O O O B-Citation I-Citation I-Citation O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-CelestialObject B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-CelestialObject B-Citation I-Citation I-Citation O O B-CelestialObject B-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O
tokens: can be estimated combining the observed secular frequency shift (almost 0.8Hz over 17yr of observations) with that caused by the material torque (ranging between 0.35 and 0.56Hz, considering the NS radius and the corotation radius as possible truncation radii of the disc). The spin-down derivative required to compensate the estimated spin-up material torque and to produce the observed spin-down effect should range between 2.210 15 and 2.710 15 Hzs 1 , a factor of almost 1.5 and 1.8 higher, respectively, than the spin-down frequency derivative estimated ignoring the material torque. Using equation ( 5 ) and adopting the FPS equation of state previously described, we can estimate the NS dipole magnetic moment, hence the magnetic field at the magnetic caps in the range 2.210 8 B PC 310 8 G, very similar to the value suggested by Burderi etal. ( 2006 ). However, we note that other mechanisms such as magnetic propeller torque and gravitational radiation torque (see e.g. Hartman etal. 2008 , and references therein for more details) could contribute to the spin-down torque required to describe the observed secular spin evolution of SAXJ1808.43658. 4.2 Pulse energy dependence SAXJ1808.43658 shows an interesting behaviour of its pulse profile as a function of energy. As shown in Fig. 5 , the pulse fractional amplitude estimated from the fundamental component varies significantly between the XMMNewton and the NuSTAR observations of the source. We can exclude instrumental effects between the two satellites to explain such a discrepancy. Indeed, phase-coherence analyses on almost simultaneous XMMNewton and NuSTAR have been carried out on other sources (see e.g. Sanna etal. 2017 , for the AMXP IGRJ00291+5934) and they did not show any peculiar difference between the two detectors. Therefore, a possible explanation may be a significant source state variation occurred in the 3d gap between the two observations. A detailed study of this phenomenon is beyond the scope of this work, however, further investigations on the subject will be reported in a follow-up paper focusing on the spectral properties of SAXJ1808.43658 during its 2015 outburst (Di Salvo etal., in preparation). The peculiar trend showed by the fundamental component is consistent with that observed by the Rossi X-ray Timing Explorer during the 1998 outburst while it significantly differs from that of the 2002 (see e.g. Cui, Morgan Titarchuk 1998 ; Falanga Titarchuk 2007 ; Hartman, Watts Chakrabarty 2009a ). A similar behaviour has been observed for the other AMXPs such as IGRJ00291+5934 (Falanga etal. 2005 ; Sanna etal. 2017 ), IGRJ175113057 (Papitto etal. 2010 ) and XTEJ1751305 (Falanga Titarchuk 2007 ), although for the latter a good coverage of the trend below 4keV is lacking. On the other hand, the constant energy dependence of the fractional amplitude inferred from the second harmonic component seems to remain unvaried over the outbursts (see e.g. Cui etal. 1998 ; Hartman etal. 2009a ). The