Physics of accretion in the millisecond pulsar XTE J1751-305

We have undertaken an extensive study of X-ray data from the accreting millisecond pulsar XTE J1751 - 305 observed by RXTE and XMM-Newton during its 2002 outburst. In all aspects this source is similar to the prototypical millisecond pulsar SAX J1808.4 - 3658, except for the higher peak luminosity of 13 per cent of Eddington, and the optical depth of the hard X-ray source, which is larger by a factor similar to 2. Its broad-band X-ray spectrum can be modelled by three components. We interpret the two soft components as thermal emission from a colder (kT similar to 0.6 keV) accretion disc and a hotter (similar to 1 keV) spot on the neutron star surface. We interpret the hard component as thermal Comptonization in plasma of temperature similar to 40 keV and optical depth similar to 1.5 in a slab geometry. The plasma is heated by the accretion shock as the material collimated by the magnetic field impacts on to the surface. The seed photons for Comptonization are provided by the hotspot, not by the disc. The Compton reflection is weak and the disc is probably truncated into an optically thin flow above the magnetospheric radius. Rotation of the emission region with the star creates an almost sinusoidal Pulse profile with an rms amplitude of 3.3 per cent. The energy-dependent soft phase lags can be modelled by two pulsating components shifted in phase, which is naturally explained by a different character of emission of the optically thick spot and optically thin shock combined with the action of the Doppler boosting. The observed variability amplitude constrains the hotspot to lie within 3 degrees-4 degrees of the rotational pole. We estimate the inner radius of the optically thick accreting disc to be about 40 km. In that case, the absence of emission from the antipodal spot, which can be blocked by the accretion disc, gives the inclination of the system as greater than or similar to 70 degrees.