We have investigated the pulse shape evolution of the Crab pulsar emission in the hard X-ray domain of the electromagnetic spectrum .
In particular , we have studied the alignment of the Crab pulsar phase profiles measured in the hard X - rays and in other wavebands .
To obtain the hard X - ray pulse profiles , we have used six year ( 2003 - 2009 , with a total exposure of about 4 Ms ) of publicly available data of the SPI telescope on-board of the INTEGRAL observatory , folded with the pulsar time solution derived from the Jodrell Bank Crab Pulsar Monthly Ephemeris ( http : //www.jb.man.ac.uk ) .
We found that the main pulse in the hard X - ray 20 - 100 keV energy band is leading the radio one by 8.18 \pm 0.46 milliperiods in phase , or 275 \pm 15 ~ { } \mu s in time .
Quoted errors represent only statistical uncertainties .
Our systematic error is estimated to be \sim 40 \mu s and is mainly caused by the radio measurement uncertainties .
In hard X - rays , the average distance between the main pulse and interpulse on the phase plane is 0.3989 \pm 0.0009 .
To compare our findings in hard X - rays with the soft 2 - 20 keV X-ray band , we have used data of quasi-simultaneous Crab observations with the PCA monitor on-board the Rossi X-Ray Timing Explorer ( RXTE ) mission .
The time lag and the pulses separation values measured in the 3 - 20 keV band are 0.00933 \pm 0.00016 ( corresponding to 310 \pm 6 ~ { } \mu s ) and 0.40016 \pm 0.00028 parts of the cycle , respectively .
While the pulse separation values measured in soft X - rays and hard X - rays agree , the time lags are statistically different .
Additional analysis show that the delay between the radio and X-ray signals varies with energy in the 2 - 300 keV energy range .
We explain such a behaviour as due to the superposition of two independent components responsible for the Crab pulsed emission in this energy band .