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The Fermi Large Area Telescope (LAT) discovered the time signature of a radio-silent pulsar coincident with RX J0007.0+7302, a plerion-like X-ray source at the centre of the CTA 1 supernova remnant. The inferred timing parameters of the gamma-ray pul sar PSR J0007+7303 (P=315.8 ms; dot{P}sim3.6 10^{-13} s s^{-1}) point to a Vela-like neutron star, with an age comparable to that of CTA 1. The PSR J0007+7303 low distance (sim 1.4 kpc), interstellar absorption (A_Vsim 1.6), and relatively high energy loss rate (dot{E} sim4.5 10^{35} erg s^{-1}), make it a suitable candidate for an optical follow-up. Here, we present deep optical observations of PSR J0007+7303. The pulsar is not detected in the Gran Telescopio Canarias (GTC) images down to a limit of rsim 27.6 (3 sigma), the deepest ever obtained for this pulsar, while William Herschel Telescope (WHT) images yield a limit of V sim 26.9. Our r-band limit corresponds to an optical emission efficiency eta_{opt}= L_{opt}/dot{E} < 9.4 10^{-8}. This limit is more constraining than those derived for other Vela-like pulsars, but is still above the measured optical efficiency of the Vela pulsar. We compared the optical upper limits with the extrapolation of the XMM-Newton X-ray spectrum and found that the optical emission is compatible with the extrapolation of the X-ray power-law component, at variance with what is observed, e.g. in the Vela pulsar.
We performed a statistical analysis of half-power pulse-widths of the core components in average pulsar profiles. We confirmed an existence of the lower bound of the distribution of half-power pulse-width versus the pulsar period W50~2.45deg P^(-0.5) found by Rankin (1990). Using our much larger database we found W50= (2.51 +/- 0.08)deg P^(-0.50 +/-0.02) for 21 pulsars with double-pole interpulses for which measurement of the core component width was possible. On the other hand, all single-pole interpulse cases lie in the swarm of pulsars above the boundary line. Using the Monte Carlo simulations based on exact geometrical calculations we found that the Rankins method of estimation of the inclination angle alpha ~ asin(2.45deg P^(-0.5)/W50) in pulsars with core components is quite good an approximation, except for very small angles alpha in almost aligned rotators.
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