4. Discussion and conclusions
So far we have focused on the evolution of the magnetic inclination of canonical pulsars. It appears that our model cannot explain millisecond pulsars which are generally believed to be spun up by accretion, (so they are called recycled pulsars,) because these millisecond pulsars have typical magnetic field around to gauss, characteristic ages of at least years, and some of theses pulsars possess large inclination angle extending even to . First, we want to point out that it is very misleading to use the spin-down age () to estimate the age of weak field millisecond pulsars, the actual age of those pulsars should be younger than the spin-down age. Second, it has been suggested that the accretion can reduce the surface magnetic field of pulsars(Shibazaki et al 1989; Zhang et al 1994; Zhang 1998; Van den Heuvel & Bitzaraki 1995; Taam & Van den Heuvel 1986). In this case, most of the stellar magnetic field may be just buried inside the crust. In other words, the crustal field B could be larger than the original field by one or two order of magnitudes because it has been squeezed into a smaller volume resulting in a surface field of only gauss. Thirdly, the mass of the star is very likely larger than 1.4 solar masses due to accretion which reduces (Cheng & Dai 1997). Therefore, we can expand the logarithmic term in Eq. (18) and obtain
We can see that the initial angular velocity plays a very important role in determining if the inclination will decay. Table 4 lists those millisecond pulsars with known inclination angle. It is interesting to point out that even if the crustal magnetic field is actually gauss, our model cannot explain the inclination angles of PSR1953+29 and PSR1937+214 unless their ages are less than years. Perhaps the magnetic field of these two pulsars orginates from quantized flux tubes in the superconducting core and the interaction between the flux and the superfluid vortex lines can force the magnetic fluxoids to always be perpendicular to the rotation axis (Ruderman 1991).
Table 4. Recycled pulsar parameters
Finally, we conclude that our model predictions can explain the evolution of the magnetic inclination of most pulsars including those accretion spun up pulsars, but can only explain those pulsars with periods less than a few millisecond if their ages are actually less than years old.
© European Southern Observatory (ESO) 1998
Online publication: March 23, 1998