3 Discussion

One of the main astrophysical reasons for the investigation of the spindown of neutron stars is the existence of X-ray sources which display pulses with long periods (in excess of 100s). On the basis of their calculations Davies & Pringle suggested that the periods of neutron stars spinning down due to propeller mechanism can be as long as 100s only if the stars are situated in the weak stellar wind, i.e. $\dot{M}_0 < 4 ~ 10^{14}\,{\rm g\,s^{-1}}$. They also pointed out that in this case however it is difficult to account for a substantial population of long period pulsators.

In the light of the recalculated value of the break period obtained in this paper (Eq. (8)) I find that the propeller mechanism can be responsible for the long spin period of a neutron star even if it is situated in the essentially stronger stellar wind:

$$\dot{M}_0 \mathrel{\mathchoice {\vcenter{\offinterlineskip\ha... ... \mu_{30}^{16/15}\ m^{-4/15}\ P_{100}^{-7/5} {\rm g\,s^{-1}},$$ (9)

where P₁₀₀ is the observed spin period of the neutron star expressed in units of 100s. The corresponding spindown time-scale of the neutron star in the state of subsonic propeller is

$$\tau_{\rm d} \simeq 10^5\ \mu_{30}^{-2}\ m\ I_{45}\ P_{100}\ {\rm yr},$$ (10)

i.e. smaller that the characteristic evolutionary time-scale of the early spectral type supergiants. Here I₄₅ is the moment of inertia of the neutron star expressed in units of $10^{45}\,{\rm g\,cm^2}$.