On the role of the current loss in radio pulsar evolution

The aim of this article is to draw attention to the importance of the electric current loss in the energy output of radio pulsars. We remind that even the losses attributed to the magneto-dipole radiation of a pulsar in vacuum can be written as a result of an Ampere force action of the electric currens flowing over the neutron star surface [1], [2]. It is this force that is responsible for the transfer of angular momentum of a neutron star to an outgoing magneto-dipole wave. If a pulsar is surrounded by plasma, and there is no longitudinal current in its magnetosphere, there is no energy loss [2], [3]. It is the longitudinal current closing within the pulsar polar cap that exerts the retardation torque acting on the neutron star. This torque can be determined if the structure of longitudinal current is known. Here we remind of the solution by Beskin, Gurevitch & Istomin (1993) and discuss the validity of such an assumption. The behavior of the recently observed " part-time job " pulsar B1931+24 can be naturally explained within the model of current loss while the magneto-dipole model faces difficulties. 1 Magneto-dipole loss The first idea to explain the energy loss of radio pulsars was to consider the magneto-dipole radiation [4]. Indeed, the magneto-dipole formula gives for the radiation power W md = 1 6 B 2 0 Ω 4 R 6 c 3 sin 2 χ, (1) where χ is the angle between rotational and magnetic axis, R is a neutron star radius ∼ 10 km, and Ω is a pul-sar angular velocity. This formula explains pulsar activity and observed energy loss for expected large magnetic field near the surface B 0 ∼ 10 12 Gs. Let us recall that the physical reason of such energy loss is the action of the torque exerted on the pulsar by the Ampere force of the electric currens flowing over the neutron star surface [5]. The electric and magnetic fields in the outgoing magneto-dipole wave in vacuum can be found by solving the wave equations ∇ 2 B + Ω 2 /c 2 B = 0 and ∇ 2 E + Ω 2 /c 2 E = 0 with the boundary conditions stated as the fields corresponding components E t and B n being continuous through the neutron star surface. Inside the star one can consider magnetic field as homogeneous, and find …