Energy budget of the bifurcated component in the radio pulsar profile of PSR J1012+5307

Abstract

The bifurcated emission component (BEC) in the radio profile of the millisecond pulsar J1012+5307 can be interpreted as the signature of the curvature radiation beam polarised orthogonally to the plane of electron trajectory. Since the beam is intrinsically narrow (~1 deg), the associated emission region must be small for the observed BEC to avoid smearing out by spatial convolution. We estimate whether the energy available in the stream is sufficient to produce such a bright feature in the averaged profile. The energy considerations become complicated by the angular constraints imposed by the width of the microbeam, and by the specific spectrum of the BEC which is found to have the spectral index xi ~ -0.9 in comparison to the index of xi ~ -2 for the total profile. For typical parameters, the luminosity of the BEC is determined to be 4 10^{25} erg/s, whereas the maximum-possible beam-size-limited power of the stream is L_max ~ 2 10^{29} erg/s. This implies the minimum energy-conversion efficiency of eta ~ 2 10^{-4}. The BEC's luminosity does not exceed any absolute limits of energetics, in particular, it is smaller than the power of primary electron and/or secondary plasma stream. However, the implied efficiency of energy transfer into the radio band is extreme if the coherently emitting charge-separated plasma density is limited to the Goldreich-Julian value. This suggests that the bifurcated shape of the BEC has macroscopic origin, however, several uncertainties (eg. the dipole inclination and spectral shape) make this conclusion not firm.