Deviation of the arrival-time delay of pulses for the Crab pulsar from a quadratic frequency region

Abstract

Our measurements of the arrival-time delays of radio pulses from the Crab pulsar, PSR B0531+21, at low frequencies 111, 63, and 44 MHz revealed additional delays compared to the usual quadratic frequency relation, Δt(v) ∝ v−2. These additional delays are 65 ms between 63 MHz and 111 MHz—i.e., a factor of two longer than the pulsar’s period, i.e., a factor of five longer than the pulsar period—and cannot be explained by the “twisting” of the magnetic-field lines by the rotation of the pulsar. We suggest the model in which a previously unknown high-density plasma layer with a high electron concentration is present along the line of sight in the Crab nebula, causing an additional frequency-dependent delay of the observed radio pulses at low frequencies due to the contribution of the ne2v−4 term in the dispersion-delay formula. The parameters of this inferred layer have been derived: emission measure EM ≅ 4 × 106 pc/cm6, electron density ne ≅ 106 cm−3, depth along the line of sight d ≅ 4 × 10−6 pc, and electron temperature Te ≥ 2 × 106 K.