Two‐Pole Caustic Model for High‐Energy Light Curves of Pulsars

Abstract

We present a new model of high-energy light curves from rotation-powered pulsars. The key ingredient of the model is the gap region (i.e., the region where particle acceleration is taking place and high-energy photons originate) that satisfies the following assumptions: (1) the gap region extends from each polar cap to the light cylinder; (2) the gap is thin and confined to the surface of last open magnetic-field lines; (3) photon emissivity is uniform within the gap region. The model light curves are dominated by strong peaks (either double or single) of caustic origin. Unlike other pulsar models with caustic effects, the double peaks arise from a crossing two caustics, each of which is associated with a different magnetic pole. The generic features of the light curves are consistent with the observed characteristics of pulsar light curves: (1) the most natural (in terms of probability) shape consists of two peaks (separated by 0.4 to 0.5 in phase for large viewing angles); (2) the peaks possess well-developed wings; (3) there is a bridge (interpeak) emission component; (4) there is a nonvanishing off-pulse emission level; (5) the radio pulse occurs before the leading high-energy peak. The model is well suited for four gamma-ray pulsars-Crab, Vela, Geminga, and B1951+32-with double-peak light curves exhibiting the peak separation of 0.4 to 0.5 in phase. Here we apply the model to the Vela pulsar. Moreover, we indicate the limitation of the model in accurate reproducing of the light curves with single pulses and narrowly separated (about 0.2 in phase) pulse peaks. We also discuss the optical polarization properties for the Crab pulsar in the context of the two-pole caustic model.

Relativistic Effects and Polarization in Three High‐Energy Pulsar Models

“…The value of P is especially low (P ∼ 2 %) within the phase intervals trailing both peaks. Dyks & Rudak (2003) suggested that the minima in polarization percentage P could naturally result from the caustic nature of the peaks: superposition of emission from different altitudes (ie. with different position angles), which produces the peaks, could ensure both the decrease in P and the fast swings of ψ.…”

“…In Fig. 4 of Dyks & Rudak (2003) we chose α = 70 • and ζ obs = 61 • to reproduce the observed peak separation of ∼ 0.43 while keeping the difference α − ζ obs smaller than ∼ 10 • to ensure the close approach to the narrow radio beam centered at the dipole axis. Given the relatively weak sensitivity of the peak locations to α and ζ obs (eg.…”

Order parameters for the high-energy spectra of pulsars

“…The model also explains the flattening of the X-ray spectra at soft energies as a result of propagating particles being subject to synchrotron losses all along their trajectories. Using this model, we show how observations in gamma-rays can predict the detectability of the pulsar in X-rays, and viceversa.Curvature and synchrotron emission from particles accelerated in magnetospheric gaps or reconnection (see e.g., Cheng et al 1986a,b;Romani 1996;Zhang & Cheng 1997;Hirotani & Shibata 1999;Muslimov & Harding 2003;Dyks & Rudak 2003;Kalapotharakos et al 2012;Philippov & Spitkovsky 2017) has been thought to be behind non-thermal pulsations. However, a simplified, unifying interpretation of pulsar spectra is still lacking.…”

Current Flows in Pulsar Magnetospheres

“…Certainly, extra acceleration due to ρ = ρ GJ exists too. As demonstrated in Fig.3, a very large acceleration may exist near the last open field lines, which could be favorable for the high energy emission in the caustic model (Dyks & Rudak 2003). An outer gap may not be possible if particles can flow out freely either from the surface (for negligible binding energy) or from the pair-formation-front (for enough binding energy) of a charged pulsar.…”