Through a simple model of particle acceleration and pair creation above the polar caps of rotationpowered pulsars, we calculate the height of the pair formation front (PFF) and the dominant photon emission mechanism for the pulsars in the Princeton catalog. We Ðnd that for most low-and moderateÐeld pulsars, the height of the PFF and the Ðnal Lorentz factor of the primary beam is set by nonresonant inverse Compton scattering (NRICS), in the Klein-Nishina limit. NRICS is capable of creating pairs over a wide range of pulsar parameters without invoking a magnetic Ðeld more complicated than a centered dipole, although we still require a reduced radius of curvature for most millisecond pulsars. For short-period pulsars, the dominant process is curvature radiation, while for extremely high Ðeld pulsars, it is resonant inverse Compton scattering (RICS). The dividing point between NRICS dominance and curvature dominance is very temperature dependent ; large numbers of pulsars dominated by NRICS at a stellar temperature of 106 K are dominated by curvature at 105 K. Our principle result is a new determination of the theoretical pulsar death line. Proper inclusion of ICS allows us to reach the conclusion that all known radio pulsars are consistent with pair creation above their polar caps, assuming steady acceleration of a space chargeÈlimited particle beam. We identify a new region of the diagram where P-P0 slow pulsars with narrow radiation beams should be found in sufficiently large surveys. We also show that the injection rate of electrons and positrons into the Crab Nebula inferred from the polar cap pair creation model at the present epoch (1039 electrons and positrons s~1) suffices to explain the nebular X-ray and c-ray emission, the best empirical measure of the instantaneous particle-loss rate from any pulsar, but that the contemporary injection rate is about a factor of 5 below the rate averaged over the nebulaÏs history required to explain the nebular radio emission (assuming that the nebular radio source is homogeneous). It is not clear whether this discrepancy can be resolved by evolutionary e †ects and by better treatment of nebular inhomogeneity or is an indication of another particle source in the pulsarÏs magnetosphere.
We discuss the creation of electron-positron cascades in the context of pulsar polar cap acceleration models and derive several useful analytic and semianalytic results for the spatial extent and energy response of the cascade. Instead of Monte Carlo simulations, we use an integrodi †erential equation that describes the development of the cascade energy spectrum in one space dimension quite well, when it is compared to existing Monte Carlo models. We reduce this full equation to a single integral equation, from which we can derive useful results, such as the energy loss between successive generations of photons and the spectral index of the response. We Ðnd that a simple analytic formula represents the pair cascade multiplicity quite well, provided that the magnetic Ðeld is below 1012 G and that an only slightly more complex formula matches the numerically calculated cascade at all other Ðeld strengths. Using these results, we Ðnd that cascades triggered by c-rays emitted through inverse Compton scattering of thermal photons from the neutron starÏs surface, both resonant and nonresonant, are important for the dynamics of the polar cap region in many pulsars. In these objects, the expected multiplicity of pairs generated by a single input particle is lower than previously found in cascades initiated by curvature emission, frequently being on the order of 10 rather than D1000 as usually quoted. Such pulsars also are expected to be less luminous in polar cap c-rays than when curvature emission triggers the cascade, a topic that will be the subject of a subsequent paper.
We re-examine the characteristic polarization angle sweep of rotation-powered pulsars and calculate the expected deviations from this sweep caused by aberrational effects and by polar-cap current flow. We find that in addition to the previously known phase shift of the entire sweep by ∆Φ = −4r/R L , aberration shifts the polarization angle itself by ∆Ψ = −(10/3)(r/R L ) cos α. Similarly, current flow above the polar cap shifts the polarization sweep by ∆Ψ = (10/3)(r/R L )(J/J GJ ) cos α, potentially providing a method of directly measuring the magnitude of the current. The competition between these two effects produces a potentially observable signature in the polarization angle sweep. Although these effects may appear similar to orthogonal mode shifts, they are an independent phenomenon with distinct observational characteristics.
Using a simplified model of cascade pair creation over pulsar polar caps presented in two previous papers, we investigate the expected gamma-ray output from pulsars' low altitude particle acceleration and pair creation regions. We divide pulsars into several categories, based on which mechanism truncates the particle acceleration off the polar cap, and give estimates for the expected luminosity of each category.We find that inverse Compton scattering above the pulsar polar cap provides the primary gamma rays which initiate the pair cascades in most pulsars. This reduces the expected γ-ray luminosity below previous estimates which assumed curvature gamma ray emission was the dominant initiator of pair creation in all pulsars. Even for the brightest pulsars where curvature radiation sets the height of the pair formation front (PFF), we find predicted luminosities too low to explain the EGRET pulsars, suggesting that the source of that emission is an outer magnetosphere accelerator. The predicted polar cap luminosities are large enough, however, to be observable by upcoming γ-ray instruments, which provides a firm test for this theory.
A b s t r a c t . Upon re-examining the characteristic polarization angle sweep of rotation-powered pulsars, we find that the sweep is perceptibly shifted by aberrational effects and by polar-cap current flow. In addition to the previously known phase shift of the entire sweep by A<1? = -ir/RL, aberration shifts the polarization angle itself by A*I/ = -( 1 0 / 3 ) ( r / i ? i ) cos a. Similarly, current flow above the polar cap shifts the polarization sweep by A*? = (10/3)(r/i2z,)(J/ JGJ) COS a, potentially providing a method of directly measuring the magnitude of the current. The competition between these two effects produces a potentially observable signature in the polarization angle sweep. I n t r o d u c t i o nMost pulsars emit radiation containing a significant linearly polarized component. Over the course of a pulse, the observed polarization angle of this component changes, forming the characteristic Radhakrishnan and Cooke S-curve (Radhakrishnan & Cooke 1969). The theoretical understanding of this curve depends on three assumptions about the pulsar emission mechanism. First, radiation is beamed along the magnetic field. Second, the polarization of the emission is along (or at a fixed angle to) the radius of curvature of the magnetic field. Third, the magnetic field is a dipole. In this work, we relax the first and third assumptions in an attempt to bring the phenomenological model closer to a real physical model.The effects we consider tend to scale as r/Ri, where r is the height above the polar cap and Ri is the light cylinder radius, the radius at which an object rotating along with the pulsar would be moving at the speed of light. Since the amplitude is inversely proportional to Ri, we expect these effects to be strongest for millisecond pulsars (MSPs), since they have the smallest values of Ri. P e r t u r b a t i o n sWe considered two main perturbations: aberrational effects and the effects of polar-cap current flow. Both effects perturb the paths of the emitting particles, 253terms of use, available at https://www.cambridge.org/core/terms. https://doi
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