Low bounds for pulsar γ-ray radiation altitudes

Abstract

The observational determination of radiation locations can constrain pulsar radiation models. The γ -B process in a strong magnetic field is one of the fundamental physical processes contributing to pulsar radiation mechanisms. Photons generated near a pulsar surface with sufficient energy will be absorbed in the magnetosphere. Considering aberrational, rotational and general relativistic effects, we calculate the γ -B optical depth for γ -ray photons, and we use the derived optical depth to determine the lower bounds of the radiation altitude for photons with given energies. As a case study, we obtain the low bounds of radiation altitude for the Crab pulsar for photons with energies of 5 GeV-1 TeV.

Revealing the Most Energetic Light from Pulsars and Their Nebulae

“…the second Fermi-lat Pulsar Catalog (2pc), settled the long-standing debate on the origin of the gamma rays in the inner or outer parts of the pulsar magnetosphere. The strong magnetic field above the neutron star's polar caps prevents the escape of photons with an energy above ε max due to magnetic pair creation and photon splitting (Baring, 2004;Lee et al, 2010). Close to the stellar surface such processes thus yield steep, super-exponential⁴ cut-offs in the gamma-ray spectra above a few GeV, which have not been observed so far.…”

The annular gap model for γ-ray emission from young and millisecond pulsars

“…The polar angle and azimuthal angle in the laboratory polar coordinate are denoted as , φ, while the polar angle and azimuthal angle in the magnetic polar coordinate as θ, ψ. Similar to Lee et al (2010), we use bold italic type to label the vectors; while Figure 1. The coordinate systems for an oblique rotator.…”

“…Then we calculate the emissivities projected on to the sky I(θ j , ψ j ) and direction n B (θ j , ψ j ) of the emission spot (θ j , ψ j ) on each open field line of each ring in the magnetic frame. We also take the aberration effect into account, and use the Lorentz transformation matrix to transform the emission direction n B (θ j , ψ j ) to the direction n ν (φ j , ζ j ) in the lab frame (observer frame), where φ j = arctan(n ν,y /n ν,x ) is the emission spot's rotation phase with respect to the pulsar rotation axis, and ζ j = arccos(n ν,z / n ν,x 2 + n ν,y 2 + n ν,z 2 ) is the viewing angle for a distant, non-rotating observer (see details for aberration effect in Lee et al 2010). We also add the phase shift δφ ret = −r n cos(θ μ,j − θ j ), the first order of equation (33) in Gangadhara (2005), caused by the retardation effect to φ j , where r n = r/R LC is the emission radius in units of the light cylinder radius and θ μ,j is the half opening angle of the emission beam at the emission spot (θ j , ψ j ).…”

“…An important result is that the γ -ray emission with higher photon energy comes from higher altitudes in the magnetosphere. This is probably caused by strong γ -B absorption effect for emission from lower altitudes (Lee et al 2010). In addition, the parameters of α and ζ in our model are based on the adopted value (Wang 2003;Harding et al 2008) and the results of X-ray torus simulation (Ng & Romani 2008).…”

“…a nearly aligned rotator. The γ -ray emission region is so close to the neutron star surface that high-energy γ -ray photons could be absorbed in the strong magnetic field (Lee et al 2010). The polar cap model was combined with the slot gap model recently to explain the pulsar γ -ray radiation (Muslimov & Harding 2003, 2004.…”