The Net Advance of Physics: Gamma-Ray Pulsar Emission Models, by Alice K. Harding -- Section 3B.
Next: Inverse-Compton induced pair cascades
Up: Polar Cap Models
Previous: Polar Cap Models
The -ray emission from pair cascades induced by curvature radiation
of accelerated particles has been investigated by Daugherty & Harding
(1982, 1994, 1996) and Chiang & Romani (1992), assuming a space-charge
limited electron acceleration model (e.g. Arons 1983) is operating.
DH96 found that if the primary electron acceleration is assumed to occur
over several stellar radii, then the cascade -ray emission
shows agreement with several key features of the observed emission, including
the double-peaked light curves with bridge emission (as discussed above) as
well as phase-averaged and phase-resolved spectra. In particular, the
CRPC models predict high-energy spectral cutoffs, due to magnetic pair
production,
at several GeV. The pair production attenuation cutoffs are much sharper
than exponential cutoffs due to a cutoff in the particle distribution, and
can fit the very steep cutoffs in observed -ray pulsar spectra.
Some correlation of surface magnetic field with pair production or photon
splitting (in the case of PSR1509-58, see Harding & Baring 1996) cutoff
energy is predicted, with higher B producing lower cutoff energies.
The CRPC models can account for the systematic soft-hard-soft hardness
variation of the pulse profile of Vela (Kanbach et al. 1994).
The hardest emission is predicted
to occur near the pole, where the emission is pure curvature radiation
that is not softened by cascading. Near the polar cap rim, where the peak
emission originates, the cascades are most extended, producing a softer
spectrum with a lower cutoff energy. The emission outside the rim, and
outside the peaks in the pulse profile, comes from high-altitude curvature
radiation from primary particles that have lost most of their energy and
has the lowest cutoff, but not as sharp as that of the peak spectra.
Very importantly, the CRPC/SPC model predicts pulsed emission at all phases,
as has been observed (Fierro et al. 1996).
The observed increase in hardness of the phase-averaged spectrum with age
can also be understood in the CRPC model. The hardness of a CRPC cascade
spectrum primarily depends on the number of photon generations in the cascade.
As noted by Lu et al. (1994), there is a rough correlation between the
spectral indices of the observed -ray pulsars and a theoretical
estimate of the number of polar cap cascade generations. The primary
curvature radiation spectrum has a photon index of 5/3 if the particles have
significant energy loss and 2/3 if they do not. Significant energy loss of
the primary particles will occur for short period ( )
pulsars,
where the polar cap half-angle, , is larger and
thus the field line radius of curvature at the polar cap rim, is smaller.
The input curvature spectrum is then softened on each generation of pair
production and synchrotron emission. The spectral index of the escaping
-ray spectrum will be (Harding & Daugherty 1996)
where the number of cascade generations, , is allowed to be a
non-integer and is the spectral index of the primary curvature
spectrum. The number of generations will generally increase with
decreasing pulsar period and increasing surface magnetic field strength
,
because the mean free path for pair production will decrease. The
generation number will also decrease with the height above the surface at
which the bulk of the cascade occurs. Figure 3 shows the predicted
dependence of spectral index with the parameter for different
radii r of the cascade. Since the pulsar characteristic age , a correlation of spectral index with age is predicted. Figure 3
also shows a comparison of predicted and observed for the
observed -ray pulsars. Several pulsars
with ages larger than yr and low magnetic fields, PSR1929+10 and
PSR0950+08, that should
be detectable by EGRET based on their predicted fluxes, have extremely
low predicted spectral indices, indicating that the bulk of their -ray
emission could lie above the EGRET range.
Curvature radiation induced pair cascades
Figure 3: Predicted -ray spectral index vs. .
Next: Inverse-Compton induced pair cascades
Up: Polar Cap Models
Previous: Polar Cap Models
BIBLIOGRAPHY