The two known gamma ray pulsars, the Crab and Vela, were used as guides for the development of models of high-energy radiation from spinning neutron stars. Two general classes of models were developed: those with the gamma radiation originating in the pulsar magnetosphere far from the neutron star surface (outer gap models) and those with the gamma radiation coming from above the polar cap (polar cap models). The goal is to indicate how EGRET can contribute to understanding gamma-ray pulsars, and especially how it can help distinguish between models for emission

Thompson, David J.

English

NASA Technical Reports Server

N90-23304
GAMMA RAY PULSARS: MODELS AND OBSERVATIONS
DAVID J. THOMPSON
NASA/Goddard Space Flight Center
Greenbelt, MD 20771
ABSTRACT
Data from the EGRET instrument on the Gamma Ray Observatory
will be useful in examining predictions made by models of gamma-ray
pulsars. The high-energy spectra of pulsars and the luminosities of
pulsars other than the Crab and Vela can be used to study and
possibly differentiate such models.
I. INTRODUCTION
The two known gamma-ray pulsars, the Crab and Vela, have been
used as guides for the development of models of high-energy
radiation from spinning neutron stars. Two general classes of
models have been developed: those with the gamma radiation
originating in the pulsar magnetosphere far from the neutron star
surface (outer gap models) and those with the gamma radiation coming
from above the polar cap (polar cap models). The goal of this paper
is to indicate how EGRET can contribute to understanding gamma ray
pulsars, and especially how it can help distinguish between models
for emission.
In the outer gap model (Cheng, Ho, and Ruderman, 1986a, 1986b;
Ruderman, 1990), electron acceleration in a pulsar magnetosphere
takes place in a charge-depleted region well away from the neutron
star surface. Model calculations show that the Crab and Vela
pulsars are different from one another. For a Crab-type gap, the
primary photons are produced by curvature radiation of the
electrons. The primary photons annihilate with X-rays to produce
secondary electrons. These secondary electrons produce X-rays by
synchrotron radiation and also inverse Compton scatter these X-rays
up to gamma ray energies. The radiation in the EGRET energy range
will originate from inverse Compton scattering.
The Vela pulsar for the outer gap model is different in that the
primary photons are inverse Compton scattered infrared photons with
much higher energy than thos_e of the Crab. These photons also
produce electron secondaries, and the gamma rays which are seen are
synchrotron radiation from the secondary electrons.
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In a polar cap model (e.g. Daugherty and Harding, 1982),the
particle acceleration takes place just above the polar cap of the
neutron star. Here the magnetic field is much stronger than in the
outer gap. The accelerated particles form a cascade. Electrons
produce curvature radiation photons, which annihilate. The
secondary electrons produce photons by both curvature and
synchrotron radiation. These photons may also annihilate, until the
cascade reaches th_ point where the photons (gamma rays) _an escape.
The Crab and Vela in this model are similar.
With a reasonable choice of assumptions, either of these models
can reproduce the observations of the Crab and Vela. They are
fundamentally different models, however. The polar cap model sees
gamma ray emission as a general property of young radio pulsars,
with the Crab and Vela working by similar mechanisms (Harding,
1981). The outer gap model, on the other hand, not only views the
Crab and Vela as different from each other, but suggests that gamma-
ray emission is limited to a subset of all pulsars, and that gamma-
ray pulsars do not evolve into older radio pulsars (Ruderman and
Cheng, 1988).
II. ENERGY SPECTRA OF GAMMA RAY PULSARS
One characteristic of EGRET compared to previous high energy
gamma-ray telescopes like SAS-2 and COS-B is its broader energy
range (about 20 MeV to 30,000 MeV) and better energy resolution
(Hughes, et al., 1986). Features not seen previously in the Crab
and Vela energy spectra might be visible to EGRET.
For the outer gap model, the feature in the gamma-ray range is
a break in the spectrum above a few GeV. in the case of Vela, this
results from the maximum energy that the secondary electrons can
have in the outer gap (1013 eV), assuming that the synchrotron
radiation occurs in a field of about 5000 gauss (Cheng, Ho, and
Ruderman, 1986b). The Crab spectrum in the outer gap model shows a
similar fall-off in the few GeV range, in this case resulting from
the combination of the upper limit on the secondary electron
energies and the energies of the X-rays which are being inverse
Compton scattered to the gamma-ray range (Ho, 1989).
The polar cap model also shows a fall-off in the few GeV range
for both the Crab and Vela pulsars (Harding, 1981, Daugherty and
Harding, 1982). This turnover in the cascade model results from two
factors: I. the curvature radiation gamma-ray spectrum has a
maximum for a given set of conditions; and 2. the higher energy
gamma rays are more likely to convert to pairs in the magnetic
field, because they can convert farther out where the field is
lower. Both these effects serve to suppress the high energy gamma
rays.
116
These two models predict such similar high-energy _pectral
shapes that EGRET cannot expect to distinguish them. Nevertheless,
EGRET can address the question of whether there is such a turnover
in the spectrum. Figure 1 shows the COS-B data for the Crab
spectrum (Lichti, et al., 1980), along with a model calculation
(Harding, 1981) and a power law fit to the COS-B data. Although the
final analysis of the EGRET response above a few GeV is not
complete, the estimated sensitivity (Hughes, et al., 1980; Thompson,
1986) can be used to calculated the relative response to the
different spectra. For a two week exposure, a continuing power law
spectrum would yield about 30 photons above 5 GeV detected by EGRET.
Under similar conditions, a spectrum with a break near 2 GeV would
produce fewer than i0 photons above 5 GeV. Although the numbers are
small, the difference is significant, because at these energies the
angular resolution of EGRET allows the source to be separated
clearly from any galactic or extragalactic diffuse gamma radiation.
A similar change of spectral shape would be even more significant
for Vela, because it is a factor of 3 more intense than the Crab.
If the spectrum extends in a near power law beyond i0 GeV, however,
a higher energy cutoff would probably not be visible to EGRET.
10 4
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Figure 1 -- High-energy
spectrum of the Crab pulsar.
Data points from COS-B:
Lichti, et al. (1980).
Solid curve: model of
Harding (1981).
Dashed curve: E -2-I fit to
data.
O_?IGINAL PAGE IS
OF POOR QUALITY
Ey (GeV)
117
III. MODEL PREDICTIONS FOR OTHER PULSARS
Another approach to distinguishing models is to look at the
model predictions for other pulsars. It is, of course, possible
that the Crab and Vela are so different from other pulsars that they
are the only gamma-ray pulsars, but there are enough other
candidates around that that seems unlikely. Ruderman and Cheng
(1988) suggested, for example, that some of the other COS-B sources
might be undiscovered pulsars• The concept used in the present work
is to start from the radio pulsar direction, looking for
characteristics which might indicate gamma ray emission from some
sources which are already known to be pulsars•
The solid line in Figure 2 (based on the work of Ruderman and
Cheng 1988) shows the estimated gamma ray luminosity for short-
period pulsars with characteristics like those of the Crab and Vela.
This figure has been normalized to the Crab and Vela observations,
assuming radiation into approximately one steradian. Pulsars with
periods shorter than about 50 msec are Crab-like, while those with
longer periods are similar to Vela. In the outer gap model, the
luminosity function cuts off at about 125 msec for Vela-like
pulsars. This occurs when the outer gap essentially fills the
magnetosphere and is quenched. Pulsars with longer periods are
expected to have no gamma-ray emission.
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118
Following Cheng, Ho, and Ruderman (1986b), the luminosity for
other pulsars should be proportional,'at least in first
approximation, to B/P 2 where P is the pulsar period and B is the
calculated magnetic field at the surface. This comes from the fact
that the potential drop in the outer gap and the particle flow are
both proportional to this quantity. For pulsars with a given
period, this implies that the luminosity should be proportional to
the surface magnetic field, calculated from the standard formula
B = ( 1030 I P P / a 6 )1/2 gauss (1)
where P is the pulsar period, P the period derivative, and a
the pulsar radius, generally assumed to be 1 * 106 cm. Parameters
for the other pulsars shown on this figure are drawn from a recent
update (Taylor, 1988) of the Manchester and Taylor (1981)
compilation.
Two pulsars in this figure are shown with periods just beyond
the 125 msec cutoff• These are pulsars with calculated fields
greater than those of the Crab and Vela. Such pulsars should be
able to sustain an outer gap out to longer periods, and should fall
somewhere on the rising part of the curve. Clearly, estimates for
these two pulsars are very uncertain, but they are potentially
luminous gamma-ray pulsars.
The polar cap model is in some sense easier, because it is
based on the idea that pulsars follow a common evolutionary path.
This means that the Crab and Vela parameters can be used to
extrapolate to other pulsars in the context of the model. Harding's
(1981) fit to the observations gave
L (>i00) = 1.2 * 1035 BI20.95 p-l.7 photons s -I (2)
where BI2 is the pulsar field in units of 1012 gauss.
is also based on an assumption of radiation into about one
steradian•
This fit
In the polar cap model, there is no explicit mechanism which
limits the gamma-ray emission (as the quenching of the outer gap
does), but the ultimate limiting factor is still the same: the
power source for the pulsar is its_rotational energy loss, and no
process can expect to extract all that energy in the form of gamma
rays. In applying this formula, it is important to look at what
fraction of the total energy loss it represents, and realize that
too large a fraction is not physically meaningful.
Table 1 shows the results of both model calculations for some
of the most interesting pulsars, including the Crab and Vela for
reference. Luminosities have been converted to flux values, using
the estimated pulsar distances and the same 1 steradian emission
solid angle assumed in the model calculations.
119
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120
The pulsars in addition to the Crab and Vela fall into three
groups:
The first six are ones for which both models predict gamma-ray
emission at about the same level, within a factor of three. These
are the ones most like the Crab and Vela and should tell if the Crab
and Vela are really different from other radio pulsars in some
feature relevant to gamma-ray emission.
The second two are those near the limit of the outer gap model.
If this model is correct, then they may be on the upward part of the
curve and be strong sources, or they may be over the edge and non-
sources. The question marks indicate the high degree of uncertainty
in these estimates.
The third group contains pulsars with periods and fields which
should not be able to sustain an outer gap, but which might be gamma
ray sources in the polar cap model. This group in particular could
be much larger if equation (2) extrapolates to pulsars with longer
periods. The pulsars shown are some which are relatively fast
(periods shorter than 200 msec), relatively nearby (distances less
than 2 kiloparsecs), and energetically reasonable (less than 10% of
their rotational energy loss appears in the form of gamma rays).
IV. OBSERVATIONAL CONSIDERATIONS
The next question is: Which of these might EGRET see? Based
on simple counting statistics, the estimated EGRET sensitivity, and
the known diffuse galactic and extragalactic radiation, here are
some guidelines:
i. EGRET should be able to see an pulsar with a flux above
i00 MeV of a few * 10 -7 photons cm -2 s-{ in a single good two week
exposure. This is an intensity about 0.i of the Crab pulsar.
Figure 3 is a simulation of a phase plot of a pulsar with this flux
(and a Crab-like double peak structure) seen in the galactic center
region.
2. In a two week exposure, EGRET will have trouble detecting
pulsars at the 1 * 10 -7 photons cm -2 s -I level in the galactic
center region, due to the high intensity galactic radiation, but
should be able to see pulsars with this intensity in regions away
from the center. Away from the high intensity portion of the
galactic ridge, the galactic radiation is a factor of five or more
less intense.
3. Even under the best of circumstances, EGRET will be
unlikely to detect pulsars with a flux less than 10 -8 photons cm -2
s-l.
121
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Figure 3 - Simulated phase plot of a pulsar with 0.i the Crab
flux and a double-peak emission, in the high-intensity region
near the galactic center. Two week exposure with EGRET, with
the pulsar on-axis.
From these guidelines and Table i, it is clear that these model
predictions span this range -- pulsars 0114+58 and 1951+32 should be
detectable if either model is a good description of the gamma-ray
emission process; 0540-69 (which is in the Large Magellanic Cloud)
and 1830-08 are not likely candidates due primarily to their
distance; and all the rest are in between. If the outer gap model
is an accurate representation of the gamma-ray emission process,
then pulsars 0906-49, 1509-38, and 1800-21 could all be detectable.
In light of the large uncertainty at the limit of the outer gap
model, however, the best discriminator between the models will
probably be the longer period pulsars 0355+54, 0740-28, and 1055-52.
Detection of any of these (which should not be able to support an
outer gap) would suggest particle acceleration and gamma-ray
production in some other region of the magnetosphere, such as the
polar cap model predicts.
In summary, EGRET should be able to contribute to an improved
understanding of gamma ray pulsars. It should be able to look for
the predicted turnover in the high energy spectrum of the more
intense pulsars. More significant is the prospect of being able to
detect additional pulsars which may distinguish models of gamma ray
emission.
122
REFERENCES
Cheng, K.S., Ho, C., and Ruderman, M. 1986a, Ap. J. 300, 500.
Cheng, K.S., Ho, C., and Ruderman, M. 1986b, Ap. J. 300, 522.
Daugherty, J.K., and Harding, A. 1982, Ap. J. 252, 337.
Harding, A.K. 1981, Ap. J. 245, 267.
Ho, C. 1989, Proc. Gamma Ray Observatory Science Workshop, ed. W. N.
Johnson, p. 4-174.
Hughes, E.B., et al. 1986, IEEE Trans. Nucl. Sci. NS-33, 728.
Hughes, E.B., et al. 1980, IEEE Trans. Nucl. Sci. NS-27, 364.
Lichti, G.G., et al. 1980, Non-Solar Gamma Rays (COSPAR), ed. R.
Cowsik and R.D. Wills (New York, Pergamon), p. 49.
Manchester, R.N., and Taylor, J.H. 1981, Astron. J. 86, 1953.
Ruderman, M. 1990, these proceedings.
Ruderman, M. and Cheng, K.S. 1988, Ap. J. 335, 306.
Taylor, J.H. 1988, private communication.
Thompson, D.J. 1986, Nuc. Inst. and Meth. A251, 390.
DISCUSSION
Alice Harding:
The polar cap model predicts a sharp cutoff in the gamma-ray spectrum above a few GeV,
which is due to pair production in the strong magnetic field. Thus, the break in the
spectrum would have a different shape from that predicted by the outer gap model.
R.J. Slobodrian:
I am glad that ions have been mentioned. A recent review article on double layers has
suggested that they are relevant as astrophysical accelerators to 1014 - 1015 eV -- for
example, in pulsars (young), where both ions and electrons are available. I would like to
know the opinion of experts on the possible relevance of such double layers in young
pulsars (only thus far proven gamma-ray emitters).
123
Mal Ruderman:
Wherever the magnetic field is very strong, e.g. near the surface of a magnetized neutron
star, there is copious pair production if the potential drop (along B) exceeds 10 lz volts.
This would be expected to keep such accelerator potentials there well below the 1014 - 10 _5
volt range. Far away, e.g. in the outer magnetosphere, an accelerator "gap" is a kind of
double layer in this range.
Chip Meegan:
In the gap model, what distinguishes the gamma ray pulsars, which turn off, from pulsars
that evolve into longer-period radio pulsars?
Mal Ruderrnan:
A growing charge depletion region in the outer magnetosphere may be limited by e-*
production there as proposed for the Crab and Vela pulsars, but also by transport into
that region of e-* made elsewhere. These may be separated far from the star by electric
fields much weaker than those needed to make them in the outer magnetosphere. It is
very much easier to make pairs in the very large B above a part of the polarcap than in
an accelerator near the light cylinder. Possible transport of such pairs to where they are
needed in the outer magnetosphere depends upon the magnetic field structure around the
neutron star; it would not generally occur for a pure dipole but may for somewhat more
complicated fields. Another possibility is a switching to real pair production from quasi-
pair production from ion stripping above the polarcap as a neutron star cools with age.
124


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