A model is proposed for the Vela pulsar in which the radio emission originates near the surface of the neutron star while the pulsed gamma ray emission is produced by synchrotron radiation near the speed of light cylinder. This model can explain the energy flux, double pulse structure, and phase shift with respect to the radio of the gamma ray emission and offers approximate quantitative predictions for other X-ray and gamma-ray fluxes

Thompson, D. J.

English

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MEN T.: X-
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eREPR1NT
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INTERPRETATION OF THE PULSED
GAMMA RAY EMISSION FROM VELA
(NASA - TM - n- 7C935)	 INTE	 -k IATION OF 7NE	 N75-28y97
FUISEC CAM.?A FAY EMISSIC.a FBCC VELA (NASA)
11 F hC $3.25
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D. J. THOMPSON
JUNE 1975
GODDARD SPACE FLIGHT CENTER
GREENBELT, MARYLAND
JINTERPRETATION OF THE PULSED GAMMA RAY EMISSION FROM VELA
D. J. Thompson
NASA/Goddard Space Flight Center
Greenbelt, Maryland
ABSTRACT
A model is proposed for the Vela pulsar in which the radio emission
originates near the surface of the neutron star while the pulsed y-ray
emission (Thompson et al., 1975) is produced by synchrotron radiation
near the speed of light cylinder. This model can explain the energy
flux, double pulse structure, and phase shift with respect to the radio
of the y-ray emission and offers approximate quantitative predictions
for other X- and y-ray fluxes.
I. INTRODUCTION
Recent results from the SAS-2 high energy (> 35 MeV) y-ray experi-
ment have shown a strong emission from the direction of the Vela supernova
remnant, a large fraction of which is pulsed at the radio period of
PSR 0833-45 (Thompson et a1., 1975). The y-ray emission shows a double
pulse structure, in contrast to the radio pulsar, which has only one
pulse. Based on detailed. comparison with two independent sets of radio
data, the 7 -ray pulses are both out of phase with the radio peak, follow-
ing it by 13 and 48 msee.-
3
I- 2 -
Searches for the Vela pulsar in the optical have given negative
results (Kristian, 1970; Chiu, Lynda, and Maran, 1970; Lasker, Bracker,
and Sea, 1974) although a tentative identification of a non-pulsing star
associated with PSR 0833-45 has been made (Lasker, 1975). Several X-
and y-ray experiments have found small positive pulsed results (Harnden
at al., 1972; Harnden and Gorenstein, 1973; Grindley at al., 1973;
Albats et al., 1974). All of these are of substantially lower statistical
significance than the SAS-2 result, and none show the double pulse structure.
Also, none of these positive results has been confirmed, and unless the
pulsar is strongly time-varying, the X-ray observations appear to be in
conflict or near-conflict with other measurements (Ricker et al., 1973;
Rappaport et al., 1974; Moore et al., 1974). In light of these uncertainties,
this discussion will concentrate on the radio and y-ray observations.
II. THE MODEL
The appearance of two pulses in the 7 -ray energy range and the
phase shift of both of these pulses from the single radio peak suggest
strongly that the radio and y-ray I emissions originate in different
physical regions of the pulsar. The basic feature of the model proposed
here is that the pulsed radio emission is produced near the surface of
the star while the pulsed y-ray flux originates near the speed of light
cylinder.
PSR 0833-45, the Vela pulsar, is assumed to consist of a spinning
neutron star with the axis of its dipole magnetic field oriented approx-
imately, but not exactly, at right angles to the spin axis. If the two
axes were exactly at right angles, then the radio observations would be
expected to show two pulses, one from each polar cap, if any pulsed
- 3 -
emission at all were seen. The production of radio photons in this model
is assumed to take place near the surface of the neutron star. The
production mechanism could be coherent curvature radiation by electrons
(Sturrock, 1971; Tademaru, 1971; Ruderman and Sutherland, 1975) or some
other mechanism, as reviewed, for example by ter Haar (1972). For the
present discussion, the exact radio emission mechanism is not crucial,
as long as the radio photons are produced near the polar caps of the
neutron star. The appearance of a single radio pulse can then be explained
as an orientation effect. The emission region is small in both extent
and angle; therefore, the radio beam is sufficiently narrow that only
the beam from one of the two polar caps reaches the earth.
In contrast to the radio emission, the observed high-energy y-ray
flux is produced, according to this model, near the speed of light cylinder
by synchrotron radiation of electrons which have followed the field lines
of the pulsar's dipole magnetic field. This model is, therefore, similar
to the one proposed by Shklovsky (1970) for the Crab. A qualitative
description of the y-ray production will show how the observed character-
istics can be explain .--d. Following this discussion, a quantitative approach
will indicate the feasibility of the proposed mechanisms.
In order for the radio emission to originate near the polar caps
of the neutron star, electron acceleration must take place in this region.
Once accelerated, the electrons are assumed to propagate through the
pulse' magnetosphere along the magnetic dipole field lines. As long as
the electrons move strictly along the field lines, they experience no
transverse magnetic field. The only energy loss mechanism for such electrons,
r
- 4 -
curvature radiation, causes only a small degradation of the electron
energies. At the speed of light cylinder, the electron trajectories are
assumed to deviate slightly from the field lines. The electrons then see
a transverse magnetic field and rapidly radiate away most of their energy
as synchrotron radiation peaked in the y-ray energy range. Since the
deviation from the field lines is small, the radiation itself occurs
principally along the direction of the field lines. The geometric con-
figuration of the magnetic field at the speed of light cylinder therefore
determines the characteristics of the y-radiation.
The magnetic field configuration is that of a dipole, but this
field cannot corotate with the star all the way from the surface to the
speed of light cylinder. The shearing effect of the star's rotation
causes the projection of the magnetic field lines on the equatorial
plane to show a spiral structure, with a spiral angle of about 45 0 at
the speed of light cylinder due to the approximate equality of the plasma
energy density and the magnetic field energy density in this region
(Sturrock, 1971). The 13 +2 msec delay between the radio pulse and the
first y-ray pulse is equivalent to an angle of 52° +8°. This delay
arises naturally in this model from the fact that the radio emission
originates near the surface, where the magnetic field does corotate with
the polar caps, while the y-ray flux comes from the speed of light
cylinder, where the field lines lag behind the polar caps by the spiral
angle.
The appearance of two y-ray pulses can also be explained in geo-
metric terms. The magnetic dipole field lines above the polar caps
't
- 5 -
diverge rapidly with increasing distance from the surface. A narrow beam
of electrons at the surface will, therefore, have much larger extent in
both spatial and angular dimensions at the speed of light cylinder.
i
Because of this divergence of the field lines, it then becomes possible
to see tFe second polar cap y-ray emission as well as the first. The
larger emitting region at the speed of light cylinder also accounts for
the larger widths of the pulses in the y-ray energy range as compared
to the radio. The y-ray pulse which follows the radio peak by 13 msec
is the one which is associated with the polar cap where the radio emission
takes place. The other X-ray pulse comes from the region above the second
polar cap, which has a less favorable geometry w:.th respect to the line
of sight from the earth. The second pulse could then be expected to be
less intense than the first, and the y-ray data do suggest that the
second pulse is weaker. The reason why the two pulses are separated by
0.4 period rather than 0.5 period is not clear, although this effect
could also be the result of the asymmetry between the line of sight to
the two polar caps.
Based on these largely geometric arguments, this model for the Vela
pulsar appears to be promising. The quantitative feasibility of the model
remains to be shown below. In this preliminary analysis, some details
of the complex problems of particle acceleration and propagation in the
pulsar magnetosphere are not treated explicity, or the work of other
authors has been assumed to apply to this model.
For a dipole magnetic field, the radial dependence of the field
strength is given by
- 6 -
Br = BR (R/r)3
	
(1)
where BR is the field at the surface of a neutron star with radius R
a-nd Br is the field at radius r. In particular, for r = Ry = cT/2xr
(the speed of light cylinder), where c is the velocity of light and T is
the pulsar period, Br = 104 gauss, assuming that B R = 1012 gauss.
Production of 100 MeV y-rays by synchrotron radiation in a 10 4
 ,gauss field
requires electrons with energies of about 10 12 ev. Acceleration of
electrons to energies greater than 10 13 ev has been predicted for the
Vela pulsar (Sturrock, 1971).
If the electron acceleration near the surface of the star takes
place along the magnetic field lines, as assumed, for example, by
Sturrock (1971), then the particles will move along the field lines with
essentially no transverse momentum. The only energy loss mechanism for
the electrons will be through curvature radiation, but if the radius of
curvature is assumed large (^- 108 cm), then 1012 ev electrons will lose
less than 10% of their energy in the total travel time from the surface
to the speed of light cylinder. This constraint on the radius of curvature
means that the electrons must be accelerated principally along field
lines which lie very close to the axis of the magnetic dipole.
The mechanism by which the electrons deviate from the magnetic
field lines near the speed of light cylinder is uncertain. Some external
source of energy would be necessary to force the electrons away from these
.,ines. Although they consider the possibility unlikely, Sturrock,
Petrosian and Turk (1975) suggest that a high-frequency radio field could
couple with the electron, gyromotion to produce the required transverse
(2)
ar
- 7 -
motion. For this calculation, the existence of a mechanism of this type
will be assumed.
Once the electron trajectories separate from the field lines, the
electrons will begin to radiate. The total power emitted as synchrotron
radiation by an electron with energy E (in ev) in a field B l (in gauss) is
P = 5 x 10-15E 2 B.2	 ev s-1y
If the transverse magnetic field seen by the electrons is taken to be
103gauss, i.e. 10% of the total field at the speed of light cylinder,
'I
then a 1012 ev electron will radiate away over 80% of its energy in the
form of y-rays with a time scale of about 1 msec. Since the electron
path is still predominantly in the direction of the field lines, the
synchrotron radiation will be strongly peaked along the direction of the
field lines, as assumed earlier.
Because the synchrotron mechanism converts electron energy into
y-radiation with high efficiency, the rotational energy loss of the Vela
pulsar is ample to explain the observed y-ray energy flux. The observed
time-averaged y-ray flux F can be expressed in terms of the pulsar
luminosity L by
F	 A_D	 (3)
where D is the distance to the pulsar, assumed to be 460 pc (Brandt at al.,
1971) and ACS is the solid angle swept out by the beam, taken to be 1 sr
for this calculation. The observed pulsed flux of about 10 -5 photons
cm 2 s -1 above 35 MeV from Vela implies a y-ray luminosity of 2 x 1037
photons (R > 35 MeV) s -1 for PSR 0833-45. Assuming a characteristic
energy of 100 MeV for the-y-rays, this luminosity is equivalent to 3 x 1033
ergs s -1 , which is about 0.5% of the estimated 7 x 1035 ergs s-1 rotational
energy loss of the Vela pulsar (ter Haar, 1972). 	 As a
- B -
first approximation, consider thtu case in which electrons are accelerated
to energies on the order of 10 12 ev and then injected into the region
near the speed of light cylinder. From equation (2), the rate of energy
loss as y-rays of these high energy electrons is such that less than 1%
of the rotational energy loss of the pulsar needs to appear in the form
of high energy electrons at the speed of light cylinder to explain the
observed y-ray emission.
III. DISCUSSION
The implications of this model for other measurements and theoretical
studies are significant. Before such applications are discussed, one
important consideration is the possible comparison of this model with the
Crab pulsar, the only other pulsar known to emit in both radio and y-rays.
The apparent continuity of the NP0532 pulsed spectrum from the optical
through y-ray energy ranges, together with the agreement in phase between
the radio and high-energy photon pulses and the relatively narrow y-ray
pulses, argue that the mechanism described here is not responsible for
the Crab emission. The Crab is considered to be the only pulsar capable
of accelerating protons as well as electrons from its surface (Ruderman
and Sutherland, 1975). One possibility, therefore, would be that the
Crab emission at all photon energies is due to proton-induced cascades
near the surface of the star, and that few energetic particles reach the
speed of light cylinder except directly along the field lines, in which
case they would not radiate by the synchrotron mechanism. Another pos-
sibility would be that the electrons in the Crab are accelerated along
field lines with smaller radius of curvature than those postulated for
- 9 -
the Vela pulsar. In this case, the curvature radiation losses would result
in few energetic electrons reaching the speed of light cylinder. Until
other y-ray pulsars are discovered, it appears impossible to say whether
the present model is a general case or one which applies only to Vela.
Th°s model can also be used to predict pulsed fluxes to be expected
at other X-and y-ray energies. A first approximation to the energy
spectrum can be obtained by assuming that the electrons are all injected
into the emitting region with the same energy. This delta function
approximation was used by Sturrock (1971), who calculated a photon energy
spectrum with an E-0.5 dependence, where .]F is the photon energy. Normal-
izing to the SAS-2 measurements, the energy spectrum in the X- and y-ray
range would be 1.4 x 10-3 E-0.5 KeV cm-2 a -1 KeV-1 , with E expressed in
KeV. The expected flux at 1 KeV of 1.4 x 10 -3 is well below the pulsed
result of Harnden and Gorenstein (1973) but is consistent with the upper
limit of Moore et al.,(1974). At 5 KeV, the predicted pulsed flux is
well below the upper limit of Rappaport et al. (1974). At 50 KeV, the
prediction is an order of magnitude below the pulsed observations of
Harnden et al. (1972): If the results of Harnden and Gorenstein or
Harnden et a1. are confirmed, then the possibility would have to be
considered that a second pulse mechanism is responsible for the X-ray
emission. More sensitive measurements at X-ray energies should be able
to detect the pulsed emission predicted by the present model.
In summary, the model described here offers an explanation of several
important features of the radio and y-ray pulsed radiation from PSR 0833-45.
The fact that the model can explain the y-ray energy flux, double pulse
j
t_^
- 10 -
structure, and phase shift with respect to the radio indicates that
more detailed work along these lines may be profitable.
I would like to thank J. K. Daugherty, C. E. Fichte., D. A. Kniffen,
.
and H. B. Ogelman for their suggestions, which contributed greatly to
this work.
REFERENCES
Albats, P., Frye, 0, M., Jr., Thomson, G. B., Hopper, V. D., Mace, 0 B.,
Thomas, J. A., Staib, J. A. 1974, Nature 251, 400.
Brandt, J. C., Stecher, T. P., Crawford, D. L., and Maran, S. P. 1971,
Ap. J. 163, L99.
Chiu, H. Y., Lynda, R., and Maran, Sw.P. 1970, Ap. J. 162, L99.
Grindley, J. E., Brown, R. H., Davis, J. and Allen, L. R. 1973,
Proc. 13th Intl. Cosmic Ray Conf. Denver, 439.
Harnden, F. R., Jr. and Gorenstein, P. 1973, Nature 241, 107.
Harnden, F. R., Jr., Johnson, W. N., III, and Haymes, R. C. 1972,
Ap. J. 172, L91.
Kristian, J. 1970, Ap. J. 162, L1031.
Lasker, B. M. 1975, preprint.
Lasker, $•. M., Bracker, S. D., and Saa, 0. 1972, Ap. J. 176, L65.
j^	
Moore, W. E., Agrawal, P. C., and Garmire, G. 1974, Ap. J. 189, L117.
Rappaport, S., Bradt, H., Doxsey, R., Levine, A., and Spada, G. 1974,
Nature 251, 471.
I
I.	 Ricker, G. R., Gerassimenko, M., McClintock, J. E., Ryckman, S. G., and
Lewin, W. H. G. 1973, Ap. J. 186, Llll.
Ruderman, M. A. and Sutherland, P. G. 1975, Ap. J. 196, 51.
^F
- 11 -
Shklovsky, I. S. 1970, Ap. J. 159, L77.
Sturrock, P. A. 1971, Ap. J. 164, 529.
Sturrock, P. A., Petrosian, V., and Turk, J. S. 1975, Ap. J. 196, 73.
Tademaru, E. 1971, Ap. and Sp. Sci. 12, 193.
Ter Haar, D. 1972, Phys. Reports 3, 57.
Thompson, D. J., Fichtel, C. E., Kniffen, D. A., and Ogelman, H. B.,
1975, Ap. J. (in press).
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Interpretation of the pulsed gamma ray emission from Vela

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