The synchrotron radiation expected at Earth from the region L=2.9-5 R sub J of Jupiter's magnetosphere is calculated using the Pioneer 10 electron model. The result is approximately 21 flux units (f.u.). This value is to be compared with 6.0 + or - 0.7 f.u., the flux density of synchrotron radiation measured from Jupiter's entire magnetosphere in ground-based radio observations. Most of the radiation at 375 cm is emitted by electrons in the 1 to 10 MeV range. If the electron model used for calculations is cut off below 10 MeV, the calculated flux is reduced to approximately 4 f.u., a level compatible with the radio observations

Birmingham, T. J.

English

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The Jovian Electron Spectrum and Synchrotron Radiation at 375 cm
by
Thomas J. Birmingham
Theoretical Studies Group
Goddard Space Flight Center
Greenbelt, Maryland 20771
The Jovian Electron Spectrum and Synchrotron Radiation at 375cm
Thomas J. Birmingham
Theoretical Studies Group
Goddard Space Flight Center
Greenbelt, Maryland 20771
ABSTRACT
Using the University of Iowa's Pioneer 10 electron model, we have
calculated the synchrotron radiation at 375 cm expected at Earth from the
region L=2.9-5 RJ of Jupiter's magnetosphere. The result is %21 flux
units (f.u.). This value is to be compared with 6.0+0.7 f.u., the flux
density of synchrotron radiation measured from Jupiter's entire magnetosphere
in ground based radio observations. We find that most of the radiation
at 375 cm is emitted by electrons in the 1-10 MeV range. If the Iowa
model is cut off below 10 MeV, our calculated flux is reduced to r4 f.u.,
a level compatible with the radio observations.
2In the year since Pioneer 10's encounter with Jupiter there has been
considerable discussion and concern that the energetic electron experiments
aboard are yielding results incompatible with ground based observations
of synchrotron radiation, which presumably is produced by these same
electrons. Northrop and Birmingham (1974) previously showed that their
Pioneer 10 -based calculations of the synchrotron emission at 10.4 cm are
reasonably consistent with interferometric measurements at that wavelength.
The concern, however, is that Pioneer 10 level fluxes produce increasingly
too much synchrotron radiation at longer wavelengths, Luthey et al, 1975.
Again using the spectrum derived from the University of Iowa electron
measurements, we have calculated the incoherent synchrotron emission at
375 cm, the longest wavelength at which Jovian synchrotron radiation has
been observed by radio astronomers. For this calculation, we adopt the
geometry shown in Fig. 1. Jupiter's magnetic field B is taken to be that of
a centered dipole oriented perpendicular to Earth's line of sight. The
strength of the field is 4 Gauss at the surface of Jupiter at the magnetic
equator. Convenient spatial coordinates are dipole L, latitude X, and
azimuth 4.
The radio measurements at 375 cm are flux values for Jupiter's entire
magnetosphere. For comparison purposes we therefore evaluate the emission
in the x-direction from each infinitesimal volume element of the Jovian
magnetosphere and then integrate over , A and finally L. (A p-dependence
to the emission enters because at fixed A, Earth's look angle 0 with respect
to the magnetic field depends on C).
The radiation P1 (in mks units) emitted per steradian, per, Af (Hertz)
centered at frequency f(=2-), in the direction 0 by one electron of speed
3v= 5c and local pitch angle 6, is the sum of two terms
P = e2w 2  2 sin2 6 J 2o sin e sin 6)
+ cos - cos 6 2  8 sin 0 sin 6) (1)
sin 
W
w,(v,L,X) is the relativistic gyrofrequency and Jv the ordinary Bessel
function of order v = w(1- I cos 6 cos 0)//o>>i. The first term represents
radiation polarized I to the local B and the second radiation polarized
to B. Each term contributes to both orthogonal polarizations received
at Earth in an amount which depends on L, A, and c. For the region of
Jupiter's magnetosphere that we have considered, the perpendicular polarization
is about a factor of 10 larger than the parallel; we shall henceforth consider
only the term in (1) proportional to (JN)2
To determine the total emission in the x direction from the magneto-
spheric point L, A, p, we integrate (1) over the density of electrons
n(T,6,L,A) = j(T,6,L,A)/v
P 2 (L,X,f) = fdT fdT j(T,S,L,A) P1 (T,6,L,A,f)/v (2)
0 0
(T is electron kinetic energy). For the electron flux j, differential in
T and solid angle, we again use the Iowa empirical model
k(L)F(L) -(1+1) cos 3 n(L)X n(T,6,L,A) = 2S(n) (1+3 sin A)n/4 sin T in MeVI (3)
This formula has been developed from the Pioneer 10 electron measurements
of the Iowa group (Van Allen et al, 1974). It is based primarily on integral
flux measurements above thresholds of 21 MeV and 31 MeV; its use at energies
far below 21 MeV is an extrapolation. The parameters of the model are
discussed in Northrop and Birmingham (1974) and are listed in Table 1 for
4the region between periapsis at L=2.9 R and an outer limit of L=4.9 R
at which synchrotron radiation has become very small. We have made no attempt
as yet to extrapolate to the region L<2.9 R.
The energy integral in (2) is effectively cut off at a lower limit
Tmin by the ineffective radiative capacity of low energy electrons and at
an upper limit Tmax determined by the fall-off of the electron number density.
For each value of L, we have next integrated P2 over X and , P3 (L) =
fdX fd P2 (L,X,f) cos 7 X. The cos7 X is the proper volume weighting factor.
Because of the symmetry of our model only the single octant 0 < X < /2
0 < <7 T/2 need be considered. Convergence at large A results dominantly
from the strong peaking of j at the magnetic equator. In Figure 2, Curve
1 depicts as a function of L the total radiation intensity P(L)=.l L2P 3 (L)
in Watts/Hz steradian) emitted in the direction of the Earth by all the
electrons in a dipole L shell of equatorial thickness'.l Rj; the Iowa
electron model has been assumed to be applicable from T=0 to T=-. The
inflection in the region L=3.1 -3.5 Rj is a recurrent feature and is due to
the canplicated interplay of a) the radial dependence of the electron model
(cf.Table 1), b) the drop-off with L in the dipole magnetic field strength,
and c) the increase with L of the volume of a 0.1 R thick dipole drift
shell.
The intensity in f.u. (1 f.u. = 10- 2 6 Watts/m2-Hz) received at Earth
at a distance 4.04 A.U. from Jupiter is obtained by integrating f4.9 dL P(L)
2.9
and multiplying by 2.8 x 10-24 ster./m 2. For Curve 1 the result is 21.4 f.u.
By contrast, the flux intensity from Jupiter's entire magnetosphere
has been measured radio-astronomically by Slee and Dulk (1972) to be
6.0 + 0.7 f.u. at 80 MHz. (A value of 4.5 + 1.0 f.u. was previously reported
by Gower (1968) at 81.5 MHz, but Slee and Dulk point out that the Gower
5observation is plagued by the presence of radiation from extra-Jovian
sources). Even neglecting the strong magnetic field region L<2.9 R , we come
up with a value based on the model electron flux which is 3.5 times larger.
The discrepancy is the more disturbing when one appreciates that the radio-
astronomical error estimates are <25% at these frequencies.
Obscuration of portions of Jupiter's magnetosphere by the planet has
been neglected in Figure 2. We have roughly evaluated this effect and find
that it leads to a reduction of fPdL by less than 10%.
We have noted that a large portion of the radiation at 375 cm is
produced by <10 MeV electrons, i.e., by electrons in the energy regime where
the Iowa model is unverified. This situation at 375 cm is in contrast with
that at 10.4 cm, where we found previously (Northrop and Birmingham, 1974)
that scarcely any synchrotron radiation was produced by such low energy
electrons. To assess quantitatively the effect of low energy electrons
we ran two further cases, one in which the Iowa model, Eq. 3, was abruptly
truncated so that no electrons existed below 5 MeV and a second in which
the cut-off was taken to be 10 MeV. Curves 2 and 3 are the results. The
discrepancy among the three curves is most pronounced at the smallest values
of L, where the strongest magnetic fields exist and hence where the lower
energy electrons can radiate most effectively.
Curves 2 and 3 correspond respectively to intensities of 13 f.u. and
4 f.u. at Earth. The lower value is compatible with Slee and Dulk's
(1972) 6 f.u. if one assumes that an extra 2 f.u. comes from the Jovian
magnetospheric region L<2.9 Rj unexplored by Pioneer 10.
To us, Figure 2 plus the Slee and Dulk radio observations are convincing
evidence that there are active in the Jovian magnetospheric region L<5 RJ
6processes which diminish greatly the flux of T< 10 MeV electrons. We have
no idea at the present time what such processes might be. A similar low energy
cut-off was postulated by Gleeson et al (1970) on the basis of their
attempted theoretical fit to the complete frequency spectrum of Jupiter's
synchrotron emission.
The possibility that our naive magnetic field model might be at fault
can be eliminated: we find that Curve 1 scales as approximately B2 (Curves 2 and
3 are much less sensitive). Tilting the dipole by 100 while maintaining fixed
x, y, and z axes in Fig. 1 leads to a maximum change in JBI of 13% at a
fixed spatial position and hence to a maximum 25% change in Curve 1. (The
variations of flux density with System III longitude measured by Slee and
Dulk (1972) are 25%-type variations and lend credence to this estimate.)
Offsetting the dipole by jArl .1 R leads to additional corrections of
J
order .1 % 3% which are yet smaller. We therefore do not see that use of a
3
more refined model (Smith et al. 1974, Acuna and Ness, 1975) of Jupiter's
magnetic field will substantially change our conclusions.
Finally, we remark that although experimental uncertainties are large
close in to Jupiter, Pioneer electron experiments have noted either a leveling
off (McIlwain and Fillius, 1975) or even an erosion (Fillius et al, 1975;
Van Allen et al, 1975) of the differential flux in the < 10 MeV region.
Acknowledgement: The numerical-integrations were very ably carried out
by J. Bredekamp. My concern with Jupiter's synchrotron radiation at long
wavelengths was stimulated by a personal conversation with J. Luthey
and by a lecture he gave at Goddard Space Flight Center. I have also
profited from discussions of Jovian and synchrotron physics with J. Alexander,
F. Jones, and T. Northrop.
7Figure Captions
1. The model on which this calculation is based. Jupiter's magnetic
field is that of a planet-centered dipole perpendicular to the line of
sight from Earth. It has an equatorial surface strength of 4 Gauss.
An electron at position L, A, p with local pitch angle 6 and kinetic
energy T is radiating. The intensity received from this electron is a
sensitive function of 8, the angle between the line of sight and the local
magnetic vector B.
2. The synchrotron flux P in Watts/(Hz-steradian) emitted in the direction
of Earth by electrons in a dipole flux shell of equatorial thickness 0.1
R at a distance L in R from the center of Jupiter. Curve 1 includes
electrons of all energies; Curve 2 is the radiation only from electrons
with energy >5 MeV; and Curve 3 is the radiation only from electrons with
energy >10 MeV.
8Table 1 Parameters of the Iowa Electron Model
L (in Rj) K(m- 2 sec-1) r n
2.9 1.38 x 1014 2.00 11.31
3.1 1.08 x 1014 1.91 8.18
3.3 1.12 x 1014 1.93 6.44
3.5 7.52 x 1013 1.84 5.43
3.7 6.44 x 1013 1.84 .4.83
3.9 6.36 x 1013 1.89 4.46
4.1 6.23 x 1013 1.93 4.23
4.3 6.26 x 101 3  1.97 4.07
4.5 6.08 x 1013 2.02 3.97
4.7 5.96 x 1013 2.06 3.91
4.9 5.93 x 1013 2.11 3.86
9References
Acuna, M. H. and N. F. Ness, Jupiter's main magnetic field measured by
Pioneer 11, 1975, Nature, 253, 327-328.
Fillius, R. W., C. E. McIlwain, and A. C. Mogro-Campero, Preliminary
results from the UCSD trapped radiation detector on Pioneer 11, 1975,
University of California, San Diego preprint.
Gleeson, L. J., M. P. C. Legg, and K. C. Westfold, On the radio frequency
spectrum of Jupiter, 1970, Proc. of Astron. Soc. of Australia, 1, 320-322.
Gower, J. F. R., The flux density of Jupiter at 81.5 Mc/s, 1968, Observatory
88, 264-267.
Luthey, J. L., S. Gulkis, and M. J. Klein, Synchrotron Radiation from
Jupiter: Comparison of Earth based data with calculations based on
Pioneer 10 data, Submitted to J. Geophys. Res. 1975.
McIlwain, C. E. and R. W. Fillius, Differential spectra and phase space
densities of trapped electrons at Jupiter, 1975, to appear in J. Geophys.
Res.
Northrop, T. G. and T. J. Birmingham, The magnetosphere of Jupiter as observed
with Pioneer 10, 3, Jovian synchrotron radiation at 10.4 cm as deduced
from observed electron fluxes, 1974, J. Geophys. Res., 79, 3583-3587.
Slee, O. B., and G. A. Dulk, 80 MHz measurements of Jupiter's synchrotron
emission, 1972, Aust. J. Phys., 25, 103-105.
Smith, E. J., L. Davis, Jr., D. E. Jones, P. J. Coleman, Jr., D. S. Colburn,
P. Dyal, C. P. Sonett, and A. M. A. Frandsen, The planetary magnetic
field and magnetosphere of Jupiter, 1974, J. Geophys. Res., 79, 3501-
3513.
10
Van Allen, J. A., D. N. Baker, B. A. Randall, and D. D. Sentman, The
magnetosphere of Jupiter as observed with Pioneer 10, 1, Instrument
and principal findings, 1974, J. Geophys. Res., 79, 3559-3577.
Van Allen, J. A., B. A. Randall, D. N. Baker, C. K. Goertz, D. D. Sentman,
M. F. Thomsen, and H. R. Flindt, Pioneer 11 observations of energetic
particles in the Jovian magnetosphere, 1975, to appear in Science.
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The Jovian electron spectrum and synchrotron radiation at 375 cm

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