It is important to discuss the significance of the measured
temperature, since the electron velocity distribution is not
Maxwellian in the region explored. The electron analyzers
aboard Voyager ([Scudder et al. 1981], [Sittler and Strobel 1987]) detected
at this Jovicentric
distance ( ) a suprathermal population 10-30 times
hotter
than the main (cold) population, and representing a few percent
of the total density. The presence of such a population was
confirmed by Ulysses data, since it allowed us to interpret
quantitatively the suprathermal level of electrostatic
fluctuations in Bernstein waves ([Meyer-Vernet et al. 1993]). This minor hot
population does not affect significantly the part of the
dispersion relation used in our temperature measurements ([Moncuquet et al. 1995]
), so that, if the velocity distribution were a mere
superposition of a cold and such a hot population - both being
Maxwellian, the measured temperature plotted in Fig.1
would
be approximately that of the main (cold) population.
However, the velocity distribution is expected to be more
complex than a superposition of two Maxwellians. Firstly, the
Voyager electron analyzer results clearly showed that the hot
electrons were not Maxwellian distributed ([Scudder et al. 1981]). Secondly,
these analyzers had a low-energy threshold of 10 eV, and the
spacecraft was negatively charged, thereby yielding a higher
effective threshold ([Scudder et al. 1981], [Sittler and Strobel 1987]); since
10 eV
K in temperature units, this implies that a significant part of
the main (cold) population could not be detected, so that the
precise shape of the distribution at low energies is unknown.
Hence, although the cold electron distribution could be roughly
fitted to a Maxwellian, it is not certain that it was precisely
Maxwellian. On the other hand, aboard Ulysses, the particle
analyzers were unfortunately not operating in the torus, and the
frequency range in which we measured the dispersion relation
was not large enough to settle that question.
Hence, let us consider a more general case: a
non-Maxwellian distribution made of a superposition
of several Maxwellians of densities and temperatures
.
Since our Bernstein wave measurements were mostly made in the middle
of the
first gyroharmonic band, it can be shown ([Moncuquet et al. 1995]) that
they
are not sensitive to the mean energy of the distribution, i.e.,
to the traditional temperature
. Instead, our
measurements give an effective temperature
defined by:
if the densities and temperatures of the individual populations
have similar orders of magnitude, or if the hot population
densities are much smaller than that of the coldest one. In this
case, the temperature plotted here is
thus . This
effective temperature
is defined from the mean inverse
energy of the particles, and is thus mainly sensitive to the cold electrons;
this is reminiscent of the classical Debye shielding, which
depends on the same effective temperature, albeit for different
reasons ([Meyer-Vernet 1993]).