Let us now compare the measured density profile to the
theoretical profile (23), where 
is
deduced from the polytrope exponent found in Section 3.
Since the Ulysses trajectory was not exactly normal to equator, we first correct the variation with Jovicentric distance. This is done by normalizing the measured density to the equatorial density at the same Jovicentric distance, deduced from Voyager measurements ([Sittler and Strobel 1987]) by Bagenal (1994) (Fig.5 of that paper, without current sheet). This assumes that the variation of density with Jovicentric distance was similar for Ulysses and Voyager (apart for a constant multiplicative factor
A) in the small range of distances considered here. Such a
procedure may be questionable owing to the differences in epoch
and longitude of the spacecraft trajectories; it seems, however,
reasonable since it allows to correct completely the small
observed latitudinal asymmetry. In order to match our Ulysses
results at equator, the densities of the Voyager model must be
multiplied by the factor 
, as in Hoang et al. (1993)
(i.e., the torus was denser at the time and longitude of the Ulysses
traversal, compared to what Voyager measured.)
Figure 5: Theoretical density profile across the Io torus
given in Eq.(23) with given in (19) - as deduced from the observed
polytrope law - and 
, superimposed to the normalized
measured density profile (corrected for the variation with Jovicentric
distance). The horizontal axis is sign(z) 
, z being the
latitudinal distance in Jovian radii. Dotted error bars identify the data for
which 
and 
are measured independently. The sigma of the fit is
0.04.
Our observed profile corrected
in this way is plotted in Fig.5. We have superimposed the
Kappa-like profile (23), with given in (
19), and the scale height
The distance z (in Jovian radii) is counted from the plane of
symmetry of the torus as determined from our measurements, which
is tilted by 
( 
) to the magnetic
equator; this value is
roughly equal to the nominal 
tilt of the centrifugal
equator, within the precision of the magnetic field model used.
All three parameters (H, A, 
) are deduced from a chi-square
fit involving the data points with solid error bars in
Fig.5. The fit is quite good; the mean-square
relative error between the measurements and the model is 0.04.
Substituting in Eq.(25) the Kappa scale height H
= 0.91 
found above, with the Jovian parameters 
m and
rad/s, one finds
( 
being the proton mass). Assuming an effective ion mass of
at 
([Bagenal 1994]),
this gives
K, which is close to the result found by
Hoang et al. (1993). It may be noted that in the same range of radial
distance, the Voyager measurements imply 
eV and
eV ([Bagenal 1994]). This gives 
K, which is
about 2.5 times larger
than our Ulysses determination. Such a difference (if it is not due to
the simplifications of our model) is not
surprising since (i) with a non-Maxwellian (core) distribution,
the Voyager ion (core) temperature, which is determined by
assuming the ion (core) distribution to be Maxwellian, is not
necessarily equal to the temperature defined from the mean
random energy of these particles,
(ii) the spacecraft explored different longitude sectors, and
(iii) the variability of the torus is known to be significant (see
[Strobel 1989]): for example, the 1981 observations by Morgan (1985)
also imply an ion temperature twice smaller than that
derived from the Voyager analyzers. One may also note that
the radio occultation experiment aboard Ulysses measured a
line-of-sight electron content in the torus which similarly
suggested an ion temperature twice smaller than the value
inferred from Voyager measurements ([Bird et al. 1993]).
We have not included in the fitting the measurements
acquired at negative latitudes beyond 
(dotted bars in
Fig.5) because in that region the measurements of and
are not independent. One may note, however, that
these points also match the theoretical Kappa-like profile within the
error bars,
except for the three southern most points, which do not either follow
the polytrope law. Noting that the Jovicentric distance of these
points is nearly 9 , this might suggest a different origin or behaviour
of the
plasma beyond this distance, where the torus merges into the
magnetodisc, and where the influence of the satellite Europa -
which orbits Jupiter at 9.4 - may be significant ([Intriligator and Miller, 1982]).
It would be interesting to extend the comparison farther from
the equator. This is, however, difficult, since Ulysses explored
high latitudes in very different longitudes sectors and at very
different Jovicentric distances. For an order of
magnitude comparison, we note that Ulysses passed at 
at
the radial distance 
, where the Voyager analyzers found
an
ion temperature 
roughly 0.6 times smaller than
at .
This yields a scale height roughly 
times smaller than the
value above, i.e. 
. With this parameter, the profile
(23) yields 
. Taking 
cm 
as
determined by Voyager at that radial distance, we obtain
6 cm , which is comparable
to the values measured
aboard Ulysses at this location ([Desch et al. 1994]).