We have computed the time evolution of a static loop model
with the new code. The loop is stable for very long times (several thousands
of seconds): the initial configuration of the atmosphere does not change
significantly when we let it relax maintaining only the steady heating. The
solutions are still stable if we perturb the initial temperature and
density profiles, for example giving small amplitude isobaric
perturbations as those in Peres et al. (1982). Plasma velocities (
km/s) are always
negligible compared to the local sound speed everywhere in
the loop, and decrease in time in all the relaxation tests we have performed.
We typically use relaxed atmospheres as initial configurations for any
further investigation of the plasma evolution.
As a second representative test we report the results of a simulation of a flare in an active region loop and compare them to the results obtained with the previous PH code. We have chosen the model of the well-studied flare observed by SMM on the sun on November 12 1980 at 17:00 UT (Peres et al. 1987) obtained by using the previous PH code, with a satisfactory fitting of the XRP/SMM observations. The transient heating in Eq. (7) has been placed at the top of the loop with a Gaussian spatial distribution,
where 
cm, 
cm; it is
constant for the first 180 seconds and then decays exponentially with an
e-folding time of 60 seconds; 
is 10 erg 
while the
steady heating term is uniform in the corona, with 
erg cm
s
. The half-length of the loop is 
cm,
and the pressure at the base of the transition region is initially 
dyne 
.
A first important point to check is how the more accurate numerical computation of temperature and density gradients in the transition region improves the results. It appears that we have overcome one of the difficulties which plagued the computation of hydrodynamics of flaring plasmas as discussed in the introduction.
Figure 2: Comparison between the evolution of the plasma temperature and
density during a typical flare, computed with the new code, and that
obtained with the previous code.
The parameters of the simulation are reported in the text; the initial
configuration of the atmosphere (
) is the one shown in Fig.
1 (click here). We have joined by short-dashed lines the points calculated with the
previous code to guide the eye.
The curves are taken every 5 seconds for a total time of 30 seconds.
The transition region, both in the temperature and density profiles,
moves from right toward the left after the beginning of the impulsive
heating
Figure 2 (click here) shows the hydrodynamical results obtained with the new PH code along with the corresponding results from the previous code (dashed lines); the initial conditions are the same as in Fig. 1 (click here). We show results focusing on the transition region, because this is the part of the loop atmosphere where the new code is apt to probe the behavior of the plasma in a way inaccessible to the previous PH code. The parameters of the simulations are identical apart from the numerical grid. The time profiles of temperature and density sample the first 30 seconds of the flare evolution. The total number of grid points is also approximatively the same: the simulations of Peres et al. (1987) were done on a fixed grid with 256 logarithmically spaced points; now the number of points is typically around 275, and in this case varies from a minimum of 242 (at 10 s) to a maximum of 343 (at 5 s) along the whole loop.
Figure 3: Displacement of the transition region during the flare
evolution. We have plotted vs. time the spatial coordinate of the point
at 
K.
The results obtained with the new code (solid line) are compared with
the previous ones (dashed line)
Snapshots taken at the same times are different, and now with a
significantly higher resolution, the computed gradients are also
steeper. The plasma condensation, which typically forms in the
chromosphere after a few seconds since the impulsive heating is turned
on (
s for this flare), is now resolved much better and the
density maximum is higher. The transition region of the flaring
atmosphere, at any time after 10 s, is located lower than
predicted with the previous code. These results show, once again, the
improvement produced by the adaptive grid, since under-resolving the
transition region results in an underestimation of the speed with which
chromospheric evaporation occurs. The proper resolution therefore
produces significantly more accurate results for the diagnostics of UV
lines formed in the transition region and for the plasma dynamics
during the chromospheric evaporation.
Another large
difference with the old results is that we no longer find
oscillations of the position of the transition region. This aspect is
shown in Fig. 3 (click here) where the displacement along the loop of
the volume element corresponding to a temperature 
K is plotted,
both for runs using the old and new version of the code.