## 4. Comparison with observations and diagnostic diagrams## 4.1. Observed value of the ortho:para ratioThe ortho:para ratio, The method by which the ortho:para ratio is determined
observationally is illustrated in Fig. 4a. This method makes use
of the excitation diagram, which is a plot of
against
, where
is the column density measured in
rotational level and the excitation diagram is a straight line of slope
. The downwards displacement of the
line joining points corresponding to odd where the excitation temperature between levels and , , is given by and is the column density obtained by linear interpolation between the points and in the excitation diagram (see Fig. 4a). In practice, the excitation diagram may exhibit curvature, indicative of the emitting gas having a range of kinetic temperatures. The curvature is small for C-type and greater for J-type shocks, owing to the very rapid variation of the kinetic temperature in the post J-shock flow. Curvature can introduce systematic errors in the ortho:para ratio determined from Eq. (5), but we find that averaging over an equal number of ortho and para levels yields a reliable value (with error %).
It is important to realize that the ortho:para ratio derived
empirically depends on the lines that are observed: levels with
differing excitation energies are populated in different parts of the
shock wave, where the (local) values of the ortho:para ratio may also
differ. To illustrate this important point, we plot in Fig. 4b
the variations of measures of the ortho:para ratio through a C-type
shock wave in which = 30
km s In emission line studies, the column densities of levels with
2 are measured, and the inferred
ortho:para ratio differs from Finally, Fig. 4b also plots , the mean value of the ortho:para ratios empirically derived from column densities of the levels (corresponding to the upper levels of the ro-vibrational lines observable from the ground). These levels have higher energies (6000 to 14000 K) than the levels; thus, the column density ratios become "frozen" even sooner after the temperature maximum, and remains smaller than . We conclude that an object where cannot be explained by the presence of a single stationary-state planar shock wave within the observing beam. ## 4.2. Diagnostic diagrams and application to HH 54## 4.2.1. Pure rotational lines in C-type shocksNeufeld et al. (1998) have used ISO SWS02 (grating mode)
observations of the E,K emission knots in HH 54, together with
the C-shock models of Timmermann (1998), to constrain the shock speed
and preshock ortho:para ratio in this object. They have shown that a
useful diagnostic diagram is obtained by plotting the line intensity
ratio S(3)/S(1) (a measure of the excitation temperature
) as a function of S(2)/S(1) (a
measure of both and the ortho:para
ratio) for a range of shock models with fixed preshock density. With
an arbitrarily chosen =
cm In view of the improvements that we have made, in the treatment of
H Fig. 5a is such a diagnostic diagram, for
= ,
, ,
and cm
Fig. 5a shows that the rise in the ortho:para ratio occurs at lower excitation temperatures as decreases. This shift of the diagnostic curves with has two important consequences. First, any given observed point, when plotted in this diagram, does not correspond to unique values of both the initial ortho:para ratio and . Adopting a lower yields a lower initial ortho:para ratio and a higher ; this introduces an intrinsic uncertainty in the determination of the preshock parameters. Second, the curve corresponding to a very low initial ortho:para ratio (0.01 in Fig. 5a) defines for each the minimum ortho:para ratio at a given excitation temperature. An observed point located below this curve is incompatible with the models at the corresponding value of and implies a higher preshock density. As an illustration, we plot as a star symbol in Fig. 5a the
point which derives from the SWS observations of HH 54 (Neufeld
et al. 1998). We see that values of
cm
We conclude that the initial ortho:para ratio in the region of HH 54 observed by SWS but that the uncertainties in are such that it is not possible to decide whether the ratio has reached thermal equilibrium in the preshock gas. ## 4.2.2. Pure rotational lines in J-type shocksFig. 5b is the diagnostic diagram for our grid of J-type shock
models with =
, ,
and cm In Fig. 6 are plotted the fluxes in the 0-0 S(5) line, as a
function of the excitation temperature, for our J-type shock models.
The line flux is slightly more sensitive to
than is the case for C-type shocks.
However, the predicted line fluxes for J-type shocks are at least an
order of magnitude below the flux observed in HH 54 by ISO SWS. A
J-type shock could account for the observed flux only if the preshock
gas is dense ( =
cm ## 4.2.3. Rovibrational transitions as diagnosticsPrior to the launch of ISO, H In principle, such observations may also be used to constrain the
initial ortho:para ratio in the pre-shock gas. We present in
Fig. 7 diagnostic diagrams equivalent to those in Fig. 5,
but for the levels of
H
Once again, we use the knots E,K in HH 54 as an illustration.
The dashed rectangle in Fig. 7 indicates the range of parameters
compatible with near infrared observations of these emission knots by
Gredel (1994). We first note that
is larger than , which suggests that
a single planar shock wave within the SWS beam cannot account for all
of the observations (cf. Sect. 4.1). Indeed, the rotational
excitation temperature in ,
2900 K, implies a faster C-type shock
( 35
km s The situation that vibrational transitions imply a higher shock
speed than pure rotational transitions is also found in other
protostellar outflows observed with ISO (e.g. Cep A; Wright et
al. 1996). Similar difficulties were already encountered when trying
to reconcile all H An alternative explanation of the rotational and vibrational line emission is that the shock wave has not reached steady-state (Chièze et al. 1998). In this model, the rotational lines arise mainly in the C-type component, whilst the vibrational lines come from the following J-type component (Flower & Pineau des Forêts 1999). The initial ortho:para ratio, ahead of the shock wave, could be low ( 0.8), as required by the pure rotational lines, but the ratio could increase in the magnetic precursor to a local value of 2.0 just ahead of the J-discontinuity, as required by the vibrational lines. A more detailed investigation of these possibilities in relation to HH 54 and other objects is deferred to a subsequent paper. © European Southern Observatory (ESO) 2000 Online publication: April 17, 2000 |