## 3. The cross-section of a mixing layerWith the equations and numerical method described in Sect. 2, we
compute three models. These models correspond to cross-sections with
widths ,
and
cm of a mixing layer at the edge of
a beam of velocity
km s The temperature and density obtained from these three models are
shown in panels a and b of Fig. 2. From this figure, it is clear
that while for the smallest
In panel c of Fig. 2, we have plotted the ionization fraction that would be obtained from the coronal ionization equilibrium condition at the local temperature , i.e. from setting the turbulent diffusion term to zero in Eq. (4). A comparison of these ionization fractions with those in panel d obtained from the full solutions of Eqs. (1-4) shows that the isothermal regions of the temperature cross-sections are less ionized than predicted for coronal ionization equilibrium at the local temperature. This deviation from ionization equilibrium is due to turbulent diffusion of neutral gas from the jet and ambient medium into the layer. Although this departure from equilibrium ionization in mixing layers is less pronounced than that encountered in shock wave calculations, it is not negligible and the diffusion term cannot be neglected in Eq. (4) [even though the turbulent conductivity in Eq. (2) can be neglected with respect to the viscous heating term]. To verify the analytical argument of Eq. (7) that the temperature
of radiative layers is mainly determined by the parameter
, we have also run a broader grid of
mixing layer models. All of the models have
K and one of the following
three densities: ,
or
cm In Fig. 3 we plot the calculated average temperature,
, across the mixing layer as a
function of the parameter . Sequences
of mixing layers with constant but
different are shown as asterisks
connected by a long dash line
( cm
Above g cm which is represented in Fig. 3 by a short dash line. This interpolation formula can be used to estimate the approximate temperature of a mixing layer as a function of the parameter , or conversely for determining for an emitting layer of known temperature. These results suggest that the spectrum emitted by mixing layers is quite stable over a large range in . This result is quantified in the following section. The overlap in Fig. 3 of the three sequences is explained as follows: the amount of energy to be radiated in the mixing layer is while the cooling rate is , therefore (as in plane parallel shock waves where the column of recombining gas is independent of the preshock density), the cooling history remains the same when the product is kept constant (the same argument applies to the ionization history). is a representation of such a product provided one compares models with the same , and . © European Southern Observatory (ESO) 1999 Online publication: May 6, 1999 |