$\begin{figure} \par\includegraphics[width=5.3cm,clip]{10188f27.eps} \end{figure}$

Figure 18: Models CBOW with bow shape 1.4 (dashed) along with the data from the S2 position of L1448. Bow speed 100kms^-1, pre-shock density of 10⁶cm^-3, molecular fraction of 0.5n, ion fraction $2\times 10^{-7}$ , and CO and O abundances both $1\times 10^{-5}$ . Two lower density models are also shown with s = 1.2 (dot-dash) and s = 1.4(dashed), for a density of 10⁵cm^-3, but a standard CO abundance of $2\times 10^{-4}$ .

Our main result is that we can model the ISO data of CepA and L1448 with a broad distribution of shock strengths, as typified by bow shocks with long flanks. The implied ensembles of shocks are remarkably similar. CO and O abundances in the range $2{-}4\times 10^{-4}$ and $0.5{-}1\times 10^{-4}$ are predicted, with the 63 $\mu$ m oxygen fine-structure line optically thick.

This study emphasizes the future need for comparable apertures across the infrared so that we can model the abundances with more confidence. A higher sensitivity for CO rotational levels above J=20 would aid the interpretation. Simultaneous K-band and H-band spectra would also provide the type of constraint which would reveal the shock physics. ISO had a very extensive programme of observations, making it impossible to carry out measurements also achievable from the ground.

8.1 CepheusA

Shock configurations with a strong weighting towards the weaker shocks are necessary to explain the H₂ excitation.

C-type physics provides the best interpretation of the low excitation, the CO high-J fluxes and the [OI] 63 $\mu$ m fine-structure emission line.

The two lobes, although far apart, and dynamically distinct, both contain high density shocked gas ( $1{-}3\times 10^6$ cm^-3), both with the same very low overall excitation. Such low excitation has been found previously for the CepheusE outflow (Eislöffel et al. 1996) from the vibrational H₂ lines, and also for DR21 (Smith et al. 1998) from SWS rotational H₂ line data. The low excitation thus appears quite common in the high-powered outflows (with OMC-1, where a paraboloidal bow (s=2) provides a fit, as the exception).

The inferred bow shocks are of the shape $s\sim 1.4$ . High resolution observations reveal a mixed H₂ bag in CepheusA West: numerous linear features and clumps, especially in the south and centre, bow shocks to the west and magnetic precursors to the north (Hartigan et al. 2000).

The energetics of outflows can be determined from ISO data without the uncertainties introduced by extinction. The C-type bow shock models yield the total radiated luminosity from the C-type sections. For the most plausible models we calculate total shock luminosities of 52.8 $L_{\odot}$ and 61.6 $L_{\odot}$ for CepheusA East and West from within the LWS apertures (assuming a distance of 725pc). This compares to a mechanical luminosity of 37 $L_{\odot}$ for the bipolar outflow derived from CO observations (Narayanan & Walker 1996). This suggests that the outflow is still being strongly driven by the shocks. When the energy source weakens, we expect the driving shocks to rapidly fade while the outflow switches from a driven into a coasting mode.

The predicted width of both CO and H₂ lines from bow shocks are narrow, even in high magnetic field models (FWHM < 10kms^-1, see Sect.5.12). Hence, if wide lines were detected, other larger internal motions must be dominant. Then, intrinsic line profiles are probably very similar in shape and width from all transitions, as apparent in CepA East (Fig.3).

The total radiation and mechanical luminosity is only a small fraction of the luminosity generated by the central group of hot stars, estimated to be $1.4\times 10^4\,L_{\odot}$ . Hence over 1% must be channeled into the outflow. If this outflow is to be driven by the momentum of the radiation then it must have a speed in excess of 0.01c. Therefore, we conclude that the outflow is not radiatively driven.

Our SWS aperture covers the central turbulent region in the west. Indeed, a model for decaying supersonic turbulence is a viable explanation. However, one must catch the decay at a specific time to provide a fit. Will a time-averaged decaying turbulent field yield an interpretation? Integrating the turbulent spectra over time yields a high excitation prediction: the emission is dominated by the strong shocks which form early in the flow. This then implies that the injected shock spectrum itself is responsible for what is observed.

Turbulence is inevitably created behind bow shocks: a curved shock generates vorticity and supersonic vorticity dissipates in shocks. Smith (1995) estimated that a sizeable fraction of the available energy of a bow shock is dissipated in this manner, and this energy would be channeled into low velocity shocks within the wake.

8.2 L1448

L1448 possesses no significant spatial variation in H₂ excitation. We find $s\sim1.3{-}1.4$ for C-type bows.

Densities or filling factors are a factor of 10 lower than in CepA. The gas is not fully molecular. Then (1) H-H₂ collisions maintain high 2-1/1-0 K-band ratios, as observed, and (2) the CO/H₂ line ratios are boosted in the models without an excessively high CO/H abundance (see also Nisini et al. 1999).

The spatially turbulent region of the southern lobe is characterised by very low CO/H2 flux ratios. The data here is of poor quality. If confirmed, then we suggest that this is most likely due to CO depletion onto grains.

The lower density in L1448 is consistent with the lower power of the outflow and luminosity of the protostar. For the N1 beam, we calculate a total shocked luminosity of 1.5 $L_{\odot}$ , and estimate a total shocked output from L1448 of $\sim$ 6 $L_{\odot}$ . The outflow mechanical luminosity is estimated at 6.5 $L_{\odot}$ (Barsony et al. 1998). It is most plausible that the mechanical and radiated luminosities should again be equal since L1448 is a Class0 protostar: the driving jets should be at their strongest (Smith 2000) and the energies which are transferred into heat and bulk motion are roughly equal in a shock.

The total power radiated in the molecular lines over the whole outflow is estimated from the overlapping LWS beams. Most of the radiation is predicted to be emitted in the mid-J CO lines originating from the J=3 to the J=10 levels (independent of the particular model). These lines were not observed by ISO. The total radiated power for the L1448 models is $\sim$ 0.9 $L_{\odot}$ , about 10% of the bolometric luminosity of the driving protostar (9 $L_{\odot}$ , Barsony et al. 1998). The mechanical luminosity is $\sim$ 3 $L_{\odot}$ . In a momentum-driven outflow, one expects that the shocked emission would equal the mechanical power supplied to the environment since the driving shocks are dissipative. We suggest that the protostar accretes non-uniformly, and hence ejects material non-uniformly. At present, the protostar is inbetween such pulsations. Then, during active phases the bolometric luminosity, followed by the shocked luminosity, could increase by a factor of perhaps 10. The mechanical luminosity, on the other hand, varies little since it is the power averaged over the outflow lifetime. That the ejections are pulsed is supported by the presence of CO bullets (Bachiller et al. 1998). It should be remarked, however, that extended dust emission associated with the outflow has a luminosity $\sim$ 6 $L_{\odot}$ . Hence, the estimates for either the mechanical or shock powers may be in error.

8 Implications and conclusions

8.1 CepheusA

8.2 L1448