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Shortcomings of the model
The shock model described here is not complete and do not, at the moment, include all known physical and chemical processes which are thought to be occuring in interstellar shocks. Below I list some examples.
• Geometry: in the 1D model, when the postshock gas has been compressed it remains compressed at a higher pressure than the preshock gas. In nature the postshock gas would diffuse into the surrounding medium seeking to equilibrate the pressure. This is especially important in J-type shocks where compression factors of more than 104 are predicted from the models. This could
in some cases lead to number densities greater than 1010 cm−3. It is unlikely that such high densities exist in the ISM, except in regions close to massive stars. In C-type shocks the problem is also important. Here the compression is not as high as in J-type shocks, but the compression remains for a much longer period of time. Therefore H2 emission, for example, may be over-estimated because the number density in the hot postshock gas is overestimated.
• Doubly ionized species: doubly ionized species are not included in the models, and they will probably not be included in the very near-future. For the work and observations presented here, this is not a big problem. The problem arises in J-type shocks with velocities greater than ∼60-70 kms−1, where temperatures reach more than a few 100 000 K. Thus at the moment the model is best adapted to reproduce molecular shocks.
• Grains: currently there is work in progress to treat the grains in a more realistic manner in the model. This is done by determining the 2D grain dynamics, including effects of grain inertia and charge fluctuations. In particular the gyration of charged grains around magnetic field lines is calculated (V. Guillet et al. in preparation).
Verifying model results
Sometimes a model will produce results that are not trustworthy or wrong. It is important to weed out models that do not produce credible results and to have methods to recognize whether a model result should be considered as faulty or not. The sources for wrong results are summarized here and detailed below:
• C- to J-type shock (sonic point; only valid for C-type shocks).
• No shock (pushed gas; only valid for C-type shocks).
• Unphysical results.
• Random, but persistent errors.
As the temperature in a C-type shock increases H2 will eventually be dissociated. When H2 dissociates the main coolant of the shock is removed causing a rapid increase in temperature. A sonic point forms which in effect turns the C-type shock into a J-type. The velocity at which this happens is called the critical velocity, 3crit . It is not possible to treat this in the models and it is not possible to predict 3crit analytically. Therefore if the input velocity is greater than 3crit the model will collapse. In this case the model always collapses at the point of maximum temperature. Hence all models where the last point contains the maximum temperature are excluded.
Strategy for reproducing observations
With the above discussed results and predictions it is possible to construct a strategy for reproducing observations effectively. Ideally the following constraints are possible to observe directly:
• Velocity: Proper motion and/or radial velocity.
• [FeII] emission.
• Shock width.
• Dynamical age.
• Absolute H2 brightness of at least one line.
• Line ratios of several H2 lines (excitation diagram).
The input parameters that we wish to determine are: shock type, shock velocity, preshock density, b, initial ortho/para ratio.
Absolute H2 brightness and H2 excitation diagram
The absolute H2 brightness and H2 line ratios depends on all five input parameters (shock type, preshock density, shock velocity, b, initial ortho/para ratio). Previously we have used the observational constraints to determine four of them, shock type, preshock density, shock velocity and b, it is now possible to determine the initial ortho/para ratio.
The above strategy is very idealized. In general it is necessary to have at least five constraints to determine the five input parameters. But even with five constraints it is not always possible to reproduce observations. There may be several reasons for this. First of all, the preshock density may be lower than the densities in the grid, the velocity higher, etc. Second of all, the shock may be a non-steady state C-type shock. In this case we may observe a shock that emits [FeII] emission indicating it is a dissociative J-type shock. But at the same time the H2 emission, which is primarily generated in the magnetic precursor, may indicate that we are observing a C-type shock. Or we may resolve the shock width, which clearly indicates a C-type shock. But, as is often observed, HH-objects are capped by atomic and ionic emission (such as [FeII] emission) and in the wake H2 emission is observed in C-type shocks.
All in all, a good common physical sense is needed when interpreting observations. Even though the grid proposes one model as a best-fit model, it may not necessarily be the best-fit model when considering all the data available. Examples of this is given in Chapter 6.
Table of contents :
1.1 Star Formation
1.1.1 Molecular clouds
1.1.2 Jets and outflows
1.1.3 Star formation in associations
1.1.4 Isolated star formation
1.2 H2 Molecule
1.2.1 Rovibrational transitions
1.2.2 Excited H2
1.2.3 Ortho/para ratio
1.3 H2 excitation mechanisms
1.3.1 H2 formation excitation
1.3.3 Photo-Dissociation Regions
1.4.1 Outflows in the BN-KL nebula
1.4.2 Central engine
1.4.3 Observations of H2 emission in OMC1
1.4.4 Distance to Orion
1.4.5 Magnetic field
1.5 BHR71 and BHR137
1.5.1 BHR71 outflow
1.5.2 BHR137 outflow
1.6 Star formation in the Large Magellanic Cloud
2 Theoretical shock models
2.1 Model description
2.1.1 Input parameters
2.1.2 Output parameters
2.1.3 Shortcomings of the model
2.2 Grid of models
2.2.1 Grid description
2.2.2 Model predictions
2.2.3 Verifying model results
2.2.4 Strategy for reproducing observations
2.3 3D model construction
2.3.1 Recipe for model construction
2.4 Concluding remarks
3 Observations of the Orion Molecular Cloud
3.1 Adaptive optics
3.1.1 Strehl ratio
3.2 Observation runs
3.2.1 CFHT December 2000
3.2.2 VLT/NACO-FP December 2004
3.3 Comparing emission maps of different lines
3.3.1 Image registration
3.3.2 Differential reddening
3.3.3 Atmospheric absorption
3.3.4 Relative calibration of line emissivities
3.3.5 Contamination from other lines
4 CFHT observations of OMC1: Results and discussion
4.1 o/p ratios and their relationship to v=1-0 S(1) and S(0)
4.1.1 Variations caused by differential extinction?
4.2 Observational constraints on models
4.3 PDR as a possible source of excitation
4.4 Shocks as a source of H2 excitation
4.4.1 C-type vs. J-type shocks
4.4.2 Different clases of data
4.4.3 Individual objects in region West
4.5 Concluding remarks
5 VLT observations of OMC1: Results and discussion
5.1 Comparison of CFHT and VLT data
5.1.1 Region West
5.1.2 Region North
5.1.3 Excitation temperature
5.2 2D bow shock model
5.2.1 Results and 2D model description
5.2.2 Shock model
5.2.3 Discussion of sources of error
5.2.4 Concluding remarks
5.3 Comparison with 3D bow shock model – a first iteration
5.3.1 Model input
5.3.2 Model results
5.3.3 Sources of Error
5.3.4 Next iteration
5.4 2D bow shock model of object 1
5.4.1 Observational results
5.4.2 2D model reproduction
5.5 Conclusion and outlook
6 VLT/ISAAC observations of BHR71 and BHR137
6.1 Observations and data reduction
6.2 H2 line results
6.3 Interpretation and discussion
7 Observations of N159-5, VLT/NACO
7.1 Observations and data reduction
7.2 H2 line results
7.3 Exciting source
7.4 Interpretation and discussion
7.5 Morphological model and comparison with galactic objects
8 Conclusions and outlook
8.1.1 Shock models
8.1.3 BHR71 and BHR137
A Legends for figures
B Model input and outputs
C Model results for classes A1, A2, B and C and objects 1, 2 and 3
List of Figures
List of Tables