Observations of the Orion Molecular Cloud 

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H2 Molecule

The hydrogen molecule, H2 is the most abundant molecule in the Universe. Since it is a homonuclear molecule it posseses no permanent dipole moment and rovibra-tional transitions are forbidden electric quadrupole transitions. This implies that the lifetime of H2 in rovibrationally excited states is high, typically of the order of a year (Wolniewicz et al. 1998). Even though heteronuclear excited molecules have much shorter lifetimes, they are at least four orders of magnitude less abundant. Therefore H2 remains one of the most observed molecules.

Rovibrational transitions

In this thesis we are only considering rovibrational transitions in the electronic ground state of H2, X1 +g. For rovibrational transitions we have the following se-lection rule for the rotational quantum number, J: ΔJ=0,±2. There are no selection rules for vibrational quantum numbers, v. The nomenclature for the rotational selec-tion rules is as follows
−2 S-branch
ΔJ = 0 Q-branch
+2 O-branch
Rovibrational transitions are located in the near- and mid-infrared (NIR and MIR, respectively) part of the spectrum. A transition is denoted by first writing the vibra-tional transition followed by the relevant branch and the lower rotational level. Thus the transition from v=1 to v=0, J=3 to J=1 is written v=1-0 S(1). In this thesis the main focus is put on the three rovibrational transitions v=1-0 S(0), v=1-0 S(1) and v=2-1 S(1). In Table 1.2 some properties of these transitions are given. Because the molecule is light, the energy levels are widely spaced. For example the v=0, J=1 level has an energy of 170 K. The energy difference between the v=0, J=2 and J=0 levels is 510 K, which corresponds to the lowest rovibrational transi-tion, v=0-0 S(0) at 28 m. As we will see below, this implies that a high kinetic temperature is required to collisionally excite H2.

Excited H2

Consider a gas consisting of H2 molecules. We assume that the gas is in local ther-modynamic equilibrium (LTE). This implies that the level population distribution is a Boltzmann distribution and that for a given level i, the population is ni ∝ gI gJ exp Ei , (1.2.1) −kBT where gI gJ is the level degeneracy (see below), Ei the energy of the level, kB the Boltzmann constant and T the temperature. If the populations of two levels are known from observations, it is possible to calculate a corresponding temperature, the excitation temperature, Tex. If the H2 gas is in LTE, the excitation temperature corresponds to the kinetic temperature. In the interstellar medium this is typically not the case because of the low density.
If we assume that the line is optically thin for a given H2 line, it is possible to calculate the column density, N from the observed line brightness, I. The probability for spontaneous emission is given by the Einstein A-coefficient. The column density of the upper level is given by:
N = 4πλ I . (1.2.2)
hc A
To estimate whether the assumption that the line is optically thin, we may calculate the optical depth, τ, for a transition between an upper and lower level:
τ = A 1 gu λ3N , (1.2.3)
8π 3 g
where 3 is the line width and gu,l is the degeneracy of the upper and lower level. For the v=1-0 S(1) transition we find τ = 3.07 ×10−24 N[H2 (cm−2)] (1.2.4) 3 (km s− 1 )
In OMC1 the total H2 column density is of the order of 1022 cm−2 (e.g. Masson et al. 1987; Genzel & Stutzki 1989; Rosenthal et al. 2000) and v=1-0 S(1) linewidths are of the order of ∼30 km s−1 (e.g. Chrysostomou et al. 1997). The optical depth is ∼10−3. Therefore the assumption that the line is optically thin to H2 emission is fulfilled. Typically only dust grains will prevent H2 emission from escaping the gas.
To evaluate the state of the gas, it is often usefull to make a Boltzmann plot or excitation diagram. In such a diagram log(N/gI gJ ) is plotted versus the upper level energy. If the gas is in LTE the points will lie on a straight line with a slope of −1/T according to Eqn. 1.2.1. If the gas is not in LTE, the points will typically lie on a curve and display a range of excitation temperatures.

Ortho/para ratio

H2 is a diatomic, homonuclear molecule, and as such the total nuclear spin will be either I=0 or 1 corresponding to the nuclear spins being anti-parallel or parallel, respectively. The degeneracy caused by the nuclear spin is given by gI =2I+1 and is thus either 1 or 3. The rotational degeneracy is gJ =2J+1. The total wave-function of the molecule must be anti-symmetric which means that if the nuclear spins are anti-parallel the rotational quantum number must be even and vice versa. These two states are known as para-H2 and ortho-H2 respectively. For any H2 molecule it is only possible to change the rotational quantum number, J, by 0 or ±2, so if a H2 molecule is in the para-state, it will remain there, unless it exchanges a proton with another species (e.g. H, H+, H+3; see below). The same is true for ortho-H2 .
In the high temperature limit the LSE ortho/para ratio is equal to 3. This is illustrated in Fig. 1.2 where it may be seen that for temperatures greater than ∼300 K the ortho/para ratio is equal to 3. As it is possible to determine an excitation temperature observationally, so it is also possible to determine an ortho/para ratio observationally by using a Boltzmann diagram. If the ortho/para ratio is different from 3, the high temperature LSE value, ortho-points will be displaced with respect to their para-counterparts. The amplitude of the displacement will give the ortho/para ratio. If the displacement is independent of the level, then the measured ortho/para ratio will be equal to the total ortho/para ratio. In general this is not the case in the interstellar medium.
In this case it is necessary to evaluate the ortho/para ratio for each level. For a given level, (v,J), this is done by first calculating the excitation temperatu re from the levels (v,J−1) and (v,J+1). This temperature is then inserted into Eqn. 1.2.5 and the ortho/para ratio is calculated (Wilgenbus et al. 2000).
It is only possible to change the ortho/para ratio through reactive collisions in-volving proton exchange reactions. According to Schofield ( 1967) the exchange re-action between H2 and H shows an activation energy of ∼3900 K and is therefore insignificant in the cold interstellar medium. In a cold dark cloud, only slow ex-change reactions with H+, H+3 and other protonated species will occur (Flower et al. 2006). In a cold dark cloud with T = 10 K, density nH = 105 cm−3, cosmic ray ionization rate 5×10−17 s−1 per H atom and an initial degree of ionization of ∼10−8 it will take more than 107 years to go from an ortho/para ratio of 3 to the equilibrium value at 10 K of ∼2×10−3 as illustrated in Fig. 1.3. The conversion timescale is only weakly dependent on density.
In hot gas it is possible to overcome the activation energy barrier, and exchange reactions with H are the most efficient method for interconversion. In Sect. 2.2.2 we show that this process will become efficient at kinetic temperatures greater than ∼800 K.

H2 excitation mechanisms

It is possible to excite H2 in one of three ways (e.g. Tielens 2005; Habart et al. 2005):
1. Formation excitation, in which a H2 molecule is formed in an excited state
2. Collisional excitation, where the gas is heated, and collisions with other molecules excite H2
3. Radiative excitation, where the gas is subjected to a strong radiation field and H2 molecules are excited by absorbing this radiation
In the following I will briefly go through each of these three m echanisms. Of the three mechanisms I will focus on collisional excitation, as this is the main interest of this thesis.

H2 formation excitation

The binding energy of H2 is ∼4.5 eV or ∼51 000 K. This binding energy is divided between the grain (internal heating), kinetic energy of the H2 and internal energy in H2 (i.e. the molecule is formed in a rovibrationally excited state). At the moment several experiments are underway to determine how the binding energy is partitioned among the constituents, and in particular what the internal energy distribution is and what the ortho/para ratio is.
In cold molecular clouds H2 is formed on the surface of ice-covered dust grains, the ice is primarily composed of H2O and CO. Experiments have already shown that the formation of H2 may proceed quite rapidly on ice surfaces (e.g. Manicò et al. 2001; Hornekær et al. 2003; Perets et al. 2005; Amiaud et al. 2 007).
In hot regions, such as close to stars or in shocks, the icy mantles covering the dust grains will evaporate. Therefore it is also necessary to perform the experiments on grain surfaces that simulate bare grains, such as silicate and carbonaceous sur-faces. This is also currently a work in progress (e.g. Pirronello et al. 1997a,b; Perry & Price 2003; Hornekær et al. 2006).
The energetics of the formation process has been measured by different groups, both on bare grain analogues and ice-covered grain analogues (e.g. Hornekær et al. 2003; Creighan et al. 2006; Amiaud et al. 2007). Very recently the ortho/para ratio of newly formed H2 has also been measured (Amiaud et al. 2007, F. Dulieu, priv. comm.).
In principle it should be possible to observe the formation excitation directly in cold dark clouds. As mentioned previously, H2 lines are optically thin under inter-stellar conditions, so any H2 emission will escape the gas. Several surveys have been performed of dark clouds, but so far without results (Tiné etal. 2003, and references therein).

Shocks

A shock may be defined as  » any pressure-driven disturbance which is time-independent (in a co-moving reference frame) and which effects an irreversible change in the state of the medium » (Draine 1980). A more popular definition of a shock is that it is a « hydrodynamical surprise » (Chernoff 1987). For a few reviews of shock physics and chemistry I refer the reader to e.g. Draine (1980); McKee & Hollenbach (1980); Chernoff (1987); Hollenbach et al. (1989); Hollenbach & McKee (1989); Draine & McKee (1993); Hartigan (2003).
Rankine-Hugoniot Equations
The Rankine-Hugoniot equations are the fundamental equations describing how physical properties of a medium change across a shock front. The derivation of the equations is made by assuming the shock-front is infinite and plane-parallel. Using the conservation laws for mass (ρ), momentum and energy flux over the shock front it is now possible to derive the following equations (subscript 1 denotes the pre-shock zone and 2 the post-shock zone):
ρ1 31 = ρ2 32 (1.3.1)
ρ 32 + p = ρ 32 + p (1.3.2)
1 1 1 2 2 2
ρ 3 1 U 1 + p 3 1 + 1 ρ 33 = ρ 3 2 U 2 + p 3 2 + 1 ρ 33 , (1.3.3)
where p is the pressure, U is the internal energy of the molecules and 3 the velocity of the flow in the reference frame of the shock. The first equati on (1.3.1) concerns the conservation of mass across the shock front, the second (1.3.2) the conservation of momentum and the third (1.3.3) the conservation of energy.
The above equations are only valid in the absence of a magnetic field. In the presence of a magnetic field the Rankine-Hugoniot equations are somewhat modified (e.g. de Hoffmann & Teller 1950; Draine 1980).
J-Type versus C-Type Shocks
In the absence of a transverse magnetic field neutral particl es (atoms, molecules and grains) and charged particles (ions, electrons and grains) all behave in the same way, as a single-fluid medium with the same velocity and temperatu re. It is impossible for the medium in the preshock zone to receive information about the shock-front, as the shock-front is moving at a supersonic speed. Thus the temperature and density changes over a distance corresponding to the mean free path of the particles. This type of shock is called a jump-type shock (J-type), as the change in temperature and density resembles a discontinuity. In the post-shock zone the medium cools under constant pressure.
Introducing a non-zero transversal magnetic field will sepa rate the constituents into neutral, positively and negatively charged particles and it behaves as a multifluid medium. In a multifluid medium the charged particles couple t o the magnetic field and they will gyrate around the magnetic field lines. The neut ral particles are not directly affected by the magnetic field, only through collisions with cha rged particles. Charged dust grains will also couple to the magnetic field.
A mechanical signal can propagate at several distinct velocities: The sound speed, cs, the Alfvén velocity,3A and the ion magnetosonic speed, 3ims. The sound speed is c = γkBT , (1.3.4)  where γ is the heat capacity ratio (5/3 for a monatomic gas and 7/3 for a diatomic gas), kB Boltzmann’s constant, T the temperature and the mean molecular weight. cs is typically less than ∼1 km s−1 in a cold dark cloud. The Alfvén velocity is given as (Alfven 1950)
B2 (1.3.5)
3A = , 4πρ
where B is the transverse magnetic field strength and ρ the density. In a cold dark cloud it is of the order of a few km s−1. Similarly the ion magnetosonic speed is given as
B2 (1.3.6)
3ims = , 4πρi
where ρi is the ion density. A typical value is ∼1000 km s−1 in a cold dark cloud. For small transverse magnetic fields the shock still contain s a J-type shock front, because, even though the charged particles react to the magnetic field and form mag-netic precursors, the neutral particles will not have time to recouple to the ions before the arrival of the discontinuity. When the magnetic field sur passes a critical value, Bcrit the neutrals have time to recouple to the ions (Draine 1980). When the magnetic field strength is greater than Bcrit the precursor is long enough that the neutrals do not undergo a discontinuity, and the shock is now a continuous (C) type shock. This evolution is illustrated in fig. 1.4, where a J-type shock progresses into a C-type shock as the magnetic field increases. The value of Bcrit can only be determined analytically for adiabatic shocks.
In a C-type shock the shock velocity must be greater than the Alfvén velocity and the local sound speed. Otherwise information about the arrival of the shock front is directly relayed to the neutrals and the gas will only be pushed, not shocked. In fact in the reference frame of a C-type shock, the gas flow is always su personic. Information about the shock front can travel faster than the shock through the charged particles if the shock speed is lower than 3ims. The information is then relayed to the neutral particles through collisions with the charged particles.
The magnetic field is usually assumed to be frozen into the int o the charged particles (Draine 1980). The parametrization of the preshock transverse magnetic field is B0 = b × nH (cm−3) Gauss, (1.3.7) where nH is the number density of the ambient medium in units of cm−3, and b is the magnetic scaling factor. In the interstellar medium b is typically 0.1–3 (Draine 1980). This relation has been validated for regions with densities higher than ∼103 cm−3 both through observations (e.g. Troland et al. 1986; Crutcher & Troland 2007; Crutcher 2007) and simulations (e.g. Padoan & Nordlund 1999).
The heating associated with the passing of a shock wave causes excitation and (possibly) dissociation of H2. The main coolant in the wake of a shock is H2. If 2 is dissociated, the gas temperature will increase rapidly because the main coolant is lost. The sound speed increases as T so the temperature increase leads to an increase in sound speed. However, as the sound speed increases rapidly the gas flow will become subsonic in the reference frame of the shock. The point of transition between super- and subsonic gas flow is known as a sonic point. During such a transition, the C-type shock will collapse into a J-type shock.
Figure 1.4: Evolution from a J-type shock to a C-type shock by increasing the magnetic field. In the top panel (a) there is no mag-netic field, and the shock is a J-type shock. Increasing the mag-netic field causes the origin of magnetic precursors, and when the magnetic field is larger than some critical value, the shock is a C-type shock. L is the typical length scale. Velocities are given in the restframe of the shock-front (Draine 1980).
Jets, outflows and bow shocks
Shock waves in the interstellar medium are observed through their cooling mech-anisms. The origin of these shock waves includes numerous phenomena such as supernova explosions, supersonic turbulent motion (which again may originate in different ways), cloud-cloud collisions, jets and outflows from young stellar objects or from active galactic nuclei. In this thesis I only consider shock waves originating in young stellar objects.
Shock waves may either be created by jets impinging in the ambient material or by bullets which are individual clumps of gas moving at supersonic velocities. In both cases the shock wave will take the shape of a bow as preshock material is being shocked and pushed aside.
At the head of the bow the shock speed will be at a maximum leading to a max-imum in temperature. Often, but not always, the shock at the tip of a bow shock will be a dissociative J-type shock. The main coolants are then atomic or ionic, as molecules have been dissociated. Further down the wings the shock velocity will decrease. This leads to a decrease in temperature. In this part of the shock the molecules will not dissociate and they will be the dominants coolants. This is illustrated in Fig. 1.5 and has been observed in a number of objects, e.g. several Herbig-Haro (HH) objects (Bally et al. 2007, and references therein) and the Orion bullets (Allen & Burton 1993).
If the shock wave is generated by a jet, the structure is more complex as illustrated in Fig. 1.6. We here follow the description outlined in Raga & Cabrit (1993). As the jet reaches the ambient medium it is slowed down. However as material from the jet is continuously flowing from behind the shock surface at a velocity 3s, this creates an internal working surface (also known as the Mach disk) where the jet is pushing from behind and the ambient material is pushing from the front. The trapped material is ejected sideways and interacts with the ambient gas. The ejected material will form a bow shock on the outside and a jet-shock on the inside. In between the two is a mixing layer consisting of a mixture of the jet material and the ambient gas. The mixing layer expands and fills the cavity created by the bo w shock.
Shock velocity
Observationally, it is often difficult to measure the shock velocity. While it is rela-tively straightforward to measure the velocity of an object, 3obj, through radial ve-locity and proper motion studies, this is typically not the shock velocity, 3s. If the preshock medium is moving at a certain velocity, 3pre with respect to the shock wave, the shock velocity is given as 3s = 3obj − 3pre .
This has been observed with knots of excitation in protostellar jets, where the preshock gas has been swept up by previous shocks, and is then being overrun by new shock waves (e.g. Arce & Goodman 2002). It has also been observed in large scale outflows, where an initial outflow accelerates the surr ounding gas. Outflow events following the initial one will then encounter the postshock gas of the first shock wave, and the shock velocity is lower than the observed velocity of the shock wave. this has been observed in planetary nebulae (e.g. NGC 7027; Latter et al. 2000) and regions of massive star formation (e.g. OMC1; Stone et al. 1995, and see below, Sect. 1.4).
Models
Some of the first shock models created were published in 1977 ( Hollenbach & Shull 1977; Kwan 1977; London et al. 1977). These were all planar J-type shock models. Later Draine (1980) introduced C-type shocks and provided the first planar C-type shock model (Draine & Roberge 1982; Draine et al. 1983). Over the years several groups have published planar shock models, but a general review is considered be-yond the scope of this thesis. The shock model used in this work was first described in Flower et al. (1985) and most recently in Flower et al. (2003) and Flower & Pineau des Forêts (2003).
What is common for these models is that they model a 1D plane-parallel shock front impinging on a preshock medium. In the model the MHD equations are in-tegrated and typically the chemistry is rather extended with at least several tens of different chemical species linked by hundreds of reactions. Because the models are 1D, it possible to calculate the models self-consistently (see Chapter 2 for details).
It is also possible to put more emphasis on the 2D or 3D geometry rather than the detailed physical and chemical modelling. Usually the chemistry is rudimentary at best. For examples of this type of model, see e.g. Smith et al. (2003); Raga et al. (2002); Smith & Brand (1990) for 3D models or e.g. Raga & Cabrit (1993); Lee et al. (2001); Ostriker et al. (2001); Lim et al. (2002); Fragile et al. (2005) for 2D models. 1D models have also been combined to produce 2D or 3D models. This has previously been done by e.g. Smith & Brand (1990); Smith et al. (2003). Here we will also construct a 3D model from 1D models, this is the subject of Sect. 2.3.

Photo-Dissociation Regions

Another important excitation mechanism of H2 in the interstellar medium is found in photodissociation regions or photon dominated regions (PDRs). Here the UV and far UV radiation fields of massive OB stars are strong enough t o excite a substantial part the surrounding molecular gas. Close to massive stars the gas is ionized and we find the bright HII regions. As we move away from the star the radiation field weakens and at a certain point H recombination is more effective than ionization.

Table of contents :

1 Introduction 
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
1.3.2 Shocks
1.3.3 Photo-Dissociation Regions
1.4 Orion
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
1.7 Outline
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
2.1.4 Future
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
5.1.4 Conclusion
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
5.4.3 Conclusion
5.5 Conclusion and outlook
6 VLT/ISAAC observations of BHR71 and BHR137 
6.1 Observations and data reduction
6.2 H2 line results
6.2.1 BHR71
6.2.2 BHR137
6.3 Interpretation and discussion
6.3.1 BHR71
6.3.2 BHR137
6.4 Conclusion
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
7.6 Conclusion
8 Conclusions and outlook 
8.1 Conclusions
8.1.1 Shock models
8.1.2 OMC1
8.1.3 BHR71 and BHR137
8.1.4 N159-5
8.2 Outlook
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
D Publications
List of Figures
List of Tables
Bibliography

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