<figure><img src="image_1.png" /></figure>

# Dynamics of the galactic matter cycle

Pierre Lesaffre

► To cite this version:

Pierre Lesaffre. Dynamics of the galactic matter cycle. Astrophysics [astro-ph]. Observatoire de Paris
- PSL, 2018. tel-04418186

HAL Id: tel-04418186

https://hal.science/tel-04418186

Submitted on 25 Jan 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Observatoire de Paris - PSL Research University
Unité Formation-Enseignement

MÉMOIRE D'HABILITATION À DIRIGER DES
RECHERCHES

présenté par
PIERRE LESAFFRE

DYNAMICS OF THE GALACTIC MATTER CYCLE

Soutenu le 14 février 2018 devant le jury composé de:

<table><tr><td>Mme</td><td>Sylvaine TÜRCK-CHIÈZE</td><td>Rapportrice</td></tr><tr><td>Mme</td><td>Katia FERRIÈRE</td><td>Rapportrice</td></tr><tr><td>M.</td><td>Romain TEYSSIER</td><td>Rapporteur</td></tr><tr><td>M.</td><td>Jens NIEMEYER</td><td>Examinateur</td></tr><tr><td>M.</td><td>Édouard AUDIT</td><td>Examinateur</td></tr><tr><td>M.</td><td>Jacques LASKAR</td><td>Président</td></tr></table>

Laboratoire de Radioastronomie
École Normale Supérieure & LERMA, Observatoire de Paris,
CNRS UMR 8112
24 rue Lhomond, 75231 Paris Cedex 05
Foreword & Acknowledgements

I write this manuscript to apply for the right to supervise PhD students. I view this exercise very differently to writing a PhD thesis or a paper. This is not going to be a document of reference, and I apologies in advance if your work is not cited, or if you cannot find extended and exhaustive introductions to the variety of subjects I tackle here. I will not dwell on lengthy descriptions of the shoulders of giants on which I am standing, but I will rather paint the view I get from up there. This is an account of some of the most daring, craziest and fuzziest ideas I entertain, of some of the incomplete works I undertook and where I feel they can lead, as well as a map of the very clear paths I see laying ahead, leading to almost certain progress. All these could germinate and grow in a PhD student's hands depending on his/her affinity with this or that subject, and I would be happy to accompany him/her along.

I also mean this account of my research projects as a hommage to Jean-Pierre Chièze, my first guide on the convoluted trails of research. Jean-Pierre had a unique way of looking at physics and shared it generously with the young ones. His style in a classroom was inimitable: he staged physical phenomena as in a play and brought illuminating connections to life between transverse fields of research. He had a good sense of humour and self-derision, emphasised by his talent for making a miraculous tale out of the least story. He was some sort of a Cyrano de Bergerac brought to life. This love of the nice and well balanced sentence, he shared with my dad, to whom I also want to pay tribute here, as he passed away while I was writing this document. Although neither mom nor dad are scientists, they both conveyed to me simple but solid life principles which greatly helped me as a researcher: willfulness, awareness of others. keeping the objective in sight, do what you love, love what you do, be true to yourself. Dad was a pionneer of sustainability and effectiveness of action in developing countries. The Inter-Aide chart, now signed by many other NGOs, summarises well his legacy. Its primary item is that field work must take precedence over collecting funds. This explains my conviction that researchers should be funded on what they do rather than on what they claim they are going to do... but that's another
story.

Next, I want to deeply thank all my friends and collegues who helped
me in this work. To grind at the unknown can sometimes be a strenuous
and tedious task. But to be on the road with so many great companions
is a bliss. I apologise for not citing them all here, and I mean not only all
my co-authors, but also the students, office mates, computer system guys
and last but not least the administrative staff who strive to make our work
environment viable despite ever increasing bureaucratic constraints. Special
thanks go to Antoine Gusdorf who proof read the whole manuscript and Edith
Falgarone who checked the chapter on dissipation. They provided invaluable
comments which no doubt contributed to the quality of the present document
(I stand responsible for the defects). François Levrier and my daughter Claire
helped me with the layout.

Finally, I apologise to the french reader for writing in english, and to the
english reader for writing in frenglish. My french writing is usually more
fluent, but I reckoned this document might be useful to a broader panel of
readers if written in english.
# Contents

<table><tbody><tr><td>1</td><td>Introduction: fluid dynamics throughout the galactic cycle</td><td>9</td></tr><tr><td>1.1</td><td>Summary</td><td>9</td></tr><tr><td>1.2</td><td>Fluid dynamics</td><td>11</td></tr><tr><td>1.2.1</td><td>Single fluid dynamics</td><td>11</td></tr><tr><td>1.2.2</td><td>Multi-fluid dynamics</td><td>12</td></tr><tr><td>1.2.3</td><td>Ambipolar diffusion regime</td><td>13</td></tr><tr><td>1.3</td><td>Physical scales and dimensionless numbers</td><td>14</td></tr><tr><td>1.4</td><td>Thermochemistry</td><td>18</td></tr><tr><td>1.5</td><td>Outline</td><td>20</td></tr><tr><td>2</td><td>Instabilities</td><td>21</td></tr><tr><td>2.1</td><td>Magneto-rotational instability (MRI)</td><td>22</td></tr><tr><td>2.2</td><td>Convective instability</td><td>25</td></tr><tr><td>2.3</td><td>Thermal instability</td><td>28</td></tr><tr><td>3</td><td>Mixing</td><td>31</td></tr><tr><td>3.1</td><td>Prescribed mixing at cloud interfaces</td><td>32</td></tr><tr><td>3.2</td><td>Self-consistent mixing in stellar interiors</td><td>34</td></tr><tr><td>4</td><td>Dissipation</td><td>39</td></tr><tr><td>4.1</td><td>Intermittency</td><td>40</td></tr><tr><td>4.2</td><td>Dissipation in MHD</td><td>43</td></tr><tr><td>4.3</td><td>Dissipation impact on thermochemistry in 2D turbulence</td><td>46</td></tr><tr><td>5</td><td>Time-dependence and quasi-steadyness</td><td>53</td></tr><tr><td>5.1</td><td>Steady-state in shocks</td><td>54</td></tr><tr><td>5.2</td><td>Quasi-steady state in shocks</td><td>57</td></tr><tr><td>5.3</td><td>Quasi-static star formation</td><td>58</td></tr><tr><td>5.4</td><td>Steady inviscid hypersonic flows</td><td>60</td></tr><tr><td>5.5</td><td>Chemical networks optimisation</td><td>61</td></tr></tbody></table>
6 Conclusion 65

7 Curriculum vitae 75

8 Note d'accompagnement 81

8.1 Encadrement informel 81

8.2 Encadrement formel 82

8.2.1 Stagiaires M1 et M2 82

8.2.2 Thésards 82

8.3 Vulgarisation scientifique 83

8.4 Organisation d'événements scientifiques 84

8.5 Enseignement 85

8.6 Animation scientifique 86
List of Figures

<table><tbody><tr><td>1</td><td>Our Galaxy as seen from the Sun</td><td>9</td></tr><tr><td>2</td><td>The galactic cycle in a density-temperature diagram</td><td>15</td></tr><tr><td>3</td><td>Convective instability in a saucepan</td><td>21</td></tr><tr><td>4</td><td>Rendering of 3D simulations of MRI</td><td>24</td></tr><tr><td>5</td><td>Comparison of reduced models and simulations of MRI.</td><td>25</td></tr><tr><td>6</td><td>Convective models vs numerical simulations</td><td>28</td></tr><tr><td>7</td><td>Density maps in simulations of thermal instability</td><td>30</td></tr><tr><td>8</td><td>Pouring milk in your tea.</td><td>31</td></tr><tr><td>9</td><td>Bioluminescent plankton as probe of energy dissipation</td><td>39</td></tr><tr><td>10</td><td>Intermittency models vs wind tunnel data</td><td>41</td></tr><tr><td>11</td><td>Cuts and maps of dissipation in simulations and for a β-model</td><td>42</td></tr><tr><td>12</td><td>Comparison between observation synthesis and dissipation maps</td><td>44</td></tr><tr><td>13</td><td>Chemical evolution in decaying 2D turbulence</td><td>47</td></tr><tr><td>14</td><td>Dissipation map in 2D decaying turbulence</td><td>51</td></tr><tr><td>15</td><td>Steady shock modeling in 2D decaying turbulence</td><td>52</td></tr><tr><td>16</td><td>Water flows from taps</td><td>53</td></tr><tr><td>17</td><td>Spiraling shock in a binary wind</td><td>63</td></tr><tr><td>18</td><td>Two water flows collide</td><td>64</td></tr><tr><td>19</td><td>Une vue du centre ICISE de nuit.</td><td>87</td></tr></tbody></table>
# Chapter 1

## Introduction: fluid dynamics throughout the galactic cycle

<figure><img src="image_3.png" /><figcaption>Figure 1: Our Galaxy as seen from the Sun in the visible wavelength range (credits ESO): an island of stars and gas in the intergalactic darkness.</figcaption></figure>

### 1.1 Summary

My research activity is devoted to the interplay between fluid motions and their thermal and chemical evolution. This coupling is at the heart of a great range of astrophysics puzzles and I lead you here through a brief round trip through the galactic cycle to emphasise where it matters.
Stars, etymologically the main objects of study of astrophysics, are the melting pots of almost all the elements as we know them today. Most atoms which compose our familiar environment on earth have been processed through stars. Stellar nucleosynthesis involves boiling motions for which the models we have at hand are still rather crude: most stellar evolution models today include a mixing length theory prescription which is not too far from the original work by Böhm-Vitense (1958). But even this simple prescription has allowed a tremendous progress in our understanding of the life of stars and their chemical yields into the Galaxy. A notable exception, however, is the simmering phase preceding thermonuclear supernovae explosion, for which there existed not even a valid descriptive model a few years ago. Stellar winds throughout the stars life and their final explosion release into the interstellar medium (ISM) the newly made elements along with some thermal and mechanical energy. This kinetic and magnetic energy input is degraded to turbulence which helps to stir the fresh gas and mix it with its environment. The dissipation of these complex motions is likely to happen in a very small fraction of the volume, into tiny hot spots where the temperature may help to assemble more complex molecules, which produce a variety of tracers we observe from earth. Some of the chemical elements in the ISM are very efficient coolants which force the gas to condense from place to place and shape it into molecular clouds. When the thermal or magnetic support of the gas becomes so weak that it cannot resist gravitational collapse, a new generation of stars will eventually be born, thus closing the cycle of galactic matter. As molecular cloud material gathers towards its gravitational collapse, key chemical reactions such as deuteration can be used by observers as a clock to time the star formation process. Around the newly formed stars, the gas which could not get rid of its angular momentum orbits in a disc. The ionisation degree which results from the chemistry in these discs is critical for their further dynamical evolution. Indeed, free electrons and ions are necessary to couple the gas to the magnetic field, an essential mediator for the angular momentum transport. Sufficiently ionised regions will get rid of angular momentum and plummet onto the star, but neutral regions will continue to orbit and form solid bodies and planets, thus leaking some of the material out of the galactic cycle.

Throughout this cycle of matter in our Galaxy, chemistry and temperature control the magnetised fluids' motions, and in return these dynamics imprint the chemical composition and thermal state of the gas. Thus, fluid dynamics and thermochemistry are strongly connected to each other, although each one has its own characteristics.
## 1.2 Fluid dynamics

Fluid dynamics is all about conservation of mass, momentum and energy, with a hint of microscopic transport at the smallest scales, at the limit where the fluid approximation itself becomes questionable. This section introduces only a minimal set of the equations required to model fluid dynamics throughout the galactic matter cycle. In particular, I will not consider here the dynamics of the cosmic rays or the dust grains, which other authors would consider as crucial actors (and rightly so !). On the other hand, the set of equations I present here should cover most of the background needed to appreciate my own work.

### 1.2.1 Single fluid dynamics

The equations of compressible fluid dynamics (Navier-Stokes) apply to most astrophysical fluids. The conservation of mass and momentum are expressed as

$$ \partial_t \rho + \partial_i (\rho u_i) = 0 \qquad (1.2.1) $$

$$ \partial_t \rho u_i + \partial_i (\rho u_i u_j + p \delta_{ij} + \nu \rho S_{ij}[u]) = \rho \partial_i \Phi \qquad (1.2.2) $$

where $\rho$ is the mass density, $u_i$ are the component of the velocity vector in a Cartesian frame, $p$ is the pressure, $\delta_{ij}$ is the Kronecker symbol (I use Einstein's summation convention), $\nu$ is the viscous coefficient, I use $\partial_t$ and $\partial_i$ to denote derivation with respect to time and the $i$-th space coordinate, and I have included the gravitational field $\Phi$ for completeness. The viscous stress tensor takes the form:

$$ S_{ij}[u] = \frac{1}{2}(\partial_i u_j + \partial_j u_i) - \frac{1}{3}\partial_k u_k \delta_{ij}. \qquad (1.2.3) $$

I postpone the energy conservation equation on purpose: I will present heating and cooling processes in section 1.4 as part of the thermochemical evolution. These first two equations govern the trajectories of fluid particles. One can integrate them provided $\nu$ and $p$ are known. In most situations of interest $\nu$ can be considered constant (although in principle it depends on temperature and mass density). For an isothermal or a polytropic gas, the pressure $p$ depends only on the mass density $\rho$ and the above system is closed. But in general, pressure requires the knowledge of the temperature $T$ and the chemical composition $\{X_k\}_{1,...,N}$ (the set of mass fractions of all chemical components) in addition to the mass density $\rho$. Hence thermochemistry needs to be solved coupled to fluid dynamics. For stellar mixtures, the
equation of state which provides $p$ can be quite complicated, but in the case of the ISM, the ideal gas equation of state makes a very good approximation:

$$p(\rho, T, \{X_k\}_{k=1,...,N}) = \frac{\rho k_B T}{\mu(\{X_k\}_{k=1,...,N})} \quad (1.2.4)$$

where $k_B$ is the Boltzmann constant and $\mu(\{X_k\}_{k=1,...,N})$ is the mean molecular weight.

If it were not for the pressure and dissipation coefficients, the temperature and chemical composition could be considered as completely *passive* scalars. If that were the case, the evolution of the quantities $(T, \{X_k\}_{k=1,...,N})$ could be computed *after* the fluid dynamics has been solved for, or even assuming a prescribed dynamical background. Thus the temperature and chemical composition are *active* scalars only through their backreaction on the pressure or on the values of the dissipative coefficients. For example, the gas cooling in molecular clouds can bring motion into supersonic regimes and generate shocks. In another example, a varying ionisation degree can dynamically stabilise or destabilise magnetised regions in protoplanetary discs (see section 2.1).

### 1.2.2 Multi-fluid dynamics

In a dilute magnetised fluid such as the ISM, the ionised and neutral components of the fluid do not experience the same external forces because charged particles feel the Lorentz force while the neutrals do not. This induces a drift velocity between the velocities of the charges $v$ and that of the neutrals $u$. Momentum conservation has to be expressed for both fluids independently:

$$\partial_t \rho u_i + \partial_i (\rho u_i u_j + p \delta_{ij} + \rho \nu S_{ij}[u]) = F_{in}(v_i - u_i) - \rho \partial_i \Phi \quad (1.2.5)$$

and

$$\partial_t \rho_c v_i + \partial_i \left( \rho_c v_i v_j + \left(p_c + \frac{B^2}{8\pi}\right) \delta_{ij} + \frac{B_i B_j}{4\pi} \right) = F_{in}(u_i - v_i) - \rho_c \partial_i \Phi \quad (1.2.6)$$

where $\rho_c$ is the density of charges, $B$ is the magnetic vector field, and $F_{in}$ is the rate of momentum exchange between the charged and neutral fluid. The gravitational field obeys the Poisson equation:

$$\partial_i \partial_i \Phi = -4\pi G(\rho + \rho_c). \quad (1.2.7)$$
The conservation of the total mass of the fluid now becomes:

$$ \partial_t(\rho + \rho_c) + \partial_i(\rho u_i + \rho_c v_i) = 0 \qquad (1.2.8) $$

but $\rho$ and $\rho_c$ can exchange mass via charge exchange, ionisation or recombination reactions.

The induction equation describes the evolution of the magnetic field attached to the charged fluid:

$$ \partial_t \mathbf{B} - \nabla \times (\mathbf{v} \times \mathbf{B} - \eta \nabla \times \mathbf{B}) = 0 \qquad (1.2.9) $$

where $\eta$ is the resistive dissipation due to electron-ion currents (we neglect Hall currents here, but they may play a rôle in accretion discs, for example). Only Ohmic resistivity can dissipate and reconnect magnetic fields: without it they will be distorted, dispersed, stretched, compressed and entangled as they flow along the charged fluid, but they will never be destroyed! In the case of the ISM, Ohmic resistivity is so small (see below, section 1.3) that it is actually hard to understand how the growth of magnetic fields can be impeded: this would require very thin current sheets, and presumably quite violent reconnection events.

### 1.2.3 Ambipolar diffusion regime

Ambipolar diffusion results when equation (1.2.9) is written with the velocity of the neutrals $\mathbf{u}$ rather than with that of the charges:

$$ \partial_t \mathbf{B} - \nabla \times (\mathbf{u} \times \mathbf{B} + (\mathbf{v} - \mathbf{u}) \times \mathbf{B} - \eta \nabla \times \mathbf{B}) = 0. \qquad (1.2.10) $$

The drift velocity is recovered when neglecting the inertia of charges (i.e.: by setting $\rho_c \ll \rho$) in their momentum evolution equation (1.2.6):

$$ \mathbf{v} - \mathbf{u} = \mathbf{J} \times \mathbf{B} / F_{in} \qquad (1.2.11) $$

with $\mathbf{J} = \frac{1}{4\pi} \nabla \times \mathbf{B}$ as the magnetic current vector, which allows to rewrite the induction equation as

$$ \partial_t \mathbf{B} - \nabla \times \left( \mathbf{u} \times \mathbf{B} + \frac{1}{F_{in}} (\mathbf{J} \times \mathbf{B}) \times \mathbf{B} - \eta \nabla \times \mathbf{B} \right) = 0. \qquad (1.2.12) $$

One uses this equation along with conservation equations for charges and neutrals combined as a single fluid equation: this constitutes the ambipolar diffusion regime, appropriate when the ions inertia is negligible before that of
the neutrals. This approximation is valid throughout most of the low-ionised interstellar medium. It is distinct from the often used (but in my opinion less appropriate) *heavy ions* approximation which consists in using the two-fluids equations with higher ion inertia to stabilise numerical solvers. My guess is that the ambipolar diffusion regime is more accurate than the heavy ion regime, and one could presumably check this on C-shocks models (see section 5.1): I expect the ambipolar diffusion regime captures the ion-neutral coupling distance, while the heavy-ion approximation describes only the fast early rise of temperature in the C-shock structure, which is less critical for its global properties. However, the ambipolar diffusion regime is numerically less stable than the heavy-ion approximation and requires very small time-steps where the magnetic field is large (where the ambipolar term in the induction equation acts as a strong diffusion term).

## 1.3 Physical scales and dimensionless numbers

<table><caption>Table 1: Characteristic scales and dimensionless numbers for various phases and objects in the Galaxy, from the most dilute to the densest. HIM: Hot Ionised Medium, WNM: Warm Neutral Medium, CNM: Cold Neutral Medium, Diffuse and Dense: diffuse and dense molecular gas. ISM phases values are from Draine (2011) and Hennebelle and Falgarone (2012). Sun values are quoted near centre. I also give the ionisation fraction and mass per ion assumed in the computation of the values of $R_m$ and $R_{AD}$.</caption><thead><tr><th></th><th>HIM</th><th>WNM</th><th>CNM</th><th>Diffuse</th><th>Dense</th><th>Discs</th><th>Sun</th></tr></thead><tbody><tr><td>Density ρ [cm<sup>-3</sup>]</td><td>0.004</td><td>0.6</td><td>30</td><td>200</td><td>10<sup>4</sup></td><td>10<sup>10</sup></td><td>1 g.cm<sup>-3</sup></td></tr><tr><td>Temperature T [K]</td><td>3.10<sup>5</sup></td><td>5000</td><td>100</td><td>50</td><td>10</td><td>300</td><td>10<sup>6</sup></td></tr><tr><td>Length scale L [pc]</td><td>100</td><td>50</td><td>10</td><td>3</td><td>0.1</td><td>200 AU</td><td>5.10<sup>-3</sup> AU</td></tr><tr><td>Velocity U [km.s<sup>-1</sup>]</td><td>10</td><td>10</td><td>10</td><td>3</td><td>0.1</td><td>0.1</td><td>1</td></tr><tr><td>M</td><td>0.2</td><td>2</td><td>13</td><td>7</td><td>0.5</td><td>0.1</td><td>0.02</td></tr><tr><td>M<sub>G</sub></td><td>130</td><td>20</td><td>15</td><td>6</td><td>0.8</td><td>0.08</td><td>0.003</td></tr><tr><td>R</td><td>10<sup>2</sup></td><td>10<sup>5</sup></td><td>10<sup>7</sup></td><td>10<sup>7</sup></td><td>10<sup>6</sup></td><td>10<sup>9</sup></td><td>10<sup>17</sup></td></tr><tr><td>R<sub>m</sub></td><td>10<sup>21</sup></td><td>10<sup>20</sup></td><td>10<sup>18</sup></td><td>10<sup>17</sup></td><td>10<sup>15</sup></td><td>10<sup>9</sup></td><td>10<sup>10</sup></td></tr><tr><td>R<sub>AD</sub></td><td>10<sup>3</sup></td><td>10<sup>3</sup></td><td>10<sup>2</sup></td><td>10<sup>3</sup></td><td>10<sup>4</sup></td><td>10<sup>5</sup></td><td>10<sup>20</sup></td></tr><tr><td>Ionisation fraction</td><td>1</td><td>10<sup>-2</sup></td><td>10<sup>-4</sup></td><td>10<sup>-4</sup></td><td>10<sup>-4</sup></td><td>10<sup>-7</sup></td><td>1</td></tr><tr><td>Mass per ion [amu]</td><td>1</td><td>1</td><td>12</td><td>12</td><td>12</td><td>24</td><td>1</td></tr></tbody></table>
<figure><img src="image_4.png" /></figure>

Figure 2: This diagram shows where various phases of the ISM gas and stars stand in the temperature - density plane. Note that the average baryon density of the observable universe as probed by Planck is about $4 \times 10^{-31} \text{g.cm}^{-3}$. The dark gray area spans the range of values obtained in stellar interiors. The dotted line shows the locus of constant pressure $P = 3000k_B.K$. The arrows depict changes undergone through various astrophysical processes.

The first four rows of table 1 form an attempt to list typical density, temperature, length scales, and velocity dispersion for various stable objects or phases through which the matter cycles in our Galaxy. They are ordered by increasing density, which spans about 30 orders of magnitude, and by decreasing size, which spans about 10 decades. Roughly speaking each typical object or phase component hence represents about the same mass (between one and a hundred solar masses). Indeed, given the huge span in orders of magnitude, we are not striving to be precise by more than a factor of ten, here... Temperatures live in a comparatively narrower range of values, between 10 and $10^7$K, and typical velocity dispersion values vary even less. On a density - temperature diagram such as shown in figure 2, these phases assume a 'V' shape, with two different behaviours left and right of $n_H = 10^4 \text{cm}^{-3}$. The most dilute phases (in fact, the ISM) have temperature inversely propor-
tional to density, in such a way that pressure remains roughly uniform. The densest phases however have a slowly increasing temperature with respect to density (between $T \propto \rho^{1/4}$ and $T \propto \rho^{1/3}$) which corresponds to the path they take through gravitational collapse. If we follow a parcel of fluid through its galactic cycle starting from the most dilute phase, it first undergoes isobaric cooling and then polytropic (nearly isothermal) collapse. It goes back to its original state either through jets and winds (AGB winds, coronal winds or disc winds) where it roughly takes backward its former collapsing path, or through supernovae explosions, where it is re-initialised in very little time to its original extremely hot and dilute state. This energy feedback from stellar objects to the ISM is a key ingredient which controls in part the star formation efficiency. However, it depends on a great variety of physical processes which range from angular momentum and magnetic fields in the early stages of star formation, via radiation pressure throughout the stars lives, to nuclear energy, neutrinos, cosmic rays and gravitational waves radiation in supernovae phases.

In the previous section, I was careful to write all fluid dynamics equations in a conservative form, i.e.:

$$ \partial_t \text{Quantity} + \nabla \cdot \text{Flux} = \text{Source.} \qquad (1.3.1) $$

To compute non-dimensional ratios between those terms, physical dimensions require a time and a length scale: it is in fact more customary to set a typical length scale $L$ and a typical velocity scale $U$. One can then easily normalise the equations and get a set of dimensionless numbers characterising the flow: two situations at very different scales can thus be matched provided they have the same characterising dimensionless numbers.

For instance, if one looks at the relative strengths of the terms within the momentum flux, one can define:

* the thermal to ram pressure ratio $p/\rho U^2 \sim 1/M^2$ which involves the Mach number $M = U/c_s$ (velocity relative to sound speed).

* the viscous stress to ram pressure ratio $S_{ij}/U^2 \sim 1/R$ which involves the Reynolds number $R = UL/\nu$, very large (much greater than $10^3$) for developed turbulence.

A similar treatment to the induction equation flux yields:

* the magnetic to ram pressure ratio $B^2/\rho U^2 = 1/\beta$ (from the charges momentum equation) which involves the plasma $\beta$ parameter, not too far from 1 throughout the ISM.
* the resistive stress to magnetic flux ratio yields $\eta/UL = 1/R_m$, which involves the magnetic Reynolds number $R_m = UL/\eta$. Many astrophysical systems have a large $R_m$ which is required for turbulent generation of magnetic field (dynamo effect).

* the ambipolar stress to magnetic flux ratio yields $1/R_a$ with the ambipolar diffusion Reynolds number defined as $R_a = L/(Ut_a)$ where $t_a = 1/F_{in}$. Note that $R_a$ is the only dimensionless number inversely proportional to $U$.

The gravitational source over ram pressure ratio $M_G^2 = U^2/(L^2G\rho)$ measures the strength of self-gravity, which will come as a $1/M_G^2$ term in the right hand side of non-dimensionalised equations.

Typical scales and values for these dimensionless numbers are given in table 1.

* Speeds are generally trans-sonic (sonic Mach numbers are order 1), which makes shocks ubiquitous.

* The gravitational parameter $M_G$ is below one for the ISM phases (below $n_H = 10^4 \text{cm}^{-3}$), where all phases are approximately in pressure equilibrium and equipartition holds for a large number of energy forms (thermal, kinetic, gravitational, magnetic, cosmic ray energy density, radiation energy density). Although $1/M_G^2$ is small in the ISM, gravity can be important on the long term and it remains a strong organising force. For denser gas, $M_G < 1$ and gravity controls the pressure, down to stellar interiors, where hydrostatic equilibrium rules.

* Reynolds numbers are always large, and increase drastically towards larger densities, mainly because the mean free path becomes smaller: turbulence in the ISM is usually fully developed except perhaps in the HIM. Although the inverse of the Reynolds numbers can be minute, the corresponding dissipative terms can nevertheless play an important rôle in fluid dynamics because of the existence of energy transfer from large scales to small scales, where sharp gradients can make up for the small diffusion coefficients.

* Magnetic Reynolds numbers are even larger (except in stars), and with values as high as $R_m = 10^{21}$ (HIM) it is hard to imagine how magnetic fields can ever reconnect in the ISM. $R_m$ decreases with increasing density because magnetic resistivity is propotional to density.
* Ambipolar diffusion scales as $1/R_{AD}$ and is seen to be moderately important throughout the galactic matter cycle except in stellar interiors: despite this, its dynamical effect on the ISM still remains poorly studied, which opens large avenues for future research.

## 1.4 Thermochemistry

In this section we are interested in the evolution equations for the thermodynamical quantities ($T, \{X_k\}_{k=1,...,N}$). Here, I understand chemistry in its largest acceptable sense, including nuclear reactions or molecular chemistry depending on the context. In general, the evolution of a single species on its Lagrangian path can be followed as:

$$ 
\begin{aligned}
D_t X_k &= \partial_t X_k + w_i \partial_i X_k \\
&= R_k(T, \{X_k\}_{k=1,...,N}, \rho, u-v, G_0, A_v, \zeta) + \frac{1}{\rho} \partial_i [\rho \chi_k^{\text{chem}} \partial_i X_k]
\end{aligned}
\quad (1.4.1) $$

where $R_k$ is the net rate of change of species $k$ and $\chi_k^{\text{chem}}$ is the diffusion coefficient (dimensions length×velocity) for this species. $w_i$ is the velocity of the charged fluid $v_i$ or neutral fluid $u_i$ depending on the charge of the species $k$ considered. The chemical rates $R_k$ depend naturally on the whole list of thermodynamical quantities ($T, \{X_k\}_{k=1,...,N}$), but they also are sensitive directly to some of the dynamical variables such as $\rho$ which governs the rate of collisions and the ion-neutral drift $u-v$ which provides extra energy in the centre of mass frame for ion-neutral reactions (important for endoergic chemistry in the dilute ISM). In addition, photo-reactions may play a crucial role in some regions of the interstellar medium and they require the knowledge of the local irradiation conditions $G_0$ and $A_v$ (respectively, the normalised intensity of the irradiation source and the extinction between the source and the local position). In principle, $G_0$ and $A_v$ require radiative transfer equations to be solved along the dynamical and thermochemical systems of equations. Finally, cosmic rays bring into play another external parameter of the system: the primary ionisation rate $\zeta$ which provides the ionisation source in shielded environments of the ISM. The last term in equation (1.4.1) is the molecular diffusion. It couples together the chemical composition of different fluid particles, which makes it inherently dependent on the fluid dynamics. When this term is negligible, it becomes possible to post-process the chemistry on individual Lagrangian tracers for those species which have no back-reaction on dynamics.
To the full list of reactions, I finally adjoin the evolution of the gas temperature, subject to cooling and heating just as a given species is subject to production and destruction:

$$ \frac{p}{\gamma - 1} D_t \ln(\rho^{\gamma-1} T) = \Gamma_{\text{heat}} - \Lambda_{\text{cool}} + \partial_i \left[ \frac{\gamma}{\gamma - 1} p \chi_{\text{therm.}} \partial_i \ln T \right] \quad (1.4.2) $$

where we have assumed the gas follows a perfect gas equation of state with adiabatic index $\gamma$ and where $\chi_{therm.}$ is the thermal diffusion coefficient (dimensions length×velocity). This form for the heat transport equation emphasises the parallel with the chemical composition evolution equation 1.4.1. Here I have combined both the charged and neutral fluids into a single temperature, which is sometimes inappropriate: at least two temperatures should be used for charges and neutrals in dilute media, when the collisional coupling between them is weak or when they experience a large contrast in cooling/heating processes. The thermal evolution equation depends on the fluid dynamics both via the compression term $pD_t \ln \rho$ and because of the thermal diffusion term (in much the same way as for the chemical species). The heating and cooling terms also depend on the same variables as the chemical rates do. Indeed, the heating depends on how much the gas intercepts the irradiation field via the opacities (which depend on all thermochemical quantities in general) and the cooling depends on the full thermochemical state of the gas (through temperature sensitivity and composition in specific cooling agents). In addition, the dissipation of kinetic and magnetic energy yields an extra additive contribution in the form of irreversible dissipative heating $\epsilon_{diss}$:

$$ \Gamma_{\text{heat}} = \Gamma_{\text{ext.heat}} + \epsilon_{\text{diss}} \quad (1.4.3) $$

where $\Gamma_{ext.heat}$ is the external heating due to radiative processes and interaction with cosmic rays. The dissipative heating can be decomposed into three terms:

$$ \epsilon_{\text{diss}} = \nu \rho S_{ij}[u] \partial_i u_j + \eta |\nabla \times B|^2 + \rho F_{in} |u - v|^2. \quad (1.4.4) $$

They correspond to the three forms that turbulence dissipation can take: viscous, Ohmic or ion-neutral friction. This dissipation heating is highly bursty for large Reynolds number, hence in general in astrophysical fluids (see section 4.1).
1.5 Outline

Physical processes prevail over the astrophysical context in the organisation
of this document. The next three chapters consider aspects of turbulence
from the largest scales (driving by instabilities and effective mixing) to the
smallest scales (intermittency of dissipative structures). The chapter 5 is
devoted to variations around the concept of quasi-steadyness, which I found
to be really powerful for detailed astrophysical models, and suitable in a sur-
prising number of dynamical situations. The sections of each chapter unfold
several aspects of the main theme of their parent chapter, and most often
narrow it down to a more specific astrophysical context. Chapter 6 concludes
the scientific document and places this work in the current scientific land-
scape. The remaining two chapters contain my CV and the accompaniment
note (in french).
Chapter 2

Instabilities

<figure><img src="image_5.png" /><figcaption>Figure 3: This saucepan does not need stirring: the convective instability does it for you !</figcaption></figure>

Gas dynamics imply that one sets the fluid into motion. This may happen
only if there is somewhere a reservoir of energy from which we can tap.
Astrophysical objects usually provide us with many forms of energy: kinetic
energy from larger scales, differential rotation, magnetic fields, gravitational
potential energy, nuclear or chemical energy, etc...

For example, rotation and inflow of gas in and onto our Galaxy are the
most likely sources for its largest scale motions. The compression motions
and elongation of vortices in these large scale coherent flows give rise to
dynamics at smaller and smaller scales. Given enough time, a turbulent
cascade develops which connects the large scales to the dissipative scales
where the kinetic energy input is finally dissipated into heat or radiation.
For instance, if we follow Hennebelle and Falgarone (2012) and take 300 pc
for the thickness of our Galaxy and 6 km.s⁻¹ as a typical velocity for this
scale, we get a turnover time-scale of 50 Myr at the largest scales which
indicates that the bulk of the ISM has had time to grow a fully developed
turbulent cascade over the course of even a fraction of a rotation period of
the Galaxy.

However, paths from these energy reservoirs to kinetic energy of the gas
do not always exist. Linear stability studies provide a way to find out such
paths whenever the system is prone to an instability. Unstable systems are
problems of choice for who strives to understand physics. They are naturally
self-driven, have their forcing built in and are often amenable to analytical
considerations, which allow to link the properties of the resulting turbulence
to external physical parameters.

## 2.1 Magneto-rotational instability (MRI)

One of the most exciting problems of the physics of accretion discs regards
angular momentum transport. When a protostar forms out of a contracting
molecular cloud, the conservation of its initial angular momentum forces the
gas to orbit around the newly formed star. The combined gravitational and
centrifugal forces quickly shape the surrounding mass reservoir of the proto-
star into a Keplerian disc. The only way for this orbiting gas to fall on the
central well is to lose angular momentum. The observation of high accretion
rates on young stars requires a mechanism for the angular momentum trans-
port which is many orders of magnitude more efficient than what microscopic
viscous friction alone would provide. For a long time, this process was sim-
ply parametrised by an effective viscosity calibrated on observations, until
Balbus and Hawley (1991) discovered that weakly magnetised discs were sub-
ject to a strong instability: the magneto-rotational instability (MRI). When
a magnetic field threads rotating gas, differential rotation yields a transfer
of angular momentum, with a positive feedback loop when the inside rotates
faster (which is the case in Keplerian discs). The MRI unstable modes, and
more generally the turbulent motions generated by the MRI, were shown
to possess precisely the right correlation properties necessary to transport
angular momentum.

The MRI is still nowadays the most appealing candidate to explain angu-
lar momentum transport in accretion discs. However, it requires a sufficient degree of coupling between the gas and the magnetic field: when the fraction of free electrons is too low, the Lorentz force on the gas is too weak and the disc becomes stable against MRI. This happens when the gas is cold enough and shielded from external radiation fields, so that recombination of electrons wins over photo-ionisation. This may potentially happen in regions of accretion discs which are not too close to the central star and far enough from the illuminated disc surface. These regions where MRI does not operate are called *dead zones* although they might not be as quiet as one would think, since they can be stirred by waves coming from nearby more turbulent regions. On the other hand, regions where the gas is hot enough or which are affected by the radiation from the central star are subject to MRI turbulence, which helps outward angular momentum transport and favours accretion onto the star. These regions are called *active zones*.

Whatever the nature of the turbulent motions in accretion discs, this kinetic energy needs to be dissipated at small scales, thus providing heat to raise the temperature of the gas. For instance, Ohmic heating in MRI turbulence may heat the gas and sustain a degree of ionisation high enough for the gas to remain MRI unstable, even in the deep interiors of the discs where the radiation field does not penetrate. Hence, these shielded media can harbour two stable states: active (hot) and dead (cold). With Steve Balbus, we designed a very simple dynamical system which retained the essential linear properties of MRI turbulence along with an ad hoc saturation prescription (Balbus and Lesaffre, 2008). The phase space diagram for this simple model featured the two active and dead stable states along with a third marginally unstable state in between.

We tested quantitatively this simple model with simulations where we included all the necessary physical ingredients (Lesaffre et al., 2009): a magnetised shearing box with a temperature-dependent resistivity and a prescribed cooling function to balance the Ohmic heating. Thanks to this set-up, we were first able to identify the variables of the simple model with quantitative properties of the magnetised fluid in the computational domain, and we reproduced the phase diagram for a cubic shearing box (see figures 4 and 5). In the process, we realised that other aspect ratios for the box lead to quite different dynamical behaviour. In particular, a simulation box elongated in the azimuthal direction displayed eruptions where a channel mode (the most unstable mode of the MRI instability) would flare to huge amplitude before disrupting into random turbulent motions from which a new channel mode would grow to a new cycle. In order to understand this behaviour, we incorporated parasitic instabilities in our simple model. These secondary modes grow on the main channel mode and we carefully analysed their linear prop-
<figure><img src="image_6.png" /><figcaption>Figure 4: Isometric rendering of the density field (normalised by average) in shearing box computations. Inlets show the time evolution of the momentum transfer rate (Reynolds plus Maxwell stress) normalised by *initial* pressure. Channel flows can be persistent, eruptive or intermittent depending on the aspect ratio of the box (cube, bar or slab, see Lesaffre et al., 2009 or Bodo et al., 2008).</figcaption></figure>

erties in a companion paper (Latter et al., 2009). Our refined dynamical system had one more variable (the amplitude of the parasites) and lead to a steady stable point (dead zone) and a steady cycle (active eruptive cycles). It demonstrated the crucial role of the parasitic instabilities in the saturation of the MRI and in the prediction of its final amplitude. In this process, I discovered that some of the channel modes remain solution of the non-linear equations for specific values of the parameters: this yields unprecedented numerical benchmarks for complex codes including shear, cooling, viscous, and resistive dissipation all at the same time. Another by-product of this study is the stability analysis of interfaces between dead and active zones, which Latter and Balbus (2012) showed as dynamically complex.

Our reduced system opens the way to refined sub-grid models in accretion discs where the angular transport is not an effective enhanced viscous coefficient, but is computed dynamically. I have started to build a model along those lines in the framework of 2D stellar evolution, where the comparatively long shearing time scale allows for easier simplifications (see section
<figure><img src="image_7.png" /></figure>

Figure 5: Reduced models of MRI turbulence (left) compared to the results of actual shearing box simulations (right). Top panels show the phase diagrams in a cubic set-up while bottom panels display the time evolution of various forms of energy (ordered, turbulent and thermal) for a computational domain with a bar aspect ratio. Energy amplitudes are displayed normalised by initial pressure, and the time unit is an orbital period.

2.2). Eventually, one can hope to design a complete model of transport for accretion discs which would enable calculation of the long term evolution of these objects. In particular, it will quantify how much heat MRI turbulence is able to transport vertically in the disc, an often overlooked question. For instance, such models can hope to capture the eruptive cycles of dwarf-novae in accretion discs around white dwarfs (Gammie and Menou, 1998).

## 2.2 Convective instability

One of the major ingredients of stellar evolution is the transport of heat, angular momentum and chemical elements via the motion generated by the convective instability. Convection is triggered whenever radiative diffusion is too weak to carry a heat flux generated from below (like in a boiling pan)
or forced from above (like in a pan left cooling). Then convective drafts or
bubbles carry vertically temperature excesses to provide the necessary miss-
ing flux. Today's stellar evolution models use a very simple one-dimensional
prescription based on the mixing length theory (Böhm-Vitense, 1958). In
this framework, bubbles are assumed to disrupt and mix their chemical and
thermal content with the background after they travel a given parametrized
distance: the mixing length, usually taken as a fraction of the pressure scale
height. This simple hypothesis allows to close the system of equations and
find the convective fluxes as a function of the stellar structure variables.

The vast majority of stellar models deals with spherically symmetric stars.
However, the last two decades of helioseismic measurements have revealed
with a high degree of accuracy the two-dimensional nature of the rotation
profile inside our sun (Schou et al., 1998). Thus, even stars with a spherical
surface may not necessarily possess an internal spherical symmetry. In fact,
as soon as a star rotates, the properties of the fluid inside are likely to
depend on the angle which the rotation axis makes with the local direction of
the gravity (which points very close to the centre for slowly rotating stars),
i.e.: on the latitude. Tomorrow's models, if they aim at accounting for the
helioseismic measurements, need to incorporate at least an axisymmetric
(2D) prescription. The behaviour of the MRI unstable modes saturated by
their parasites (see section 2.1) suggests that one can find out their saturation
amplitude when their growth rate is on the order of their own shear rate.
With Kumar Chitre and Chris Tout, we used this idea to come up with a
convective model for 2D axisymmetric stars (Lesaffre et al., 2013a).

We smooth the stellar fluid equations at a given scale $\lambda_m$. This yields the 2D stellar evolution equations in which unknown fluxes appear. These fluxes depend on the correlation at scales below $\lambda_m$ between the convective velocities and transported quantities such as temperature differences and angular momentum. We then consider perturbations at smaller scales. We linearise the fluid equations and consider only the unstable modes. At the scale $\lambda_m$ we decide that each one of these modes is saturated by its own parasitic modes: this provides the amplitude for each one of these modes. At these scales, the linear physics of the instability will hence set the amplitude and anisotropy of the convective perturbations. For the smaller scales, we consider that the modes are in stronger interaction and we use a prescribed Kolmogorov scaling which propagates this anisotropy down the cascade of scales. We therefore probably overestimate the anisotropy of the perturbations, but as is usual in convective instabilities, the transport properties are dominated by the largest scales so this approximation is probably not crucial. Our theory thus prescribes the 3D Fourier spectrum of the convective perturbations, which we use to close our system and compute the unknown convective fluxes. The
only parameter of our theory is the smoothing length $\lambda_m$, which we identify to the mixing length when we match our theory to the 1D mixing length theory.

At first, we derived explicit expressions for the convective fluxes only in the case of slow rotation, where the thermal structure of the star is still spherically symmetric, but the rotation profile is 2D. In this case, there are only a handful of simulations to which we could compare to figure 6. The work of Gough (1977), who also uses linear eigen vectors to compute the fluxes, is close to ours. However, in his theory, the anisotropy of the turbulent velocity is a free parameter which was calibrated on the simulation, whereas the comparison with our predictions does not introduce any parameter (the mixing length simplifies out of the ratio we choose to plot here).

With Adam Jermyn, we have started to consider faster rotation and magnetic fields. When strong shear is present, the linear analysis needs to be refined because Fourier modes are not solutions of the time-dependent linear system any more. We found two independent ways around: on the one hand a generalised version of the Liouville-Green method for multi-dimensional systems, and on the other hand a new time series expansion which allows to compute arbitrary orders in time. With this, we can compute the convective transport fluxes in a great variety of cases (Jermyn et al. 2017, submitted). In particular, we recover the correct order of magnitude for the MRI angular momentum transport as measured in simulations and as required by observations. We also account for some of the behaviour of convection simulations (Käpylä et al., 2004; Chan, 2001) although we over predict the anisotropy by up to a factor 3.

In the future, we will perform dedicated simulations to calibrate and verify our non-linear prescription. To this purpose, we will plan local simulations of rotating convection (in the nearly incompressible Boussinesq regime) with various rotation speeds and in the presence of weak shear, which applies both to our formalism and to the situation in our Sun. These will allow to pin point which of our assumptions can break down and a careful investigation of the simulation results will hopefully guide us towards more refined saturation prescriptions. The final aim of this series of work is to provide a reliable framework for 2D stellar evolution, which the recent advances in asteroseismology require (Miesch, 2007). As a first step, I envisage to compute the rotational profile in a case where the 1D thermal structure of the star is only weakly affected by rotation (slow rotation case). This is likely to be the case of the Sun, for instance. In this situation, the rotation profile can be found by solving the corresponding linear system of differential equations governing angular momentum transport, meridional circulation and residual entropy. This will yield a direct way to assess the rotation profile in slowly
rotating stars by post-processing thermal structure snapshots from classical 1D stellar evolution codes. A more speculative outcome of these models is how they modify the mixing in the radiative zones nearing convective regions. In particular, A. Jermyn has recently proposed that the resulting faster core growth could help to explain the existence of large black holes binaries as measured by the LIGO/Virgo collaboration.

<figure><img src="image_8.png" /><figcaption>Figure 6: Various convective models for angular momentum transport com-
pared with simulation results of Käpylä et al. (2004), LCT refers to Lesaffre
et al. (2013b), and KR to Kichatinov and Rudiger (1993). Note that works
by Gough and KR both introduce an extra parameter which is fitted to the
anisotropy of the convection.</figcaption></figure>

2.3 Thermal instability

Thermal instability occurs whenever there is runaway cooling, i.e. when
the cooling time-scale shortens with lower temperature. When this is the
case, parcels of fluid which started slightly cooler than their neighbours end
up to their final cold equilibrium much earlier and separate from them into
individual clumps surrounded by gas which is still warm (see figure 7). The
way such a medium behaves at large scales is still largely unknown: how
does mass decide to be shared between the cold and the warm phase ? What
happens when two clumpy media meet each other, do they just pass through
each other in a collisionless way or do they feel each other ? Do they exchange
momentum and what is the effective resulting pressure ? Is the clumpy
structure affected by the collision ? How is the turbulent energy cascade
affected by the fragmentation ?

Thermal instability (TI) is a crucial actor which shapes astrophysical
objects in many contexts. In its seminal paper about TI, Field (1965) re-
views some of the aspects of the formation of structures by other means
than gravity. He considers various contexts where TI may be at play: stellar
atmospheres, solar corona, planetary nebulae, galactic halo and the forma-
tion of galaxies themselves. Even though the initial formation of galaxies is
now understood to be triggered by dark matter gravitational wells, galactic
formation could still occur nowadays via TI. It is likely to explain part of
the baryonic dark matter, as a population of massive dense clumps can hide
matter from the observations and behave in a collisionless way. Exactly how
much remains an open question. The interpretation of some galactic scale
dynamics (large scale molecular shocks, cooling flows, cold streams, high-z
molecules tracing turbulent dissipation as in Falgarone et al., 2017) requires
a multiphase cascade. Finally, it has been shown to be one of the main actor
shaping molecular clouds and pre-stellar condensations (Chièze and Pineau
Des Forêts, 1987; Chièze, 1987), and as a result has a central role in star
formation.

Near the end of my PhD thesis I studied TI with J.-P. Chièze and E.
Audit. I realised that TI (without thermal diffusion) is not scale free. Linear
analysis demonstrates that it is only at small scales that its growth rate
becomes a constant: TI has a well-defined fragmentation scale (close to the
Field length for a simple cooling function, but possibly quite different for
more complex cases). I plan to show by simulations and theory that we
can predict the mass and shapes of the resulting fragments. TI is usually
considered near thermal equilibrium, but it can operate in a globally cooling
medium, far from thermal equilibrium, and the linear theory of TI can also
be used to interpret what happens in this case (in cooling flows and cold
streams, for example, but also fragmentation through a shock as in Koyama
and Inutsuka, 2002). Current simulations (with notable exceptions dedicated
to TI such as Audit and Hennebelle, 2005) generally have too low resolution
to properly account for TI: one needs to have the capability not only to resolve
the cooling length, at which the seeds of thermal fragmentation begin to
grow, but also to trace the condensation through its compression to higher
and higher density (i.e.: smaller and smaller scales). This is still largely
infeasible in 3D and I intend to strive to find sub-grid models or refinement
strategies which properly describe the behaviour of a thermally unstable
medium without having to resort to exceedingly high resolution. Gravity is
usually invoked for the fragmentation process and shaping of interstellar gas.
But gravitational instability is faster at large scales than at small scales: it
will slowly collect large chunks of gas rather than fragment. I rather believe
that TI shapes most of the interstellar medium, and then gravity organises
the resulting fragments into some sort of virial equilibrium.

I remain convinced that there is still a lot of knowledge to be gained from
a detailed study of TI. It will help making progress in solving the obser-
vational puzzles above mentioned (large scale shock in the Stefan's Quintet
observed by Guillard et al., 2009, or galactic CH+ seen by Falgarone et al.,
2017). It will allow us to assess many of the above mentioned questions,
such as the momentum and energy transfers in clumpy media. It should
thus considerably improve the underlying physics in the simulations of star
and galaxies formation. In particular, it is likely to explain part of the star
formation inefficiency: TI can fragment the gas to bits so small that they are
thermally supported, thus preventing collapse.

<figure><img src="image_9.png" /><figcaption>Figure 7: Density map in a 2D simulations of colliding flows, with overlayed velocity vectors (Audit and Hennebelle, 2005): the right panel is a zoom of the left panel. The longest overlayed velocity arrows represent 17 km.s⁻¹ for the right panel and 13 km.s⁻¹ for the left zoomed in panel.</figcaption></figure>
Chapter 3

Mixing

<figure><img src="image_10.png" /><figcaption>Figure 8: Pouring milk in your tea.</figcaption></figure>

In the previous chapter, I have dealt with possible ways to generate tur-
bulence. In this chapter, I focus on the mixing properties of the turbulent
motions. As mentioned in the introduction, the mixing of chemical or ther-
mal characteristics of the gas is realised by the microscopic diffusion terms.
However, these microscopic processes are very slow at the usually large as-
trophysical scales. The turbulent cascade helps transferring thermochemical
patterns to smaller scales, where they can be smoothed and connected.

When you pour milk in your tea, you first see a well defined white cloud
spiralling as you turn the spoon in your cup. Shortly thereafter, your tea
has changed to a nicely uniform colour. The transfer of patterns through
the turbulent cascade happens very fast: on the order of a spoon turn. At
the microscopic scales where the patterns have been transferred, diffusion is
nearly instantaneous. Your milk and tea are now well mixed and on average
everything has happened as if it evolved under a very fast effective diffusion
process. We leave the small scales details for the next chapter and we will
deal here only with the resulting turbulent mixing processes at large scales.

3.1 Prescribed mixing at cloud interfaces

In this section, a background turbulence is prescribed and acts only as an
effective increased diffusion. The possible heating caused by its dissipation
is neglected.

Although astrophysicists lack the possibility to experiment directly with
their objects of study, numerical physicists have the privilege of playing demi-
urge. With the help of a computer, it is comparatively easy to shake a tea cup
in interstellar space. Let's take a magnifying glass to examine carefully the
edge of a molecular piece of cold neutral medium (CNM) embedded in a sur-
rounding atomic warm neutral medium (WNM). We explore what happens
on the dynamics and chemistry at this interface when the cloud is subject to
enhanced mixing.

The numerical set-up we choose to experiment in Lesaffre et al. (2007)
is a planar box of 1 to 10 pc illuminated from one side with the standard
interstellar irradiation field. The code we use contains the full 1D multi-
fluid equations including the relevant thermochemistry of the diffuse ISM
(see sections 1.2.2 and 1.4). Its time integration method is fully implicit so
that the code is able to converge reasonably easily towards the final nearly
steady state. The treatment of the radiation field transfer is done in a very
simple manner: the external field is exponentially attenuated according to
the total column-density between the edge of the box and the local position
in the box. The natural thermo-chemical equilibrium in the box is a warm
neutral phase on the side where the irradiation field impinges the box, and a
cold neutral phase on the side where the irradiation field is attenuated. The
dynamical evolution ensures that the pressure equilibrium is reached after
viscous damping has relaxed all sound waves due to pressure imbalance in
the initial conditions. The final steady state corresponds to an advancing or receding thermal and chemical diffusion front between the WNM and the CNM.

One must be very careful when enforcing the initial pressure balance, otherwise shock waves quickly appear: sound waves in the WNM become shock waves in the CNM because of the temperature difference. This illustrates how easily the multiphase ISM can generate shocks. Another note regarding the final pressure balance is the impossibility to get both chemical equilibrium and partial pressure balance between the charged and neutral fluids. Indeed, the irradiated fluid has more ions, and the pressure gradient in the charged fluid generates an ion current towards the inside of the molecular cloud. This effect is similar to the osmotic pressure at play in our cells. Unfortunately, its time scales are very long compared to the dynamical scales otherwise experienced by these clouds, which renders this mechanism probably irrelevant, although elegant and appealing to a theory oriented mind...

When the diffusion coefficients are only molecular, the width of the diffusion front between CNM and WNM is very small, on the order of the mean free path (a moving grid algorithm allowed us to deal with such sharp features). We now increase the diffusion coefficient by setting the mean free path for diffusion to a prescribed correlation length of the background turbulence. This considerably increases the abundance of some chemical species at the cloud interface. The most spectacular enhancement is realised for the molecule CH⁺. Indeed, this molecule depends mainly on the reaction C⁺ + H₂ → CH⁺ + H which is subject a temperature barrier of 4640 K. In the WNM which would have the temperature required, H₂ molecules are absent, but the molecular CNM is too cold and this reaction channel is suppressed there. Turbulent diffusion (or mixing) allows to bring together hot C⁺ and cold H₂ to favour the formation of CH⁺ at the surface. Other molecules such as H₃⁺ are enhanced and we also expect to excite H₂ molecules at these interfaces, as seen by Gry et al. (2002). This gives us hope that other observational puzzles may be solved thanks to this new channel for molecular production and excitation.

However, the treatment of the turbulent mixing by an increased chemical and thermal diffusion is questionable. With a proper multidimensional treatment, we expect turbulence to entangle the interface between the CNM and the WNM, thus increasing the surface of interaction between the CNM and the WNM. Whether or not this can be assimilated as an effective diffusion remains to be checked. In Valdivia et al. (2016) we start to examine the influence of the multiphase structure of the ISM on H₂ production and excitation. In these 3D simulations, H₂ formation and photo-dissociation is followed alongside the thermal instability. They show the presence of large
amounts of warm $H_2$, which we attribute to its slow photo-dissociation rate: $H_2$ is formed in compressed or shadowed regions, and survives subsequent dilatation or irradiation episodes. Diffusion is dominated by grid scale diffusion in these simulations devoid of a physical diffusion term: by increasing the resolution two-fold, we could demonstrate that diffusion at the cloud interface was not responsible for the warm $H_2$. A subsequent paper (Valdivia et al., 2017) post-processes a much more complex chemistry on these simulations, and shows how warm $H_2$ can generate other molecules (notably $CH^+$, although not enough yet to explain the huge amounts seen in the ISM). Given the large dynamics of scales still remaining between these simulations and the actual dissipative scales, it is desirable to further these studies by more resolved simulations, with extra care on the dissipative processes and their effects on the chemistry.

## 3.2 Self-consistent mixing in stellar interiors

In the previous section, we have considered mixing of heat and chemicals under a prescribed turbulent field. If we add to that picture the mixing of momentum, we get a quantitative way to model the decay of kinetic energy in the turbulent field. We can then balance this decline rate with any driving instability to get prescriptions for the saturation amplitude of the turbulent flow. This idea is at the heart of the classical 1D MLT theory (Böhm-Vitense, 1958) where eddies merge their chemical, heat and momentum content into their surroundings after they have travelled one mixing length, the main control parameter of the theory. In one very specific astrophysical situation, however, the various mixing processes for heat, chemicals and momentum become so intricately coupled to each other that no theory of transport was able to emerge before a very long time: the convective Urca process forced us to build a fully self-consistent theory of convective mixing.

The term Urca was coined after George Gamow met Mario Schoenberg in Rio de Janeiro to discuss the astrophysical implications of a process Gamow had discovered: the emission of a neutrino when a proton captures an electron, and conversely the emission of an anti-neutrino when a neutron emits an electron. Mario Schoenberg took Gamow to a casino in Urca, a district in Rio de Janeiro at the feet of the sugar loaf. There, Gamow saw money flowing out of the hands of gamblers whatever they did, just as energy flows out of the system during an electronic capture or emission. On top of that, Urca sounded like the word 'ypka' (gangster) in his Russian dialect (Rachid Sunyaev private communication), and they quickly adopted the word to design the process by which neutrinos and anti-neutrinos are lost during emissions
and captures on mother and daughter nuclei. Pairs of nuclei which had the same number of nucleons, but one proton difference were called Urca pairs, mother and daughter nuclei, with the mother nucleus having more protons. $^{23}$Na-$^{23}$Ne is the most common Urca pair in stellar matter.

Emissions or captures happen when they are energetically favourable, i.e. above and below a threshold density where the Fermi energy of the electrons is close to the rest mass energy difference between the mother and the daughter nuclei. Even when emissions and captures are in equilibrium, there is still a net loss of energy which is largest when the rate of capture and emission are comparable, around the threshold density. For the $A=23$ $^{23}$Na-$^{23}$Ne pair, the threshold density is about $1.7 \times 10^9$ g.cm$^{-3}$. This density is reached only in the densest C/O white dwarfs, when they accrete mass on their way to ignite Carbon at the centre, and the resulting cooling helps them reaching slightly higher densities before ignition.

Shortly after they ignite Carbon, which usually happens at the centre, a convective core grows to transport heat outwards. However, due to the high degree of degeneracy of the white dwarf matter and to the high temperature sensitivity of the Carbon burning reaction, the core grows quickly in order to evacuate the energy excess. While it grows, the upper edge of the convective region reaches lower and lower densities, until it meets the point where the density is equal to the threshold density of the $A=23$ Urca pair. At this point, nobody really knows what happens...

Paczyński (1972) was the first to recognise that a convective region which engulfs the threshold density for an Urca pair will strongly enhance both captures and emissions, since both processes are going to be outside equilibrium throughout the convective region. Thus the neutrino cooling would be strongly enhanced: the *convective Urca process* was born. During the next three decades, a succession of authors tackled the subject and each of them discovered new elements of the problem which brought successive conclusions mutually exclusive. Some claimed the process was cooling, others reckoned it was heating or simply not important (Paczyński, 1972; Couch and Arnett, 1975; Bruenn, 1973; Iben, 1978a,b; Barkat and Wheeler, 1990; Mochkovitch, 1996; Gutierrez et al., 1996; Stein et al., 1999).

In order to settle down the matter, I strove to work out a framework where there was no room for hesitation for the energy budget equation. The simplest set-up I came up with was inspired by geophysicists who use convective models with up- and down-drafting columns of fluid. I considered the conservation of mass, vertical momentum and energy in two columns which could exchange mass, momentum and energy horizontally after a vertical displacement over one mixing length (Lesaffre et al., 2005b).

In the limit when the properties of the two columns of fluid are not very
different, I could recover the MLT formalism, with interesting extra terms. The work term could be properly derived and was shown to naturally depend on the definition of the luminosity (consistent with which thermodynamical variables are used to write the first principle of thermodynamics). Terms due to the difference in chemical rates in the two columns arouse, which are usually neglected in the MLT (such as differential radiative diffusion).

In particular, the proper energy equation one should use when dealing with the Urca process was finally laid down. So, was the problem going to be solved ? Unfortunately not... It turns out these equations are awfully difficult to solve numerically, and for reasons which are still unclear to me, I still have not come up with an accurate algorithm which enables the computation of the growth of the convective core through the Urca shell with reasonable Urca abundances.

In the process of trying, though, I managed to improve greatly the stability of the existing stellar evolution code of Cambridge (STARS). The improvements I incorporated concerned resolution at the white dwarf surface: by using an extra variable for the size of the zones, zones with sizes down to $10^{-17} R$ (where R is the radius of the white dwarf) could be used at the surface. White dwarfs are very compact objects where the scale height near the surface can be much smaller than the typical radius. I greatly improved the stability of the time integration scheme by using a staggered mesh for the luminosity and chemical flows, and I incorporated my own robust Newton-Raphson solver. Finally, I designed a tracking algorithm for the moving edge of the convective region, which allowed to smooth the incoming mass and energy fluxes in the growing convective core. This last improvement in particular was critical to allow computations of the latest stages of the white dwarf until the deflagration starts (and triggers a type Ia supernova). This had been achieved only once before by Nomoto (Nomoto and Sugimoto, 1977) with a simplified treatment of the energetics.

I met Bill Paxton at KITP Santa Barbara for a supernovae conference where I presented these results. Bill was working at the time on his MESA (modules for experiments in stellar astrophysics) project and he included most of the above technical tricks (except for the convective boundaries tracking) into the stellar evolution solver of MESA. MESA is a collection of numerical modules that Bill almost single handedly coded. It gathers all the best parts of existing stellar evolution codes at the time. It has now grown up to be the most widely used stellar evolution code thanks to a friendly community of expert users which discuss openly many aspects of stellar evolution.

During my stay in Cambridge in 2009, I developed a new idea to stabilise the treatment of advancing convective-radiative interfaces. Most of
the convergence problems during the Carbon flash occur near the top of the convective region, where the last zone oscillates between a radiative and a convective state in the successive iterations towards the final solution. The cases where the code stalls almost invariably involve an iteration process unable to decide whether one zone needs to be convective or radiative. I hence designed a scheme where the top of the convective zone is always affixed to a given interface. This requires re-meshing when a new convective region appears, and assumes one understands well the inner boundary conditions between radiative and convective zones. I managed to implement this technique for the heat transport equation, and the result was astonishingly efficient for chemically homogeneous stars. Used on the structure equations alone, this appears to solve the Carbon flash convergence issues which every other stellar evolution algorithm struggles with. This scheme achieves straightforward and painless Newton-Raphson convergence until the last microseconds when the deflagration begins. Unfortunately, I was never able to apply the same treatment to the chemical equations, and whether this is due to bad implementation (coding problems) or wrong inner boundary conditions, I still don't know... (while entropy is continuous in chemically homogeneous stars, chemical mixing introducing discountinuities at convective/radiative boundaries). Nevertheless, I set up an analytical benchmark for moving convective boundaries where I could readily test the accuracy of the method: surprisingly, the most accurate scheme was not the most conservative one, which is usually used in standard stellar evolution codes...(Lesaffre, 2010)
# Chapter 4

## Dissipation

<figure><img src="image_11.png" /><figcaption>Figure 9: Mechanical energy dissipation is emphasised by blue bioluminescent plankton on this night-time picture of a beach in the Maldives.</figcaption></figure>

I focus in this section on the nature and geometry of the dissipation, which often occurs at the bottom of the energy cascade, down to the very smallest scales where sharp gradients can make up for the small microscopic diffusion coefficients. Joule's heating, viscous heating and ion-neutral friction are several of a few irreversible processes able to degrade kinetic or magnetic energy into heat. In the ISM, the large scale velocity dispersion is often largely supersonic compared to the sound speed in the cold neutral medium, and at least part of this dissipation will occur in shock structures. The remainder is dissipated in structures such as current sheets, vortices or shearing sheets.
Bioluminescent plankton such as a few species of dinoflagellates are small animals (about 20 µm) which react to sudden changes in acceleration or shear by triggering a conversion of chemical energy into light. They hence reveal the sharp small scale velocity gradients in the ocean (see figure 9) in much the same way as we think the CH⁺ molecule can testify for turbulent dissipation in the ISM<fnref n="1" />. Indeed, CH⁺ is easily destroyed and is formed through endothermic reactions: we see it where there is local heating. Already shortly after world war II, radio antennae were turned to the sky and molecules such as CH⁺ were detected in the cold and dilute ISM. From these days until the recent discovery of CH⁺ (Falgarone et al., 2017) in high-z galaxies this molecule continues to pose observational puzzles. The intermittency of dissipation might be a key to understand the ubiquity of CH⁺.

## 4.1 Intermittency

Intermittency is a blurry notion and it has taken some time to take shape in the physics literature. The adjective itself refers to a signal which experiences sudden unexpected changes, such as the air velocity as one moves along a turbulent atmosphere. As a result, the dissipation in a highly turbulent medium is not homogeneous, but extremely bursty (the viscous dissipation rate $\epsilon$ involves the square of the velocity gradients, see equation 1.4.4).

There are several ways to assess quantitatively the intermittency of a field $f(x, t)$ over space $x$ and time $t$, none of which is entirely satisfactory. Most of them involve the increments of the field: the difference between the values of this field at two points separated in space or time (or both...). For instance, the space increment with lag $l$ is $\delta_l f(x, t) = f(x+l, t) - f(x, t)$. The distance or absolute time difference between those two points is referred to as the lag. As noted by Frisch (1996), the square of the velocity increment $(\delta_l v)^2$ scales like the dissipation field $\langle \epsilon \rangle_l$ averaged over scale $l$ (note $\epsilon$ was defined in section 1.4).

One can first look at the statistical distribution $P(\delta_l f)$ of the increments of the field over various lags. Non-intermittent fields have Gaussian distributions at all lags. The distribution of increments for intermittent fields grows exponential wings at small lags: large jumps are much more likely to occur than for an equivalent Gaussian distribution. For instance, when travelling in a plane, you feel many more abrupt air pockets (i.e.: changes in the vertical air drafts) in a small plane than in an Airbus A380.

Second, from these distributions, one can compute the moments of various powers of the absolute value of these increments: the structure functions.

<footnote n="1">¹The idea for this beautiful comparison comes from Edith Falgarone.</footnote>
For example, the order $n$ space structure function of the above field reads: $S_n(l) = \langle |\delta_l f|^n \rangle_x$. These often exhibit power-law behaviour as a function of the lag: $S_n \approx c_n l^{\zeta_n}$ at small $l$. The intermittency exponent of order $n$ is defined as the index $\zeta_n$ of that power-law. The function $\zeta_n$ characterises the intermittency. A linear behaviour corresponds to the non-intermittent case: $\zeta_n/n$ is a constant. Intermittent fields deviate from this situation and display more and more concave behaviours. Many intermittency models strive to predict the intermittency exponents : see figure 10.

<figure><img src="image_12.png" /><figcaption>Figure 10: Intermittency exponents of the dissipation field in various models Kolmogorov (1941, 1962); She and Leveque (1994); Arimitsu and Arimitsu (2000); Ruelle (2014) compared to wind tunnel data from Jiang et al. (2002). The exponents $\tau_p$ are defined as $\langle \epsilon^p \rangle_l = \langle \epsilon \rangle^p (l/L)^{\tau_p}$ for small $l/L$. The equivalent exponents for velocity are $\zeta_m = m/3 + \tau_m/3$.</figcaption></figure>

The third way to assess intermittency is a little bit more convoluted. One now looks at the local behaviour of the field: $\delta_l f(x, t) \propto l^\alpha$ at small $l$. In most places, $\alpha = 1$ and the field is regular, but some places may have lower values with $\alpha < 1$, which means there is a singularity there, and others places may witness extra-regular behaviour with $\alpha > 1$. One then considers the set of points which bear the same $\alpha$ and examine its fractal dimension $D(\alpha)$. This function $D(\alpha)$ is the multi-fractal spectrum associated to the field $f$. One
can show it is linked to the previous intermittency function $\zeta_n$ by a Legendre transform (Frisch, 1996).

In principle, full knowledge of $P(|\delta_l f|)$ allows to compute both $\zeta_n$ and $D(\alpha)$. But to go backwards from the intermittency exponents of structure functions, you need to know in addition the normalisation coefficients $c_n$ of their scaling laws. Similarly, if you want to build $P(|\delta_l f|)$ from the multi-fractal spectrum, you need to know the weight of each singularity exponent $\alpha$ (a combination of the volume of its underlying fractal set and the missing factor in the scaling $\delta_l f(x, t) \propto l^\alpha$). In other words, each one of these three indicators emphasises a slightly different aspect of intermittency and is adapted to different kinds of data or models.

<figure><img src="image_13.png" /><figcaption>Figure 11: Left: 1D cuts of dissipation through a decaying incompressible MHD turbulence simulation (top) and a $\beta$-model realisation (bottom). Right: 2D maps of dissipation for a slice of a 3D simulation of decaying compressible MHD turbulence (top) and a $\beta$-model realisation (bottom).</figcaption></figure>

However, some crucial spatial aspects of intermittency are completely missed out by all three indicators and one should not rely exclusively on them. For instance, the typical time scale with which one fluid particle ex-
periences successive dissipation bursts is not characterised, although it is of
course crucial for the chemical outcome. Let's consider a variation of the
β-model, which allows to draw a random realisation of a 2D dissipation map
with given intermittency exponents. The map is generated recursively by
cutting each pixel of a level into four new squares. One of these squares is
randomly chosen as 'inactive' and inherits from the parent's pixel dissipation
rate decreased by a factor $p < 1$. The other three squares are enhanced to
keep the total dissipation rate the same as in the parent level. The artificial
field thus generated has intermittency exponents reasonably close to mea-
surements on experiments or direct simulations. At first glance, 1D-cuts also
display intermittency, but a closer look at the 2D map reveals the underlying
skeleton of the β-model (see figure 11). The statistics within each square
are 'frozen' and will not change if one exchanges the spatial position of two
squares which share the same parents. One can thus entirely reshuffle the
space structure of dissipation within these constraints and still get exactly
the same $P(\epsilon_l)$, so the shape of the dissipative structures is poorly charac-
terised by these measurements. Also, the above reasoning means that the
largest jumps of dissipation are more likely to occur on the interface between
low level squares. Hence these artificial models are unlikely to be good back-
ground models to probe chemical yields from actual turbulent dissipation.

Uritsky et al. (2010) have examined other complementary aspects of the
space correlation of dissipative structures by looking at the clustering of
dissipative regions and the correlation between characteristic parameters of
their shapes (see section 4.2). Although it characterises better the spatial
coherence of the dissipation structures, even this approach misses the typical
distances between structures.

## 4.2 Dissipation in MHD

Turbulence dissipation is very localised. Look at the surface of the ocean on
a windy day, and notice how only the biggest waves break. Breaking sets in
when a wave reaches a non-linear amplitude (i.e. height comparable to its
wavelength) at which point the shearing time is comparable to its free-fall
time (see also section 2.2). Only these breaking waves produce foam which
reveals the places where energy is dissipated. This picture in my opinion
illustrates well what we think happens in the turbulent interstellar medium.
Energy dissipation takes place in violent and localised events, where new
molecules are produced and excited, thus catching the eyes of the astronomi-
cal observer, who can thus probe the physics of the medium. Similarly, foam
appears at the crest of the strongest waves, leaving a white trail in their
wake, which the cunning sailor uses to estimate the wind strength...

<figure><img src="image_14.png" /><figcaption>Figure 12: Maps of line-of-sight integrated dissipation in decaying incompressible MHD turbulence with ambipolar diffusion (simulations details in Momferratos et al., 2014). *Left*: thin slice of $L_{box}/64$ where $L_{box}$ is the size of the periodic computation domain, *Right*: thick slice of length $L_{box}/2$. Colors characterise the nature of dissipation: green for viscous, red for Ohmic and blue for ambipolar dissipation. Overlayed are contours of the small lag increments of synthesised observables: line-of-sight average velocity in white, Stokes parameters Q and U in red and green, and polarisation angle in blue. Each observable characterises different parts of the dissipative structures, and the correlation does not disappear with line of sight averaging.</figcaption></figure>

To validate this scenario in MHD flows, we followed Uritsky et al. (2010) and we performed and analysed a set of 3D simulations of decaying turbulence (see Momferratos et al., 2014 for the incompressible work and Momferratos’ PhD thesis for the compressible runs). We paid particular attention to the treatment of dissipation, making sure we numerically resolve the viscous, resistive and ambipolar diffusion terms. Though the scales at play were not in the adequate physical ratios (out of reach of current numerical capabilities), our numerical experiments revealed sharp coherent dissipative structures of three distinct natures (viscous, ohmic or ambipolar), as seen on figure 12. We measured the characteristics of the statistical correlations and distributions of their various attributes as well as their characteristic intermittency exponents. We examined plane of sky projections of the dissipation to reveal their link to the increment maps of some observable (such as the line of sight velocity or the Stokes polarisation parameters). Although the dissi-
pative structures in 3D have a sheet-like structure (shocks working surfaces, shearing or current sheets), their projection onto the plane of the sky puts emphasis on caustic structures where the sheets are seen edge on. We suggest part of the resulting ridges can be detected as worm-like structures in the increment maps of observable, thus providing an observational way to detect the dissipation structures (see figure 12).

Grid based numerical schemes often yield significant amount of dissipa-
tion due to the discretisation. Beware that even conservative schemes are
subject to this defect: although the total energy is conserved, part of the
kinetic and magnetic energy can be artificially converted into heat. Even
when the scheme includes physical dissipative terms, some extra heat will be
generated by the truncation. It is rather easy to investigate the *global* total
energy budget over a computational box, i.e.: to check that the decay rate
of total energy is actually faster than what is obtained from the integral of
the physical dissipative terms. However, one can do better and estimate the
*local* dissipation due to numerical truncation only. In the case of a Godunov
scheme, I tested with isothermal shocks that one can recover local numerical
dissipation by integrating a variant of the total energy conservation equation.
This allows to study accurately the dissipative structures in simulations even
when they are not properly resolved (the isothermal shock benchmark in
Momferratos PhD thesis shows that you need 20 zones per mean free path to
get convergence on the viscous dissipative rate of heat, which is out of reach
of current numerical capabilities for 3D simulations). I expect a careful inves-
tigation of the Godunov scheme and its Riemann solver should lead to even
more accurate estimates of the grid based dissipation: the Riemann problem
solution gives how much energy is dissipated in its shocks, and the averaging
step yields the heat generation through entropy mixing. One should thus
be able to assess how the scheme differs from an actual effective viscosity,
and similar considerations can be applied to thermal and chemical diffusion
generated by the grid.

Simulations with controlled dissipation will allow us to understand the
dynamics and statistics of dissipative structure. One of my greatest hope is
that we can eventually obtain a statistical physics picture for these structures.
Validated numerically on moderate Reynolds numbers, such a model would
then predict the statistics of dissipation at high Reynolds number, in regimes
out of reach of simulations. Ideally, such a statistical theory should for
example account for the propagation speed of shocks, the collision between
shocks, and the wriggling of the dissipative sheets (for instance, how do
shearing sheets roll on themselves to make vortices at high Reynolds numbers
?). That is an ambitious programme which I will probably start working out
in a 2D or even 1D framework. Even if it does not yield immediately usable
results, it should help asking the right questions and discover new alleys.

Finally, MRI Intermittency in turbulence has often been overlooked, and there are probably many other situations where discoveries remain to be made. One potentially interesting aspect is the relationship between intermittency of MRI turbulence dissipation and meteorites. The structure of chondrules as examined in a microscope bears signatures of the heating they experienced while they were still wandering about through the protosolar nebula. Various crystals in a melted matrix hint at each grain being subject to one or more heating events above melting temperature (around 1900 K), with constraints on the subsequent cooling timescales (King and Pringle, 2010). This provides precise constraints on the extreme excursions of intermittent heating. Turbulence dissipation in the protosolar nebula might thus be one key ingredient to understand the origin of chondrules.

## 4.3 Dissipation impact on thermochemistry in 2D turbulence

In the above (section 4.2), due to our computing power limitations for 3D MHD simulations, dissipative coefficients are several orders of magnitude larger than real ones, so the size of the dissipation structures is greatly enhanced. In such simulations, what we perceive as a shearing sheet of a few computational zones in width might in fact be a full grown shearing layer in which Kelvin Helmoltz instabilities give rise to smaller vortices and perhaps even sub-shocks. Regions with strong dissipation correspond essentially to zones with exceptionally large r.m.s. velocity.

To see what happens in such regions, rather than increasing the resolution, one can also drastically decrease the size of the domain until the computational grid resolves the dissipation. Thus, let's consider a simulation of decaying turbulence without magnetic field (as resistive scales in the ISM are prohibitively small, see section 1.3). I start the initial rms velocity at $2 \text{ km s}^{-1}$, for a domain scale of $10^{16} \text{ cm}$. This corresponds to a relatively high amplitude, as if we would follow a pixel from the above 3D simulations as it flows through one of its dissipative structures, except I now use the actual physical value for the coefficients of viscous dissipation, thermal and chemical diffusion.

Furthermore, in order to probe the chemical impact of dissipation, I follow a network of 32 species and detailed associated cooling functions. The code I use, CHEMSES, results from an interface between DUMSES (a fixed grid code using the Godunov solver of RAMSES) and the Paris-Durham shock
code, which comprises all the chemistry and physics necessary to model the ISM (see section 5.1). In particular, CHEMSES is the first code which allows to follow time-dependent excitation of H₂ coupled to multi-dimensional MHD. This implementation makes it very easy to check the validity of the hydro-chemical coupling: by design the same micro-physics is present in both the 3D and the 1D steady-state codes, and so steady-state shocks should yield exactly the same chemical profiles, a fact I carefully checked. However, this code is not yet optimised (see section 5.5), so I first had to resort to 2D simulations.

<figure><img src="image_15.png" /><figcaption>Figure 13: Time evolution of the average abundance of some molecules of interest in simulation of 2D decaying hydrodynamic turbulence. The average population of the excited level of H₂ with ($v = 0, J = 3$), responsible for 0-0S(1) emission, is also given in black, scaled down by a factor of thousand.</figcaption></figure>

We can now follow the total production and excitation of molecules integrated through the computational domain. Figure 13 witnesses the enhancement of molecular abundances and excited levels of H₂. We set the initial velocity field to an incompressible flow with random phases and a top-hat spectrum in Fourier space. As this initial perturbation decays, molecular
abundances reach a peak very shortly after the maximum of the total dis-
sipation rate (around a time of 300 years), and finally relax back to their
initial state of equilibrium. This simple experiment illustrates how turbu-
lence dissipation can locally enhance observable tracers.

Chemical yields from dissipation might help us assess several observa-
tional challenges.

* First this provides a new channel for the presence of warm excited H₂ in the diffuse ISM as detected by Gry et al. (2002), for instance.

* Second, this warm H₂ triggers the formation of a large number of other molecules. For instance, I chose the conditions where PDR models such as those of Levrier et al. (2011) are the furthest away from observations for the abundance of CO molecules (predicted column-densities fall an order of magnitude short of observations at a density n<sub>H</sub> = 10<sup>2</sup> cm<sup>-3</sup> for a standard irradiation field). The present simulations show few-fold enhanced CO abundances: turbulence dissipation will help bringing Levrier et al. (2011) results towards observations, in the same manner as models from Godard et al. (2014) did. However, remember our simulation corresponds to limited regions where dissipation is enhanced, so it is not clear how this translates for the average ISM as probed by observed lines of sight.

* Third, excited states of H₂ facilitate reactions with large barriers such as C⁺+H₂ → CH⁺+H. Such simulations with time-dependent levels of H₂ will allow us to assess the impact of H₂ excitation on CH⁺ molecules production in a multi-dimsensional environment.

The present detailed simulations make unique experiments to carefully
examine both the chemistry and the dissipation at the same time. As much
as 3D dissipative structures lived on sheets, in this 2D situation, dissipation
lies on well-defined ridges (see figure 14) which I detected using the DIS-
PERSE algorithm (Sousbie, 2011; Sousbie et al., 2011). Analytical solutions
for steady state adiabatic shock fronts were then adjusted locally in the direc-
tion orthogonal to the dissipation crests. For each successful fit, I recorded
the position and entrance parameters (density, velocity, pressure, chemical
composition) of the steady shock front. I examined the statistics of these
parameters, which shows a much higher number of shocks in the lower half
range of velocities. The dissipation in all shocks accounts for nearly 80%
of the dissipation in the computational box at its highest peak. I then ran
steady-state (J-type) shock models using exactly the same thermochemistry
as in the 2D simulation and truncated them at the same age (here, 300 yr).
I was able to link most points of the 2D simulation in the wake of the dissipation ridges to its corresponding steady-state shock (see figure 15). The remaining points (about half the volume for a snapshot near the dissipation peak) were affected as background even if sometimes they were clearly linked to a messy dissipative knot or to an old shock now deceased. The comparison between the result of the steady-shock modelling and the actual simulation shows that even though locally the abundance could be a factor of a few off, the average over the shocked region matched pretty closely the actual results (to within +/-20% for most species of interest). Despite the huge number of approximations (steadiness, neglect of fronts curvature, of sideways gradients along the front, of dilution effects, etc..), the errors made locally seem to cancel when averaged globally.

The previous experiment illustrates and validates the idea that a collection of steady-shocks can well represent the dissipative yields from decaying turbulence, at least in this 2D situation without magnetic fields. One straightforward improvement would be to investigate the effect of ambipolar diffusion in the same set-up. By introducing ion-neutral drift velocities, ambipolar diffusion considerably enhances the chemical rates of ion-neutral reactions, giving birth to a specific chemistry controlled by magnetic fields, whose signatures in the diffuse ISM matches observations as demonstrated by Godard et al. (2014).

Once we understand the statistics of shocks in 3D turbulence on the one hand and the detailed chemistry and micro-physics of 1D shocks on the other hand, we can use this approach to deduce detailed observational properties of the tracers of turbulence in various environments. To paint the dissipative statistics with detailed thermal and chemical models will hopefully help us design new sub-grid models for 3D simulations, thus allowing to better take into account the effects of turbulence dissipation in large scale simulations. However, one must bear in mind that the statistics of rare events are hard to measure, and unfortunately the molecular yields and emissivities naturally give much more weight to the strongest dissipative events (i.e.: the rarest): the task at hand is reminiscent of computing nuclear rates involving a Gamow-peak effect<fnref n="2" />.

These multi-dimensional simulations will also help us improve 1D shock models in many other aspects. It will help us understand the way the post-shock pressure returns to the average pre-shock, how the shock is diluted back into the surrounded medium and dies out. We will also better understand the rate at which a given piece of fluid experiences successive shocks, thus

<footnote n="2">²The product of the fast decreasing Maxwell-Boltzmann distribution with the steep turning on of tunneling probabilities yields a sharp peak.</footnote>
giving us insight on the typical entrance conditions in these shocks (and the
variance around this typical value). Finally, the shocks 3D geometry can be
translated to 1D distribution functions allowing to build 3D models from 1D
models (cf. Lê Ngọc Trãm thesis and section 5.2).
<figure><img src="image_16.png" /><figcaption>Figure 14: Map of dissipation near the peak dissipation (ie: after 300 years) of our 2D decaying turbulence simulation. Blue: compressive heating $\frac{4}{3}\nu|\text{div}u|^2$ which emphasises the shock fronts, Green: vortical heating $\nu|\text{curl}u|^2$ which shows vorticity in the wake of shocks, Red: difference between actual local heating and the sum of the previous two $(\epsilon_\nu - \frac{4}{3}\nu|\text{div}u|^2 - \nu|\text{curl}u|^2)$ which shows that the local total heating is not quite the sum of compressional and vortical heating (the equality holds exactly only when averaged over the whole computational domain). The size of the computational box is $10^{16}$cm.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Figure 15: *Top left:* map of the relative abundance of CO in the same simulation of 2D decaying turbulence. *Top right:* map of the index of the steady shock associated to each pixel. The zero value means that no shock is associated and hence this pixel is counted as background. *Bottom left:* modelled map of CO using steady-state shock models when available, or equilibrium chemistry for background pixels, same colour scale as above. *Bottom right:* Integrated simulated or modelled abundances relative to total abundance in the simulation in various regions. Red and blue are simulated abundances in the shocked and background regions (so the sum of red and blue is always equal to one). Orange and cyan are for modelled abundances. The rightmost histograms show the results for a number of purely rotational levels of H<sub>2</sub>.</figcaption></figure>
Chapter 5

Time-dependence and
quasi-steadyness

<figure><img src="image_18.png" /><figcaption>Figure 16: Water flowing out of a tap for three different water flows. Steady-state models are overlayed: the radius of the jet $a$ relates to the height $z$ as $a/a_0 = (1 + z/z_0)^{1/4}$ with $a_0$ the jet diameter at the tap and $z_0$ a typical scale. Highschool internship at LRA for Paul Wilgenbus and Jean Gossaert in june 2017.</figcaption></figure>
Open a tap over a sink and stare at the flowing water. The envelope of the jet moving down appears stationary although the fluid parcels keep moving down and are replaced by new liquid. Most of the time, you will also notice fluctuations around this mean flow, but on average the shape will be rather stable. It turns out a very simple steady-state model of free fall for the water drops along with mass conservation allows to predict the shape of the jet even when it is rather strong and bubbly (see figure 16). Fitting this model to the shape of the jet allows to recover the speed and the flow from a single image (and the knowledge of the local gravity field). This is typically what astrophysicists do most of the time to recover rates of change from static images, as astronomical observers most often do not live to see the evolution of their objects of study.

Consider now a more general system evolving under the influence of several processes, each with its own characteristic time scales. If these time scales are well separated, the fastest process will yield a short transient initial behaviour before it goes to equilibrium. The system will then evolve according to the second fastest process and so on. It is hence often (but not always) easier and meaningful to compute the equilibrium which results from setting some given mechanisms to equilibrium. This idea is at the root of the following selection of studies. Very often, it greatly simplifies the dimensionality of the problem. On the one hand, it allows to enhance the details of the micro-physics model such as chemical composition and thermal processes, thus easing the comparison to observations. On the other hand, it can provide analytical solutions which can be used as benchmarks for codes or guides to better understand the physical behaviour of these astrophysical systems.

In the following, I will distinguish two situations: a static state (or state of equilibrium) where Lagrangian time-derivatives are assumed to vanish ($D_t \equiv 0$, nothing changes) and a steady-state (or stationary state) where Eulerian derivatives are set to zero ($\partial_t \equiv 0$, one looks at a steadily moving fluid, like in the water tap situation above).

## 5.1 Steady-state in shocks

As mentioned before (section 4.3), shocks can account for a significant fraction of the total dissipation and can be well modelled by steady-state plane-parallel (1D) shocks. These models allow to include a wealth of micro-physics and help us to characterize signatures of shock dissipation in a turbulent medium, to quantify the main lines that radiate away the kinetic energy of turbulence and the impact of dissipation on the chemical abundances.
When one sets $\partial_t \equiv 0$ in a 1D plane-parallel geometry, a set of ordinary differential equations results which governs the dynamics and evolution of all characteristics of a fluid parcel. The Paris-Durham shock code solves for the steady-state equations of fluid-dynamics in a 1D plane-parallel geometry configuration. It follows the time evolution of a multi-component magnetised fluid with a large number of species (and a arbitrary number of ro-vibrational excitation levels of the H₂ molecule). The velocities of the charges and neutrals are treated independently as in section 1.2.2. The temperatures of the ions, neutrals and electrons are also decoupled. A large number of processes are incorporated to heat and cool the gas: collisional cooling through a large number of atoms and a few molecules (OH, H₂, CO, H₂O), cosmic ray heating, photo-electric effect on grains, chemical exo- or endothermicities, collisional exchanges with grains, and ion-neutral friction. The chemistry is solved jointly with this already complex evolution and is made as modular as possible through an ASCII file which the user can easily manipulate.

Two shock types are solved with this tool. On the one hand one can introduce a small initial velocity gradient and switch on viscous diffusion: this will generate a sharp viscous jump (J-type shock) where kinetic energy is degraded into heat. Over a few mean free paths, the temperature rises almost adiabatically to a maximum governed by the conservation relations across the jump: the Hugoniot-Rankine conditions<fnref n="1" />. In the wake of this adiabatic front thermal energy is radiated away by the cooling agents present in the gas, and density rises. On the other hand one can perturb the initial state with a small velocity difference between the ions and neutrals components: this will produce a continuous transfer from kinetic energy to thermal energy via ion-neutral friction (a C-type shock structure results). In this continuous structure, the velocity remains supersonic throughout the shock, and the temperature is maintained to a warm state resulting from the balance between the frictional heating and the molecular cooling. Provided that the temperature in the post-shock comes back to its pre-shock value, isothermal Hugoniot-Rankine relations will hold globally over the shock structure between the entry point and the final exit point where the pre-shock temperature is reached. In a way, shocks help short-circuit the turbulent energy cascade: kinetic energy ordered at large scales is directly degraded into thermal energy via viscosity or ion-neutral friction over the width of the shock front.

In Lesaffre et al. (2013b), I start to revive the treatment of mild irra-

<footnote n="1">¹Those who never had a chance to attend Chièze's unrivalled hydrodynamics lectures may refer to these relations as the Rankine-Hugoniot relations.</footnote>
diation in the Paris-Durham shock code. I introduce the integration of the extinction along the structure of the shock, a large number of photo-reactions and self-shielding screening functions for the photo-dissociation of CO and H₂. I implement a new mode of integration at constant velocity which mimics a moving steady-state photon-dominated region (PDR): I checked that good agreement with classical PDR models such as the Meudon PDR code (Le Petit et al., 2006) is obtained provided the velocity is sufficiently slow to let chemistry reach equilibrium (velocities on the order of a few 10⁻⁴km.s⁻¹ or below are needed, which casts doubts on the relevance of traditional PDR chemistry). This enables the computation of shocks in diffuse media in standard irradiation conditions (G₀ ≤ 1). I investigated systematically the chemical and emission properties of magnetised shocks with low to moderate velocities (from 3 to 40 km.s⁻¹) in typical conditions of the diffuse ISM. In particular, I show the threshold velocities for molecule production can be quite low. Indeed, the generation of molecules in the interstellar medium (ISM) is initiated by the formation of the H₂ molecule on dust grains surfaces. Some of the more complex molecules then rely on the gas phase reaction between an atom (or atomic ion) and an H₂ molecule, while others are formed via the H₃⁺ ion chemistry channel. The former reactions are subject to energy barriers with high characteristic temperatures such as 2980K in the case of the oxygen atom. Nevertheless, this temperature is obtained in shocks with entrance velocity as low as and above 7.5 km.s⁻¹. Low velocity shocks may therefore play an important role in shaping the molecular chemistry of the ISM.

In the same paper, I introduce a convolution of this grid of models with a probability distribution functions (PDFs) of shock velocities. This is motivated by results on turbulence which examine the statistics of velocity jumps in numerical simulations or experiments on developed turbulence (Pety and Falgarone, 2000; Mouri et al., 2008) as well as by the above study of steady shocks in 2D turbulence (see section 4.3): I propose that one can estimate the observational signatures of such turbulence by a statistical distribution of shock models. We illustrate this method on *Spitzer* spectroscopic observations of H₂ line emission from the Galaxy-wide shock in the Stephan's Quintet (Appleton et al., 2006), and on H₂ absorption spectra obtained with FUSE towards a background star to diffuse molecular gas in the Solar Neighbourhood (Gry et al., 2002). The models fitted to the H₂ excitation diagram allow us to discuss the impact of kinetic energy dissipation on the physical state and chemistry of molecular gas in these two sources. We also make predictions on other diagnostic lines to be observed with *Herschel*. The predictions on the CII line intensity are now confirmed by new measurements (Appleton et al., 2013).
For optically thin lines, distributions of shocks also allow to model geometries other than planar. For instance, with Lê Ngọc Trâm, we find an analytical relationship between the shape of axisymmetric bow shocks and the underlying shock distribution which allows to recover their emission properties. We use this to compare H₂ emission diagrams of bow shocks to planar shocks and we show that there is a bias towards low-velocities when planar shock are adjusted to beam-averaged observations of a bow-shock structure. On the other hand, we obtain unprecedented match to H₂ observational properties (both line shapes and intensities) of bow-shocks in HH54, BHR71 and Orion. In particular, we show that emission diagrams can be used to probe the orientation of the magnetic field and that line shapes are powerful tools to probe the dynamics. It will be relatively straightforward to extend these results to optically thin CO lines and other molecules of interest.

Thanks to his expertise on the Meudon PDR code (Le Petit et al., 2006), B. Godard has now added a tremendous amount of physics to the Paris-Durham shock code relevant to higher degrees of irradiation: UV pumping, radiative transfer and linked photo-reaction rates, grain charge and discharge from irradiation, photo-desorption and thermal desorption from grains. This will allow proper prediction of shock properties in a much broader range of physical situations relevant to the ISM in strongly irradiated environments (high mass stars neighbourhoods, HII regions, moving PDRs, etc...) for which we are accumulating observational data. Finally, A. Gusdorf is developing post-processing tools to model the emissivities of a large collection of molecules: this will achieve to make the Paris-Durham code a world-wide reference in shock models.

## 5.2 Quasi-steady state in shocks

The study of time-dependent 1D planar shocks in the ISM is made very difficult by the high resolution needed to resolve the shock front while computing the chemistry. Indeed, if the adiabatic shock front is smeared out over a too large scale due to weak resolution, some fast chemical reactions may unduly change the composition while the fluid traverses it, and this can affect the resulting structure when the abundance of major coolants is modified. During my PhD thesis with Jean-Pierre Chièze, we designed a 1D moving grid algorithm able to provide exponentially high resolution at a fixed number of zones. Coupled to a fully implicit time integration scheme, this produced a very robust laboratory for 1D time-dependent studies of the ISM, such as time-dependent molecular shocks (Lesaffre et al., 2004a).

Thanks to a careful analysis of the latter simulations, I demonstrated that
time-dependent snapshots were composed of pieces of steady-state models for a wide variety of entrance conditions (Lesaffre et al., 2004b). I provided an algorithm to guide how to build a snapshot at a given age from pieces of steady-state models and this was implemented in the Paris-Durham model. For instance, the early stages of C-type shocks are composed of a piece of C-type shock forming the magnetic precursor followed by a trailing J-type shock triggered by a viscous term when the time-flow in the charged fluid reaches the desired age. The trailing J-type shock is cut when the neutral flow-time through its own structure reaches the same desired age.

Quasi-steadyness in these shocks opens the road for a lot of further studies. First, this makes time-dependence accessible to very detailed stationary models of shocks. For instance, shocks in jets with very short dynamical ages (such as BHR71, see Gusdorf et al. 2015 and Tram et al. 2018) or in supernovae remnants (such as Cepheus E, see Gusdorf et al. 2017) benefit from these models. Second, it yields approximate solutions for time-dependent shocks with cooling (Lesaffre, 2006) which could serve as code benchmarks or even as a building block for Rieman solvers with cooling. Third, it provides a frame with which to consider the stability of these shocks: the quasi-steady state can serve as a reference state for linear studies (looking at the growth of 3D modes feeding on the shock structure).

## 5.3 Quasi-static star formation

Collapse is usually viewed as a violent event. Stellar clusters are commonly found at the edge of compact HII regions or near OB associations, thus hinting at triggered star formation. Some stellar clusters are born in association and are nearly coeval: this is often used to argue for fast, violent star formation. However, it only means that the time scale for individual star formation is shorter than the dispersion time of the cluster's parent cloud (on the order of its free-fall time if it is roughly virialised). Because this parent cloud is likely to have a mean density much lower than that of the protostellar clumps, that dispersion time is actually much larger than the individual free-fall time of the proto-stellar clumps. Hence there is ample room for slower than free-fall star formation. In fact, at least some modes of star formation are on the contrary very slow, with support leaking out very progressively (this could be through magnetic field dispersion, ambipolar diffusion, cooling, turbulence decay, slow push from outside from a nearby star lighting up, a cloud slowly entering the shadow of another cloud, etc...).

The first evidence for this was the case of IRAM04191, a spherical clump where a nascent jet signals the existence of an obscured new born star and al-
lows to estimate the age past the star formation. The in-fall signatures from
the molecular line shapes allows to put upper very stringent upper limits on
the in-fall velocities (Belloche et al., 2002). Lesaffre et al. (2005a) shows that
even the slowest isothermal collapse had a hard time accounting for such low
velocities (this was recently rediscovered in the case of L1544 by Keto et al.,
2015). Simulations which account for the dynamical cooling of the collapsing
gas are the only ones compatible with observations. It seems at first glance
surprising that a phenomenon which suppresses thermal support allows for
a milder collapse, but a quasi-static reasoning solves the paradox. Because
cooling is stronger in the denser central zones, it introduces a steeper pressure
gradient, and yields a more extended envelope: the resulting contraction at
fixed mass is slower. A careful analysis of the simulations reveals a collapse
in four phases. The first stage is hydrostatic: the cloud is still stable and
whatever external parameter forces it towards the critical collapsing state
evolves over time scales longer than the sound crossing time. There comes a
time when the acceleration time scale ($t_r = r/\sqrt{|\ddot{r}|}$) is shorter than the ex-
ternal forcing time, but still longer than the sound crossing time: hydrostatic
equilibrium is still valid even though evolution time scales are shorter than
the forcing. This detaching phase is amenable to a quasi-static treatment.
The third stage occurs when the acceleration time scale becomes shorter than
the sound crossing time: this is the collapsing phase, where pressure gradi-
ents and gravitational acceleration are on the same order. This is the most
difficult phase to handle, but it occurs quite late in the process. Finally, the
gravitational acceleration dominates pressure gradients completely and we
enter the free-fall phase. The first two stages can be described with simple
hydrostatic models, which would allow for a detailed chemical treatment at a
low cost: this fruitful idea has yet to be developed but promises a lot of pre-
dictive power for synthesising observations of slowly collapsing protostellar
envelopes.

Incidentally, the simulations of Lesaffre et al. (2005b) were almost the
first to compute the dynamics of collapse alongside chemistry and detailed
thermodynamics (the work of Li et al. (2002), which included magnetic fields
as an isotropic pressure, preceded ours, but was isothermal, and had no ability
to go past the central object formation). We later used this tool in Pagani
et al. (2013) to probe deuteration of some tracer molecules as a chemical
clock for the collapse. With observational constraints on the N₂D⁺/N₂H⁺
ratio, we demonstrated that the collapse of L183 had to take place rather
rapidly (less than 0.4 Myr from the beginning of the cloud contraction).
## 5.4 Steady inviscid hypersonic flows

We examine here a particularly fruitful case where a full 3D time-dependent problem can be split into a bundle of 0D time-dependent problems. As noted in section 1.3, the ram pressure term in the Euler equation scales like the inverse of the Mach number: it does not take a very large Mach number for it to become small. In addition, most astrophysical conditions yield an extremely small viscous coefficient. When both the pressure and the viscous terms can be neglected in the Euler equation, the system can be simplified into:

$$D_t v = F(r, v, t) \qquad (5.4.1)$$

$$D_t r = v \qquad (5.4.2)$$

where $D_t = \partial_t + v \cdot \nabla$ denotes the Lagrangian time derivative along $v$, $r$ and $v$ are the position and velocity, and we have assumed the external forces $F$ depend on position and velocity only at a given time. If in addition one assumes $F$ does not depend on time, then it is straightforward to integrate the trajectories given initial conditions. For instance, one can prescribe the wind velocity close to the surface of an AGB star and get the full 3D kinematics of the resulting wind, even in the presence of a perturbing binary companion. One can even prescribe a time evolution of the wind mass-loss rate on the surface of initial conditions (provided the velocities at the base of the wind remain constant in time, which is usually a good approximation for winds).

The main difficulty in this process is to find out where trajectories meet each other, at which point a shock will be triggered (because of the high Mach number assumption). I have started to devise techniques to find the position of the spiral shock in the equatorial plane of a binary wind, but the extension of this technique above and below the symmetry plane is proving to be quite tricky. Mean while, the good match with existing spiral shock observations and the computation gain from 3D simulations currently used to interpret these spiral patterns is very promising (see figure 17) !

The whole thermal and chemical history can then be recovered by post-processing on the trajectories. One can “paint” back all the trajectories with their temperature, chemical content and line emission properties. In the context of wind models this will allow detailed modelling of the molecular emission maps, precisely as ALMA is retrieving unprecedented high resolution data on these objects. This is one of the main purpose of the collaboration undergoing with the VNSC/DAP group in Hanoï through the PhD of Lê Ngọc Trãm. We have already started to include the relevant physics
in the Paris-Durham code: geometrical dilution, momentum transfer from
grains due to radiation pressure, gravitational force, three-body reactions,
handling of the sonic point crossing and a crude treatment of grains conden-
sation. Preliminary tests are very satisfactory and we should be soon in good
shape to investigate the formation and dissociation of H₂ in these winds. We
hope these models will help to interpret the difficulty to observe HI in high
mass-loss rate AGB stars: because of their low surface temperature, we ex-
pect hydrogen might remain in molecular form throughout the wind. This
will also provide the initial conditions for the reverse shock in bow-shocks
trailing AGB stars, to assess its observational properties thanks to our shock
distribution technique.

The large Mach number approximation is also used in the study the shape
of bow shocks around stellar winds. Wilkin (1996) simply computes the
balance of ram pressures to get a very neat derivation of the analytical shape
of the bow-shock. I tested his approximation in a simple shallow water
experiment where I measure the shape of the hydraulic jump between the
flows coming from two taps and compare it to a semi-analytical solution
using the same ram pressure balance as in Wilkin (see figure 18). It is indeed
relatively easy to obtain largely supersonic flows in shallow water, because
the gravity wave propagation speed in a thin fluid film is proportional to its
height. Hence, the ram pressure balance could be used in the Paris-Durham
shock code to predict the shape of the bow-shock self-consistently.

**5.5 Chemical networks optimisation**

The code CHEMSES makes direct use of the rich ISM micro-physics of the Paris-Durham code, carefully updated through the last few decades as more and more observational problems were addressed. The modularity of the Paris-Durham code is also ported to CHEMSES and allows to easily probe a wide variety of networks. However, the resulting tool is rather slow to run. In particular, 3D simulations cannot be run in a reasonable time (50 000 CPU hours) on more than 100³ pixels domains. This is why with Benjamin Godard we have started to devise ways to optimise the treatment of chemistry.

The cost of chemistry is due in part to the large number of chemical sub-
steps required when a rapid reaction takes place and in part to the matrix
inversion for each chemical sub-step, which scales like N<sup>3</sup><sub>species</sub> where N<sub>species</sub>
is the number of species. There are hence two ways to gain speed: smaller
equivalent networks or a decrease in the number of chemical sub-steps.

One drastic way to reduce the sub-stepping of chemistry is to perform
a single fully implicit integration step. However, this in general introduces
a considerable loss of accuracy. We are hence trying to devise an efficient
method to regain precision. Our idea is to assume chemical equilibrium for
some of the species and time-dependence for others. We have come up with
an iterative way to estimate the time-scale of variation of each chemical specie
and we plan to use it to assess which species need to include time-dependence,
and which species are computed at equilibrium with respect to the remainder
set of species. This has not yet been ported to CHEMSES, but we expect a
large speed-up should result with little or no loss of precision.

There exist a few situations where one can easily get rid of an independent
species or a chemical reaction. For example, when reactions of a chain of
reactions have a very large flow rate, one can usually short circuit the chain
and replace it by a single reaction. Or even more simple, one can deduce the
abundance of a specie using an elemental conservation equation. We managed
to extend this last situation to a whole set of species (which interact only
linearly with the others through the network) thanks to our understanding
of the Chemical Network Reaction theory (CNRT, see the nice introduction
by Gunawardena, 2003, for example). We also tried some other sophisticated
automated reduction methods of the CNRT, but they unfortunately turned
out inefficient for our ISM specific reaction networks. We are still of course
surveying the large body of literature on chemical reactions or biological
models reduction in the hope of finding an efficient method well suited to our
networks. We are also investigating ways to automatically reduce networks
as we would do it by hand for simple test networks, but this is proving a
sophisticated and convoluted task. Network analysis is also interesting per se
as a tool to understand the chemical outcomes and the structure of networks
which are growing richer and richer as observations reveal increasingly more
complex molecules.
<figure><img src="image_19.png" /><figcaption>Figure 17: Top: Binary wind trajectories in the orbital plane (distances in units of the stellar radius). The circle around the '+' sign is the surface of the AGB star. The 'x' sign marks the position of the secondary star. The black curve marks the position of the shock. Blue and red trajectories hit the shock from one side or the other. Green trajectories never hit the shock. Trajectories which fall on the secondary are not shown. Bottom: ALMA image of LL Pegasi showing nice spiral patterns in its planetary nebula. The companion, too faint, is not seen on this image.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Figure 18: Intersection of two shallow water flows originating from two taps (viewed from above, '+' and 'x' signs mark the positions where both taps hit the experimental plane). The dashed line marks the position of the hydraulic jump as computed from ram pressure balance. The dimensionless parameter $\alpha = (D_1/D_2)^{3/4}$ where $D_1$ and $D_2$ are the flows at both taps can be measured from adjusting the theoretical curve by eye ($\alpha \approx 5 \pm 1$) or by measuring the flows at the two taps ($\alpha \approx 7 \pm 1.6$ for $D_1 \approx 200 \text{ mL.s}^{-1}$ and $D_2 \approx 15 \text{ mL.s}^{-1}$, assuming a 30% relative uncertainty while measuring the flows' ratio). Experiment conducted with Merwan Ouldelhkim during his internship at ENS in may 2017.</figcaption></figure>
# Chapter 6

## Conclusion

I wish the organisation of these chapters by physical concepts did not put you off and that perhaps it brought light on hidden alleys between poorly connected areas of research, and more generally that you enjoyed reading this document. I also hope I managed to convince you that there is material here for a few sound PhDs. I want to add here that I feel these proposed lines of research are also timely.

The newly started ERC project MIST (Molecules, magnetic fields, Inter-mittency in coSmic Turbulence) conducted by Edith Falgarone at LRA will allow a good number of these projects to come to life (irradiated and self-irradiated shock models, dissipative structures analysis and study of thermal instability). I secretly wish the grant application time thus freed will give me enough freedom to investigate some of the craziest ideas I entertain.

LOFAR and in the future SKA will provide a rich handle on the structure of MHD turbulence in our Galaxy. The complexity of this data however requests detailed physical models and complex observation synthesis to extract the essence of the message it bears. The ANR BxB recently obtained by François Boulanger at LRA will grant the resources to develop these tools.

In a nearer future, the launch of JWST will hopefully unveil more of this warm H₂ component, with new observational puzzles which my work on mixing or dissipation might help to address.

ALMA is now revealing a wealth of details on the dynamics, small scale structure and chemical composition of astrophysical gases. The interpretation of these data requires more and more sophisticated models which steady-state approximations can provide (see chapter 5). These models are easy to manipulate even with low computational resources. Combined with the easy accessibility of ALMA data, this makes it a fantastic opportunity for small teams in fast developing countries such as Vietnam. This is the favourable context of my collaboration with VNSC/DAP (Vietnam National Satellite
Center / Department of Astrophysics) with which I work in the framework of
the PhD of Lê Ngọc Trâm (who I hope will become my first official student).
Bibliography

P. N. Appleton, K. C. Xu, W. Reach, M. A. Dopita, Y. Gao, N. Lu, C. C. Popescu, J. W. Sulentic, R. J. Tuffs, and M. S. Yun. Powerful High-Velocity Dispersion Molecular Hydrogen Associated with an Intergalactic Shock Wave in Stephan's Quintet. *Astrophys. Journal Letters*, 639: L51-L54, March 2006. doi: 10.1086/502646.

P. N. Appleton, P. Guillard, F. Boulanger, M. E. Cluver, P. Ogle, E. Falgarone, G. Pineau des Forêts, E. O'Sullivan, P.-A. Duc, S. Gallagher, Y. Gao, T. Jarrett, I. Konstantopoulos, U. Lisenfeld, S. Lord, N. Lu, B. W. Peterson, C. Struck, E. Sturm, R. Tuffs, I. Valchanov, P. van der Werf, and K. C. Xu. Shock-enhanced C⁺ Emission and the Detection of H₂O from the Stephan's Quintet Group-wide Shock Using Herschel. *Astrophysical Journal*, 777:66, November 2013. doi: 10.1088/0004-637X/777/1/66.

T. Arimitsu and N. Arimitsu. Analysis of fully developed turbulence in terms of Tsallis statistics. *Phys. Rev. E*, 61:3237-3240, March 2000. doi: 10.1103/PhysRevE.61.3237.

P. E. Arratia and J. P. Gollub. Predicting the Progress of Diffusively Limited Chemical Reactions in the Presence of Chaotic Advection. *Physical Review Letters*, 96(2):024501, January 2006. doi: 10.1103/PhysRevLett.96.024501.

E. Audit and P. Hennebelle. Thermal condensation in a turbulent atomic hydrogen flow. *Astron. and Astrophys.*, 433:1-13, April 2005. doi: 10.1051/0004-6361:20041474.

S. A. Balbus and J. F. Hawley. A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution. *Astrophysical Journal*, 376:214-233, July 1991. doi: 10.1086/170270.

S. A. Balbus and P. Lesaffre. The effects of Prandtl number on black hole
accretion flows. *New. Astron. Review*, 51:814–818, May 2008. doi: 10.1016/j.newar.2008.03.010.

Z. Barkat and J. C. Wheeler. The convective URCA mechanism. *Astrophysical Journal*, 355:602–616, June 1990. doi: 10.1086/168793.

A. Belloche, P. André, D. Despois, and S. Blinder. Molecular line study of the very young protostar IRAM 04191 in Taurus: infall, rotation, and outflow. *Astron. and Astrophys.*, 393:927–947, October 2002. doi: 10.1051/0004-6361:20021054.

G. Bodo, A. Mignone, F. Cattaneo, P. Rossi, and A. Ferrari. Aspect ratio dependence in magnetorotational instability shearing box simulations. *Astron. and Astrophys.*, 487:1–5, August 2008. doi: 10.1051/0004-6361:200809730.

E. Böhm-Vitense. Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Mit 5 Textabbildungen. *Zeitschrift für Astrophysik*, 46:108–+, 1958.

S. W. Bruenn. Thermal Consequences of the Convectively Driven URCA Process. *Astrophys. Journal Letters*, 183:L125, August 1973. doi: 10.1086/181269.

K. L. Chan. Rotating Convection in F-Planes: Mean Flow and Reynolds Stress. *Astrophysical Journal*, 548:1102–1117, February 2001. doi: 10.1086/318989.

J. P. Chièze. The fragmentation of molecular clouds. I - The mass-radius-velocity dispersion relations. *Astron. and Astrophys.*, 171:225–232, January 1987.

J.-P. Chièze and G. Pineau Des Forêts. The fragmentation of molecular clouds. II - Gravitational stability of low-mass molecular cloud cores. *Astron. and Astrophys.*, 183:98–108, September 1987.

R. G. Couch and W. D. Arnett. Carbon ignition and burning in degenerate stellar cores. *Astrophysical Journal*, 196:791–803, March 1975. doi: 10.1086/153470.

B. T. Draine. *Physics of the Interstellar and Intergalactic Medium*. 2011.

E. Falgarone, M. A. Zwaan, B. Godard, E. Bergin, R. J. Ivison, P. M. Andreani, F. Bournaud, R. S. Bussmann, D. Elbaz, A. Omont, I. Oteo,
and F. Walter. Large turbulent reservoirs of cold molecular gas around high-redshift starburst galaxies. *Nature*, 548:430–433, August 2017. doi: 10.1038/nature23298.

G. B. Field. Thermal Instability. *Astrophysical Journal*, 142:531, August 1965. doi: 10.1086/148317.

U. Frisch. *Turbulence*. January 1996.

C. F. Gammie and K. Menou. On the Origin of Episodic Accretion in Dwarf Novae. *Astrophys. Journal Letters*, 492:L75–L78, January 1998. doi: 10.1086/311091.

B. Godard, E. Falgarone, and G. Pineau des Forêts. Chemical probes of turbulence in the diffuse medium: the TDR model. *Astron. and Astrophys.*, 570:A27, October 2014. doi: 10.1051/0004-6361/201423526.

D. O. Gough. Mixing-length theory for pulsating stars. *Astrophysical Journal*, 214:196–213, May 1977. doi: 10.1086/155244.

C. Gry, F. Boulanger, C. Nehmé, G. Pineau des Forêts, E. Habart, and E. Falgarone. H₂ formation and excitation in the diffuse interstellar medium. *Astron. and Astrophys.*, 391:675–680, August 2002. doi: 10.1051/0004-6361:20020691.

P. Guillard, F. Boulanger, G. Pineau Des Forêts, and P. N. Appleton. H₂ formation and excitation in the Stephan's Quintet galaxy-wide collision. *Astron. and Astrophys.*, 502:515–528, August 2009. doi: 10.1051/0004-6361/200811263.

Jeremy Gunawardena. Chemical reaction network theory for in-silico biologists. 01 2003.

A. Gusdorf, D. Riquelme, S. Anderl, J. Eislöffel, C. Codella, A. I. Gómez-Ruiz, U. U. Graf, L. E. Kristensen, S. Leurini, B. Parise, M. A. Requena-Torres, O. Ricken, and R. Güsten. Impacts of pure shocks in the BHR71 bipolar outflow. *Astron. and Astrophys.*, 575:A98, March 2015. doi: 10.1051/0004-6361/201425142.

A. Gusdorf, S. Anderl, B. Lefloch, S. Leurini, H. Wiesemeyer, R. Güsten, M. Benedettini, C. Codella, B. Godard, A. I. Gómez-Ruiz, K. Jacobs, L. E. Kristensen, P. Lesaffre, G. Pineau des Forêts, and D. C. Lis. Nature of shocks revealed by SOFIA OI observations in the Cepheus E protostellar outflow. *Astron. and Astrophys.*, 602:A8, June 2017. doi: 10.1051/0004-6361/201730454.
J. Gutierrez, E. Garcia-Berro, I. Iben, Jr., J. Isern, J. Labay, and R. Canal. The Final Evolution of ONeMg Electron-Degenerate Cores. *Astrophysical Journal*, 459:701, March 1996. doi: 10.1086/176934.

P. Hennebelle and E. Falgarone. Turbulent molecular clouds. *A. & A. Review*, 20:55, November 2012. doi: 10.1007/s00159-012-0055-y.

I. Iben, Jr. URCA neutrino-loss rates under conditions found in the carbon-oxygen cores of intermediate-mass stars. *Astrophysical Journal*, 219: 213-225, January 1978a. doi: 10.1086/155769.

I. Iben, Jr. Thermal oscillations during carbon burning in an electron-degenerate stellar core. *Astrophysical Journal*, 226:996-1033, December 1978b. doi: 10.1086/156680.

Nan Jiang, Yu-chun Wang, Wei shu, and Zhen-dong Wang. Experimental study of measurement for dissipation rate scaling exponent in heated wall turbulence. *Applied Mathematics and Mechanics-Amsterdam*, 23 (9):1035-1044, 2002.

P. J. Käpylä, M. J. Korpi, and I. Tuominen. Local models of stellar convection: Reynolds stresses and turbulent heat transport. *Astron. and Astrophys.*, 422:793-816, August 2004. doi: 10.1051/0004-6361:20035874.

E. Keto, P. Caselli, and J. Rawlings. The dynamics of collapsing cores and star formation. *M. N. R. A. S.*, 446:3731-3740, February 2015. doi: 10.1093/mnras/stu2247.

L. L. Kichatinov and G. Rudiger. A-effect and differential rotation in stellar convection zones. *Astron. and Astrophys.*, 276:96, September 1993.

A. R. King and J. E. Pringle. The accretion disc dynamo in the solar nebula. *M. N. R. A. S.*, 404:1903-1909, June 2010. doi: 10.1111/j.1365-2966.2010.16405.x.

A. N. Kolmogorov. Dissipation of Energy in Locally Isotropic Turbulence. *Akademiia Nauk SSSR Doklady*, 32:16, April 1941.

A. N. Kolmogorov. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. *Journal of Fluid Mechanics*, 13:82-85, 1962. doi: 10.1017/S0022112062000518.
H. Koyama and S.-i. Inutsuka. An Origin of Supersonic Motions in Interstellar Clouds. Astrophys. Journal Letters, 564:L97-L100, January 2002. doi: 10.1086/338978.

H. N. Latter and S. Balbus. The dynamics of inner dead-zone boundaries in protoplanetary discs. M. N. R. A. S., 424:1977-1990, August 2012. doi: 10.1111/j.1365-2966.2012.21334.x.

H. N. Latter, P. Lesaffre, and S. A. Balbus. MRI channel flows and their parasites. M. N. R. A. S., 394:715-729, April 2009. doi: 10.1111/j.1365-2966.2009.14395.x.

F. Le Petit, C. Nehmé, J. Le Bourlot, and E. Roueff. A Model for Atomic and Molecular Interstellar Gas: The Meudon PDR Code. Astrophys. Journal Supp., 164:506-529, June 2006. doi: 10.1086/503252.

P. Lesaffre. Time-dependent analytic solutions of quasi-steady shocks with cooling. Geophysical and Astrophysical Fluid Dynamics, 100:265-278, June 2006. doi: 10.1080/03091920600738416.

P. Lesaffre. (Semi-)Analytical Solutions of 1D Partial Differential Equations. In N. V. Pogorelov, E. Audit, and G. P. Zank, editors, Numerical Modeling of Space Plasma Flows, Astronum-2009, volume 429 of Astronomical Society of the Pacific Conference Series, page 253, September 2010.

P. Lesaffre, J.-P. Chièze, S. Cabrit, and G. Pineau des Forêts. Temporal evolution of magnetic molecular shocks. I. Moving grid simulations. Astron. and Astrophys., 427:147-155, November 2004a. doi: 10.1051/0004-6361:20035867.

P. Lesaffre, J.-P. Chièze, S. Cabrit, and G. Pineau des Forêts. Temporal evolution of magnetic molecular shocks. II. Analytics of the steady state and semi-analytical construction of intermediate ages. Astron. and Astrophys., 427:157-167, November 2004b. doi: 10.1051/0004-6361:20035873.

P. Lesaffre, A. Belloche, J.-P. Chièze, and P. André. The dynamical influence of cooling in the envelope of prestellar and protostellar cores. Astron. and Astrophys., 443:961-971, December 2005a. doi: 10.1051/0004-6361:20053388.

P. Lesaffre, P. Podsiadlowski, and C. A. Tout. A two-stream formalism for the convective Urca process. M. N. R. A. S., 356:131-144, January 2005b. doi: 10.1111/j.1365-2966.2004.08428.x.
P. Lesaffre, Z. Han, C. A. Tout, P. Podsiadlowski, and R. G. Martin. The C flash and the ignition conditions of Type Ia supernovae. *M. N. R. A.* S., 368:187-195, May 2006. doi: 10.1111/j.1365-2966.2006.10068.x.

P. Lesaffre, M. Gerin, and P. Hennebelle. Effects of turbulent diffusion on the chemistry of diffuse clouds. *Astron. and Astrophys.*, 469:949-961, July 2007. doi: 10.1051/0004-6361:20066807.

P. Lesaffre, S. A. Balbus, and H. Latter. A comparison of local simulations and reduced models of MRI-induced turbulence. *M. N. R. A. S.*, 396: 779-787, June 2009. doi: 10.1111/j.1365-2966.2009.14798.x.

P. Lesaffre, S. M. Chitre, A. T. Potter, and C. A. Tout. A two-dimensional mixing length theory of convective transport. *M. N. R. A. S.*, 431: 2200-2208, May 2013a. doi: 10.1093/mnras/stt317.

P. Lesaffre, G. Pineau des Forêts, B. Godard, P. Guillard, F. Boulanger, and E. Falgarone. Low-velocity shocks: signatures of turbulent dissipation in diffuse irradiated gas. *Astron. and Astrophys.*, 550:A106, February 2013b. doi: 10.1051/0004-6361/201219928.

F. Levrier, F. Le Petit, P. Hennebelle, P. Lesaffre, M. Gerin, and E. Falgarone. Applying the Meudon PDR code on dense structures from MHD simulations of the ISM. In J. Cernicharo and R. Bachiller, editors, *IAU Symposium*, volume 280 of *IAU Symposium*, page 233P, May 2011.

Z.-Y. Li, V. I. Shematovich, D. S. Wiebe, and B. M. Shustov. A Coupled Dynamical and Chemical Model of Starless Cores of Magnetized Molecular Clouds. I. Formulation and Initial Results. *Astrophysical Journal*, 569:792-802, April 2002. doi: 10.1086/339353.

M. S. Miesch. Differential rotation and meridional circulation in global models of solar convection. *Astronomische Nachrichten*, 328:998-1001, December 2007. doi: 10.1002/asna.200710841.

R. Mochkovitch. The thermodynamics of the convective URCA process. *Astron. and Astrophys.*, 311:152-154, July 1996.

G. Momferratos, P. Lesaffre, E. Falgarone, and G. Pineau des Forêts. Turbulent energy dissipation and intermittency in ambipolar diffusion magnetohydrodynamics. *M. N. R. A. S.*, 443:86-101, September 2014. doi: 10.1093/mnras/stu853.
H. Mouri, A. Hori, and M. Takaoka. Fluctuations of statistics among subregions of a turbulence velocity field. *Physics of Fluids*, 20(3):035108–+, March 2008. doi: 10.1063/1.2890499.

K. Nomoto and D. Sugimoto. Rejuvenation of Helium White Dwarfs by Mass Accretion. *P. A. S. J.*, 29:765–780, 1977.

B. Paczyński. Carbon Ignition in Degenerate Stellar Cores. *Astrophysical Letters*, 11:53, May 1972.

L. Pagani, P. Lesaffre, M. Jorfi, P. Honvault, T. González-Lezana, and A. Faure. Ortho-$H_2$ and the age of prestellar cores. *Astron. and Astrophys.*, 551:A38, March 2013. doi: 10.1051/0004-6361/201117161.

B. Paxton, L. Bildsten, A. Dotter, F. Herwig, P. Lesaffre, and F. Timmes. Modules for Experiments in Stellar Astrophysics (MESA). *Astrophys. Journal Supp.*, 192:3, January 2011. doi: 10.1088/0067-0049/192/1/3.

J. Pety and E. Falgarone. The elusive structure of the diffuse molecular gas: shocks or vortices in compressible turbulence? *Astron. and Astrophys.*, 356:279–286, April 2000.

D. Ruelle. Non-Equilibrium Statistical Mechanics of Turbulence. *Journal of Statistical Physics*, 157:205–218, October 2014. doi: 10.1007/s10955-014-1086-8.

J. Schou, H. M. Antia, S. Basu, R. S. Bogart, R. I. Bush, S. M. Chitre, J. Christensen-Dalsgaard, M. P. Di Mauro, W. A. Dziembowski, A. Eff-Darwich, D. O. Gough, D. A. Haber, J. T. Hoeksema, R. Howe, S. G. Korzennik, A. G. Kosovichev, R. M. Larsen, F. P. Pijpers, P. H. Scherrer, T. Sekii, T. D. Tarbell, A. M. Title, M. J. Thompson, and J. Toomre. Helioseismic Studies of Differential Rotation in the Solar Envelope by the Solar Oscillations Investigation Using the Michelson Doppler Imager. *Astrophysical Journal*, 505:390–417, September 1998. doi: 10.1086/306146.

Z.-S. She and E. Leveque. Universal scaling laws in fully developed turbulence. *Physical Review Letters*, 72:336–339, January 1994. doi: 10.1103/PhysRevLett.72.336.

T. Sousbie. The persistent cosmic web and its filamentary structure - I. Theory and implementation. *M. N. R. A. S.*, 414:350–383, June 2011. doi: 10.1111/j.1365-2966.2011.18394.x.
T. Sousbie, C. Pichon, and H. Kawahara. The persistent cosmic web and its filamentary structure - II. Illustrations. *M. N. R. A. S.*, 414:384-403, June 2011. doi: 10.1111/j.1365-2966.2011.18395.x.

J. Stein, Z. Barkat, and J. C. Wheeler. The Role of Kinetic Energy Flux in the Convective URCA Process. *Astrophysical Journal*, 523:381-385, September 1999. doi: 10.1086/307715.

L. N. Tram, P. Lesaffre, S. Cabrit, A. Gusdorf, and P. T. Nhung. H₂ emission from non-stationary magnetized bow shocks. *M. N. R. A. S.*, 473:1472–1488, January 2018. doi: 10.1093/mnras/stx2334.

V. M. Uritsky, A. Pouquet, D. Rosenberg, P. D. Mininni, and E. F. Donovan. Structures in magnetohydrodynamic turbulence: Detection and scaling. *Phys. Rev. E*, 82(5):056326, November 2010. doi: 10.1103/Phys-RevE.82.056326.

V. Valdivia, P. Hennebelle, M. Gérin, and P. Lesaffre. H₂ distribution during the formation of multiphase molecular clouds. *Astron. and Astrophys.*, 587:A76, March 2016. doi: 10.1051/0004-6361/201527325.

V. Valdivia, B. Godard, P. Hennebelle, M. Gerin, P. Lesaffre, and J. Le Bourlot. Origin of CH⁺ in diffuse molecular clouds. Warm H₂ and ion-neutral drift. *Astron. and Astrophys.*, 600:A114, April 2017. doi: 10.1051/0004-6361/201629905.

F. P. Wilkin. Exact Analytic Solutions for Stellar Wind Bow Shocks. *Astro-phys. Journal Letters*, 459:L31, March 1996. doi: 10.1086/309939.
# Chapter 7

## Curriculum vitae
# Pierre LESAFFRE

LRA, ENS
24, rue Lhomond
75231 Paris Cedex 05
France
tel: 0033 (0)1 44 32 33 49

Email : pierre.lesaffre@lra.ens.fr
Born May 21st, 1975
Married, four children
French nationality

<figure><img src="image_21.png" /></figure>

## EDUCATION / POSITIONS HELD

<table><thead><tr><th></th><th></th></tr></thead><tbody><tr><td><strong>Université des Sciences et des Technologies de Hanoï (USTH, Vietnam)</strong><br>Driving Committee of the master 'Space & Applications'<br>Teaching coordination of the M2 'Space & Applications'<br>Long term visitor researcher in the Vietnam-Auger Training Laboratory for the Young (VATLY) group, Hanoi</td><td>2012-2013-2016<br>2013-2014</td></tr><tr><td><strong>Computing meso-centers</strong><br>meso-PSL (computing center of Paris Science & Lettre) driving committee<br>Centre de Calcul des Écoulements Magnétisés (CEMAG) science expert</td><td>2013-2010-2013</td></tr><tr><td>In charge of the <strong>general colloquium at ENS</strong> physics department</td><td>2009-2011</td></tr><tr><td><strong>Chargé de recherche 1ère classe CNRS</strong><br>Churchill College (UK) french overseas fellow<br>Chargé de recherche 2ème classe CNRS (ranked 1<sup>st</sup>) (LERMA/ENS, Paris)<br>Post-doc in the Chaire d'excellence of Steve Balbus (LERMA/ENS, Paris)<br><strong>Laboratoire de Radioastronomie (LERMA/ENS, Paris)</strong></td><td>2012-2008-2009<br>2007-2012<br>2005-2007<br>2005-</td></tr><tr><td><strong>Institute of Astronomy (IoA, Cambridge) and Oxford university, UK.</strong><br>Post-Doc in the European Supernova Community (ESC)<br>Advisors C. A. Tout (Cambridge) and Ph. Podsiadlowski (Oxford)</td><td>2002-2005</td></tr><tr><td><strong>Commissariat à l'Energie Atomique (CEA), Saclay, France.</strong><br>Ph.D: Dynamical aspects of the interstellar medium. Advisor J.-P. Chièze</td><td>1999-2002</td></tr><tr><td><strong>Meudon Observatory, France.</strong><br>Equivalent M.Sc. : Magistère des sciences de la matière (Physics)<br>Diplôme d'Etudes Approfondies (DEA) in « Techniques in Space Science »</td><td>1998-1999</td></tr><tr><td><strong>Ecole Normale Supérieure de Lyon (ENSL), Lyon, France.</strong><br>Agrégation in Mathematics (national exam for teaching in colleges and university).<br>Master in physics. Bachelor in mathematics.</td><td>1995-1998<br>July 1998<br>1995-1998</td></tr></tbody></table>
RESEARCH

**Research at LRA.** 2005-

- **Turbulence dissipation**

I examine the role of **turbulence** and its dissipation onto the chemistry of the **interstellar medium**.

I study **stellar winds** with the Vietnam Satellite Center / Department of Astrophysics (VNSC/DAP) group in Hanoi. And I show how a distribution of 1D shocks can model 3D **bow shocks** (Le Ngoc Tram PhD thesis). 2013-

I interface the Paris-Durham shock code and the RAMSES 3D MHD into **CHEMSES**, first hydro+chemistry code with time-dependent excitation of H2.

I start to implement irradiation physics in the **Paris-Durham** shock code.

I study the statistics of **dissipative structures** and design techniques to recover dissipative losses in Godunov schemes (Momferratos PhD thesis). 2012-2015

- **Stellar physics**

I study the **convection in stars** and the rotational profile of the sun.

I formulate a general turbulence closure for mixing length theories (Adam Jermyn PhD thesis). 2015-

I improve **stellar evolution algorithms** and incorporate some of my findings in the **MESA** stellar evolution code written by Bill Paxton.

I examine **deuteration chemistry** to time the spherical collapse of protostellar clouds.

**Post-Doc. (ENS/LRA)** 2005-2007

I work with Steve Balbus on the interplay between thermal and magnetorotational instabilities in **proto-planetary disks**. I develop numerical extensions to 3D MHD codes such as **RAMSES** and **ZEUS** on the 256 CPU computer of the lab.

**Post-Doc. (at Oxford & Cambridge universities)** 2002-2005

With C.A. Tout and Ph. Podsiadlowski, I link **type Ia supernovae** progenitors to explosion models. In particular, I produced a new model for the convective Urca process and developed a new stellar evolution code **Flash_the_Tortoise**.

I work with R. Stancliffe and C.A.Tout on **TP-AGB stars** (IoA, Cambridge).

I study **electron-capture supernovae** with Ph. Podsiadlowski, J. Dewi, J. Willer and W. Newton (Oxford).

**Ph.D. (at Paris 7 university)** 1999-2002

I developed a **high resolution computational model for time dependent mono-dimensional MHD shocks**.

I applied this model to **proto-stellar jets**, **photo-ionising** and **photo-dissociating fronts** and spherical collapse of dense cores.

I also derived analytical results on the **thermal instability in the interstellar medium**.
Master 2 Internship.
I developed a **Zel'dovich multi-scale approximation algorithm**.
Advisor S. Colombi. Institut d'Astrophysique de Paris, France.
Apr-Jun 1998

Master 1 Internship.
I reduced **photometry of dwarf galaxies in the local group of M81**.
Advisor Ph. Prugniel. Lyon Observatory, France.
Jun-Aug 1996

Bachelor Internship.
I developed a code for **digital spectrophotometry**.
Advisor P. B. Stetson. Dominion Astrophysical Observatory, Canada.
Jun-Aug 1995

TEACHING

Lecturer in the Space and Application master at USTH (average 20h / year)
Astrophysics. Celestial Mechanics. Optical Astronomy. Probabilities&Statistics.
Introduction to programming with python.
2012-

Graduate teaching assistant, Paris 7 Jussieu University, France.
Introductory courses to the theory of probability for undergraduate students.
1999-2002

STUDENTS SUPERVISION

<table><tr><td>L3 Merwan Ouldelhkim (100%) (effective fraction of the supervision)</td><td>June 2017</td></tr><tr><td>PhD Adam Jermyn (50% during first year)</td><td>2016-2017</td></tr><tr><td>PhD Le Ngoc Tram (90%)</td><td>2015-2018</td></tr><tr><td>PhD Giorgos Momferratos (90%)</td><td>2011-2015</td></tr><tr><td>M1 Valeska Valdivia (50%)</td><td>summer 2012</td></tr><tr><td>M2 Hoàng Thanh Phi Hùng (100%)</td><td>summer 2011</td></tr><tr><td>M2 Petar Todorov (100%)</td><td>summer 2011</td></tr><tr><td>M2 Clothilde Busschaert (100%)</td><td>summer 2009</td></tr><tr><td>PhD Ludovic Petitdemange (10%)</td><td>2006-2009</td></tr><tr><td>PhD Richard Stancliffe (20%)</td><td>2002-2005</td></tr></table>

LANGUAGES

<table><tr><td>French</td><td>Mother tongue</td></tr><tr><td>English</td><td>Fluent</td></tr><tr><td>German</td><td>Basic</td></tr><tr><td>Vietnamese</td><td>Basic</td></tr></table>

PROGRAMMING

<table><tr><td>Programming</td><td>FORTRAN 90, C</td></tr><tr><td>Parallelisation</td><td>MPI, openMP</td></tr><tr><td>Data handling</td><td>IDL, Perl, Ruby, Python</td></tr></table>
## OTHER FIELDS OF INTERESTS: Music

### Piano solo performances

with Cambridge Sinfonieta, St Saens 5th piano concerto, at Milton, UK April 2016

with l'Odysée Symphonique, Gershwin's Rhapsodie in Blue, at les Ulis and Paris June 2013

with the "Britton's peers" in Mozart's 21st concerto, at West Road, Cambridge March 2012

with 'l'Odyssée Symphonique' in Beethoven's 5th concerto at Gif-sur-Yvette January 2011

with Cambridge Sinfonieta in Beethoven's 5th concerto at Fitzwilliam college June 2010

with 'l'orchestre de la garde républicaine' in Weber's Konzertstück, la Sorbonne December 2007

2nd prize at the international competition for outstanding piano amateurs, Paris, Sorbonne. January 2003

Finalist at the international competition for outstanding piano amateurs, Paris maison de la radio January 1999
# Chapter 8

## Note d'accompagnement

D'après le site de l'observatoire, cette note doit servir à montrer mes capacités à “concevoir, diriger, animer et coordonner des activités de recherche et de valorisation”. Je préfère de beaucoup le terme “superviser” à celui de diriger. À mon sens, mon rôle est de montrer l’objectif lointain où l’on souhaite aller, et l’étudiant doit pouvoir choisir sa propre voie. Pour moi, une thèse se conçoit mieux comme une collaboration fructueuse plutôt qu’un lien hiérarchique, et finalement le terme “accompagnement” me paraît sans doute encore plus approprié, même si ce n’est sans doute pas le sens que l’observatoire voulu donner au titre de ce document. Enfin, j’ai déjà fait une part de la “mise en perspective” demandée par l’observatoire dans la conclusion du document scientifique (voir section 2.2) et je ne vais pas la répéter ici.

### 8.1 Encadrement informel

J'ai été amené très tôt à accompagner des étudiants, en qualité de collègue et conseiller. Dès mon premier post-doc à Cambridge, j'ai pris beaucoup de plaisir à échanger avec Richard Stancliffe et ai contribué à le former sur la physique numérique du code d'évolution stellaire de Cambridge, dans lequel j'étais en train de porter les techniques de maillage glissant mises au point pendant ma thèse. J'ai finalement été appelé à siéger dans son jury de thèse en tant qu'examineur interne. Il m'a ensuite été donné d'interagir avec Ludovic Petitdemange au cours de sa thèse avec Steve Balbus pour lui faire prendre en main une version du code MHD parallèle Zeus3D et l'aider à y implémenter la physique qu'il avait à coeur de modéliser (pour tester la MRI dans les intérieurs stellaires ou planétaires).
## 8.2 Encadrement formel

### 8.2.1 Stagiaires M1 et M2

J'ai encadré mon premier stagiaire M2 dans le cadre du master de physique nucléaire de l'université de Bordeaux 1 délocalisé à Hanoï. Hoàng Thanh Phi Hùng était désireux d'acquérir une expérience en astrophysique et nous avons examiné pendant son séjour à Paris les caractéristiques des étoiles progénitrices des supernovae de type Ia, en utilisant la version de l'époque du code d'évolution stellaire MESA (publiée sous la forme Paxton et al., 2011). Il travaille aujourd'hui au Vietnam comme ingénieur nucléaire dans un service d'imagerie hospitalier.

Sur une prolongation de ce sujet, j'ai ensuite accueilli Clotilde Buschaert lors de mon séjour à Cambridge. Elle a donc pu réaliser l'étape suivante, qui fait croître les naines blanches vers l'explosion finale. Elle a ainsi pu tester l'efficacité de l'algorithme de suivi des interfaces convectives/radiatives que j'avais conçu, et a reproduit sans effort les résultats d'une précédente étude réalisée avec le code STARS de Cambridge (Lesaffre et al., 2006). Elle a aujourd'hui décroché un poste d'ingénieur de recherche au CEA de Cadarache.

J'ai supervisé le stage M2 de Petar Todorov, qui a essuyé les premiers plâtres de mes essais avec CHEMSES. Il a examiné à 2D l'effet d'une turbulence entretenue sur la réactivité d'une réaction acide-base. Il a ainsi été en mesure de reproduire numériquement les résultats expérimentaux de Arratia and Gollub (2006). Il travaille aujourd'hui en tant qu'ingénieur informati-cien dans une start-up parisienne. J'ai realyé Patrick Hennebelle pour la superivsion du stage de M1 de Valeska Valdivia avec qui nous avons calibré la diffusivité du code CHEMSES en analysant la vitesse de propagation de fronts de réaction/diffusion pour diverses résolutions et coefficients de diffu-sion. Valeska Valdivia est aujourd'hui en post-doc avec Annaëlle Maury au CEA.

### 8.2.2 Thésards

Mon premier thésard "à temps complet" est Giorgos Momferratos, un étudiant passionné par la turbulence. Il a contacté Edith Falgarone en lisant un su-jet de thèse qui n'avait pas trouvé preneur. Il avait écrit seul pendant son master un code pseudo-spectral et avait réalisé à son université des simu-lations lourdes de turbulence hydrodynamique pour mesurer les propriétés d'aggrégation d'un scalaire passif. Son travail de master nous a tellement im-pressionné que nous l'avons fait venir au laboratoire pour le jauger et nous
avons décidé de lui réécrire un sujet sur mesure. Il a donc étudié avec moi
les structures dissipatives dans de la turbulence MHD en déclin avec ou sans
diffusion ambipôlaire (voir Momferratos et al., 2014 et section 4.2). Comme
je n'avais pas obtenu ma HDR avant la fin de sa soutenance, c'est Guillaume
Pineau des Forêts qui a constitué son directeur de thèse officiel.

Mon second thésard est Lê Ngọc Trâm, rencontré au travers du master
'Espace et Applications' que j'ai contribué à développer à Hanoï. Nous avons
ensemble examiné en détails l'émission de la molécule H₂ dans des modèles
3D de chocs magnétisés (Tram et al., 2018) et nous incluons la physique des
vents stellaires dans le code de Paris-Durham dans le but ultime de modéliser
le choc en retour dans le vent. Cet outil servira aussi pour interpréter les
observations ALMA que l'équipe de Hanoï (au VNSC/DAP) exploite grâce
à la politique de mise à disposition rapide de ces données: une réelle aubaine
pour des pays dont la recherche est pauvre en moyens mais riche en idées.

Enfin, j'ai participé pour moitié à l'encadrement de la première année de
thèse d'Adam Jermyn. Cet étudiant américain à Cambridge (UK) a souhaité
travaillé sur la prolongation de mes travaux sur la convection stellaire. Il
s'est très vite approprié les équations et est venu travailler avec moi à l'ENS
pendant un bon mois début 2016. Cet étudiant extrêmement brillant ne pêche
que par excès de confiance, qui est un atout lorsqu'on souhaite débrider sa
créativité. L'une de ses idées a fini par résister à mon filtre correcteur et
elle nous a permi d'étendre notre modèle convectif à un grand nombre de cas
supplémentaires (rotation et gradient de température arbitraires, en présence
de champ magnétique, voir section 2.2).

8.3 Vulgarisation scientifique

La prospection d'étudiants pour le master Hanoïen et mes multiples voyages
au Vietnam m'ont donné l'occasion à de nombreuses reprises de vulgariser
la science auprès d'une grande variété de publics à travers ce pays où à ma
connaissance la motivation des jeunes ne connait pas d'égal.

En France, j'ai récemment donné la conférence grand public pour le col-
loque bisannuel PCMI (physico-chimie du milieu interstellaire) qui se tenait
à Lille. J'y ai brossé un tableau des activités PCMI organisées autour
de l'origine des molécules du vivant. C'est un exercice très sain, que je
trouve très gratifiant, utile pour notre propre connaissance de ce que font
nos collègues, qui permet une meilleure compréhension de la physique et
qui, en élargissant notre perspective, nous fait parfois entrevoir de nouvelles
articulations entre différents domaines de recherche.

Je suis assez régulièrement désigné pour présenter aux nouveaux entrants
de l'école normale les activités de notre laboratoire de radioastronomie. J'ai aussi réalisé quelques visites de l'observatoire de Paris pour des groupes de lycéens, et suis intervenu dans quelques classes primaires pour répondre aux questions d'enfants qui avaient travaillé sur ce thème. J'ai pris beaucoup de plaisir à échanger avec eux et ai pu admirer la profondeur de leurs questions et leur capacité de concentration sur ces sujets pourtant réputés comme difficiles. Mes interventions face aux primaires étaient avec questions libres: je n'ai rien préparé à l'avance, et ne leur ai pas fait d'exposé préalable, sauf pour expliquer en deux phrases le quotidien du chercheur astrophysicien. Ces sessions ont toutes duré plus d'une heure et demie, se sont déroulées sans heurt ni chahut et se clôturaient systématiquement faute de temps restant. Un seul exemple, face aux quelques mains impatientes encore levées à la fin d'une session: "Bon d'accord, encore une dernière question... - monsieur, pourquoi le ciel est bleu le jour et noir la nuit ?". Deux des plus merveilleuses questions auxquelles puisse rêver un astrophysicien, réunies en une seule...

## 8.4 Organisation d'événements scientifiques

J'aide Phan Bao Ngọc à organiser chaque été l'école Vietnam School Of Astrophysics qui regroupe une quinzaine d'étudiants d'Asie du Sud-Est triés sur le volet. Au cours d'une semaine de cours et travaux pratiques sur un thème différent chaque été ils côtoient une poignée de professeurs choisis parmis les participants des conférences internationales données à l'ICISE. C'est l'occasion pour eux de pratiquer leur anglais, d'approfondir des sujets qui ne sont pas enseignés au Vietnam, et d'avoir un aperçu du quotidien de scientifiques chevronnés. Réciproquement, c'est pour ces professeurs une chance de trouver un futur étudiant de thèse brillant et motivé.

Cédant à l'amicale pression de Tràn Thanh Vân et son épouse, j'ai organisé une conférence internationale à l'ICISE au cours de l'été 2016 sur le thème des vents stellaires: "Blowing in the wind". Ce thème permet de couper horizontalement à travers de multiples sujets astrophysiques, réalisant un pont entre le milieu interstellaire et les intérieurs stellaires. Bien que cette conférence fut un réel succès, son organisation m'a coûté un temps infini. Pour couvrir les frais de la conférence (qui restent modestes car les frais locaux sont très faibles), il m'a fallu une vingtaine de demandes de fonds (dont seules six couronnées de succès) pour récolter 12 000 euros à mettre en regard de la contribution de l'ICISE (environ 10 000 euros). La diversité des guichets des demandes nous force ensuite à jongler avec les règles propres à chacun d'entre eux et constitue un véritable casse-tête pour les accomoder aux demandes particulières de chaque participant. J'ai d'autre
part pu constater que j'avais beaucoup de mal à déléguer (ou tout du moins
à faire réaliser certaines tâches à d'autres personnes). Malgré un SOC très
nombreux, l'essentiel a reposé sur ma propre personne: j'ai donc fait un très
mauvais manager.

Plus tôt dans la même année, j'ai participé à l'organisation de l'hommage
à Jean-Pierre Chièze avec Chantal Stehle, Édouard Audit, Sylvaine Türck-
Chièze, et Xavier Fresquet dont l'extraordinaire efficacité a joué pour beau-
coup dans le succès de cette événement. J'ai aussi accompagné François
Dulieu dans la mise en place d'un atelier sur la physique des grains qui a réuni
les pôles 2 et 3 du LERMA. Bien qu'uniquement prête-nom dans l'édition
V de 'Magnetic Fields in the Universe' (Cargèse 2015), j'ai été témoin de
l'immense travail d'Edith Falgaronne et celà a constitué ma première expérience
en matière d'organisation de conférences.

Ma conclusion est que je suis bien meilleur en tant que second-couteau
dans ce type d'aventure. Aujourd'hui, j'accompagne Anne Dutrey dans
l'organisation de la prochaine conférence d'astrophysique à ICISE ('the cos-
mic cycle of dust and gas in our Galaxy') et sers de trait d'union entre Tràn
Thanh Vân et de futurs organisateurs de conférences dans ce lieu qui fait
penser à un Cargèse Vietnamien.

8.5 Enseignement

Mon premier contact avec des étudiants était lors du monitorat qui allait avec
ma thèse: j'ai supervisé des TDs de statistiques et probablités à Jussieu. Ces
cours m'ont par la suite été très utile lorsque j'ai pris en charge les cours de
probabilités et statistiques au master 'Espace et Applications' de l'USTH,
jusqu'à il y a deux ans. J'ai assuré par ailleurs au même master le cours
d'introduction à l'astrophysique et de mécanique céleste (la première année).
J'ai donné un cours d'introduction à la programmation en python l'année où
j'étais établi à Hanoï. Et je gère aujourd'hui la session de méthodologie des
observations optiques dont j'espère arriver à passer la main aux enseignants
vientamiens l'année prochaine. À cette occasion, j'organise tous les ans
des sessions pratiques au télescope de 30 cm de l'Université d'Éducation de
Hanoï. En moyenne ces enseignements représentent une vingtaine d'heures
par an (soixante la première année où j'avais trois cours simultanément à
cause d'un remplacement). L'anglais très basique et l'inhomogénéité des
profils de ces étudiants sont largement compensés par leur motivation et leur
enthousiasme. Un bon nombre d'enseignants en France envoyés à Hanoï y
retrouvent le goût d'enseigner qu'ils avaient perdu dans nos universités.
8.6 Animation scientifique

J'ai animé pendant deux ans le séminaire général de l'ENS, en tâchant de trouver des thèmes réellement généraux, touchant à des problèmes de société ou bien d'actualité. Je suis responsable de la petite bibliothèque du laboratoire LRA et j'organise de temps en temps des journal clubs ou des réunions de groupe au labo. Je siège au comité de pilotage du méso-centre de calcul mésoPSL, mais il faut bien avouer qu'à part lors de la création du centre, ce comité n'a eu que peu de problèmes à traiter.

J'ai découvert la petite communauté astrophysique du Vietnam lors d'une conférence à Hanoï organisée par Pierre Encrenaz à laquelle j'ai eu l'occasion de participer en remplacement d'un orateur malade. J'ai été conquis par l'énergie et la motivation de ces jeunes chercheurs. C'est au cours de ce voyage qu'est née l'idée de démarrer un master Hanoïen sur les sciences spatiales et je me suis rapidement embarqué dans l'aventure de l'USTH (Université Science et Technique de Hanoï) au master Espace et Applications (en passe de devenir 'Espace et Aéronautique), dont je suis toujours membre du bureau. Quelques années plus tard, j'ai ainsi profité d'une année à Hanoï (2013-2014, en partie en mise à disposition) pour coordonner la mise en place de la deuxième année du master. J'en ai assuré la coordination pédagogique jusqu'en 2016. J'ai profité de mon année à Hanoï pour prospecter la pertinence d'un centre de calcul informatique à l'USTH. J'ai ainsi rencontré un à un tous les acteurs du numérique à Hanoï: ma conclusion était qu'ils ont suffisamment de machines à leur disposition, mais les moyens humains pour les utiliser manquent cruellement... Ce besoin de formation plutôt que d'équipement forme un stat assez général au Vietnam, qui justifie notre action à l'USTH. Le centre ICISE (International center for Interdisciplinary Science and Education) est né à peu près au même moment, et Tràn Thanh Vân et son épouse Kim Ngọc m'ont aussi mis à contribution pour rédiger le cahier des charges scientifique pour la conception des expositions du planétarium qui ouvrira au cours de l'année prochaine au côté de l'ICISE à Quy Nhon (voir photo figure 19).

Le Vietnam est riche en étudiants très motivés, qui savent bien calculer (mais mal parler anglais...). À court terme, l'université USTH représente une ressource riche en moyens matériels mais manquant encore de moyens humains (pour un temps seulement, car les thésards vietnamiens sont appelés à prendre notre relève d'ici quelques années). À moyen terme, le VNSC se constituera comme un vrai centre de réalisation de satellites, avec sans-doute à long terme une plate-forme de lancement convoitée par les japonais qui manquent de lanceurs à basse latitude. L'astrophysique au Vietnam est encore balbutiante, mais prend d'autant plus de sens d'une part avec la mise en accès libre aux données de plus en plus rapide dans les très grands
<figure><img src="image_22.png" /><figcaption>Figure 19: Une vue du centre ICISE de nuit.</figcaption></figure>

équipements tels ALMA, et d'autre part comme un moyen de drainer des
bons étudiants vers le centre spatial. L'USTH est certes fragile à cause du
contexte politique au Vietnam, où le fonctionnement déplorable des uni-
versités nationales menace de prendre le dessus (une crainte d'autant plus
forte que la Vietnam Academy of Science and Technology en a récemment
repris le contrôle). Mais sa pérennité sera bien mieux assurée tant que de
la recherche solide y est menée. Il est par exemple difficile de contester le
succès de l'USTH en termes de ses publications, grâce auxquelles elle tient
le rang de 7ème université au Vietnam (Nature Index) malgré son jeune âge
(5 ans). Mon intention est donc de continuer à soutenir d'une façon pratique
les équipes de recherche astrophysique au Vietnam en poursuivant une col-
laboration continue avec elles. C'est de plus un sentiment très exhaltant de
participer à l'éclosion de cette discipline dans ce pays.