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Molecules, magnetic fields and Intermittency in coSmic Turbulence – Following the energy trail.

Periodic Reporting for period 4 - MIST (Molecules, magnetic fields and Intermittency in coSmic Turbulence – Following the energy trail.)

Reporting period: 2022-04-01 to 2023-09-30

Stars are the long-lived building blocks of galaxies. While most of the stars and galaxies of our present-day universe formed, almost all together, 10 billion years ago when the universe was very young, new stars are still forming now, at a much lower pace. A major step forward occurred, decades ago, with the discovery that star formation is the outcome of simultaneous accretion, driven by gravity, and ejection, powered by and gravitational energy of stars (and black holes).

A most vexing concern, however, is that everywhere at the scale of galaxies and giant molecular clouds, in the early universe as in our own Galaxy, star formation is 10 to 100 times less efficient than predicted by theory. What is the missing piece in the puzzle?
Turbulence, among others, is a critical player, and the far-reaching question addressed in the MIST project is the following: can we measure the fraction of the large-scale gravitational energy stored in turbulent motions in the violent interplay between accretion and ejection?

Turbulence is a cascade where the energy injection and dissipation rates balance each other. This is key because the former may be inferred from the latter, in spite of a major additional complexity: turbulence is intermittent in space and time, so that its dissipation is not uniform but occurs in rare bursts that fill only a tiny fraction of the volume. The origin of turbulent intermittency is an on-going and intense theoretical debate.
As almost nothing is known theoretically on the intermittency in a highly turbulent, magnetized, compressible and partially ionized plasma - the medium where stars form - the MIST project is rooted on original observations. This is so because nature is providing invaluable beacons. In the same way as glitters of luminescent plankton image the small scale extrema of shear stress in the breaking waves of tropical seas, one molecular species, CH+ - ironically one of the three first ever discovered in interstellar space in the 1940's, is one such beacon. This molecule highlights the sites of turbulent dissipation because only in such regions can atomic collisions overcome the 0.5 eV endothermicity of its formation route.
On the theoretical side, the main challenge is the impressive range of scales and thermal phases that are coupled by gravitation and turbulence in space. Dissipation occurs at scales presumably smaller than the viscous length i.e. the mean free path of particles, about one astronomical unit in the cold medium of interest for star formation. Gravitational energy is fed at the largest scales, those of galaxies and galaxy clusters, more than 10 orders of magnitude larger than the dissipation scales. This is a challenge that cannot be tackled by one single methodology.
The milestones of the MIST project therefore include:
(1) Molecular line observations in the nearby and high-redshift universe that provide local and global perspectives of this fundamental process,
(2) Statistical studies of the velocity and magnetic fields to characterize intermittency of turbulence at the smallest possible scales in the nearby interstellar medium,
(3) Numerical simulations of magnetized turbulence dedicated to dissipation to provide a census of the different kinds of magnetic, velocity and density structures causing dissipation,
(4) Models of the non-equilibrium chemistry triggered in these dissipation structures
Turbulence is a resilient unsolved problem in physics and the energy dissipation it generates is in focus of many industrial investigations in aeronautics, maritime transport, space missions, etc. Cosmic turbulence provides a unique field of investigation because it is extreme, in the sense that the ratio of the energy injection scales to the dissipative scales is larger than in any other known system.
The MIST project is providing insights on a fundamental property of turbulence, its space-time intermittency. This is an active field in laboratory experiments, in the spatial exploration of the solar wind, in the physics of plasma confinement in the perspective of mastering nuclear fusion. It is a key phenomenon that couples the fluid and plasma properties of cosmic turbulence at small scale. The challenge of the prodigious range of scales coupled by turbulence is shared by many other fields of physics, climate sciences in particular, where turbulence in the oceans and in the atmosphere plays a crucial role in their exchange of matter and energy.
Astronomy is an important driver of advanced technology. In the present case, interferometry and spectroscopy in the sub-millimeter and far-infrared ranges are making giant leaps forward in the domain of detectors, mixers and correlators, not to mention the prospective of space missions in that field.
Last, human beings are naturally curious of the nature of the universe and are often most grateful to researchers who dedicate their life to acquire this knowledge. As one of the 2020 Nobel prize of physics winners says " It is important to get people excited about research. And astronomy has a special role to play". Humanity would not have evolved as it did without a knowledge of their sky. This knowledge opens up to timescales that are immensely beyond the human lifetime.
The goal of the MIST project is therefore to follow the energy trail of baryonic matter in the star (and galaxy) formation processes from its source, the gravitational energy of the largest scales to its fate, the loss in radiative cooling. The turbulent energy cascade is a clue because it grows way faster than the warm gas can cool down.
The practical question is to be able to measure how much of the total energy is entering the turbulent cascade. As said above, the molecular species, CH+, called methylidinium, plays the role of the plankton in cosmic turbulence because its presence highlights the bursts of turbulence dissipation. Another peculiar property of this species is its short lifetime. Unlike most molecules, it is destroyed by collisions faster than by photons. Therefore, it cannot be transported by fluid motions away from its formation site. It is this property that is used to estimate the amount of turbulent energy injected in the medium to form the number of molecules we observe. It is robust and simple.
The second objective of the MIST project is the modeling of the formation of CH+ and its link with turbulent dissipation. This is why numerical simulations of compressible magnetized turbulence dedicated to dissipation are performed to characterize the different kinds of dissipative processes, followed by detailed models of the micro-physics and chemistry at the scale of these dissipative structures.
This modeling step is conducted in parallel to novel statistical approaches performed in the nearest observed regions, to characterize the velocity and magnetic fields in these dissipation structures.
The discovery with the ALMA interferometer of CH+ emission lines broader than1000 km/s
in the circumgalactic medium of starburst galaxies at redshift ~3 is a new milestone in the MIST project. These linewidths, far too large to allow molecule survival, are a challenge to turbulent cascade theories in multi-phasic media. They are the signposts of kiloparsec-scale shocks found to highlight the long-sought interface between accretion and ejection i.e. infalling matter and outflows.

At the other end of the scales accessible to the NOEMA and ALMA interferometers, i.e. close to the dissipation scales, the CO lines are used to trace the velocity field in diffuse molecular gas. Elongated and sharp-edged structures are detected. A spatial coherence, never seen before, is found in the orientation of these CO-edges at the milliparsec- and parsec-scale. This is both a robust observational breakthrough and a challenge for theory. The still unresolved sharpness of these features suggests a dynamical generation of CO by some dissipative process operating at scales smaller than 300 au.

Numerical simulations of compressible magnetized turbulence dedicated to dissipation scales show that dissipation is concentrated in sheet-like fractal structures that fill only a tiny fraction of the whole volume (see Figure) and that rotational discontinuities and Parker sheets play a major role, in spite of the high compressibility of turbulence.

The state-of-the-art Paris-Durham shock model has been augmented to treat the combined impact of mechanical and UV irradiation energy inputs. When UV irradiation is external, the outcome is the time-dependent chemistry and the energy radiated by specific molecules, such as H2 and CH+ of major interest to the MIST project. The CH+ abundance in these shocks is enhanced by UV-photons while that of CO and H2O is reduced.

We also model UV self-irradiated shocks. UV self-generation turns on sharply at shock velocities of 30 km/s. As much as 20% of the shock initial kinetic energy escapes in the Ly alpha and Ly beta lines. These shocks produce enhanced abundances of molecules such as CO, HCO+ and CH+ while H2O is destroyed. Atomic and molecular lines reprocess the quasi totality of the kinetic energy, allowing the connection of observable emission, in the H2 lines, for instance, to the driving kinetic energy source.
The MIST team has developed a collaboration with mathematicians to apply their method - e.g. the Wavelet Scattering Transform (WST) - to numerical simulations and observations of interstellar matter. This approach is inspired by neural networks but, unlike those, the statistical descriptors are obtained without any learning step, an essential asset as we have one unique sky. The WST describes sky maps with only a few tens of coefficients, which allows the creation of synthetic emission maps with the same statistical characteristics as the input data.

The final steps of the MIST project - bridging theory and observations - have been initiated with two-dimensional small-scale simulations of hydrodynamic turbulence using the CHEMSES code, with fully resolved viscous dissipation, time-dependent heating, cooling, chemistry and excitation of H2 (see Figure). Molecules are produced and excited in the wake of strong dissipation ridges. Shocks are identified: they open endothermic chemical routes that allow the formation of CH+, HCO+ and CO.

In parallel, numerical simulations of turbulence (RAMSES code) have been dedicated to the role of supersonic turbulence in triggering phase transitions in the warm diffuse interstellar medium of our Galaxy. The atomic-molecular transition, that has a very characteristic shape as a function of the UV-shielding in our Galaxy, is shown to be a robust feature in well-defined domains of parameters. These results suggest that a strong self-regulation operates to bring this transition as observed when large fluctuations of these parameters perturb the system.
(1) In the irradiated shock models, new types of shocks, intermediate between the C- and J-shocks, have been shown to exist in the presence of UV photons. A new and robust algorithm has been developed to find steady-state solutions, to cross sonic points and identify non physical trajectories.
(2) In the UV self-irradiated shock models, the complex radiative transfer of Lyman alpha and Lyman beta photons is treated self-consistently with a doubly iterative method between the shock evolution and the radiative transfer. The extreme optical depths of Lyman alpha photons are computed with a multi-level accelerated Lambda iteration. Calculations in quadruple precision is necessary.
(3) In these two shock models, non-equilibrium chemistry is a prerequisite since the timescales of the dissipative dynamics (∼100 year or less) are far smaller than the time it takes to reach chemical equilibrium.
(4) In the numerical simulations of compressible magneto-hydrodynamical turbulence dedicated to dissipation, algorithms have been developed to control and estimate the numerical dissipation.
(5) The work with the WST is opening new perspectives for the analysis of observations of interstellar matter and their comparison with numerical simulations. We are extending it to analyze the all-sky Planck observations in total intensity and polarization.
(6) The size and topology in space and velocity of the smallest-scale molecular structures that we are able to detect with interferometers in diffuse molecular gas are opening a new field of investigation on the emergence of molecules in atomic gas.
(7) The ALMA discovery of emission and absorption lines of CH+ in high-redshift starburst galaxies is a breakthrough because this unique species is shedding a new light on dissipative processes in the process of galaxy growth.

Anticipating on the end of the project, we could expect:
- success in many upcoming JWST (November 2020) and ALMA (March 2021) proposals
- the achievement of a complete census of the CH+ emission regions in several starburst galaxy fields already observed
- finalizing the predictive power of intermediate velocity shock models in terms of H2 and CH+ emission lines, in particular
- the implementation of the ion-neutral drift in the numerical simulations dedicated to dissipation
- the tracing of the time evolution of the structures of dissipation extrema
- further developments of the numerical simulations of turbulence in multi-phasic media
- coupling chemistry and dissipation in the dedicated numerical simulations to start exploring the link with molecular line observations at the 300 au scale.

Figure caption: Left: Regions of extrema of dissipation in numerical simulations of magnetized turbulence dedicated to dissipation. The different colors show different kinds of dissipation due to compressible viscosity (blue), solenoidal viscosity (green) and ohmic resistivity (red). These regions are those that have received bursts of kinetic energy from
the turbulent cascade and in which dissipation is concentrated. The small white box shows the size of the simulations displayed in the right column, meant to compute the evolution of one parcel of gas, after receiving the burst of energy.
Upper right: Dissipation rate in a 2-dimensional simulation of hydrodynamic turbulence with chemistry and radiative cooling (CHEMSES code). The two viscous dissipations are shown (green and blue) as above. The difference between the total dissipation and viscous dissipation is shown in red. Lower right: CO abundance in the same simulation. The color display is logarithmic (red is 10 x blue). The black contours show the dissipation extrema (here, shocks). CO is generated in the wake of the dissipation structures.
Regions of extrema of dissipation in magnetized turbulence and CO production