Angular momentum is one of the most fundamental properties of matter in our universe, which has deep consequences on its evolution. In particular, the formation and the physical characteristics of cosmic structures such as galaxies, stars and planets are intimately linked to the amount of angular momentum they carry, to the way it is redistributed within the system and exchanged with the surrounding environment. Considerable efforts have been undertaken during the last decades to identify and quantify the various physical mechanisms responsible for the transport of angular momentum in these objects. While some of them are relatively well understood, in many circumstances the underlying mechanism turns out to be extremely complex and very challenging. In this introductory chapter, we first introduce some general considerations on the angular momentum impact and transport. We then derive the MHD equations both in the ideal and non-ideal limit. Finally, after deriving the conservative form of the angular momentum equation, we discuss in more details some of the mechanisms that can contribute to the transport of angular momentum in various astrophysical contexts.

Angular momentum plays a crucial role in the formation of stars and planets. It has long been noticed that parcels of gas in molecular clouds need to reduce their specific angular momentum by 6 to 7 orders of magnitude to participate in the building of a typical star like the Sun. Several physical processes on different scales and at different stages of evolution can contribute to this loss of angular momentum. In order to set constraints on these processes and better understand this transfer of angular momentum, a detailed observational census and characterization of rotation at all stages of evolution and over all scales of star forming regions is necessary. This review presents the main results obtained in low-mass star forming regions over the past four decades in this field of research. It addresses the search and characterization of rotation in molecular clouds, prestellar and protostellar cores, circumstellar disks, and jets. Perspectives offered by ALMA are briefly discussed.

Angular momentum is playing a key role during the collapse of prestellar cores since it is leading to disk formation and to some extent to binary formation. On the other hand, it has long been recognized that the stars possess a tiny fraction of the initial momentum that their parent clouds retain, an issue known as the “angular momentum problem”. In these lectures, we attempt to present the most recent calculations performed to investigate the angular momentum transport and the influence angular momentum has, during the collapse of prestellar cores. After a brief introduction of the star formation context and a broad description of the important features within collapsing cores, we discuss the so-called catastrophic braking. Indeed when magnetic field and rotation axis are aligned, the magnetic braking is so efficient that the formation of early disks is completely prevented. We then present the various studies which have attempted to explore the robustness of this efficient transport including influence of non-ideal MHD, misalignment between magnetic field and rotation axis and turbulence. While the role of the first, is not entirely clear; the two other effects diminish the efficacity of the magnetic braking making the issue less severe than in the pure ideal MHD aligned configuration. Finally, we discuss the fragmentation of low and high mass cores with particular emphasis on the impact of the magnetic field. In particular, we discuss the drastic stabilization that magnetic field has on low mass cores and the possible solution to this apparent conundrum. In the context of high mass stars, its influence is much more limited reducing the number of fragments by a factor of the order of two. However when both radiative feedback and magentic field are included, the fragmentation is very significantly reduced.

Angular momentum transport in accretion disk has been the focus of intense research in theoretical astrophysics for many decades. In the past twenty years, MHD turbulence driven by the magnetorotational instability has emerged as an efficient mechanism to achieve that goal. Yet, many questions and uncertainties remain, among which the saturation level of the turbulence. The consequences of the magnetorotational instability for planet formation models are still being investigated. This lecture, given in September 2012 at the school “Role and mechanisms of angular momentum transport in the formation and early evolution of stars” in Aussois (France), aims at introducing the historical developments, current status and outstanding questions related to the magnetorotational instability that are currently at the forefront of academic research.

This course reviews the rotational properties of non- degenerate stars as observed from the protostellar stage to the end of the main sequence. It includes an introduction to the various observational techniques used to measure stellar rotation. Angular momentum evolution models developed over the mass range from the substellar domain to high-mass stars are briefly discussed.

Classical T Tauri stars are low mass young forming stars that are surrounded by a circumstellar accretion disc from which they gain mass. Despite this accretion and their own contraction that should both lead to their spin up, these stars seem to conserve instead an almost constant rotational period as long as the disc is maintained. Several scenarios have been proposed in the literature in order to explain this puzzling “disc-locking” situation: either deposition in the disc of the stellar angular momentum by the stellar magnetosphere or its ejection through winds, providing thereby an explanation of jets from Young Stellar Objects.

In this lecture, these various mechanisms will be critically detailed, from the physics of the star-disc interaction to the launching of self-confined jets (disc winds, stellar winds, X-winds, conical winds). It will be shown that no simple model can account alone for the whole bulk of observational data and that “disc locking” requires a combination of some of them.

The Sun has been known to rotate for more than 4 centuries, and evidence is also available through direct measurements, that almost all stars rotate. In this lecture, I will propose a review of the different physical processes associated to rotation that are expected to impact the evolution of stars. I will describe in detail the way these physical processes are introduced in 1D stellar evolution codes and how their introduction in the modelling has impacted our understanding of the internal structure, nucleosynthesis and global evolution of stars.

Magnetic field are ubiquitous to young and mature low-mass stars, and can potentially impact their formation, their evolution and their internal structure; yet the physical processes that succeed at amplifying and sustaining these fields (called dynamo processes), like those capable of changing the fate of the host stars (and in particular their rotation rates), are still somewhat enigmatic. Although theoretical modelling and numerical simulations (e.g., of stellar dynamo action and magnetospheric accretion processes) showed breathtaking progress in the last decade, they are not yet in the state of accurately predicting the various magnetic topologies that different low-mass stars can generate nor the impact such fields can have on stellar formation.

Thanks to the advent of new-generation instruments, spectropolarimetric observations coupled to tomographic techniques can now reveal the large-scale magnetic topologies of both young and mature low-mass stars, and in particular their poloidal and toroidal components. More specifically, one can now investigate magnetic topologies of cool dwarfs, all the way from the brown dwarf threshold (spectral type M8) where stars are fully convective up to the limit beyond which outer convective zones get vanishingly small (spectral type F5); one can also explore the magnetic topologies of young low-mass stars that are still accreting mass from their circumstellar disc (i.e., the classical T Tauri stars) and study how such fields can impact mass accretion processes from the surrounding discs.

We review herein the latest observational advances in this field, showing in particular that large-scale magnetic topologies of low-mass stars and protostars can drastically vary with mass and rotation rate, and discuss their implications for our understanding of dynamo processes, stellar formation and stellar evolution.

In this lecture I present the way stars can be modeled in two dimensions and especially the fluid flows that are driven by rotation. I discuss some of the various ways of taking into account turbulence and conclude this contribution by a short presentation of some of the first results obtained with the ESTER code on the modeling of interferometrically observed fast rotating early-type stars.

Internal waves and tidal interactions constitute powerful mechanisms for angular momentum exchanges in star-planet systems. In this lecture, we review the state of the art of their modelling and we discuss their impact on the evolution of stellar systems. In this context, we first show how internal waves are able to deeply modify the secular transport of angular momentum in stellar interiors in the whole Hertzsprung-Russelll diagram. Then, we show how tidal waves, as well as the related exchanges of angular momentum, strongly depend on the internal structure of stars and planets.