Abstract

We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement (AMR) in both codes, as well as the most promising directions for future developments.

Introduction

The dynamics of astrophysical systems described by the equations of radiation magnetohydrodynamics (MHD) span a tremendous range of scales and parameter regimes, from the interiors of stars (Kippenhahn & Weigert 1994), to accretion disks around compact objects (Turner et al. 2003), to dusty accretion flows around massive protostars (Krumholz et al. 2005, 2007a), to galactic-scale flows onto AGN (Thompson et al. 2005). All of these systems have in common that matter, radiation and magnetic fields are strongly interacting and that the energy and momentum carried by the radiation field is significant in comparison to that carried by the gas. Thus, an accurate treatment of the problem must include analysis of both the matter and the radiation, as well as the magnetic fields, and their mutual interaction.

Understanding the formation of gravitationally bound structures at all scales in the universe is one of the most fascinating challenges of modern astronomy. It is now realized that the initial building blocks of galaxies were small collapsing dark matter halos, produced by the primordial fluctuations. These blocks then merged and were assembled into progressively larger galaxies, a scheme generally described as the hierarchical model of galaxy formation. The modern understanding of star formation involves large-scale turbulent motions producing local overdensities which eventually collapse and form prestellar cores under the action of gravity. The most likely scenario for planet formation is the collapse of a vast gaseous envelope onto a central dense core formed from the aggregation of millimetre-size grains in the original protoplanetary nebula, although disk fragmentation could remain an alternative scenario in some situations. The detailed processes responsible for the formation of these structures, however, remain poorly understood. Many important issues remain unsettled, so the robustness of these general paradigms is still ill determined. All these scenarios for the formation of galaxies, stars and planets, although involving vastly different scales, share many underlying physical mechanisms.They all involved hydrodynamical processes, generally leading to turbulent motions, but the very nature of these motions and their real role in structure formation remains unclear. The role of magnetic fields, in the collapse itself and in the generation of winds and jets, remains one of the major unknowns in the formation of structures.

Abstract

Astrophysical jets are associated with the formation of young stars of all masses, stellar and massive black holes, and perhaps even with the formation of massive planets. Their role in the formation of planets, stars and galaxies is increasingly appreciated and probably reflects a deep connection between the accretion flows – by which stars and black holes may be formed – and the efficiency by which magnetic torques can remove angular momentum from such flows. We compare the properties and physics of jets in both non-relativistic and relativistic systems and trace, by means of theoretical argument and numerical simulations, the physical connections between these different phenomena. We discuss the properties of jets from young stars and black holes, give some basic theoretical results that underpin the origin of jets in these systems, and then show results of recent simulations on jet production in collapsing star-forming cores as well as from jets around rotating Kerr black holes.

Introduction

The goal of this book, to explore structure formation in the cosmos and the physical linkage of astrophysical phenomena on different physical scales, is both timely and important. The emergence of multi-wavelength astronomy in the late twentieth century with its unprecedented ground- and space-based observatories, as well as the arrival of powerful new computational capabilities and numerical codes, has opened up unanticipated new vistas in understanding how planets, stars and galaxies form.

Introduction

This chapter is devoted to planet formation and to the early stages of evolution of low-mass objects, including low-mass stars, brown dwarfs and exoplanets. We first summarize the general properties of current exoplanet observations (Section 15.2) and describe the two main planet formation models based on disk instability and on the core-accretion scenario, respectively (Section 15.3). Recent progress of the latter formation model allows sophisticated population synthesis analyses which provide fully quantitative predictions that can be compared to the observed statistical properties of exoplanets (Section 15.3.5). The last part of this chapter is devoted to the distinction between brown dwarfs and planets, in terms of structure and evolutionary properties. The existence of a mass overlap between these two distinct populations of low-mass objects is highlighted by the increasing discoveries of very massive exoplanets (M ≳ 5MJ) and by the identification of planetary mass brown dwarfs in young clusters (M ≲ 10MJ) These discoveries stress the importance to define signatures which could allow to disentangle a brown dwarf from a planet. We first analyse the effect of accretion on the evolution of young brown dwarfs and the resulting uncertainties of evolutionary models at ages of a few million years. We also analyse different specific signatures of brown dwarfs and planets such as their luminosity at young ages, their radii and their atmospheric properties.

Abstract

The formation of massive stars is currently an unsolved problem in astrophysics. Understanding the formation of massive stars is essential because they dominate the luminous, kinematic and chemical output of stars. Furthermore, their feedback is likely to play a dominant role in the evolution of molecular clouds and any subsequent star formation therein. Although significant progress has been made observationally and theoretically, we still do not have a consensus as to how massive stars form. There are two contending models to explain the formation of massive stars: core accretion and competitive accretion. They differ primarily in how and when the mass that ultimately makes up the massive star is gathered. In the core accretion model, the mass is gathered in a pre-stellar stage due to the overlying pressure of a stellar cluster or a massive pre-cluster cloud clump. In contrast, competitive accretion envisions that the mass is gathered during the star formation process itself, being funnelled to the centre of a stellar cluster by the gravitational potential of the stellar cluster. Although these differences may not appear overly significant, they involve significant differences in terms of the physical processes involved. Furthermore, the differences also have important implications in terms of the evolutionary phases of massive star formation and ultimately that of stellar clusters and star formation on larger scales. Here, we review the dominant models and discuss prospects for developing a better understanding of massive star formation in the future.

Introduction

During the last two decades, the focus of star formation research has shifted from understanding the collapse of a single dense core into a star to studying the formation of hundreds to thousands of stars in molecular clouds. In this chapter, we overview recent observational and theoretical progress towards understanding star formation on the scale of molecular clouds and complexes, i.e. the macrophysics of star formation (McKee & Ostriker 2007). We begin with an overview of recent surveys of young stellar objects (YSOs) in molecular clouds and embedded clusters, and we outline an emerging picture of cluster formation. We then discuss the role of turbulence to both support clouds and create dense, gravitationally unstable structures, with an emphasis on the role of magnetic fields (in the case of distributed stars), and feedback (in the case of clusters) to slow turbulent decay and mediate the rate and density of star formation. The discussion is followed by an overview of how gravity and turbulence may produce observed scaling laws for the properties of molecular clouds, stars and star clusters and how the observed, star formation rate (SFR) may result from self-regulated star formation. We end with some concluding remarks, including a number of questions to be addressed by future observations and simulations.

Observations of clustered and distributed populations in molecular clouds

Our knowledge of the distribution and kinematics of young stars, protostars and dense cores in molecular clouds is being rapidly improved by wide-field observations at X-ray, optical, infrared and (sub)millimeter wavelengths (Allen et al. 2007; Feigelson et al. 2007).

Abstract

Computational gas dynamics has become a prominent research field in both astrophysics and cosmology. In the first part of this chapter, we intend to briefly describe several of the numerical methods used in this field, discuss their range of application and present strategies for converting conditionally stable numerical methods into unconditionally stable solution procedures. The underlying aim of the conversion is to enhance the robustness and unification of numerical methods and subsequently enlarge their range of applications considerably. In the second part, Heitsch presents and discusses the implementation of a time-explicit magneto hydrodynamic (MHD) Boltzmann solver.

PART I

Numerical methods in AFD

Astrophysical fluid dynamics (AFD) deals with the properties of gaseous matter under a wide variety of circumstances. Most astrophysical fluid flows evolve over a large variety of different time and length scales, henceforth making their analytical treatment unfeasible.

On the contrary, numerical treatments by means of computer codes have witnessed an exponential growth during the last two decades due to the rapid development of hardware technology. Nowadays, the vast majority of numerical codes are capable of treating large and sophisticated multi-scale fluid problems with high resolutions and even in 3D.

The numerical methods employed in AFD can be classified into two categories (see Figure 5.1):

1. Microscopic-oriented methods: These are mostly based on N-body (NB), Monte Carlo (MC) and on the Smoothed Particle Hydrodynamics (SPH).

2. Grid-oriented methods: To this category belong the finite difference (FDM), finite volume (FVM) and finite element methods (FEM).

We conducted an optical survey (Keck Telescope, 3,700–7,000 Å) of 24 high-metallicity (Z) starburst galaxies to investigate whether high-Zenvironments favor the formation of Wolf–Rayet (WR) stars. We searched for the presence of the He II 4686 Å line produced by the massive WR stars. We detected this feature in six galaxies (25% of the sample). We also used a stellar-population-synthesis code to determine their ages. We find that (i) all galaxies hosting considerable numbers of WR stars are very young systems, with ages log(t) > 8, with t in years; (ii) not all young star-forming galaxies host WR stars, or at least that population cannot be detected in their integrated spectra; and (iii) most galaxies hosting WR populations are found in interacting systems. We for the first time detect WR populations in galaxies ESO 485-G003, NGC 6090, and NGC 2798.

Reports of high metallicities in galactic systems have always been controversial. I disuss whether observational claims both for nebulae and for stars are well-founded, and try to form a rational view of just how metal-rich some regions of galaxies do become. Metallicity is linked to the evolution of star formation in a galaxy through the yield, the mass of metals produced each time star formation locks up unit mass of interstellar material. The mechanisms by which real or apparent high yields might be achieved are examined – global and local gas flows, poor mixing, star formation and metallicity effects in stellar evolution. As perhaps expected, it turns out to be not so easy to ‘get rich’, quickly or otherwise – suggesting that sorting out the lingering uncertainties in the abundance analysis of H ii regions and stars remains a priority.

We review some of the models of chemical evolution of ellipticals and bulges of spirals. In particular, we focus on the star-formation histories of ellipticals and their influence on chemical properties such as [α/Fe] versus [Fe/H], galactic mass and visual magnitudes. By comparing models with observational properties, we can constrain the timescales for the formation of these galaxies. The observational properties of stellar populations suggest that the more-massive ellipticals formed on a shorter timescale than less-massive ones, in the sense that both the star-formation rate and the mass-assembly rate, strictly linked properties, were greater for the most-massive objects. Observational properties of true bulges seem to suggest that they are very similar to ellipticals and that they formed on a very short timescale: for the bulge of the Milky Way we suggest a timescale of 0.1 Gyr. This leads us to conclude that the bulge evolved in a quite independent way from the Galactic disk.

We present results for the chemical evolution of the Galactic bulge in the context of an inside-out formation model of the Galaxy. A supernovadriven wind was also included in analogy with elliptical galaxies. New observations of chemical-abundance ratios and the metallicity distribution have been employed in order to check the model results. We confirm previous findings that the bulge formed on a very short timescale with quite a high star-formation efficiency and an initial mass function more skewed towards high masses than the one suitable for the Solar neighbourhood. A certain amount of primary nitrogen from massive stars might be required in order to reproduce the nitrogen data at low and intermediate metallicities.

We have derived metallicity, masses, and ages for two samples of nearby giant stars, which have been observed with the aim of understanding their nature of the radial-velocity (RV) variability and to search for planetary companions. Our stars have reliable Hipparcos parallaxes, and for several we also have measured angular diameters; the parameters we retrieve from our inversion process are in very good agreement with the observed ones. Among our results, we find that the stars regarded as candidates to host planetary companions are not preferencially metal-rich, which is at odds with what is found for main-sequence stars. We also find that stars younger than ∼1 Gyr can be described by a single metallicity and that an age–metallicity relationship applies to our samples.

Galactic open clusters provide a key tool to address a variety of issues related to the formation and evolution of stars and the Galactic disk. In the last few years a metallicity higher than Solar has been derived/confirmed spectroscopically for a few clusters, the most famous example being the very old NGC 6791, for which a metallicity [Fe/H] ∼ 0.4 has recently been reported. In this paper current knowledge of these supersolarmetallicity clusters is reviewed and their properties and abundance patterns are compared with those of non-metal-rich clusters and other Galactic populations. Possible implications for their origin and for the metallicity gradient in the disk are briefly discussed. A summary of recent surveys for planets in metal-rich clusters is also provided, together with new results on Li abundances for the 3-Gyr-old metal-rich cluster NGC 6253.

The chemical evolution of the Galactic bulge is calculated by adopting a single-zone framework, with accretion of primordial gas on a free-fall timescale, assuming (i) a correspondingly rapid timescale for star formation and (ii) an initial mass function biased towards massive stars. We emphasise here the uncertainties associated with the underlying physics (specifically, stellar nucleosynthesis) and how those uncertainties are manifested in the predicted abundance-ratio patterns in the resulting present-day Galactic-bulge stellar populations.

Does the initial mass function (IMF) vary? Is it significantly different in metal-rich environments versus metal-poor ones? Theoretical work predicts this to be the case, but in order to provide robust empirical evidence for this, the researcher must understand all possible biases affecting the derivation of the stellar mass function. Apart from the very difficult observational challenges, this turns out to be highly non-trivial, relying on an exact understanding of how stars evolve, how stellar populations in galaxies are assembled dynamically and how individual star clusters and associations evolve. N-body modelling is therefore an unavoidable tool in this game: the case can be made that without complete dynamical modelling of star clusters and associations any statements about the variation of the IMF with physical conditions are most probably wrong. The calculations that do exist demonstrate time and again that the IMF is invariant: there exists no statistically meaningful evidence for a variation of the IMF on going from metal-poor to metal-rich populations. This means that currently existing star-formation theory fails to describe the stellar outcome. Indirect evidence, based on chemical-evolution calculations, however, indicates that the extreme starbursts that assembled bulges and elliptical galaxies may have had a top-heavy IMF.

Galactic chemical evolution witnesses the enrichment of the interstellar medium with elements heavier than H, He, and Li that originate from the Big Bang. These heavier elements can be traced via the surface compositions of low-mass stars of various ages, which have remained unaltered since their formation and therefore measure the composition in the interstellar medium at the time of their birth. Thus, the metallicity [Fe/H] is a measure of the enrichment with nucleosynthesis products and indirectly of the ongoing duration of galactic evolution. For very early times, when the interstellar medium was essentially pristine, this interpretation might be wrong and perhaps we see the ejecta of individual supernovae where the amount of H with which these ejecta mix is dependent on the energy of the explosion and the mass of the stellar progenitor. Certain effects are qualitatively well understood, i.e. the early ratios of alpha elements (O, Ne, Mg, Si, S, Ar, Ca, Ti) to Fe, which represent typical values from Type-II supernova explosions that originate from rapidly evolving massive stars. On the other hand, Type-Ia supernovae, which are responsible for the majority of Fe-group elements and are the products of binary evolution of lower-mass stars, later emit their ejecta and reduce the alpha/Fe ratio. In addition to being a measure of time, the metallicity [Fe/H] also enters stellar nucleosynthesis in two other ways. (i) Some nucleosynthesis processes are of secondary nature, e.g. the s-process, requiring initial Fe in stellar He-burning. (ii) Other processes are of primary nature, e.g. the production of Fe-group elements in both types of supernovae.