We examine variations of the stellar initial mass function (IMF) in extreme environments within the formalism derived by Hennebelle & Chabrier. We focus on conditions encountered in progenitors of massive early type galaxies and starburst regions. We
show that, when applying the concept of turbulent Jeans mass as the characteristic mass for fragmentation in a turbulent medium, instead of the standard thermal Jeans mass for purely gravitational fragmentation, the peak of the IMF in such environments is shifted towards smaller masses, leading to a bottom-heavy IMF, as suggested by various observations. In very dense and turbulent environments, we predict that the high-mass tail of the IMF can become even steeper than the standard Salpeter IMF, with a limit for the power law exponent $alphasimeq -2.7$, in agreement with recent observational determinations. This steepening is a direct consequence of the high densities and Mach values in such regions but also of the time dependence of the fragmentation process, as incorporated in the Hennebelle-Chabrier theory. We provide analytical parametrizations of these IMFs in such environments, to be used in galaxy evolution calculations. We also calculate the star formation rates and the mass-to-light ratios expected under such extreme conditions and show that they agree well with the values inferred in starburst environments and massive high-redshift galaxies. This reinforces the paradigm of star formation as being a universal process, i.e. the direct outcome of gravitationally unstable fluctuations in a density field initially generated by large scale shock-dominated turbulence. This globally enables us to infer the variations of the stellar IMF and related properties for atypical galactic conditions.
Understanding the dominant brown dwarf and giant planet formation processes, and finding out whether these processes rely on completely different mechanisms or share common channels represents one of the major challenges of astronomy and remains the
subject of heated debates. It is the aim of this review to summarize the latest developments in this field and to address the issue of origin by confronting different brown dwarf and giant planet formation scenarios to presently available observational constraints. As examined in the review, if objects are classified as Brown Dwarfs or Giant Planets on the basis of their formation mechanism, it has now become clear that their mass domains overlap and that there is no mass limit between these two distinct populations. Furthermore, while there is increasing observational evidence for the existence of non-deuterium burning brown dwarfs, some giant planets, characterized by a significantly metal enriched composition, might be massive enough to ignite deuterium burning in their core. Deuterium burning (or lack of) thus plays no role in either brown dwarf or giant planet formation. Consequently, we argue that the IAU definition to distinguish these two populations has no physical justification and brings scientific confusion. In contrast, brown dwarfs and giant planets might bear some imprints of their formation mechanism, notably in their mean density and in the physical properties of their atmosphere. Future direct imaging surveys will undoubtedly provide crucial information and perhaps provide some clear observational diagnostics to unambiguously distinguish these different astrophysical objects.
We present a simple dimensional argument to illustrate the impact of nonthermal support from turbulent velocity dispersion on the shape of the prestellar core mass function (CMF), precursor of the stellar initial mass function (IMF). The argument dem
onstrates the need to invoke such support to recover the Salpeter slope in the high-mass part of the CMF/IMF, whereas pure thermal support leads to a much steeper slope. This simple dimensional argument clearly highlights the results obtained in the complete Hennebelle-Chabrier theory of the IMF.
In this short review, we summarize our present understanding (and non-understanding) of exoplanet formation, structure and evolution, in the light of the most recent discoveries. Recent observations of transiting massive brown dwarfs seem to remarkab
ly confirm the predicted theoretical mass-radius relationship in this domain. This mass-radius relationship provides, in some cases, a powerful diagnostic to distinguish planets from brown dwarfs of same mass, as for instance for Hat-P-20b. If confirmed, this latter observation shows that planet formation takes place up to at least 8 Jupiter masses. Conversely, observations of brown dwarfs down to a few Jupiter masses in young, low-extinction clusters strongly suggest an overlapping mass domain between (massive) planets and (low-mass) brown dwarfs, i.e. no mass edge between these two distinct (in terms of formation mechanism) populations. At last, the large fraction of heavy material inferred for many of the transiting planets confirms the core-accretion scenario as been the dominant one for planet formation.
We present a simple statistical analysis of recent numerical simulations exploring the correlation between the core mass function obtained from the fragmentation of a molecular cloud and the stellar mass function which forms from these collapsing cor
es. Our analysis shows that the distributions of bound cores and sink particles obtained in the simulations are consistent with the sinks being formed predominantly from their parent core mass reservoir, with a statistical dispersion of the order of one third of the core mass. Such a characteristic dispersion suggests that the stellar initial mass function is relatively tightly correlated to the parent core mass function, leading to two similar distributions, as observed. This in turn argues in favor of the IMF being essentially determined at the early stages of core formation and being only weakly affected by the various environmental factors beyond the initial core mass reservoir, at least in the mass range explored in the present study. Accordingly, the final IMF of a star forming region should be determined reasonably accurately, statistically speaking, from the initial core mass function, provided some uniform efficiency factor. The calculations also show that these statistical fluctuations, due e.g. to variations among the core properties, broaden the low-mass tail of the IMF compared with the parent CMF, providing an explanation for the fact that this latter appears to underestimate the number of pre brown dwarf cores compared with the observationally-derived brown dwarf IMF.
In this review, I briefly summarize the present status of experimental and theoretical investigations of the properties of matter under conditions characteristic of planetary interiors, from terrestrial to jovian planets. I first focus on the two lig
htest elements, hydrogen and helium, and discuss recent theoretical and experimental investigations of their properties at high pressure and temperature. Then, I discuss the impact of these properties, as well as of the equation of state of heavier elements, on planetary interiors. Finally, I highlight the importance of exoplanet transit observations and of the inferred mass-radius relationships to determine the planetary interior compositions.
We revisit the tidal stability of extrasolar systems harboring a transiting planet and demonstrate that, independently of any tidal model, none but one (HAT-P-2b) of these planets has a tidal equilibrium state, which implies ultimately a collision of
these objects with their host star. Consequently, conventional circularization and synchronization timescales cannot be defined because the corresponding states do not represent the endpoint of the tidal evolution. Using numerical simulations of the coupled tidal equations for the spin and orbital parameters of each transiting planetary system, we confirm these predictions and show that the orbital eccentricity and the stellar obliquity do not follow the usually assumed exponential relaxation but instead decrease significantly, reaching eventually a zero value, only during the final runaway merging of the planet with the star. The only characteristic evolution timescale of {it all} rotational and orbital parameters is the lifetime of the system, which crucially depends on the magnitude of tidal dissipation within the star. These results imply that the nearly circular orbits of transiting planets and the alignment between the stellar spin axis and the planetary orbit are unlikely to be due to tidal dissipation. Other dissipative mechanisms, for instance interactions with the protoplanetary disk, must be invoked to explain these properties.
In this review, we summarize our present knowledge of the behaviour of the mass-radius relationship from solar-type stars down to terrestrial planets, across the regime of substellar objects, brown dwarfs and giant planets. Particular attention is pa
id to the identification of the main physical properties or mechanisms responsible for this behaviour. Indeed, understanding the mechanical structure of an object provides valuable information about its internal structure, composition and heat content as well as its formation history. Although the general description of these properties is reasonably well mastered, disagreement between theory and observation in certain cases points to some missing physics in our present modelling of at least some of these objects. The mass-radius relationship in the overlaping domain between giant planets and low-mass brown dwarfs is shown to represent a powerful diagnostic to distinguish between these two different populations and shows once again that the present IAU distinction between these two populations at a given mass has no valid foundation.
We derive an analytical theory of the prestellar core initial mass function based on an extension of the Press-Schechter statistical formalism. With the same formalism, we also obtain the mass spectrum for the non self-gravitating clumps produced in
supersonic flows. The mass spectrum of the self-gravitating cores reproduces very well the observed initial mass function and identifies the different mechanisms responsible for its behaviour. The theory predicts that the shape of the IMF results from two competing contributions, namely a power-law at large scales and an exponential cut-off (lognormal form) centered around the characteristic mass for gravitational collapse. The cut-off exists already in the case of pure thermal collapse, provided that the underlying density field has a lognormal distribution. Whereas pure thermal collapse produces a power-law tail steeper than the Salpeter value, dN/dlog Mpropto M^{-x}, with x=1.35, this latter is recovered exactly for the (3D) value of the spectral index of the velocity power spectrum, nsimeq 3.8, found in observations and in numerical simulations of isothermal supersonic turbulence. Indeed, the theory predicts that x=(n+1)/(2n-4) for self-gravitating structures and x=2-n/3 for non self-gravitating structures, where n is the power spectrum index of log(rho). We show that, whereas supersonic turbulence promotes the formation of both massive stars and brown dwarfs, it has an overall negative impact on star formation, decreasing the star formation efficiency. This theory provides a novel theoretical foundation to understand the origin of the IMF and to infer its behaviour in different environments. It also provides a complementary approach and useful guidance to numerical simulations exploring star formation, while making testable predictions.
