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.
The equation of state (EOS) for partially ionized carbon, oxygen, and carbon-oxygen mixtures at temperatures 3times10^5 K <~ T <~ 3times10^6 K is calculated over a wide range of densities, using the method of free energy minimization in the framework
of the chemical picture of plasmas. The free energy model is an improved extension of our model previously developed for pure carbon (Phys. Rev. E, 72, 046402; arXiv:physics/0510006). The internal partition functions of bound species are calculated by a self-consistent treatment of each ionization stage in the plasma environment taking into account pressure ionization. The long-range Coulomb interactions between ions and screening of the ions by free electrons are included using our previously published analytical model, recently improved, in particular for the case of mixtures. We also propose a simple but accurate method of calculation of the EOS of partially ionized binary mixtures based on detailed ionization balance calculations for pure substances.
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 briefly review analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasmas, applicable in a wide range of plasma parameters, including the domains of nondegenerate and degenerate, nonrelativistic and relativis
tic electrons, weakly and strongly coupled Coulomb liquids, classical and quantum Coulomb crystals. We present improvements to previously published approximations. Our code for calculation of thermodynamic functions based on the reviewed approximations is made publicly available.
Recently developed analytic approximation for the equation of state of fully ionized nonideal electron-ion plasma mixtures [Potekhin et al., Phys. Rev. E, 79, 016411 (2009); arXiv:0812.4344], which covers the transition between the weak and strong Co
ulomb coupling regimes and reproduces numerical results obtained in the hypernetted chain (HNC) approximation, is modified in order to fit the small deviations from the linear mixing in the strong coupling regime, revealed by recent Monte Carlo simulations. In addition, a mixing rule is proposed for the regime of weak coupling, which generalizes post-Debye density corrections to the case of mixtures and numerically agrees with the HNC approximation in that regime.
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.
We develop analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasma mixtures. In the regime of strong Coulomb coupling, we use our previously developed analytic approximations for the free energy of one-compone
nt plasmas with rigid and polarizable electron background and apply the linear mixing rule (LMR). Other thermodynamic functions are obtained through analytic derivation of this free energy. In order to obtain an analytic approximation for the intermediate coupling and transition to the Debye-Hueckel limit, we perform hypernetted-chain calculations of the free energy, internal energy, and pressure for mixtures of different ion species and introduce a correction to the LMR, which allows a smooth transition from strong to weak Coulomb coupling in agreement with the numerical results.
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.
