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Register a new userHow first hydrostatic cores, tidal forces and gravo-turbulent fluctuations set the characteristic mass of stars
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The stellar initial mass function (IMF) is playing a critical role in the history of our universe. We propose a theory that is based solely on local processes, namely the dust opacity limit, the tidal forces and the properties of the collapsing gas envelope. The idea is that the final mass of the central object is determined by the location of the nearest fragments, which accrete the gas located further away, preventing it to fall onto the central object. To estimate the relevant statistics in the neighbourhood of an accreting protostar, we perform high resolution numerical simulations. We also use these simulations to further test the idea that fragmentation in the vicinity of an existing protostar is determinant in setting the peak of the stellar mass spectrum. We develop an analytical model, which is based on a statistical counting of the turbulent density fluctuations, generated during the collapse, that are at least equal to the mass of the first hydrostatic core, and sufficiently important to supersede tidal and pressure forces to be self-gravitating. The analytical mass function presents a peak located at roughly 10 times the mass of the first hydrostatic core in good agreement with the numerical simulations. Since the physical processes involved are all local, i.e. occurs at scales of a few 100 AU or below, and do not depend on the gas distribution at large scale and global properties such as the mean Jeans mass, the mass spectrum is expected to be relatively universal.
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We investigate the dependence of the peak of the IMF on the physics of the so-called first Larson core, which corresponds to the point where the dust becomes opaque to its own radiation. We perform numerical simulations of collapsing clouds of $1000 M_odot$ for various gas equation of state (eos), paying great attention to the numerical resolution and convergence. The initial conditions of these numerical experiments are varied in the companion paper. We also develop analytical models that we confront to our numerical results. If an isothermal eos is used, we show that the peak of the IMF shifts to lower masses with improved numerical resolution. When an adiabatic eos is employed, numerical convergence is obtained. The peak position varies with the eos and we find that the peak position is about ten times the mass of the first Larson core. By analyzing the stability of non-linear density fluctuations in the vicinity of a point mass and then summing over a reasonable density distribution, we find that tidal forces exert a strong stabilizing effect and likely lead to a preferential mass several times larger than that of the first Larson core. We propose that in a sufficiently massive and cold cloud, the peak of the IMF is determined by the thermodynamics of the high density adiabatic gas as well as the stabilizing influence of tidal forces. The resulting characteristic mass is about ten times the mass of the first Larson core, which altogether leads to a few tenths of solar masses. Since these processes are not related to the large scale physical conditions and to the environment, our results suggest a possible explanation for the apparent universality of the peak of the IMF.
Star formation in our Galaxy occurs in molecular clouds that are self-gravitating, highly turbulent, and magnetized. We study the conditions under which cloud cores inherit large-scale magnetic field morphologies and how the field is governed by cloud turbulence. We present four moving-mesh simulations of supersonic, turbulent, isothermal, self-gravitating gas with a range of magnetic mean-field strengths characterized by the Alfvenic Mach number $mathcal{M}_{{rm A}, 0}$, resolving pre-stellar core formation from parsec to a few AU scales. In our simulations with the turbulent kinetic energy density dominating over magnetic pressure ($mathcal{M}_{{rm A}, 0}>1$), we find that the collapse is approximately isotropic with $Bproptorho^{2/3}$, core properties are similar regardless of initial mean-field strength, and the field direction on $100$ AU scales is uncorrelated with the mean field. However, in the case of a dominant large-scale magnetic field ($mathcal{M}_{{rm A}, 0}=0.35$), the collapse is anisotropic with $Bproptorho^{1/2}$. This transition at $mathcal{M}_{{rm A}, 0}sim1$ is not expected to be sharp, but clearly signifies two different paths for magnetic field evolution in star formation. Based on observations of different star forming regions, we conclude that star formation in the interstellar medium may occur in both regimes. Magnetic field correlation with the mean-field extends to smaller scales as $mathcal{M}_{{rm A}, 0}$ decreases, making future ALMA observations useful for constraining $mathcal{M}_{{rm A}, 0}$ of the interstellar medium.
Observations of pre-/proto-stellar cores in young star-forming regions show them to be mass segregated, i.e. the most massive cores are centrally concentrated, whereas pre-main sequence stars in the same star-forming regions (and older regions) are not. We test whether this apparent contradiction can be explained by the massive cores fragmenting into stars of much lower mass, thereby washing out any signature of mass segregation in pre-main sequence stars. Whilst our fragmentation model can reproduce the stellar initial mass function, we find that the resultant distribution of pre-main sequence stars is mass segregated to an even higher degree than that of the cores, because massive cores still produce massive stars if the number of fragments is reasonably low (between one and five). We therefore suggest that the reason cores are observed to be mass segregated and stars are not is likely due to dynamical evolution of the stars, which can move significant distances in star-forming regions after their formation.
Most stars in the Galaxy, including the Sun, were born in high-mass star-forming regions. It is hence important to study the chemical processes in these regions to better understand the chemical heritage of both the Solar System and most stellar systems in the Galaxy. The molecular ion HCNH+ is thought to be a crucial species in ion-neutral astrochemical reactions, but so far it has been detected only in a handful of star-forming regions, and hence its chemistry is poorly known. We have observed with the IRAM-30m Telescope 26 high-mass star-forming cores in different evolutionary stages in the J=3-2 rotational transition of HCNH+. We report the detection of HCNH+ in 16 out of 26 targets. This represents the largest sample of sources detected in this molecular ion so far. The fractional abundances of HCNH+, [HCNH+], w.r.t. H2, are in the range 0.9 - 14 X $10^{-11}$, and the highest values are found towards cold starless cores. The abundance ratios [HCNH+]/[HCN] and [HCNH+]/[HCO+] are both < 0.01 for all objects except for four starless cores, for which they are well above this threshold. These sources have the lowest gas temperature in the sample. We run two chemical models, a cold one and a warm one, which attempt to match as much as possible the average physical properties of the cold(er) starless cores and of the warm(er) targets. The reactions occurring in the latter case are investigated in this work for the first time. Our predictions indicate that in the warm model HCNH+ is mainly produced by reactions with HCN and HCO+, while in the cold one the main progenitor species of HCNH+ are HCN+ and HNC+. The results indicate that the chemistry of HCNH+ is different in cold/early and warm/evolved cores, and the abundance ratios [HCNH+]/[HCN] and [HCNH+]/[HCO+] is a useful astrochemical tool to discriminate between different evolutionary phases in the process of star formation.
In stars with $M_ast lesssim 2 M_odot$, nuclear burning of helium starts under degenerate conditions and, depending on the efficiency of neutrino cooling, more or less off-center. The behavior of the centers of low-mass stars undergoing core helium ignition on the $logrho - log T$ plane is not thoroughly explained in the textbooks on stellar evolution and the appropriate discussions remain scattered throughout the primary research literature. Therefore, in the following exposition we collect the available knowledge, we make use of computational data obtained with the open-source star-modeling package MESA, and we compare them with the results in the existing literature. The line of presentation follows essentially that of Thomas (1967) who was the first who outlined correctly the stellar behavior during the off-center helium flashes that lead to central helium burning. The exposition does not contain novel research results; it is intended to be a pedagogically oriented, edifying compilation of pertinent physical aspects which help to emph{understand} the nature of the stars.
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