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Register a new userStellar mass spectrum within massive collapsing clumps II. Thermodynamics and tidal forces of the first Larson core
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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.
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The stellar mass spectrum is an important property of the stellar cluster and a fundamental quantity to understand our Universe. The fragmentation of diffuse molecular cloud into stars is subject to physical processes such as gravity, turbulence, thermal pressure, and magnetic field. The final mass of a star is believed to be a combined outcome of a virially unstable reservoir and subsequent accretion. We aim to clarify the roles of different supporting energies, notably the thermal pressure and the magnetic field, in determining the stellar mass. Following previous studies by Lee & Hennebelle (2018a,b), we perform a series of numerical experiments of stellar cluster formation inside an isolated molecular clump. By changing the effective equation of state (EOS) of the diffuse gas (that is to say gas whose density is below the critical density at which dust becomes opaque to its radiation) and the strength of the magnetic field, we investigate whether any characteristic mass is introduced into the fragmentation processes. The EOS of the diffuse gas, including the bulk temperature and the polytropic index, does not affect significantly the shape of the stellar mass spectrum. The presence of magnetic field slightly modifies the shape of the mass spectrum only when extreme values are applied. This study confirms that the peak of the IMF is primarily determined by the adiabatic high-density end of the EOS that mimics the radiation inside the high-density gas. Furthermore, the shape of the mass spectrum is mostly sensitive to the density PDF, and the magnetic field has likely only a secondary role. In particular, we stress that the Jeans mass at the mean cloud density and at the critical density are not responsible of setting the peak.
The connection between the pre-stellar core mass function (CMF) and the stellar initial mass function (IMF) lies at the heart of all star formation theories. In this paper, we study the earliest phases of star formation with a series of high-resolution numerical simulations that include the formation of sinks. In particular, we focus on the transition from cores to sinks within a massive molecular filament. We compare the CMF and IMF between magnetized and unmagnetized simulations, and between different resolutions. We find that selecting cores based on their kinematic virial parameter excludes collapsing objects because they host large velocity dispersions. Selecting only the thermally unstable magnetized cores, we observe that their mass-to-flux ratio spans almost two orders of magnitude for a given mass. We also see that, when magnetic fields are included, the CMF peaks at higher core mass values with respect to pure hydrodynamical simulations. Nonetheless, all models produce sink mass functions with a high-mass slope consistent with Salpeter. Finally, we examine the effects of resolution and find that, in isothermal simulations, even models with very high dynamical range fail to converge in the mass function. Our main conclusion is that, although the resulting CMFs and IMFs have similar slopes in all simulations, the cores have slightly different sizes and kinematical properties when a magnetic field is included. However, a core selection based on the mass-to-flux ratio alone is not enough to alter the shape of the CMF, if we do not take thermal stability into account. Finally, we conclude that extreme care should be given to resolution issues when studying sink formation with an isothermal equation of state.
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.
Star-forming clumps dominate the rest-frame ultraviolet morphology of galaxies at the peak of cosmic star formation. If turbulence driven fragmentation is the mechanism responsible for their formation, we expect their stellar mass function to follow a power-law of slope close to $-2$. We test this hypothesis performing the first analysis of the stellar mass function of clumps hosted in galaxies at $zsim 1-3.5$. The clump sample is gathered from the literature with similar detection thresholds and stellar masses determined in a homogeneous way. To overcome the small number statistics per galaxy (each galaxy hosts up to a few tens of clumps only), we combine all high-redshift clumps. The resulting clump mass function follows a power-law of slope $sim -1.7$ and flattens at masses below $2times 10^7$ M$_{odot}$. By means of randomly sampled clump populations, drawn out of a power-law mass function of slope $-2$, we test the effect of combining small clump populations, detection limits of the surveys, and blending on the mass function. Our numerical exercise reproduces all the features observed in the real clump mass function confirming that it is consistent with a power-law of slope $simeq -2$. This result supports the high-redshift clump formation through fragmentation in a similar fashion as in local galaxies, but under different gas conditions.
Different studies have reported a power-law mass-size relation $M propto R^q$ for ensembles of molecular clouds. In the case of nearby clouds, the index of the power-law $q$ is close to 2. However, for clouds spread all over the Galaxy, indexes larger than 2 are reported. We show that indexes larger than 2 could be the result of line-of-sight superposition of emission that does not belong to the cloud itself. We found that a random factor of gas contamination, between 0.001% and 10% of the line-of-sight, allows to reproduce the mass-size relation with $q sim 2.2-2.3$ observed in Galactic CO surveys. Furthermore, for dense cores within a single cloud, or molecular clouds within a single galaxy, we argue that, even in these cases, there is observational and theoretical evidence that some degree of superposition may be occurring. However, additional effects may be present in each case, and are briefly discussed. We also argue that defining the fractal dimension of clouds via the mass-size relation is not adequate, since the mass is not {necessarily} a proxy to the area, and the size reported in $M-R$ relations is typically obtained from the square root of the area, rather than from an estimation of the size independent from the area. Finally, we argue that the statistical analysis of finding clouds satisfying the Larsons relations does not mean that each individual cloud is in virial equilibrium.
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