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Register a new userAnalytical theory for the initial mass function: CO clumps and prestellar cores
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Patrick Hennebelle
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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.
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Stars form from dense molecular cores, and the mass function of these cores (the CMF) is often found to be similar to the form of the stellar initial mass function (IMF). This suggests that the form of the IMF is the result of the form of the CMF. However, most stars are thought to form in binary and multiple systems, therefore the relationship between the IMF and the CMF cannot be trivial. We test two star formation scenarios - one in which all stars form as binary or triple systems, and one in which low-mass stars form in a predominantly single mode. We show that from a log-normal CMF, similar to those observed, and expected on theoretical grounds, the model in which all stars form as multiples gives a better fit to the IMF.
We report the detection of D2CO in a sample of starless dense cores, in which we previously measured the degree of CO depletion. The deuterium fractionation is found extremely high, [D2CO]/[H2CO] ~ 1-10 %, similar to that reported in low-mass protostars. This provides convincing evidence that D2CO is formed in the cold pre-stellar cores, and later desorbed when the gas warms up in protostars. We find that the cores with the highest CO depletions have also the largest [D2CO]/[H2CO] ratios, supporting the theoretical prediction that deuteration increases with increasing CO depletion.
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 cores. 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.
Context. The different theoretical models concerning the formation of high-mass stars make distinct predictions regarding their progenitors, i.e. the high-mass prestellar cores. However, so far no conclusive observation of such objects has been made. Aims. We aim to study the very early stages of high-mass star formation in two infrared-dark, massive clumps, to identify the core population that they harbour. Methods. We obtained ALMA observations of continuum emission at 0.8mm and of the ortho-$rm H_2D^+$ transition at 372GHz towards the two clumps. We use the SCIMES algorithm to identify cores in the position-position-velocity space, finding 16 cores. We model their observed spectra in the LTE approximation, deriving the centroid velocity, linewidth, and column density maps. We also study the correlation between the continuum and molecular data, which in general do not present the same structure. Results. We report for the first time the detection of ortho-$rm H_2D^+$ in high-mass star-forming regions performed with an interferometer. The molecular emission shows narrow and subsonic lines, suggesting that locally the temperature of the gas is less than 10K. From the continuum emission we estimate the cores total masses, and compare them with the respective virial masses. We also compute the volume density values, which are found to be higher than $10^{6}, rm cm^{-3}$. Conclusions. Our data confirm that ortho-$rm H_2D^+$ is an ideal tracer of cold and dense gas. Interestingly, almost all the $rm H_2D^+$-identified cores are less massive than 13M_sun , with the exception of one core in AG354. Furthermore, most of them are subvirial and larger than their Jeans masses. These results are difficult to explain in the context of the turbulent accretion models, which predict massive and virialised prestellar cores.
We review the properties of low mass dense molecular cloud cores, including starless, prestellar, and Class 0 protostellar cores, as derived from observations. In particular we discuss them in the context of the current debate surrounding the formation and evolution of cores. There exist several families of model scenarios to explain this evolution (with many variations of each) that can be thought of as a continuum of models lying between two extreme paradigms for the star and core formation process. At one extreme there is the dynamic, turbulent picture, while at the other extreme there is a slow, quasi-static vision of core evolution. In the latter view the magnetic field plays a dominant role, and it may also play some role in the former picture. Polarization and Zeeman measurements indicate that some, if not all, cores contain a significant magnetic field. Wide-field surveys constrain the timescales of the core formation and evolution processes, as well as the statistical distribution of core masses. The former indicates that prestellar cores typically live for 2--5 free-fall times, while the latter seems to determine the stellar initial mass function. In addition, multiple surveys allow one to compare core properties in different regions. From this it appears that aspects of different models may be relevant to different star-forming regions, depending on the environment. Prestellar cores in cluster-forming regions are smaller in radius and have higher column densities, by up to an order of magnitude, than isolated prestellar cores. This is probably due to the fact that in cluster-forming regions the prestellar cores are formed by fragmentation of larger, more turbulent cluster-forming cores, which in turn form as a result of strong external compression.
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