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Register a new userCore Mass Function: The Role of Gravity
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Sami Dib
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We analyze the mass distribution of cores formed in an isothermal, magnetized, turbulent, and self-gravitating nearly critical molecular cloud model. Cores are identified at two density threshold levels. Our main results are that the presence of self-gravity modifies the slopes of the core mass function (CMF) at the high mass end. At low thresholds, the slope is shallower than the one predicted by pure turbulent fragmentation. The shallowness of the slope is due to the effects of core coalescence and gas accretion. Most importantly, the slope of the CMF at the high mass end steepens when cores are selected at higher density thresholds, or alternatively, if the CMF is fitted with a log-normal function, the width of the lognormal distribution decreases with increasing threshold. This is due to the fact that gravity plays a more important role in denser structures selected at higher density threshold and leads to the conclusion that the role of gravity is essential in generating a CMF that bears more resemblance with the IMF when cores are selected with an increasing density threshold in the observations.
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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.
Numerical simulations of star formation have found that a power-law mass function can develop at high masses. In a previous paper, we employed isothermal simulations which created large numbers of sinks over a large range in masses to show that the power law exponent of the mass function, $dN/dlog M propto M^{Gamma}$, asymptotically and accurately approaches $Gamma = -1.$ Simple analytic models show that such a power law can develop if the mass accretion rate $dot{M} propto M^2$, as in Bondi-Hoyle accretion; however, the sink mass accretion rates in the simulations show significant departures from this relation. In this paper we show that the expected accretion rate dependence is more closely realized provided the gravitating mass is taken to be the sum of the sink mass and the mass in the near environment. This reconciles the observed mass functions with the accretion rate dependencies, and demonstrates that power-law upper mass functions are essentially the result of gravitational focusing, a mechanism present in, for example, the competitive accretion model.
We have re-analysed all of the SCUBA archive data of the Orion star-forming regions. We have put together all of the data taken at different times by different groups. Consequently we have constructed the deepest submillimetre maps of these regions ever made. There are four regions that have been mapped: Orion A North & South, and Orion B North & South. We find that two of the regions, Orion A North and Orion B North, have deeper sensitivity and completeness limits, and contain a larger number of sources, so we concentrate on these two. We compare the data with archive data from the Spitzer Space Telescope to determine whether or not a core detected in the submillimetre is pre-stellar in nature. We extract all of the pre-stellar cores from the data and make a histogram of the core masses. This can be compared to the stellar initial mass function (IMF). We find the high-mass core mass function follows a roughly Salpeter-like slope, just like the IMF, as seen in previous work. Our deeper maps allow us to see that the core mass function (CMF) turns over at ~ 1.3 Mo, about a factor of 4 higher than our completeness limit. This turnover has never previously been observed, and is only visible here due to our much deeper maps. It mimics the turnover seen in the stellar IMF at ~ 0.1 Mo. The low-mass side of the CMF is a power-law with an exponent of 0.35 +/- 0.2, which is consistent with the low-mass slope of the young cluster IMF of 0.3 +/- 0.1. This shows that the CMF continues to mimic the shape of the IMF all the way down to the lower completeness limit of these data at ~ 0.3 Mo.
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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.
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