Mapping the core mass function on to the stellar initial mass function: Multiplicity matters

Holman, Katy, Walch, Stefanie, Goodwin, S. P. and Whitworth, A. P. 2013. Mapping the core mass function on to the stellar initial mass function: Multiplicity matters. Monthly Notices of the Royal Astronomical Society 432 (4) , pp. 3534-3543. 10.1093/mnras/stt705

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Abstract

Observations indicate that the central portions of the present-day prestellar core mass function (hereafter CMF) and the stellar initial mass function (hereafter IMF) both have approximately log-normal shapes, but that the CMF is displaced to higher mass than the IMF by a factor F ∼ 4 ± 1. This has led to suggestions that the shape of the IMF is directly inherited from the shape of the CMF – and therefore, by implication, that there is a self-similar mapping from the CMF on to the IMF. If we assume a self-similar mapping, it follows (i) that F=NO/η, where η is the mean fraction of a core’s mass that ends up in stars and NO is the mean number of stars spawned by a single core; and (ii) that the stars spawned by a single core must have an approximately log-normal distribution of relative masses, with universal standard deviation σO. Observations can be expected to deliver ever more accurate estimates of F, but this still leaves a degeneracy between η and NO, and  σO is also unconstrained by observation. Here we show that these parameters can be estimated by invoking binary statistics. Specifically, if (a) each core spawns one long-lived binary system, and (b) the probability that a star of mass M is part of this long-lived binary is proportional to Mα, current observations of the binary frequency as a function of primary mass, b(M1), and the distribution of mass ratios, pq, strongly favour  η ∼ 1.0 ± 0.3, NO∼4.3±0.4,  σO ∼ 0.3 ± 0.03  and  α ∼ 0.9 ± 0.6;  η > 1 just means that, between when its mass is measured and when it finishes spawning stars, a core accretes additional mass, for example from the filament in which it is embedded. If not all cores spawn a long-lived binary system, db/dM1 < 0, in strong disagreement with observation; conversely, if a core typically spawns more than one long-lived binary system, then NO and η have to be increased further. The mapping from CMF to IMF is not necessarily self-similar – there are many possible motivations for a non-self-similar mapping – but if it is not, then the shape of the IMF cannot be inherited from the CMF. Given the limited observational constraints currently available and the ability of a self-similar mapping to satisfy them, the possibility that the shape of the IMF is inherited from the CMF cannot be ruled out at this juncture.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Physics and Astronomy
Subjects:	Q Science > QB Astronomy
Uncontrolled Keywords:	binaries: general; stars: formation; stars: luminosity function, mass function; stars: statistics
Publisher:	Oxford University Press
ISSN:	0035-8711
Last Modified:	10 Sep 2023 16:48
URI:	https://orca.cardiff.ac.uk/id/eprint/47816

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