The minimum mass for opacity-limited fragmentation in turbulent cloud cores

Abstract

Abstract. We present a new analysis of the minimum mass for star formation, based on opacity-limited fragmentation. Our analysis differs from the standard one, which considers hierarchical fragmentation of a 3D medium, and yields M MIN ∼ 0.007 to 0.010 M for Population I star formation. Instead we analyse the more realistic situation in which there is one-shot fragmentation of a shock-compressed layer, of the sort which arises in turbulent star-forming clouds. In this situation, M MIN can be smaller than 0.003 M . Our analysis is more stringent than the standard one in that (a) it requires fragments to have condensation timescales shorter than all competing mass scales, and (b) it takes into acount that a fragment grows by accretion whilst it is condensing out, and therefore has to radiate away the energy dissipated in the associated accretion shock (in addition to the PdV work done by internal compression). It also accords with the recent detection, in young star clusters, of free-floating star-like objects having masses as low as 0.003 M .

HSTNICMOS Imaging of the Planetary‐mass Companion to the Young Brown Dwarf 2MASSW J1207334−393254

“…Calculations of opacity-limited fragmentation in a turbulent three-dimensional medium yield minimum masses k7M J (e.g., Low & Lynden-Bell 1976;Boyd & Whitworth 2005;Bate 2005 and references therein). Given the uncertainties in these calculations and in evolutionary models of young, planetary-mass objects, our 5M J AE 3M J estimate for 2M 1207b is likely not in conflict with the 7M J fragmentation mass.…”

“…Given the uncertainties in these calculations and in evolutionary models of young, planetary-mass objects, our 5M J AE 3M J estimate for 2M 1207b is likely not in conflict with the 7M J fragmentation mass. Alternatively, perhaps a different model, for example, two-dimensional fragmentation of a shock-compressed layer (Boyd & Whitworth 2005), would ultimately be needed to account for the properties of 2M 1207b.…”

The minimum Jeans mass, brown dwarf companion IMF, and predictions for detection of Y-type dwarfs

“…Furthermore, as Low & Lynden-Bell pointed out, (a) for a fragment to split it must have at least twice the minimum mass and (b) since a Jeans mass perturbation has a zero growth rate, one would expect a real growing perturbation to be somewhat more massive than a Jeans mass. Subsequently, Bate and collaborators (see Bate 2005, and references therein), Boyd & Whitworth (2005), Padoan & Nordlund (2004), Padoan et al (2005), Whitworth & Stamatellos (2006), and Padoan et al (2007) considered additional processes such as turbulence, shock compression and the role of magnetic fields and derived fragment masses that could be as low as three times Jupiter's mass.…”

The formation of planets by disc fragmentation

“…objects with masses below the hydrogen-burning limit (∼ 80 M J ): brown dwarfs (m ∼ 13 − 80 M J ; they are able to burn deuterium), and planets (m < 13 M J ; they cannot sustain deuterium burning). There is no reason for gas fragmentation to stop either at the hydrogen-burning limit or the deuterium-burning limit: the minimum mass of an object that forms by gas fragmentation is given from the opacity limit for fragmentation which is thought to be ∼ 1 − 5 M J [6][7][8][9][10][11][12][13][14][15]. Substellar objects may form either from the collapse of very low-mass gravitationally-bound cores, which are produced by turbulent fragmentation of larger molecular clouds [16,17], or by disc fragmentation [11,[18][19][20][21][22].…”