The first low-mass stars: critical metallicity or dust-to-gas ratio?

Abstract

We explore the minimal conditions which enable the formation of metal-enriched solar and sub-solar mass stars. We find that in the absence of dust grains, gas fragmentation occurs at densities nH ~ [10^4-10^5]cm^{-3} when the metallicity exceeds Z ~ 10^{-4} Zsun. The resulting fragmentation masses are > 10 Msun. The inclusion of Fe and Si cooling does not affect the thermal evolution as this is dominated by molecular cooling even for metallicities as large as Z = 10^{-2} Zsun. The presence of dust is the key driver for the formation of low-mass stars. We focus on three representative core-collapse supernova (SN) progenitors, and consider the effects of reverse shocks of increasing strength: these reduce the depletion factors, fdep = Mdust/(Mdust+Mmet), alter the shape of the grain size distribution function and modify the relative abundances of grain species and of metal species in the gas phase. We find that the lowest metallicity at which fragmentation occurs is Z=10^{-6} Zsun for gas pre-enriched by the explosion of a 20 Msun primordial SN (fdep > 0.22) and/or by a 35 Msun, Z=10^{-4} Zsun SN (fdep > 0.26); it is ~ 1 dex larger, when the gas is pre-enriched by a Z = 10^{-4} Zsun, 20 Msun SN (fdep > 0.04). Cloud fragmentation depends on the depletion factor and it is suppressed when the reverse shock leads to a too large destruction of dust grains. These features are all consistent with the existence of a minimum dust-to-gas ratio, Dcr, above which fragmentation is activated. We derive a simple analytic expression for Dcr which, for grain composition and properties explored in the present study, reads Dcr = [2.6 - 6.3] x 10^{-9}. When the dust-to-gas ratio of star forming clouds exceeds this value, the fragmentation masses range between 0.01 Msun and 1 Msun, thus enabling the formation of the first low-mass stars.Comment: accepted by MNRAS, 12 pages, 8 figure

TOPoS

“…On the other hand, all forms of dust cooling (Schneider et al 2006(Schneider et al , 2012aOmukai et al 2008;Dopcke et al 2011Dopcke et al , 2013 are viable for all the UIP stars, CEMP or not. Disc fragmentation (Clark et al 2011a;Greif et al 2011bGreif et al , 2012, is also a possible formation mechanism for all these stars, and it would also allow the formation of primordial low-mass stars.…”

“…Although these systems have a low dust content, it may still be sufficient to act as a coolant for the formation of low-mass stars. The existing studies of this topic (Schneider et al 2006(Schneider et al , 2012aOmukai et al 2008;Dopcke et al 2011Dopcke et al , 2013 find that if one assumes that the dust-to-gas ratio D scales with the metallicity Z, one only needs a metallicity of the order of 10 −5 solar to get effective dust cooling. This means that if we relax the assumption that D scales with Z, for example assuming a constant dust-to-gas ratio, we only need an absolute dust abundance of the order of 10 −7 solar.…”

“…Omukai et al 2005;Schneider et al 2012a;Glover 2013), two main cooling channels emerge which could lead to the efficient formation of low-mass stars and result in a stellar mass spectrum similar to the present-day IMF (Kroupa 2002;Chabrier 2003). These cooling processes are -fine structure transitions of C ii and O i (Bromm & Loeb 2003) and; -dust cooling (Schneider et al 2006(Schneider et al , 2012aOmukai et al 2008;Dopcke et al 2011Dopcke et al , 2013.…”

Classification of extremely metal-poor stars: absent region in A(C)–[Fe/H] plane and the role of dust cooling

“…The critical condition for cloud fragmentation can be described by the comparison of gas cooling owing to dust thermal emission with gas compressional heating (Schneider et al 2012). With condensation efficiency fij of a key element j onto a grain species i and a characteristic grain radius r cool i , the fragmentation condition can be written using the number abundance y(j) as…”

“…The radius r cool i is defined as r 3 i / r 2 i characterizing the efficiency of gas cooling, where x i = xϕ i (r)dr is the average of a physical quantity x weighted by the size distribution ϕ i (r) of a grain species i. Equation (1) is given at the gas density n H = 10 14 cm −3 and temperature T = 1000 K where dust cooling is dominant over gas compressional heating in clouds with [Fe/H] ∼ −5 (Schneider et al 2012). X H is the mass fraction of hydrogen nuclei, and X H = 0.75 throughout this Letter.…”