Evolution of First Cores in Rotating Molecular Cores

Abstract

We investigate the effect of rotation on the star formation process quantitatively using axisymmetric numerical calculations. An adiabatic hydrostatic object (the so-called first core) forms in a contracting cloud core, after the central region becomes optically thick and continues to contract, driven by mass accretion onto it. The structure of a rotating first core is characterized by its total angular momentum J core and mass M core , both of which increase by accretion with time. We find that the first core evolves with a constant J core /M 2 core . Evolutionary paths of first cores can be classified into two types. In a slowly rotating core with J core /M 2 core < 0:015G/( ffiffi ffi 2 p c iso ), where c iso and G represent the isothermal sound speed in the molecular cloud core and the gravitational constant, respectively, the core begins ''second collapse'' after the central density exceeds the H 2 dissociation density. This is the same evolution as a standard scenario for a spherically symmetric, nonrotating core. On the other hand, a core with J core /M 2 core > 0:015G/( ffiffi ffi 2 p c iso ) stops its contraction before the central density reaches the H 2 dissociation density and does not begin the second collapse. These rapidly rotating first cores suffer from nonaxisymmetric instabilities, such as formation of massive spiral arms, deformation into a bar, or fragmentation. Although the rotating first cores have small average luminosities of L core ¼ 0:003 0:03Ṁ core /10 À5 M yr À1 À Á L , assuming a constant mass accretion rateṀ core . Their lifetimes last several thousand years or more, which is much longer than those expected for nonrotating clouds ($1000 yr). We expect that at least several percent of prestellar cores contain first cores as very low luminosity objects. Furthermore, we find a core with 0:012G/( ffiffi ffi 2 p c iso ) < J core /M 2 core < 0:015G/( ffiffi ffi 2 p c iso ) may form close binary systems with initial separation of 0.02-0.1 AU after the second collapse phase.

The end of star formation in Chamaeleon I?

“…With a 70 μm flux of ∼200 mJy (Belloche et al 2006), this correlation implies that Cha-MMS1 has a very low internal luminosity of ∼0.015 L . Luminosities ranging between 10 −4 and 0.1 L have been theoretically predicted at the stage of the first core, depending on the collapse model and the amount of rotation (Saigo & Tomisaka 2006;Omukai 2007). The faint luminosity of Cha-MMS1 looks therefore consistent with the luminosity of a first core.…”

ALMA Observations of SMM11 Reveal an Extremely Young Protostar in Serpens Main Cluster

“…Nevertheless, none of these sources can be unambiguously characterized as true FHSCs partly because the theoretically-predicted parameter space of first cores is wide-spread; mass, lifetime, internal luminosity 1 and radius of 0.01 − 0.1 M ⊙ , 500-5×10 4 yr, 10 −4 − 0.1 L ⊙ , and 5-100 AU, respectively (Boss & Yorke 1995;Masunaga et al 1998;Omukai 2007;Commerçon et al 2012;Saigo & Tomisaka 2006;Saigo et al 2008;Tomida et al 2010). In addition, observations have not strongly constrained properties such as the rotation and mass accretion rate in the early phases of star formation.…”

Different modes of star formation: gravitational collapse of magnetically subcritical cloud

“…Note that the first core lifetime is roughly determined by t fc = M fc /(Ṁ fc ), where M fc andṀ fc are the mass of the first core and the mass accretion rate onto the first core, and the first core becomes massive with rotation (Saigo & Tomisaka 2006). Thus, assuming a constant mass accretion rate, the rotating first core has a longer lifetime than the non-rotating first core.…”

“…Therefore, magnetic braking is alleviated in the first core and the first core remnant evolves into a rotationally supported disc following protostar formation (Bate 1998(Bate , 2010Walch et al 2009;Machida & Matsumoto 2011c;Walch et al 2012). In addition, the low-velocity outflow is driven by the outer edge of the rotating first core where the magnetic field is coupled with neutral gas ( On the other hand, the lifetime of the first core is as short as t ∼ < 100 yr when the angular momentum of the first core is sufficiently small (Masunaga & Inutsuka 2000;Saigo & Tomisaka 2006;Saigo et al 2008). In such a case, there is not enough time for dissipation of the magnetic field, and the magnetic field continues to be amplified without dissipation (Machida et al 2007).…”

“…Note that the first core is partly supported by the centrifugal force in magnetically supercritical models (Saigo & Tomisaka 2006;Saigo et al 2008). Since the dissipation of the magnetic field mainly occurs inside the first core, the magnetic field might become weaker in calculations that consider the heating by magnetic dissipation than in those that consider a barotropic equation of state due to the long lifetime of the first core.…”