The first stars are known to form in primordial gas, either in minihalos with about 10 6 M or so-called atomic cooling halos of about 10 8 M . Simulations have shown that gravitational collapse and disk formation in primordial gas yield dense stellar clusters. In this paper, we focus particularly on the formation of protostellar binary systems, and aim to quantify their properties during the early stage of their evolution. For this purpose, we combine the smoothed particle hydrodynamics code GRADSPH with the astrochemistry package KROME. The GRADSPH-KROME framework is employed to investigate the collapse of primordial clouds in the high-density regime, exploring the fragmentation process and the formation of binary systems. We observe a strong dependence of fragmentation on the strength of the turbulent Mach number M and the rotational support parameter β. Rotating clouds show significant fragmentation, and have produced several Pop. III proto-binary systems. We report maximum and minimum mass accretion rates of 2.31 × 10 −1 M yr −1 and 2.18 × 10 −4 M yr −1 . The mass spectrum of the individual Pop III proto-binary components ranges from 0.88 M to 31.96 M and has a sensitive dependence on the Mach number M as well as on the rotational parameter β. We also report a range from ∼ 0.01 to ∼ 1 for the mass ratio of our proto-binary systems.

We report the results of a numerical study on the initial formation stages of lowmass protostellar binary systems. We determine the separation of protostellar binaries formed as a function of the initial thermal state by varying the initial temperature in a slightly modified version of the Burkert and Bodenheimer collapse test. We find that the outcome is highly sensitive to both the initial temperature of the cloud and the initial amplitude of azimuthal density perturbation A. For A=10 %, variations of only 1 unit Kelvin below 10 K lead to changes of up to 100 AU ( i.e. of order 30 %) in the instantaneous separation, whereas for this small A the initial temperatures above 10 K yield, instead of a binary, a single low-mass fragment that never reaches protostellar densities. Protostellar binaries, however, do emerge when the perturbation amplitude is increased from 10 % to 25 %. We also investigate the impact of the critical density which governs the transition from isothermal to adiabatic thermodynamic behaviour of the collapsing gas. We find that the critical density not only affects the overall structural evolution of the gas envelope, but also the size of the rotating disk structures formed during collapse as well as the number of protostellar fragments resulting from the final fragmentation of the disks. This mechanism can give rise to young protostellar objects constituting bound multiple stellar systems.

While the stellar Initial Mass Function (IMF) appears to be close to universal within the Milky Way galaxy, it is strongly suspected to be different in the primordial Universe, where molecular hydrogen cooling is less efficient and the gas temperature can be higher by a factor of 30. In between these extreme cases, the gas temperature varies depending on the environment, metallicity and radiation background. In this paper we explore if changes of the gas temperature affect the IMF of the stars considering fragmentation and accretion. The fragmentation behavior depends mostly on the Jeans mass at the turning point in the equation of state where a transition occurs from an approximately isothermal to an adiabatic regime due dust opacities. The Jeans mass at this transition in the equation of state is always very similar, independent of the initial temperature, and therefore the initial mass of the fragments is very similar. Accretion on the other hand is strongly temperature dependent. We argue that the latter becomes the dominant process for star formation efficiencies above 5−7 %, increasing the average mass of the stars.The formation of low-mass stars in the primordial regime has also been suggested in earlier studies (e.g. Nakamura and Umemura 2002; Palla et al. 1983). Already at metallicities Z ∼ 10 −5 Z Clark et al. (2008) have reported vigorous fragmentation due to efficient dust cooling that leads to densely-packed clusters of low-mass stars in which the IMF of stars peaks below 1 M .With the ejection of metals, the stellar mass decreases due to the increasing efficiency of cooling. In particular, metal line cooling predominantly proceeds via oxygen, carbon and nitrogen lines (Bromm and Loeb 2003). This cooling mechanism becomes quite efficient for metal abundances of about 0.3 % of the solar value, and operates already at low densities, of the order 1−100 cm −3 depending on metallicity (Omukai and Palla 2001;Glover and Jappsen 2007;Safranek et al. 2014).An alternative cooling mechanism is provided by the injection of dust via AGB stars or supernovae, which provides a cooling mechanism that operates even at ∼ 0.01% of the dust abundance in the solar neighborhood, but kicks in at much higher densities (> 10 6 cm −3 ) than the metal line cooling (Schneider et al. 2003; Schneider and Omukai arXiv:2003.07639v1 [astro-ph.GA]

The origin of very low-mass stars (VLMS) and brown dwarfs (BDs) is still an unresolved topic of star formation. We here present numerical simulations of the formation of VLMS, BDs, and planet mass objects (planemos) resulting from the gravitational collapse and fragmentation of solar mass molecular cores with varying rotation rates and initial density perturbations. Our simulations yield various types of binary systems including the combinations VLMS-VLMS, BD-BD, planemo-planemo, VLMS-BD, VLMS-planemos, BD-planemo. Our scheme successfully addresses the formation of wide VLMS and BD binaries with semi-major axis up to 441 AU and produces a spectrum of mass ratios closer to the observed mass ratio distribution (q > 0.5). Molecular cores with moderate values of the ratio of kinetic to gravitational potential energy (0.16 β 0.21) produce planemos. Solar mass cores with rotational parameters β outside of this range yield either VLMS/BDs or a combination of both. With regard to the mass ratios we find that for both types of binary systems the mass ratio distribution varies in the range 0.31 q 0.74. We note that in the presence of radiative feedback, the length scale of fragmentation would increase by approximately two orders of magnitude, implying that the formation of binaries may be efficient for wide orbits, while being suppressed for short-orbit systems.

Observations show a large spread in the luminosities of young protostars, which are frequently explained in the context of episodic accretion. We here test this scenario using numerical simulations following the collapse of a solar mass molecular cloud using the GRADSPH code, varying the strength of the initial perturbations and the temperature of the cores. A specific emphasis of this paper is to investigate the role of binaries and multiple systems in the context of episodic accretion, and to compare their evolution to the evolution in isolated fragments. Our models form a variety of low mass protostellar objects including single, binary and triple systems with binaries more active in exhibiting episodic accretion than isolated protostars. We also find a general decreasing trend for the average mass accretion rate over time, suggesting that the majority of the protostellar mass is accreted within the first 10 5 years. This result can potentially help to explain the surprisingly low average luminosities in the majority of the protostellar population.