Primordial Star-forming Clouds Research Articles

Exponential amplification of the magnetic field in the primordial star-forming cloud

In the study of the initial mass function associated with the first generation of stars, known as Population III (Pop III) stars, a fundamental yet unresolved question pertains to the ultimate destiny of the secondary protostars emerging within the accretion disk – specifically, their likelihood of either merging or persisting as distinct entities. Our research concentrates on the magnetic influences affecting the genesis of these first stars under the conditions set by the cosmological initial magnetic field strength. We employ ideal magnetohydrodynamic simulations, utilizing a stiff equation-of-state (EOS) model, to accurately depict the magnetic field structure interconnecting these protostars. We observe that the magnetic field experiences rapid intensification due to the gas near the protostar completing multiple tens of orbital rotations in the initial decade following the formation of the protostar. Concurrently, as mass accretion continues, the region influenced by the significant magnetic field expands outward. This process of magnetic braking effectively curtails the disk fragmentation that would typically occur without a magnetic field. The resulting exponential augmentation of the magnetic field is posited to facilitate the formation of supermassive first stars.

Low-mass Population III Star Formation due to the HD Cooling Induced by Weak Lyman–Werner Radiation

Lyman–Werner (LW) radiation photodissociating molecular hydrogen (H2) influences the thermal and dynamical evolution of the Population III (Pop III) star-forming gas cloud. The effect of powerful LW radiation has been well investigated in the context of supermassive black hole formation in the early Universe. However, the average intensity in the early Universe is several orders of magnitude lower. For a comprehensive study, we investigate the effects of LW radiation at 18 different intensities, ranging from J LW/J 21 = 0 (no radiation) to 30 (H-cooling cloud), on the primordial star-forming gas cloud obtained from a three-dimensional cosmological simulation. The overall trend with increasing radiation intensity is a gradual increase in the gas cloud temperature, consistent with previous works. Due to the HD cooling, however, the dependence of gas cloud temperature on J LW deviates from the aforementioned increasing trend for a specific range of intensities (J LW/J 21 = 0.025–0.09). In HD-cooling clouds, the temperature remained below 200 K during 105 yr after the first formation of the high-density region, maintaining a low accretion rate. Finally, the HD-cooling clouds have only a low-mass dense core (above 108 cm−3) with about 1–16 M ⊙, inside of which a low-mass Pop III star with ≤0.8 M ⊙ (a so-called “surviving star”) could form. The upper limit of star formation efficiency Mcore/Mvir,gas significantly decreases from 10−3 to 10−5 as HD cooling becomes effective. This tendency indicates that, whereas the total gas mass in the host halo increases with the LW radiation intensity, the total Pop III stellar mass does not increase similarly.

Clumpy structures within the turbulent primordial cloud

ABSTRACT The primordial clouds in the mini-haloes hatch the first generation stars of the Universe, which play a crucial role in cosmic evolution. In this paper, we investigate how turbulence impacts the structure of primordial star-forming clouds. Previous cosmological simulations of the first star formation predicted a typical mass of around $\mathrm{ 100 \, M_\odot }$. This conflicts with recent observations of extremely metal-poor stars, suggesting a lower mass scale of about $\mathrm{25 \, M_\odot }$. The discrepancy may arise from unresolved turbulence in the star-forming cloud, driven by primordial gas accretion during mini-halo formation in the previous simulations. To quantitatively examine the turbulence effect on the primordial cloud formation, we employ the adaptive mesh refinement code Enzo to model the gas cloud with primordial composition, including artificially driven turbulence on the cloud scale and relevant gas physics. This artificially driven turbulence utilizes a stochastic forcing model to mimic the unresolved turbulence inside mini-haloes. Our results show that the turbulence with high Mach number and compressional mode effectively fragments the cloud into several clumps, each with dense cores of $\mathrm{22.7 - 174.9 \, M_\odot }$ that undergo Jeans instability to form stars. Fragmentation caused by intense and compressive turbulence prevents a runaway collapse of the cloud. The self-bound clumps with smaller masses in the turbulent primordial clouds suggest a possible pathway to decrease the theoretical mass scale of the first stars, further reconciling the mass discrepancy between simulations and observations.

The Birth of a Massive First-star Binary

Abstract We study the formation of massive Population III binary stars using a newly developed radiation hydrodynamics code with the adaptive mesh refinement and adaptive ray-tracing methods. We follow the evolution of a typical primordial star-forming cloud obtained from a cosmological hydrodynamics simulation. Several protostars form as a result of disk fragmentation and grow in mass by the gas accretion, which is finally quenched by the radiation feedback from the protostars. Our code enables us, for the first time, to consider the feedback by both the ionizing and dissociating radiation from the multiple protostars, which is essential for self-consistently determining their final masses. At the final step of the simulation, we observe a very wide (≳104 au) binary stellar system consisting of 60 and 70 M ⊙ stars. One of the member stars also has two smaller mass (10 M ⊙) companion stars orbiting at 200 and 800 au, making up a mini-triplet system. Our results suggest that massive binary or multiple systems are common among Population III stars.

Ionization degree and magnetic diffusivity in the primordial star-forming clouds

ABSTRACTMagnetic fields play such roles in star formation as the angular momentum transport in star-forming clouds, thereby controlling circumstellar disc formation and even binary star formation efficiency. The coupling between the magnetic field and gas is determined by the ionization degree in the gas. Here, we calculate the thermal and chemical evolution of the primordial gas by solving chemical reaction network where all the reactions are reversed. We find that at ∼1014–1018 cm−3, the ionization degree becomes 100–1000 times higher than the previous results due to the lithium ionization by thermal photons trapped in the cloud, which has been omitted so far. We construct the minimal chemical network which can reproduce correctly the ionization degree as well as the thermal evolution by extracting 36 reactions among 13 species. Using the obtained ionization degree, we evaluate the magnetic field diffusivity. We find that the field dissipation can be neglected for global fields coherent over ≳ a tenth of the cloud size as long as the field is not so strong as to prohibit the collapse. With magnetic fields strong enough for ambipolar diffusion heating to be significant, the magnetic pressure effects to slow down the collapse and to reduce the compressional heating become more important, and the temperature actually becomes lower than in the no-field case.

Angular momentum transfer in primordial discs and the rotation of the first stars

We investigate the rotation velocity of the first stars by modelling the angular momentum transfer in the primordial accretion disc.Assessing the impact of magnetic braking, we consider the transition in angular momentum transport mode at the Alfv$\acute{\rm e}$n radius, from the dynamically dominated free-fall accretion to the magnetically dominated solid-body one.The accreting protostar at the centre of the primordial star-forming cloud rotates with close to breakup speed in the case without magnetic fields.Considering a physically-motivated model for small-scale turbulent dynamo amplification, we find that stellar rotation speed quickly declines if a large fraction of the initial turbulent energy is converted to magnetic energy ($\gtrsim 0.14$). Alternatively, if the dynamo process were inefficient, for amplification due to flux-freezing, stars would become slow rotators if the pre-galactic magnetic field strength is above a critical value, $\simeq 10^{-8.2}$G, evaluated at a scale of $n_{\rm H} = 1 {\rm cm}^{-3}$, which is significantly higher than plausible cosmological seed values ($\sim 10^{-15}$G). Because of the rapid decline of the stellar rotational speed over a narrow range in model parameters, the first stars encounter a bimodal fate: rapid rotation at almost the breakup level, or the near absence of any rotation.

Angular momentum distribution during the collapse of primordial star-forming clouds

It is generally believed that angular momentum is distributed during the gravitational collapse of the primordial star forming cloud. However, so far there has been little understanding of the exact details of the distribution. We use the modified version of the Gadget-2 code, a three-dimensional smoothed-particle hydrodynamics simulation, to follow the evolution of the collapsing gas in both idealized as well as more realistic minihalos. We find that, despite the lack of any initial turbulence and magnetic fields in the clouds the angular momentum profile follows the same characteristic power-law that has been reported in studies that employed fully self-consistent cosmological initial conditions. The fit of the power-law appears to be roughly constant regardless of the initial rotation of the cloud. We conclude that the specific angular momentum of the self-gravitating rotating gas in the primordial minihalos maintains a scaling relation with the gas mass as $L \propto M^{1.125}$. We also discuss the plausible mechanisms for the power-law distribution.

On the effects of rotation in primordial star-forming clouds

The thermodynamical evolution of gas during the collapse of the primordial star-forming cloud depends significantly on the initial degree of rotation. However, there is no clear understanding of how the initial rotation can affect the heating and cooling process and hence the temperature that leads to the fragmentation of the gas during Population III star formation. We report the results from three\hbox{-}dimensional, smoothed-particle hydrodynamics (SPH) simulations of a rotating self-gravitating primordial gas cloud with a modified version of the Gadget-2 code, in which the initial ratio of the rotational to the gravitational energy ($\beta_0$) is varied over two orders of magnitude. We find that despite the lack of any initial turbulence and magnetic fields in the clouds, the angular momentum distribution leads to the formation and build-up of a disk that fragments into several clumps. We further examine the behavior of the protostars that form in both idealized as well as more realistic minihalos from the cosmological simulations. The thermodynamical evolution and the fragmentation behavior of the cosmological minihalos are similar to that of the artificial cases, especially in those with a similar $\beta_0$-parameter. Protostars with a higher rotation support exhibit spiral-arm-like structures on several scales, and have lower accretion rates. These type of clouds tend to fragment more, while some of the protostars escape from the cluster with the possibility of surviving until the present day. They also take much longer to form compared to their slowly rotating counterparts. We conclude that the use of appropriate initial conditions of the gas in minihalos is a pivotal and decisive quantity to study the evolution and final fate of the primordial stars.

Chemical Enrichment of the First Binaries

AbstractRecent studies of Population III (Pop III) star formation suggest that the primordial star-forming clouds can fragment to form binary or multiple stellar systems inside dark matter minihalos. Here, we briefly present the chemical enrichment of the Pop III binary scenarios.

ONE HUNDRED FIRST STARS: PROTOSTELLAR EVOLUTION AND THE FINAL MASSES

We perform a large set of radiation hydrodynamics simulations of primordial star formation in a fully cosmological context. Our statistical sample of 100 First Stars show that the first generation of stars have a wide mass distribution M_popIII = 10 ~ 1000 M_sun. We first run cosmological simulations to generate a set of primordial star-forming gas clouds. We then follow protostar formation in each gas cloud and the subsequent protostellar evolution until the gas mass accretion onto the protostar is halted by stellar radiative feedback. The accretion rates differ significantly among the primordial gas clouds which largely determine the final stellar masses. For low accretion rates the growth of a protostar is self-regulated by radiative feedback effects and the final mass is limited to several tens of solar masses. At high accretion rates the protostar's outer envelope continues to expand and the effective surface temperature remains low; such protostars do not exert strong radiative feedback and can grow in excess to one hundred solar masses. The obtained wide mass range suggests that the first stars play a variety of roles in the early universe, by triggering both core-collapse supernovae and pair-instability supernovae as well as by leaving stellar mass black holes. We find certain correlations between the final stellar mass and the physical properties of the star-forming cloud. These correlations can be used to estimate the mass of the first star from the properties of the parent cloud or of the host halo, without following the detailed protostellar evolution.

On the operation of the chemothermal instability in primordial star-forming clouds

We investigate the operation of the chemothermal instability in primordial star-forming clouds with a suite of three-dimensional, moving-mesh simulations. In line with previous studies, we find that the gas at the centre of high-redshift minihaloes becomes chemothermally unstable as three-body reactions convert the atomic hydrogen into a fully molecular gas. The competition between the increasing rate at which the gas cools and the increasing optical depth to H2 line emission creates a characteristic dip in the cooling time over the free-fall time on a scale of 100 au. As a result, the free-fall time decreases to below the sound-crossing time, and the cloud may become gravitationally unstable and fragment on a scale of a few tens of au during the initial free-fall phase. In three of the nine haloes investigated, secondary clumps condense out of the parent cloud, which will likely collapse in their own right before they are accreted by the primary clump. In the other haloes, fragmentation at such an early stage is less likely. However, given that previous simulations have shown that the infall velocity decreases substantially once the gas becomes rotationally supported, the amount of time available for perturbations to develop may be much greater than is evident from the limited period of time simulated here.

RADIATIVE COOLING IMPLEMENTATIONS IN SIMULATIONS OF PRIMORDIAL STAR FORMATION

We study the thermal evolution of primordial star-forming gas clouds using three-dimensional cosmological simulations. We critically examine how assumptions and approximations made in calculating radiative cooling rates affect the dynamics of the collapsing gas clouds. We consider two important molecular hydrogen cooling processes that operate in a dense primordial gas; H_2 line cooling and continuum cooling by H_2 collision-induced emission. To calculate the optically thick cooling rates, we follow the Sobolev method for the former, whereas we perform ray-tracing for the latter. We also run the same set of simulations using simplified fitting functions for the net cooling rates. We compare the simulation results in detail. We show that the time- and direction-dependence of hydrodynamic quantities such as gas temperature and local velocity gradients significantly affects the optically thick cooling rates. Gravitational collapse of the cloud core is accelerated when the cooling rates are calculated by using the fitting functions. The structure and evolution of the central pre-stellar disk are also affected. We conclude that physically motivated implementations of radiative transfer are necessary to follow accurately the thermal and chemical evolution of a primordial gas to high densities.

Dissipation of Magnetic Flux in Primordial Star Formation: From Run-away Phase to Mass-Accretion Phase

Abstract We investigate the dissipation of magnetic flux in primordial star-forming clouds throughout their collapse, including the run-away collapse phase as well as the accretion phase. We solve the energy equation and the non-equilibrium chemical reactions in the collapsing gas, in order to obtain the radial distribution of the ionized fraction during the collapse. As a result, we find that the ionized fraction is high enough for the magnetic field to couple with the gas throughout evolution of the cloud. This result suggests that the jet formation from protostars as well as the activation of magneto–rotational instability in the accretion disk are enabled in the presence of the cosmological seed magnetic flux proposed by Langer, Puget, and Aghanim (2003, Phys. Rev. D67, 43505).

Dissipation of Magnetic Flux in Primordial Gas Clouds

We report the strength of seed magnetic flux of accretion disk surrounding the PopIII stars. The magnetic field in accretion disk might play an important role in the transport of angular momentum because of the turbulence induced by Magneto-Rotational Instability (MRI). On the other hand, since the primordial star-forming clouds contain no heavy elements and grains, they experience much different thermal history and different dissipation history of the magnetic field in the course of their gravitational contraction, from those in the present-day star-forming molecular clouds. In order to assess the magnetic field strength in the accretion disk of PopIII stars, we calculate the thermal history of the primordial collapsing clouds, and investigate the coupling of magnetic field with primordial gas. As a result, we find that the magnetic field strongly couple with primordial gas cloud throughout the collapse, i.e. the magnetic field are frozen to the gas as far as initial field strength satisfies $ B\lesssim 10^{-5}(n_{\rm H}/10^3{\rm cm^{-3}})^{0.55}{\rm G}$.