The formation process of Population III (PopIII) stars in the mass-accretion phase is investigated by numerical experiments. The barotropic relation of primordial gas and artificial stiffening of the ...equation of state in very dense regions (>1015 cm−3) enables us to follow the fragmentation of PopIII circumstellar disks and the merging processes of the fragments. The disk becomes gravitationally unstable to fragmentation, followed by a rapid merger process typically within 100 yr, which roughly corresponds to one orbital time of the circumstellar disk. We also find that the fragmentation of the gas disk around a multiple system, a circumbinary disk, is rare; however, it is frequent in the disk around an individual protostar. We also perform a simulation with standard sink particles, where the number and total mass of sink particles are in rough agreement with those of the stiff equation of state runs. Based on the results of these numerical results, we model the evolution of the number of fragments with a simple phenomenological equation. We find that the average number of fragments is roughly proportional to t0.3, where t is the elapsed time since the formation of the first protostar. Next, we compare this trend with a number of published numerical studies by scaling the elapsed time according to the scale-free nature of the system. As a result, we find most of the results in the literature agree well with the relation. The present results, combined with previous studies in the literature, imply that the PopIII stars tend to be born not as single stars, but in multiple systems.
Abstract
We present the merger rate density of Population III binary black holes (BHs) by means of a widely used binary population synthesis code
BSE
with extensions to very massive and extreme ...metal-poor stars. We consider not only low-mass BHs (lBHs: 5–50
M
⊙
) but also high-mass BHs (hBHs: 130–200
M
⊙
), where lBHs and hBHs are below and above the pair-instability mass gap (50–130
M
⊙
), respectively. Population III BH–BHs can be categorized into three subpopulations: BH–BHs without hBHs (hBH0s:
m
tot
≲ 100
M
⊙
), with one hBH (hBH1s:
m
tot
∼ 130–260
M
⊙
), and with two hBHs (hBH2s:
m
tot
∼ 270–400
M
⊙
), where
m
tot
is the total mass of a BH–BH. Their merger rate densities at the current universe are ∼0.1 yr
−1
Gpc
−3
for hBH0s, and ∼0.01 yr
−1
Gpc
−3
for the sum of hBH1s and hBH2s, provided that the mass density of Population III stars is ∼10
13
M
⊙
Gpc
−3
. These rates are modestly insensitive to initial conditions and single star models. The hBH1 and hBH2 mergers can dominate BH–BHs with hBHs discovered in the near future. They have low effective spins ≲0.2 in the current universe. The number ratio of hBH2s to hBH1s is high, ≳0.1. We also find that BHs in the mass gap (up to ∼85
M
⊙
) merge. These merger rates can be reduced to nearly zero if Population III binaries are always wide (≳100
R
⊙
), and if Population III stars always enter into chemically homogeneous evolution. The presence of close Population III binaries (∼10
R
⊙
) is crucial for avoiding the worst scenario.
Abstract
We investigate the amplification of turbulence through gravitational contraction of the primordial gas in minihalos. We perform numerical simulations to follow the cloud collapse, assuming ...polytropic equations of state for different initial turbulent Mach numbers and resolutions. We find that the turbulent velocity is amplified solely by gravitational contraction, and eventually becomes comparable to the sound speed, even for small initial turbulent Mach numbers (
0
≳
0.05
). We derive an analytic formula for the amplification of turbulent velocity in a collapsing cloud, and find that our numerical results are consistent with the formula. These results suggest that the turbulence can play an important role in collapsing clouds for general cases.
Abstract
Recent numerical studies suggest that magnetic fields play an important role in primordial star formation in the early Universe. However, the detailed evolution of the magnetic field in the ...collapse phase still has uncertainties because of the complicated physics associated with turbulence in a collapsing magnetized system. Here, we perform a suite of numerical MHD simulations that follow the collapse of magnetized, turbulent primordial gas clouds to investigate the evolution of the magnetic field associated with the turbulence, assuming a polytropic equation of state with exponent
γ
eff
and with various numerical resolutions. In addition, we generalize the analytic theory of magnetic field growth/saturation so that it can deal with various exponents
γ
eff
and turbulence energy spectra. We find that the numerical results are well reproduced by the theory for various
γ
eff
through the collapse phase during the formation of the first stars. The magnetic field is eventually amplified by a factor of 10
12
–10
15
due to kinematic and nonlinear turbulent dynamo effects and reaches 3%–100% of the equipartition level, depending on
γ
eff
. We also find that the transition between the kinematic and nonlinear stages can be analytically estimated. These results indicate that the strong magnetic field accompanied by supersonic turbulence is a general property and suggest that it can play a crucial role in the formation of the first stars.
Abstract
We investigate the physical mechanism that determines the saturation level of the turbulence in collapsing gas clouds. We perform a suite of high-resolution numerical simulations that follow ...the collapse of turbulent gas clouds, with various effective polytropic exponents
γ
eff
, initial Mach numbers
0
, and initial turbulent seeds. Equating the energy injection rate from gravitational contraction and the dissipation rate of the turbulence, we obtain an analytic expression for the saturation level of the turbulence, and compare it with the numerical results. Consequently, the numerical results are well described by the analytic model, given that the turbulent driving scale in collapsing gas clouds is one-third the Jeans length of the collapsing core. These results indicate that the strength of the turbulence at first-core formations in the early universe/the present-day star formation process can be estimated solely by
γ
eff
.
Abstract
We investigate the formation of merging binary black holes (BHs) through isolated binary evolution, performing binary population synthesis calculations covering an unprecedentedly wide ...metallicity range of Population (Pop) I, II, III, and extremely metal-poor (EMP) binary stars. We find that the predicted merger rate density and primary BH mass (
m
1
) distribution are consistent with the gravitational wave (GW) observations. Notably, Population III and EMP (<10
−2
Z
⊙
) binary stars yield most of the pair instability (PI) mass gap events with
m
1
= 65–130
M
⊙
. Population III binary stars contribute more to the PI mass gap events with increasing redshift, and all the PI mass gap events have the Population III origin at redshifts ≳8. Our result can be assessed by future GW observations in the following two points. First, there are no binary BHs with
m
1
= 100–130
M
⊙
in our result, and thus the
m
1
distribution should suddenly drop in the range of
m
1
= 100–130
M
⊙
. Second, the PI mass gap event rate should increase toward higher redshift up to ∼11, since those events mainly originate from the Population III binary stars. We find that the following three assumptions are needed to reproduce the current GW observations: a top-heavy stellar initial mass function and the presence of close binary stars for Population III and EMP binary stars, and inefficient convective overshoot in the main-sequence phase of stellar evolution. Without any of the above, the number of PI mass gap events becomes too low to reproduce current GW observations.
ABSTRACT We study the number and the distribution of low-mass Population III (Pop III) stars in the Milky Way. In our numerical model, hierarchical formation of dark matter minihalos and ...Milky-Way-sized halos are followed by a high-resolution cosmological simulation. We model the Pop III formation in H2 cooling minihalos without metal under UV radiation of the Lyman-Werner bands. Assuming a Kroupa initial mass function (IMF) from 0.15 to 1.0 M for low-mass Pop III stars, as a working hypothesis, we try to constrain the theoretical models in reverse by current and future observations. We find that the survivors tend to concentrate on the center of halo and subhalos. We also evaluate the observability of Pop III survivors in the Milky Way and dwarf galaxies, and constraints on the number of Pop III survivors per minihalo. The higher latitude fields require lower sample sizes because of the high number density of stars in the galactic disk, the required sample sizes are comparable in the high- and middle-latitude fields by photometrically selecting low-metallicity stars with optimized narrow-band filters, and the required number of dwarf galaxies to find one Pop III survivor is less than 10 at <100 kpc for the tip of red giant stars. Provided that available observations have not detected any survivors, the formation models of low-mass Pop III stars with more than 10 stars per minihalo are already excluded. Furthermore, we discuss the way to constrain the IMF of Pop III stars at a high mass range of 10 M .
ABSTRACT
Magnetic 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.
Low-mass population III (PopIII) stars of could survive up until the present. The nondetection of low-mass PopIII stars in our Galaxy has already put a stringent constraint on the initial mass ...function (IMF) of PopIII stars, suggesting that PopIII stars have a top-heavy IMF. On the other hand, some claim that the lack of such stars stems from metal enrichment of their surfaces by the accretion of heavy elements from the interstellar medium (ISM). We investigate the effects of the stellar wind on metal accretion onto low-mass PopIII stars because accretion of the local ISM onto the Sun is prevented by the solar wind, even for neutrals. The stellar wind and radiation of low-mass PopIII stars are modeled based on knowledge of nearby low-mass stellar systems, including our Sun. We find that low-mass PopIII stars traveling across the Galaxy form a stellar magnetosphere in most of their life. Once the magnetosphere is formed, most of the neutral interstellar particles are photoionized before reaching the stellar surface and are blown away by the wind. Especially, the accretion abundance of iron will be reduced by a factor of compared with Bondi-Hoyle-Lyttleton accretion. The metal accretion can enhance iron abundance Fe/H only up to ∼−14. This demonstrates that low-mass PopIII stars remain pristine and will be found as metal-free stars and that further searches for them are valuable in constraining the IMF of PopIII stars.
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