We report results from numerical simulations of star formation in the early universe that focus on the role of subsonic turbulence, and investigate whether it can induce fragmentation of the gas. We find that dense primordial gas is highly susceptible to fragmentation, even for rms turbulent velocity dispersions as low as 20% of the initial sound speed. The resulting fragments cover over two orders of magnitude in mass, ranging from 0.1 to 40 solar masses. However, our results suggest that the details of the fragmentation depend on the local properties of the turbulent velocity field and hence we expect considerable variations in the resulting stellar mass spectrum in different halos.
The collapse of the primordial gas in the density regime $\sim 10^{8}\hbox{--}10^{10}$ cm$^{-3}$ is controlled by the three-body $\rm H_2$ formation process, in which the gas can cool faster than free-fall time $\hbox{--}$ a condition proposed as the chemothermal instability. We investigate how the heating and cooling rates are affected during the rapid transformation of atomic to molecular hydrogen. With a detailed study of the heating and cooling balance in a 3D simulation of Pop~III collapse, we follow the chemical and thermal evolution of the primordial gas in two dark matter minihaloes. T…
We present the first 3D simulations to include the effects of dark matter annihilation feedback during the collapse of primordial mini-halos. We begin our simulations from cosmological initial conditions and account for dark matter annihilation in our treatment of the chemical and thermal evolution of the gas. The dark matter is modelled using an analytical density profile that responds to changes in the peak gas density. We find that the gas can collapse to high densities despite the additional energy input from the dark matter. No objects supported purely by dark matter annihilation heating …
We develop an analytic framework to understand fragmentation in turbulent, self-gravitating media. Previously, we showed some properties of turbulence can be predicted with the excursion-set formalism. Here, we generalize to fully time-dependent gravo-turbulent fragmentation & collapse. We show that turbulent systems are always gravitationally unstable (in a probabilistic sense). The fragmentation mass spectra, size/mass relations, correlation functions, range of scales over which fragmentation occurs, & time-dependent rates of fragmentation are predictable. We show how this depends on bulk tu…
We show that fragmentation of the inflaton into long-lived spatially localized oscillon configurations can lead to copious production of black holes. In a single-field inflation model primordial black holes of sublunar mass can form, and they can account for all of the dark matter. We also explore the possibility that solar-mass primordial black holes, particularly relevant for gravitational wave astronomy, are produced from the same mechanism.
We perform a set of cosmological simulations of early structure formation with incorporating baryonic streaming motions. We present a case where a significantly elongated gas cloud with $\sim\!10^4\,$solar masses (${\rm M_\odot}$) is formed in a pre-galactic ($\sim\!10^7\,{\rm M_\odot}$) dark halo. The gas streaming into the halo compresses and heats the massive filamentary cloud to a temperature of $\sim\!10,000\,$Kelvin. The gas cloud cools rapidly by atomic hydrogen cooling, and then by molecular hydrogen cooling down to $\sim\!400\,$Kelvin. The rapid decrease of the temperature and hence o…
Population III stars form in groups due to the fragmentation of primordial gas. While uniform magnetic fields have been shown to support against fragmentation in present day star formation, it is unclear whether realistic k^3/2 primordial fields can have the same effect. We bypass the issues associated with simulating the turbulent dynamo by introducing a saturated magnetic field at equipartition with the velocity field when the central densities reaches 10-13 g cm-3. We test a range of sink particle creation densities from 10-10-10-8 g cm-3. Within the range tested, the fields did not suppres…
A fundamental assumption in our understanding of disks is that when the Toomre Q>>1, the disk is stable against fragmentation into self-gravitating objects (and so cannot form planets via direct collapse). But if disks are turbulent, this neglects a spectrum of stochastic density fluctuations that can produce rare, high-density mass concentrations. Here, we use a recently-developed analytic framework to predict the statistics of these fluctuations, i.e. the rate of fragmentation and mass spectrum of fragments formed in a turbulent Keplerian disk. Turbulent disks are never completely stable: we…
We present a derivation of the time evolution equations for the energy content of nonhelical magnetic fields and the accompanying turbulent flows from first principles of incompressible magnetohydrodynamics in the general framework of homogeneous and isotropic turbulence. This is then applied to the early Universe, i.e., the evolution of primordial magnetic fields. Numerically integrating the equations, we find that most of the energy is concentrated at an integral wavenumber scale k_I where the turbulence turn over time equals the Hubble time. At larger length scales L, i.e., smaller wavenumb…
The very first stars to form in the Universe heralded an end to the cosmic dark ages and introduced new physical processes that shaped early cosmic evolution. Until now, it was thought that these stars lived short, solitary lives, with only one extremely massive star, or possibly a very wide binary system, forming in each dark matter minihalo. Here we describe numerical simulations that show that these stars were, to the contrary, often members of tight multiple systems. Our results show that the disks that formed around the first young stars were unstable to gravitational fragmentation, possi…
Supermassive stars (SMSs; >10^5 Msun) formed in the first protogalaxies with virial temperature T_vir>10^4 K are expected to collapse into seeds of supermassive black hole (SMBHs) in the high-redshift universe (z>7). Fragmentation of the primordial gas is, however, a possible obstacle to SMS formation. We discuss the expected properties of a compact, metal-free, marginally unstable nuclear protogalactic disk, and the fate of the clumps formed in the disk by gravitational instability. Interior to a characteristic radius R_f=few*10^{-2} pc, the disk fragments into massive clumps with M_c~30 Msun…
We study the influence of gas metallicity, turbulence, and non-equilibrium chemistry on the evolution of the two-phase interstellar medium (warm and cold atomic phases), and thereby constrain the initial conditions for star formation prevailing in turbulent gas. We perform high-resolution simulations in three dimensions, including a realistic non-equilibrium treatment of the ionization state of the gas, and examine both driven and decaying turbulence. This allows us to explore variations in the metallicity Z. In this paper, we study solar metallicity, Z=Z_sun, and low metallicity, Z=1d-3 Z_sun…
Magnetic fields in extreme primordial halos: turbulent collapse and implications for early quasar formation
Hamburger Sternwarte, Universität Hamburg（汉堡天文台，汉堡大学）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；Physics Department, College of Science, United Arab Emirates University（阿拉伯联合酋长国大学理学院物理系）
We have used the IRAM Plateau de Bure Interferometer and the Expanded Very Large Array to obtain a high resolution map of the CO(6-5) and CO(1-0) emission in the lensed, star-forming galaxy SMMJ2135-0102 at z=2.32. The kinematics of the gas are well described by a model of a rotationally-supported disk with an inclination-corrected rotation speed, v_rot = 320+/-25km/s, a ratio of rotational- to dispersion- support of v/sigma=3.5+/-0.2 and a dynamical mass of 6.0+/-0.5x10^10Mo within a radius of 2.5kpc. The disk has a Toomre parameter, Q=0.50+/-0.15, suggesting the gas will rapidly fragment int…
It has been shown that fragmentation within self-gravitating, turbulent molecular clouds ("turbulent fragmentation") can naturally explain the observed properties of protostellar cores, including the core mass function (CMF). Here, we extend recently-developed analytic models for turbulent fragmentation to follow the time-dependent hierarchical fragmentation of self-gravitating cores, until they reach effectively infinite density (and form stars). We show that turbulent fragmentation robustly predicts two key features of the IMF. First, a high-mass power-law scaling very close to the Salpeter …
Primordial black hole (PBH) formation is a more generic phenomenon than was once thought. The dynamics of a scalar field in inflationary universe can produce PBHs under mild assumptions regarding the scalar potential. In the early universe, light scalar fields develop large expectation values during inflation and subsequently relax to the minimum of the effective potential at a later time. During the relaxation process, an initially homogeneous scalar condensate can fragment into lumps via an instability similar to the gravitational (Jeans) instability, where the scalar self-interactions, rath…
We present the first study on the amplification of magnetic fields by the turbulent dynamo in the highly subsonic regime, with Mach numbers ranging from $10^{-3}$ to $0.4$. We find that for the lower Mach numbers the saturation efficiency of the dynamo, $(E_{\mathrm{mag}}/E_{\mathrm{kin}})_{\mathrm{sat}}$, increases as the Mach number decreases. Even in the case when injection of energy is purely through longitudinal forcing modes, $(E_{\mathrm{mag}}/E_{\mathrm{kin}})_{\mathrm{sat}}$ $\gtrsim 10^{-2}$ at a Mach number of $10^{-3}$. We apply our results to magnetic field amplification in the ea…
Primordial turbulence from inflation: a new inflaton-driven turbulent regime
Nordita, KTH Royal Institute of Technology and Stockholm University（诺尔迪塔，皇家理工学院与斯德哥尔摩大学）；The Oskar Klein Centre, Stockholm University（奥斯卡·克莱因中心，斯德哥尔摩大学）；Instituut-Lorentz of Theoretical Physics, Universiteit Leiden（莱顿大学洛伦兹理论物理研究所）；McWilliams Center for Cosmology & Department of Physics, Carnegie Mellon University（卡内基梅隆大学麦克威廉姆斯宇宙学中心与物理系）；School of Natural Sciences and Medicine, Ilia State University（伊利亚州立大学自然科学与医学院）
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…
We report results from a cosmological simulation with non-equilibrium chemistry of 21 species, including H2, HD, and LiH molecular cooling. Starting from cosmological initial conditions, we focus on the evolution of the central 1.8 Kpc region of a 3 x 10^7 Msun halo. The crossing of a few 10^6 Msun halos and the gas accretion through larger scale filaments generate a turbulent environment within this region. Due to the short cooling time caused by the non-equilibrium formation of H2, the supersonic turbulence results in a very fragmented mass distribution, where dense, gravitationally unstable…
(abridged) This comment is intended to show that simulations by Smith et al. (S12) support the Dark Star (DS) scenario and even remove some potential obstacles. Our previous work illustrated that the initial hydrogen densities of the first equilibrium DSs are high, ~10^{17}/cm^3 for the case of 100 GeV WIMPs, with a stellar radius of ~2-3 AU. Subsequent authors have somehow missed the fact that equilibrium DSs have the high densities they do. S12 have numerically simulated the effect of dark matter annihilation on the contraction of a protostellar gas cloud en route to forming the first stars.…
The origin and maintenance of coherent magnetic fields in the Universe is reviewed with an emphasis on the possible challenges that arise in their theoretical understanding. We begin with the interesting possibility that magnetic fields originated at some level from the early universe. This could be during inflation, the electroweak or the quark-hadron phase transitions. These mechanisms can give rise to fields which could be strong, but often with much smaller coherence scales than galactic scales. Their subsequent turbulent decay decreases their strength but increases their coherence. We the…
Radiative feedback from populations II stars played a vital role in early structure formation. Particularly, photons below the Lyman limit can escape the star forming regions and produce a background ultraviolet (UV) flux which consequently may influence the pristine halos far away from the radiation sources. These photons can quench the formation of molecular hydrogen by photo-detachment of $\rm H^{-}$. In this study, we explore the impact of such UV radiation on fragmentation in massive primordial halos of a few times $\rm 10^{7}$~M${_\odot}$. To accomplish this goal, we perform high resolut…
We present coupled stellar evolution (SE) and 3D radiation-hydrodynamic (RHD) simulations of the evolution of primordial protostars, their immediate environment, and the dynamic accretion history under the influence of stellar ionizing and dissociating UV feedback. Our coupled SE-RHD calculations result in a wide diversity of final stellar masses covering 10 Msun $\lesssim M_* \lesssim$ 1000 Msun. The formation of very massive ($\gtrsim$ 250 Msun) stars is possible under weak UV feedback, whereas ordinary massive (a few x 10 Msun) stars form when UV feedback can efficiently halt the accretion.…
Numerous cosmological simulations have been performed to study the formation of the first objects. We present the results of high resolution 3-D cosmological simulations of primordial objects formation using the adaptive mesh refinement code FLASH by including in an approximate manner the radiative transfer effects of Lyman alpha photons. We compare the results of a Lyman alpha trapping case inside gas clouds with atomic and molecular hydrogen cooling cases.The principal objective of this research is to follow the collapse of a zero metallicity halo with an effective equation of state (that ac…
In massive primordial galaxies, the gas may directly collapse and form a single central massive object if cooling is suppressed. Line cooling by molecular hydrogen can be suppressed in the presence of a strong soft-ultraviolet radiation field, but the role played by other cooling mechanisms is less clear. In optically thin gas, Lyman-Alpha cooling can be very effective, maintaining the gas temperature below 10^4 K over many orders of magnitude in density. However, the large neutral hydrogen column densities present in primordial galaxies render them highly optically thick to Lyman-Alpha photon…
A popular theory of star formation is gravito-turbulent fragmentation, in which self-gravitating structures are created by turbulence-driven density fluctuations. Simple theories of isothermal fragmentation successfully reproduce the core mass function (CMF) which has a very similar shape to the initial mass function (IMF) of stars. However, numerical simulations of isothermal turbulent fragmentation thus far have not succeeded in identifying a fragment mass scale that is independent of the simulation resolution. Moreover, the fluid equations for magnetized, self-gravitating, isothermal turbul…
We have performed a cosmological numerical simulation of primordial baryonic gas collapsing onto a $3\times10^7$M$_{\odot}$ dark matter (DM) halo. We show that the large scale baryonic accretion process and the merger of few $\sim10^6$ M$_{\odot}$ DM halos, triggered by the gravitational potential of the biggest halo, is enough to create super sonic ($\mathcal{M}>10$) shocks and develop a turbulent environment. In this scenario the post shocked regions are able to produced both H$_2$ and HD molecules very efficiently reaching maximum abundances of $n_\mathrm{H_2}\sim10^{-2}n_\mathrm{H}$ and $n…
We use cosmological simulations of high-redshift minihalos to investigate the effect of dark matter annihilation (DMA) on the collapse of primordial gas. We numerically investigate the evolution of the gas as it assembles in a Population III stellar disk. We find that when DMA effects are neglected, the disk undergoes multiple fragmentation events beginning at ~ 500 yr after the appearance of the first protostar. On the other hand, DMA heating and ionization of the gas speeds the initial collapse of gas to protostellar densities and also affects the stability of the developing disk against fra…
Understanding the physics of inflaton condensate fragmentation in the early Universe is crucial as the existence of fragments in the form of non-topological solitons (oscillons or Q-balls) may potentially modify the evolution of the post-inflation Universe. Furthermore, such fragments may evolve into primordial black holes and form dark matter, or emit gravitational waves. Due to the non-perturbative and non-linear nature of the dynamics, most of the studies rely on numerical lattice simulations. Numerical simulations of condensate fragmentation are, however, challenging and, without knowing w…
