A generic consequence of supersymmetry is formation of a scalar condensate along the flat directions of the potential at the end of cosmological inflation. This condensate is usually unstable, and it can fragment into non-topological solitons, Q-balls. The gravitational waves produced by the fragmentation can be detected by Laser Interferometer Space Antenna (LISA), Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), and Big Bang Observer (BBO), which can offer an important window on the early universe and the physics at some very high energy scales.
We discuss the fragmentation of primordial gas clouds in the universe after decoupling. Comparing the time scale of collapse with that of fragmentation, we obtain the typical mass of a fragment both numerically and analytically. It is shown that the estimated mass gives the minimum mass of a fragment which is formed from the primordial gas cloud and is essentially determined by the Chandrasekhar mass.
In order to constrain the initial mass function of the first generation of stars (Population III), one has to study the fragmentation properties of primordial gas. We present results from 3D simulations, based on Smoothed Particle Hydrodynamics, which explore the idea that small-scale fluctuations in the (cold) dark matter recreate a filamentary and clumpy structure in the gas component on scales smaller than the initial Jeans mass, where all primordial fluctuations would have been wiped out.
We briefly review the motivations for studying the formation of the first ``Population III'' stars and present recent results from our numerical simulations in this area. We discuss the new questions raised as a result of the simulations presented by us and others at this meeting.
We study the excited states of the Q-balls by performing stationary perturbation on the spherical Q-balls. We find the exact solution of the stationary perturbation of the global Q-ball with thin wall approximation. For local Q-balls we solve the equations of motion for the perturbative part approximately by using expansion about the coupling constant. Furthermore we comment on the magnetic field generated by the excited Q-balls during the phase transition precipitated by solitosyhthesis and give an implication into cosmology.
We present numerical simulations of fragmentation of the Affleck-Dine condensate in two spatial dimensions. We argue analytically that the final state should consist of both Q-balls and anti-Q-balls in a state of maximum entropy, with most of the balls small and relativistic. Such a behaviour is found in simulations on a 100x100 lattice with cosmologically realistic parameter values. During fragmentation process, we observe filament-like texture in the spatial distribution of charge. The total charge in Q-balls is found to be almost equal to the charge in anti-Q-balls and typically orders of m…
The first structures were proto-voids formed in the primordial plasma. Viscous and weak turbulence forces balanced gravitational forces when the scale of causal connection at time 30,000 years matched the viscous and turbulent Schwarz scales of hydro-gravitational theory (Gibson 1996). The photon viscosity allows only weak turbulence from the Reynolds number Re = 200, with fragmentation to give proto-supercluster voids, buoyancy forces, fossil vorticity turbulence, and strong sonic damping. The expanding, cooling, plasma continued fragmentation to proto-galaxy-mass with the density and rate-of…
Many questions in physical cosmology regarding the thermal history of the intergalactic medium, chemical enrichment, reionization, etc. are thought to be intimately related to the nature and evolution of pregalactic structure. In particular the efficiency of primordial star formation and the primordial IMF are of special interest. We present results from high resolution three--dimensional adaptive mesh refinement simulations that follow the collapse of primordial molecular clouds and their subsequent fragmentation within a cosmologically representative volume. Comoving scales from 128 kpc down…
Many questions in physical cosmology regarding the thermal history of the intergalactic medium, chemical enrichment, reionization, etc. are thought to be intimately related to the nature and evolution of pregalactic structure. In particular the efficiency of primordial star formation and the primordial IMF are of special interest. We present results from high resolution three-dimensional adaptive mesh refinement simulations that follow the collapse of primordial molecular clouds and their subsequent fragmentation within a cosmologically representative volume. Comoving scales from 128 kpc down …
The mechanisms which could lead to chemo-thermal instabilities and fragmentation during the formation of primordial protostars are investigated analytically. We introduce approximations for H2 cooling rates bridging the optically thin and thick regimes. These allow us to discuss instabilities up to densities when protostars become optically thick to continuum radiation (n~10^16 cm^-3). During the collapse, instability arises at two different stages: at low density (n~10^8-10^11 cm^-3), it is due to fast 3-body reactions converting H into H2; at high density (n>10^13 cm^-3), it is due to Collis…
The Padoan and Nordlund model of the stellar initial mass function (IMF) is derived from low order statistics of supersonic turbulence, neglecting gravity (e.g. gravitational fragmentation, accretion and merging). In this work the predictions of that model are tested using the largest numerical experiments of supersonic hydrodynamic (HD) and magneto-hydrodynamic (MHD) turbulence to date (~1000^3 computational zones) and three different codes (Enzo, Zeus and the Stagger Code). The model predicts a power law distribution for large masses, related to the turbulence energy power spectrum slope, an…
In order to constrain the initial mass function (IMF) of the first generation of stars (Population III), we investigate the fragmentation properties of metal-free gas in the context of a hierarchical model of structure formation. We investigate the evolution of an isolated 3-sigma peak of mass 2x10^6 M_solar which collapses at z_coll=30 using Smoothed Particle Hydrodynamics. We find that the gas dissipatively settles into a rotationally supported disk which has a very filamentary morphology. The gas in these filaments is Jeans unstable with M_J~10^3 M_solar. Fragmentation leads to the formatio…
Recent theoretical investigations have suggested that the formation of the very first stars, forming out of metal-free gas, was fundamentally different from the present-day case. In this paper, we study the effect of metallicity on the evolution of the gas in a collapsing dark matter mini-halo. We model such a system as an isolated 3σpeak of mass 2x10^6 M_sun that collapses at z_coll=30, using smoothed particle hydrodynamics. The gas has a supposed level of pre-enrichment of either 10^-4 Z_sun or 10^-3 Z_sun. We find that the evolution proceeds very differently for the two cases. The gas in th…
We show that the explosion of the first supernovae can trigger low-mass star formation via gravitational fragmentation of the supernova-driven gas shell. If the shell mass does not exceed the host galaxy gas mass, all explosions with energies E_SN > 10^{51} erg can lead to shell fragmentation. However, the minimum ambient density required to induce such fragmentation is much larger, n_0 > 300 cm^{-3}, for Type II supernovae than for pair-instability ones, which can induce star formation even at lower ambient densities. The typical mass of the unstable fragments is 10^{4-7} Msun; their density …
We investigate the formation of molecular hydrogen (H_2) in a primordial H+He gas cloud irradiated by a power-law UV flux. We find that at high densities (>1 cm^{-3}) and low temperatures (<10^4 K), the background radiation enhances the formation of H_2 and results in molecular cooling dominating over photoionization heating. This process could accelerate the collapse and fragmentation of dense objects at high redshifts.
Primordial star formation appears to result in stars at least an order of magnitude more massive than modern star formation. It has been proposed that the transition from primordial to modern initial mass functions occurs due to the onset of effective metal line cooling at a metallicity Z/Z_sun = 10^{-3.5}. However, these simulations neglected molecular hydrogen cooling. We perform simulations using the same initial conditions, but including molecular cooling, using a complex network that follows molecular hydrogen formation and also directly follows carbon monoxide and water. We find that mol…
Fragmentation of the Affleck-Dine condensate into Q-balls could fill the Universe with dark matter either in the form of stable baryonic balls, or LSP produced from the decay of unstable Q-balls. The dark matter and the ordinary matter in the Universe may share the same origin.
Fragmentation of the planetesimals is found to play a role whose importance is greater than previously believed and depends on the average characteristic size of the primordial planetesimals but not on their mass distribution. In the small size range the mass spectrum is strongly modified with the formation of a small bodies tail but, on the other hand, the growth of the most massive objects is significantly slowed down. The formation of planetary embryos much more massive than the rest of the swarm is delayed; nevertheless the time-scale problem for the growth of the outer planets is not revi…
Astrophysical bounds on the properties and abundances of primordial quark nuggets and cosmic ray strangelets are reviewed. New experiments to search for cosmic ray strangelets in lunar soil and from the International Space Station are described. Analogies with baryonic and supersymmetric Q-balls are briefly mentioned, as are prospects for strangelets as ultra-high energy cosmic rays.
Stephan's Quintet (SQ) is a compact group of galaxies that has been well studied since its discovery in 1877 but is mysterious using cold dark matter hierarchical clustering cosmology (CDMHCC). Anomalous red shifts $z = (0.0027,0.019, 0.022, 0.022, 0.022)$ among galaxies in SQ either reduce it to a Trio with two highly improbable intruders from CDMHCC or support the Arp (1973) hypothesis that its red shifts are intrinsic. An alternative is provided by the Gibson 1996-2006 hydro-gravitational-dynamics (HGD) theory where superclusters, clusters and galaxies all originate by gravitational fragmen…
Thermal and chemical evolution of primordial gas clouds irradiated with far-ultraviolet (FUV; < 13.6 eV) radiation is investigated. In clouds irradiated by intense FUV radiation, sufficient hydrogen molecules to be important for cooling are never formed. However, even without molecular hydrogen, if the clouds are massive enough, they start collapsing via atomic hydrogen line cooling. Such clouds continue to collapse almost isothermally owing to successive cooling by H^{-} free-bound emission up to the number density of 10^{16} cm^{-3}. Inside the clouds, the Jeans mass eventually falls well be…
We study the formation of the first generation of stars in the standard cold dark matter model, using a very high-resolution hydordynamic simulations. Our simulation achieves a dynamic range of 10^{10} in length scale. With accurate treatment of atomic and molecular physics, it allows us to study the chemo-thermal evolution of primordial gas clouds to densities up to n = 10^{16}/cc without assuming any a priori equation of state; a six orders of magnitudes improvement over previous three-dimensional calculations. All the relevant atomic and molecular cooling and heating processes, including co…
We investigate the thermal and dynamical evolution of primordial gas clouds in the universe after decoupling. Comparing the time-scale of dynamical evolution with that of fragmentation, we can estimate the typical fragmentation scale. We propose the following scenario of the formation process of first luminous objects consisting of large number stars. First, by pancake collapse of the overdensity regions in the expanding universe or collision between clouds in potential wells, quasi-plane shocks form. If the shock-heated temperature is higher than about $10^4$ K, the postshock gas cools down t…
The MSSM has flat directions in its scalar potential, along which it is natural for Bose condensates of squarks to form in the early Universe. A baryon asymmetry can be induced in these condensates via Affleck-Dine baryogenesis. The condensates are unstable with respect to fragmentation to "B-balls", solitons made of squarks and carrying baryon number, which, if they survive thermalization, fill the Universe down to low temperatures, much lower than that of the electroweak phase transition, with interesting cosmological consequences. In particular, their decay implies a similar number density …
Cloud evolution for various metallicities is investigated by three-dimensional nested grid simulations, in which the initial ratio of rotational to gravitational energy of the host cloud β_0 (=10^-1 - 10^-6) and cloud metallicity Z (=0 - Z_\odot) are parameters. Starting from a central number density of n = 10^4 cm^-3, cloud evolution for 48 models is calculated until the protostar is formed (n \simeq 10^23 cm^-3) or fragmentation occurs. The fragmentation condition depends both on the initial rotational energy and cloud metallicity. Cloud rotation promotes fragmentation, while fragmentation t…
Jet driving and fragmentation process in collapsing primordial cloud are studied using three-dimensional MHD nested grid simulations. Starting from a rotating magnetized spherical cloud with the number density of n=10^3 cm^-3, we follow the evolution of the cloud up to the stellar density n=10^22 cm^-3. We calculate 36 models parameterizing the initial magnetic and rotational energies (γ_0, β_0). In the collapsing primordial clouds, the cloud evolutions are characterized by the ratio of the initial rotational to magnetic energy, γ_0/β_0. The Lorentz force significantly affects the cloud evolut…
The initial mass function (IMF) of metal-free stars that form in the initial starburst of massive (virial temperatures >10^4K) metal-free protogalaxies is studied. In particular, we focus on the effect of H2 photodissociation by pre-existing stars on the fragmentation mass scale, presumedly determined by the Jeans mass at the end of the initial free-fall phase, i.e., at the so-called ``loitering phase,'' characterized by the local temperature minimum. Photodissociation diminishes the Jeans mass at the loitering phase, thereby reducing the fragmentation mass scale of primordial clouds. Thus, in…
We discuss results from numerical simulations of star cluster formation in the turbulent interstellar medium (ISM). The thermodynamic behavior of the star-forming gas plays a crucial role in fragmentation and determines the stellar mass function as well as the dynamic properties of the nascent stellar cluster. This holds for star formation in molecular clouds in the solar neighborhood as well as for the formation of the very first stars in the early universe. The thermodynamic state of the ISM is a result of the balance between heating and cooling processes, which in turn are determined by ato…
The role of HD cooling in the formation of primordial objects is examined by means of a great number of 1-D models of the collapse of halos, exploring a wide range of masses and virialization redshifts. We find that HD has very little effect upon the critical mass separating the objects which are likely to form stars from those which are not. We also find that, once the proto-stellar collapse has started, HD effects are quite negligible. Instead, HD effects can be important during the intermediate stage of gas fragmentation: objects below a certain mass scale (~3x10^5 Msun at z_vir=20 in our `…
We study numerically the effect of varying the equation of state (EOS) on the formation of stellar clusters in turbulent molecular clouds. Our results show that the EOS plays an important role in the fragmentation of the clouds, and the determination of the initial mass function (IMF) of the protostellar cores. Fragmentation decreases with increasing adiabatic index $γ$ in the range $0.2 < γ< 1.4$, although the total amount of mass accreted appears to remain roughly constant through that range, resulting in more massive cores at higher $γ$. Fragmentation and collapse ceases entirely for $γ> 1.…
The fragmentation process of primordial-gas cores during prestellar collapse is studied using three-dimensional nested-grid hydrodynamics. Starting from the initial central number density of n \sim10^3 cm^-3, we follow the evolution of rotating spherical cores up to the stellar density n \simeq 10^{22} cm^-3. An initial condition of the cores is specified by three parameters: the ratios of the rotation and thermal energies to the gravitational energy (β_0, and α_0, respectively), and the amplitude of the bar-mode density perturbation (A_ϕ). Cores with rotation β_0 > 10^{-6} are found to fragme…
Accretion discs at sub-pc distances around supermassive black holes are likely to cool rapidly enough that self-gravity results in fragmentation. Here, we use high-resolution hydrodynamic simulations of a simplified disc model to study how the outcome of fragmentation depends upon numerical resolution and cooling time, and to investigate the incidence of binary formation within fragmenting discs. We investigate a range of cooling times, from the relatively long cooling time-scales that are marginally unstable to fragmentation down to highly unstable cooling on a time-scale that is shorter than…
To constrain the nature of the very first stars, we investigate the collapse and fragmentation of primordial, metal-free gas clouds. We explore the physics of primordial star formation by means of three-dimensional simulations of the dark matter and gas components, using smoothed particle hydrodynamics, under a wide range of initial conditions, including the initial spin, the total mass of the halo, the redshift of virialization, the power spectrum of the DM fluctuations, the presence of HD cooling, and the number of particles employed in the simulation. We find characteristic values for the t…
