Primordial Turbulence Research Articles

The scalar, vector, and tensor modes in gravitational wave turbulence simulations

We study the gravitational wave (GW) signal sourced by primordial turbulence that is assumed to be present at cosmological phase transitions like the electroweak and quantum chromodynamics phase transitions. We consider various models of primordial turbulence, such as those with and without helicity, purely hydrodynamical turbulence induced by fluid motions, and magnetohydrodynamic turbulence whose energy can be dominated either by kinetic or magnetic energy, depending on the nature of the turbulence. We also study circularly polarized GWs generated by parity violating sources such as helical turbulence. Our ultimate goal is to determine the efficiency of GW production through different classes of turbulence. We find that the GW energy and strain tend to be large for acoustic or irrotational turbulence, even though its tensor mode amplitude is relatively small at most wave numbers. Only at very small wave numbers is the spectral tensor mode significant, which might explain the efficient GW production in that case.

Dynamo effect in decaying helical turbulence

We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity - regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t^{-1/2}. This is even slower than in the fully helical case, where it decays like t^{-2/3}. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity, is approximately constant. This scaling of magnetic energy persists over long time scales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a cross-over to the t^{-2/3} decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe.

Magnetism in the Early Universe

AbstractBlazar observations point toward the possible presence of magnetic fields over intergalactic scales of the order of up to ∼1 Mpc, with strengths of at least ∼10−16 G. Understanding the origin of these large-scale magnetic fields is a challenge for modern astrophysics. Here we discuss the cosmological scenario, focussing on the following questions: (i) How and when was this magnetic field generated? (ii) How does it evolve during the expansion of the universe? (iii) Are the amplitude and statistical properties of this field such that they can explain the strengths and correlation lengths of observed magnetic fields? We also discuss the possibility of observing primordial turbulence through direct detection of stochastic gravitational waves in the mHz range accessible to LISA.

Unveiling the cosmological QCD phase transition through the eLISA/NGO detector

We study the evolution of turbulence in the early Universe at the QCD epoch using a state-of-the-art equation of state derived from lattice QCD simulations. Since the transition is a crossover we assume that temperature and velocity fluctuations were generated by some event in the previous history of the Universe and survive until the QCD epoch due to the extremely large Reynolds number of the primordial fluid. The fluid at the QCD epoch is assumed to be nonviscous, based on the fact that the viscosity per entropy density of the quark gluon plasma obtained from heavy-ion collision experiments at the Relativistic Heavy Ion Collider and the LHC is extremely small. Our hydrodynamic simulations show that the velocity spectrum is very different from the Kolmogorov power law considered in studies of primordial turbulence that focus on first order phase transitions. This is due to the fact that there is no continuous injection of energy into the system and the viscosity of the fluid is negligible. Thus, as kinetic energy cascades from the larger to the smaller scales, a large amount of kinetic energy is accumulated at the smallest scales due to the lack of dissipation. We have obtained the spectrum of the gravitational radiation emitted by the motion of the fluid finding that, if typical velocity and temperature fluctuations have an amplitude $(\ensuremath{\Delta}v)/c\ensuremath{\gtrsim}{10}^{\ensuremath{-}2}$ and/or $\ensuremath{\Delta}T/{T}_{c}\ensuremath{\gtrsim}{10}^{\ensuremath{-}3}$, they would be detected by eLISA at frequencies larger than $\ensuremath{\sim}{10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{Hz}$.

A Study of Multiscale Density Fluctuation Measurements

Intriguing parallels between density fluctuation power versus wavenumber on small (mm) and large (Mpc) scales are presented. The comparative study is carried out between fusion plasma measurements and cosmological data. Based on predictions from classical fluid turbulence theory, we argue that our observations are consistent with 2D turbulence. The similar dependencies of density fluctuations on these disparate scales might indicate that primordial turbulence has been expanded to cosmological proportions.

Spectrum of gravitational radiation from primordial turbulence

Energy injection into the early universe can induce turbulent motions of the primordial plasma, which in turn act as a source for gravitational radiation. Earlier work computed the amplitude and characteristic frequency of the relic gravitational wave background, as a function of the total energy injected and the stirring scale of the turbulence. This paper computes the frequency spectrum of relic gravitational radiation from a turbulent source of the stationary Kolmogoroff form which acts for a given duration, making no other approximations. We also show that the limit of long source wavelengths, commonly employed in aeroacoustic problems, is an excellent approximation. The gravitational waves from cosmological turbulence around the electroweak energy scale will be detectable by future space-based laser interferometers for a substantial range of turbulence parameters.

Gravitational waves from stochastic relativistic sources: Primordial turbulence and magnetic fields

The power spectrum of a homogeneous and isotropic stochastic variable, characterized by a finite correlation length, does not, in general, vanish on scales larger than the correlation scale. If the variable is a divergence-free vector field, we demonstrate that its power spectrum is blue on large scales. Accounting for this fact, we compute the gravitational waves induced by an incompressible turbulent fluid and by a causal magnetic field present in the early universe. The gravitational wave power spectra show common features: they are both blue on large scales, and they both peak at the correlation scale. However, the magnetic field can be treated as a coherent source and it is active for a long time. This results in a very effective conversion of magnetic energy in gravitational wave energy at horizon crossing. Turbulence instead acts as a source for gravitational waves over a time interval much shorter than a Hubble time, and the conversion into gravitational wave energy is much less effective. We also derive a strong constraint on the amplitude of a primordial magnetic field when the correlation length is much smaller than the horizon.

Cluster Formation in Protostellar Outflow-driven Turbulence

Most, perhaps all, stars go through a phase of vigorous outflow during formation. We examine, through three-dimensional MHD simulation, the effects of protostellar outflows on cluster formation. We find that the initial turbulence in the cluster-forming region is quickly replaced by motions generated by outflows. The protostellar outflow-driven turbulence (protostellar turbulence for short) can keep the region close to a virial equilibrium long after the initial turbulence has decayed away. We argue that there exist two types of turbulence in star-forming clouds: a primordial (or interstellar) turbulence and a protostellar turbulence, with the former transformed into the latter mostly in embedded clusters such as NGC 1333. Since the majority of stars are thought to form in clusters, an implication is that the stellar initial mass function is determined to a large extent by the stars themselves, through outflows that individually limit the mass accretion onto forming stars and collectively shape the environments (density structure and velocity field) in which most cluster members form. We speculate that massive cluster-forming clumps supported by protostellar turbulence gradually evolve toward a highly centrally condensed pivotal state, culminating in rapid formation of massive stars in the densest part through accretion.

Multiscaling of cosmic microwave background radiation

The multiscaling features of structure functions of cosmic microwave background (CMB) radiation have been studied using the new data available with the resolution of the order of a degree (combined QMAP and Saskatoon CMB radiation maps). It is shown that the scaling exponents of the CMB structure functions in the angular scale interval 0.9–4° are nearly identical to those of universal velocity structure functions in fluid turbulence. This indicates a strong connection between fluid turbulence and the origin of the observed CMB angular anisotropy in this interval of scales. Since the atmosphere and foreground radiation give minor contribution to these data the most likely explanation for this finding is primordial turbulence.

On the Origin of Cosmic Magnetic Fields

In the past investigations of cosmological magnetic fields, Harrison (1970) assumed primordial turbulence with nonzero vorticity. More recently this idea lost favor with most cosmologists, primarily because vortices decay during the cosmic expansion (Rees, 1987). In contrast to these works we resort to no assumption as for the primordial condition but for the thermal equilibrium in the following. A plasma with temperature T in the early universe sustains fluctuations of electromagnetic fields and density even if it is in a thermal equilibrium. The level of fluctuations in the plasma for a given wavelength of electromagnetic fields, for example, can be rigorously computed by the fluctuation-dissipation theorem (Geary et al. 1986; Kubo 1957; Sitenko 1967). In particular, without assuming any turbulence we show that very low (or ~ zero) frequency magnetic fluctuations can also be excited and the level of these is computedr where summation on k is over all the available wavenumbers V the volume of the Universe, and ωp the plasma frequency (4πe2n/m)1/2. The level of fluctuation is given approximately by the equipartition value of T/2 for kωωp/c and much less than that for k>ωp/c. These fields at the early radiation epoch t=10°sec (we call the radiation epoch in which the radiation effects dominate that of gravity in the universe as the plasma epoch: tε10−2 − 1013 sec) can act as seed fields and can evolve during the plasma epoch. The result is shown in Fig. 1. We show that magnetic fields with the size of λ≤108cm can be amplified by the dynamo effect and that the field strength corresponding to this size is greater than 10–19 Gauss.

Star formation - The influence of velocity fields and turbulence

It is shown that the Jeans mass for gravitational collapse can be very much reduced by the influence velocity fields, even when allowance is made for non-isothermal gas behavior. We examine the role of turbulence in establishing the initial stellar mass function and show that the flattening and/or turnover at the low mass end may be a signature of interstellar turbulence. We consider also the implications of primordial turbulence for the formation of stars in the early universe.

On the Acoustic Decay of Primordial Cosmic Turbulence

On the basis .of Nariai's new formalism for dealing with the generation of sound from primordial cosmic turbulence, the intensity of sound (at the center of an expanding turbulent fluid sphere within the acoustic event horizon) an.d the ratio of sound energy to that of turbulence are numerically calculated for several values of n (a parameter specifying the decay law of cosmic turbulence) and M, (an .initial Mach number). It is shown that, con­ trary to Jones's assertion, the acoustic decay ,of, primordial cosmic turbulence is negligible irrespective of a concrete form of the spectral fQnction. It is also shown that a more reli­ able fixation of n is necessary to make clearer the formation of galaxies ·from cosmic tur­ bulence.

Galaxy Formation Without Primordial Turbulence: Mechanisms for Generating Cosmic Vorticity

It is shown that neither the tidal interaction between protogalaxies nor turbulent dynamo action can account for the observed vorticities of spiral galaxies. Doroshkevich's suggestion that vorticity generated in shock waves might account for the rotation of spiral galaxies is then investigated. A relation is obtained for the vorticity generated in a generally curved shock front. Applying this result to a collapsing protocluster of galaxies it is found that this mechanism does indeed provide more than adequate vorticity to account for spiral galaxy formation. On the basis of this model there is a natural explanation of the tendency of spiral or elliptical galaxies to cluster together. There should also be a correlation between the relative proportions of spirals and ellipticals and the shape of a cluster itself. The application of this analysis to the Virgo Supercluster gives a different pattern of peculiar velocities for the galaxies in the solar neighbourhood from that expected on the basis of the primordial turbulence model. When more precise data on the anisotropy of the 2.7 K background becomes available, this may enable us to choose between these two theories.

On the Generation of Sound from the Primordial Turbulence in an Expanding Universe. II: Refinement of the Formalism

On the Generation of Sound from the Primordial Turbulence in an Expanding Universe. II: Refinement of the Formalism

Magnetic Fields in the Early Universe

Primordial turbulence in the radiation-dominated era of the early Universe has an associated weak seed magnetic field on all scales of the turbulence. This seed field is stochastically amplified by the small-scale rapidly fluctuating turbulence motions and it is possible, in principle at least, for magnetic and small-scale kinetic energies to attain equipartition within an expansion time. It is unlikely that the magnetic energy attains equipartition with the large-scale kinetic energy of the turbulence. The intensity of the field is ~ 10 9 Gauss at temperature T = 10 9 K and ~ 10 2 Gauss at T = 10 5 K. Field generation ceases at approximately the epoch of equal radiation and matter densities. Some implications of the primordially generated field are considered. It is shown that the Jeans mass, owing to magnetic stresses, is of galactic magnitude and plays a crucial role in galaxy formation. It is estimated that the present intergalactic magnetic field has an intensity of ~ 10 −8 Gauss and a dominant scale-length ~ 10 kpc. Some brief comments are made on the possibility of ion acceleration by agitated magnetic fields during and after the radiation era.

On the Generatin of Sound from the Primordial Turbulence in an Expanding Universe

In order that galaxies may be formed from the primordial turbulence in a big-bang universe, the cosmic turbulence with suitable scales must survive up to the decoupling epoch of matter from radiation against its decay due to the generation of sound as envisaged by Lighthill and Crighton. To attack the problem with due consideration of the effect of cosmic expansion neglected in the Lighthill-- Crighton theory, the generation of sound from the cosmic turbulence is dealt with by constructing the appropriate retarded Oreen's function in which all significant influences of the cosmic expansion upon the propagation of sound waves to be generated are woven. rt is shown that the expanding turbulent fluid is inevitably of a diffusive nature in such a way that its physical radius is equal to the acoustical event horizon. The latter situation means that the retardation effect is essential in the evaluation of the intensity of sound at the center of the turbulent fluid sphere, while the effect was discarded in the Crighton formula for a static diffusive medium. In other words, the formalism is superior to Crighton's for the examination of the aforementioned problem. (auth)

Origin of Magnetic Fields in the Early Universe

Primordial turbulence in the radiation era generates a weak seed magnetic field on all scales of the turbulence. This field is stochastically amplified by turbulence motions, and it is possible for magnetic and small-scale kinetic energies to attain equipartition within an expansion time. Field generation ceases at the epoch of equal radiation and matter densities, when the field strength is of the order of 1 G. It is estimated that the present intergalactic magnetic field has an intensity of \ensuremath{\sim}${10}^{\ensuremath{-}8}$ G and a scale-length of \ensuremath{\sim}Mparsec.

Primordial Turbulence and the FORMAT10N of Galaxies

The development of turbulence at early epochs in a Friedmann universe is studied, giving primary attention to the density fluctuations generated by vortical turbulence. Aspects of turbulence theory in a cosmogonical context are discussed together with a theory of turbulence in an expanding universe. It is suggested that small-amplitude density fluctuations generated by primordial turbulence before decoupling, rather than by the onset of supersonic turbulence after decoupling, can best account for the formation of galaxies. On the other hand, the requisite amount of angular momentum per unit mass to account for the rotation of galaxies is well explained by the turbulence parameters.

Dissipation of Primordial Turbulence and Thermal History of the Universe

The assumption that in the early stage of the universe there existed turbulence of photons and plasma dragged by them can explain the formation of galaxies plausibly. Using simple expressions to represent the decay law of the primordial turbulence, the thermal history of gas at the pre-galactic stage is followed and the residual ionization degree of hydrogen is computed. It is found that maximum temperatures attainable are about 104 oK for a wide range of heating paramaters. This is because a kind of thermostat that keeps gas temperature below 104 OK operates: the increase of temperature above 10 4 oK is prevented by the increase of the ionization degree and the resultant increase of cooling rate. Therefore, it can be concluded that galaxies cannot be formed through the thermal instability due to the heating by the primordial turbulence.

The Rotation and Angular Momentum of Galaxies

view Abstract Citations (8) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Rotation and Angular Momentum of Galaxies Hunter, C. Abstract Current explanations attribute the rotation of galaxies either to primordial turbulence or else to tidal interactions between protogalaxies during their formation. The latter effect gives rise to angular momentum in the form of straining motion and asymmetrical shape rather than purely circular motion. Simple models of protogalaxies considered here show a strong tendency to contract to high-density asymmetrical states, and a variety of steady states of this kind can be achieved with angular momentum in both straining and rotational forms. Publication: The Astrophysical Journal Pub Date: November 1970 DOI: 10.1086/150677 Bibcode: 1970ApJ...162..445H full text sources ADS |