Structure formation

Last updated June 07, 2024

In physical cosmology, structure formation is the formation of galaxies, galaxy clusters and larger structures from small early density fluctuations. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.8 billion years ago.^[1] However, looking at the night sky today, structures on all scales can be seen, from stars and planets to galaxies. On even larger scales, galaxy clusters and sheet-like structures of galaxies are separated by enormous voids containing few galaxies.^[2] Structure formation attempts to model how these structures were formed by gravitational instability of small early ripples in spacetime density^[3]^[4]^[5]^[6].

The modern Lambda-CDM model is successful at predicting the observed large-scale distribution of galaxies, clusters and voids; but on the scale of individual galaxies there are many complications due to highly nonlinear processes involving baryonic physics, gas heating and cooling, star formation and feedback. Understanding the processes of galaxy formation is a major topic of modern cosmology research, both via observations such as the Hubble Ultra-Deep Field and via large computer simulations.

Overview

Under present models, the structure of the visible universe was formed in the following stages:

Very early universe

In this stage, some mechanism, such as cosmic inflation, was responsible for establishing the initial conditions of the universe: homogeneity, isotropy, and flatness.^[4]^[7] Cosmic inflation also would have amplified minute quantum fluctuations (pre-inflation) into slight density ripples of overdensity and underdensity (post-inflation).

Growth of structure

The early universe was dominated by radiation; in this case density fluctuations larger than the cosmic horizon grow proportional to the scale factor, as the gravitational potential fluctuations remain constant. Structures smaller than the horizon remained essentially frozen due to radiation domination impeding growth. As the universe expanded, the density of radiation drops faster than matter (due to redshifting of photon energy); this led to a crossover called matter-radiation equality at ~ 50,000 years after the Big Bang. After this all dark matter ripples could grow freely, forming seeds into which the baryons could later fall. The particle horizon at this epoch induces a turnover in the matter power spectrum which can be measured in large redshift surveys.

Recombination

The universe was dominated by radiation for most of this stage, and due to the intense heat and radiation, the primordial hydrogen and helium were fully ionized into nuclei and free electrons. In this hot and dense situation, the radiation (photons) could not travel far before Thomson scattering off an electron. The universe was very hot and dense, but expanding rapidly and therefore cooling. Finally, at a little less than 400,000 years after the 'bang', it became cool enough (around 3000 K) for the protons to capture negatively charged electrons, forming neutral hydrogen atoms. (Helium atoms formed somewhat earlier due to their larger binding energy). Once nearly all the charged particles were bound in neutral atoms, the photons no longer interacted with them and were free to propagate for the next 13.8 billion years; we currently detect those photons redshifted by a factor 1090 down to 2.725 K as the Cosmic Microwave Background Radiation (CMB) filling today's universe. Several remarkable space-based missions (COBE, WMAP, Planck), have detected very slight variations in the density and temperature of the CMB. These variations were subtle, and the CMB appears very nearly uniformly the same in every direction. However, the slight temperature variations of order a few parts in 100,000 are of enormous importance, for they essentially were early "seeds" from which all subsequent complex structures in the universe ultimately developed.

The theory of what happened after the universe's first 400,000 years is one of hierarchical structure formation: the smaller gravitationally bound structures such as matter peaks containing the first stars and stellar clusters formed first, and these subsequently merged with gas and dark matter to form galaxies, followed by groups, clusters and superclusters of galaxies.

Before the first structures

Structure formation began some time after recombination, when the early universe cooled enough from expansion to allow the formation of stable hydrogen and helium atoms.^[8]^: 6 At this point the the cosmic microwave background(CMB) is emitted; many careful measurements of the CMB provide key information about the initial state of the universe before structure formation. The measurements support a model of small fluctuations in density, critical seeds for structures to come.

Linear structure

Dark matter plays a crucial role in structure formation because it feels only the force of gravity: the gravitational Jeans instability which allows compact structures to form is not opposed by any force, such as radiation pressure. As a result, dark matter begins to collapse into a complex network of dark matter halos well before ordinary matter, which is impeded by pressure forces. Without dark matter, the epoch of galaxy formation would occur substantially later in the universe than is observed.

The physics of structure formation in this epoch is particularly simple, as dark matter perturbations with different wavelengths evolve independently. As the Hubble radius grows in the expanding universe, it encompasses larger and larger disturbances. During matter domination, all causal dark matter perturbations grow through gravitational clustering. However, the shorter-wavelength perturbations that are included during radiation domination have their growth suppressed until matter domination. At this stage, luminous, baryonic matter is expected to mirror the evolution of the dark matter simply, and their distributions should closely trace one another.

It is straightforward to calculate this "linear power spectrum" and, as a tool for cosmology, it is of comparable importance to the cosmic microwave background. Galaxy surveys have measured the power spectrum, such as the Sloan Digital Sky Survey, and by surveys of the Lyman-α forest. Since these studies observe radiation emitted from galaxies and quasars, they do not directly measure the dark matter, but the large-scale distribution of galaxies (and of absorption lines in the Lyman-α forest) is expected to mirror the distribution of dark matter closely. This depends on the fact that galaxies will be larger and more numerous in denser parts of the universe, whereas they will be comparatively scarce in rarefied regions.

Nonlinear structure

When the perturbations have grown sufficiently, a small region might become substantially denser than the mean density of the universe. At this point, the physics involved becomes substantially more complicated. When the deviations from homogeneity are small, the dark matter may be treated as a pressureless fluid and evolves by very simple equations. In regions which are significantly denser than the background, the full Newtonian theory of gravity must be included. (The Newtonian theory is appropriate because the masses involved are much less than those required to form a black hole, and the speed of gravity may be ignored as the light-crossing time for the structure is still smaller than the characteristic dynamical time.) One sign that the linear and fluid approximations become invalid is that dark matter starts to form caustics in which the trajectories of adjacent particles cross, or particles start to form orbits. These dynamics are best understood using N-body simulations (although a variety of semi-analytic schemes, such as the Press–Schechter formalism, can be used in some cases). While in principle these simulations are quite simple, in practice they are tough to implement, as they require simulating millions or even billions of particles. Moreover, despite the large number of particles, each particle typically weighs 10⁹ solar masses and discretization effects may become significant. The largest such simulation as of 2005 is the Millennium simulation.^[9]

The result of N-body simulations suggests that the universe is composed largely of voids, whose densities might be as low as one-tenth the cosmological mean. The matter condenses in large filaments and haloes which have an intricate web-like structure. These form galaxy groups, clusters and superclusters. While the simulations appear to agree broadly with observations, their interpretation is complicated by the understanding of how dense accumulations of dark matter spur galaxy formation. In particular, many more small haloes form than we see in astronomical observations as dwarf galaxies and globular clusters. This is known as the Dwarf galaxy problem, and a variety of explanations have been proposed. Most account for it as an effect in the complicated physics of galaxy formation, but some have suggested that it is a problem with our model of dark matter and that some effect, such as warm dark matter, prevents the formation of the smallest haloes.

Gas evolution

The final stage in evolution comes when baryons condense in the centres of galaxy haloes to form galaxies, stars and quasars. Dark matter greatly accelerates the formation of dense haloes. As dark matter does not have radiation pressure, the formation of smaller structures from dark matter is impossible. This is because dark matter cannot dissipate angular momentum, whereas ordinary baryonic matter can collapse to form dense objects by dissipating angular momentum through radiative cooling. Understanding these processes is an enormously difficult computational problem, because they can involve the physics of gravity, magnetohydrodynamics, atomic physics, nuclear reactions, turbulence and even general relativity. In most cases, it is not yet possible to perform simulations that can be compared quantitatively with observations, and the best that can be achieved are approximate simulations that illustrate the main qualitative features of a process such as a star formation.

Modelling structure formation

Snapshot from a computer simulation of large scale structure formation in a Lambda-CDM universe. LCDM.jpg — Snapshot from a computer simulation of large scale structure formation in a Lambda-CDM universe.

Cosmological perturbations

Much of the difficulty, and many of the disputes, in understanding the large-scale structure of the universe can be resolved by better understanding the choice of gauge in general relativity. By the scalar-vector-tensor decomposition, the metric includes four scalar perturbations, two vector perturbations, and one tensor perturbation. Only the scalar perturbations are significant: the vectors are exponentially suppressed in the early universe, and the tensor mode makes only a small (but important) contribution in the form of primordial gravitational radiation and the B-modes of the cosmic microwave background polarization. Two of the four scalar modes may be removed by a physically meaningless coordinate transformation. Which modes are eliminated determine the infinite number of possible gauge fixings. The most popular gauge is Newtonian gauge (and the closely related conformal Newtonian gauge), in which the retained scalars are the Newtonian potentials Φ and Ψ, which correspond exactly to the Newtonian potential energy from Newtonian gravity. Many other gauges are used, including synchronous gauge, which can be an efficient gauge for numerical computation (it is used by CMBFAST). Each gauge still includes some unphysical degrees of freedom. There is a so-called gauge-invariant formalism, in which only gauge invariant combinations of variables are considered.

Inflation and initial conditions

The initial conditions for the universe are thought to arise from the scale invariant quantum mechanical fluctuations of cosmic inflation. The perturbation of the background energy density at a given point $\rho (\mathbf {x} ,t)$ in space is then given by an isotropic, homogeneous Gaussian random field of mean zero. This means that the spatial Fourier transform of $\rho$ – ${\hat {\rho }}(\mathbf {k} ,t)$ has the following correlation functions

\langle {\hat {\rho }}(\mathbf {k} ,t){\hat {\rho }}(\mathbf {k} ',t)\rangle =f(k)\delta ^{(3)}(\mathbf {k} -\mathbf {k'} )

,

where $\delta ^{(3)}$ is the three-dimensional Dirac delta function and $k=|\mathbf {k} |$ is the length of $\mathbf {k}$ . Moreover, the spectrum predicted by inflation is nearly scale invariant, which means

\langle {\hat {\rho }}(\mathbf {k} ,t){\hat {\rho }}(\mathbf {k} ',t)\rangle =k^{n_{s}-1}\delta ^{(3)}(\mathbf {k} -\mathbf {k'} )

,

where $n_{s}-1$ is a small number. Finally, the initial conditions are adiabatic or isentropic, which means that the fractional perturbation in the entropy of each species of particle is equal. The resulting predictions fit very well with observations.

Related Research Articles

Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood.

The cosmic microwave background is microwave radiation that fills all space in the observable universe. It is a remnant that provides an important source of data on the primordial universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dark. However, a sufficiently sensitive radio telescope detects a faint background glow that is almost uniform and is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1965 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s.

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are farther away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the farther away that an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.

The Friedmann–Lemaître–Robertson–Walker metric is a metric based on an exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.

The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components:

a cosmological constant, denoted by lambda (Λ), associated with dark energy
the postulated cold dark matter, denoted by CDM
ordinary matter

The flatness problem is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that small deviations from these values would have extreme effects on the appearance of the universe at the current time.

Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. Currently, the most widely accepted explanation for their origin is in the context of cosmic inflation. According to the inflationary paradigm, the exponential growth of the scale factor during inflation caused quantum fluctuations of the inflaton field to be stretched to macroscopic scales, and, upon leaving the horizon, to "freeze in". At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the initial conditions for structure formation.

In modern models of physical cosmology, a dark matter halo is a basic unit of cosmological structure. It is a hypothetical region that has decoupled from cosmic expansion and contains gravitationally bound matter. A single dark matter halo may contain multiple virialized clumps of dark matter bound together by gravity, known as subhalos. Modern cosmological models, such as ΛCDM, propose that dark matter halos and subhalos may contain galaxies. The dark matter halo of a galaxy envelops the galactic disc and extends well beyond the edge of the visible galaxy. Thought to consist of dark matter, halos have not been observed directly. Their existence is inferred through observations of their effects on the motions of stars and gas in galaxies and gravitational lensing. Dark matter halos play a key role in current models of galaxy formation and evolution. Theories that attempt to explain the nature of dark matter halos with varying degrees of success include cold dark matter (CDM), warm dark matter, and massive compact halo objects (MACHOs).

In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the Big Bang model. Cosmological perturbation theory may be broken into two categories: Newtonian or general relativistic. Each case uses its governing equations to compute gravitational and pressure forces which cause small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. Both cases apply only to situations where the universe is predominantly homogeneous, such as during cosmic inflation and large parts of the Big Bang. The universe is believed to still be homogeneous enough that the theory is a good approximation on the largest scales, but on smaller scales more involved techniques, such as N-body simulations, must be used. When deciding whether to use general relativity for perturbation theory, note that Newtonian physics is only applicable in some cases such as for scales smaller than the Hubble horizon, where spacetime is sufficiently flat, and for which speeds are non-relativistic.

In physics and astronomy, an N-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity. N-body simulations are widely used tools in astrophysics, from investigating the dynamics of few-body systems like the Earth-Moon-Sun system to understanding the evolution of the large-scale structure of the universe. In physical cosmology, N-body simulations are used to study processes of non-linear structure formation such as galaxy filaments and galaxy halos from the influence of dark matter. Direct N-body simulations are used to study the dynamical evolution of star clusters.

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In modern cosmological theory, diffusion damping, also called photon diffusion damping, is a physical process which reduced density inequalities (anisotropies) in the early universe, making the universe itself and the cosmic microwave background radiation (CMB) more uniform. Around 300,000 years after the Big Bang, during the epoch of recombination, diffusing photons travelled from hot regions of space to cold ones, equalising the temperatures of these regions. This effect is responsible, along with baryon acoustic oscillations, the Doppler effect, and the effects of gravity on electromagnetic radiation, for the eventual formation of galaxies and galaxy clusters, these being the dominant large scale structures which are observed in the universe. It is a damping by diffusion, not of diffusion.

The chronology of the universe describes the history and future of the universe according to Big Bang cosmology.

In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way that supernovae provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler" for length scale in cosmology. The length of this standard ruler is given by the maximum distance the acoustic waves could travel in the primordial plasma before the plasma cooled to the point where it became neutral atoms, which stopped the expansion of the plasma density waves, "freezing" them into place. The length of this standard ruler can be measured by looking at the large scale structure of matter using astronomical surveys. BAO measurements help cosmologists understand more about the nature of dark energy by constraining cosmological parameters.

The Press–Schechter formalism is a mathematical model for predicting the number of objects of a certain mass within a given volume of the Universe. It was described in an academic paper by William H. Press and Paul Schechter in 1974.

The Mészáros effect "is the main physical process that alters the shape of the initial power spectrum of fluctuations in the cold dark matter theory of cosmological structure formation". It was introduced in 1974 by Péter Mészáros considering the behavior of dark matter perturbations in the range around the radiation-matter equilibrium redshift $and up to the radiation decoupling redshift . This showed that, for a non-baryonic cold dark matter not coupled to radiation, the small initial perturbations expected to give rise to the present day large scale structures experience below an additional distinct growth period which alters the initial fluctuation power spectrum, and allows sufficient time for the fluctuations to grow into galaxies and galaxy clusters by the present epoch. This involved introducing and solving a joint radiation plus dark matter perturbation equation for the density fluctuations,$

<span class="mw-page-title-main">Cosmic microwave background spectral distortions</span> Fluctuations in the energy spectrum of the microwave background

CMB spectral distortions are tiny departures of the average cosmic microwave background (CMB) frequency spectrum from the predictions given by a perfect black body. They can be produced by a number of standard and non-standard processes occurring at the early stages of cosmic history, and therefore allow us to probe the standard picture of cosmology. Importantly, the CMB frequency spectrum and its distortions should not be confused with the CMB anisotropy power spectrum, which relates to spatial fluctuations of the CMB temperature in different directions of the sky.

References

↑ "Cosmic Detectives". The European Space Agency (ESA). 2013-04-02. Retrieved 2013-04-15.
↑ Einasto, J.; Longair, M.S. (1978). "The Large Scale Structure of the Universe Symposium". Large Scale Structures in the Universe. 79. Reidel: 247. Bibcode:1978IAUS...79..241J.
↑ Dodelson, Scott (2003). Modern Cosmology. Academic Press. ISBN 978-0-12-219141-1.
1 2 Liddle, Andrew; David Lyth (2000). Cosmological Inflation and Large-Scale Structure. Cambridge. ISBN 978-0-521-57598-0.
↑ Padmanabhan, T. (1993). Structure formation in the universe. Cambridge University Press. ISBN 978-0-521-42486-8.
↑ Peebles, P. J. E. (1980). The Large-Scale Structure of the Universe. Princeton University Press. ISBN 978-0-691-08240-0.
↑ Kolb, Edward; Michael Turner (1988). The Early Universe. Addison-Wesley. ISBN 978-0-201-11604-5.
↑ Dayal, Pratika; Ferrara, Andrea (2018). "Early galaxy formation and its large-scale effects". Physics Reports. 780–782: 1–64. doi:10.1016/j.physrep.2018.10.002.
↑ Springel, V.; et al. (2005). "Simulations of the formation, evolution and clustering of galaxies and quasars". Nature. 435 (7042): 629–636. arXiv: astro-ph/0504097 . Bibcode:2005Natur.435..629S. doi:10.1038/nature03597. PMID 15931216. S2CID 4383030.

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[1] "Cosmic Detectives". The European Space Agency (ESA). 2013-04-02. Retrieved 2013-04-15.

[2] Einasto, J.; Longair, M.S. (1978). "The Large Scale Structure of the Universe Symposium". Large Scale Structures in the Universe. 79. Reidel: 247. Bibcode:1978IAUS...79..241J.

[dodelson-3] Dodelson, Scott (2003). Modern Cosmology. Academic Press. ISBN 978-0-12-219141-1.

[liddle-4] 1 2 Liddle, Andrew; David Lyth (2000). Cosmological Inflation and Large-Scale Structure. Cambridge. ISBN 978-0-521-57598-0.

[padmanabhan-5] Padmanabhan, T. (1993). Structure formation in the universe. Cambridge University Press. ISBN 978-0-521-42486-8.

[peebles-6] Peebles, P. J. E. (1980). The Large-Scale Structure of the Universe. Princeton University Press. ISBN 978-0-691-08240-0.

[kolb-7] Kolb, Edward; Michael Turner (1988). The Early Universe. Addison-Wesley. ISBN 978-0-201-11604-5.

[DayalFerrara2018-8] Dayal, Pratika; Ferrara, Andrea (2018). "Early galaxy formation and its large-scale effects". Physics Reports. 780–782: 1–64. doi:10.1016/j.physrep.2018.10.002.

[9] Springel, V.; et al. (2005). "Simulations of the formation, evolution and clustering of galaxies and quasars". Nature. 435 (7042): 629–636. arXiv: astro-ph/0504097 . Bibcode:2005Natur.435..629S. doi:10.1038/nature03597. PMID 15931216. S2CID 4383030.

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