Shape of the universe

From Wikipedia, the free encyclopedia

The shape of the universe is the local and global geometry of the Universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as of a continuous object. The shape of the universe is related to general relativity which describes how spacetime is curved and bent by mass and energy.

Cosmologists distinguish between the observable universe and the global universe. The observable universe consists of the part of the universe that can, in principle, be observed by light reaching Earth within the age of the universe. It encompasses a region of space which currently forms a ball centered at Earth of estimated radius 46 billion light-years (4.4×10²⁶ m). This does not mean the universe is 46 billion years old; in fact the universe is believed to be 13.799 billion years old but space itself has also expanded causing the size of the observable universe to be as stated. (However, it is possible to observe these distant areas only in their very distant past, when the distance light had to travel was much less). Assuming an isotropic nature, the observable universe is similar for all contemporary vantage points.

According to the book Our Mathematical Universe^{[clarification needed]}, the shape of the global universe can be explained with three categories:^[1]

1. Finite or infinite
2. Flat (no curvature), open (negative curvature), or closed (positive curvature)
3. Connectivity, how the universe is put together, i.e., simply connected space or multiply connected.

There are certain logical connections among these properties. For example, a universe with positive curvature is necessarily finite.^[2] Although it is usually assumed in the literature that a flat or negatively curved universe is infinite, this need not be the case if the topology is not the trivial one.^[2]

The exact shape is still a matter of debate in physical cosmology, but experimental data from various, independent sources (WMAP, BOOMERanG, and Planck for example) confirm that the observable universe is flat with only a 0.4% margin of error.^[3][4][5] Theorists have been trying to construct a formal mathematical model of the shape of the universe. In formal terms, this is a 3-manifold model corresponding to the spatial section (in comoving coordinates) of the 4-dimensional space-time of the universe. The model most theorists currently use is the Friedmann–Lemaître–Robertson–Walker (FLRW) model. Arguments have been put forward that the observational data best fit with the conclusion that the shape of the global universe is infinite and flat,^[6] but the data are also consistent with other possible shapes, such as the so-called Poincaré dodecahedral space^[7][8] and the Sokolov-Starobinskii space (quotient of the upper half-space model of hyperbolic space by 2-dimensional lattice).^[9]

Shape of the observable universe

As stated in the introduction, there are two aspects to consider:

1. its local geometry, which predominantly concerns the curvature of the universe, particularly the observable universe, and
2. its global geometry, which concerns the topology of the universe as a whole.

The observable universe can be thought of as a sphere that extends outwards from any observation point for 46.5 billion light years, going farther back in time and more redshifted the more distant away one looks. Ideally, one can continue to look back all the way to the Big Bang; in practice, however, the farthest away one can look using light and other electromagnetic radiation is the cosmic microwave background (CMB), as anything past that was opaque. Experimental investigations show that the observable universe is very close to isotropic and homogeneous.

If the observable universe encompasses the entire universe, we may be able to determine the global structure of the entire universe by observation. However, if the observable universe is smaller than the entire universe, our observations will be limited to only a part of the whole, and we may not be able to determine its global geometry through measurement. From experiments, it is possible to construct different mathematical models of the global geometry of the entire universe all of which are consistent with current observational data and so it is currently unknown whether the observable universe is identical to the global universe or it is instead many orders of magnitude smaller than it. The universe may be small in some dimensions and not in others (analogous to the way a cuboid is longer in the dimension of length than it is in the dimensions of width and depth). To test whether a given mathematical model describes the universe accurately, scientists look for the model's novel implications—what are some phenomena in the universe that we have not yet observed, but that must exist if the model is correct—and they devise experiments to test whether those phenomena occur or not. For example, if the universe is a small closed loop, one would expect to see multiple images of an object in the sky, although not necessarily images of the same age.

Cosmologists normally work with a given space-like slice of spacetime called the comoving coordinates, the existence of a preferred set of which is possible and widely accepted in present-day physical cosmology. The section of spacetime that can be observed is the backward light cone (all points within the cosmic light horizon, given time to reach a given observer), while the related term Hubble volume can be used to describe either the past light cone or comoving space up to the surface of last scattering. To speak of "the shape of the universe (at a point in time)" is ontologically naive from the point of view of special relativity alone: due to the relativity of simultaneity we cannot speak of different points in space as being "at the same point in time" nor, therefore, of "the shape of the universe at a point in time". However, the comoving coordinates (if well-defined) provide a strict sense to those by using the time since the Big Bang (measured in the reference of CMB) as a distinguished universal time.

Curvature of the universe

The curvature is a quantity describing how the geometry of a space differs locally from the one of the flat space. The curvature of any locally isotropic space (and hence of a locally isotropic universe) falls into one of the three following cases:

1. Zero curvature (flat); a drawn triangle's angles add up to 180° and the Pythagorean theorem holds; such 3-dimensional space is locally modeled by Euclidean space E³.
2. Positive curvature; a drawn triangle's angles add up to more than 180°; such 3-dimensional space is locally modeled by a region of a 3-sphere S³.
3. Negative curvature; a drawn triangle's angles add up to less than 180°; such 3-dimensional space is locally modeled by a region of a hyperbolic space H³.

Curved geometries are in the domain of Non-Euclidean geometry. An example of a positively curved space would be the surface of a sphere such as the Earth. A triangle drawn from the equator to a pole will have at least two angles equal 90°, which makes the sum of the 3 angles greater than 180°. An example of a negatively curved surface would be the shape of a saddle or mountain pass. A triangle drawn on a saddle surface will have the sum of the angles adding up to less than 180°.

The local geometry of the universe is determined by whether the density parameter Ω is greater than, less than, or equal to 1.
From top to bottom: a spherical universe with Ω > 1, a hyperbolic universe with Ω < 1, and a flat universe with Ω = 1. These depictions of two-dimensional surfaces are merely easily visualizable analogs to the 3-dimensional structure of (local) space.

General relativity explains that mass and energy bend the curvature of spacetime and is used to determine what curvature the universe has by using a value called the density parameter, represented with Omega (Ω). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way,

• If Ω = 1, the universe is flat
• If Ω > 1, there is positive curvature
• if Ω < 1 there is negative curvature

One can experimentally calculate this Ω to determine the curvature two ways. One is to count up all the mass-energy in the universe and take its average density then divide that average by the critical energy density. Data from Wilkinson Microwave Anisotropy Probe (WMAP) as well as the Planck spacecraft give values for the three constituents of all the mass-energy in the universe - normal mass (baryonic matter and dark matter), relativistic particles (photons and neutrinos), and dark energy or the cosmological constant:^[10][11]

Ω_mass ≈ 0.315±0.018
Ω_relativistic ≈ 9.24×10⁻⁵
Ω_Λ ≈ 0.6817±0.0018
Ω_total= Ω_mass + Ω_relativistic + Ω_Λ= 1.00±0.02

The actual value for critical density value is measured as ρ_critical= 9.47×10⁻²⁷ kg m⁻³. From these values, within experimental error, the universe seems to be flat.

Another way to measure Ω is to do so geometrically by measuring an angle across the observable universe. We can do this by using the CMB and measuring the power spectrum and temperature anisotropy. For an intuition, one can imagine finding a gas cloud that is not in thermal equilibrium due to being so large that light speed cannot propagate the thermal information. Knowing this propagation speed, we then know the size of the gas cloud as well as the distance to the gas cloud, we then have two sides of a triangle and can then determine the angles. Using a method similar to this, the BOOMERanG experiment has determined that the sum of the angles to 180° within experimental error, corresponding to an Ω_total ≈ 1.00±0.12.^[12]

These and other astronomical measurements constrain the spatial curvature to be very close to zero, although they do not constrain its sign. This means that although the local geometries of spacetime are generated by the theory of relativity based on spacetime intervals, we can approximate 3-space by the familiar Euclidean geometry.

The Friedmann–Lemaître–Robertson–Walker (FLRW) model using Friedmann equations is commonly used to model the universe. The FLRW model provides a curvature of the universe based on the mathematics of fluid dynamics, that is, modeling the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. Another way of saying this is that if all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies). This assumption is justified by the observations that, while the universe is "weakly" inhomogeneous and anisotropic (see the large-scale structure of the cosmos), it is on average homogeneous and isotropic.

Global universe structure

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Also see: Human timeline and Life timeline

Global structure covers the geometry and the topology of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. The universe is often taken to be a geodesic manifold, free of topological defects; relaxing either of these complicates the analysis considerably. A global geometry is a local geometry plus a topology. It follows that a topology alone does not give a global geometry: for instance, Euclidean 3-space and hyperbolic 3-space have the same topology but different global geometries.

As stated in the introduction, investigations within the study of the global structure of the universe include:

• Whether the universe is infinite or finite in extent
• Whether the geometry of the global universe is flat, positively curved, or negatively curved
• Whether the topology is simply connected like a sphere or multiply connected, like a torus^[13]

Infinite or finite

One of the presently unanswered questions about the universe is whether it is infinite or finite in extent. For intuition, it can be understood that a finite universe has a finite volume that, for example, could be in theory filled up with a finite amount of material, while an infinite universe is unbounded and no numerical volume could possibly fill it. Mathematically, the question of whether the universe is infinite or finite is referred to as boundedness. An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the universe, in which case the universe has a well-defined "volume" or "scale."

With or without boundary

Assuming a finite universe, the universe can either have an edge or no edge. Many finite mathematical spaces, e.g., a disc, have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is very difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration.

However, there exist many finite spaces, such as the 3-sphere and 3-torus, which have no edges. Mathematically, these spaces are referred to as being compact without boundary. The term compact basically means that it is finite in extent ("bounded") and complete. The term "without boundary" means that the space has no edges. Moreover, so that calculus can be applied, the universe is typically assumed to be a differentiable manifold. A mathematical object that possesses all these properties, compact without boundary and differentiable, is termed a closed manifold. The 3-sphere and 3-torus are both closed manifolds.

Curvature

The curvature of the universe places constraints on the topology. If the spatial geometry is spherical, i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite.^[14] Many textbooks erroneously state that a flat universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe.^[14] For example, Euclidean space is flat, simply connected, and infinite, but the torus is flat, multiply connected, finite, and compact.

In general, local to global theorems in Riemannian geometry relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in Thurston geometries.

The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10⁻⁴. If the true value of the cosmological curvature parameter is larger than 10⁻³ we will be able to distinguish between these three models even now.^[15]

Results of the Planck mission released in 2015 show the cosmological curvature parameter, Ω_K, to be 0.000±0.005, consistent with a flat universe.^[16]

Universe with zero curvature

In a universe with zero curvature, the local geometry is flat. The most obvious global structure is that of Euclidean space, which is infinite in extent. Flat universes that are finite in extent include the torus and Klein bottle. Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. These are the Bieberbach manifolds. The most familiar is the aforementioned 3-torus universe.

In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The ultimate fate of the universe is the same as that of an open universe.

A flat universe can have zero total energy.

Universe with positive curvature

A positively curved universe is described by elliptic geometry, and can be thought of as a three-dimensional hypersphere, or some other spherical 3-manifold (such as the Poincaré dodecahedral space), all of which are quotients of the 3-sphere.

Poincaré dodecahedral space, a positively curved space, colloquially described as "soccerball-shaped", as it is the quotient of the 3-sphere by the binary icosahedral group, which is very close to icosahedral symmetry, the symmetry of a soccer ball. This was proposed by Jean-Pierre Luminet and colleagues in 2003^[7][17] and an optimal orientation on the sky for the model was estimated in 2008.^[8]

Universe with negative curvature

Universe in an expanding sphere. The galaxies farthest away are moving fastest and hence experience length contraction and so become smaller to an observer in the centre.

A hyperbolic universe, one of a negative spatial curvature, is described by hyperbolic geometry, and can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. There are a great variety of hyperbolic 3-manifolds, and their classification is not completely understood. Those of finite volume can be understood via the Mostow rigidity theorem. For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called "horn topologies", so called because of the shape of the pseudosphere, a canonical model of hyperbolic geometry. An example is the Picard horn, a negatively curved space, colloquially described as "funnel-shaped".^[9]

Curvature: open or closed

When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive. These meanings of open and closed are different from the mathematical meaning of open and closed used for sets in topological spaces and for the mathematical meaning of open and closed manifolds, which gives rise to ambiguity and confusion. In mathematics, there are definitions for a closed manifold (i.e., compact without boundary) and open manifold (i.e., one that is not compact and without boundary). A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the Friedmann–Lemaître–Robertson–Walker (FLRW) model the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.

Milne model ("spherical" expanding)

If one applies Minkowski space-based special relativity to expansion of the universe, without resorting to the concept of a curved spacetime, then one obtains the Milne model. Any spatial section of the universe of a constant age (the proper time elapsed from the Big Bang) will have a negative curvature; this is merely a pseudo-Euclidean geometric fact analogous to one that concentric spheres in the flat Euclidean space are nevertheless curved. Spatial geometry of this model is an unbounded hyperbolic space. The entire universe is contained within a light cone, namely the future cone of the Big Bang. For any given moment t> 0 of coordinate time (assuming the Big Bang has t = 0), the entire universe is bounded by a sphere of radius exactly c t. The apparent paradox of an infinite universe contained within a sphere is explained with length contraction: the galaxies farther away, which are travelling away from the observer the fastest, will appear thinner.
This model is essentially a degenerate FLRW for Ω = 0. It is incompatible with observations that definitely rule out such a large negative spatial curvature. However, as a background in which gravitational fields (or gravitons) can operate, due to diffeomorphism invariance, the space on the macroscopic scale, is equivalent to any other (open) solution of Einstein's field equations.

Quantum fluctuation

From Wikipedia, the free encyclopedia

In quantum physics, a quantum fluctuation (or quantum vacuum fluctuation or vacuum fluctuation) is the temporary change in the amount of energy in a point in space,^[1] as explained in Werner Heisenberg's uncertainty principle.

This allows the creation of particle-antiparticle pairs of virtual particles. The effects of these particles are measurable, for example, in the effective charge of the electron, different from its "naked" charge.
Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of expansive inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure. Vacuum energy may also be responsible for the current accelerating expansion of the universe (cosmological constant).

According to one formulation of the principle, energy and time can be related by the relation^[2]

${\displaystyle \Delta E\Delta t\geq {h \over 4\pi }}$

In the modern view, energy is always conserved, but because the particle number operator does not commute with a field's Hamiltonian or energy operator, the field's lowest-energy or ground state, often called the vacuum state, is not, as one might expect from that name, a state with no particles, but rather a quantum superposition of particle number eigenstates with 0, 1, 2...etc. particles.

Quantum fluctuations of a field

A quantum fluctuation is the temporary appearance of energetic particles out of empty space, as allowed by the uncertainty principle. The uncertainty principle states that for a pair of conjugate variables such as position/momentum or energy/time, it is impossible to have a precisely determined value of each member of the pair at the same time. For example, a particle pair can pop out of the vacuum during a very short time interval.

An extension is applicable to the "uncertainty in time" and "uncertainty in energy" (including the rest mass energy ${\displaystyle mc^{2}}$). When the mass is very large like a macroscopic object, the uncertainties and thus the quantum effect become very small, and classical physics is applicable.

In quantum field theory, fields undergo quantum fluctuations. A reasonably clear distinction can be made between quantum fluctuations and thermal fluctuations^[how?] of a quantum field (at least for a free field; for interacting fields, renormalization substantially complicates matters). For the quantized Klein–Gordon field in the vacuum state, we can calculate the probability density that we would observe a configuration ${\displaystyle {\displaystyle \varphi _{t}(x)}}$ at a time ${\displaystyle t}$ in terms of its Fourier transform ${\displaystyle {\displaystyle {\tilde {\varphi }}_{t}(k)}}$ to be

${\displaystyle \rho _{0}[\varphi _{t}]=\exp {\left[-{\frac {1}{\hbar }}\int {\frac {d^{3}k}{(2\pi )^{3}}}{\tilde {\varphi }}_{t}^{*}(k){\sqrt {|k|^{2}+m^{2}}}\;{\tilde {\varphi }}_{t}(k)\right]}.}$

In contrast, for the classical Klein–Gordon field at non-zero temperature, the Gibbs probability density that we would observe a configuration ${\displaystyle {\displaystyle \varphi _{t}(x)}}$ at a time ${\displaystyle t}$ is

${\displaystyle \rho _{E}[\varphi _{t}]=\exp {[-H[\varphi _{t}]/k_{\mathrm {B} }T]}=\exp {\left[-{\frac {1}{k_{\mathrm {B} }T}}\int {\frac {d^{3}k}{(2\pi )^{3}}}{\tilde {\varphi }}_{t}^{*}(k){\scriptstyle {\frac {1}{2}}}(|k|^{2}+m^{2})\;{\tilde {\varphi }}_{t}(k)\right]}.}$

The amplitude of quantum fluctuations is controlled by Planck's constant ${\displaystyle \hbar }$, just as the amplitude of thermal fluctuations is controlled by ${\displaystyle k_{\mathrm {B} }T}$, where ${\displaystyle k_{\mathrm {B} }}$ is Boltzmann's constant. Note that the following three points are closely related:

1. Planck's constant has units of action (joule-seconds) instead of units of energy (joules),
2. the quantum kernel is ${\displaystyle {\sqrt {|k|^{2}+m^{2}}}}$ instead of ${\displaystyle {\scriptstyle {\frac {1}{2}}}(|k|^{2}+m^{2})}$ (the quantum kernel is nonlocal from a classical heat kernel viewpoint, but it is local in the sense that it does not allow signals to be transmitted),^{[citation needed]}
3. the quantum vacuum state is Lorentz invariant (although not manifestly in the above), whereas the classical thermal state is not (the classical dynamics is Lorentz invariant, but the Gibbs probability density is not a Lorentz invariant initial condition).

We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory (measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible — in quantum mechanical terms they always commute). Quantum effects that are consequences only of quantum fluctuations, not of subtleties of measurement incompatibility, can alternatively be models of classical continuous random fields.

In the 1930s, Pascual Jordan knew that a star could equal zero energy because its matter energy was positive and its gravitational energy was negative and they cancelled each other out. And this led him to speculate what would prevent a quantum transition from creating a new star. And he had this idea because he was trying to figure out where matter might come from if we existed in an always-here universe.^[3]

In December, 1973, the British scientific journal Nature published an article by Edward P. Tryon titled "Is the Universe a Vacuum Fluctuation?" In this paper Tryon said our universe may have originated as a quantum fluctuation of the vacuum.^[3] Yet, the idea of our universe coming from a quantum fluctuation or quantum process was not taken seriously until inflationary theory came and was able to explain how our universe could inflate from a tiny particle.^[4]

Interpretations

The success of quantum fluctuation theories have given way to metaphysical interpretations on the nature of reality and their potential role in the origin and structure of the universe:

• The fluctuations are a manifestation of the innate uncertainty on the quantum level^[5]
• Fluctuations of the fields in each element of our universe's spacetime could be coherent throughout the universe by mesoscopic quantum entanglement.

A fundamental particle arising out of its quantum field is always inescapably subject to this reality and is thus describable by an associated wave function.

The wave function of a quantum particle represents the reality of the innate quantum fluctuations at the core of the universe and bestows the particle its counter intuitive quantum behavior.

In the double slit experiment each particle makes an unpredictable choice between alternative possibilities, consistent with an interference pattern with the inherent fluctuations of the underlying quantum field rendering the electron to do so.^[6]

Such an underlying immutable quantum field by which quantum fluctuations are correlated in a universal scale may explain the non-locality of quantum entanglement as a natural process^[7]

Galaxy formation and evolution

From Wikipedia, the free encyclopedia

The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have generated the variety of structures observed in nearby galaxies.

Galaxy formation is hypothesized to occur, from structure formation theories, as a result of tiny quantum fluctuations in the aftermath of the Big Bang. The simplest model for this that is in general agreement with observed phenomena is the Λ-Cold Dark Matter cosmology; that is to say that clustering and merging is how galaxies gain in mass, and can also determine their shape and structure.

Commonly observed properties of galaxies

Hubble tuning fork diagram of galaxy morphology

Because of the inability to conduct experiments in outer space, the only way to “test” theories and models of galaxy evolution is to compare them with observations. Explanations for how galaxies formed and evolved must be able to predict the observed properties and types of galaxies.
Edwin Hubble created the first galaxy classification scheme known as the Hubble tuning-fork diagram. It partitioned galaxies into ellipticals, normal spirals, barred spirals (such as the Milky Way), and irregulars. These galaxy types exhibit the following properties which can be explained by current galaxy evolution theories:

• Many of the properties of galaxies (including the galaxy color–magnitude diagram) indicate that there are fundamentally two types of galaxies. These groups divide into blue star-forming galaxies that are more like spiral types, and red non-star forming galaxies that are more like elliptical galaxies.
• Spiral galaxies are quite thin, dense, and rotate relatively fast, while the stars in elliptical galaxies have randomly-oriented orbits.
• The majority of mass in galaxies is made up of dark matter, a substance which is not directly observable, and might not interact through any means except gravity.
• The majority of giant galaxies contain a supermassive black hole in their centers, ranging in mass from millions to billions of times the mass of our Sun. The black hole mass is tied to the host galaxy bulge or spheroid mass.
• Metallicity has a positive correlation with the absolute magnitude (luminosity) of a galaxy.

There is a common misconception that Hubble believed incorrectly that the tuning fork diagram described an evolutionary sequence for galaxies, from elliptical galaxies through lenticulars to spiral galaxies. This is not the case; instead, the tuning fork diagram shows an evolution from simple to complex with no temporal connotations intended.^[1] Astronomers now believe that disk galaxies likely formed first, then evolved into elliptical galaxies through galaxy mergers.

Formation of disk galaxies

The earliest stage in the evolution of galaxies is the formation. When a galaxy forms, it has a disk shape and is called a spiral galaxy due to spiral-like "arm" structures located on the disk. There are different theories on how these disk-like distributions of stars develop from a cloud of matter: however, at present, none of them exactly predicts the results of observation.

Top-down theories

Olin Eggen, Donald Lynden-Bell, and Allan Sandage^[2] in 1962, proposed a theory that disk galaxies form through a monolithic collapse of a large gas cloud. The distribution of matter in the early universe was in clumps that consisted mostly of dark matter. These clumps interacted gravitationally, putting tidal torques on each other that acted to give them some angular momentum. As the baryonic matter cooled, it dissipated some energy and contracted toward the center. With angular momentum conserved, the matter near the center speeds up its rotation. Then, like a spinning ball of pizza dough, the matter forms into a tight disk. Once the disk cools, the gas is not gravitationally stable, so it cannot remain a singular homogeneous cloud. It breaks, and these smaller clouds of gas form stars. Since the dark matter does not dissipate as it only interacts gravitationally, it remains distributed outside the disk in what is known as the dark halo. Observations show that there are stars located outside the disk, which does not quite fit the "pizza dough" model. It was first proposed by Leonard Searle and Robert Zinn ^[3] that galaxies form by the coalescence of smaller progenitors. Known as a top-down formation scenario, this theory is quite simple yet no longer widely accepted.

Bottom-up theories

More recent theories include the clustering of dark matter halos in the bottom-up process. Instead of large gas clouds collapsing to form a galaxy in which the gas breaks up into smaller clouds, it is proposed that matter started out in these “smaller” clumps (mass on the order of globular clusters), and then many of these clumps merged to form galaxies,^[4] which then were drawn by gravitation to form galaxy clusters. This still results in disk-like distributions of baryonic matter with dark matter forming the halo for all the same reasons as in the top-down theory. Models using this sort of process predict more small galaxies than large ones, which matches observations.

Astronomers do not currently know what process stops the contraction. In fact, theories of disk galaxy formation are not successful at producing the rotation speed and size of disk galaxies. It has been suggested that the radiation from bright newly formed stars, or from an active galactic nuclei can slow the contraction of a forming disk. It has also been suggested that the dark matter halo can pull the galaxy, thus stopping disk contraction.^[5]

The Lambda-CDM model is a cosmological model that explains the formation of the universe after the Big Bang. It is a relatively simple model that predicts many properties observed in the universe, including the relative frequency of different galaxy types; however, it underestimates the number of thin disk galaxies in the universe.^[6] The reason is that these galaxy formation models predict a large number of mergers. If disk galaxies merge with another galaxy of comparable mass (at least 15 percent of its mass) the merger will likely destroy, or at a minimum greatly disrupt the disk, and the resulting galaxy is not expected to be a disk galaxy (see next section). While this remains an unsolved problem for astronomers, it does not necessarily mean that the Lambda-CDM model is completely wrong, but rather that it requires further refinement to accurately reproduce the population of galaxies in the universe.

Galaxy mergers and the formation of elliptical galaxies

Artist image of a firestorm of star birth deep inside core of young, growing elliptical galaxy.

NGC 4676 (Mice Galaxies) is an example of a present merger.

Antennae Galaxies are a pair of colliding galaxies - the bright, blue knots are young stars that have recently ignited as a result of the merger.

ESO 325-G004, a typical elliptical galaxy.

Elliptical galaxies (such as IC 1101) are among some of the largest known thus far. Their stars are on orbits that are randomly oriented within the galaxy (i.e. they are not rotating like disk galaxies). A distinguishing feature of elliptical galaxies is that the velocity of the stars does not necessarily contribute to flattening of the galaxy, such as in spiral galaxies.^[7] Elliptical galaxies have central supermassive black holes, and the masses of these black holes correlate with the galaxy’s mass.
Elliptical galaxies have two main stages of evolution. The first is due to the supermassive black hole growing by accreting cooling gas. The second stage is marked by the black hole stabilizing by suppressing gas cooling, thus leaving the elliptical galaxy in a stable state.^[8] The mass of the black hole is also correlated to a property called sigma which is the dispersion of the velocities of stars in their orbits. This relationship, known as the M-sigma relation, was discovered in 2000.^[9] Elliptical galaxies mostly lack disks, although some bulges of disk galaxies resemble elliptical galaxies. Elliptical galaxies are more likely found in crowded regions of the universe (such as galaxy clusters).

Astronomers now see elliptical galaxies as some of the most evolved systems in the universe. It is widely accepted that the main driving force for the evolution of elliptical galaxies is mergers of smaller galaxies. Many galaxies in the universe are gravitationally bound to other galaxies, which means that they will never escape their mutual pull. If the galaxies are of similar size, the resultant galaxy will appear similar to neither of the progenitors,^[10] but will instead be elliptical. There are many types of galaxy mergers, which do not necessarily result in elliptical galaxies, but result in a structural change. For example, a minor merger event is thought to be occurring between the Milky Way and the Magellanic Clouds.

Mergers between such large galaxies are regarded as violent, but because of the vast distances between stars, there are essentially no stellar collisions. However, the frictional interaction of the gas between the two galaxies can cause gravitational shock waves, which are capable of forming new stars in the new elliptical galaxy.^[11] By sequencing several images of different galactic collisions, one can observe the timeline of two spiral galaxies merging into a single elliptical galaxy.^[12]

In the Local Group, the Milky Way and the Andromeda Galaxy are gravitationally bound, and currently approaching each other at high speed. Simulations show that the Milky Way and Andromeda are on a collision course, and are expected to collide in less than five billion years. During this collision, it is expected that the Sun and the rest of the Solar System will be ejected from its current path around the Milky Way. The remnant could be a giant elliptical galaxy.^[13]

Galaxy quenching

Star formation in what are now "dead" galaxies sputtered out billions of years ago.^[14]

One observation (see above) that must be explained by a successful theory of galaxy evolution is the existence of two different populations of galaxies on the galaxy color-magnitude diagram. Most galaxies tend to fall into two separate locations on this diagram: a "red sequence" and a "blue cloud". Red sequence galaxies are generally non-star-forming elliptical galaxies with little gas and dust, while blue cloud galaxies tend to be dusty star-forming spiral galaxies.^[15][16]

As described in previous sections, galaxies tend to evolve from spiral to elliptical structure via mergers. However, the current rate of galaxy mergers does not explain how all galaxies move from the "blue cloud" to the "red sequence". It also does not explain how star formation ceases in galaxies. Theories of galaxy evolution must therefore be able to explain how star formation turns off in galaxies. This phenomenon is called galaxy "quenching".^[17]

Stars form out of cold gas (see also the Kennicutt-Schmidt law), so a galaxy is quenched when it has no more cold gas. However, it is thought that quenching occurs relatively quickly (within 1 billion years), which is much shorter than the time it would take for a galaxy to simply use up its reservoir of cold gas.^[18][19] Galaxy evolution models explain this by hypothesizing other physical mechanisms that remove or shut off the supply of cold gas in a galaxy. These mechanisms can be broadly classified into two categories: (1) preventive feedback mechanisms that stop cold gas from entering a galaxy or stop it from producing stars, and (2) ejective feedback mechanisms that remove gas so that it cannot form stars.^[20]

One theorized preventive mechanism called “strangulation” keeps cold gas from entering the galaxy. Strangulation is likely the main mechanism for quenching star formation in nearby low-mass galaxies.^[21] The exact physical explanation for strangulation is still unknown, but it may have to do with a galaxy’s interactions with other galaxies. As a galaxy falls into a galaxy cluster, gravitational interactions with other galaxies can strangle it by preventing it from accreting more gas.^[22] For galaxies with massive dark matter halos, another preventive mechanism called “virial shock heating” may also prevent gas from becoming cool enough to form stars.^[19]

Ejective processes, which expel cold gas from galaxies, may explain how more massive galaxies are quenched.^[23] One ejective mechanism is caused by supermassive black holes found in the centers of galaxies. Simulations have shown that gas accreting onto supermassive black holes in galactic centers produces high-energy jets; the released energy can expel enough cold gas to quench star formation.^[24]

Our own Milky Way and the nearby Andromeda Galaxy currently appear to be undergoing the quenching transition from star-forming blue galaxies to passive red galaxies.^[25]

Gallery

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  NGC 3610 shows some structure in the form of a bright disc implies that it formed only a short time ago.^[26]
  
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  NGC 891, a very thin disk galaxy
  
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  An image of Messier 101, a prototypical spiral galaxy seen face-on
  
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  A spiral galaxy, ESO 510-G13, was warped as a result of colliding with another galaxy. After the other galaxy is completely absorbed, the distortion will disappear. The process typically takes millions if not billions of years.