HOME

TheInfoList



OR:

In
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
, recombination refers to the
epoch In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided ...
during which charged
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
s and
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s first became bound to form
electrically neutral Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons resp ...
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s. Recombination occurred about 370,000 yearsRecombination time frames: *
Edward L. Wright Edward L. (Ned) Wright (born August 25, 1947 in Washington, D.C.) is an American astrophysicist and cosmologist, well known for his achievements in the COBE, WISE, and WMAP projects and as a strong Big Bang proponent in web tutorials on cosmolog ...
'
Javascript Cosmology Calculator
(last modified 23 July 2018). With a default H_0 =  (based on ), the calculated age of the universe with a redshift of ''z'' =  is in agreement with Olive and Peacock (about 370,000 years). * : "Going forward in time now, the temperature declined, and at ''T''∼3000 K, few of the photons in the radiation field, even in its high-energy tail, had the energy required to ionize a hydrogen atom. Most of the electrons and protons then recombined. Once this happened, at a time ''t''rec = 380,000 yr after the Big Bang, the major source of opacity disappeared, and the Universe became transparent to radiation of most frequencies." * : "The million dollar question is now, 'when did recombination happen?' In other words, when did electrons and protons combine to form neutral hydrogen (...) e epoch of recombination ''t''rec for a matter dominated universe is then...≈400,000 yr ('Epoch of Recombination')."
after the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
(at a
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
of ''z'' = ). The word "recombination" is misleading, since the Big Bang theory doesn't posit that protons and electrons had been combined before, but the name exists for historical reasons since it was named before the Big Bang hypothesis became the primary theory of the creation of the universe. Immediately after the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
, the universe was a hot, dense plasma of
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
s,
lepton In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
s, and
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly ...
s: the quark epoch. At 10−6 seconds, the Universe had expanded and cooled sufficiently to allow for the formation of
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s: the hadron epoch. This plasma was effectively opaque to electromagnetic radiation due to Thomson scattering by free electrons, as the
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as ...
each photon could travel before encountering an electron was very short. This is the current state of the interior of the Sun. As the universe expanded, it also cooled. Eventually, the universe cooled to the point that the formation of neutral hydrogen was energetically favored, and the fraction of free electrons and protons as compared to neutral hydrogen decreased to a few parts in 10,000. Recombination involves electrons binding to protons (hydrogen nuclei) to form neutral
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s. Because direct recombinations to the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
(lowest energy) of hydrogen are very inefficient, these hydrogen atoms generally form with the electrons in a high energy state, and the electrons quickly transition to their low energy state by emitting
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
s. Two main pathways exist: from the ''2p'' state by emitting a Lyman-a photon - these photons will almost always be reabsorbed by another hydrogen atom in its ground state - or from the ''2s'' state by emitting two photons, which is very slow. This production of photons is known as decoupling, which leads to recombination sometimes being called photon decoupling, but recombination and photon decoupling are distinct events. Once photons decoupled from matter, they traveled freely through the universe without interacting with matter and constitute what is observed today as cosmic microwave background radiation (in that sense, the cosmic background radiation is
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...
nd some red
black-body radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spe ...
emitted when the universe was at a temperature of some 3000 K,
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
ed by a factor of from the visible spectrum to the
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...
spectrum).


The recombination history of hydrogen

The cosmic ionization history is generally described in terms of the free electron fraction ''x''e as a function of
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
. It is the ratio of the abundance of free electrons to the total abundance of hydrogen (both neutral and ionized). Denoting by ''n''e the number density of free electrons, ''n''H that of atomic hydrogen and ''n''p that of ionized hydrogen (i.e. protons), ''x''e is defined as : x_\text = \frac. Since hydrogen only recombines once helium is fully neutral, charge neutrality implies ''n''e = ''n''p, i.e. ''x''e is also the fraction of ionized hydrogen.


Rough estimate from equilibrium theory

It is possible to find a rough estimate of the redshift of the recombination epoch assuming the recombination reaction p + e^ \longleftrightarrow H + \gamma is fast enough that it proceeds near thermal equilibrium. The relative abundance of free electrons, protons and neutral hydrogen is then given by the
Saha equation In physics, the Saha ionization equation is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure. The equation is a result of combining ideas of quantum mechanics and statistical mechanics ...
: : \frac = \left(\frac\right)^\frac \exp\left(-\frac\right), where ''m''e is the mass of the electron, ''k''B is Boltzmann's constant, ''T'' is the temperature, ''ħ'' is the reduced Planck's constant, and ''E''I = 13.6 eV is the
ionization energy Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule ...
of hydrogen. Charge neutrality requires ''n''e = ''n''p, and the Saha equation can be rewritten in terms of the free electron fraction ''x''e: : \frac = (n_\text + n_\text)^ \left(\frac\right)^\frac \exp\left(-\frac\right). All quantities in the right-hand side are known functions of z, the
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
: the temperature is given by , and the total density of hydrogen (neutral and ionized) is given by ''n''p + ''n''H = 1.6 (1+z)3 m−3. Solving this equation for a 50 percent ionization fraction yields a recombination temperature of roughly , corresponding to redshift ''z'' = .


The effective three-level atom

In 1968, physicists Jim Peebles in the US and Yakov Borisovich Zel'dovich and collaborators in the USSR independently computed the non-equilibrium recombination history of hydrogen. The basic elements of the model are the following. * Direct recombinations to the ground state of hydrogen are very inefficient: each such event leads to a photon with energy greater than 13.6 eV, which almost immediately re-ionizes a neighboring hydrogen atom. * Electrons therefore only efficiently recombine to the excited states of hydrogen, from which they cascade very quickly down to the first excited state, with
principal quantum number In quantum mechanics, the principal quantum number (symbolized ''n'') is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. A ...
''n'' = 2. * From the first excited state, electrons can reach the ground state ''n'' =1 through two pathways: ** Decay from the ''2p'' state by emitting a Lyman-α photon. This photon will almost always be reabsorbed by another hydrogen atom in its ground state. However, cosmological redshifting systematically decreases the photon frequency, and there is a small chance that it escapes reabsorption if it gets redshifted far enough from the Lyman-α line resonant frequency before encountering another hydrogen atom. ** Decay from the ''2s'' state by emitting two photons. This two-photon decay process is very slow, with a rate of 8.22 s−1. It is however competitive with the slow rate of Lyman-α escape in producing ground-state hydrogen. * Atoms in the first excited state may also be re-ionized by the ambient
CMB In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space ...
photons before they reach the ground state. When this is the case, it is as if the recombination to the excited state did not happen in the first place. To account for this possibility, Peebles defines the factor ''C'' as the probability that an atom in the first excited state reaches the ground state through either of the two pathways described above before being photoionized. This model is usually described as an "effective three-level atom" as it requires keeping track of hydrogen under three forms: in its ground state, in its first excited state (assuming all the higher excited states are in Boltzmann equilibrium with it), and in its ionized state. Accounting for these processes, the recombination history is then described by the
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
\frac = - C\left( \alpha_\text(T) n_\text x_e - 4 (1-x_\text) \beta_\text(T)e^ \right), where is the "case B" recombination coefficient to the excited states of hydrogen, is the corresponding photoionization rate and ''E''21 = 10.2 eV is the energy of the first excited state. Note that the second term in the right-hand side of the above equation can be obtained by a detailed balance argument. The equilibrium result given in the previous section would be recovered by setting the left-hand side to zero, i.e. assuming that the net rates of recombination and photoionization are large in comparison to the
Hubble expansion Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
rate, which sets the overall evolution timescale for the temperature and density. However, is comparable to the Hubble expansion rate, and even gets significantly lower at low redshifts, leading to an evolution of the free electron fraction much slower than what one would obtain from the Saha equilibrium calculation. With modern values of cosmological parameters, one finds that the universe is 90% neutral at ''z'' ≈ 1070.


Modern developments

The simple effective three-level atom model described above accounts for the most important physical processes. However it does rely on approximations which lead to errors on the predicted recombination history at the level of 10% or so. Due to the importance of recombination for the precise prediction of
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
anisotropies, several research groups have revisited the details of this picture over the last two decades. The refinements to the theory can be divided into two categories: * Accounting for the non-equilibrium populations of the highly excited states of hydrogen. This effectively amounts to modifying the recombination coefficient ''α''B. * Accurately computing the rate of Lyman-α escape and the effect of these photons on the ''2s-1s'' transition. This requires solving a time-dependent
radiative transfer Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative trans ...
equation. In addition, one needs to account for higher-order Lyman transitions. These refinements effectively amount to a modification of Peebles' ''C'' factor. Modern recombination theory is believed to be accurate at the level of 0.1%, and is implemented in publicly available fast recombination codes.


Primordial helium recombination

Helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
nuclei are produced during Big Bang nucleosynthesis, and make up about 24% of the total mass of
baryonic matter In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classifie ...
. The
ionization energy Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule ...
of helium is larger than that of hydrogen and it therefore recombines earlier. Because neutral helium carries two electrons, its recombination proceeds in two steps. The first recombination, \mathrm^ + \mathrm^ \longrightarrow \mathrm^+ + \gamma proceeds near Saha equilibrium and takes place around redshift ''z''≈ 6000. The second recombination, \mathrm^ + \mathrm^ \longrightarrow \mathrm + \gamma, is slower than what would be predicted from Saha equilibrium and takes place around redshift ''z''≈ 2000. The details of helium recombination are less critical than those of hydrogen recombination for the prediction of
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
anisotropies, since the universe is still very optically thick after helium has recombined and before hydrogen has started its recombination.


Primordial light barrier

Prior to recombination, photons were not able to freely travel through the universe, as they constantly
scattered Scattered may refer to: Music * ''Scattered'' (album), a 2010 album by The Handsome Family * "Scattered" (The Kinks song), 1993 * "Scattered", a song by Ace Young * "Scattered", a song by Lauren Jauregui * "Scattered", a song by Green Day from ' ...
off the free electrons and protons. This scattering causes a loss of information, and "there is therefore a photon barrier at a redshift" near that of recombination that prevents us from using photons directly to learn about the universe at larger redshifts. Once recombination had occurred, however, the mean free path of photons greatly increased due to the lower number of free electrons. Shortly after recombination, the photon mean free path became larger than the Hubble length, and photons traveled freely without interacting with matter. For this reason, recombination is closely associated with the last scattering surface, which is the name for the last time at which the photons in the cosmic microwave background interacted with matter. However, these two events are distinct, and in a universe with different values for the baryon-to-photon ratio and matter density, recombination and photon decoupling need not have occurred at the same epoch.


See also

* Chronology of the universe * Age of the universe *
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...


Notes


References


Bibliography

* * * * * * * * {{Portal bar, Physics, Astronomy, Stars, Spaceflight, Outer space, Solar System, Science Physical cosmology