HOME

TheInfoList



OR:

In modern
cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...
theory, diffusion damping, also called photon diffusion damping, is a physical process which reduced density inequalities ( anisotropies) in the early
universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
, making the universe itself and the
cosmic microwave background radiation The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dar ...
(CMB) more uniform. Around 300,000 years after the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
, 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 The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The ''Doppler effect'' is named after the physicist Christian Doppler, who described ...
, and the effects of gravity on electromagnetic radiation, for the eventual formation of
galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar Sys ...
and
galaxy clusters A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. Clusters consist of galax ...
, these being the dominant large scale structures which are observed in the universe. It is a damping ''by'' diffusion, not ''of'' diffusion.Hu, Sugiyama &
Silk Silk is a natural fiber, natural protein fiber, some forms of which can be weaving, woven into textiles. The protein fiber of silk is composed mainly of fibroin and is most commonly produced by certain insect larvae to form cocoon (silk), c ...
(1996-04-28), p. 2
The strength of diffusion damping is calculated by a mathematical expression for the ''
damping factor In an audio system, the damping factor is defined as the ratio of the rated impedance of the loudspeaker (usually assumed to be ) to the Output impedance, source impedance of the power amplifier. It was originally proposed in 1941. Only the magni ...
'', which figures into the
Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G ...
, an equation which describes the amplitude of perturbations in the CMB. The strength of the diffusion damping is chiefly governed by the distance photons travel before being scattered (diffusion length). The primary effects on the diffusion length are from the properties of the plasma in question: different sorts of plasma may experience different sorts of diffusion damping. The evolution of a plasma may also affect the damping process. The scale on which diffusion damping works is called the Silk scale and its value corresponds to the size of galaxies of the present day. The mass contained within the Silk scale is called the Silk mass and it corresponds to the mass of the galaxies.


Introduction

Diffusion damping took place about 13.8 billion years ago, during the stage of the early universe called '' recombination'' or matter-radiation ''decoupling''. This period occurred about 320,000 years after the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
. This is equivalent to 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 increase in frequency and e ...
of around '' z'' = 1090. Recombination was the stage during which simple
atoms Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other ...
, e.g.
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
and
helium Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...
, began to form in the cooling, but still very hot, soup of
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
s,
electrons The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
and
photons 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 particles that ...
that composed the universe. Prior to the recombination epoch, this ''soup'', a plasma, was largely opaque to the
electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
of photons. This meant that the permanently excited photons were scattered by the protons and electrons too often to travel very far in straight lines.Hu (1995-08-26), p. 6 During the recombination epoch, the universe cooled rapidly as free electrons were captured by atomic nuclei; atoms formed from their constituent parts and the universe became transparent: the amount of photon scattering decreased dramatically. Scattering less, photons could diffuse (travel) much greater distances.Liddle & Lyth (2000-04-13), p. 63, 120 There was no significant diffusion damping for electrons, which could not diffuse nearly as far as photons could in similar circumstances. Thus all damping by electron diffusion is negligible when compared to photon diffusion damping.Padmanabhan (1993-06-25), p. 171–2 Acoustic perturbations of initial density fluctuations in the universe made some regions of space hotter and denser than others.Harrison (1970-05-15) These differences in
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
and
density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
are called '' anisotropies''. Photons diffused from the hot, overdense regions of plasma to the cold, underdense ones: they dragged along the protons and electrons: the photons pushed electrons along, and these, in turn, pulled on protons by the
Coulomb force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the ''electrostatic ...
. This caused the temperatures and densities of the hot and cold regions to be averaged and the universe became less
anisotropic Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ver ...
(characteristically various) and more ''isotropic'' (characteristically uniform). This reduction in anisotropy is the ''damping'' of diffusion damping. Diffusion damping thus damps temperature and density anisotropies in the early universe. With baryonic matter (protons and electrons) escaping the dense areas along with the photons; the temperature and density inequalities were ''
adiabatically Adiabatic (from ''Gr.'' ἀ ''negative'' + διάβασις ''passage; transference'') refers to any process that occurs without heat transfer. This concept is used in many areas of physics and engineering. Notable examples are listed below. A ...
'' damped. That is to say the ratios of photons to baryons remained constant during the damping process.Madsen (1996-05-15), p. 99–100Longair (2008-01-08), p. 355Jetzer & Pretzl (2002-07-31), p. 6Rich (2001-06-15), p. 256 Photon diffusion was first described in
Joseph Silk Joseph Ivor Silk (born 3 December 1942) is a British-American astrophysicist. He was the Savilian Chair of Astronomy at the University of Oxford from 1999 to September 2011. He is an Emeritus Fellow of New College, Oxford and a Fellow of th ...
's 1968 paper entitled "Cosmic Black-Body Radiation and Galaxy Formation",Silk (1968-02-01) which was published in ''
The Astrophysical Journal ''The Astrophysical Journal'' (''ApJ'') is a peer-reviewed scientific journal of astrophysics and astronomy, established in 1895 by American astronomers George Ellery Hale and James Edward Keeler. The journal discontinued its print edition and ...
''. As such, diffusion damping is sometimes also called Silk damping, though this term may apply only to one possible damping scenario.Partridge (1995-09-29), p. 302Bonometto, Gorini & Moschella (2001-12-15), p. 55 Silk damping was thus named after its discoverer.Madsen (1996-05-15), p. 99–101Hu (1994-06-28), p. 15


Magnitude

The magnitude of diffusion damping is calculated as a ''damping factor'' or ''suppression factor'', represented by the symbol \mathcal , which figures into the
Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G ...
, an equation which describes the amplitude of perturbations in the CMB. The strength of the diffusion damping is chiefly governed by the distance photons travel before being scattered (diffusion length). What affect the diffusion length are primarily the properties of the plasma in question: different sorts of plasma may experience different sorts of diffusion damping. The evolution of a plasma may also affect the damping process. : \mathcal(\mathit) = \int_^ \left(\dote^\right)e^\; d\eta. Where: * \eta is the conformal time. * \dote^ is the visibility function, giving the probability that a CMB photon observed today last scattered at a conformal time \eta . The quantity \tau is the optical depth to
Thomson scattering Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is the low-energy limit of Compton scattering: the particle's kinetic energy and photon frequency ...
in the plasma, which is roughly the integrated number of scatterings undergone by a given photon. * \mathit is the
wave number In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of r ...
of the wave being suppressed.Longair (2008-01-08), p. 450 * e^ is the exponential damping envelope due to diffusion. * (\eta) = /\lambda_\mathit The damping factor \mathcal , when factored into the
Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G ...
for the cosmic microwave background radiation (CMB), reduces the amplitude of perturbations: : Theta_0+\Psi\eta_\ast) = hat_0+\Psi\eta_\ast)\mathcal(\mathit). Where:Jungman, Kamionkowski, Kosowsky & Spergel (1995-12-20), p. 2–4Hu (1995-08-26), p. 146 *\mathit_\ast is the conformal time at decoupling. * \Theta_0 is the "monopole erturbationof the photon distribution function" * \Psi is a "gravitational-potential erturbationin the Newtonian gauge". The
Newtonian gauge In general relativity, the Newtonian gauge is a perturbed form of the FLRW metric, Friedmann–Lemaître–Robertson–Walker line element. The gauge theory, gauge freedom of general relativity is used to eliminate two scalar degrees of freedom of t ...
is a quantity with importance in the
General Theory of Relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physi ...
. * Theta_0+\Psi\eta) is the effective temperature. Mathematical calculations of the damping factor depend on \mathit_\mathit , or the ''effective diffusion scale'', which in turn depends on a crucial value, ''the diffusion length'', \lambda_\mathit .Hu, Sugiyama & Silk (1996-04-28), p. 5 The diffusion length relates how far photons travel during diffusion, and comprises a finite number of short steps in random directions. The average of these steps is the ''Compton
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 a ...
'', and is denoted by \lambda_\mathit. As the direction of these steps are randomly taken, \lambda_\mathit is approximately equal to \sqrt \lambda_\mathit , where \mathit is the number of steps the photon takes before the conformal time at decoupling (\mathit_\ast).Hu (1995-08-26), p. 12–13 The diffusion length increases at recombination because the mean free path does, with less photon scattering occurring; this increases the amount of diffusion and damping. The mean free path increases because the ''electron ionisation fraction'', \mathit_\mathit , decreases as ionised
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
and
helium Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...
bind with the free, charged electrons. As this occurs, the mean free path increases proportionally: \lambda_\mathit \varpropto ^ . That is, the mean free path of the photons is
inversely proportional In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called ''coefficient of proportionality'' (or ''proportionality ...
to the electron ionisation fraction and the baryon number density (\mathit_\mathit). That means that the more baryons there were, and the more they were ionised, the shorter the average photon could travel before encountering one and being scattered. Small changes to these values before or during recombination can augment the damping effect considerably. This dependence on the baryon density by photon diffusion allows scientists to use analysis of the latter to investigate the former, in addition to the history of ionisation. The effect of diffusion damping is greatly augmented by the finite width of the
surface of last scattering The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely da ...
(SLS).(1995-08-26), p. 137 The finite width of the SLS means the CMB photons we see were not all emitted at the same time, and the fluctuations we see are not all in phase.Durrer (2001-09-17), p. 5 It also means that during recombination, the diffusion length changed dramatically, as the ionisation fraction shifted.Hu (1995-08-26), pp. 156–7


Model dependence

In general, diffusion damping produces its effects independent of the cosmological model being studied, thereby masking the effects of other, model-''dependent'' phenomena. This means that without an accurate model of diffusion damping, scientists cannot judge the relative merits of cosmological models, whose theoretical predictions cannot be compared with observational data, this data being obscured by damping effects. For example, the peaks in the power spectrum due to acoustic oscillations are decreased in amplitude by diffusion damping. This deamplification of the power spectrum hides features of the curve, features that would otherwise be more visible.Hu (1995-08-26), p. 136–8Hu & White (1997-04-20), p. 568–9 Though general diffusion damping can damp perturbations in collisionless dark matter simply due to photon dispersion, the term ''Silk damping'' applies only to damping of adiabatic models of baryonic matter, which is coupled to the diffusing photons, not
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
, and diffuses with them. Silk damping is not as significant in models of cosmological development which posit early isocurvature fluctuations (i.e. fluctuations which do not require a constant ratio of baryons and photons). In this case, increases in baryon density do not require corresponding increases in photon density, and the lower the photon density, the less diffusion there would be: the less diffusion, the less damping. Photon diffusion is not dependent on the causes of the initial fluctuations in the density of the universe.


Effects


Speed

Damping occurs at two different scales, with the process working more quickly over short ranges than over longer distances. Here, a short length is one that is lower than the mean free path of the photons. A long distance is one that is greater than the mean free path, if still less than the diffusion length. On the smaller scale, perturbations are damped almost instantaneously. On the larger scale, anisotropies are decreased more slowly, with significant degradation happening within one unit of Hubble time.


The Silk scale and the Silk mass

Diffusion damping exponentially decreases anisotropies in the CMB on a scale (the Silk scale) much smaller than a degree, or smaller than approximately 3 megaparsecs.Bonometto, Gorini & Moschella (2001-12-15), p. 227–8 This angular scale corresponds to a multipole moment \mathit \gtrsim 800.Papantonopoulos (2005-03-24), p. 63 The mass contained within the Silk scale is the ''silk mass''. Numerical evaluations of the Silk mass yield results on the order of 10^ solar masses at recombinationJedamzik, Katalinić & Olinto (1996-06-13), p. 1–2 and on the order of the mass of a present-day
galaxy A galaxy is a Physical system, system of stars, stellar remnants, interstellar medium, interstellar gas, cosmic dust, dust, and dark matter bound together by gravity. The word is derived from the Ancient Greek, Greek ' (), literally 'milky', ...
or
galaxy cluster A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. Clusters consist of galax ...
in the current era. : \mathit_\mathit \approx \frac. Scientists say diffusion damping affects ''small'' angles and corresponding anisotropies. Other effects operate on a scale called ''intermediate'' 10 \lesssim \mathit \lesssim 100 or ''large'' \mathit \lessapprox 10 . Searches for anisotropies on a small scale are not as difficult as those on larger scales, partly because they may employ ground-based telescopes and their results can be more easily predicted by current theoretical models.Kaiser & Silk (1986-12-11), p. 533


Galaxy formation

Scientists study photon diffusion damping (and CMB anisotropies in general) because of the insight the subject provides into the question, "How did the universe come to be?". Specifically, primordial anisotropies in the temperature and density of the universe are supposed to be the causes of later large-scale structure formation. Thus it was the amplification of small perturbations in the pre-recombination universe that grew into the galaxies and galaxy clusters of the present era. Diffusion damping made the universe isotropic within distances on the order of the Silk Scale. That this scale corresponds to the size of observed galaxies (when the passage of time is taken into account) implies that diffusion damping is responsible for limiting the size of these galaxies. The theory is that clumps of matter in the early universe became the galaxies that we see today, and the size of these galaxies is related to the temperature and density of the clumps.Hu & Sugiyama (1994-07-28), p. 2Sunyaev & Zel'dovich (Sept. 1980), p. 1 Diffusion may also have had a significant effect on the evolution of primordial cosmic magnetic fields, fields which may have been amplified over time to become galactic magnetic fields. However, these cosmic magnetic fields may have been damped by radiative diffusion: just as acoustic oscillations in the plasma were damped by the diffusion of photons, so were
magnetosonic wave In physics, magnetosonic waves, also known as magnetoacoustic waves, are low-frequency Compression (physics), compressive waves driven by mutual interaction between an electrically conducting fluid and a magnetic field. They are associated with Co ...
s (waves of ions travelling through a magnetised plasma). This process began before the era of
neutrino decoupling In Big Bang cosmology, neutrino decoupling was the epoch at which neutrinos ceased interacting with other types of matter, and thereby ceased influencing the dynamics of the universe at early times. Prior to decoupling, neutrinos were in thermal equ ...
and ended at the time of recombination.Brandenburg, Enqvist & Olesen (January 1997), p. 2


See also

* Chronology of the universe *
Joseph Silk Joseph Ivor Silk (born 3 December 1942) is a British-American astrophysicist. He was the Savilian Chair of Astronomy at the University of Oxford from 1999 to September 2011. He is an Emeritus Fellow of New College, Oxford and a Fellow of th ...
*
Photon diffusion Photon diffusion is a situation where photons travel through a material without being absorbed, but rather undergoing repeated scattering events which change the direction of their path. The path of any given photon is then effectively a random wal ...
* Timeline of cosmological theories


Notes


References


Bibliography

* * * * * * * * * * * * * * * * * * * * * * *


External links


Diffusion damping explained in a "1997 Travelguide to CMB physics" by Wayne Hu
{{good article Physical cosmology