Phase shift induced by free-streaming neutrinos and other light relics in the spectrum of baryon acoustic oscillations. Credit: Daniel Baumann, Florian Beutler, Raphael Flauger, Daniel Green, Anže Slosar, Mariana Vargas-Magaña, Benjamin Wallisch & Christophe Yèche.{{fairuse}}

"A pattern caused by sound waves in the early universe — known as baryon acoustic oscillations — should be distorted by the [early] neutrinos. Those sound waves spread outward through the universe like circular ripples on a pond, compressing matter into denser pockets. Eventually, that process resulted in galaxies having a tendency to cluster in rings across the sky [...]."[1]

"Using data from the Baryon Oscillation Spectroscopic Survey, or BOSS, [to study] the circular patterns of galaxies [produced] evidence that the [early] neutrinos were, in fact, pulling matter around from the inner side of the ring band toward the outer side."[1]

"A complementary and more robust probe [of the cosmic neutrino background] is provided by a distinct shift in the temporal phase of sound waves in the primordial plasma that is produced by fluctuations in the neutrino density."[2]

"The effect of neutrinos on perturbations in the primordial plasma has been shown to be a more robust probe of the CνB4. Neutrinos travel near the speed of light in the early Universe, significantly faster than sound waves in the hot plasma of photons and baryons, and can therefore propagate information ahead of the sound horizon of the plasma. The gravitational influence of this supersonic propagation induces a shift in the phase of the acoustic oscillations that cannot be mimicked by other properties of the plasma4,5. This phase shift has recently been detected in the CMB5,6, adding to the robustness of the cosmological evidence for the CνB."[2]

"After recombination, photons decoupled from baryons and the sound waves lost their pressure support. The sudden halt to the propagation of these density waves leaves an overdensity of baryons at the scale of the acoustic horizon at recombination. Subsequent gravitational evolution transfers this overdensity to the matter distribution. The power spectrum of galaxies inherits this feature in the form of baryon acoustic oscillations (BAOs). It was recently pointed out that the BAO spectrum should not only exhibit the same phase shift from the supersonic propagation of neutrinos, but that this shift should also be robust to nonlinear gravitational evolution in the late Universe7."[2]

"A key property of neutrinos is that they do not behave as a fluid, but as a collection of ultra-relativistic free-streaming particles. As a consequence, neutrinos travel at the speed of light c while the sound waves in a relativistic fluid, like the photon–baryon fluid, travel at cs ≈ c/√3. The supersonic propagation speed of neutrino perturbations creates a characteristic phase shift [see image on the right (a)] in the sound waves of the primordial plasma. A useful way to understand the effect is to consider the evolution of a single initial overdensity11,12. (For adiabatic fluctuations, the primordial density field is a superposition of such point-like overdensities.) The overdensities of photons, baryons and neutrinos will spread out as spherical shells, while the dark matter perturbation does not move much and will be left behind at the centre. Because the neutrinos travel faster than all other perturbations, they induce metric perturbations ahead of the sound horizon rs of the acoustic waves of the photon–baryon fluid."[2]

Image on the right part (a) shows the template "of the phase shift f(k) (blue) [...[, with the fitting function [...] shown as the red curve. The template was obtained numerically in ref.8 by sampling the phase shift in 100 different cosmologies with varying free-streaming radiation density. The blue bands indicate the 1σ and 2σ contours in these measurements."[2]

In the image on the right part (b), "Linear BAO spectrum O(k) [is] a function of the amplitude of the phase shift β."[2]

## Acoustics

This image is an acoustic profile of castanets. Credit: Acapulco007.

"Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound."[3]

"Indeed, among the dominant group of signals, ie, whistles (W), we did not detect any signals of this type."[4]

"This ridge can be used to trace out the dominant group velocity packet as a function of frequency for this site."[5]

"The number of modes having a reverberation time in a specified time interval is expressed as a function of the total allowed degrees of freedom and it is shown that even when the number of degrees of freedom of the model is large there is, in general, no one dominant group."[6]

"Acoustical measurements are being increasingly used in exploring the properties of matter; the interaction between sound fields and electromagnetic waves is an important part of plasma physics; and magneto-hydrodynamic wave motion is a phenomenon of growing importance in the sciences of meteorology and of astrophysics."[7]

## Minerals

The photomicrographs show of a sand grain held in an amorphous matrix, in plane-polarized light on top, cross-polarized light on bottom. Scale box in mm. Credit: Qfl247.

This is a thin section with cross-polarized kight through a sand-sized quartz grain of 0.13 mm diameter. Credit: Glen A. Izett, USGS.

This is a thin section of a shocked quartz grain. Credit: Martin Schmieder.

Alpha-quartz (space group P3121, no. 152, or P3221, no. 154) under a high pressure of 2-3 gigapascals and a moderately high temperature of 700°C changes space group to monoclinic C2/c, no. 15, and becomes the mineral coesite. It is "found in extreme conditions such as the impact craters of meteorites.

Shocked quartz is associated with two high pressure polymorphs of silicon dioxide: coesite and stishovite. These polymorphs have a crystal structure different from standard quartz. Again, this structure can only be formed by intense pressure, but moderate temperatures. High temperatures would anneal the quartz back to its standard form. Stishovite may be formed by an instantaneous over pressure such as by an impact or nuclear explosion type event.

So far several of the polymorphs of α-quartz formed at high temperature and pressure occur with rock types away from meteorite impact craters.

At lower left is a thin section through a sand-sized quartz grain "from the USGS-NASA Langley core showing two well-developed, intersecting sets of shock lamellae produced by the late Eocene Chesapeake Bay bolide impact. This shocked quartz grain is from the upper part of the crater-fill deposits at a depth of 820.6 ft in the core. The corehole is located at the NASA Langley Research Center, Hampton, VA, near the southwestern margin of the Chesapeake Bay impact crater."[8] "Very high pressures produced by strong shock waves cause dislocations in the crystal structure of quartz grains along preferred orientations. These dislocations appear as sets of parallel lamellae in the quartz when viewed with a petrographic microscope. Bolide impacts are the only natural process known to produce shock lamellae in quartz grains."[8]

Lower right shows another thin section in plane polarized light of a shocked quartz grain with two sets of decorated planar deformation features (PDFs) surrounded by a cryptocrystalline matrix from the Suvasvesi South impact structure, Finland.

In a specimen of shocked quartz, stishovite can be separated from quartz by applying hydrogen fluoride (HF); unlike quartz, stishovite will not react.[9]

Minute amounts of stishovite has been found within diamonds.[10]

The major evidence for a volcanic origin for tektites "includes: close analogy between shaped tektites and small volcanic bombs, and between layered tektites and lava or tuff-lava flows or huge bombs; analogy between flanged tektites and volcanic bombs ablated by gasjets: long-time, multistage formation of some tektites that corresponds to wide variations in their radiometric ages; well-ordered long compositional trends (series) typical of magmatic differentiation; different compositional tektite families (subseries) comparable to different stages (phases) of the volcanic process."[11]

"As with the North American microtektite-bearing cores, all the Australasian microtektite-bearing cores containing coesite and shocked quartz also contained volcanic ash, which complicated the search."[12]

Def. the "physical quality of a space for conveying sound"[13] or the "science of sounds, teaching their nature, phenomena and laws"[14] is called acoustics.

Def. the turning or bending of any wave, such as a light or sound wave, when it passes from one medium into another of different optical density is called refraction.

Def. the "quantum of acoustic or vibrational energy [(sound)][15], considered a discrete particle [rather than a wave][16]"[17] is called a phonon.

## Colors

WMAP 3-year Power spectrum of CMB is compared to recent measurements of BOOMERanG, CBI, VSA and ACBAR. Credit: NASA/WMAP Science Team.

The figure at the right "shows the three-year [Wilkinson Microwave Anisotropy Probe] WMAP spectrum compared to a set of recent balloon and ground-based measurements that were selected to most complement the WMAP data in terms of frequency coverage and l range. The non-WMAP data points are plotted with errors that include both measurement uncertainty and cosmic variance, while the WMAP data in this l range are largely noise dominated, so the effective error is comparable. When the WMAP data are combined with these higher resolution CMB measurements, the existence of a third acoustic peak is well established, as is the onset of Silk damping beyond the 3rd peak."[18]

## Absorptions

This image shows the crater created by the Sedan shallow underground nuclear test explosion. Credit: National Nuclear Security Administration, Federal Government of the United States.

This diagram depicts a stylized cross-section of a crater formed by a below-ground explosion. Credit: JBel.

Post-shot subsidence crater and Operation Tinderbox Huron King test chamber is from an explosion of less than 20 TNT equivalent kilotons (1980). Credit: .

The image shows a Galileo image of Tindr. Credit: .

Sub-Level Caving Subsidence reaches surface at the Ridgeway underground mine. Credit: Rolinator.

This is the gorge where the Reka River disappears underground. Credit: Dennis Tang from London, UK.

A photograph shows a collapsed mine tunnel to the west of № VI Conow adit. Credit: Bernd Triller, Bergamt Stralsund; Recherche:Berginspektor.

This image is an oblique aerial photo of Makhtesh Hazera. Credit: N. Fruchter, A. Matmon, Y. Avni, and D. Fink.

The image at right shows the crater created by the Sedan shallow underground nuclear test explosion.

At left is a stylised cross-section of a crater formed by a below-ground explosion.

A crater is formed by an explosive event through the displacement and ejection of material from the ground. It is typically bowl-shaped. High pressure gas and pressure waves are responsible for the creation of the crater by three processes

1. plastic deformation of the ground
2. projection of material (ejecta) from the ground by the expansion of gases in the ground
3. spallation of the ground surface and two processes partially fill it back in
4. fall-back of ejecta
5. erosion and landslides of the crater lip and wall[19]

The relative importance of the five processes varies depending on the height above or depth below the ground surface at which the explosion occurs, and the material composing the ground.

A subsidence crater is a hole or depression left on the surface of an area which has had an underground (usually nuclear) explosion.

Subsidence craters are created as the roof of the cavity caused by the explosion collapses. This causes the surface to depress into a sink (which subsidence craters are sometimes called). It is possible for further collapse to occur from the sink into the explosion chamber. When this collapse reaches the surface, and the chamber is exposed atmospherically to the surface, it is referred to as a chimney.

When a drilling oil well encounters high-pressured gas which cannot be contained either by the weight of the drilling mud or by blow-out preventers, the resulting violent eruption can create a large crater which can swallow up a drilling rig. This phenomenon is called "cratering" in oil field slang.

An image of Tindr is shown at right. It is a pit crater.

Tindr is a crater on Jupiter's moon Callisto. It is named after one of the ancestors of Ottar in Norse mythology. This is an example of a central pit impact crater.[20]

Removal of material and rock beneath a surface may result in a collapse of material above into the cavern below.

"In accordance with its definition, a makhtesh (Hebrew for "mortar" or "crater"; plural, makhteshim) is an erosion structure incised into an anticline and having a single drainage system with one outlet."[21]

"Erosional craters (Makhtesh) were formed by truncation and erosion of several of these anticlinal crests."[22]

At lower left, the image is an oblique aerial photo of Makhtesh Hazera. The Makhtesh drainage divide is outlined by a bold black line, with both of its constituent features (the anticlinal valley and the Upper Basin) located.[22]

## Bands

The prominent impact crater is Tycho on the Moon. Credit: NASA.
A laboratory simulation of an impact event and crater formation is shown. Credit: .

Impact crater structure is diagrammed. Credit: .

Close-up of shatter cones developed in fine grained dolomite from the Wells Creek crater, USA, are shown. Credit: .

U.S. Geological Survey aerial electromagnetic resistivity map of the Decorah crater has been produced. Credit: .

The image shows a crater produced by missile impact in silty sand and sandy silt, oblique view. Credit: US Army.

In the broadest sense, the term impact crater can be applied to any depression, natural or manmade, resulting from the high velocity impact of a projectile with a larger body. In most common usage, the term is used for the approximately circular depression in the surface of a planet, moon or other solid body in the Solar System, formed by the hypervelocity impact of a smaller body with the surface. In contrast to volcanic craters, which result from explosion or internal collapse,[23] impact craters typically have raised rims and floors that are lower in elevation than the surrounding terrain.[24] Impact craters range from small, simple, bowl-shaped depressions to large, complex, multi-ringed impact basins. Meteor Crater is perhaps the best-known example of a small impact crater on the Earth.

Impact cratering involves high velocity collisions between solid objects, typically much greater than the velocity of sound in those objects. Such hyper-velocity impacts produce physical effects such as melting and vaporization that do not occur in familiar sub-sonic collisions. On Earth, ignoring the slowing effects of travel through the atmosphere, the lowest impact velocity with an object from space is equal to the gravitational escape velocity of about 11 km/s. The fastest impacts occur at more than 80 km/s in the "worst case" scenario which the asteroid hits the earth in a retrograde parabolic orbit (because kinetic energy scales as velocity squared, earth's gravity only contributes 1 km/s to this figure, not 11 km/s). The median impact velocity on Earth is about 20 to 25 km/s.

Impacts at these high speeds produce shock waves in solid materials, and both impactor and the material impacted are rapidly compressed to high density. Following initial compression, the high-density, over-compressed region rapidly depressurizes, exploding violently, to set in train the sequence of events that produces the impact crater. Impact-crater formation is therefore more closely analogous to cratering by high explosives than by mechanical displacement. Indeed, the energy density of some material involved in the formation of impact craters is many times higher than that generated by high explosives. Since craters are caused by explosions, they are nearly always circular – only very low-angle impacts cause significantly elliptical craters.[25]

The distinctive mark of an impact crater is the presence of rock that has undergone shock-metamorphic effects, such as shatter cones, melted rocks, and crystal deformations. The problem is that these materials tend to be deeply buried, at least for simple craters. They tend to be revealed in the uplifted center of a complex crater, however.

Impacts produce distinctive shock-metamorphic effects that allow impact sites to be distinctively identified. Such shock-metamorphic effects can include:

• A layer of shattered or "brecciated" rock under the floor of the crater. This layer is called a "breccia lens".
• Shatter cones, which are chevron-shaped impressions in rocks. Such cones are formed most easily in fine-grained rocks.
• High-temperature rock types, including laminated and welded blocks of sand, spherulites and tektites, or glassy spatters of molten rock. The impact origin of tektites has been questioned by some researchers; they have observed some volcanic features in tektites not found in impactites. Tektites are also drier (contain less water) than typical impactites. While rocks melted by the impact resemble volcanic rocks, they incorporate unmelted fragments of bedrock, form unusually large and unbroken fields, and have a much more mixed chemical composition than volcanic materials spewed up from within the Earth. They also may have relatively large amounts of trace elements that are associated with meteorites, such as nickel, platinum, iridium, and cobalt. Note: scientific literature has reported that some "shock" features, such as small shatter cones, which are often associated only with impact events, have been found also in terrestrial volcanic ejecta.
• Microscopic pressure deformations of minerals. These include fracture patterns in crystals of quartz and feldspar, and formation of high-pressure materials such as diamond, derived from graphite and other carbon compounds, or stishovite and coesite, varieties of shocked quartz.
• Buried craters can be identified through drill coring, aerial electromagnetic resistivity imaging, and airborne gravity gradiometry.[26]

At right is a "[r]ecent airborne geophysical surveys near Decorah, Iowa [which is] providing an unprecedented look at a 470- million-year-old meteorite crater concealed beneath bedrock and sediments."[27]

"Capturing images of an ancient meteorite impact was a huge bonus," said Dr. Paul Bedrosian, a USGS geophysicist in Denver who is leading the effort to model the recently acquired geophysical data.[27] "These findings highlight the range of applications that these geophysical methods can address."[27]

"In 2008-09, geologists from the Iowa Department of Natural Resources' (Iowa DNR) Iowa Geological and Water Survey hypothesized what has become known as the Decorah Impact Structure. The scientists examined water well drill-cuttings and recognized a unique shale unit preserved only beneath and near the city of Decorah. The extent of the shale, which was deposited after the impact by an ancient seaway, defines a "nice circular basin" of 5.5 km width, according to Robert McKay, a geologist at the Iowa Geological Survey."[27]

"Bevan French, a scientist the Smithsonian's National Museum of Natural History, subsequently identified shocked quartz - considered strong evidence of an extra-terrestrial impact - in samples of sub-shale breccia from within the crater."[27]

"The recent geophysical surveys include an airborne electromagnetic system, which is sensitive to how well rocks conduct electricity, and airborne gravity gradiometry, which measures subtle changes in rock density. The surveys both confirm the earlier work and provide a new view of the Decorah Impact Structure. Models of the electromagnetic data show a crater filled with electrically conductive shale and the underlying breccia, which is rock composed of broken fragments of rock cemented together by a fine-grained matrix."[27]

"The shale is an ideal target and provides the electrical contrast that allows us to clearly image the geometry and internal structure of the crater," Bedrosian said.[27]

The image at the right shows a crater produced by missile impact in silty sand and sandy silt photographed in an oblique view. The "[m]issile traveled along an oblique trajectory, 45.8° from the horizontal with a kinetic energy of 25.1 x 1014 ergs. The crater, about 6 metres across, and ejecta have bilateral symmetry because of the oblique trajectory. [The t]race of path of [the] missile is shown by [the] arrow. Small depressions in foreground are footprints."[28]

"Craters in natural materials at White Sands Missile Range, N. Mex., were produced by the impact of high-velocity to hypervelocity missiles traveling along oblique trajectories with kinetic energies between 2.1 and 81 x 1014 ergs. The oblique impacts produce craters 2 to 10 m across with morphologies and ejecta that are bilaterally symmetrical with respect to the plane of the missile trajectory. Rims are high and the amount of ejecta large in down-trajectory and lateral directions, whereas rims are low to nonexistent and ejecta thin to absent up-trajectory. Symmetry development and modifications of the symmetry are a function of target material, local topography, and angle of impact."[28]

## Continua

"It [the Solar Oscillation Imager (SOI) onboard Ulysses] will provide high precision solar images 1024x1024 of line-of-sight velocity, line intensity, continuum intensity, longitudinal magnetic field and limb position."[29] Bold added.

## Neutrals

"Neutral current single π0 production induced by neutrinos with a mean energy of 1.3GeV is measured at a 1000 ton water Cherenkov detector as a near detector of the K2K long baseline neutrino experiment."[30]

"The single π0 production rate by atmospheric neutrinos could be usable to distinguish between the νµ ↔ ντ and νµ ↔ νs oscillation hypotheses. The NC rate is attenuated in the case of transitions of νµ’s into sterile neutrinos, while it does not change in the νµ ↔ ντ scenario."[30]

## Neutrinos

Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo[31] whereby a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates. Neutrino oscillation is of theoretical and experimental interest since observation of the phenomenon implies that the neutrino has a non-zero mass.

A great deal of evidence for neutrino oscillation has been collected from many sources, over a wide range of neutrino energies and with many different detector technologies.[32]

## Ultraviolets

STEREO—First images is a slow animation of a mosaic of the extreme ultraviolet images taken on December 4, 2006. These false color images show the Sun's atmospheres at a range of different temperatures. Clockwise from top left: 1 million degrees C (171 Å—blue), 1.5 million °C (195 Å—green), 60,000–80,000 °C (304 Å—red), and 2.5 million °C (286 Å—yellow). Credit: NASA.

This image of the Sun is taken on December 16, 2008, during sunspot-minimum conditions, using light produced at a wavelength of 19.5 nanometers by the ion Fe XII. Credit: NASA/ESA, SOHO/EIT.

In the corona thermal conduction occurs from the external hotter atmosphere towards the inner cooler layers. Responsible for the diffusion process of the heat are the electrons, which are much lighter than ions and move faster.

Ultraviolet telescopes such as TRACE and SOHO/EIT can observe individual micro-flares as small brightenings in extreme ultraviolet light,[33] but there seem to be too few of these small events to account for the energy released into the corona.

The first direct observation of waves propagating into and through the solar corona was made in 1997 with the SOHO space-borne solar observatory, the first platform capable of observing the Sun in the extreme ultraviolet (EUV) for long periods of time with stable photometry. Those were magneto-acoustic waves with a frequency of about 1 millihertz (mHz, corresponding to a 1,000 second wave period), that carry only about 10% of the energy required to heat the corona. Many observations exist of localized wave phenomena, such as Alfvén waves launched by solar flares, but those events are transient and cannot explain the uniform coronal heat.

"Ultraviolet irradiance (EUV) varies by approximately 1.5 percent from solar maxima to minima, for 200 to 300 nm UV.[34]

"1 percent of the sun's energy is emitted at ultraviolet wavelengths between 200 and 300 nanometers, the decrease in this radiation from 1 July 1981 to 30 June 1985 accounted for 19 percent of the decrease in the total irradiance".[34]

Energy changes in the UV wavelengths involved in production and loss of ozone have atmospheric effects.

The 30 hPa atmospheric pressure level has changed height in phase with solar activity during the last 4 solar cycles.

UV irradiance increase causes higher ozone production, leading to stratospheric heating and to poleward displacements in the stratospheric and tropospheric wind systems.

A proxy study estimates that UV has increased by 3.0% since the Maunder Minimum.[35]

"Solar satellite observatories such as ESA/NASA's Solar and Heliospheric Observatory (SOHO) have been studying the sun for over 10 years, and have created images of the entire solar surface using spectroscopic techniques. [The second image at right] shows a recent full-sun image created by the Extreme-ultraviolet Imaging Telescope (EIT) taken during sunspot-minimum conditions in 2008. [...] By using the techniques of imaging spectroscopy, solar physicists can isolate gases heated to temperatures of 1,500,000 K and study their motions and evolution over time."[36]

The second image at right is "taken on December 16, 2008 during sunspot-minimum conditions, was created by isolating the light produced at a wavelength of 195 Angstroms (19.5 nanometers) by the ion Fe XII. By selecting the light from only one spectral line, a spectroheliograph works like a high-precision light filter and lets astronomers map, or image, a distant object in the light from a single spectral line. This information can be used to map the temperature and density changes in the gas."[36]

## Opticals

The Variability of Solar Irradiance and Gravity Oscillations (VIRGO) on board SOHO "characterises solar intensity oscillations and measures the total solar irradiance (known as the ‘solar constant’) to quantify its variability over periods of days to the duration of the mission."[37]

## Plasma objects

This is a photo of the kink instability in action - the 3 by 25 cm pyrex tube at Aldermaston. Credit: Alan Sykes, UK Atomic Energy Authority.

Plasma instabilities can be divided into two general groups:

1. hydrodynamic instabilities
2. kinetic instabilities.

Plasma instabilities are also categorised into different modes:[38]

 Mode(azimuthal wave number) Note Description Radial modes Description m=0 Sausage instability:displays harmonic variations of beam radius with distance along the beam axis n=0 Axial hollowing n=1 Standard sausaging n=2 Axial bunching m=1 Sinuous, kink or hose instability:represents transverse displacements of the beam cross-section without change in the form or in a beam characteristics other than the position of its center of mass m=2 Filamentation modes:growth leads towards the breakup of the beam into separate filaments. Gives an elliptic cross-section m=3 Gives a pyriform (pear-shaped) cross-section

Ideal MHD instabilities driven by current or pressure gradients.

A kink instability, also oscillation or mode, is a class of magnetohydrodynamic instabilities which sometimes develop in a thin plasma column carrying a strong axial current. If a "kink" begins to develop in a column the magnetic forces on the inside of the kink become larger than those on the outside, which leads to growth of the perturbation.[39] As it develops at fixed areas in the plasma, kinks belong to the class of "absolute plasma instabilities", as opposed to convective processes.

## Space plasma characteristics

Space plasma pioneers Hannes Alfvén and Carl-Gunne Fälthammar divided the plasmas in the solar system into three different categories:

Classification of Magnetic Cosmic Plasmas

 Characteristic Space plasma density categories(Note that density does not refer to only particle density) Ideal comparison High density Medium Density Low Density Criterion λ << ρ λ << ρ << lc lc << λ lc << λD Examples Stellar interiorSolar photosphere Solar chromosphere/coronaInterstellar/intergalactic spaceIonosphere above 70 km Magnetosphere duringmagnetic disturbance.Interplanetary space Single chargesin a high vacuum Diffusion Isotropic Anisotropic Anisotropic and small No diffusion Conductivity Isotropic Anisotropic Not defined Not defined Electric field parallel to Bin completely ionized gas Small Small Any value Any value Particle motion in planeperpendicular to B Almost straight pathbetween collisions Circlebetween collisions Circle Circle Path of guiding centreparallel to B Straight pathbetween collisions Straight pathbetween collisions Oscillations(e.g. between mirror points) Oscillations(e.g. between mirror points) Debye Distance λD λD << lc λD << lc λD << lc λD >> lc Magnetohydrodynamicssuitability Yes Approximately No No

λ=Mean free path. ρ= Larmor radius (gyroradius) of electron. λD=Debye length. lc=Characteristic length
Adapted From Cosmical Electrodynamics (2nd Ed. 1952) Alfvén and Fälthammar

## Magnetohydrodynamic waves

There are several distinct kinds of MHD modes which have quite different dispersive, polarisation, and propagation properties:

• Kink (or transverse) modes, which are oblique fast magnetoacoustic (also known as magnetosonic waves) guided by the plasma structure; the mode causes the displacement of the axis of the plasma structure. These modes are weakly compressible, but could nevertheless be observed with imaging instruments as periodic standing or propagating displacements of coronal structures, e.g. coronal loops. The frequency of transverse or "kink" modes is given by the following expression:
${\displaystyle \omega _{K}={\sqrt {\frac {2k_{z}B^{2}}{\mu (\rho _{i}+\rho _{e})}}}}$

For kink modes the parameter ${\displaystyle m}$  is equal to 1.

• Sausage modes, which are also oblique fast magnetoacoustic waves guided by the plasma structure; the mode causes expansions and contractions of the plasma structure, but does not displace its axis. These modes are compressible and cause significant variation of the absolute value of the magnetic field in the oscillating structure. The frequency of sausage modes is given by the following expression:
${\displaystyle \omega _{S}={\sqrt {\frac {k_{z}^{2}B^{2}}{\mu \rho _{e}}}}}$

For sausage modes the parameter ${\displaystyle m}$  is equal to 0.

• Longitudinal (or slow, or acoustic) modes, which are slow magnetoacoustic waves propagating mainly along the magnetic field in the plasma structure; these mode are essentially compressible. The magnetic field perturbation in these modes is negligible. The frequency of slow modes is given by the following expression:
${\displaystyle \omega _{L}={\sqrt {k_{z}^{2}\left({\frac {C_{s}^{2}C_{A}^{2}}{C_{s}^{2}+C_{A}^{2}}}\right)}}}$

Where we define ${\displaystyle C_{s}}$  as the sound speed and ${\displaystyle C_{A}}$  as the Alfvèn speed.

• Torsional (Alfvén or twist) modes are incompressible transverse perturbations of the magnetic field along certain individual magnetic surfaces. In contrast with kink modes, torsional modes cannot be observed with imaging instruments, as they do not cause the displacement of either the structure axis or its boundary.
${\displaystyle \omega _{A}={\sqrt {\frac {k_{z}^{2}B^{2}}{\mu \rho _{i}}}}}$

Waves in plasmas are an interconnected set of particles and fields which propagates in a periodically repeating fashion. A plasma is a quasineutral, electrically conductive fluid. In the simplest case, it is composed of electrons and a single species of positive ions, but it may also contain multiple ion species including negative ions as well as neutral particles. Due to its electrical conductivity, a plasma couples to electric and magnetic fields. This complex of particles and fields supports a wide variety of waves.

Waves in plasmas can be classified as electromagnetic or electrostatic according to whether or not there is an oscillating magnetic field. Applying Faraday's law of induction to plane waves, we find ${\displaystyle \mathbf {k} \times {\tilde {\mathbf {E} }}=\omega {\tilde {\mathbf {B} }}}$ , implying that an electrostatic wave must be purely longitudinal. An electromagnetic wave, in contrast, must have a transverse component, but may also be partially longitudinal.

Waves can be further classified by the oscillating species. In most plasmas of interest, the electron temperature is comparable to or larger than the ion temperature. This fact, coupled with the much smaller mass of the electron, implies that the electrons are much faster than the ions. An electron mode depends on the mass of the electrons, but the ions may be assumed to be infinitely massive, i.e. stationary. An ion mode depends on the ion mass, but the electrons are assumed to be massless and to redistribute themselves instantaneously according to the Boltzmann relation. Only rarely, e.g. in the lower hybrid oscillation, will a mode depend on both the electron and the ion mass.

The various modes can also be classified according to whether they propagate in an unmagnetized plasma or parallel, perpendicular, or oblique to the stationary magnetic field. Finally, for perpendicular electromagnetic electron waves, the perturbed electric field can be parallel or perpendicular to the stationary magnetic field.

Summary of elementary plasma waves
EM character oscillating species conditions dispersion relation name
electrostatic electrons ${\displaystyle {\vec {B}}_{0}=0\ {\rm {or}}\ {\vec {k}}\|{\vec {B}}_{0}}$  ${\displaystyle \omega ^{2}=\omega _{p}^{2}+3k^{2}v_{th}^{2}}$  plasma oscillation (or Langmuir wave)
${\displaystyle {\vec {k}}\perp {\vec {B}}_{0}}$  ${\displaystyle \omega ^{2}=\omega _{p}^{2}+\omega _{c}^{2}=\omega _{h}^{2}}$  upper hybrid oscillation
ions ${\displaystyle {\vec {B}}_{0}=0\ {\rm {or}}\ {\vec {k}}\|{\vec {B}}_{0}}$  ${\displaystyle \omega ^{2}=k^{2}v_{s}^{2}=k^{2}{\frac {\gamma _{e}KT_{e}+\gamma _{i}KT_{i}}{M}}}$  ion acoustic wave
${\displaystyle {\vec {k}}\perp {\vec {B}}_{0}}$  (nearly) ${\displaystyle \omega ^{2}=\Omega _{c}^{2}+k^{2}v_{s}^{2}}$  electrostatic ion cyclotron wave
${\displaystyle {\vec {k}}\perp {\vec {B}}_{0}}$  (exactly) ${\displaystyle \omega ^{2}=[(\Omega _{c}\omega _{c})^{-1}+\omega _{i}^{-2}]^{-1}}$  lower hybrid oscillation
electromagnetic electrons ${\displaystyle {\vec {B}}_{0}=0}$  ${\displaystyle \omega ^{2}=\omega _{p}^{2}+k^{2}c^{2}}$  light wave
${\displaystyle {\vec {k}}\perp {\vec {B}}_{0},\ {\vec {E}}_{1}\|{\vec {B}}_{0}}$  ${\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}}$  O wave
${\displaystyle {\vec {k}}\perp {\vec {B}}_{0},\ {\vec {E}}_{1}\perp {\vec {B}}_{0}}$  ${\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}\,{\frac {\omega ^{2}-\omega _{p}^{2}}{\omega ^{2}-\omega _{h}^{2}}}}$  X wave
${\displaystyle {\vec {k}}\|{\vec {B}}_{0}}$  (right circ. pol.) ${\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}/\omega ^{2}}{1-(\omega _{c}/\omega )}}}$  R wave (whistler mode)
${\displaystyle {\vec {k}}\|{\vec {B}}_{0}}$  (left circ. pol.) ${\displaystyle {\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}/\omega ^{2}}{1+(\omega _{c}/\omega )}}}$  L wave
ions ${\displaystyle {\vec {B}}_{0}=0}$    none
${\displaystyle {\vec {k}}\|{\vec {B}}_{0}}$  ${\displaystyle \omega ^{2}=k^{2}v_{A}^{2}}$  Alfvén wave
${\displaystyle {\vec {k}}\perp {\vec {B}}_{0}}$  ${\displaystyle {\frac {\omega ^{2}}{k^{2}}}=c^{2}\,{\frac {v_{s}^{2}+v_{A}^{2}}{c^{2}+v_{A}^{2}}}}$  magnetosonic wave

${\displaystyle \omega }$  - wave frequency, ${\displaystyle k}$  - wave number, ${\displaystyle c}$  - speed of light, ${\displaystyle \omega _{p}}$  - plasma frequency, ${\displaystyle \omega _{i}}$  - ion plasma frequency, ${\displaystyle \omega _{c}}$  - electron gyrofrequency, ${\displaystyle \Omega _{c}}$  - proton gyrofrequency, ${\displaystyle \omega _{h}}$  - upper hybrid frequency, ${\displaystyle v_{s}}$  - plasma "sound" speed, ${\displaystyle v_{A}}$  - plasma Alfven speed

## Acoustic oceanography

Sound "waves tend to bend downward as they travel at shallow depths. Conversely, the waves bend upward as they propagate at deeper depths."[40]

Def. "a continuous layer in the deep ocean where sound waves are focused, thus providing a mechanism for a long-range communications system"[40] is called a Sound Fixing and Ranging (SOFAR) channel.

"The depth of this channel varies in different oceans depending on the salinity, temperature, and depth of the water. It may be anywhere from 600 to 1500 meters below the surface, depending on these variables."[40]

"[L]ow-frequency waves are less vulnerable than higher frequencies to scattering and absorption."[40]

An "underwater TNT explosion [was set off] in the Bahamas at a depth of 1500 meters, which was easily detected by receivers 2,000 miles away on the coast of West Africa."[40]

Sound "propagating through the SOFAR channel [may be used] to study underwater earthquakes, volcanoes and whales."[40]

"SOFAR floats [were used] in the 1970s to measure and track oceanic currents. The floats were free- drifting underwater buoys. The floats sent out acoustic pulses, typically at 260 Hz. Moored listening stations at known locations received the sound signals. The position of each float was determined using time of arrival of the signal at three or more hydrophones. SOFAR floats worked at ranges of up to 2500 km, which is about half-way across the Atlantic Ocean."[40]

"The ocean is divided into horizontal layers. The speed of sound is greatly influenced by temperature in the upper layers and by pressure in the deeper layers. The speed of sound decreases as temperature decreases. The speed of sound increases as the pressure (depth) increases. The two effects do not cancel, however. The "channeling" of sound occurs because there is a minimum in the vertical sound speed profile in the ocean caused by the changes in temperature and pressure."[40]

"The principle of sound propagation is that sound rays always bend towards the region of lower sound speed. The refraction of sound waves from higher velocities above and below the sound channel axis thus bends the sound back towards the axis. Sound energy is refracted towards the axis of the sound channel away from the surface and the bottom of the ocean. Furthermore, sound propagates in the SOFAR channel without interacting with either the sea surface or seafloor. These sound waves thus travel with relatively little attenuation beyond that due to geometric spreading."[40]

## Sound waves

The recordings of the acceleration of the ground include from left to right: acceleration, velocity, and displacement. Credit: Charles Ammon, Penn State University.

Def. vibrations that travel through the air or another medium, some of which may be heard by a human or animal's ear is called sound.

These vibrations may be recorded by an accelerometer and discriminated into displacement, velocity, or acceleration as shown in the images on the right.

## Body waves

Speed of seismic waves is versus depth into the Earth. Credit: Brews ohare.

Cross section of the whole Earth shows the complexity of paths of seismic waves. Credit: Eugene C. Robertson, USGS.

Def. a seismic wave that travels through the earth's interior is called a body wave.

"Primary or P-waves are the fastest seismic waves, and they propagate through solids and liquids."[41]

"Secondary or S-waves travel only through solid materials, at a slower speed than P- waves."[41]

"Cross section of the whole Earth, [in the image on the left shows] the complexity of paths of [seismic] waves. The paths curve because the different rock types found at different depths change the speed at which the waves travel. Solid lines marked P are compressional waves; dashed lines marked S are shear waves. S waves do not travel through the core but may be converted to compressional waves (marked K) on entering the core (PKP, SKS). Waves may be reflected at the surface (PP, PPP, SS)."[42]

## Primary waves

The velocity profile is a cross-section of a velocity model. Credit: Southern California Earthquake Center.

P waves' arrival can be easily identified on a seismogram. Credit: Southern California Earthquake Center.

"P waves [primary waves] are longitudinal [along the axis of propagation] compressional waves. Just like sound waves, they travel through matter causing compression and dilatation [expansion] in an orientation parallel to their direction of propagation. As with sound, the speed at which P waves travel depends upon the properties of the matter through which they propagate. In general, the less dense the matter, the slower the waves."[43]

A "velocity model [is] a three-dimensional map [such as in the image on the right] of the variations in P-wave velocity throughout the crust [here] beneath southern California. The velocity profile at [on the right] is a cross-section of such a model. It shows that P waves typically travel through the rocks below southern California at speeds between 5 and 7 kilometers per second, though in sediment-filled basins (like the Los Angeles Basin), they may move as slowly as 3 km/sec. That's still very fast; the speed of sound in air is only 0.3 km/sec!"[43]

"Because P waves are the first seismic waves to reach any given location after an earthquake occurs, their arrival can be easily identified on a seismogram, like the example [on the right]. This record is read from left to right, as time elapsed during the recording. You can see how the trace (the dark line) starts out, at far left, as a flat line, meaning all was "quiet". The first deflection of the trace from this quiet mode represents the arrival of the P wave."[43]

## Secondary waves

Typically, the more obvious indicator of an S-wave's arrival is a sudden increase in the amplitude of deflection. Credit: Southern California Earthquake Center.

"Travelling at a speed typically around 60% that of P waves, S waves always arrive at a location after them -- the "S" stands for secondary. S waves are transverse shear waves. This means that they create a shearing, side-to-side motion transverse (perpendicular) to their direction of propagation (but in any possible orientation, unlike Love waves). Because of this, they can only travel through a substance that has shear strength -- the ability to elastically resist this kind of motion. Liquids and gases have no shear strength, meaning S waves cannot travel through water, air, or even molten rock. It may thus help to think of the "S" as meaning "shear", in addition to "secondary"."[44]

"Identifying the exact time of the initial S-wave arrival [... ] is [usually] accomplished by noting two features of the waveform trace: amplitude and wavelength. S-waves, in addition to being slower than P-waves, also tend to be lower in frequency and longer in wavelength. A sudden increase in wavelength is one way to recognize the arrival of an S-wave on a seismogram. Typically, the more obvious indicator of an S-wave's arrival is a sudden increase in the amplitude of deflection. In cases where the earthquake is large and the source is nearby, however, this method is often not feasible, because the P-wave shaking has not yet decayed to the point where the S-wave arrival "overpowers" it. The image at right, like that [for the primary waves], is a link to an example of an identified S-wave arrival time, on the same seismogram used before."[44]

"When body waves [as opposed to surface waves] encounter a boundary across which their velocity changes -- a contact between two different types of rock, for example, or the ground surface, where rock ends and air begins -- they will reflect and refract, sometimes spawning other body waves, or even surface waves. Large earthquakes can produce body waves detectable all across the globe. Their reflections and refractions as they pass through the planet produce identifiable phases that allow researchers to detect structural and compositional boundaries deep within the Earth. This phenomenon is also responsible for one of the most eerie of earthquake effects: "earth noises"."[44]

## Tertiary waves

The measured sound pressure time history of T-waves for the Sumatra earthquake captured by hydrophones located at Diego Garcia, more than 1700 miles (2740 km) from the epicenter. Credit: Tom Irvine.

"Tertiary or T-waves are the slowest of the three types."[41]

"T-waves can be partially converted to other seismic waveforms at a continental or insular shoreline. T-waves can thus be recorded by seismic stations in the vicinity of the coastline."[41]

"The T-waves for the Sumatra earthquake were captured by hydrophones located at Diego Garcia, more than 1700 miles (2740 km) from the epicenter. The measured sound pressure time history is shown in [the figure on the right]."[41]

Monochromatic "seismic signals, typically between 3 and 12 Hz, with a lack of overtones [occurred on some seismic recordings from French Polynesia]. The signals were due to oceangoing T- waves, which were particularly active in 1991 and in the early months of 1992. The duration of individual blasts lasted from a few seconds to several minutes. [...] earthquakes and whales [were ruled out] as the source of the T-waves."[41]

The "waves originated at an underwater volcanic ridge in a poorly surveyed region of the South Pacific. New probing showed a flat-topped undersea volcano that rose to within 130 meters of the surface. [...] undersea volcanoes at shallow depths [are] capable of producing T-waves, where the pressure is low enough that bubbles can form in the hot lava."[41]

"Sound waves normally travel at about 1500 meters per second in seawater, but they can slow to one meter per second in a cloud of bubbles generated by the steam from a volcano."[41]

"The cloud becomes sandwiched between the top of the seamount and the ocean surface, forming a resonant cavity. The cavity behaves as an organ pipe, with acoustic waves reflecting back and forth between the boundaries. A standing wave could thus be generated. The standing wave would emit a fundamental tone with overtones, but the gas bubbles would damp out the higher frequency overtones."[41]

## Surface waves

The 3D images describe body waves and surface waves. Credit: USGS.

Def. a seismic wave that travels along the earth's surface is called a surface wave.

"Surface waves travel only within the uppermost layers of the Earth -- i.e. along its surface. The two types of surface waves are called Rayleigh waves and Love waves."[45]

"Each of the two surface waves travels literally along the surface of the Earth; the farther below the surface a point is, the smaller the displacement it will experience. Each wave produces a distinct type of motion. Love waves produce transverse motion -- perpendicular to the direction of wave propagation -- in a horizontal orientation only. This kind of horizontal shearing can be devastating to the foundations of buildings."[45]

"Rayleigh waves produce a rolling motion analogous to waves on the surface of a body of water. An object on the surface will experience both an up-and-down motion transverse to, and a back-and-forth motion parallel to, the propagation direction of the Rayleigh wave. The two components combine to produce a rolling, elliptical motion."[45]

## Love waves

Def. a seismic surface shock wave, which is also known as a Q-wave, with a lateral horizontal movement perpendicular to the direction of propagation is called a Love wave.

## Rayleigh waves

Def. an undulating wave that travels over the surface of a solid, with a speed independent of wavelength, the motion of the particles being in ellipses, is called a Rayleigh wave.

## Longitudinal waves

Propagation is of a plane compression wave (impulse). Credit: Christophe Dang Ngoc Chan.

Surface propagation is for a point source compressional or longitudinal wave. Credit: Christophe Dang Ngoc Chan.

Def. a wave vibrating in the direction of propagation is called a longitudinal wave.

## Transverse waves

Propagation is of a plane shear wave (impulse). Credit: Christophe Dang Ngoc Chan.

This shear wave is a transverse wave. Credit: Christophe Dang Ngoc Chan.

## Neons

The neutrino oscillation signatures are discussed regarding "flavor conversion of neutrinos from core-collapse supernovae that have oxygen-neon-magnesium (ONeMg) cores."[46]

## Sun

Global Oscillations at Low Frequencies (GOLF) aboard SOHO "studies the internal structure of the Sun by measuring velocity oscillations over the entire solar disc."[47]

The Michelson Doppler Imager/Solar Oscillations Investigation (MDI/SOI) aboard SOHO records the vertical motion (“tides”) of the Sun's surface at a million different points for each minute. By measuring the acoustic waves inside the Sun as they perturb the photosphere, scientists can study the structure and dynamics of the Sun’s interior. MDI also measures the longitudinal component of the Sun’s magnetic field."[48]

## Solar coronal cloud

This image shows the Sun as viewed by the Soft X-Ray Telescope (SXT) onboard the orbiting Yohkoh satellite. Credit: NASA Goddard Laboratory for Atmospheres.

Although a coronal cloud (as part or all of a stellar or galactic corona) is usually "filled with high-temperature plasma at temperatures of T ≈ 1–2 (MK), ... [h]ot active regions and postflare loops have plasma temperatures of T ≈ 2–40 MK."[49]

Waves & Oscillations occur in the Solar Atmosphere: Heating and Magneto-Seismology.

In the image at right, the photosphere of the Sun is dark in X-rays. However, apparently associated with the Sun is a high-temperature plasma that radiates in X-rays at temperatures 1,000 times as hot as the photosphere.

## Heliognosy

This computer-generated diagram of internal rotation in the Sun shows differential rotation in the outer convective region and almost uniform rotation in the central radiative region. Credit: Global Oscillation Network Group (GONG).

Stellar astrognosy, or perhaps stellagnosy as Latin for "star" is stella, deals with the materials of stars and their general exterior and interior constitution.

At right is a diagram of the internal rotation in the Sun, showing differential rotation in the outer convective region and almost uniform rotation in the central radiative region. The transition between these regions is called the tachocline.

Until the advent of helioseismology, the study of wave oscillations in the Sun, very little was known about the internal rotation of the Sun. The differential profile of the surface was thought to extend into the solar interior as rotating cylinders of constant angular momentum.[50] Through helioseismology this is now known not to be the case and the rotation profile of the Sun has been found. On the surface the Sun rotates slowly at the poles and quickly at the equator. This profile extends on roughly radial lines through the solar convection zone to the interior. At the tachocline the rotation abruptly changes to solid body rotation in the solar radiation zone.[51]

## Solar neutrinos

This "neutrino image" of the Sun is produced by using the Super-Kamiokande to detect the neutrinos from nuclear fusion coming from the Sun. Credit: R. Svoboda and K. Gordan (LSU).

Neutrinos are hard to detect. The Super-Kamiokande, or "Super-K" is a large-scale experiment constructed in an unused mine in Japan to detect and study neutrinos. The image at right required 500 days worth of data to produce the "neutrino image" of the Sun. The image is centered on the Sun's position. It covers a 90° x 90° octant of the sky (in right ascension and declination). The higher the brightness of the color, the larger is the neutrino flux.

"The detection of solar neutrinos demonstrates that fusion energy is the basic source of energy received from the sun."[52]

In detecting solar neutrinos, it became clear that the number detected was half or a third than that predicted by models of the solar interior. The problem was solved by revising the properties of neutrinos and understanding the limits of the detection mechanisms - only one third of the forms of neutrinos coming in was being detected and all neutrinos oscillate between the three forms.

The first experiment to detect the effects of neutrino oscillation was Ray Davis's Homestake Experiment in the late 1960s, in which he observed a deficit in the flux of solar neutrinos with respect to the prediction of the Standard Solar Model, using a chlorine-based detector. This gave rise to the Solar neutrino problem. Many subsequent radiochemical and water Cherenkov detectors confirmed the deficit, but neutrino oscillation was not conclusively identified as the source of the deficit until the Sudbury Neutrino Observatory provided clear evidence of neutrino flavor change in 2001. Solar neutrinos have energies below 20 MeV and travel an astronomical unit between the source in the Sun and detector on the Earth. At energies above 5 MeV, solar neutrino oscillation actually takes place in the Sun through a resonance known as the Mikheyev–Smirnov–Wolfenstein effect (MSW) effect, a different process from the vacuum oscillation.

Most neutrinos passing through the Earth emanate from the Sun. About 65 billion (6.5 x 1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun in the region of the Earth.[53]

The Mikheyev Smirnov Wolfenstein (MSW) effect is important at the very large electron densities of the Sun where electron neutrinos are produced. The high-energy neutrinos seen, for example, in the Sudbury Neutrino Observatory (SNO) and in Super-Kamiokande, are produced mainly as the higher mass eigenstate in matter ν2m, and remain as such as the density of solar material changes. (When neutrinos go through the MSW resonance the neutrinos have the maximal probability to change their nature, but it happens that this probability is negligibly small—this is sometimes called propagation in the adiabatic regime). Thus, the neutrinos of high energy leaving the sun are in a vacuum propagation eigenstate, ν2, that has a reduced overlap with the electron neutrino νe = ν1 cosθ + ν2 sinθ seen by charged current reactions in the detectors.

For high-energy solar neutrinos the MSW effect is important, and leads to the expectation that Pee = sin²θ, where θ = 34° is the solar mixing angle. This was dramatically confirmed in the Sudbury Neutrino Observatory (SNO), which has resolved the solar neutrino problem. SNO measured the flux of Solar electron neutrinos to be ~34% of the total neutrino flux (the electron neutrino flux measured via the charged current reaction, and the total flux via the neutral current reaction). The SNO results agree well with the expectations.

For the low-energy solar neutrinos, on the other hand, the matter effect is negligible, and the formalism of oscillations in vacuum is valid. The size of the source (i.e. the Solar core) is significantly larger than the oscillation length, therefore, averaging over the oscillation factor, one obtains Pee = 1 − sin²2θ / 2. For the same value of the solar mixing angle (θ = 34°) this corresponds to a survival probability of Pee ≈ 60%. This is consistent with the experimental observations of low energy Solar neutrinos by the Homestake experiment (the first experiment to reveal the solar neutrino problem), followed by GALLEX, the Gallium Neutrino Observatory (GNO), and Soviet–American Gallium Experiment (SAGE) (collectively, gallium radiochemical experiments), and, more recently, the Borexino experiment. These experiments provided further evidence of the MSW effect.

The transition between the low energy regime (the MSW effect is negligible) and the high energy regime (the oscillation probability is determind by matter effects) lies in the region of about 2 MeV for the Solar neutrinos.

## Earth

"For outside wave fields of the Moon and the Earth accept seismic and acoustic waves which characteristic frequencies first of all coincide with frequencies of orbital and own rotation of cosmogony objects (planets and their satellites, multiple star systems, pulsars)."[54]

"Besides wave (acoustic) processes in the top Earth atmosphere and also those from that its are accompanied also by optical effects (polar lights) and strongly connected with gas dust streams acting [4]."[54]

## Geoseismology

The key principle of plate tectonics is that the lithosphere exists as separate and distinct tectonic plates, which float on the fluid-like (visco-elastic solid) asthenosphere. Credit: USGS.

Sound "propagating through the [Sound Fixing and Ranging] SOFAR channel [may be used] to study underwater earthquakes, volcanoes and whales."[40]

"Between 100 and 200 kilometers below the Earth's surface, the temperature of the rock is near the melting point; molten rock erupted by some volcanoes originates in this region of the mantle."[42]

Monochromatic "seismic signals, typically between 3 and 12 Hz, with a lack of overtones [occurred on some seismic recordings from French Polynesia]. The signals were due to oceangoing T- waves, which were particularly active in 1991 and in the early months of 1992. The duration of individual blasts lasted from a few seconds to several minutes. [...] earthquakes and whales [were ruled out] as the source of the T-waves."[41]

The "waves originated at an underwater volcanic ridge in a poorly surveyed region of the South Pacific. New probing showed a flat-topped undersea volcano that rose to within 130 meters of the surface. [...] undersea volcanoes at shallow depths [are] capable of producing T-waves, where the pressure is low enough that bubbles can form in the hot lava."[41]

"Sound waves normally travel at about 1500 meters per second in seawater, but they can slow to one meter per second in a cloud of bubbles generated by the steam from a volcano."[41]

Def. the "study of the vibration of the Earth's interior caused by natural and unnatural sources,[55] such as earthquakes[56]" is called seismology.

Def. "Earth"[57] is prefixed with geo-.

Def. the seismology of the Earth is called geoseismology.

## Velocity structures

A velocity structure is a generalized regional model of the Earth's crust. Credit: Canales, Detrick, Lin Collins, and Toomey.

Def. "a generalized regional model of the earth's crust that represents crustal structure using layers having different assumed seismic velocities"[58] is called a velocity structure.

## Thunderstorms

Stages of a thunderstorm's life.

Anvil-shaped thundercloud in the mature stage. Credit: .

Lightning, which is responsible for the majority of fires in the American West. Credit: Jrmichae.

A thunderstorm, also known as an electrical storm or a lightning storm, is a storm characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere, known as thunder.[59] Relatively weak thunderstorms are sometimes called thundershowers.[60]

Thunderstorms can form and develop in any geographic location but most frequently within the mid-latitude, where warm, moist air from tropical latitudes collides with cooler air from polar latitudes.[61]

Warm air has a lower density than cool air, so warmer air rises upwards and cooler air will settle at the bottom[62] (this effect can be seen with a hot air balloon).[63] Clouds form as relatively warmer air, carrying moisture, rises within cooler air. The moist air rises, and, as it does so, it cools and some of the water vapor in that rising air condenses.[64] When the moisture condenses, it releases energy known as latent heat of condensation, which allows the rising packet of air to cool less than the cooler surrounding air[65] continuing the cloud's ascension. If enough instability is present in the atmosphere, this process will continue long enough for cumulonimbus clouds to form and produce lightning and thunder. Meteorological indices such as convective available potential energy (CAPE) and the lifted index can be used to assist in determining potential upward vertical development of clouds.[66] Generally, thunderstorms require three conditions to form:

1. Moisture
2. An unstable airmass
3. A lifting force (heat)

All thunderstorms, regardless of type, go through three stages: the developing stage, the mature stage, and the dissipation stage.[67] The average thunderstorm has a 24 km (15 mi) diameter. Depending on the conditions present in the atmosphere, each of these three stages take an average of 30 minutes.[68]

A "thunderstorm supplies a negative charge to the Earth. The net positive space charge in the air between the ground and a height of ~ 10 km is nearly equal to the negative charge on the Earth's surface".[69]

'Giant' "thunderclouds can produce transverse electric fields of tens of microvolts per meter in the equatorial plane of the midlatitude magnetosphere."[70]

The "contribution to global thunderstorm activity by oceanic thunderstorms should be regarded as itself having a diurnal variation of some 18% in amplitude."[71]

Pyrocumulonimbus are cumuliform clouds that can form over a large fire and that are particularly dry.[72]

There is "a decrease in thunderstorms at the time of high cosmic rays and an increase in thunderstorms 2-4 days later."[73]

## Heat lightning

Heat Lightning occurs near Louisville, Kentucky. Credit: Bbadgett.{{free media}}

Heat lightning, sometimes known as silent lightning, 'summer lightning, or dry lightning (mainly used in the American south; not to be confused with dry thunderstorms, which are also often called dry lightning), is a misnomer[74] used for the faint flashes of lightning on the horizon or other clouds from distant thunderstorms that do not appear to have accompanying sounds of thunder.

Heat lightning is a lightning flash that appears to produce no discernible because it occurs too far away for the thunder to be heard; the sound waves dissipate before they reach the observer.[75]

## Moon

NASA’s Apollo missions installed four solar-powered seismometers on the moon. Credit: Astronauts at Apollo landing sites.{{fairuse}}

Features like the curving outcrop of a lobate fault scarp, a steplike cliff on the moon (white arrows), indicate where the moon’s surface is compressing as its interior cools. Credit: GSFC/NASA, Arizona State University, Smithsonian.{{fairuse}}

Moonquakes recorded during those missions installing the seismometers shown on the right have now been linked to faults scattered across the lunar surface.

"Rumbles recorded decades ago by seismometers at Apollo landing sites are probably linked to young faults mapped by NASA’s Lunar Reconnaissance Orbiter."[76]

"Eight of those moonquakes occurred within 30 kilometers of fault scarps, steplike cliffs on the lunar crust that mark places where one side of a fault has thrust up or slipped down."[77]

Like Mercury and Mars, "the moon is basically a one-plate planet."[76]

Even "one-plate objects can have quakes [...]. As those objects cool over time and the interior contracts, their hard outer shell, or lithosphere, also compresses and cracks. That compression can produce quakes. As the moon’s interior has cooled, its radius is thought to have shrunk by about 100 meters."[77]

Images examined "from the Lunar Reconnaissance Orbiter, launched in 2009, [...] identified numerous sinuous cliffs distributed widely across the surface. Called lobate scarps, those features, from tens to a few hundreds of meters high, represent thrust faults, places where the surface is contracting as the moon cools. [Those] scarps were [estimated] no older than 50 million years."[77]

The "faults might be much, much younger."[76]

Thousands "of moonquakes detected from 1969 to 1977 by NASA’s Passive Seismic Experiment, consisting of four seismometers installed by astronauts at Apollo landing sites [...] were small and originated deep inside the moon. But 28 quakes were larger and shallower, originating within just 200 kilometers of the surface. Even then, some [...] suspected that the moonquakes might be related to ongoing tectonic activity."[77]

"They had the seismic data, but what they didn’t have was potential sources."[76]

Now, the Lunar Reconnaissance Orbiter had provided evidence of abundant faults, "thousands of potential sources."[77]

"We found eight of these within that 30-kilometer, cutoff distance, close matches that suggest that the moon is still actively contracting. This is data that’s just 40 years old. If we detected these slip events 40 years ago, then these faults are still active. That must also mean that the moon still has a lot of heat in its interior."[76]

The "faults had a distinct pattern: In the equatorial and mid-latitude regions, they tended to run north-south. Near the poles, they were oriented east-west."[77]

"18 of the 28 recorded shallow quakes happened when the moon was farthest from Earth, called its apogee."[77]

"Stress is force over a unit area. When the moon is at apogee, the unit area the Earth is acting on is actually greater. The moon also slows down just a bit as it reaches apogee, giving stresses caused by changes in the pull of Earth’s gravity more time to accumulate, and making quakes more likely."[76]

"The moon is no longer considered to be ‘dead.’"[78]

The "proximity of moonquakes to the young thrust faults together with evidence of regolith disturbance and boulder movements on and near the fault scarps strongly suggest the Moon is tectonically active."[79]

## Solar and Heliospheric Observatory

Artist's concept shows SOHO. Credit: .{{free media}}

The Solar and Heliospheric Observatory (SOHO) is a spacecraft built by a European industrial consortium led by Matra Marconi Space (now Astrium) that was launched on a Lockheed Martin Atlas II AS launch vehicle on December 2, 1995 to study the Sun. SOHO has also discovered over 3,000 comets.[80] It began normal operations in May 1996. It is a joint project of international cooperation between the European Space Agency (ESA) and NASA. Originally planned as a two-year mission, SOHO continues to operate after over 20 years in space: the mission is extended until the end of 2020 with a likely extension until 2022.[81]

GOLF, MDI, and VIRGO are used for helioseismology:

• Global Oscillations at Low Frequencies which measures velocity variations of the whole solar disk to explore the core of the Sun.[82]
• Michelson Doppler Imager which measures velocity and magnetic fields in the photosphere to learn about the convection zone which forms the outer layer of the interior of the Sun and about the magnetic fields which control the structure of the corona. The MDI is the biggest producer of data by far on SOHO. In fact, two of SOHO's virtual channels are named after MDI, VC2 (MDI-M) carries MDI magnetogram data, and VC3 (MDI-H) carries MDI Helioseismology data.[83] MDI has not been used for scientific observation since 2011, because it was superseded by the Solar Dynamics Observatory's Helioseismic and Magnetic Imager.[84]
• Variability of solar IRradiance and Gravity Oscillations[85] which measures oscillations and solar constant both of the whole solar disk and at low resolution, again exploring the core of the Sun.

## Seismometers

In the torsion seismometer motion is generated from the rotation of a small, copper, inertial mass, when the instrument is shaken. Credit: Harry O. Wood and J.A. Anderson.

This is a Kinemetrics FBA-23 accelerograph. Credit: Kinemetrics.

This is an accelerograph. Credit: USGS.

Def. a seismic "instrument designed specifically to record ... strong ground accelerations"[86] is called an accelerograph.

Def. a "computer software that includes digital mapping with a linked database"[86] is called a Geographic Information System (GIS).

In the torsion seismometer [in the image on the right], motion is generated from the rotation of a small, copper, inertial mass, when the instrument is shaken.

"The Wood-Anderson seismometer was designed to be as sensitive and as nearly frictionless as possible. Damping of the torsional motion was accomplished using magnets (M)."[87]

Def. an "instrument that records the acceleration of the ground during" the [generation or conduction of vibrations][88] is called an accelerograph, or accelerometer.

Def. a form of microphone that detects and records seismic vibrations is called a geophone.

## Seismographs

Kinemetrics seismograph is formerly used by United States Department of the Interior. Credit: Kinemetrics.

"A seismograph, or seismometer, is an instrument used to detect and record earthquakes. Generally, it consists of a mass attached to a fixed base. During an earthquake, the base moves and the mass does not. The motion of the base with respect to the mass is commonly transformed into an electrical voltage. The electrical voltage is recorded on paper, magnetic tape, or another recording medium. This record is proportional to the motion of the seismometer mass relative to the earth, but it can be mathematically converted to a record of the absolute motion of the ground. Seismograph generally refers to the seismometer and its recording device as a single unit."[89]

## Quantum microphone

"Phonons are individual packets of vibrational energy that often manifest as sound or heat."[90]

"One phonon corresponds to an energy ten trillion trillion times smaller than the energy required to keep a lightbulb on for one second."[91]

"Rather than sound moving a membrane inside an ordinary microphone, the quantum microphone uses supercooled resonators [...] — so small they can only be seen through an electron microscope — that act as a “mirror of sound.”"[90]

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