Abandoned village

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https://en.wikipedia.org/wiki/Abandoned_village

Abandoned village in Russia

The remains of a fieldstone church in Dangelsdorf, ^{[de ]} Germany, from the 14th century

Moggessa di Qua near Moggio Udinese / Italy

Glanzenberg, a 13th-century town in Unterengstringen, Switzerland

Villa Epecuén (Argentina)

An abandoned village is a village that has, for some reason, been deserted. In many countries, and throughout history, thousands of villages have been deserted for a variety of causes. Abandonment of villages is often related to epidemic, famine, war, climate change, economic depressions, environmental destruction, or deliberate clearances.

Armenia and Azerbaijan

Hundreds of villages in Nagorno-Karabakh were deserted following the First Nagorno-Karabakh War. Between 1988 and 1993, 400,000 ethnic Azeris, and Kurds fled the area and nearly 200 villages in Armenia itself populated by Azeris and Kurds were abandoned by 1991. Likewise, nearly 300,000 Armenians fled from Azerbaijan between 1988 and 1993, including 50 villages populated by Armenians in Northern Nagorno Karabakh that were abandoned. Some of the Armenian settlements and churches outside Armenia and the Nagorno-Karabakh Republic have either been destroyed or damaged including those in Nakhichevan.

Australia

In Australia, the government requires operators of mining towns to remove all traces of the town when it is abandoned. This has occurred in the cases of Mary Kathleen, Goldsworthy and Shay Gap, but not in cases such as Wittenoom and Big Bell. Some towns have been lost or moved when dams are built. Others when the settlement was abandoned for any number of other reasons such as recurring natural disasters such as bushfires or changed circumstances. In Australia, an abandoned settlement that has infrastructure remaining is synonymous with ghost town.

Belarus

In 1988, two years after the Chernobyl disaster, the Belarusian government created the Polesie State Radioecological Reserve, a 1,313 km² (507 sq mi) exclusion zone to protect people against the effects of radiation. Twenty-two thousand people lived there in the 96 settlements that were abandoned, including Aravichy and Dzernavichy, and the area has since been expanded by a further 849 km² (328 sq mi).

Belgium

In 1968 in the town of Doel, a building ban was implemented so that the Port of Antwerp could expand. Then an economic crisis occurred and this plan for expansion was halted. Then in 1998 another plan for expansion for the Port of Antwerp was released and most of the inhabitants left.

China

Many villages in remote parts of the New Territories, Hong Kong, usually in valleys or on islands, have been abandoned due to inaccessibility. Residents go to live in urban areas with better job opportunities. Some villages have been moved to new sites to make way for reservoirs or new town development. See also walled villages of Hong Kong and list of villages in Hong Kong.

Cyprus

Villages have been abandoned as a result of the Cyprus dispute. Some of these are reported to be landmined.

Finland

On the western edge of Vantaa's Ilola district, there is an illegal village called Simosenkylä, where the houses are mainly dilapidated, some completely abandoned.

France

See also: List of French villages destroyed in World War I

A number of villages, mainly in the north and north western areas of the country, were destroyed during World War I and World War II. A percentage of them were rebuilt next to the original sites, with the original villages remaining in a ruined state.

Germany

Winnefeld church ruin

There are hundreds of abandoned villages, known as Wüstungen, in Germany. Geographer Kurt Scharlau categorized the different types in the 1930s, making distinctions between temporary and permanent Wüstung, settlements used for different purposes (farms or villages), and the extent of abandonment (partial or total). His scheme has been expanded, and has been criticized for not taking into account expansion and regression. Archaeologists commonly distinguish between Flurwüstungen (farmed areas) and Ortswüstungen (sites where buildings formerly stood). The most drastic period of abandonment in modern times was during the 14th and 15th centuries—before 1350, there were about 170,000 settlements in Germany, and this had been reduced by nearly 40,000 by 1450. As in Britain, the Black Death played a large role in this, as did the growth of large villages and towns, the Little Ice Age, the introduction of crop rotation, and war (in Germany, particularly the Thirty Years' War). In later times, the German Empire demolished villages for the creation of training grounds for the military. As a result of the Potsdam conference the southern part of “east Prussia” became “Kaliningrad oblast” with the majority of villages permanently destroyed after the German population had been driven out. The same applied to villages of ethnic Germans at the prewar borders of the now Czech Republic and Germany or Austria respectively as all ethnic Germans were expelled from the then Czechoslovakia.

Hungary

Hundreds of villages were abandoned during the Ottoman wars in the Kingdom of Hungary in the 16th–17th centuries. Many of them were never repopulated, and they generally left few visible traces. Real ghost towns are rare in present-day Hungary, except the abandoned villages of Derenk (left in 1943) and Nagygéc (left in 1970). Due to the decrease in rural population beginning in the 1980s, dozens of villages are now threatened with abandonment. The first village officially declared as "died out" was Gyűrűfű at the end of the 1970s, but it was later repopulated as an "eco-village". Sometimes depopulated villages were successfully saved as small rural resorts like Kán, Tornakápolna, Szanticska, Gorica and Révfalu.

India

One significant event of abandonment in Indian history was due to the Bengal famine of 1770. About ten million people, approximately one-third of the population of the affected area, are estimated to have died in the Bengal famine of 1770. Regions where the famine occurred included especially the modern Indian states of Bihar and West Bengal, but the famine also extended into Odisha and Jharkhand as well as modern Bangladesh. Among the worst affected areas were Birbhum and Murshidabad in Bengal, and Tirhut, Champaran and Bettiah in Bihar. As a result of the famine, these large areas were depopulated and returned to jungle for decades to come as the survivors migrated en masse in a search for food. Many cultivated lands were abandoned—much of Birbhum, for instance, returned to jungle and was virtually impassable for decades afterwards. From 1772 on, bands of bandits and thugs became an established feature of Bengal, and were only brought under control by punitive actions in the 1780s.

Indonesia

Due to natural disasters, many villages are destroyed and abandoned.

• Petobo

Ireland

Several villages in Ireland have been abandoned during the Middle Ages or later: Oliver Goldsmith's poem "The Deserted Village" (1770) being a famous commentary on rural depopulation. Notable deserted villages include:

• Cannakill, County Offaly
• Clonmines, County Wexford
• Kilcornan, County Galway
• Port, County Donegal
• Rindoon, County Roscommon
• Scattery Island, County Clare
• Slievemore, Achill Island, County Mayo
• Tonaroasty, County Galway

Smaller rural settlements, known as clachans, were also abandoned in large numbers during the Great Famine (1845–50).

In 1940 the town of Ballinahown in West Wicklow was evacuated for the construction of the Blessington Lakes and Poulaphouca Reservoir.

Territory of the former British Mandate of Palestine

Main articles: List of villages depopulated during the Arab–Israeli conflict and Depopulated Palestinian locations in Israel

As a consequence of the 1948 Palestinian expulsion and flight during the 1948 Palestine war, around 720,000 Palestinian Arabs were displaced, leaving around 400 Palestinian Arab towns and villages depopulated in what became Israel. In addition, several Jewish communities in what became the West Bank and Gaza Strip were also depopulated.

In August 2005, Israel evacuated Gush Katif and all other Jewish settlements in the Gaza Strip. Some structures in these settlements, including greenhouses and synagogues, were left standing after the withdrawal.

Malta

Ruins of Tal-Baqqari, an abandoned village near Żurrieq

Many small villages around Malta were abandoned between the 14th and 18th centuries. They were abandoned for several reasons, including corsair raids (such as the raids of 1429 and 1551), slow population decline, migration to larger villages as well as political changes such as the transfer of the capital from Mdina to Birgu in 1530, and to Valletta in 1571. Many villages were depopulated after a plague epidemic in 1592–93.

Of Malta's ten original parishes in 1436, two (Ħal Tartarni and Bir Miftuħ) no longer exist, while others such as Mellieħa were abandoned but rebuilt at a later stage. The existence of many of the other villages is known only from militia lists, ecclesiastical or notarial documents, or lists of lost villages compiled by scholars such as Giovanni Francesco Abela.

The villages usually consisted of a chapel surrounded by a number of farmhouses and other buildings. In some cases, such as Ħal-Millieri and Bir Miftuħ, the village disappeared but the chapel still exists.

North Africa

Oases and villages in North Africa have been abandoned due to the expansion of the Sahara desert.

Romania

Many Saxon villages in Transylvania became depopulated or abandoned when their German-speaking inhabitants emigrated to Germany in the 1990s.

Russia

Abandoned village in the Tver Oblast of Russia

Thousands of abandoned villages are scattered across Russia.

Narmeln, the westernmost point of Russia, was a German village on the Vistula Spit until it became depopulated in 1945 during World War II. The Vistula Spit was split between Poland and the Soviet Union after the war, with Narmeln as the only settlement on the Soviet side. Narmeln was never repopulated as the Soviet side was made into an exclusion zone.

Spain

The abandoned village of Merades, Spain; part of the northernmost section of the ruins

Large zones of the mountainous Iberian System and the Pyrenees have undergone heavy depopulation since the early 20th century. In Spain there are many ghost towns scattered across mountain areas especially in Teruel Province.

The traditional agricultural practices such as sheep and goat rearing on which the village economy was based were not taken over by the local youth after the lifestyle changes that swept over rural Spain during the second half of the 20th century. The exodus from the rural mountainous areas in Spain rose steeply after General Franco's Plan de Estabilización in 1959. The population declined steeply as people emigrated towards the industrial areas of the large cities and the coastal towns where tourism grew exponentially.

The abandonment of agricultural land use practices drives the natural establishment of forests through ecological succession in Spain. This spontaneous forest establishment has several consequences for society and nature, such as increase of fire risk and frequency and biodiversity loss. Regarding biodiversity loss, The risk, research findings from Mediterranean showed that this is very site dependent. More recently, the abandonment of land is also discussed by some as an opportunity for rewilding in rural areas in Spain.

Syria

The Dead Cities are a group of abandoned villages in Northern Syria dating back to the times of Late Antiquity and the Byzantine Empire. They are a World Heritage Site.

After the occupation of the Golan Heights by Israel after its victory during the Six-Day War, more than 130,000 Syrians were expelled, and two towns as well as 163 villages were abandoned and destroyed.

In the 2010s, as a result of the Syrian civil war, many villages in Syria, both in areas under government control and under rebel control, have been depopulated. For example, the town of Darayya in Rural Damascus Governorate, with a pre-war population of 225,000 was completely depopulated during the war, and since its return to government control in 2016, only between 10% and 30% of its population have returned. Further north in Idlib Governorate, the two villages of Al-Fu'ah and Kafriya for example, were depopulated completely as their Twelver Shia population were evacuated.

Ukraine

Abandoned village near Chernobyl

Following the 1986 Chernobyl disaster, a 2,600 km² (1,000 sq mi) zone of exclusion was created and the entire population was evacuated to prevent exposure to radiation. Since then, a limited number of people have been allowed to return: 197 lived in the zone in 2012, down from 328 in 2007 and 612 in 1999. However, all of the villages and the main city of the region, Pripyat, are falling into decay. The only lived in settlement is Chernobyl which houses maintenance staff and scientists working at the nuclear power plant, although they can only live there for short periods of time.

United Kingdom

See also: List of lost settlements in the United Kingdom

St Mary Church in West Tofts, Norfolk, a village which had its population relocated and was then incorporated into the Stanford Training Area facility.

Many villages in the United Kingdom have been abandoned throughout history. Some cases were the result of natural events, such as rivers changing course or silting up, or coastal and estuarine erosion.

Sometimes villages were deliberately cleared: the Harrying of the North caused widespread devastation in the winter of 1069–1070. In the 12th and 13th centuries, many villages were removed to make way for monasteries, and in the 18th century, it became fashionable for land-owning aristocrats to live in large mansions set in large landscaped parklands. Villages that obstructed the view were removed, although by the early 19th century it had become common to provide replacements.

In modern times, a few villages have been abandoned due to reservoirs being built and the location being flooded. These include Capel Celyn in Gwynedd, Wales, Mardale Green in the English Lake District and two villages—Ashopton and Derwent—drowned by the Ladybower Reservoir in Derbyshire. In other cases, such as Tide Mills, East Sussex, Imber and Tyneham, the village lands have been converted to military training areas. Villages in Northumberland have been demolished to make way for open-cast mines. Hampton-on-Sea was abandoned due to coastal erosion thought to have been exacerbated by the building of a pier. Several other villages had their populations relocated to make way for military installations; these include a group of villages in the vicinity of Thetford, Norfolk, which were emptied in 1942 to allow for the establishment of the Stanford Training Area, which incorporates the villages as part of the facility's training areas.

Deserted medieval villages

Main article: Deserted medieval village

In the United Kingdom, a deserted medieval village (DMV) is a settlement that was abandoned during the Middle Ages, typically leaving no trace apart from earthworks or cropmarks. If there are three or fewer inhabited houses, the convention is to regard the site as deserted; if there are more than three houses, it is regarded as shrunken. The commonest causes of DMVs include failure of marginal agricultural land and clearance and enclosure following depopulation after the Black Death. The study of the causes of each settlement's desertion is an ongoing field of research.

England has an estimated 3,000 DMVs. One of the best known is Wharram Percy in North Yorkshire, where extensive archaeological excavations were conducted between 1948 and 1990. Its ruined church and former fishpond are still visible. Some other examples are Gainsthorpe in Lincolnshire, and Old Wolverton in Milton Keynes.

Cosmic dust

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Cosmic_dust

Porous chondrite dust particle

Cosmic dust – also called extraterrestrial dust, space dust, or star dust – is dust that occurs in outer space or has fallen onto Earth. Most cosmic dust particles measure between a few molecules and 0.1 mm (100 μm), such as micrometeoroids. Larger particles are called meteoroids. Cosmic dust can be further distinguished by its astronomical location: intergalactic dust, interstellar dust, interplanetary dust (as in the zodiacal cloud), and circumplanetary dust (as in a planetary ring). There are several methods to obtain space dust measurement.

In the Solar System, interplanetary dust causes the zodiacal light. Solar System dust includes comet dust, planetary dust (like from Mars), asteroidal dust, dust from the Kuiper belt, and interstellar dust passing through the Solar System. Thousands of tons of cosmic dust are estimated to reach Earth's surface every year, with most grains having a mass between 10⁻¹⁶ kg (0.1 pg) and 10⁻⁴ kg (0.1 g). The density of the dust cloud through which the Earth is traveling is approximately 10⁻⁶ dust grains/m³.

Cosmic dust contains some complex organic compounds (amorphous organic solids with a mixed aromatic–aliphatic structure) that could be created naturally, and rapidly, by stars. A smaller fraction of dust in space is "stardust" consisting of larger refractory minerals that condensed as matter left by stars.

Interstellar dust particles were collected by the Stardust spacecraft and samples were returned to Earth in 2006.

Study and importance

Artist's impression of dust formation around a supernova explosion.

Cosmic dust was once solely an annoyance to astronomers, as it obscures objects they wished to observe. When infrared astronomy began, the dust particles were observed to be significant and vital components of astrophysical processes. Their analysis can reveal information about phenomena like the formation of the Solar System. For example, cosmic dust can drive the mass loss when a star is nearing the end of its life, play a part in the early stages of star formation, and form planets. In the Solar System, dust plays a major role in the zodiacal light, Saturn's B Ring spokes, the outer diffuse planetary rings at Jupiter, Saturn, Uranus and Neptune, and comets.

Zodiacal light caused by cosmic dust.

The interdisciplinary study of dust brings together different scientific fields: physics (solid-state, electromagnetic theory, surface physics, statistical physics, thermal physics), fractal mathematics, surface chemistry on dust grains, meteoritics, as well as every branch of astronomy and astrophysics. These disparate research areas can be linked by the following theme: the cosmic dust particles evolve cyclically; chemically, physically and dynamically. The evolution of dust traces out paths in which the Universe recycles material, in processes analogous to the daily recycling steps with which many people are familiar: production, storage, processing, collection, consumption, and discarding.

Observations and measurements of cosmic dust in different regions provide an important insight into the Universe's recycling processes; in the clouds of the diffuse interstellar medium, in molecular clouds, in the circumstellar dust of young stellar objects, and in planetary systems such as the Solar System, where astronomers consider dust as in its most recycled state. The astronomers accumulate observational ‘snapshots’ of dust at different stages of its life and, over time, form a more complete movie of the Universe's complicated recycling steps.

Parameters such as the particle's initial motion, material properties, intervening plasma and magnetic field determined the dust particle's arrival at the dust detector. Slightly changing any of these parameters can give significantly different dust dynamical behavior. Therefore, one can learn about where that object came from, and what is (in) the intervening medium.

Detection methods

Cosmic dust of the Andromeda Galaxy as revealed in infrared light by the Spitzer Space Telescope.

A wide range of methods is available to study cosmic dust. Cosmic dust can be detected by remote sensing methods that utilize the radiative properties of cosmic dust particles, c.f. Zodiacal light measurement.

Cosmic dust can also be detected directly ('in-situ') using a variety of collection methods and from a variety of collection locations. Estimates of the daily influx of extraterrestrial material entering the Earth's atmosphere range between 5 and 300 tonnes.

NASA collects samples of star dust particles in the Earth's atmosphere using plate collectors under the wings of stratospheric-flying airplanes. Dust samples are also collected from surface deposits on the large Earth ice-masses (Antarctica and Greenland/the Arctic) and in deep-sea sediments.

Don Brownlee at the University of Washington in Seattle first reliably identified the extraterrestrial nature of collected dust particles in the latter 1970s. Another source is the meteorites, which contain stardust extracted from them. Stardust grains are solid refractory pieces of individual presolar stars. They are recognized by their extreme isotopic compositions, which can only be isotopic compositions within evolved stars, prior to any mixing with the interstellar medium. These grains condensed from the stellar matter as it cooled while leaving the star.

Cosmic dust of the Horsehead Nebula as revealed by the Hubble Space Telescope.

In interplanetary space, dust detectors on planetary spacecraft have been built and flown, some are presently flying, and more are presently being built to fly. The large orbital velocities of dust particles in interplanetary space (typically 10–40 km/s) make intact particle capture problematic. Instead, in-situ dust detectors are generally devised to measure parameters associated with the high-velocity impact of dust particles on the instrument, and then derive physical properties of the particles (usually mass and velocity) through laboratory calibration (i.e. impacting accelerated particles with known properties onto a laboratory replica of the dust detector). Over the years dust detectors have measured, among others, the impact light flash, acoustic signal and impact ionisation. Recently the dust instrument on Stardust captured particles intact in low-density aerogel.

Dust detectors in the past flew on the HEOS 2, Helios, Pioneer 10, Pioneer 11, Giotto, Galileo, Ulysses and Cassini space missions, on the Earth-orbiting LDEF, EURECA, and Gorid satellites, and some scientists have utilized the Voyager 1 and 2 spacecraft as giant Langmuir probes to directly sample the cosmic dust. Presently dust detectors are flying on the Ulysses, Proba, Rosetta, Stardust, and the New Horizons spacecraft. The collected dust at Earth or collected further in space and returned by sample-return space missions is then analyzed by dust scientists in their respective laboratories all over the world. One large storage facility for cosmic dust exists at the NASA Houston JSC.

Infrared light can penetrate cosmic dust clouds, allowing us to peer into regions of star formation and the centers of galaxies. NASA's Spitzer Space Telescope was the largest infrared space telescope, before the launch of the James Webb Space Telescope. During its mission, Spitzer obtained images and spectra by detecting the thermal radiation emitted by objects in space between wavelengths of 3 and 180 micrometres. Most of this infrared radiation is blocked by the Earth's atmosphere and cannot be observed from the ground. Findings from the Spitzer have revitalized the studies of cosmic dust. One report showed some evidence that cosmic dust is formed near a supermassive black hole.

Another detection mechanism is polarimetry. Dust grains are not spherical and tend to align to interstellar magnetic fields, preferentially polarizing starlight that passes through dust clouds. In nearby interstellar space, where interstellar reddening is not intense enough to be detected, high precision optical polarimetry has been used to glean the structure of dust within the Local Bubble.

In 2019, researchers found interstellar dust in Antarctica which they relate to the Local Interstellar Cloud. The detection of interstellar dust in Antarctica was done by the measurement of the radionuclides Fe-60 and Mn-53 by highly sensitive Accelerator mass spectrometry.

Radiation properties

HH 151 is a bright jet of glowing material trailed by an intricate, orange-hued plume of gas and dust.

A dust particle interacts with electromagnetic radiation in a way that depends on its cross section, the wavelength of the electromagnetic radiation, and on the nature of the grain: its refractive index, size, etc. The radiation process for an individual grain is called its emissivity, dependent on the grain's efficiency factor. Further specifications regarding the emissivity process include extinction, scattering, absorption, or polarisation. In the radiation emission curves, several important signatures identify the composition of the emitting or absorbing dust particles.

Dust particles can scatter light nonuniformly. Forward scattered light is light that is redirected slightly off its path by diffraction, and back-scattered light is reflected light.

The scattering and extinction ("dimming") of the radiation gives useful information about the dust grain sizes. For example, if the object(s) in one's data is many times brighter in forward-scattered visible light than in back-scattered visible light, then it is understood that a significant fraction of the particles are about a micrometer in diameter.

The scattering of light from dust grains in long exposure visible photographs is quite noticeable in reflection nebulae, and gives clues about the individual particle's light-scattering properties. In X-ray wavelengths, many scientists are investigating the scattering of X-rays by interstellar dust, and some have suggested that astronomical X-ray sources would possess diffuse haloes, due to the dust.

Stardust

Main article: Presolar grains

Stardust grains (also called presolar grains by meteoriticists) are contained within meteorites, from which they are extracted in terrestrial laboratories. Stardust was a component of the dust in the interstellar medium before its incorporation into meteorites. The meteorites have stored those stardust grains ever since the meteorites first assembled within the planetary accretion disk more than four billion years ago. So-called carbonaceous chondrites are especially fertile reservoirs of stardust. Each stardust grain existed before the Earth was formed. Stardust is a scientific term referring to refractory dust grains that condensed from cooling ejected gases from individual presolar stars and incorporated into the cloud from which the Solar System condensed.

Many different types of stardust have been identified by laboratory measurements of the highly unusual isotopic composition of the chemical elements that comprise each stardust grain. These refractory mineral grains may earlier have been coated with volatile compounds, but those are lost in the dissolving of meteorite matter in acids, leaving only insoluble refractory minerals. Finding the grain cores without dissolving most of the meteorite has been possible, but difficult and labor-intensive (see presolar grains).

Many new aspects of nucleosynthesis have been discovered from the isotopic ratios within the stardust grains. An important property of stardust is the hard, refractory, high-temperature nature of the grains. Prominent are silicon carbide, graphite, aluminium oxide, aluminium spinel, and other such solids that would condense at high temperature from a cooling gas, such as in stellar winds or in the decompression of the inside of a supernova. They differ greatly from the solids formed at low temperature within the interstellar medium.

Also important are their extreme isotopic compositions, which are expected to exist nowhere in the interstellar medium. This also suggests that the stardust condensed from the gases of individual stars before the isotopes could be diluted by mixing with the interstellar medium. These allow the source stars to be identified. For example, the heavy elements within the silicon carbide (SiC) grains are almost pure S-process isotopes, fitting their condensation within AGB star red giant winds inasmuch as the AGB stars are the main source of S-process nucleosynthesis and have atmospheres observed by astronomers to be highly enriched in dredged-up s process elements.

Another dramatic example is given by the so-called supernova condensates, usually shortened by acronym to SUNOCON (from SUperNOva CONdensate) to distinguish them from other stardust condensed within stellar atmospheres. SUNOCONs contain in their calcium an excessively large abundance of ⁴⁴Ca, demonstrating that they condensed containing abundant radioactive ⁴⁴Ti, which has a 65-year half-life. The outflowing ⁴⁴Ti nuclei were thus still "alive" (radioactive) when the SUNOCON condensed near one year within the expanding supernova interior, but would have become an extinct radionuclide (specifically ⁴⁴Ca) after the time required for mixing with the interstellar gas. Its discovery proved the prediction from 1975 that it might be possible to identify SUNOCONs in this way. The SiC SUNOCONs (from supernovae) are only about 1% as numerous as are SiC stardust from AGB stars.

Stardust itself (SUNOCONs and AGB grains that come from specific stars) is but a modest fraction of the condensed cosmic dust, forming less than 0.1% of the mass of total interstellar solids. The high interest in stardust derives from new information that it has brought to the sciences of stellar evolution and nucleosynthesis.

Laboratories have studied solids that existed before the Earth was formed. This was once thought impossible, especially in the 1970s when cosmochemists were confident that the Solar System began as a hot gas virtually devoid of any remaining solids, which would have been vaporized by high temperature. The existence of stardust proved this historic picture incorrect.

Some bulk properties

Smooth chondrite interplanetary dust particle.

Cosmic dust is made of dust grains and aggregates into dust particles. These particles are irregularly shaped, with porosity ranging from fluffy to compact. The composition, size, and other properties depend on where the dust is found, and conversely, a compositional analysis of a dust particle can reveal much about the dust particle's origin. General diffuse interstellar medium dust, dust grains in dense clouds, planetary rings dust, and circumstellar dust, are each different in their characteristics. For example, grains in dense clouds have acquired a mantle of ice and on average are larger than dust particles in the diffuse interstellar medium. Interplanetary dust particles (IDPs) are generally larger still.

Major elements of 200 stratospheric interplanetary dust particles.

Most of the influx of extraterrestrial matter that falls onto the Earth is dominated by meteoroids with diameters in the range 50 to 500 micrometers, of average density 2.0 g/cm³ (with porosity about 40%). The total influx rate of meteoritic sites of most IDPs captured in the Earth's stratosphere range between 1 and 3 g/cm³, with an average density at about 2.0 g/cm³.

Other specific dust properties: in circumstellar dust, astronomers have found molecular signatures of CO, silicon carbide, amorphous silicate, polycyclic aromatic hydrocarbons, water ice, and polyformaldehyde, among others (in the diffuse interstellar medium, there is evidence for silicate and carbon grains). Cometary dust is generally different (with overlap) from asteroidal dust. Asteroidal dust resembles carbonaceous chondritic meteorites. Cometary dust resembles interstellar grains which can include silicates, polycyclic aromatic hydrocarbons, and water ice.

In September 2020, evidence was presented of solid-state water in the interstellar medium, and particularly, of water ice mixed with silicate grains in cosmic dust grains.

Dust grain formation

The large grains in interstellar space are probably complex, with refractory cores that condensed within stellar outflows topped by layers acquired during incursions into cold dense interstellar clouds. That cyclic process of growth and destruction outside of the clouds has been modeled to demonstrate that the cores live much longer than the average lifetime of dust mass. Those cores mostly start with silicate particles condensing in the atmospheres of cool, oxygen-rich red-giants and carbon grains condensing in the atmospheres of cool carbon stars. Red giants have evolved or altered off the main sequence and have entered the giant phase of their evolution and are the major source of refractory dust grain cores in galaxies. Those refractory cores are also called stardust (section above), which is a scientific term for the small fraction of cosmic dust that condensed thermally within stellar gases as they were ejected from the stars. Several percent of refractory grain cores have condensed within expanding interiors of supernovae, a type of cosmic decompression chamber. Meteoriticists who study refractory stardust (extracted from meteorites) often call it presolar grains but that within meteorites is only a small fraction of all presolar dust. Stardust condenses within the stars via considerably different condensation chemistry than that of the bulk of cosmic dust, which accretes cold onto preexisting dust in dark molecular clouds of the galaxy. Those molecular clouds are very cold, typically less than 50K, so that ices of many kinds may accrete onto grains, in cases only to be destroyed or split apart by radiation and sublimation into a gas component. Finally, as the Solar System formed many interstellar dust grains were further modified by coalescence and chemical reactions in the planetary accretion disk. The history of the various types of grains in the early Solar System is complicated and only partially understood.

Astronomers know that the dust is formed in the envelopes of late-evolved stars from specific observational signatures. In infrared light, emission at 9.7 micrometres is a signature of silicate dust in cool evolved oxygen-rich giant stars. Emission at 11.5 micrometres indicates the presence of silicon carbide dust in cool evolved carbon-rich giant stars. These help provide evidence that the small silicate particles in space came from the ejected outer envelopes of these stars.

Conditions in interstellar space are generally not suitable for the formation of silicate cores. This would take excessive time to accomplish, even if it might be possible. The arguments are that: given an observed typical grain diameter a, the time for a grain to attain a, and given the temperature of interstellar gas, it would take considerably longer than the age of the Universe for interstellar grains to form. On the other hand, grains are seen to have recently formed in the vicinity of nearby stars, in nova and supernova ejecta, and in R Coronae Borealis variable stars which seem to eject discrete clouds containing both gas and dust. So mass loss from stars is unquestionably where the refractory cores of grains formed.

Most dust in the Solar System is highly processed dust, recycled from the material out of which the Solar System formed and subsequently collected in the planetesimals, and leftover solid material such as comets and asteroids, and reformed in each of those bodies' collisional lifetimes. During the Solar System's formation history, the most abundant element was (and still is) H₂. The metallic elements: magnesium, silicon, and iron, which are the principal ingredients of rocky planets, condensed into solids at the highest temperatures of the planetary disk. Some molecules such as CO, N₂, NH₃, and free oxygen, existed in a gas phase. Some molecules, for example, graphite (C) and SiC would condense into solid grains in the planetary disk; but carbon and SiC grains found in meteorites are presolar based on their isotopic compositions, rather than from the planetary disk formation. Some molecules also formed complex organic compounds and some molecules formed frozen ice mantles, of which either could coat the "refractory" (Mg, Si, Fe) grain cores. Stardust once more provides an exception to the general trend, as it appears to be totally unprocessed since its thermal condensation within stars as refractory crystalline minerals. The condensation of graphite occurs within supernova interiors as they expand and cool, and do so even in gas containing more oxygen than carbon, a surprising carbon chemistry made possible by the intense radioactive environment of supernovae. This special example of dust formation has merited specific review.

Planetary disk formation of precursor molecules was determined, in large part, by the temperature of the solar nebula. Since the temperature of the solar nebula decreased with heliocentric distance, scientists can infer a dust grain's origin(s) with knowledge of the grain's materials. Some materials could only have been formed at high temperatures, while other grain materials could only have been formed at much lower temperatures. The materials in a single interplanetary dust particle often show that the grain elements formed in different locations and at different times in the solar nebula. Most of the matter present in the original solar nebula has since disappeared; drawn into the Sun, expelled into interstellar space, or reprocessed, for example, as part of the planets, asteroids or comets.

Due to their highly processed nature, IDPs (interplanetary dust particles) are fine-grained mixtures of thousands to millions of mineral grains and amorphous components. We can picture an IDP as a "matrix" of material with embedded elements which were formed at different times and places in the solar nebula and before the solar nebula's formation. Examples of embedded elements in cosmic dust are GEMS, chondrules, and CAIs.

From the solar nebula to Earth

A dusty trail from the early Solar System to carbonaceous dust today.

The arrows in the adjacent diagram show one possible path from a collected interplanetary dust particle back to the early stages of the solar nebula.

We can follow the trail to the right in the diagram to the IDPs that contain the most volatile and primitive elements. The trail takes us first from interplanetary dust particles to chondritic interplanetary dust particles. Planetary scientists classify chondritic IDPs in terms of their diminishing degree of oxidation so that they fall into three major groups: the carbonaceous, the ordinary, and the enstatite chondrites. As the name implies, the carbonaceous chondrites are rich in carbon, and many have anomalies in the isotopic abundances of H, C, N, and O. From the carbonaceous chondrites, we follow the trail to the most primitive materials. They are almost completely oxidized and contain the lowest condensation temperature elements ("volatile" elements) and the largest amount of organic compounds. Therefore, dust particles with these elements are thought to have been formed in the early life of the Solar System. The volatile elements have never seen temperatures above about 500 K, therefore, the IDP grain "matrix" consists of some very primitive Solar System material. Such a scenario is true in the case of comet dust. The provenance of the small fraction that is stardust (see above) is quite different; these refractory interstellar minerals thermally condense within stars, become a small component of interstellar matter, and therefore remain in the presolar planetary disk. Nuclear damage tracks are caused by the ion flux from solar flares. Solar wind ions impacting on the particle's surface produce amorphous radiation damaged rims on the particle's surface. And spallogenic nuclei are produced by galactic and solar cosmic rays. A dust particle that originates in the Kuiper Belt at 40 AU would have many more times the density of tracks, thicker amorphous rims and higher integrated doses than a dust particle originating in the main-asteroid belt.

Based on 2012 computer model studies, the complex organic molecules necessary for life (extraterrestrial organic molecules) may have formed in the protoplanetary disk of dust grains surrounding the Sun before the formation of the Earth. According to the computer studies, this same process may also occur around other stars that acquire planets.

In September 2012, NASA scientists reported that polycyclic aromatic hydrocarbons (PAHs), subjected to interstellar medium (ISM) conditions, are transformed, through hydrogenation, oxygenation and hydroxylation, to more complex organics – "a step along the path toward amino acids and nucleotides, the raw materials of proteins and DNA, respectively". Further, as a result of these transformations, the PAHs lose their spectroscopic signature which could be one of the reasons "for the lack of PAH detection in interstellar ice grains, particularly the outer regions of cold, dense clouds or the upper molecular layers of protoplanetary disks."

In February 2014, NASA announced a greatly upgraded database for detecting and monitoring polycyclic aromatic hydrocarbons (PAHs) in the universe. According to NASA scientists, over 20% of the carbon in the Universe may be associated with PAHs, possible starting materials for the formation of life. PAHs seem to have been formed shortly after the Big Bang, are abundant in the Universe, and are associated with new stars and exoplanets.

In March 2015, NASA scientists reported that, for the first time, complex DNA and RNA organic compounds of life, including uracil, cytosine and thymine, have been formed in the laboratory under outer space conditions, using starting chemicals, such as pyrimidine, found in meteorites. Pyrimidine, like polycyclic aromatic hydrocarbons (PAHs), the most carbon-rich chemical found in the Universe, may have been formed in red giants or in interstellar dust and gas clouds, according to the scientists.

Some "dusty" clouds in the universe

The Solar System has its own interplanetary dust cloud, as do extrasolar systems. There are different types of nebulae with different physical causes and processes: diffuse nebula, infrared (IR) reflection nebula, supernova remnant, molecular cloud, HII regions, photodissociation regions, and dark nebula.

Distinctions between those types of nebula are that different radiation processes are at work. For example, H II regions, like the Orion Nebula, where a lot of star-formation is taking place, are characterized as thermal emission nebulae. Supernova remnants, on the other hand, like the Crab Nebula, are characterized as nonthermal emission (synchrotron radiation).

Some of the better known dusty regions in the Universe are the diffuse nebulae in the Messier catalog, for example: M1, M8, M16, M17, M20, M42, M43.

Some larger dust catalogs are Sharpless (1959) A Catalogue of HII Regions, Lynds (1965) Catalogue of Bright Nebulae, Lynds (1962) Catalogue of Dark Nebulae, van den Bergh (1966) Catalogue of Reflection Nebulae, Green (1988) Rev. Reference Cat. of Galactic SNRs, The National Space Sciences Data Center (NSSDC), and CDS Online Catalogs.

Dust sample return

The Discovery program's Stardust mission, was launched on 7 February 1999 to collect samples from the coma of comet Wild 2, as well as samples of cosmic dust. It returned samples to Earth on 15 January 2006. In 2007, the recovery of particles of interstellar dust from the samples was announced.

Zero to the power of zero

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero 

Zero to the power of zero, denoted by 0⁰, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra and combinatorics, one typically defines  0⁰ = 1. In mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression.

Discrete exponents

Many widely used formulas involving natural-number exponents require 0⁰ to be defined as 1. For example, the following three interpretations of b⁰ make just as much sense for b = 0 as they do for positive integers b:

• The interpretation of b⁰ as an empty product assigns it the value 1.
• The combinatorial interpretation of b⁰ is the number of 0-tuples of elements from a b-element set; there is exactly one 0-tuple.
• The set-theoretic interpretation of b⁰ is the number of functions from the empty set to a b-element set; there is exactly one such function, namely, the empty function.

All three of these specialize to give 0⁰ = 1.

Polynomials and power series

When evaluating polynomials, it is convenient to define 0⁰ as 1. A (real) polynomial is an expression of the form a₀x⁰ + ⋅⋅⋅ + a_nxⁿ, where x is an indeterminate, and the coefficients a_i are real numbers. Polynomials are added termwise, and multiplied by applying the distributive law and the usual rules for exponents. With these operations, polynomials form a ring R[x]. The multiplicative identity of R[x] is the polynomial x⁰; that is, x⁰ times any polynomial p(x) is just p(x). Also, polynomials can be evaluated by specializing x to a real number. More precisely, for any given real number r, there is a unique unital R-algebra homomorphism ev_r : R[x] → R such that ev_r(x) = r. Because ev_r is unital, ev_r(x⁰) = 1. That is, r⁰ = 1 for each real number r, including 0. The same argument applies with R replaced by any ring.

Defining 0⁰ = 1 is necessary for many polynomial identities. For example, the binomial theorem (1 + x)ⁿ = Σⁿ
_k=0 (ⁿ
_k) x^k holds for x = 0 only if 0⁰ = 1.

Similarly, rings of power series require x⁰ to be defined as 1 for all specializations of x. For example, identities like 1/1−x = Σ^∞
_n=0 xⁿ and e^x = Σ^∞
_n=0 xⁿ/n! hold for x = 0 only if 0⁰ = 1.

In order for the polynomial x⁰ to define a continuous function R → R, one must define 0⁰ = 1.

In calculus, the power rule d/dxxⁿ = nxⁿ⁻¹ is valid for n = 1 at x = 0 only if 0⁰ = 1.

Continuous exponents

Plot of z = x^y. The red curves (with z constant) yield different limits as (x, y) approaches (0, 0). The green curves (of finite constant slope, y = ax) all yield a limit of 1.

Limits involving algebraic operations can often be evaluated by replacing subexpressions by their limits; if the resulting expression does not determine the original limit, the expression is known as an indeterminate form. The expression 0⁰ is an indeterminate form: Given real-valued functions f(t) and g(t) approaching 0 (as t approaches a real number or ±∞) with f(t) > 0, the limit of f(t)^g(t) can be any non-negative real number or +∞, or it can diverge, depending on f and g. For example, each limit below involves a function f(t)^g(t) with f(t), g(t) → 0 as t → 0⁺ (a one-sided limit), but their values are different:

$${\displaystyle \underset{t\to 0^{+}}{lim}{t}^t=1,}$$

$${\displaystyle \underset{t\to 0^{+}}{lim}{\left(e^{-1/t^2}\right)}^t=0,}$$

$${\displaystyle \underset{t\to 0^{+}}{lim}{\left(e^{-1/t^2}\right)}^{-t}=+\mathrm{\infty },}$$

$${\displaystyle \underset{t\to 0^{+}}{lim}{\left(e^{-1/t}\right)}^{at}=e^{-a}.}$$

Thus, the two-variable function x^y, though continuous on the set {(x, y) : x > 0}, cannot be extended to a continuous function on {(x, y) : x > 0} ∪ {(0, 0)}, no matter how one chooses to define 0⁰.

On the other hand, if f and g are analytic functions on an open neighborhood of a number c, then f(t)^g(t) → 1 as t approaches c from any side on which f is positive. This and more general results can be obtained by studying the limiting behavior of the function ln(f(t)^g(t)) = g(t) ln f(t).

Complex exponents

In the complex domain, the function z^w may be defined for nonzero z by choosing a branch of log z and defining z^w as e^{w log z}. This does not define 0^w since there is no branch of log z defined at z = 0, let alone in a neighborhood of 0.

History

As a value

In 1752, Euler in Introductio in analysin infinitorum wrote that a⁰ = 1 and explicitly mentioned that 0⁰ = 1. An annotation attributed to Mascheroni in a 1787 edition of Euler's book Institutiones calculi differentialis offered the "justification"

$${\displaystyle 0^0=(a-a{)}^{n-n}=\frac{(a-a{)}^n}{(a-a{)}^n}=1}$$

as well as another more involved justification. In the 1830s, Libri published several further arguments attempting to justify the claim 0⁰ = 1, though these were far from convincing, even by standards of rigor at the time.

As a limiting form

Euler, when setting 0⁰ = 1, mentioned that consequently the values of the function 0^x take a "huge jump", from ∞ for x < 0, to 1 at x = 0, to 0 for x > 0. In 1814, Pfaff used a squeeze theorem argument to prove that x^x → 1 as x → 0⁺.

On the other hand, in 1821 Cauchy explained why the limit of x^y as positive numbers x and y approach 0 while being constrained by some fixed relation could be made to assume any value between 0 and ∞ by choosing the relation appropriately. He deduced that the limit of the full two-variable function x^y without a specified constraint is "indeterminate". With this justification, he listed 0⁰ along with expressions like 0/0 in a table of indeterminate forms.

Apparently unaware of Cauchy's work, Möbius in 1834, building on Pfaff's argument, claimed incorrectly that f(x)^g(x) → 1 whenever f(x),g(x) → 0 as x approaches a number c (presumably f is assumed positive away from c). Möbius reduced to the case c = 0, but then made the mistake of assuming that each of f and g could be expressed in the form Pxⁿ for some continuous function P not vanishing at 0 and some nonnegative integer n, which is true for analytic functions, but not in general. An anonymous commentator pointed out the unjustified step; then another commentator who signed his name simply as "S" provided the explicit counterexamples (e^−1/x)^x → e⁻¹ and (e^−1/x)^2x → e⁻² as x → 0⁺ and expressed the situation by writing that "0⁰ can have many different values".

Current situation

• Some authors define 0⁰ as 1 because it simplifies many theorem statements. According to Benson (1999), "The choice whether to define 0⁰ is based on convenience, not on correctness. If we refrain from defining 0⁰, then certain assertions become unnecessarily awkward. ... The consensus is to use the definition 0⁰ = 1, although there are textbooks that refrain from defining 0⁰." Knuth (1992) contends more strongly that 0⁰ "has to be 1"; he draws a distinction between the value 0⁰, which should equal 1, and the limiting form 0⁰ (an abbreviation for a limit of f(t)^g(t) where f(t), g(t) → 0), which is an indeterminate form: "Both Cauchy and Libri were right, but Libri and his defenders did not understand why truth was on their side."
• Other authors leave 0⁰ undefined because 0⁰ is an indeterminate form: f(t), g(t) → 0 does not imply f(t)^g(t) → 1.

There do not seem to be any authors assigning 0⁰ a specific value other than 1.

Treatment on computers

IEEE floating-point standard

The IEEE 754-2008 floating-point standard is used in the design of most floating-point libraries. It recommends a number of operations for computing a power:

• pown (whose exponent is an integer) treats 0⁰ as 1; see § Discrete exponents.
• pow (whose intent is to return a non-NaN result when the exponent is an integer, like pown) treats 0⁰ as 1.
• powr treats 0⁰ as NaN (Not-a-Number) due to the indeterminate form; see § Continuous exponents.

The pow variant is inspired by the pow function from C99, mainly for compatibility. It is useful mostly for languages with a single power function. The pown and powr variants have been introduced due to conflicting usage of the power functions and the different points of view (as stated above).

Programming languages

The C and C++ standards do not specify the result of 0⁰ (a domain error may occur). But for C, as of C99, if the normative annex F is supported, the result for real floating-point types is required to be 1 because there are significant applications for which this value is more useful than NaN (for instance, with discrete exponents); the result on complex types is not specified, even if the informative annex G is supported. The Java standard, the .NET Framework method System.Math.Pow, Julia, and Python also treat 0⁰ as 1. Some languages document that their exponentiation operation corresponds to the pow function from the C mathematical library; this is the case with Lua and Perl's ** operator (where it is explicitly mentioned that the result of 0**0 is platform-dependent).

Mathematical and scientific software

APL, R, Stata, SageMath, Matlab, Magma, GAP, Singular, PARI/GP, and GNU Octave evaluate x⁰ to 1. Mathematica and Macsyma simplify x⁰ to 1 even if no constraints are placed on x; however, if 0⁰ is entered directly, it is treated as an error or indeterminate. SageMath does not simplify 0^x. Maple, Mathematica and PARI/GP further distinguish between integer and floating-point values: If the exponent is a zero of integer type, they return a 1 of the type of the base; exponentiation with a floating-point exponent of value zero is treated as undefined, indeterminate or error.