A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth; the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the estimated 300 sextillion stars in the Universe are invisible to the naked eye from Earth, including all stars outside our galaxy, the Milky Way. For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and radiates into outer space. All occurring elements heavier than helium are created by stellar nucleosynthesis during the star's lifetime, for some stars by supernova nucleosynthesis when it explodes.
Near the end of its life, a star can contain degenerate matter. Astronomers can determine the mass, age and many other properties of a star by observing its motion through space, its luminosity, spectrum respectively; the total mass of a star is the main factor. Other characteristics of a star, including diameter and temperature, change over its life, while the star's environment affects its rotation and movement. A plot of the temperature of many stars against their luminosities produces a plot known as a Hertzsprung–Russell diagram. Plotting a particular star on that diagram allows the age and evolutionary state of that star to be determined. A star's life begins with the gravitational collapse of a gaseous nebula of material composed of hydrogen, along with helium and trace amounts of heavier elements; when the stellar core is sufficiently dense, hydrogen becomes converted into helium through nuclear fusion, releasing energy in the process. The remainder of the star's interior carries energy away from the core through a combination of radiative and convective heat transfer processes.
The star's internal pressure prevents it from collapsing further under its own gravity. A star with mass greater than 0.4 times the Sun's will expand to become a red giant when the hydrogen fuel in its core is exhausted. In some cases, it will fuse heavier elements in shells around the core; as the star expands it throws a part of its mass, enriched with those heavier elements, into the interstellar environment, to be recycled as new stars. Meanwhile, the core becomes a stellar remnant: a white dwarf, a neutron star, or if it is sufficiently massive a black hole. Binary and multi-star systems consist of two or more stars that are gravitationally bound and move around each other in stable orbits; when two such stars have a close orbit, their gravitational interaction can have a significant impact on their evolution. Stars can form part of a much larger gravitationally bound structure, such as a star cluster or a galaxy. Stars have been important to civilizations throughout the world, they have used for celestial navigation and orientation.
Many ancient astronomers believed that stars were permanently affixed to a heavenly sphere and that they were immutable. By convention, astronomers grouped stars into constellations and used them to track the motions of the planets and the inferred position of the Sun; the motion of the Sun against the background stars was used to create calendars, which could be used to regulate agricultural practices. The Gregorian calendar used nearly everywhere in the world, is a solar calendar based on the angle of the Earth's rotational axis relative to its local star, the Sun; the oldest dated star chart was the result of ancient Egyptian astronomy in 1534 BC. The earliest known star catalogues were compiled by the ancient Babylonian astronomers of Mesopotamia in the late 2nd millennium BC, during the Kassite Period; the first star catalogue in Greek astronomy was created by Aristillus in 300 BC, with the help of Timocharis. The star catalog of Hipparchus included 1020 stars, was used to assemble Ptolemy's star catalogue.
Hipparchus is known for the discovery of the first recorded nova. Many of the constellations and star names in use today derive from Greek astronomy. In spite of the apparent immutability of the heavens, Chinese astronomers were aware that new stars could appear. In 185 AD, they were the first to observe and write about a supernova, now known as the SN 185; the brightest stellar event in recorded history was the SN 1006 supernova, observed in 1006 and written about by the Egyptian astronomer Ali ibn Ridwan and several Chinese astronomers. The SN 1054 supernova, which gave birth to the Crab Nebula, was observed by Chinese and Islamic astronomers. Medieval Islamic astronomers gave Arabic names to many stars that are still used today and they invented numerous astronomical instruments that could compute the positions of the stars, they built the first large observatory research institutes for the purpose of producing Zij star catalogues. Among these, the Book of Fixed Stars was written by the Persian astronomer Abd al-Rahman al-Sufi, who observed a number of stars, star clusters and galaxies.
According to A. Zahoor, in the 11th century, the Persian polymath scholar Abu Rayhan Biruni described the Milky
A spectrum is a condition, not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism; as scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the "spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with quantifiable numbers or definitions; such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. Nonscientific uses of the term spectrum are sometimes misleading. For instance, a single left–right spectrum of political opinion does not capture the full range of people's political beliefs. Political scientists use a variety of biaxial and multiaxial systems to more characterize political opinion.
In most modern usages of spectrum there is a unifying theme between the extremes at either end. This was not always true in older usage. In Latin, spectrum means "image" or "apparition", including the meaning "spectre". Spectral evidence is testimony about what was done by spectres of persons not present physically, or hearsay evidence about what ghosts or apparitions of Satan said, it was used to convict a number of persons of witchcraft at Salem, Massachusetts in the late 17th century. The word "spectrum" was used to designate a ghostly optical afterimage by Goethe in his Theory of Colors and Schopenhauer in On Vision and Colors; the prefix "spectro-" is used to form words relating to spectra. For example, a spectrometer is a device used to record spectra and spectroscopy is the use of a spectrometer for chemical analysis. In the 17th century, the word spectrum was introduced into optics by Isaac Newton, referring to the range of colors observed when white light was dispersed through a prism.
Soon the term referred to a plot of light intensity or power as a function of frequency or wavelength known as a spectral density plot. The term spectrum was expanded to apply to other waves, such as sound waves that could be measured as a function of frequency, frequency spectrum and power spectrum of a signal; the term now applies to any signal that can be measured or decomposed along a continuous variable such as energy in electron spectroscopy or mass-to-charge ratio in mass spectrometry. Spectrum is used to refer to a graphical representation of the signal as a function of the dependent variable. Electromagnetic spectrum refers to the full range of all frequencies of electromagnetic radiation and to the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object. Devices used to measure an electromagnetic spectrum are called spectrometer; the visible spectrum is the part of the electromagnetic spectrum. The wavelength of visible light ranges from 390 to 700 nm.
The absorption spectrum of a chemical element or chemical compound is the spectrum of frequencies or wavelengths of incident radiation that are absorbed by the compound due to electron transitions from a lower to a higher energy state. The emission spectrum refers to the spectrum of radiation emitted by the compound due to electron transitions from a higher to a lower energy state. Light from many different sources contains various colors, each with its own brightness or intensity. A rainbow, or prism, sends these component colors in different directions, making them individually visible at different angles. A graph of the intensity plotted against the frequency is the frequency spectrum of the light; when all the visible frequencies are present the perceived color of the light is white, the spectrum is a flat line. Therefore, flat-line spectra in general are referred to as white, whether they represent light or another type of wave phenomenon. In radio and telecommunications, the frequency spectrum can be shared among many different broadcasters.
The radio spectrum is the part of the electromagnetic spectrum corresponding to frequencies lower below 300 GHz, which corresponds to wavelengths longer than about 1 mm. The microwave spectrum corresponds to frequencies between 300 MHz and 300 GHz and wavelengths between one meter and one millimeter; each broadcast radio and TV station transmits a wave on an assigned frequency range, called a channel. When many broadcasters are present, the radio spectrum consists of the sum of all the individual channels, each carrying separate information, spread across a wide frequency spectrum. Any particular radio receiver will detect a single function of amplitude vs. time. The radio uses a tuned circuit or tuner to select a single channel or frequency band and demodulate or decode the information from that broadcaster. If we made a graph of the strength of each channel vs. the frequency of the tuner, it would be the frequency spectrum of the antenna signal. In astronomical spectroscopy, the strength and position of absorption and emission lines, as well as the overall spectral energy distribution of the continuum, reveal many properties of astronomical objects.
Stellar classification is the categorisation of stars based on their characteristic electromagnetic spectra. The spectral flux density is used to represent the spectrum such as a star. In radiometry and colorimetry, the spectral power distribution of a light source is a measure o
Mixing length model
In fluid dynamics, the mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a Newtonian fluid boundary layer by means of an eddy viscosity. The model was developed by Ludwig Prandtl in the early 20th century. Prandtl himself had reservations about the model, describing it as, "only a rough approximation," but it has been used in numerous fields since, including atmospheric science and stellar structure; the mixing length is conceptually analogous to the concept of mean free path in thermodynamics: a fluid parcel will conserve its properties for a characteristic length, ξ ′, before mixing with the surrounding fluid. Prandtl described that the mixing length, In the figure above, temperature, T, is conserved for a certain distance as a parcel moves across a temperature gradient; the fluctuation in temperature that the parcel experienced throughout the process is T ′. So T ′ can be seen as the temperature deviation from its surrounding environment after it has moved over this mixing length ξ ′.
To begin, we must first be able to express quantities as the sums of their varying components and fluctuating components. This process is known as Reynolds decomposition. Temperature can be expressed as: T = T ¯ + T ′, where T ¯, is the varying component and T ′ is the fluctuating component. In the above picture, T ′ can be expressed in terms of the mixing length: T ′ = − ξ ′ ∂ T ¯ ∂ z; the fluctuating components of velocity, u ′, v ′, w ′, can be expressed in a similar fashion: u ′ = − ξ ′ ∂ u ¯ ∂ z, v ′ = − ξ ′ ∂ v ¯ ∂ z, w ′ = − ξ ′ ∂ w ¯ ∂ z. although the theoretical justification for doing so is weaker, as the pressure gradient force can alter the fluctuating components. Moreover, for the case of vertical velocity, w ′ must be in a neutrally stratified fluid. Taking the product of horizontal and vertical fluctuations gives us: u ′ w ′ ¯ = ξ ′ 2 ¯ | ∂ w ¯ ∂ z | ∂ u ¯ ∂ z; the eddy viscosity is defined from the equation above as: K m = ξ ′ 2 ¯ | ∂ w ¯ ∂ z |, so we have the eddy viscosity, K m expressed in terms of the mixing length, ξ ′.
Reynolds stress equation model Law of the wall
Wolf–Rayet stars abbreviated as WR stars, are a rare heterogeneous set of stars with unusual spectra showing prominent broad emission lines of ionised helium and ionised nitrogen or carbon. The spectra indicate high surface enhancement of heavy elements, depletion of hydrogen, strong stellar winds, their surface temperatures range from 30,000 K to around 200,000 K, hotter than all other stars. Classic Wolf–Rayet stars are evolved, massive stars that have lost their outer hydrogen and are fusing helium or heavier elements in the core. A subset of the population I WR stars show hydrogen lines in their spectra and are known as WNh stars. A separate group of stars with WR spectra are the central stars of planetary nebulae, post asymptotic giant branch stars that were similar to the Sun while on the main sequence, but have now ceased fusion and shed their atmospheres to reveal a bare carbon-oxygen core. All Wolf–Rayet stars are luminous objects due to their high temperatures—thousands of times the bolometric luminosity of the Sun for the CSPNe, hundreds of thousands L☉ for the Population I WR stars, to over a million L☉ for the WNh stars—although not exceptionally bright visually since most of their radiation output is in the ultraviolet.
The naked-eye stars Gamma Velorum and Theta Muscae, as well as the most massive known star, R136a1 in 30 Doradus, are all Wolf–Rayet stars. In 1867, using the 40 cm Foucault telescope at the Paris Observatory, astronomers Charles Wolf and Georges Rayet discovered three stars in the constellation Cygnus that displayed broad emission bands on an otherwise continuous spectrum. Most stars only display absorption lines or bands in their spectra, as a result of overlying elements absorbing light energy at specific frequencies, so these were unusual objects; the nature of the emission bands in the spectra of a Wolf–Rayet star remained a mystery for several decades. Edward C. Pickering theorized that the lines were caused by an unusual state of hydrogen, it was found that this "Pickering series" of lines followed a pattern similar to the Balmer series, when half-integer quantum numbers were substituted, it was shown that the lines resulted from the presence of helium. Pickering noted similarities between Wolf–Rayet spectra and nebular spectra, this similarity led to the conclusion that some or all Wolf Rayet stars were the central stars of planetary nebulae.
By 1929, the width of the emission bands was being attributed to Doppler broadening, hence that the gas surrounding these stars must be moving with velocities of 300–2400 km/s along the line of sight. The conclusion was that a Wolf–Rayet star is continually ejecting gas into space, producing an expanding envelope of nebulous gas; the force ejecting the gas at the high velocities observed is radiation pressure. It was well known that many stars with Wolf Rayet type spectra were the central stars of planetary nebulae, but that many were not associated with an obvious planetary nebula or any visible nebulosity at all. In addition to helium, emission lines of carbon and nitrogen were identified in the spectra of Wolf–Rayet stars. In 1938, the International Astronomical Union classified the spectra of Wolf–Rayet stars into types WN and WC, depending on whether the spectrum was dominated by lines of nitrogen or carbon-oxygen respectively. In 1969, several CSPNe with strong OVI emissions lines were grouped under a new "OVI sequence", or just OVI type.
These were subsequently referred to as stars. Similar stars not associated with planetary nebulae were described shortly after and the WO classification was also adopted for population I WR stars; the understanding that certain late, sometimes not-so-late, WN stars with hydrogen lines in their spectra are at a different stage of evolution from hydrogen-free WR stars has led to the introduction of the term WNh to distinguish these stars from other WN stars. They were referred to as WNL stars, although there are late-type WN stars without hydrogen as well as WR stars with hydrogen as early as WN5. Wolf–Rayet stars were named on the basis of the strong broad emission lines in their spectra, identified with helium, carbon and oxygen, but with hydrogen lines weak or absent; the first system of classification split these into stars with dominant lines of ionised nitrogen and those with dominant lines of ionised carbon and sometimes oxygen, referred to as WN and WC respectively. The two classes WN and WC were further split into temperature sequences WN5-WN8 and WC6-WC8 based on the relative strengths of the 541.1nm HeII and 587.5 nm HeI lines.
Wolf–Rayet emission lines have a broadened absorption wing suggesting circumstellar material. A WO sequence has been separated from the WC sequence for hotter stars where emission of ionised oxygen dominates that of ionised carbon, although the actual proportions of those elements in the stars are to be comparable. WC and WO spectra are formally distinguished based on the absence of CIII emission. WC spectra generally lack the OVI lines that are strong in WO spectra; the WN spectral sequence was expanded to include WN2 - WN9, the definitions refined based on the relative strengths of the NIII lines at 463.4-464.1 nm and 531.4 nm, the NIV lines at 347.9-348.4 nm and 405.8 nm, the NV lines at 460.3 nm, 461.9 nm, 493.3-4
The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/phos, photos meaning "light" and σφαῖρα/sphaira meaning "sphere", in reference to it being a spherical surface, perceived to emit light, it extends into a star's surface until the plasma becomes opaque, equivalent to an optical depth of 2/3, or equivalently, a depth from which 50% of light will escape without being scattered. In other words, a photosphere is the deepest region of a luminous object a star, transparent to photons of certain wavelengths; the surface of a star is defined to have a temperature given by the effective temperature in the Stefan–Boltzmann law. Stars, except neutron stars, have no liquid surface. Therefore, the photosphere is used to describe the Sun's or another star's visual surface; the Sun is composed of the chemical elements hydrogen and helium. All heavier elements, called metals in astronomy, account for less than 2% of the mass, with oxygen, carbon and iron being the most abundant.
The Sun's photosphere has a temperature between 4,500 and 6,000 K and a density somewhere around 1×10−3 to 1×10−6 kg/m3. The Sun's photosphere is around 100 kilometers thick, is composed of convection cells called granules—cells of plasma each 1000 kilometers in diameter with hot rising plasma in the center and cooler plasma falling in the narrow spaces between them, flowing at velocities of 7 kilometer per second; each granule has a lifespan of only about twenty minutes, resulting in a continually shifting "boiling" pattern. Grouping the typical granules are super granules up to 30,000 kilometers in diameter with lifespans of up to 24 hours and flow speeds of about 500 meter per second, carrying magnetic field bundles to the edges of the cells. Other magnetically-related phenomena include sunspots and solar faculae dispersed between the granules; these details are too fine to be seen. The Sun's visible atmosphere has other layers above the photosphere: the 2,000 kilometer-deep chromosphere lies just between the photosphere and the much hotter but more tenuous corona.
Other "surface features" on the photosphere are solar sunspots. Animated explanation of the Photosphere. Animated explanation of the temperature of the Photosphere. Solar Lower Atmosphere and Magnetism