Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars. The components for proper motion in the equatorial coordinate system are given in the direction of right ascension and of declination, their combined value is computed as the total proper motion. It has dimensions of angle per time arcseconds per year or milliarcseconds per year. Knowledge of the proper motion and radial velocity allows calculations of true stellar motion or velocity in space in respect to the Sun, by coordinate transformation, the motion in respect to the Milky Way. Proper motion is not "proper", because it includes a component due to the motion of the Solar System itself. Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time.
Ursa Major or Crux, for example, looks nearly the same now. However, precise long-term observations show that the constellations change shape, albeit slowly, that each star has an independent motion; this motion is caused by the movement of the stars relative to the Solar System. The Sun travels in a nearly circular orbit about the center of the Milky Way at a speed of about 220 km/s at a radius of 8 kPc from the center, which can be taken as the rate of rotation of the Milky Way itself at this radius; the proper motion is a two-dimensional vector and is thus defined by two quantities: its position angle and its magnitude. The first quantity indicates the direction of the proper motion on the celestial sphere, the second quantity is the motion's magnitude expressed in arcseconds per year or milliarcsecond per year. Proper motion may alternatively be defined by the angular changes per year in the star's right ascension and declination, using a constant epoch in defining these; the components of proper motion by convention are arrived at.
Suppose an object moves from coordinates to coordinates in a time Δt. The proper motions are given by: μ α = α 2 − α 1 Δ t, μ δ = δ 2 − δ 1 Δ t; the magnitude of the proper motion μ is given by the Pythagorean theorem: μ 2 = μ δ 2 + μ α 2 ⋅ cos 2 δ, μ 2 = μ δ 2 + μ α ∗ 2, where δ is the declination. The factor in cos2δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cosδ, for example, zero at the pole. Thus, the component of velocity parallel to the equator corresponding to a given angular change in α is smaller the further north the object's location; the change μα, which must be multiplied by cosδ to become a component of the proper motion, is sometimes called the "proper motion in right ascension", μδ the "proper motion in declination". If the proper motion in right ascension has been converted by cosδ, the result is designated μα*. For example, the proper motion results in right ascension in the Hipparcos Catalogue have been converted. Hence, the individual proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions.
The position angle θ is related to these components by: μ sin θ = μ α cos δ = μ α ∗, μ cos θ = μ δ. Motions in equatorial coordinates can be converted to motions in galactic coordinates. For the majority of stars seen in the sky, the observed proper motions are small and unremarkable; such stars are either faint or are distant, have changes of below 10 milliarcseconds per year, do not appear to move appreciably over many millennia. A few do have significant motions, are called high-proper motion stars. Motions can be in seemingly random directions. Two or more stars, double stars or open star clusters, which are moving in similar directions, exhibit so-called shared or common proper motion, suggesting they may be gravitationally attached or share similar motion in space. Barnard's Star has the largest proper motion of all stars, moving at 10.3 seconds of arc per year. L
In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power. In SI units luminosity is measured in joules per second or watts. Values for luminosity are given in the terms of the luminosity of the Sun, L⊙. Luminosity can be given in terms of the astronomical magnitude system: the absolute bolometric magnitude of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term brightness in astronomy is used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness.
The distance determined by luminosity measures can be somewhat ambiguous, is thus sometimes called the luminosity distance. In astronomy, luminosity is the amount of electromagnetic energy; when not qualified, the term "luminosity" means bolometric luminosity, measured either in the SI units, watts, or in terms of solar luminosities. A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. A star radiates neutrinos, which carry off some energy, contributing to the star's total luminosity; the IAU has defined a nominal solar luminosity of 3.828×1026 W to promote publication of consistent and comparable values in units of the solar luminosity. While bolometers do exist, they cannot be used to measure the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum, most to match those measurements.
In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infra-red. Bolometric luminosities can be calculated using a bolometric correction to a luminosity in a particular passband; the term luminosity is used in relation to particular passbands such as a visual luminosity of K-band luminosity. These are not luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist; some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density. A star's luminosity can be determined from two stellar characteristics: size and effective temperature; the former is represented in terms of solar radii, R⊙, while the latter is represented in kelvins, but in most cases neither can be measured directly.
To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth. Both can be measured with great accuracy in certain cases, with cool supergiants having large angular diameters, some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is a number that represents the temperature of a black body that would reproduce the luminosity, it cannot be measured directly, but it can be estimated from the spectrum. An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction, present, a condition that arises because of gas and dust present in the interstellar medium, the Earth's atmosphere, circumstellar matter.
One of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium. In the current system of stellar classification, stars are grouped according to temperature, with the massive young and energetic Class O stars boasting temperatures in excess of 30,000 K while the less massive older Class M stars exhibit temperatures less than 3,500 K; because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes; the most luminous stars are always young stars, no more than a few million years for the most extreme.
In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are
Not to be confused with warm and cool colors. The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of a color comparable to that of the light source. Color temperature is a characteristic of visible light that has important applications in lighting, videography, manufacturing, astrophysics and other fields. In practice, color temperature is meaningful only for light sources that do in fact correspond somewhat to the radiation of some black body, i.e. light in a range going from red to orange to yellow to white to blueish white. Color temperature is conventionally expressed in kelvins, using the symbol K, a unit of measure for absolute temperature. Color temperatures over 5000 K are called "cool colors", while lower color temperatures are called "warm colors". "Warm" in this context is an analogy to radiated heat flux of traditional incandescent lighting rather than temperature. The spectral peak of warm-coloured light is closer to infrared, most natural warm-coloured light sources emit significant infrared radiation.
The fact that "warm" lighting in this sense has a "cooler" color temperature leads to confusion. The color temperature of the electromagnetic radiation emitted from an ideal black body is defined as its surface temperature in kelvins, or alternatively in micro reciprocal degrees; this permits the definition of a standard. To the extent that a hot surface emits thermal radiation but is not an ideal black-body radiator, the color temperature of the light is not the actual temperature of the surface. An incandescent lamp's light is thermal radiation, the bulb approximates an ideal black-body radiator, so its color temperature is the temperature of the filament, thus a low temperature emits a dull red and a high temperature emits the white of the traditional incandescent light bulb. Metal workers are able to judge the temperature of hot metals by their color, from dark red to orange-white and white. Many other light sources, such as fluorescent lamps, or LEDs emit light by processes other than thermal radiation.
This means. These sources are assigned. CCT is the color temperature of a black-body radiator which to human color perception most matches the light from the lamp; because such an approximation is not required for incandescent light, the CCT for an incandescent light is its unadjusted temperature, derived from comparison to a black-body radiator. The Sun approximates a black-body radiator; the effective temperature, defined by the total radiative power per square unit, is about 5780 K. The color temperature of sunlight above the atmosphere is about 5900 K; as the Sun crosses the sky, it may appear to be red, yellow or white, depending on its position. The changing color of the Sun over the course of the day is a result of the scattering of light and is not due to changes in black-body radiation; the blue color of the sky is caused by Rayleigh scattering of the sunlight by the atmosphere, which tends to scatter blue light more than red light. Some early morning and evening light has a lower color temperature due to increased low-wavelength light scattering by the Tyndall effect.
Daylight has a spectrum similar to that of a black body with a correlated color temperature of 6500 K or 5500 K. For colors based on black-body theory, blue occurs at higher temperatures, whereas red occurs at lower temperatures; this is the opposite of the cultural associations attributed to colors, in which "red" is "hot", "blue" is "cold". For lighting building interiors, it is important to take into account the color temperature of illumination. A warmer light is used in public areas to promote relaxation, while a cooler light is used to enhance concentration, for example in schools and offices. CCT dimming for LED technology is regarded as a difficult task, since binning and temperature drift effects of LEDs change the actual color value output. Here feedback loop systems are used, for example with color sensors, to monitor and control the color output of multiple color mixing LEDs. In fishkeeping, color temperature has different foci in the various branches. In freshwater aquaria, color temperature is of concern only for producing a more attractive display.
Lights tend to be designed to produce an attractive spectrum, sometimes with secondary attention paid to keeping the plants in the aquaria alive. In a saltwater/reef aquarium, color temperature is an essential part of tank health. Within about 400 to 3000 nanometers, light of shorter wavelength can penetrate deeper into water than longer wavelengths, providing essential energy sources to the algae hosted in coral; this is equivalent to an increase of color temperature with water depth in this spectral range. Because coral live in shallow water and receive intense, direct tropical sunlight, the focus was once on simulating this situation with 6500 K lights. In the meantime higher temperature light sources have become more popular, first with 10000 K and more 16000 K and 20000 K. Actinic lighting at the violet end of the visible range is used to allow night viewing without increasing algae bloom or enhancing photosynthesis, to make the somewhat fl
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with spectral lines; each line indicates a particular chemical element or molecule, with the line strength indicating the abundance of that element. The strengths of the different spectral lines vary due to the temperature of the photosphere, although in some cases there are true abundance differences; the spectral class of a star is a short code summarizing the ionization state, giving an objective measure of the photosphere's temperature. Most stars are classified under the Morgan-Keenan system using the letters O, B, A, F, G, K, M, a sequence from the hottest to the coolest; each letter class is subdivided using a numeric digit with 0 being hottest and 9 being coolest. The sequence has been expanded with classes for other stars and star-like objects that do not fit in the classical system, such as class D for white dwarfs and classes S and C for carbon stars.
In the MK system, a luminosity class is added to the spectral class using Roman numerals. This is based on the width of certain absorption lines in the star's spectrum, which vary with the density of the atmosphere and so distinguish giant stars from dwarfs. Luminosity class 0 or Ia+ is used for hypergiants, class I for supergiants, class II for bright giants, class III for regular giants, class IV for sub-giants, class V for main-sequence stars, class sd for sub-dwarfs, class D for white dwarfs; the full spectral class for the Sun is G2V, indicating a main-sequence star with a temperature around 5,800 K. The conventional color description takes into account only the peak of the stellar spectrum. In actuality, stars radiate in all parts of the spectrum; because all spectral colors combined appear white, the actual apparent colors the human eye would observe are far lighter than the conventional color descriptions would suggest. This characteristic of'lightness' indicates that the simplified assignment of colors within the spectrum can be misleading.
Excluding color-contrast illusions in dim light, there are indigo, or violet stars. Red dwarfs are a deep shade of orange, brown dwarfs do not appear brown, but hypothetically would appear dim grey to a nearby observer; the modern classification system is known as the Morgan–Keenan classification. Each star is assigned a spectral class from the older Harvard spectral classification and a luminosity class using Roman numerals as explained below, forming the star's spectral type. Other modern stellar classification systems, such as the UBV system, are based on color indexes—the measured differences in three or more color magnitudes; those numbers are given labels such as "U-V" or "B-V", which represent the colors passed by two standard filters. The Harvard system is a one-dimensional classification scheme by astronomer Annie Jump Cannon, who re-ordered and simplified a prior alphabetical system. Stars are grouped according to their spectral characteristics by single letters of the alphabet, optionally with numeric subdivisions.
Main-sequence stars vary in surface temperature from 2,000 to 50,000 K, whereas more-evolved stars can have temperatures above 100,000 K. Physically, the classes indicate the temperature of the star's atmosphere and are listed from hottest to coldest; the spectral classes O through M, as well as other more specialized classes discussed are subdivided by Arabic numerals, where 0 denotes the hottest stars of a given class. For example, A0 denotes A9 denotes the coolest ones. Fractional numbers are allowed; the Sun is classified as G2. Conventional color descriptions are traditional in astronomy, represent colors relative to the mean color of an A class star, considered to be white; the apparent color descriptions are what the observer would see if trying to describe the stars under a dark sky without aid to the eye, or with binoculars. However, most stars in the sky, except the brightest ones, appear white or bluish white to the unaided eye because they are too dim for color vision to work. Red supergiants are cooler and redder than dwarfs of the same spectral type, stars with particular spectral features such as carbon stars may be far redder than any black body.
The fact that the Harvard classification of a star indicated its surface or photospheric temperature was not understood until after its development, though by the time the first Hertzsprung–Russell diagram was formulated, this was suspected to be true. In the 1920s, the Indian physicist Meghnad Saha derived a theory of ionization by extending well-known ideas in physical chemistry pertaining to the dissociation of molecules to the ionization of atoms. First he applied it to the solar chromosphere to stellar spectra. Harvard astronomer Cecilia Payne demonstrated that the O-B-A-F-G-K-M spectral sequence is a sequence in temperature; because the classification sequence predates our understanding that it is a temperature sequence, the placement of a spectrum into a given subtype, such as B3 or A7, depends upon estimates of the strengths of absorption features in stellar spectra. As a result, these subtypes are not evenly divided into any sort of mathematically representable intervals; the Yerkes spectral classification called the MKK system from the authors' initial
A white dwarf called a degenerate dwarf, is a stellar core remnant composed of electron-degenerate matter. A white dwarf is dense: its mass is comparable to that of the Sun, while its volume is comparable to that of Earth. A white dwarf's faint luminosity comes from the emission of stored thermal energy; the nearest known white dwarf is Sirius B, at 8.6 light years, the smaller component of the Sirius binary star. There are thought to be eight white dwarfs among the hundred star systems nearest the Sun; the unusual faintness of white dwarfs was first recognized in 1910. The name white dwarf was coined by Willem Luyten in 1922. White dwarfs are thought to be the final evolutionary state of stars whose mass is not high enough to become a neutron star, that of about 10 solar masses; this includes over 97% of the other stars in the Milky Way. § 1. After the hydrogen-fusing period of a main-sequence star of low or medium mass ends, such a star will expand to a red giant during which it fuses helium to carbon and oxygen in its core by the triple-alpha process.
If a red giant has insufficient mass to generate the core temperatures required to fuse carbon, an inert mass of carbon and oxygen will build up at its center. After such a star sheds its outer layers and forms a planetary nebula, it will leave behind a core, the remnant white dwarf. White dwarfs are composed of carbon and oxygen. If the mass of the progenitor is between 8 and 10.5 solar masses, the core temperature will be sufficient to fuse carbon but not neon, in which case an oxygen–neon–magnesium white dwarf may form. Stars of low mass will not be able to fuse helium, hence, a helium white dwarf may form by mass loss in binary systems; the material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy. As a result, it cannot support itself by the heat generated by fusion against gravitational collapse, but is supported only by electron degeneracy pressure, causing it to be dense; the physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit—approximately 1.44 times of M☉—beyond which it cannot be supported by electron degeneracy pressure.
A carbon-oxygen white dwarf that approaches this mass limit by mass transfer from a companion star, may explode as a type Ia supernova via a process known as carbon detonation. A white dwarf is hot when it forms, but because it has no source of energy, it will cool as it radiates its energy; this means that its radiation, which has a high color temperature, will lessen and redden with time. Over a long time, a white dwarf will cool and its material will begin to crystallize, starting with the core; the star's low temperature means it will no longer emit significant heat or light, it will become a cold black dwarf. Because the length of time it takes for a white dwarf to reach this state is calculated to be longer than the current age of the universe, it is thought that no black dwarfs yet exist; the oldest white dwarfs still radiate at temperatures of a few thousand kelvins. The first white dwarf discovered was in the triple star system of 40 Eridani, which contains the bright main sequence star 40 Eridani A, orbited at a distance by the closer binary system of the white dwarf 40 Eridani B and the main sequence red dwarf 40 Eridani C.
The pair 40 Eridani B/C was discovered by William Herschel on 31 January 1783. In 1910, Henry Norris Russell, Edward Charles Pickering and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white. In 1939, Russell looked back on the discovery:, p. 1 I was visiting my friend and generous benefactor, Prof. Edward C. Pickering. With characteristic kindness, he had volunteered to have the spectra observed for all the stars—including comparison stars—which had been observed in the observations for stellar parallax which Hinks and I made at Cambridge, I discussed; this piece of routine work proved fruitful—it led to the discovery that all the stars of faint absolute magnitude were of spectral class M. In conversation on this subject, I asked Pickering about certain other faint stars, not on my list, mentioning in particular 40 Eridani B. Characteristically, he sent a note to the Observatory office and before long the answer came that the spectrum of this star was A.
I knew enough about it in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would have called "possible" values of the surface brightness and density. I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a pretty rule of stellar characteristics; the spectral type of 40 Eridani B was described in 1914 by Walter Adams. The white dwarf companion of Sirius, Sirius B, was next to be discovered. During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used position measurements to determine that the stars Sirius and Procyon were changing their positions periodically. In 1844 he predicted that both stars had unseen companions: If we were to regard Sirius and Procyon as double stars, the change of their motions would not surprise us.
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is used as an estimate of a body's surface temperature when the body's emissivity curve is not known; when the star's or planet's net emissivity in the relevant wavelength band is less than unity, the actual temperature of the body will be higher than the effective temperature. The net emissivity may be low due to surface or atmospheric properties, including greenhouse effect; the effective temperature of a star is the temperature of a black body with the same luminosity per surface area as the star and is defined according to the Stefan–Boltzmann law FBol = σTeff4. Notice that the total luminosity of a star is L = 4πR2σTeff4, where R is the stellar radius; the definition of the stellar radius is not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius, defined by a certain value of the Rosseland optical depth within the stellar atmosphere.
The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the Hertzsprung–Russell diagram. Both effective temperature and bolometric luminosity depend on the chemical composition of a star; the effective temperature of our Sun is around 5780 kelvins. Stars have a decreasing temperature gradient; the "core temperature" of the Sun—the temperature at the centre of the Sun where nuclear reactions take place—is estimated to be 15,000,000 K. The color index of a star indicates its temperature from the cool—by stellar standards—red M stars that radiate in the infrared to the hot blue O stars that radiate in the ultraviolet; the effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area. From the warmest surfaces to the coolest is the sequence of stellar classifications known as O, B, A, F, G, K, M. A red star could be a tiny red dwarf, a star of feeble energy production and a small surface or a bloated giant or supergiant star such as Antares or Betelgeuse, either of which generates far greater energy but passes it through a surface so large that the star radiates little per unit of surface area.
A star near the middle of the spectrum, such as the modest Sun or the giant Capella radiates more energy per unit of surface area than the feeble red dwarf stars or the bloated supergiants, but much less than such a white or blue star as Vega or Rigel. To find the effective temperature of a planet, it can be calculated by equating the power received by the planet to the known power emitted by a blackbody of temperature T. Take the case of a planet at a distance D from the star, of luminosity L. Assuming the star radiates isotropically and that the planet is a long way from the star, the power absorbed by the planet is given by treating the planet as a disc of radius r, which intercepts some of the power, spread over the surface of a sphere of radius D; the calculation assumes the planet reflects some of the incoming radiation by incorporating a parameter called the albedo. An albedo of 1 means that all the radiation is reflected, an albedo of 0 means all of it is absorbed; the expression for absorbed power is then: P a b s = L r 2 4 D 2 The next assumption we can make is that the entire planet is at the same temperature T, that the planet radiates as a blackbody.
The Stefan–Boltzmann law gives an expression for the power radiated by the planet: P r a d = 4 π r 2 σ T 4 Equating these two expressions and rearranging gives an expression for the effective temperature: T = L 16 π σ D 2 4 Note that the planet's radius has cancelled out of the final expression. The effective temperature for Jupiter from this calculation is 88 K and 51 Pegasi b is 1,258 K. A better estimate of effective temperature for some planets, such as Jupiter, would need to include the internal heating as a power input; the actual temperature depends on atmosphere effects. The actual temperature from spectroscopic analysis for HD 209458 b is 1,130 K, but the effective temperature is 1,359 K; the internal heating within Jupiter raises the effective temperature to about 152 K. The surface temperature of a planet can be estimated by modifying the effective-temperature calculation to account for emissivity and temperature variation; the area of the planet that absorbs the power from the star is Aabs, some fraction of the total surface area Atotal = 4πr2, where r is the radius of the planet.
This area intercepts some of the power, spread over the surface of a sphere of radius D. We allow the planet to reflect some of the incoming radiation by incorporating a parameter a called the albedo. An albedo of 1 means that all the radiation is reflected, an albedo