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
The Solar System is the gravitationally bound planetary system of the Sun and the objects that orbit it, either directly or indirectly. Of the objects that orbit the Sun directly, the largest are the eight planets, with the remainder being smaller objects, such as the five dwarf planets and small Solar System bodies. Of the objects that orbit the Sun indirectly—the moons—two are larger than the smallest planet, Mercury; the Solar System formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud. The vast majority of the system's mass is in the Sun, with the majority of the remaining mass contained in Jupiter; the four smaller inner planets, Venus and Mars, are terrestrial planets, being composed of rock and metal. The four outer planets are giant planets, being more massive than the terrestrials; the two largest and Saturn, are gas giants, being composed of hydrogen and helium. All eight planets have circular orbits that lie within a nearly flat disc called the ecliptic.
The Solar System contains smaller objects. The asteroid belt, which lies between the orbits of Mars and Jupiter contains objects composed, like the terrestrial planets, of rock and metal. Beyond Neptune's orbit lie the Kuiper belt and scattered disc, which are populations of trans-Neptunian objects composed of ices, beyond them a newly discovered population of sednoids. Within these populations are several dozen to tens of thousands of objects large enough that they have been rounded by their own gravity; such objects are categorized as dwarf planets. Identified dwarf planets include the trans-Neptunian objects Pluto and Eris. In addition to these two regions, various other small-body populations, including comets and interplanetary dust clouds travel between regions. Six of the planets, at least four of the dwarf planets, many of the smaller bodies are orbited by natural satellites termed "moons" after the Moon; each of the outer planets is encircled by planetary rings of dust and other small objects.
The solar wind, a stream of charged particles flowing outwards from the Sun, creates a bubble-like region in the interstellar medium known as the heliosphere. The heliopause is the point at which pressure from the solar wind is equal to the opposing pressure of the interstellar medium; the Oort cloud, thought to be the source for long-period comets, may exist at a distance a thousand times further than the heliosphere. The Solar System is located in the Orion Arm, 26,000 light-years from the center of the Milky Way galaxy. For most of history, humanity did not understand the concept of the Solar System. Most people up to the Late Middle Ages–Renaissance believed Earth to be stationary at the centre of the universe and categorically different from the divine or ethereal objects that moved through the sky. Although the Greek philosopher Aristarchus of Samos had speculated on a heliocentric reordering of the cosmos, Nicolaus Copernicus was the first to develop a mathematically predictive heliocentric system.
In the 17th century, Galileo discovered that the Sun was marked with sunspots, that Jupiter had four satellites in orbit around it. Christiaan Huygens followed on from Galileo's discoveries by discovering Saturn's moon Titan and the shape of the rings of Saturn. Edmond Halley realised in 1705 that repeated sightings of a comet were recording the same object, returning once every 75–76 years; this was the first evidence that anything other than the planets orbited the Sun. Around this time, the term "Solar System" first appeared in English. In 1838, Friedrich Bessel measured a stellar parallax, an apparent shift in the position of a star created by Earth's motion around the Sun, providing the first direct, experimental proof of heliocentrism. Improvements in observational astronomy and the use of unmanned spacecraft have since enabled the detailed investigation of other bodies orbiting the Sun; the principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99.86% of the system's known mass and dominates it gravitationally.
The Sun's four largest orbiting bodies, the giant planets, account for 99% of the remaining mass, with Jupiter and Saturn together comprising more than 90%. The remaining objects of the Solar System together comprise less than 0.002% of the Solar System's total mass. Most large objects in orbit around the Sun lie near the plane of Earth's orbit, known as the ecliptic; the planets are close to the ecliptic, whereas comets and Kuiper belt objects are at greater angles to it. All the planets, most other objects, orbit the Sun in the same direction that the Sun is rotating. There are exceptions, such as Halley's Comet; the overall structure of the charted regions of the Solar System consists of the Sun, four small inner planets surrounded by a belt of rocky asteroids, four giant planets surrounded by the Kuiper belt of icy objects. Astronomers sometimes informally divide this structure into separate regions; the inner Solar System includes the asteroid belt. The outer Solar System is including the four giant planets.
Since the discovery of the Kuiper belt, the outermost parts of the Solar Sys
A comet is an icy, small Solar System body that, when passing close to the Sun and begins to release gases, a process called outgassing. This produces a visible atmosphere or coma, sometimes a tail; these phenomena are due to the effects of solar radiation and the solar wind acting upon the nucleus of the comet. Comet nuclei range from a few hundred metres to tens of kilometres across and are composed of loose collections of ice and small rocky particles; the coma may be up to 15 times the Earth's diameter, while the tail may stretch one astronomical unit. If sufficiently bright, a comet may be seen from the Earth without the aid of a telescope and may subtend an arc of 30° across the sky. Comets have been recorded since ancient times by many cultures. Comets have eccentric elliptical orbits, they have a wide range of orbital periods, ranging from several years to several millions of years. Short-period comets originate in the Kuiper belt or its associated scattered disc, which lie beyond the orbit of Neptune.
Long-period comets are thought to originate in the Oort cloud, a spherical cloud of icy bodies extending from outside the Kuiper belt to halfway to the nearest star. Long-period comets are set in motion towards the Sun from the Oort cloud by gravitational perturbations caused by passing stars and the galactic tide. Hyperbolic comets may pass once through the inner Solar System before being flung to interstellar space; the appearance of a comet is called an apparition. Comets are distinguished from asteroids by the presence of an extended, gravitationally unbound atmosphere surrounding their central nucleus; this atmosphere has parts termed the tail. However, extinct comets that have passed close to the Sun many times have lost nearly all of their volatile ices and dust and may come to resemble small asteroids. Asteroids are thought to have a different origin from comets, having formed inside the orbit of Jupiter rather than in the outer Solar System; the discovery of main-belt comets and active centaur minor planets has blurred the distinction between asteroids and comets.
In the early 21st century, the discovery of some minor bodies with long-period comet orbits, but characteristics of inner solar system asteroids, were called Manx comets. They are still classified as comets, such as C/2014 S3. 27 Manx comets were found from 2013 to 2017. As of July 2018 there are 6,339 known comets, a number, increasing as they are discovered. However, this represents only a tiny fraction of the total potential comet population, as the reservoir of comet-like bodies in the outer Solar System is estimated to be one trillion. One comet per year is visible to the naked eye, though many of those are faint and unspectacular. Bright examples are called "great comets". Comets have been visited by unmanned probes such as the European Space Agency's Rosetta, which became the first to land a robotic spacecraft on a comet, NASA's Deep Impact, which blasted a crater on Comet Tempel 1 to study its interior; the word comet comētēs. That, in turn, is a latinisation of the Greek κομήτης, the Oxford English Dictionary notes that the term κομήτης meant "long-haired star, comet" in Greek.
Κομήτης was derived from κομᾶν, itself derived from κόμη and was used to mean "the tail of a comet". The astronomical symbol for comets is ☄; the solid, core structure of a comet is known as the nucleus. Cometary nuclei are composed of an amalgamation of rock, water ice, frozen carbon dioxide, carbon monoxide and ammonia; as such, they are popularly described as "dirty snowballs" after Fred Whipple's model. However, some comets may have a higher dust content, leading them to be called "icy dirtballs". Research conducted in 2014 suggests that comets are like "deep fried ice cream", in that their surfaces are formed of dense crystalline ice mixed with organic compounds, while the interior ice is colder and less dense; the surface of the nucleus is dry, dusty or rocky, suggesting that the ices are hidden beneath a surface crust several metres thick. In addition to the gases mentioned, the nuclei contain a variety of organic compounds, which may include methanol, hydrogen cyanide, formaldehyde and ethane and more complex molecules such as long-chain hydrocarbons and amino acids.
In 2009, it was confirmed that the amino acid glycine had been found in the comet dust recovered by NASA's Stardust mission. In August 2011, a report, based on NASA studies of meteorites found on Earth, was published suggesting DNA and RNA components may have been formed on asteroids and comets; the outer surfaces of cometary nuclei have a low albedo, making them among the least reflective objects found in the Solar System. The Giotto space probe found that the nucleus of Halley's Comet reflects about four percent of the light that falls on it, Deep Space 1 discovered that Comet Borrelly's surface reflects less than 3.0%. The dark surface material of the nucleus may consist of complex organic compounds. Solar heating drives off lighter volatile compounds, leaving behind larger organic compounds that tend to be dark, like tar or crude oil; the low reflectivity of cometary surfaces causes them to absorb t
ArXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, astronomy, electrical engineering, computer science, quantitative biology, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month. ArXiv was made possible by the compact TeX file format, which allowed scientific papers to be transmitted over the Internet and rendered client-side. Around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Paul Ginsparg recognized the need for central storage, in August 1991 he created a central repository mailbox stored at the Los Alamos National Laboratory which could be accessed from any computer.
Additional modes of access were soon added: FTP in 1991, Gopher in 1992, the World Wide Web in 1993. The term e-print was adopted to describe the articles, it began as a physics archive, called the LANL preprint archive, but soon expanded to include astronomy, computer science, quantitative biology and, most statistics. Its original domain name was xxx.lanl.gov. Due to LANL's lack of interest in the expanding technology, in 2001 Ginsparg changed institutions to Cornell University and changed the name of the repository to arXiv.org. It is now hosted principally with eight mirrors around the world, its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv; the annual budget for arXiv is $826,000 for 2013 to 2017, funded jointly by Cornell University Library, the Simons Foundation and annual fee income from member institutions.
This model arose in 2010, when Cornell sought to broaden the financial funding of the project by asking institutions to make annual voluntary contributions based on the amount of download usage by each institution. Each member institution pledges a five-year funding commitment to support arXiv. Based on institutional usage ranking, the annual fees are set in four tiers from $1,000 to $4,400. Cornell's goal is to raise at least $504,000 per year through membership fees generated by 220 institutions. In September 2011, Cornell University Library took overall administrative and financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a life sentence". However, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. Although arXiv is not peer reviewed, a collection of moderators for each area review the submissions; the lists of moderators for many sections of arXiv are publicly available, but moderators for most of the physics sections remain unlisted.
Additionally, an "endorsement" system was introduced in 2004 as part of an effort to ensure content is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, but to check whether the paper is appropriate for the intended subject area. New authors from recognized academic institutions receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for restricting scientific inquiry. A majority of the e-prints are submitted to journals for publication, but some work, including some influential papers, remain purely as e-prints and are never published in a peer-reviewed journal. A well-known example of the latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman in November 2002.
Perelman appears content to forgo the traditional peer-reviewed journal process, stating: "If anybody is interested in my way of solving the problem, it's all there – let them go and read about it". Despite this non-traditional method of publication, other mathematicians recognized this work by offering the Fields Medal and Clay Mathematics Millennium Prizes to Perelman, both of which he refused. Papers can be submitted in any of several formats, including LaTeX, PDF printed from a word processor other than TeX or LaTeX; the submission is rejected by the arXiv software if generating the final PDF file fails, if any image file is too large, or if the total size of the submission is too large. ArXiv now allows one to store and modify an incomplete submission, only finalize the submission when ready; the time stamp on the article is set. The standard access route is through one of several mirrors. Sev
A dwarf galaxy is a small galaxy composed of about 100 million up to several billion stars, a small number compared to the Milky Way's 200–400 billion stars. The Large Magellanic Cloud, which orbits the Milky Way and contains over 30 billion stars, is sometimes classified as a dwarf galaxy. Dwarf galaxies' formation and activity are thought to be influenced by interactions with larger galaxies. Astronomers identify numerous types of dwarf galaxies, based on their composition. Current theory states that most galaxies, including dwarf galaxies, form in association with dark matter, or from gas that contains metals. However, NASA's Galaxy Evolution Explorer space probe identified new dwarf galaxies forming out of gases with low metallicity; these galaxies were located in the Leo Ring, a cloud of hydrogen and helium around two massive galaxies in the constellation Leo. Because of their small size, dwarf galaxies have been observed being pulled toward and ripped by neighbouring spiral galaxies, resulting in galaxy merger.
There are many dwarf galaxies in the Local Group. A 2007 paper has suggested that many dwarf galaxies were created by galactic tides during the early evolutions of the Milky Way and Andromeda. Tidal dwarf galaxies are produced when their gravitational masses interact. Streams of galactic material are pulled away from the parent galaxies and the halos of dark matter that surround them. A 2018 study suggests that some local dwarf galaxies formed early, during the Dark Ages within the first billion years after the big bang. More than 20 known dwarf galaxies orbit the Milky Way, recent observations have led astronomers to believe the largest globular cluster in the Milky Way, Omega Centauri, is in fact the core of a dwarf galaxy with a black hole at its centre, at some time absorbed by the Milky Way. Elliptical galaxy: dwarf elliptical galaxy Dwarf spheroidal galaxy: Once a subtype of dwarf ellipticals, now regarded as a distinct type Irregular galaxy: dwarf irregular galaxy Spiral galaxy: dwarf spiral galaxy Magellanic type dwarfs Blue compact dwarf galaxies Ultra-compact dwarf galaxies In astronomy, a blue compact dwarf galaxy is a small galaxy which contains large clusters of young, massive stars.
These stars, the brightest of which are blue, cause the galaxy. Most BCD galaxies are classified as dwarf irregular galaxies or as dwarf lenticular galaxies; because they are composed of star clusters, BCD galaxies lack a uniform shape. They consume gas intensely, which causes their stars to become violent when forming. BCD galaxies cool in the process of forming new stars; the galaxies' stars are all formed at different time periods, so the galaxies have time to cool and to build up matter to form new stars. As time passes, this star formation changes the shape of the galaxies. Nearby examples include NGC 1705, NGC 2915, NGC 3353 and UGCA 281. Ultra-compact dwarf galaxies are a class of compact galaxies with high stellar densities, discovered in the 2000s, they are thought to be on the order of 200 light years across. It is theorised that these are the cores of nucleated dwarf elliptical galaxies that have been stripped of gas and outlying stars by tidal interactions, travelling through the hearts of rich clusters.
UCDs have been found in the Virgo Cluster, Fornax Cluster, Abell 1689, the Coma Cluster, amongst others. In particular, an unprecedentedly large sample of ~ 100 UCDs has been found in the core region of the Virgo cluster by the Next Generation Virgo Cluster Survey team; the first relatively robust studies of the global properties of Virgo UCDs suggest that UCDs have distinct dynamical and structural properties from normal globular clusters. An extreme example of UCD is M60-UCD1, about 54 million light years away, which contains 200 million solar masses within a 160 light year radius. M59-UCD3 is the same size as M60-UCD1 with a half-light radius, rh, of 20 parsecs but is 40% more luminous with an apparent relative magnitude of −14.6. This makes M59-UCD3 the densest known galaxy. Based on stellar orbital velocities, two UCD in the Virgo Cluster are claimed to have supermassive black holes weighing 13% and 18% of the galaxies' masses. Galaxy morphological classification – System for categorizing galaxies based on appearance List of nearest galaxies Pea galaxy – Possibly a type of Luminous Blue Compact Galaxy, undergoing high rates of star formation Milky Way Satellite Galaxies SPACE.com article on "hobbit galaxies" Science article on "hobbit galaxies"
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, the electric potential energy of an electric charge in an electric field; the unit for energy in the International System of Units is the joule, which has the symbol J. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space; these forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
Since the work of potential forces acting on a body that moves from a start to an end position is determined only by these two positions, does not depend on the trajectory of the body, there is a function known as potential that can be evaluated at the two positions to determine this work. There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy has two components: the kinetic energy of random motions of particles and the potential energy of their mutual positions. Forces derivable from a potential are called conservative forces; the work done by a conservative force is W = − Δ U where Δ U is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential energy.
Common notations for potential energy are PE, U, V, Ep. Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity; the action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential. This work is stored in the force field, said to be stored as potential energy. If the external force is removed the force field acts on the body to perform the work as it moves the body back to the initial position, reducing the stretch of the spring or causing a body to fall. Consider a ball whose mass is m and whose height is h; the acceleration g of free fall is constant, so the weight force of the ball mg is constant. Force × displacement gives the work done, equal to the gravitational potential energy, thus U g = m g h The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position.
Potential energy is linked with forces. If the work done by a force on a body that moves from A to B does not depend on the path between these points the work of this force measured from A assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. If the work for an applied force is independent of the path the work done by the force is evaluated at the start and end of the trajectory of the point of application; this means that there is a function U, called a "potential," that can be evaluated at the two points xA and xB to obtain the work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, W = ∫ C F ⋅ d x = U − U where C is the trajectory taken from A to B; because the work done is independent of the path taken this expression is true for any trajectory, C, from A to B.
The function U is called the potential energy associated with the applied force. Examples of forces that have potential energies are spring forces. In this section the relationship between work and potential energy is presented in more detail; the line integral that defines work along curve C takes a special form if the force F is related to a scalar field φ so that F = ∇ φ = ( ∂ φ ∂ x, ∂
Star formation is the process by which dense regions within molecular clouds in interstellar space, sometimes referred to as "stellar nurseries" or "star-forming regions", collapse and form stars. As a branch of astronomy, star formation includes the study of the interstellar medium and giant molecular clouds as precursors to the star formation process, the study of protostars and young stellar objects as its immediate products, it is related to planet formation, another branch of astronomy. Star formation theory, as well as accounting for the formation of a single star, must account for the statistics of binary stars and the initial mass function. Most stars do not form in isolation but as part of a group of stars referred as star clusters or stellar associations. A spiral galaxy like the Milky Way contains stars, stellar remnants, a diffuse interstellar medium of gas and dust; the interstellar medium consists of 10−4 to 106 particles per cm3 and is composed of 70% hydrogen by mass, with most of the remaining gas consisting of helium.
This medium has been chemically enriched by trace amounts of heavier elements that were ejected from stars as they passed beyond the end of their main sequence lifetime. Higher density regions of the interstellar medium form clouds, or diffuse nebulae, where star formation takes place. In contrast to spirals, an elliptical galaxy loses the cold component of its interstellar medium within a billion years, which hinders the galaxy from forming diffuse nebulae except through mergers with other galaxies. In the dense nebulae where stars are produced, much of the hydrogen is in the molecular form, so these nebulae are called molecular clouds. Observations indicate that the coldest clouds tend to form low-mass stars, observed first in the infrared inside the clouds in visible light at their surface when the clouds dissipate, while giant molecular clouds, which are warmer, produce stars of all masses; these giant molecular clouds have typical densities of 100 particles per cm3, diameters of 100 light-years, masses of up to 6 million solar masses, an average interior temperature of 10 K.
About half the total mass of the galactic ISM is found in molecular clouds and in the Milky Way there are an estimated 6,000 molecular clouds, each with more than 100,000 M☉. The nearest nebula to the Sun where massive stars are being formed is the Orion nebula, 1,300 ly away. However, lower mass star formation is occurring about 400–450 light years distant in the ρ Ophiuchi cloud complex. A more compact site of star formation is the opaque clouds of dense gas and dust known as Bok globules, so named after the astronomer Bart Bok; these can form in association with collapsing molecular clouds or independently. The Bok globules are up to a light year across and contain a few solar masses, they can be observed as dark clouds silhouetted against bright emission background stars. Over half the known Bok globules have been found to contain newly forming stars. An interstellar cloud of gas will remain in hydrostatic equilibrium as long as the kinetic energy of the gas pressure is in balance with the potential energy of the internal gravitational force.
Mathematically this is expressed using the virial theorem, which states that, to maintain equilibrium, the gravitational potential energy must equal twice the internal thermal energy. If a cloud is massive enough that the gas pressure is insufficient to support it, the cloud will undergo gravitational collapse; the mass above which a cloud will undergo such collapse is called the Jeans mass. The Jeans mass depends on the temperature and density of the cloud, but is thousands to tens of thousands of solar masses. During cloud collapse dozens to ten thousands of stars form more or less, observable in so-called embedded clusters; the end product of a core collapse is an open cluster of stars. In triggered star formation, one of several events might occur to compress a molecular cloud and initiate its gravitational collapse. Molecular clouds may collide with each other, or a nearby supernova explosion can be a trigger, sending shocked matter into the cloud at high speeds. Alternatively, galactic collisions can trigger massive starbursts of star formation as the gas clouds in each galaxy are compressed and agitated by tidal forces.
The latter mechanism may be responsible for the formation of globular clusters. A supermassive black hole at the core of a galaxy may serve to regulate the rate of star formation in a galactic nucleus. A black hole, accreting infalling matter can become active, emitting a strong wind through a collimated relativistic jet; this can limit further star formation. Massive black holes ejecting radio-frequency-emitting particles at near-light speed can block the formation of new stars in aging galaxies. However, the radio emissions around the jets may trigger star formation. A weaker jet may trigger star formation when it collides with a cloud; as it collapses, a molecular cloud breaks into smaller and smaller pieces in a hierarchical manner, until the fragments reach stellar mass. In each of these fragments, the collapsing gas radiates away the energy gained by the release of gravitational potential energy; as the density increases, the fragments become opaque and are thus less efficient at radiating away their energy.
This inhibits further fragmentation. The fragments now condense into rotating spheres of gas. Complicating this picture of a collapsing cloud are the effects of turbulence, macroscopic flows, magnetic f