Star formation |
---|
Object classes |
Theoretical concepts |
In astronomy, the initial mass function (IMF) is an empirical function that describes the initial distribution of masses for a population of stars during star formation. [1] IMF not only describes the formation and evolution of individual stars, it also serves as an important link that describes the formation and evolution of galaxies. [1]
The IMF is often given as a probability density function (PDF) that describes the probability of a star that has a certain mass during its formation. [2] It differs from the present-day mass function (PDMF), which describes the current distribution of masses of stars, such as red giants, white dwarfs, neutron stars, and black holes, after some time of evolution away from the main sequence stars and after a certain amount of mass loss. [2] [3] Since there are not enough young clusters of stars available for the calculation of IMF, PDMF is used instead and the results are extrapolated back to IMF. [3] IMF and PDMF can be linked through the "stellar creation function". [2] Stellar creation function is defined as the number of stars per unit volume of space in a mass range and a time interval. In the case that all the main sequence stars have greater lifetimes than the galaxy, IMF and PDMF are equivalent. Similarly, IMF and PDMF are equivalent in brown dwarfs due to their unlimited lifetimes. [2]
The properties and evolution of a star are closely related to its mass, so the IMF is an important diagnostic tool for astronomers studying large quantities of stars. For example, the initial mass of a star is the primary factor of determining its colour, luminosity, radius, radiation spectrum, and quantity of materials and energy it emitted into interstellar space during its lifetime. [1] At low masses, the IMF sets the Milky Way Galaxy mass budget and the number of substellar objects that form. At intermediate masses, the IMF controls chemical enrichment of the interstellar medium. At high masses, the IMF sets the number of core collapse supernovae that occur and therefore the kinetic energy feedback.
The IMF is relatively invariant from one group of stars to another, though some observations suggest that the IMF is different in different environments, [4] [5] [6] and potentially dramatically different in early galaxies. [7]
The mass of a star can only be directly determined by applying Kepler's third law to a binary star system. However, the number of binary systems that can be directly observed is low, thus not enough samples to estimate the initial mass function. Therefore, the stellar luminosity function is used to derive a mass function (a present-day mass function, PDMF) by applying mass–luminosity relation. [2] The luminosity function requires accurate determination of distances, and the most straightforward way is by measuring stellar parallax within 20 parsecs from the earth. Although short distances yield a smaller number of samples with greater uncertainty of distances for stars with faint magnitudes (with a magnitude > 12 in the visual band), it reduces the error of distances for nearby stars, and allows accurate determination of binary star systems. [2] Since the magnitude of a star varies with its age, the determination of mass-luminosity relation should also take into account its age. For stars with masses above 0.7 M☉, it takes more than 10 billion years for their magnitude to increase substantially. For low-mass stars with below 0.13 M☉, it takes 5 × 108 years to reach main sequence stars. [2]
The IMF is often stated in terms of a series of power laws, where (sometimes also represented as ), the number of stars with masses in the range to within a specified volume of space, is proportional to , where is a dimensionless exponent.
Commonly used forms of the IMF are the Kroupa (2001) broken power law [8] and the Chabrier (2003) log-normal. [2]
Edwin E. Salpeter is the first astrophysicist who attempted to quantify IMF by applying power law into his equations. [9] His work is based upon the sun-like stars that can be easily observed with great accuracy. [2] Salpeter defined the mass function as the number of stars in a volume of space observed at a time as per logarithmic mass interval. [2] His work enabled a large number of theoretical parameters to be included in the equation while converging all these parameters into an exponent of . [1] The Salpeter IMF is
where is a constant relating to the local stellar density.
Glenn E. Miller and John M. Scalo extended the work of Salpeter, by suggesting that the IMF "flattened" () when stellar masses fell below 1 M☉. [10]
Pavel Kroupa kept between 0.5–1.0 M☉, but introduced between 0.08–0.5 M☉ and below 0.08 M☉. Above 1 M☉, correcting for unresolved binary stars also adds a fourth domain with . [8]
Chabrier gave the following expression for the density of individual stars in the Galactic disk, in units of pc −3: [2]
This expression is log-normal, meaning that the logarithm of the mass follows a Gaussian distribution up to 1 M☉.
For stellar systems (namely binaries), he gave:
The initial mass function is typically graphed on a logarithm scale of log(N) vs log(m). Such plots give approximately straight lines with a slope Γ equal to 1–α. Hence Γ is often called the slope of the initial mass function. The present-day mass function, for coeval formation, has the same slope except that it rolls off at higher masses which have evolved away from the main sequence. [11]
There are large uncertainties concerning the substellar region. In particular, the classical assumption of a single IMF covering the whole substellar and stellar mass range is being questioned, in favor of a two-component IMF to account for possible different formation modes for substellar objects—one IMF covering brown dwarfs and very-low-mass stars, and another ranging from the higher-mass brown dwarfs to the most massive stars. This leads to an overlap region approximately between 0.05–0.2 M☉ where both formation modes may account for bodies in this mass range. [12]
The possible variation of the IMF affects our interpretation of the galaxy signals and the estimation of cosmic star formation history [13] thus is important to consider.
In theory, the IMF should vary with different star-forming conditions. Higher ambient temperature increases the mass of collapsing gas clouds (Jeans mass); lower gas metallicity reduces the radiation pressure thus make the accretion of the gas easier, both lead to more massive stars being formed in a star cluster. The galaxy-wide IMF can be different from the star-cluster scale IMF and may systematically change with the galaxy star formation history. [14] [15] [16] [17]
Measurements of the local universe where single stars can be resolved are consistent with an invariant IMF [18] [19] [20] [16] [21] but the conclusion suffers from large measurement uncertainty due to the small number of massive stars and difficulties in distinguishing binary systems from the single stars. Thus IMF variation effect is not prominent enough to be observed in the local universe. However, recent photometric survey across cosmic time does suggest a potentially systematic variation of the IMF at high redshift. [22]
Systems formed at much earlier times or further from the galactic neighborhood, where star formation activity can be hundreds or even thousands time stronger than the current Milky Way, may give a better understanding. It has been consistently reported both for star clusters [23] [24] [25] and galaxies [26] [27] [28] [29] [30] [31] [32] [33] [34] that there seems to be a systematic variation of the IMF. However, the measurements are less direct. For star clusters the IMF may change over time due to complicated dynamical evolution. [lower-alpha 1]
The Local Group is the galaxy group that includes the Milky Way, where Earth is located. It has a total diameter of roughly 3 megaparsecs (10 million light-years; 9×1019 kilometres), and a total mass of the order of 2×1012 solar masses (4×1042 kg). It consists of two collections of galaxies in a "dumbbell" shape; the Milky Way and its satellites form one lobe, and the Andromeda Galaxy and its satellites constitute the other. The two collections are separated by about 800 kiloparsecs (3×10 6 ly; 2×1019 km) and are moving toward one another with a velocity of 123 km/s. The group itself is a part of the larger Virgo Supercluster, which may be a part of the Laniakea Supercluster. The exact number of galaxies in the Local Group is unknown as some are occluded by the Milky Way; however, at least 80 members are known, most of which are dwarf galaxies.
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 (ISM) and giant molecular clouds (GMC) as precursors to the star formation process, and the study of protostars and young stellar objects as its immediate products. It is closely related to planet formation, another branch of astronomy. Star formation theory, as well as accounting for the formation of a single star, must also 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.
The Andromeda Galaxy is a barred spiral galaxy and is the nearest major galaxy to the Milky Way. It was originally named the Andromeda Nebula and is cataloged as Messier 31, M31, and NGC 224. Andromeda has a D25 isophotal diameter of about 46.56 kiloparsecs (152,000 light-years) and is approximately 765 kpc (2.5 million light-years) from Earth. The galaxy's name stems from the area of Earth's sky in which it appears, the constellation of Andromeda, which itself is named after the princess who was the wife of Perseus in Greek mythology.
A supermassive black hole is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions, of times the mass of the Sun (M☉). Black holes are a class of astronomical objects that have undergone gravitational collapse, leaving behind spheroidal regions of space from which nothing can escape, including light. Observational evidence indicates that almost every large galaxy has a supermassive black hole at its center. For example, the Milky Way galaxy has a supermassive black hole at its center, corresponding to the radio source Sagittarius A*. Accretion of interstellar gas onto supermassive black holes is the process responsible for powering active galactic nuclei (AGNs) and quasars.
A stellar black hole is a black hole formed by the gravitational collapse of a star. They have masses ranging from about 5 to several tens of solar masses. They are the remnants of supernova explosions, which may be observed as a type of gamma ray burst. These black holes are also referred to as collapsars.
In astronomy, metallicity is the abundance of elements present in an object that are heavier than hydrogen and helium. Most of the normal currently detectable matter in the universe is either hydrogen or helium, and astronomers use the word "metals" as convenient shorthand for "all elements except hydrogen and helium". This word-use is distinct from the conventional chemical or physical definition of a metal as an electrically conducting solid. Stars and nebulae with relatively high abundances of heavier elements are called "metal-rich" in astrophysical terms, even though many of those elements are nonmetals in chemistry.
A satellite galaxy is a smaller companion galaxy that travels on bound orbits within the gravitational potential of a more massive and luminous host galaxy. Satellite galaxies and their constituents are bound to their host galaxy, in the same way that planets within our own solar system are gravitationally bound to the Sun. While most satellite galaxies are dwarf galaxies, satellite galaxies of large galaxy clusters can be much more massive. The Milky Way is orbited by about fifty satellite galaxies, the largest of which is the Large Magellanic Cloud.
A super star cluster (SSC) is a very massive young open cluster that is thought to be the precursor of a globular cluster. These clusters called "super" because they are relatively more luminous and contain more mass than other young star clusters. The SSC, however, does not have to physically be larger than other clusters of lower mass and luminosity. They typically contain a very large number of young, massive stars that ionize a surrounding HII region or a so-called "Ultra dense HII region (UDHII)" in the Milky Way Galaxy or in other galaxies. An SSC's HII region is in turn surrounded by a cocoon of dust. In many cases, the stars and the HII regions will be invisible to observations in certain wavelengths of light, such as the visible spectrum, due to high levels of extinction. As a result, the youngest SSCs are best observed and photographed in radio and infrared. SSCs, such as Westerlund 1 (Wd1), have been found in the Milky Way Galaxy. However, most have been observed in farther regions of the universe. In the galaxy M82 alone, 197 young SSCs have been observed and identified using the Hubble Space Telescope.
NGC 1277 is a lenticular galaxy in the constellation of Perseus. It is a member of the Perseus Cluster of galaxies and is located approximately 73 Mpc (megaparsecs) or 220 million light-years from the Milky Way. It has an apparent magnitude of about 14.7. It was discovered on December 4, 1875 by Lawrence Parsons, 4th Earl of Rosse.
Bahcall–Wolf cusp refers to a particular distribution of stars around a massive black hole at the center of a galaxy or globular cluster. If the nucleus containing the black hole is sufficiently old, exchange of orbital energy between stars drives their distribution toward a characteristic form, such that the density of stars, ρ, varies with distance from the black hole, r, as
NGC 4203 is the New General Catalogue identifier for a lenticular galaxy in the northern constellation of Coma Berenices. It was discovered on March 20, 1787 by English astronomer William Herschel, and is situated 5.5° to the northwest of the 4th magnitude star Gamma Comae Berenices and can be viewed with a small telescope. The morphological classification of NGC 4203 is SAB0−, indicating that it has a lenticular form with tightly wound spiral arms and a weak bar structure at the nucleus.
NGC 3311 is a super-giant elliptical galaxy located about 190 million light-years away in the constellation Hydra. The galaxy was discovered by astronomer John Herschel on March 30, 1835. NGC 3311 is the brightest member of the Hydra Cluster and forms a pair with NGC 3309 which along with NGC 3311, dominate the central region of the Hydra Cluster.
NGC 708 is an elliptical galaxy located 240 million light-years away in the constellation Andromeda and was discovered by astronomer William Herschel on September 21, 1786. It is classified as a cD galaxy and is the brightest member of Abell 262. NGC 708 is a weak FR I radio galaxy and is also classified as a type 2 Seyfert galaxy.
NGC 2835 is an intermediate spiral galaxy located in the constellation Hydra. It is located at a distance of circa 35 million light years from Earth, which, given its apparent dimensions, means that NGC 2835 is about 65,000 light years across. It was discovered by Wilhelm Tempel on April 13, 1884. NGC 2835 is located only 18.5 degrees from the galactic plane.
NGC 3585 is an elliptical or a lenticular galaxy located in the constellation Hydra. It is located at a distance of circa 60 million light-years from Earth, which, given its apparent dimensions, means that NGC 3585 is about 80,000 light years across. It was discovered by William Herschel on December 9, 1784.
NGC 2974 is a lenticular galaxy located in the constellation Sextans. It is located at a distance of circa 90 million light years from Earth, which, given its apparent dimensions, means that NGC 2974 is about 90,000 light years across. It was discovered by William Herschel on January 6, 1785. NGC 2974 is located in the sky about 2 and a half degrees south-south east of Iota Hydrae and more than 6 degrees northeast of Alphard. A 10th magnitude star lies next to the galaxy, thus making it a challenging object at low magnifications. NGC 2974 is part of the Herschel 400 Catalogue.
The [α/Fe] versus [Fe/H] diagram refers to the graph, commonly used in stellar and galactic astrophysics. It shows the logarithmic ratio number densities of diagnostic elements in stellar atmospheres compared to the solar value. The x-axis represents the abundance of iron (Fe) vs. hydrogen (H), that is, [Fe/H]. The y-axis represents the combination of one or several of the alpha process elements compared to iron (Fe), denoted as [α/Fe].
NGC 4324 is a lenticular galaxy located about 85 million light-years away in the constellation Virgo. It was discovered by astronomer Heinrich d'Arrest on March 4, 1862. NGC 4324 has a stellar mass of 5.62 × 1010M☉, and a baryonic mass of 5.88 × 1010M☉. The galaxy's total mass is around 5.25 × 1011M☉. NGC 4324 is notable for having a ring of star formation surrounding its nucleus. It was considered a member of the Virgo II Groups until 1999, when its distance was recalculated and it was placed in the Virgo W Group.
NGC 4393 is a spiral galaxy about 46 million light-years away in the constellation Coma Berenices. It was discovered by astronomer William Herschel on April 11, 1785. It is a member of the NGC 4274 Group, which is part of the Coma I Group or Cloud.