Can mass loss via accretion occur on stellar remnants?

Can mass loss via accretion occur on stellar remnants?

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We know that normal stars can lose mass to a binary companion. But can this happen to neutron stars and white dwarfs? Let's say a stellar black hole is being orbited by a white dwarf or neutron star. How close would they have to orbit each other for mass loss to occur, if it is possible?

Can mass loss via accretion occur on stellar remnants? - Astronomy

Stars manufacture carbon and oxygen nuclei (part of the "stellar nucleosynthesis" process) via the reactions:

The arrow -> indicates a fusion reaction.

This carbon and oxygen settles to the core of the star. If the star has an initial mass of less than 8 solar masses, it will lose its atmosphere as a planetary nebula and leave behind a white dwarf core remnant.

A white dwarf is a carbon-oxygen core remnant supported by "electron degeneracy pressure" in its main sequence and giant stages, a star is a balance between gravity (directed inward) and gas pressure (directed outward). However, in the remnant stages, different sources of pressure dominate. Electron degeneracy pressure results because the atoms in the white dwarf are so compressed that their electrons border each other. There is a law in physics that says that you can only fit a certain number of electrons into a given volume, i.e., electrons cannot overlap. White dwarf stars have reached this limit. A white dwarf cannot be compressed any further than it is.

The maximum mass of a white dwarf is 1.4 solar masses. This limiting mass is called the Chandrasekhar limit, named after the stellar theorist Subrahmanyan Chandrasehkar. He worked first in India, then England, and then the United States.

The following table shows the white dwarf mass left by stars of different main sequence masses.

Main Sequence MassResultant white dwarf mass
3 solar masses 1.2 solar masses
1.5 0.8
0.8 0.6

White dwarfs are very dense, about 1,000 kg/cc. Their diameters are a few thousands of km, similar to that of the Earth (at 12,000 km). They are stellar cores, so initially they are very hot, emerging at 10,000 kelvin or more. They cool down over time. Below 4,000 K, the carbon and oxygen crystallizes, and the star is effectively a solid.

Their hot temperatures but small sizes (and hence luminosities) place them in the lowest region of the HR diagram.

Note that in this degenerate state, the atomic nuclei are free to move around, it is the electrons that are packed close together. At masses bbove the Chandrasekhar Limit, electron degeneracy pressure can no longer support the star, and there is further collapse.

Neutron Stars

Stars with masses above 8 solar masses lose their atmospheres in a supernova explosion. The explosion works this way: massive stars manufacture iron, which is deposited in the core and which is supported by electron degeneracy pressure. When the iron core exceeds a mass of 1.4 solar masses, electron degeneracy pressure no longer holds the core up, and it collapses suddenly the core shrinks from a radius of about 3,000 km to about 20 km in one-fifth of a second.

The surrounding atmosphere, no longer sitting on the core, rushes inward, hits the core surface, and rebounds outward. This outward-moving rebound causes a fusion wave that incinerates the entire atmosphere, creating atoms heavier than iron, like copper, silver, gold, uranium, and nickel. This element-construction process is called "explosive nucleosynthesis". The atmosphere of the star continues to rush outward and becomes a large, circular gas cloud called a supernova remnant.

What happens to the core? Electron degeneracy pressure has given out and the core has collapsed. High energy photons will disintegrate the iron and other elements to free protons, neutrons, and electrons. Under the tremendous pressure of collapse, the protons and electrons merge to form neutrons, thus the entire core becomes composed of neutrons. Neutrons also have a maximum density, and the core is now held up against gravity by "neutron degeneracy pressure".

A neutron star is like a giant atomic nucleus. Its density is 100 billion (100,000,000,000) kg/cc imagine squeezing the Earth down to the size of about 10 cubic football fields.

Neutron degeneracy pressure also has a mass limit, above which it cannot support the star. This limit occurs at 3 solar masses, and is called the Oppenheimer-Volkov limit. The neutron star collapses to a theoretical object called a quark star. Quark stars are not discovered, and have mostly unknown properties. We do not yet know if they exist.


A pulsar is a rotating, magnetized neutron star. If the spin axis and the magnetic axis are not aligned, then the rotation of the magnetic field will cause light to be emitted in the direction of the magnetic axis. This light sweeps around like a lighthouse beam. We only see the light beam if we are located along its line of projection at some time in the neutron star's spin. Then, we see the light winking on and off, a light pulse that gives pulsars their name (from "pulsating radio star").

The first pulsar was discovered in 1967 with a radio telescope, by the Cambridge astronomer Jocelyn Bell. Rotation periods vary from a few milliseconds to a few seconds. A few hundred pulsars are known in our Milky Way galaxy. They are too faint to be detected in external galaxies.

The energy to generate light comes from the rotational energy of the neutron star. As the neutron star emits light, it loses its energy of rotation and so gradually slows down.

An excellent account of the properties of a neutron star is given in Robert L. Forward's sci-fi classic, "Dragon's Egg".

Black Holes


"Escape velocity" is defined as the minimum velocity needed for one object to permanently escape the gravitational influence of another. At the surface of a neutron star, the escape velocity is about half the speed of light, written as 0.5c. If the stellar remnant is so dense and massive that its escape velocity reaches (or exceeds) the speed of light, then we call the object a black hole. Different processes can create black holes. Here, the concentration will be upon black holes as stellar remnants.

The radius at which the escape velocity equals the speed of light is called the Schwarzschild radius. It is also called the "event horizon". The Schwarzschild radius is given by:

where G is the gravitational constant, M is the object's mass, and c is the speed of light. A more convenient formula is

where R is in km and M is in solar masses.

Note that the size of the collapsed object itself is probably much smaller than the event horizon radius. At the center of the black hole is an object called the "singularity". It is the term for a region where we have no way of describing its properties using our current mathematical methods. In other words, we have no way to test what happens inside the event horizon (no light is emitted, therefore, no information is available), or to predict what happens inside the event horizon. Black holes are "black" because the collapsed object itself emits no light.


Black holes can be detected from their gravitational influence on nearby objects (recall our discussion of extrasolar planets). The first black hole candidate is called Cygnus X-1, an unseen massive companion of a B0 ("B-zero") star called HDE 226868. The B0 star has a mass of 30 solar masses, the unseen companion of 7 solar masses.

This star-plus-companion pair is also a source of X-rays, which are very high energy photons. The X-rays are produced when the black hole strips gas off the surface of the B0 star. This gas circles the black hole in a disk shape, where it is compressed and friction-heated. The hot gas emits X-rays. The X-rays can change their brightness very quickly, i.e., they flicker. This flickering is presumably from hot spots on the inner edge of the disk of gas.

Material from the disk only slowly falls into the black hole. Black holes are a source of strong gravity, but gravity does NOT reach out and drag objects down it is a common misconception that black holes create some kind of local suction. Instead, collisions between gas particles will send some of them spiralling into the black hole. Gas therefore only slowly accretes into the black hole, and thus the disk is called an "accretion disk".


Black holes can slowly lose mass over time via a process called "Hawking radiation" or the "Hawking effect". This effect is named after the celebrated Cambridge astrophysicist Stephen Hawking.

Empty space can spontaneously erupt into particles that exist only for a very short time. These particles always appear in matter/anti-matter pairs. The process is called "virtual particle pair production", where the word "virtual" comes from their extremely short lifetimes. After being produced, they come back together again and annihilate each other.

Gravitational energy can be used in pair production. Hawking proposes that virtual pairs can be produced at the event horizon. One member of the pair falls into the event horizon and one escapes. The particle that escapes is now called a "real particle", and it carries away with it some of the gravitational energy of the black hole. You have to take my word for it that mass and gravitational energy are equivalent. Therefore, the escaped particle carries away some of the mass of the black hole. In this way, the black hole evaporates.

This evaporation process is very slow, but speeds up as the black hole gets less massive. A 10 kg black hole will evaporate in 15 billion years, about the age of the universe. A 5 solar mass black hole will evaporate in 10 62 years.

Hawking radiation is very faint, so that detecting it is probably not a realistic hope until the final moments of its evaporation, when the process is fastest.

Other black holes (not required reading)

Black holes can have any mass, depending upon how they are formed. Miniature black holes may have been formed when the universe was very young and dense. These are called "primordial black holes". They have not been discovered.

The accretion model that Earth and the other terrestrial planets formed from meteoric material was proposed in 1944 by Otto Schmidt, followed by the protoplanet theory of William McCrea (1960) and finally the capture theory of Michael Woolfson. [3] In 1978, Andrew Prentice resurrected the initial Laplacian ideas about planet formation and developed the modern Laplacian theory. [3] None of these models proved completely successful, and many of the proposed theories were descriptive.

The 1944 accretion model by Otto Schmidt was further developed in a quantitative way in 1969 by Viktor Safronov. [4] He calculated, in detail, the different stages of terrestrial planet formation. [5] [6] Since then, the model has been further developed using intensive numerical simulations to study planetesimal accumulation. It is now accepted that stars form by the gravitational collapse of interstellar gas. Prior to collapse, this gas is mostly in the form of molecular clouds, such as the Orion Nebula. As the cloud collapses, losing potential energy, it heats up, gaining kinetic energy, and the conservation of angular momentum ensures that the cloud forms a flattened disk—the accretion disk.

A few hundred thousand years after the Big Bang, the Universe cooled to the point where atoms could form. As the Universe continued to expand and cool, the atoms lost enough kinetic energy, and dark matter coalesced sufficiently, to form protogalaxies. As further accretion occurred, galaxies formed. [7] Indirect evidence is widespread. [7] Galaxies grow through mergers and smooth gas accretion. Accretion also occurs inside galaxies, forming stars.

Stars are thought to form inside giant clouds of cold molecular hydrogen—giant molecular clouds of roughly 300,000 M and 65 light-years (20 pc) in diameter. [8] [9] Over millions of years, giant molecular clouds are prone to collapse and fragmentation. [10] These fragments then form small, dense cores, which in turn collapse into stars. [9] The cores range in mass from a fraction to several times that of the Sun and are called protostellar (protosolar) nebulae. [8] They possess diameters of 2,000–20,000 astronomical units (0.01–0.1 pc) and a particle number density of roughly 10,000 to 100,000/cm 3 (160,000 to 1,600,000/cu in). Compare it with the particle number density of the air at the sea level—2.8 × 10 19 /cm 3 (4.6 × 10 20 /cu in). [9] [11]

The initial collapse of a solar-mass protostellar nebula takes around 100,000 years. [8] [9] Every nebula begins with a certain amount of angular momentum. Gas in the central part of the nebula, with relatively low angular momentum, undergoes fast compression and forms a hot hydrostatic (non-contracting) core containing a small fraction of the mass of the original nebula. This core forms the seed of what will become a star. [8] As the collapse continues, conservation of angular momentum dictates that the rotation of the infalling envelope accelerates, which eventually forms a disk.

As the infall of material from the disk continues, the envelope eventually becomes thin and transparent and the young stellar object (YSO) becomes observable, initially in far-infrared light and later in the visible. [11] Around this time the protostar begins to fuse deuterium. If the protostar is sufficiently massive (above 80 M J), hydrogen fusion follows. Otherwise, if its mass is too low, the object becomes a brown dwarf. [12] This birth of a new star occurs approximately 100,000 years after the collapse begins. [8] Objects at this stage are known as Class I protostars, which are also called young T Tauri stars, evolved protostars, or young stellar objects. By this time, the forming star has already accreted much of its mass the total mass of the disk and remaining envelope does not exceed 10–20% of the mass of the central YSO. [11]

At the next stage, the envelope completely disappears, having been gathered up by the disk, and the protostar becomes a classical T Tauri star. [13] The latter have accretion disks and continue to accrete hot gas, which manifests itself by strong emission lines in their spectrum. The former do not possess accretion disks. Classical T Tauri stars evolve into weakly lined T Tauri stars. [14] This happens after about 1 million years. [8] The mass of the disk around a classical T Tauri star is about 1–3% of the stellar mass, and it is accreted at a rate of 10 −7 to 10 −9 M per year. [15] A pair of bipolar jets is usually present as well. The accretion explains all peculiar properties of classical T Tauri stars: strong flux in the emission lines (up to 100% of the intrinsic luminosity of the star), magnetic activity, photometric variability and jets. [16] The emission lines actually form as the accreted gas hits the "surface" of the star, which happens around its magnetic poles. [16] The jets are byproducts of accretion: they carry away excessive angular momentum. The classical T Tauri stage lasts about 10 million years. [8] There are only a few examples, so-called Peter Pan Disk where the accretion lasts for more than 20 million years. [17] The disk eventually disappears due to accretion onto the central star, planet formation, ejection by jets, and photoevaporation by ultraviolet radiation from the central star and nearby stars. [18] As a result, the young star becomes a weakly lined T Tauri star, which, over hundreds of millions of years, evolves into an ordinary Sun-like star, dependent on its initial mass.

Self-accretion of cosmic dust accelerates the growth of the particles into boulder-sized planetesimals. The more massive planetesimals accrete some smaller ones, while others shatter in collisions. Accretion disks are common around smaller stars, stellar remnants in a close binary, or black holes surrounded by material (such as those at the centers of galaxies). Some dynamics in the disk, such as dynamical friction, are necessary to allow orbiting gas to lose angular momentum and fall onto the central massive object. Occasionally, this can result in stellar surface fusion (see Bondi accretion).

In the formation of terrestrial planets or planetary cores, several stages can be considered. First, when gas and dust grains collide, they agglomerate by microphysical processes like van der Waals forces and electromagnetic forces, forming micrometer-sized particles during this stage, accumulation mechanisms are largely non-gravitational in nature. [19] However, planetesimal formation in the centimeter-to-meter range is not well understood, and no convincing explanation is offered as to why such grains would accumulate rather than simply rebound. [19] : 341 In particular, it is still not clear how these objects grow to become 0.1–1 km (0.06–0.6 mi) sized planetesimals [5] [20] this problem is known as the "meter size barrier": [21] [22] As dust particles grow by coagulation, they acquire increasingly large relative velocities with respect to other particles in their vicinity, as well as a systematic inward drift velocity, that leads to destructive collisions, and thereby limit the growth of the aggregates to some maximum size. [23] Ward (1996) suggests that when slow moving grains collide, the very low, yet non-zero, gravity of colliding grains impedes their escape. [19] : 341 It is also thought that grain fragmentation plays an important role replenishing small grains and keeping the disk thick, but also in maintaining a relatively high abundance of solids of all sizes. [23]

A number of mechanisms have been proposed for crossing the 'meter-sized' barrier. Local concentrations of pebbles may form, which then gravitationally collapse into planetesimals the size of large asteroids. These concentrations can occur passively due to the structure of the gas disk, for example, between eddies, at pressure bumps, at the edge of a gap created by a giant planet, or at the boundaries of turbulent regions of the disk. [24] Or, the particles may take an active role in their concentration via a feedback mechanism referred to as a streaming instability. In a streaming instability the interaction between the solids and the gas in the protoplanetary disk results in the growth of local concentrations, as new particles accumulate in the wake of small concentrations, causing them to grow into massive filaments. [24] Alternatively, if the grains that form due to the agglomeration of dust are highly porous their growth may continue until they become large enough to collapse due to their own gravity. The low density of these objects allows them to remain strongly coupled with the gas, thereby avoiding high velocity collisions which could result in their erosion or fragmentation. [25]

Grains eventually stick together to form mountain-size (or larger) bodies called planetesimals. Collisions and gravitational interactions between planetesimals combine to produce Moon-size planetary embryos (protoplanets) over roughly 0.1–1 million years. Finally, the planetary embryos collide to form planets over 10–100 million years. [20] The planetesimals are massive enough that mutual gravitational interactions are significant enough to be taken into account when computing their evolution. [5] Growth is aided by orbital decay of smaller bodies due to gas drag, which prevents them from being stranded between orbits of the embryos. [26] [27] Further collisions and accumulation lead to terrestrial planets or the core of giant planets.

If the planetesimals formed via the gravitational collapse of local concentrations of pebbles their growth into planetary embryos and the cores of giant planets is dominated by the further accretions of pebbles. Pebble accretion is aided by the gas drag felt by objects as they accelerate toward a massive body. Gas drag slows the pebbles below the escape velocity of the massive body causing them to spiral toward and to be accreted by it. Pebble accretion may accelerate the formation of planets by a factor of 1000 compared to the accretion of planetesimals, allowing giant planets to form before the dissipation of the gas disk. [28] [29] Yet, core growth via pebble accretion appears incompatible with the final masses and compositions of Uranus and Neptune. [30]

The formation of terrestrial planets differs from that of giant gas planets, also called Jovian planets. The particles that make up the terrestrial planets are made from metal and rock that condensed in the inner Solar System. However, Jovian planets began as large, icy planetesimals, which then captured hydrogen and helium gas from the solar nebula. [31] Differentiation between these two classes of planetesimals arise due to the frost line of the solar nebula. [32]

Meteorites contain a record of accretion and impacts during all stages of asteroid origin and evolution however, the mechanism of asteroid accretion and growth is not well understood. [33] Evidence suggests the main growth of asteroids can result from gas-assisted accretion of chondrules, which are millimeter-sized spherules that form as molten (or partially molten) droplets in space before being accreted to their parent asteroids. [33] In the inner Solar System, chondrules appear to have been crucial for initiating accretion. [34] The tiny mass of asteroids may be partly due to inefficient chondrule formation beyond 2 AU, or less-efficient delivery of chondrules from near the protostar. [34] Also, impacts controlled the formation and destruction of asteroids, and are thought to be a major factor in their geological evolution. [34]

Chondrules, metal grains, and other components likely formed in the solar nebula. These accreted together to form parent asteroids. Some of these bodies subsequently melted, forming metallic cores and olivine-rich mantles others were aqueously altered. [34] After the asteroids had cooled, they were eroded by impacts for 4.5 billion years, or disrupted. [35]

For accretion to occur, impact velocities must be less than about twice the escape velocity, which is about 140 m/s (460 ft/s) for a 100 km (60 mi) radius asteroid. [34] Simple models for accretion in the asteroid belt generally assume micrometer-sized dust grains sticking together and settling to the midplane of the nebula to form a dense layer of dust, which, because of gravitational forces, was converted into a disk of kilometer-sized planetesimals. But, several arguments [ which? ] suggest that asteroids may not have accreted this way. [34]

Comets, or their precursors, formed in the outer Solar System, possibly millions of years before planet formation. [36] How and when comets formed is debated, with distinct implications for Solar System formation, dynamics, and geology. Three-dimensional computer simulations indicate the major structural features observed on cometary nuclei can be explained by pairwise low velocity accretion of weak cometesimals. [37] [38] The currently favored formation mechanism is that of the nebular hypothesis, which states that comets are probably a remnant of the original planetesimal "building blocks" from which the planets grew. [39] [40] [41]

Astronomers think that comets originate in both the Oort cloud and the scattered disk. [42] The scattered disk was created when Neptune migrated outward into the proto-Kuiper belt, which at the time was much closer to the Sun, and left in its wake a population of dynamically stable objects that could never be affected by its orbit (the Kuiper belt proper), and a population whose perihelia are close enough that Neptune can still disturb them as it travels around the Sun (the scattered disk). Because the scattered disk is dynamically active and the Kuiper belt relatively dynamically stable, the scattered disk is now seen as the most likely point of origin for periodic comets. [42] The classic Oort cloud theory states that the Oort cloud, a sphere measuring about 50,000 AU (0.24 pc) in radius, formed at the same time as the solar nebula and occasionally releases comets into the inner Solar System as a giant planet or star passes nearby and causes gravitational disruptions. [43] Examples of such comet clouds may already have been seen in the Helix Nebula. [44]

The Rosetta mission to comet 67P/Churyumov–Gerasimenko determined in 2015 that when Sun's heat penetrates the surface, it triggers evaporation (sublimation) of buried ice. While some of the resulting water vapour may escape from the nucleus, 80% of it recondenses in layers beneath the surface. [45] This observation implies that the thin ice-rich layers exposed close to the surface may be a consequence of cometary activity and evolution, and that global layering does not necessarily occur early in the comet's formation history. [45] [46] While most scientists thought that all the evidence indicated that the structure of nuclei of comets is processed rubble piles of smaller ice planetesimals of a previous generation, [47] the Rosetta mission dispelled the idea that comets are "rubble piles" of disparate material. [48] [49]

The Big Problems in Star Formation: the Star Formation Rate, Stellar Clustering, and the Initial Mass Function

Mark R. Krumholz , in Physics Reports , 2014

5.2.1 General theory

At some point in the star formation process, the gas is removed, either because it has all been converted into stars, or because some stellar feedback process ejects it. The classical theory for how the stars will respond, first described by Hils [630] , is quite simple, though more sophisticated analytic models exist [631,632] . If one starts with a virialized system of gas and stars with negligible support from magnetic fields, the kinetic and potential energy are related by

and the two terms individually scale with the mass M of the system as T ∝ M and W ∝ M 2 . If one rapidly removes some of the mass, leaving a mass ϵ M behind in the form of stars, 16 then the total energy of the resulting system is

where T ′ and W ′ are the new kinetic and potential energy after gas removal. The total energy E is negative, indicating that the system is bound, only if ϵ > 1 / 2 . (Note that the exact same calculation implies that binary companions to stars that go supernova will in general become unbound, unless the asymmetric kick of the supernova happens to push the neutron star in exactly the right direction to keep the system together.) This process of star clusters disrupting due to rapid gas expulsion goes by the somewhat macabre name “infant mortality”. On the other hand, if the mass loss is slow compared to a dynamical time, then the system remains in virial equilibrium at all times, and it is straightforward to show that in this case the system always remains bound, but that its radius increases from an initial value R to a final value R ′ = R / ϵ .

Numerous authors have studied this process with N -body simulations as well. The most common procedure is to start with a star cluster in a gas potential, whose depth relative to the potential produced by the stars is specified by the star formation efficiency. The stars themselves can be either smoothly distributed and in virial equilibrium with the gas [633–642] , smooth and sub-virial [643,644] , distributed in a fractal or other sub-structured distribution [645,646] , or taken directly from the output of gas-dynamical simulations [647–649] . The cluster potential is then removed over some time scale, either via a prescribed analytic formula, or by running a fluid-dynamics simulation together with the N -body one and causing the gas to disperse using a simple prescription for the effects of stellar feedback [637,642] . The primary free parameters in this approach are the star formation efficiency ϵ , the timescale over which the gas is removed, and the virial ratio of the stars at the time the simulations begin.

The simulations generally agree with the simple analytic argument given above, but with some important differences. First, even for an initially-virialized stellar population and instantaneous gas removal, ϵ = 0.5 does not represent a hard line for cluster survival or disruption. Instead, at least some bound remnants will be left even with values of ϵ ≈ 0.33 , mainly because the kinetic energy is not uniformly distributed among the stars instead, when the potential is removed, those stars on the high-energy tail of the Maxwellian distribution carry away a disproportionate share of the energy, while those with lower energies remain behind. However, at values of ϵ < 0.5 , clusters do suffer increasing mass loss, which becomes total at ϵ ≲ 0.3 . Conversely, even if mass removal is as slow at ∼10 crossing times, for low values of ϵ substantial mass loss can still occur, thanks to the presence of the galactic tidal field. This tends to strip stars that wander too far from the cluster during mass removal, even if that removal is slow.

Second, for a cluster that is smooth but not initially virialized, clusters are much more likely to survive than if the initial conditions is virialized, and ϵ alone is not a good predictor of the outcome. Instead, the fraction of the stars that remain bound is determined primarily by the effective star formation efficiency ϵ eff , defined simply as the virial ratio of the stars immediately after gas removal. (Note that ϵ eff should not be confused with ϵ ff , the dimensionless star formation rate per free-fall time, which represents an entirely different concept—unfortunately the letter ϵ is used for too many different things in this field.) Thus if the stars are sub-virial with respect to the gas, while it is present, gas removal will result in an effective star formation efficiency that is larger than the true star formation efficiency ϵ , and the stellar cluster will be correspondingly more difficult to disrupt.

Third, in cases where the initial conditions are highly sub-structured, either through a specified structure model or by taking the results from fluid simulations, the results are highly stochastic, and can change wildly from one realization of the structure to another, even when all the parameters used to generate those realizations (e.g., the star formation efficiency and the initial virial ratio) are held fixed. Thus the amount of mass that remains in bound clusters in this case is highly random, and can only realistically be determined from very large statistical ensembles of simulations.

Black Holes

So far we have seen what happens to stellar remnants of about 3 solar masses or less. Remnants less than 1.4 solar masses become white dwarfs and will eventually cool down to black spheres of electron degenerate matter. Cores of 1.4 - 3 solar masses become neutron stars, 10 km spheres of rapidly spinning neutron degenerate matter. Young neutron stars may also be detected as pulsars if one of their beams crosses Earth. Sometimes though a star is so massive that the mass of the material left after all other mass-loss processes exceeds the limit that even neutron degeneracy pressure can withstand. At this stage then the material keeps collapsing inwards until all the mass becomes concentrated at a single point, a singularity. It is now a black hole.

Black holes are even more exotic objects than neutron stars. With all the mass concentrated at a point they have extremely high gravitational fields. They are referred to as black because not even light can escape from them once it has crossed a region known as the event horizon. At the event horizon, the escape velocity equals the speed of light, c. Black holes are therefore hard to observe because they do not emit light at any waveband. Rather than look for a black hole itself, astronomers infer their presence due to their effect on surrounding matter.

A black hole that is one component of a binary system may draw material off its nearby giant companion. As this falls towards the black hole it forms an accretion disk. The material in the accretion disk gets heated and so becomes ionised. Charged objects that get accelerated due to centripetal force emit high frequency synchrotron radiation. This is observed at UV, X-ray and Gamma-ray wavebands.

A black hole that is one component of a binary system may draw material off its nearby giant companion. As this falls towards the black hole it forms an accretion disk. The material in the accretion disk gets heated and so becomes ionised. Charged objects that get accelerated due to centripetal force emit high frequency synchrotron radiation. This is observed at UV, X-ray and Gamma-ray wavebands.

Black holes formed from core collapse of massive stars in hypernovae are thought to range in mass from about 3 to 15 solar masses. They are commonly referred to as stellar black holes so as to distinguish them from the supermassive black holes that are thought to lie at the centre of galaxies such as our own. These may range in mass from about 10 6 to 10 9 solar masses. Such supermassive black holes are likely to be responsible for phenomena such as active galactic nuclei (AGNs), Seyfert galaxies, BL Lacerate Objects and quasars or QSOs.

Some theories also predict the existence of primordial black holes formed during the Big Bang. Whilst still only theoretical in that none have ever been observed they would be very small - about the size of an atom but with a mass of 10 11 kg.

5 Discussion

In addition to producing the two-power-law mass spectrum, competitive accretion naturally results in a certain degree of mass segregation. This arises due to the accretion in the gas-dominated phase where there is a strong correlation between accretion rate, and thus the final mass, and position in the cluster (see equations 16 and 20). This direct correlation between the final mass and position in the cluster neglects variations in the initial masses and the relative movements of the stars due to their interactions. If the cluster is mass-segregated entering the stellar-dominated phase, then the implies that the mass segregation will persist. Simulations of accretion in clusters show that the mass segregation does result but that there is not a one-to-one correlation between mass and radius ( Bonnell et al. 2001). In fact, low-mass stars are located throughout the cluster, including in the core, but the high-mass stars are predominantly located in the central regions as is found in young stellar clusters such as the ONC ( Hillenbrand 1997).

It is also worth noting that, although the models presented here are meant to consider accretion on to young stars, they are equally appropriate for the growth of clumps in a molecular cloud. As the clumps evolve towards gravitational instability, they will accrete from the surrounding gas and this accretion will be governed by the physics described here. Thus, for example, the clump mass function found by Motte, André & Neri (1998) for the ρ Oph molecular cloud could be due to the accretion by the pre-stellar clumps as the whole system collapses down to form a cluster. The observed slope would imply that the whole system is in a density configuration and is subvirial (dominated by the diffuse gas not in the clumps). The steeper slope found by Motte et al. (1998) at the high-mass end of the mass spectrum can be interpreted as arising from a region of near-uniform gas density. A test of such a possibility is to estimate the degree of mass segregation of the clumps in this pre-stellar cluster system.

Finally, it is possible that the mass spectrum for massive stars, , is significantly different from that for lower-mass stars if they do not form in a similar fashion. If massive stars cannot accrete above 10 M because of the effect of radiation pressure on the infalling dust ( Yorke & Krügel 1977 Yorke 1993), but form through a merger process in a dense core ( Bonnell et al. 1998), then the expected mass spectrum could be significantly different from that presented here.

Supergiants are evolved high-mass stars, larger and more luminous than main-sequence stars. O class and early B class stars with initial masses around 10–300 M evolve away from the main sequence in just a few million years as their hydrogen is consumed and heavy elements start to appear near the surface of the star. These stars usually become blue supergiants, although it is possible that some of them evolve directly to Wolf–Rayet stars. [2] Expansion into the supergiant stage occurs when hydrogen in the core of the star is depleted and hydrogen shell burning starts, but it may also be caused as heavy elements are dredged up to the surface by convection and mass loss due to radiation pressure increase. [3]

Blue supergiants are newly evolved from the main sequence, have extremely high luminosities, high mass loss rates, and are generally unstable. Many of them become luminous blue variables (LBVs) with episodes of extreme mass loss. Lower mass blue supergiants continue to expand until they become red supergiants. In the process they must spend some time as yellow supergiants or yellow hypergiants, but this expansion occurs in just a few thousand years and so these stars are rare. Higher mass red supergiants blow away their outer atmospheres and evolve back to blue supergiants, and possibly onwards to Wolf–Rayet stars. [4] [5] Depending on the exact mass and composition of a red supergiant, it can execute a number of blue loops before either exploding as a type II supernova or finally dumping enough of its outer layers to become a blue supergiant again, less luminous than the first time but more unstable. [6] If such a star can pass through the yellow evolutionary void it is expected that it becomes one of the lower luminosity LBVs. [7]

The most massive blue supergiants are too luminous to retain an extensive atmosphere and they never expand into a red supergiant. The dividing line is approximately 40 M , although the coolest and largest red supergiants develop from stars with initial masses of 15–25 M . It is not clear whether more massive blue supergiants can lose enough mass to evolve safely into old age as a Wolf Rayet star and finally a white dwarf, or they reach the Wolf Rayet stage and explode as supernovae, or they explode as supernovae while blue supergiants. [2]

Supernova progenitors are most commonly red supergiants and it was believed that only red supergiants could explode as supernovae. SN 1987A, however, forced astronomers to re-examine this theory, as its progenitor, Sanduleak -69° 202, was a B3 blue supergiant. [8] Now it is known from observation that almost any class of evolved high-mass star, including blue and yellow supergiants, can explode as a supernova although theory still struggles to explain how in detail. [9] While most supernovae are of the relatively homogeneous type II-P and are produced by red supergiants, blue supergiants are observed to produce supernovae with a wide range of luminosities, durations, and spectral types, sometimes sub-luminous like SN 1987A, sometimes super-luminous such as many type IIn supernovae. [10] [11] [12]

Because of their extreme masses they have relatively short lifespans and are mainly observed in young cosmic structures such as open clusters, the arms of spiral galaxies, and in irregular galaxies. They are rarely observed in spiral galaxy cores, elliptical galaxies, or globular clusters, most of which are believed to be composed of older stars, although the core of the Milky Way has recently been found to be home to several massive open clusters and associated young hot stars. [13]

The best known example is Rigel, the brightest star in the constellation of Orion. Its mass is about 20 times that of the Sun, and its luminosity is around 117,000 times greater. Despite their rarity and their short lives they are heavily represented among the stars visible to the naked eye their immense brightness is more than enough to compensate for their scarcity.

Blue supergiants have fast stellar winds and the most luminous, called hypergiants, have spectra dominated by emission lines that indicate strong continuum driven mass loss. Blue supergiants show varying quantities of heavy elements in their spectra, depending on their age and the efficiency with which the products of nucleosynthesis in the core are convected up to the surface. Quickly rotating supergiants can be highly mixed and show high proportions of helium and even heavier elements while still burning hydrogen at the core these stars show spectra very similar to a Wolf Rayet star.

While the stellar wind from a red supergiant is dense and slow, the wind from a blue supergiant is fast but sparse. When a red supergiant becomes a blue supergiant, the faster wind it produces impacts the already emitted slow wind and causes the outflowing material to condense into a thin shell. In some cases several concentric faint shells can be seen from successive episodes of mass loss, either previous blue loops from the red supergiant stage, or eruptions such as LBV outbursts. [14]


Type Ia supernova Edit

White dwarfs are the remnants of low-mass stars and, if they form a binary system with another star, they can cause large stellar explosions known as type Ia supernovae. The normal route by which this happens involves a white dwarf drawing material off a main sequence or red giant star to form an accretion disc. Much more rarely, a type Ia supernova occurs when two white dwarfs orbit each other closely. [8] Emission of gravitational waves causes the pair to spiral inward. When they finally merge, if their combined mass approaches or exceeds the Chandrasekhar limit, carbon fusion is ignited, raising the temperature. Since a white dwarf consists of degenerate matter, there is no safe equilibrium between thermal pressure and the weight of overlying layers of the star. Because of this, runaway fusion reactions rapidly heat up the interior of the combined star and spread, causing a supernova explosion. [8] In a matter of seconds, all of the white dwarf's mass is thrown into space. [9]

Neutron star mergers Edit

Neutron star mergers occur in a fashion similar to the rare type Ia supernovae resulting from merging white dwarfs. When two neutron stars orbit each other closely, they spiral inward as time passes due to gravitational radiation. When they meet, their merger leads to the formation of either a heavier neutron star or a black hole, depending on whether the mass of the remnant exceeds the Tolman–Oppenheimer–Volkoff limit. This creates a magnetic field that is trillions of times stronger than that of Earth, in a matter of one or two milliseconds. Astronomers believe that this type of event is what creates short gamma-ray bursts [10] and kilonovae. [11]

Thorne–Żytkow objects Edit

If a neutron star collides with red giant of sufficiently low mass and density, both can survive in the form of a peculiar hybrid known as Thorne–Żytkow object, with a neutron star surrounded by a red giant.

Binary star mergers Edit

About half of all the stars in the sky are part of binary systems, with two stars orbiting each other. Some binary stars orbit each other so closely that they share the same atmosphere, giving the system a peanut shape. While most contact binary stars are stable, a few have become unstable and have merged in the past for reasons not well understood (see relevant section below).

When two low-mass stars in a binary system merge, mass may be thrown off in the orbital plane of the merging stars, creating an excretion disk from which new planets can form. [12]

While the concept of stellar collision has been around for several generations of astronomers, only the development of new technology has made it possible for it to be more objectively studied. For example, in 1764, a cluster of stars known as Messier 30 was discovered by astronomer Charles Messier. In the twentieth century, astronomers concluded that the cluster was approximately 13 billion years old. [13] The Hubble Space Telescope resolved the individual stars of Messier 30. With this new technology, astronomers discovered that some stars, known as “blue stragglers”, appeared younger than other stars in the cluster. [13] Astronomers then hypothesized that stars may have “collided”, or “merged”, giving them more fuel so they continued fusion while fellow stars around them started going out. [13]

While stellar collisions may occur very frequently in certain parts of the galaxy, the likelihood of a collision involving the Sun is very small. A probability calculation predicts the rate of stellar collisions involving the Sun is 1 in 10 28 years. [14] For comparison, the age of the universe is of the order 10 10 years. The likelihood of close encounters with the Sun is also small. The rate is estimated by the formula:

where N is the number of encounters per million years that come within a radius D of the Sun in parsecs. [15] For comparison, the mean radius of the Earth's orbit, 1 AU, is 4.82 × 10 −6 parsecs .

Our star will likely not be directly affected by such an event, but the Earth may be easily affected by a nearby collision. Astronomers say that if a stellar collision happens within 100 light years of the Earth, the resulting gamma-ray burst could possibly destroy all life on Earth. [14] This is still very unlikely though because there are no stellar clusters this close to the Solar System.

KIC 9832227 is an example of an eclipsing contact binary star system. It is mainly composed of two stars orbiting each other so closely that they share the same atmosphere, giving the system a peanut shape. As the orbits of the two stars decay due to stellar mass loss and internal viscosity, the two stars will eventually merge, resulting in a luminous red nova.

An analysis of the eclipses of KIC 9832227 initially suggested that its orbital period was indeed shortening, and that the cores of the two stars would merge in 2022. [16] [17] [18] [19] However subsequent reanalysis found that one of the datasets used in the initial prediction contained a 12-hour timing error, leading to a spurious apparent shortening of the stars' orbital period. [20] [21] [22] [23]

The mechanism behind binary star mergers is not yet fully understood, and remains one of the main focuses of those researching KIC 9832227 and other contact binaries.


Novae are much less luminous than Supernovae:

Like Supernovae, novae brighten quickly, and fade slowly. The remnants of the nova outburst can be seen for months to years afterward.

Novae occur in binary systems in which one star is a White Dwarf. The WD accretes matter (hydrogen) from the companion onto its surface. The accreted matter is heated by falling onto the WD, and the hydrogen "flash-fuses" into helium.

In Novae, mass is accreting onto the WD at a fairly high rate. Because of this, the material cannot get rid of its heat efficiently, reaches fusion temperatures on the surface, and is then blown off into space. Given the mechanism, it turns out that a system can go Nova several times. The typical time between nova outbursts in such systems is at least decades, and can be thousands of years. The rule here is that the more luminous the outburst, the longer the time between outbursts. So really bright novae will probably have burst intervals of thousands of years. All those that we have seen do multiple bursts in the past century are much less luminous.

But what if the mass accretion rate is slow enough for the heat to escape without a nova eruption? Then the mass of the WD will slowly increase until it reaches the Chandrasekhar limit. If the WD accretes enough mass to drive it over the Chandrasekhar limit (1.4 Solar masses), the star undergoes runaway Carbon burning, and explodes.

In other words, there are (at least) two types of Supernovae

The Type I SNe are further divided into Types Ia, Ib, and Ic. Types Ib and Ic appear to be due to exploding massive stars, like Type II SNe, but the progenitors of Types Ib and Ic are stars that managed to shed their entire Hydrogen envelope before exploding.

Type Ia SNe appear to be different beasts altogether. While Type II (and Ib and Ic) SNe are always associated with regions of recent star formation, Type Ia SNe can happen in any environment.

The current understanding is that Type Ia SNe are due to accrection onto WD stars in close binaries. If the WD accretes enough mass to drive it over the Chandrasekhar limit (1.4 Solar masses), the star undergoes runaway Carbon burning, and explodes.

Because there is no collapse to nuclear densities in Type Ia SNe, there is no neutrino burst from them. Thus, although the photon luminosities of Type Ia's is comparable to that of Type II's, the Total energy released (including neutrinos) is much less in Type Ia's.

It is possible to distinguish between Type Ia and Type II SNe just from their light curves. This means they can be distinguised at large distances, even if they are too faint for good spectroscopy.

A last comment about stellar evolution. This process, by which hydrogen is converted into heavier elements in stars, and then returned to the ISM via stellar mass loss (stellar winds, planetary nebula ejection, supernovae) is the means by which the heavy elements in our bodies were produced. The carbon, oxygen, and calcium in our bodies were made in stellar interiors. And it is via the process of stellar evolution that this material found its way back out into space to form our planet.


Accretion disk jets: Why do the disks surrounding certain objects, such as the nuclei of active galaxies, emit jets along their polar axes? These jets are invoked by astronomers to do everything from getting rid of angular momentum in a forming star to reionizing the universe (in active galactic nuclei), but their origin is still not well understood.

Accretion disks are a ubiquitous phenomenon in astrophysics active galactic nuclei, protoplanetary disks, and gamma ray bursts all involve accretion disks. These disks very often give rise to astrophysical jets coming from the vicinity of the central object. Jets are an efficient way for the star-disk system to shed angular momentum without losing too much mass.

The most spectacular accretion disks found in nature are those of active galactic nuclei and of quasars, which are thought to be massive black holes at the center of galaxies. As matter enters the accretion disc, it follows a trajectory called a tendex line, which describes an inward spiral. This is because particles rub and bounce against each other in a turbulent flow, causing frictional heating which radiates energy away, reducing the particles' angular momentum, allowing the particle to drift inwards, driving the inward spiral. The loss of angular momentum manifests as a reduction in velocity at a slower velocity, the particle must adopt a lower orbit. As the particle falls to this lower orbit, a portion of its gravitational potential energy is converted to increased velocity and the particle gains speed. Thus, the particle has lost energy even though it is now travelling faster than before however, it has lost angular momentum. As a particle orbits closer and closer, its velocity increases, as velocity increases frictional heating increases as more and more of the particle's potential energy (relative to the black hole) is radiated away the accretion disk of a black hole is hot enough to emit X-rays just outside the event horizon. The large luminosity of quasars is believed to be a result of gas being accreted by supermassive black holes. [3] Elliptical accretion disks formed at tidal disruption of stars can be typical in galactic nuclei and quasars. [4] Accretion process can convert about 10 percent to over 40 percent of the mass of an object into energy as compared to around 0.7 percent for nuclear fusion processes. [5] In close binary systems the more massive primary component evolves faster and has already become a white dwarf, a neutron star, or a black hole, when the less massive companion reaches the giant state and exceeds its Roche lobe. A gas flow then develops from the companion star to the primary. Angular momentum conservation prevents a straight flow from one star to the other and an accretion disk forms instead.

Accretion disks surrounding T Tauri stars or Herbig stars are called protoplanetary disks because they are thought to be the progenitors of planetary systems. The accreted gas in this case comes from the molecular cloud out of which the star has formed rather than a companion star.

In the 1940s, models were first derived from basic physical principles. [6] In order to agree with observations, those models had to invoke a yet unknown mechanism for angular momentum redistribution. If matter is to fall inwards it must lose not only gravitational energy but also lose angular momentum. Since the total angular momentum of the disk is conserved, the angular momentum loss of the mass falling into the center has to be compensated by an angular momentum gain of the mass far from the center. In other words, angular momentum should be transported outwards for matter to accrete. According to the Rayleigh stability criterion,

On one hand, it was clear that viscous stresses would eventually cause the matter towards the center to heat up and radiate away some of its gravitational energy. On the other hand, viscosity itself was not enough to explain the transport of angular momentum to the exterior parts of the disk. Turbulence-enhanced viscosity was the mechanism thought to be responsible for such angular-momentum redistribution, although the origin of the turbulence itself was not well understood. The conventional α -model (discussed below) introduces an adjustable parameter α describing the effective increase of viscosity due to turbulent eddies within the disk. [7] [8] In 1991, with the rediscovery of the magnetorotational instability (MRI), S. A. Balbus and J. F. Hawley established that a weakly magnetized disk accreting around a heavy, compact central object would be highly unstable, providing a direct mechanism for angular-momentum redistribution. [9]

Α-Disk model Edit

Using Kramers' law for the opacity it is found that

The Shakura–Sunyaev model assumes that the disk is in local thermal equilibrium, and can radiate its heat efficiently. In this case, the disk radiates away the viscous heat, cools, and becomes geometrically thin. However, this assumption may break down. In the radiatively inefficient case, the disk may "puff up" into a torus or some other three-dimensional solution like an Advection Dominated Accretion Flow (ADAF). The ADAF solutions usually require that the accretion rate is smaller than a few percent of the Eddington limit. Another extreme is the case of Saturn's rings, where the disk is so gas poor that its angular momentum transport is dominated by solid body collisions and disk-moon gravitational interactions. The model is in agreement with recent astrophysical measurements using gravitational lensing. [13] [14] [15] [16]

Magnetorotational instability Edit

Balbus and Hawley (1991) [9] proposed a mechanism which involves magnetic fields to generate the angular momentum transport. A simple system displaying this mechanism is a gas disk in the presence of a weak axial magnetic field. Two radially neighboring fluid elements will behave as two mass points connected by a massless spring, the spring tension playing the role of the magnetic tension. In a Keplerian disk the inner fluid element would be orbiting more rapidly than the outer, causing the spring to stretch. The inner fluid element is then forced by the spring to slow down, reduce correspondingly its angular momentum causing it to move to a lower orbit. The outer fluid element being pulled forward will speed up, increasing its angular momentum and move to a larger radius orbit. The spring tension will increase as the two fluid elements move further apart and the process runs away. [17]

It can be shown that in the presence of such a spring-like tension the Rayleigh stability criterion is replaced by

Most astrophysical disks do not meet this criterion and are therefore prone to this magnetorotational instability. The magnetic fields present in astrophysical objects (required for the instability to occur) are believed to be generated via dynamo action. [18]

Magnetic fields and jets Edit

Accretion disks are usually assumed to be threaded by the external magnetic fields present in the interstellar medium. These fields are typically weak (about few micro-Gauss), but they can get anchored to the matter in the disk, because of its high electrical conductivity, and carried inward toward the central star. This process can concentrate the magnetic flux around the centre of the disk giving rise to very strong magnetic fields. Formation of powerful astrophysical jets along the rotation axis of accretion disks requires a large scale poloidal magnetic field in the inner regions of the disk. [19]

Such magnetic fields may be advected inward from the interstellar medium or generated by a magnetic dynamo within the disk. Magnetic fields strengths at least of order 100 Gauss seem necessary for the magneto-centrifugal mechanism to launch powerful jets. There are problems, however, in carrying external magnetic flux inward towards the central star of the disk. [20] High electric conductivity dictates that the magnetic field is frozen into the matter which is being accreted onto the central object with a slow velocity. However, the plasma is not a perfect electric conductor, so there is always some degree of dissipation. The magnetic field diffuses away faster than the rate at which it is being carried inward by accretion of matter. [21] A simple solution is assuming a viscosity much larger than the magnetic diffusivity in the disk. However, numerical simulations, and theoretical models, show that the viscosity and magnetic diffusivity have almost the same order of magnitude in magneto-rotationally turbulent disks. [22] Some other factors may possibly affect the advection/diffusion rate: reduced turbulent magnetic diffusion on the surface layers reduction of the Shakura–Sunyaev viscosity by magnetic fields [23] and the generation of large scale fields by small scale MHD turbulence –a large scale dynamo. In fact, a combination of different mechanisms might be responsible for efficiently carrying the external field inwards towards the central parts of the disk where the jet is launched. Magnetic buoyancy, turbulent pumping and turbulent diamagnetism exemplify such physical phenomena invoked to explain such efficient concentration of external fields. [24]

When the accretion rate is sub-Eddington and the opacity very high, the standard thin accretion disk is formed. It is geometrically thin in the vertical direction (has a disk-like shape), and is made of a relatively cold gas, with a negligible radiation pressure. The gas goes down on very tight spirals, resembling almost circular, almost free (Keplerian) orbits. Thin disks are relatively luminous and they have thermal electromagnetic spectra, i.e. not much different from that of a sum of black bodies. Radiative cooling is very efficient in thin disks. The classic 1974 work by Shakura and Sunyaev on thin accretion disks is one of the most often quoted papers in modern astrophysics. Thin disks were independently worked out by Lynden-Bell, Pringle and Rees. Pringle contributed in the past thirty years many key results to accretion disk theory, and wrote the classic 1981 review that for many years was the main source of information about accretion disks, and is still very useful today.

A fully general relativistic treatment, as needed for the inner part of the disk when the central object is a black hole, has been provided by Page and Thorne, [25] and used for producing simulated optical images by Luminet [26] and Marck, [27] in which, although such a system is intrinsically symmetric its image is not, because the relativistic rotation speed needed for centrifugal equilibrium in the very strong gravitational field near the black hole produces a strong Doppler redshift on the receding side (taken here to be on the right) whereas there will be a strong blueshift on the approaching side. Due to light bending, the disk appears distorted but is nowhere hidden by the black hole.

When the accretion rate is sub-Eddington and the opacity very low, an ADAF is formed. This type of accretion disk was predicted in 1977 by Ichimaru. Although Ichimaru's paper was largely ignored, some elements of the ADAF model were present in the influential 1982 ion-tori paper by Rees, Phinney, Begelman and Blandford. ADAFs started to be intensely studied by many authors only after their rediscovery in the mid-1990 by Narayan and Yi, and independently by Abramowicz, Chen, Kato, Lasota (who coined the name ADAF), and Regev. Most important contributions to astrophysical applications of ADAFs have been made by Narayan and his collaborators. ADAFs are cooled by advection (heat captured in matter) rather than by radiation. They are very radiatively inefficient, geometrically extended, similar in shape to a sphere (or a "corona") rather than a disk, and very hot (close to the virial temperature). Because of their low efficiency, ADAFs are much less luminous than the Shakura–Sunyaev thin disks. ADAFs emit a power-law, non-thermal radiation, often with a strong Compton component.

Watch the video: James Bullock: Counting Black Holes: The Cosmic Stellar Remnant Population and Implications for LIGO (January 2023).