Degenerate matter

From Wikipedia, the free encyclopedia

Degenerate matter^[1][2] in physics is a collection of free, non-interacting particles with a pressure and other physical characteristics determined by quantum mechanical effects. It is the analogue of an ideal gas in classical mechanics. The degenerate state of matter, in the sense of deviant from an ideal gas, arises at extraordinarily high density (in compact stars) or at extremely low temperatures in laboratories.^[3][4] It occurs for matter particles such as electrons, neutrons, protons, and fermions in general and is referred to as electron-degenerate matter, neutron-degenerate matter, etc. In a mixture of particles, such as ions and electrons in white dwarfs or metals, the electrons may be degenerate, while the ions are not.

In a quantum mechanical description, free particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. The pressure (called degeneracy pressure or Fermi pressure) remains nonzero even near absolute zero temperature.^[3][4] Adding particles or reducing the volume forces the particles into higher-energy quantum states. This requires a compression force, and is made manifest as a resisting pressure. The key feature is that this degeneracy pressure does not depend on the temperature and only on the density of the fermions. It keeps dense stars in equilibrium independent of the thermal structure of the star.

Degenerate matter is also called a Fermi gas or a degenerate gas. A degenerate state with velocities of the fermions close to the speed of light (particle energy larger than its rest mass energy) is called relativistic degenerate matter.

Degenerate matter was first described for a mixture of ions and electrons in 1926 by Ralph H. Fowler,^[5] showing that at densities observed in white dwarfs the electrons (obeying Fermi–Dirac statistics, the term degenerate was not yet in use) have a pressure much higher than the partial pressure of the ions.

Concept

Imagine that a plasma is cooled and compressed repeatedly. Eventually, it will not be possible to compress the plasma any further, because the Pauli exclusion principle states that two fermions cannot share the same quantum state. When in this state, since there is no extra space for any particles, we can also say that a particle's location is extremely defined. Therefore, since (according to the Heisenberg uncertainty principle) ΔpΔx ≥ ħ/2 where Δp is the uncertainty in the particle's momentum and Δx is the uncertainty in position, then we must say that their momentum is extremely uncertain since the particles are located in a very confined space. Therefore, even though the plasma is cold, the particles must be moving very fast on average. This leads to the conclusion that in order to compress an object into a very small space, tremendous force is required to control its particles' momentum.

Unlike a classical ideal gas, whose pressure is proportional to its temperature (P = nkT/V, where P is pressure, V is the volume, n is the number of particles—typically atoms or molecules—k is Boltzmann's constant, and T is temperature), the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at absolute zero temperature. At relatively low densities, the pressure of a fully degenerate gas is given by P = K(n/V)5/3, where K depends on the properties of the particles making up the gas. At very high densities, where most of the particles are forced into quantum states with relativistic energies, the pressure is given by P = K′(n/V)4/3, where K′ again depends on the properties of the particles making up the gas.^[6]

All matter experiences both normal thermal pressure and degeneracy pressure, but in commonly encountered gases, thermal pressure dominates so much that degeneracy pressure can be ignored. Likewise, degenerate matter still has normal thermal pressure, but at extremely high densities the degeneracy pressure usually dominates.

Exotic examples of degenerate matter include neutronium, strange matter, metallic hydrogen and white dwarf matter. Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter because a significant contribution to their pressure is provided by electrical repulsion of atomic nuclei and the screening of nuclei from each other by electrons. In metals it is useful to treat the conduction electrons alone as a degenerate, free electron gas while the majority of the electrons are regarded as occupying bound quantum states. This contrasts with degenerate matter that forms the body of a white dwarf, where all the electrons would be treated as occupying free particle momentum states.

Degenerate gases

Degenerate gases are gases composed of fermions that have a particular configuration that usually forms at high densities. Fermions are particles with half-integer spin. Their behavior is regulated by a set of quantum mechanical rules called the Fermi–Dirac statistics. One particular rule is the Pauli exclusion principle, which states that there can be only one fermion occupying each quantum state, which also applies to electrons that are not bound to a nucleus but merely confined to a fixed volume, such as in the deep interior of a star. Such particles as electrons, protons, neutrons, and neutrinos are all fermions and obey Fermi–Dirac statistics.

A fermion gas in which all energy states below some energy level are filled is called a fully degenerate fermion gas. The difference between this energy level and the lowest energy level is known as the Fermi energy. The electron gas in ordinary metals and in the interior of white dwarf stars constitute two examples of a degenerate electron gas. Most stars are supported against their own gravitation by normal thermal gas pressure. White dwarf stars are supported by the degeneracy pressure of the electron gas in their interior, while for neutron stars the degenerate particles are neutrons.

Electron degeneracy

In an ordinary fermion gas in which thermal effects dominate, most of the available electron energy levels are unfilled and the electrons are free to move to these states. As particle density is increased, electrons progressively fill the lower energy states and additional electrons are forced to occupy states of higher energy even at low temperatures. Degenerate gases strongly resist further compression because the electrons cannot move to already filled lower energy levels due to the Pauli exclusion principle. Since electrons cannot give up energy by moving to lower energy states, no thermal energy can be extracted. The momentum of the fermions in the fermion gas nevertheless generates pressure, termed degeneracy pressure.

Under high densities the matter becomes a degenerate gas when the electrons are all stripped from their parent atoms. In the core of a star, once hydrogen burning in nuclear fusion reactions stops, it becomes a collection of positively charged ions, largely helium and carbon nuclei, floating in a sea of electrons, which have been stripped from the nuclei. Degenerate gas is an almost perfect conductor of heat and does not obey the ordinary gas laws. White dwarfs are luminous not because they are generating any energy but rather because they have trapped a large amount of heat which is gradually radiated away. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. When gas becomes super-compressed, particles position right up against each other to produce degenerate gas that behaves more like a solid. In degenerate gases the kinetic energies of electrons are quite high and the rate of collision between electrons and other particles is quite low, therefore degenerate electrons can travel great distances at velocities that approach the speed of light. Instead of temperature, the pressure in a degenerate gas depends only on the speed of the degenerate particles; however, adding heat does not increase the speed. Pressure is only increased by the mass of the particles, which increases the gravitational force pulling the particles closer together. Therefore, the phenomenon is the opposite of that normally found in matter where if the mass of the matter is increased, the object becomes bigger. In degenerate gas, when the mass is increased, the pressure is increased, and the particles become spaced closer together, so the object becomes smaller. Degenerate gas can be compressed to very high densities, typical values being in the range of 10,000 kilograms per cubic centimeter.

There is an upper limit to the mass of an electron-degenerate object, the Chandrasekhar limit, beyond which electron degeneracy pressure cannot support the object against collapse. The limit is approximately 1.44^[7]solar masses for objects with compositions similar to the sun. The mass cutoff changes with the chemical composition of the object, as this affects the ratio of mass to number of electrons present. Celestial objects below this limit are white dwarf stars, formed by the collapse of the cores of stars that run out of fuel. During collapse, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse. Above this mass limit, a neutron star (supported by neutron degeneracy pressure) or a black hole may be formed instead.

Proton degeneracy

Sufficiently dense matter containing protons experiences proton degeneracy pressure, in a manner similar to the electron degeneracy pressure in electron-degenerate matter: protons confined to a sufficiently small volume have a large uncertainty in their momentum due to the Heisenberg uncertainty principle. Because protons are much more massive than electrons, the same momentum represents a much smaller velocity for protons than for electrons. As a result, in matter with approximately equal numbers of protons and electrons, proton degeneracy pressure is much smaller than electron degeneracy pressure, and proton degeneracy is usually modeled as a correction to the equations of state of electron-degenerate matter.

Neutron degeneracy

Neutron degeneracy is analogous to electron degeneracy and is demonstrated in neutron stars, which are primarily supported by the pressure from a degenerate neutron gas.^[8] This happens when a stellar core above 1.44^{[citation needed]} solar masses, the Chandrasekhar limit, collapses and is not halted by the degenerate electrons. As the star collapses, the Fermi energy of the electrons increases to the point where it is energetically favorable for them to combine with protons to produce neutrons (via inverse beta decay, also termed electron capture and "neutralization"). The result of this collapse is an extremely compact star composed of nuclear matter, which is predominantly a degenerate neutron gas, sometimes called neutronium, with a small admixture of degenerate proton and electron gases.

Neutrons in a degenerate neutron gas are spaced much more closely than electrons in an electron-degenerate gas, because the more massive neutron has a much shorter wavelength at a given energy. In the case of neutron stars and white dwarf stars, this is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs. The pressure increase is caused by the fact that the compactness of a neutron star causes gravitational forces to be much higher than in a less compact body with similar mass. This results in a star with a diameter on the order of a thousandth that of a white dwarf.

There is an upper limit to the mass of a neutron-degenerate object, the Tolman–Oppenheimer–Volkoff limit, which is analogous to the Chandrasekhar limit for electron-degenerate objects. The precise limit is unknown, as it depends on the equations of state of nuclear matter, for which a highly accurate model is not yet available. Above this limit, a neutron star may collapse into a black hole, or into other, denser forms of degenerate matter (such as quark matter) if these forms exist and have suitable properties (mainly related to degree of compressibility, or "stiffness", described by the equations of state).

Quark degeneracy

At densities greater than those supported by neutron degeneracy, quark matter is expected to occur. Several variations of this have been proposed that represent quark-degenerate states. Strange matter is a degenerate gas of quarks that is often assumed to contain strange quarks in addition to the usual up and down quarks. Color superconductor materials are degenerate gases of quarks in which quarks pair up in a manner similar to Cooper pairing in electrical superconductors. The equations of state for the various proposed forms of quark-degenerate matter vary widely, and are usually also poorly defined, due to the difficulty of modeling strong force interactions.

Quark-degenerate matter may occur in the cores of neutron stars, depending on the equations of state of neutron-degenerate matter. It may also occur in hypothetical quark stars, formed by the collapse of objects above the Tolman–Oppenheimer–Volkoff mass limit for neutron-degenerate objects. Whether quark-degenerate matter forms at all in these situations depends on the equations of state of both neutron-degenerate matter and quark-degenerate matter, both of which are poorly known.

Preon degeneracy hypothesis

Preons are subatomic particles proposed to be the constituents of quarks, which become composite particles in preon-based models. If preons exist, preon-degenerate matter might occur at densities greater than that which can be supported by quark-degenerate matter. The expected properties of preon-degenerate matter depend very strongly on the model chosen to describe preons, and the existence of preons is not assumed by the majority of the scientific community, due to conflicts between the preon models originally proposed and experimental data from particle accelerators.

Singularity

At densities greater than those supported by any degeneracy, gravity overwhelms all other forces. To the best of our current understanding, the body collapses to form a black hole. In the frame of reference that is co-moving with the collapsing matter, all the matter ends up in an infinitely dense singularity at the center of the event horizon. In the frame of reference of an observer at infinity, the collapse asymptotically approaches the event horizon.
As a consequence of relativity, the extreme gravitational field and orbital velocity experienced by infalling matter around a black hole would "slow" time for that matter relative to a distant observer.

Neutron star

From Wikipedia, the free encyclopedia

Play media

The size of a neutron star compared to Manhattan

Radiation from the pulsar PSR B1509-58, a rapidly spinning neutron star, makes nearby gas glow in X-rays (gold, from Chandra) and illuminates the rest of the nebula, here seen in infrared (blue and red, from WISE).

A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star after a supernova. Neutron stars are the densest and smallest stars known to exist in the universe; with a radius of only about 12–13 km (7 mi), they can have a mass of about two times that of the Sun.

Neutron stars are composed almost entirely of neutrons, which are subatomic particles without net electrical charge and with slightly larger mass than protons. Neutron stars are very hot and are supported against further collapse by quantum degeneracy pressure due to the phenomenon described by the Pauli exclusion principle, which states that no two neutrons (or any other fermionic particles) can occupy the same place and quantum state simultaneously.

A typical neutron star has a mass between ~1.4 and about 3 solar masses (M_☉) with a surface temperature of ~6×10⁵ K.^{[1][2][3][4][a]} Neutron stars have overall densities of 3.7×10¹⁷ to 5.9×10¹⁷ kg/m³ (2.6×10¹⁴ to 4.1×10¹⁴ times the density of the Sun),^[b] which is comparable to the approximate density of an atomic nucleus of 3×10¹⁷ kg/m³.^[5] The neutron star's density varies from below 1×10⁹ kg/m³ in the crust – increasing with depth – to above 6×10¹⁷ or 8×10¹⁷ kg/m³ deeper inside (denser than an atomic nucleus).^[6] A normal-sized matchbox containing neutron star material would have a mass of approximately 5 billion tonnes or ~1 km³ of Earth rock.^{[citation needed]}

In general, compact stars of less than 1.44 M_☉ (the Chandrasekhar limit) are white dwarfs while compact stars weighing between that and 3 M_☉ (the Tolman–Oppenheimer–Volkoff limit) should be neutron stars. The maximum observed mass of neutron stars is about 2 M_☉. Compact stars with more than 10 M_☉ will overcome the neutron degeneracy pressure and gravitational collapse will usually occur to produce a black hole.^[7] The smallest observed mass of a black hole is about 5 M_☉. Between these, hypothetical intermediate-mass stars such as quark stars and electroweak stars have been proposed, but none have been shown to exist. The equations of state of matter at such high densities are not precisely known because of the theoretical and empirical difficulties.

Some neutron stars rotate very rapidly (up to 716 times a second,^[8][9] or approximately 43,000 revolutions per minute) and emit beams of electromagnetic radiation as pulsars. Indeed, the discovery of pulsars in 1967 first suggested that neutron stars exist. Gamma-ray bursts may be produced from rapidly rotating, high-mass stars that collapse to form a neutron star, or from the merger of binary neutron stars. There are thought to be on the order of 10⁸ neutron stars in the galaxy, but they can only be easily detected in certain instances, such as if they are a pulsar or part of a binary system. Non-rotating and non-accreting neutron stars are virtually undetectable; however, the Hubble Space Telescope has observed one thermally radiating neutron star, called RX J185635-3754.

Formation

Any main sequence star with an initial mass of around 10 M_☉ or above has the potential to become a neutron star. As the star evolves away from the main sequence, subsequent nuclear burning produces an iron-rich core. When all nuclear fuel in the core has been exhausted, the core must be supported by degeneracy pressure alone. Further deposits of material from shell burning cause the core to exceed the Chandrasekhar limit. Electron degeneracy pressure is overcome and the core collapses further, sending temperatures soaring to over 5×10⁹ K. At these temperatures, photodisintegration (the breaking up of iron nuclei into alpha particles by high- energy gamma rays) occurs. As the temperature climbs even higher, electrons and protons combine to form neutrons, releasing a flood of neutrinos. When densities reach nuclear density of 4×10¹⁷ kg/m³, neutron degeneracy pressure halts the contraction. The infalling outer atmosphere of the star is flung outwards, becoming a Type II or Type Ib supernova.
The remnant left is a neutron star. If it has a mass greater than about 5 M_☉, it collapses further to become a black hole. Other neutron stars are formed within close binaries.

As the core of a massive star is compressed during a Type II, Type Ib or Type Ic supernova, and collapses into a neutron star, it retains most of its angular momentum. Since it has only a tiny fraction of its parent's radius (and therefore its moment of inertia is sharply reduced), a neutron star is formed with very high rotation speed, and then gradually slows down. Neutron stars are known that have rotation periods from about 1.4 ms to 30 s. The neutron star's density also gives it very high surface gravity, with typical values ranging from 10¹² to 10¹³ m/s² (more than 10¹¹ times of that of Earth).^[4] One measure of such immense gravity is the fact that neutron stars have an escape velocity ranging from 100,000 km/s to 150,000 km/s, that is, from a third to half the speed of light. Matter falling onto the surface of a neutron star would be accelerated to tremendous speed by the star's gravity. The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star.

Properties

Gravitational light deflection at a neutron star. Due to relativistic light deflection more than half of the surface is visible (each chequered patch here represents 30 degrees by 30 degrees).^[10] In natural units, the mass of the depicted star is 1 and its radius 4, or twice its Schwarzschild radius.^[10]

The gravitational field at the star's surface is about 2×10¹¹ times stronger than on Earth. Such a strong gravitational field acts as a gravitational lens and bends the radiation emitted by the star such that parts of the normally invisible rear surface become visible.^[10] If the radius of the neutron star is or less, then the photons may be trapped in an orbit, thus making the whole surface of that neutron star visible, along with destabilizing orbits at that and less than that of the radius. A fraction of the mass of a star that collapses to form a neutron star is released in the supernova explosion from which it forms (from the law of mass-energy equivalence, E = mc²). The energy comes from the gravitational binding energy of a neutron star.

Neutron star relativistic equations of state provided by Jim Lattimer include a graph of radius vs. mass for various models.^[11] The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius). BE is the ratio of gravitational binding energy mass equivalent to observed neutron star gravitational mass of "M" kilograms with radius "R" meters,^[12]

      

Given current values

^[13]

and star masses "M" commonly reported as multiples of one solar mass,

then the relativistic fractional binding energy of a neutron star is

A 2 M_☉ neutron star would not be more compact than 10,970 meters radius (AP4 model). Its mass fraction gravitational binding energy would then be 0.187, −18.7% (exothermic). This is not near 0.6/2 = 0.3, −30%.

A neutron star is so dense that one teaspoon (5 milliliters) of its material would have a mass over 5.5×10¹² kg (that is 1100 tonnes per 1 nanolitre), about 900 times the mass of the Great Pyramid of Giza.^[c] Hence, the gravitational force of a typical neutron star is such that if an object were to fall from a height of one meter, it would only take one microsecond to hit the surface of the neutron star, and would do so at around 2000 kilometers per second, or 7.2 million kilometers per hour.^[14]

The temperature inside a newly formed neutron star is from around 10¹¹ to 10¹² kelvin.^[6] However, the huge number of neutrinos it emits carry away so much energy that the temperature falls within a few years to around 10⁶ kelvin.^[6] Even at 1 million kelvin, most of the light generated by a neutron star is in X-rays.

The pressure increases from 3×10³³ to 1.6×10³⁵ Pa from the inner crust to the center.^[15]
The equation of state for a neutron star is still not known. It is assumed that it differs significantly from that of a white dwarf, whose EOS is that of a degenerate gas which can be described in close agreement with special relativity. However, with a neutron star the increased effects of general relativity can no longer be ignored. Several EOS have been proposed (FPS, UU, APR, L, SLy, and others) and current research is still attempting to constrain the theories to make predictions of neutron star matter.^[4][16] This means that the relation between density and mass is not fully known, and this causes uncertainties in radius estimates. For example, a 1.5 M_☉ neutron star could have a radius of 10.7, 11.1, 12.1 or 15.1 kilometres (for EOS FPS, UU, APR or L respectively).^[16]

Structure

Cross-section of neutron star. Densities are in terms of ρ₀ the saturation nuclear matter density, where nucleons begin to touch.

Current understanding of the structure of neutron stars is defined by existing mathematical models, but it might be possible to infer through studies of neutron-star oscillations. Similar to asteroseismology for ordinary stars, the inner structure might be derived by analyzing observed frequency spectra of stellar oscillations.^[4]

On the basis of current models, the matter at the surface of a neutron star is composed of ordinary atomic nuclei crushed into a solid lattice with a sea of electrons flowing through the gaps between them. It is possible that the nuclei at the surface are iron, due to iron's high binding energy per nucleon.^[17] It is also possible that heavy element cores, such as iron, simply sink beneath the surface, leaving only light nuclei like helium and hydrogen cores.^[17] If the surface temperature exceeds 10⁶ kelvin (as in the case of a young pulsar), the surface should be fluid instead of the solid phase observed in cooler neutron stars (temperature <10 sup="">6

kelvin).^[17]
The "atmosphere" of the star is hypothesized to be at most several micrometers thick, and its dynamic is fully controlled by the star's magnetic field. Below the atmosphere one encounters a solid "crust". This crust is extremely hard and very smooth (with maximum surface irregularities of ~5 mm), because of the extreme gravitational field.^[18] The expected hierarchy of phases of nuclear matter in the inner crust has been characterized as nuclear pasta.^[19]

Proceeding inward, one encounters nuclei with ever increasing numbers of neutrons; such nuclei would decay quickly on Earth, but are kept stable by tremendous pressures. As this process continues at increasing depths, neutron drip becomes overwhelming, and the concentration of free neutrons increases rapidly. In this region, there are nuclei, free electrons, and free neutrons. The nuclei become increasingly small (gravity and pressure overwhelming the strong force) until the core is reached, by definition the point where they disappear altogether.

The composition of the superdense matter in the core remains uncertain. One model describes the core as superfluid neutron-degenerate matter (mostly neutrons, with some protons and electrons). More exotic forms of matter are possible, including degenerate strange matter (containing strange quarks in addition to up and down quarks), matter containing high-energy pions and kaons in addition to neutrons,^[4] or ultra-dense quark-degenerate matter.

History of discoveries

The first direct observation of a neutron star in visible light. The neutron star is RX J185635-3754.

In 1934, Walter Baade and Fritz Zwicky proposed the existence of the neutron star,^[20][d] only a year after the discovery of the neutron by Sir James Chadwick.^[23] In seeking an explanation for the origin of a supernova, they tentatively proposed that in supernova explosions ordinary stars are turned into stars that consist of extremely closely packed neutrons that they called neutron stars. Baade and Zwicky correctly proposed at that time that the release of the gravitational binding energy of the neutron stars powers the supernova: "In the supernova process, mass in bulk is annihilated". Neutron stars were thought to be too faint to be detectable and little work was done on them until November 1967, when Franco Pacini (1939–2012) pointed out that if the neutron stars were spinning and had large magnetic fields, then electromagnetic waves would be emitted. Unbeknown to him, radio astronomer Antony Hewish and his research assistant Jocelyn Bell at Cambridge were shortly to detect radio pulses from stars that are now believed to be highly magnetized, rapidly spinning neutron stars, known as pulsars.

In 1965, Antony Hewish and Samuel Okoye discovered "an unusual source of high radio brightness temperature in the Crab Nebula".^[24] This source turned out to be the Crab Nebula neutron star that resulted from the great supernova of 1054.

In 1967, Iosif Shklovsky examined the X-ray and optical observations of Scorpius X-1 and correctly concluded that the radiation comes from a neutron star at the stage of accretion.^[25]

In 1967, Jocelyn Bell and Antony Hewish discovered regular radio pulses from CP 1919. This pulsar was later interpreted as an isolated, rotating neutron star. The energy source of the pulsar is the rotational energy of the neutron star. The majority of known neutron stars (about 2000, as of 2010) have been discovered as pulsars, emitting regular radio pulses.

In 1971, Riccardo Giacconi, Herbert Gursky, Ed Kellogg, R. Levinson, E. Schreier, and H. Tananbaum discovered 4.8 second pulsations in an X-ray source in the constellation Centaurus, Cen X-3. They interpreted this as resulting from a rotating hot neutron star. The energy source is gravitational and results from a rain of gas falling onto the surface of the neutron star from a companion star or the interstellar medium.

In 1974, Antony Hewish was awarded the Nobel Prize in Physics "for his decisive role in the discovery of pulsars" without Jocelyn Bell who shared in the discovery.

In 1974, Joseph Taylor and Russell Hulse discovered the first binary pulsar, PSR B1913+16, which consists of two neutron stars (one seen as a pulsar) orbiting around their center of mass. Einstein's general theory of relativity predicts that massive objects in short binary orbits should emit gravitational waves, and thus that their orbit should decay with time. This was indeed observed, precisely as general relativity predicts, and in 1993, Taylor and Hulse were awarded the Nobel Prize in Physics for this discovery.

In 1982, Don Backer and colleagues discovered the first millisecond pulsar, PSR B1937+21. This objects spins 642 times per second, a value that placed fundamental constraints on the mass and radius of neutron stars. Many millisecond pulsars were later discovered, but PSR B1937+12 remained the fastest-spinning known pulsar for 24 years, until PSR J1748-2446ad was discovered.

In 2003, Marta Burgay and colleagues discovered the first double neutron star system where both components are detectable as pulsars, PSR J0737-3039. The discovery of this system allows a total of 5 different tests of general relativity, some of these with unprecedented precision.

In 2010, Paul Demorest and colleagues measured the mass of the millisecond pulsar PSR J1614–2230 to be 1.97±0.04 M_☉, using Shapiro delay.^[26] This was substantially higher than any previously measured neutron star mass (1.67 M_☉, see PSR J1903+0327), and places strong constraints on the interior composition of neutron stars.
In 2013, John Antoniadis and colleagues measured the mass of PSR J0348+0432 to be 2.01±0.04 M_☉, using white dwarf spectroscopy.^[27] This confirmed the existence of such massive stars using a different method. Furthermore, this allowed, for the first time, a test of general relativity using such a massive neutron star.

Rotation

Neutron stars rotate extremely rapidly after their creation due to the conservation of angular momentum; like spinning ice skaters pulling in their arms, the slow rotation of the original star's core speeds up as it shrinks. A newborn neutron star can rotate several times a second; sometimes, the neutron star absorbs orbiting matter from a companion star, increasing the rotation to several hundred times per second, reshaping the neutron star into an oblate spheroid.

Over time, neutron stars slow down (spin down) because their rotating magnetic fields radiate energy; older neutron stars may take several seconds for each revolution.

The rate at which a neutron star slows its rotation is usually constant and very small: the observed rates of decline are between 10⁻¹⁰ and 10⁻²¹ seconds for each rotation. Therefore, for a typical slow down rate of 10⁻¹⁵ seconds per rotation, a neutron star now rotating in 1 second will rotate in 1.000003 seconds after a century, or 1.03 seconds after 1 million years.

NASA artist's conception of a "starquake", or "stellar quake".

Sometimes a neutron star will spin up or undergo a glitch, a sudden small increase of its rotation speed. Glitches are thought to be the effect of a starquake — as the rotation of the star slows down, the shape becomes more spherical. Due to the stiffness of the "neutron" crust, this happens as discrete events when the crust ruptures, similar to tectonic earthquakes. After the starquake, the star will have a smaller equatorial radius, and since angular momentum is conserved, rotational speed increases. Recent work, however, suggests that a starquake would not release sufficient energy for a neutron star glitch; it has been suggested that glitches may instead be caused by transitions of vortices in the superfluid core of the star from one metastable energy state to a lower one.^[28]

Neutron stars have been observed to "pulse" radio and x-ray emissions believed to be caused by particle acceleration near the magnetic poles, which need not be aligned with the rotation axis of the star. Through mechanisms not yet entirely understood, these particles produce coherent beams of radio emission. External viewers see these beams as pulses of radiation whenever the magnetic pole sweeps past the line of sight. The pulses come at the same rate as the rotation of the neutron star, and thus, appear periodic. Neutron stars which emit such pulses are called pulsars.

The most rapidly rotating neutron star currently known, PSR J1748-2446ad, rotates at 716 rotations per second.^[29] A recent paper reported the detection of an X-ray burst oscillation (an indirect measure of spin) at 1122 Hz from the neutron star XTE J1739-285.^[30] However, at present, this signal has only been seen once, and should be regarded as tentative until confirmed in another burst from this star.

Population and distances

At present, there are about 2000 known neutron stars in the Milky Way and the Magellanic Clouds, the majority of which have been detected as radio pulsars. Neutron stars are mostly concentrated along the disk of the Milky Way although the spread perpendicular to the disk is large because the supernova explosion process can impart high speeds (400 km/s) to the newly created neutron star.

Some of the closest neutron stars are RX J1856.5-3754 about 400 light years away and PSR J0108-1431 at about 424 light years.^[31] RX J1856.5-3754 is a member of a close group of neutron stars called The Magnificent Seven. Another nearby neutron star that was detected transiting the backdrop of the constellation Ursa Minor has been nicknamed Calvera by its Canadian and American discoverers, after the villain in the 1960 film The Magnificent Seven. This rapidly moving object was discovered using the ROSAT/Bright Source Catalog.

Binary neutron stars

About 5% of all known neutron stars are members of a binary system. The formation and evolution scenario of binary neutron stars is a rather exotic and complicated process.^[32] The companion stars may be either ordinary stars, white dwarfs or other neutron stars. According to modern theories of binary evolution it is expected that neutron stars also exist in binary systems with black hole companions. Such binaries are expected to be prime sources for emitting gravitational waves. Neutron stars in binary systems often emit X-rays which is caused by the heating of material (gas) accreted from the companion star. Material from the outer layers of a (bloated) companion star is sucked towards the neutron star as a result of its very strong gravitational field. As a result of this process binary neutron stars may also coalesce into black holes if the accretion of mass takes place under extreme conditions.^[33] It has been proposed that coalescence of binaries consisting of two neutron stars may be responsible for producing short gamma-ray bursts. Such events may also be responsible for creating all chemical elements beyond iron,^[34] as opposed to the supernova nucleosynthesis theory.

Subtypes

• Neutron star
  • Protoneutron star (PNS), theorized.^[35]
  • Radio-quiet neutron stars
  • Radio loud neutron star
    • Single pulsars–general term for neutron stars that emit directed pulses of radiation towards us at regular intervals (due to their strong magnetic fields).
      • Rotation-powered pulsar ("radio pulsar")
        • Magnetar–a neutron star with an extremely strong magnetic field (1000 times more than a regular neutron star), and long rotation periods (5 to 12 seconds).
          • Soft gamma repeater (SGR)
          • Anomalous X-ray pulsar (AXP)
    • Binary pulsars
      • Low-mass X-ray binaries (LMXB)
      • Intermediate-mass X-ray binaries (IMXB)
      • High-mass X-ray binaries (HMXB)
      • Accretion-powered pulsar ("X-ray pulsar")
        • X-ray burster–a neutron star with a low mass binary companion from which matter is accreted resulting in irregular bursts of energy from the surface of the neutron star.
        • Millisecond pulsar (MSP) ("recycled pulsar")
          • Sub-millisecond pulsar^[36]
  • Exotic star
    • Quark star–currently a hypothetical type of neutron star composed of quark matter, or strange matter. As of 2008, there are three candidates.
    • Electroweak star–currently a hypothetical type of extremely heavy neutron star, in which the quarks are converted to leptons through the electroweak force, but the gravitational collapse of the star is prevented by radiation pressure. As of 2010, there is no evidence for their existence.
    • Preon star–currently a hypothetical type of neutron star composed of preon matter. As of 2008, there is no evidence for the existence of preons.

Giant nucleus

A neutron star has some of the properties of an atomic nucleus, including density (within an order of magnitude) and being composed of nucleons. In popular scientific writing, neutron stars are therefore sometimes described as giant nuclei. However, in other respects, neutron stars and atomic nuclei are quite different. In particular, a nucleus is held together by the strong interaction, whereas a neutron star is held together by gravity, and thus the density and structure of neutron stars is more variable. It is generally more useful to consider such objects as stars.

Examples of neutron stars

• PSR J0108-1431 – closest neutron star
• LGM-1 – the first recognized radio-pulsar
• PSR B1257+12 – the first neutron star discovered with planets (a millisecond pulsar)
• SWIFT J1756.9-2508 – a millisecond pulsar with a stellar-type companion with planetary range mass (below brown dwarf)
• PSR B1509-58 source of the "Hand of God" photo shot by the Chandra X-ray Observatory.
• PSR J0348+0432 - the most massive neutron star with a well-constrained mass, .

Solar Roadways

From Wikipedia, the free encyclopedia

Solar Roadways Inc

Type	Startup
Founded	2006 (2006)
Founder	Scott Brusaw Julie Brusaw
Headquarters	721 Pine Street, Sandpoint, Idaho 83864, United States [1]
Website	solarroadways.com

Solar Roadways Incorporated is a startup company based in Sandpoint, Idaho, that is developing solar powered road panels to form a smart highway. Their technology combines a transparent driving surface with underlying solar cells, electronics and sensors to act as a solar array with programmable capability. Solar Roadways Inc is working to develop and commercially produce road panels which are made from recycled materials and incorporate photovoltaic cells. ^[2]

History

In 2006, the company was founded by Scott and Julie Brusaw, with Scott as President and CEO. The company envisioned replacing asphalt surfaces with structurally-engineered solar panels capable of withstanding vehicular traffic."^[3] The proposed system would require the development of strong, transparent, and self-cleaning glass that has the necessary traction and impact-resistance properties. ^[4]

In 2009, Solar Roadways received a $100,000 Small Business Innovation Research (SBIR) grant from the Department of Transportation (DOT) for Phase I to develop and build a solar parking lot.^[5] In 2011, Solar Roadways received $750,000 SBIR grant from the DOT for Phase II to develop and build a solar parking lot.^[6] The DOT distinguishes the technology proposed by Solar Roadways Inc. as "Solar Power Applications in the Roadway," as compared to a number of other solar technologies categorized by the DOT as "Solar Applications along the Roadway."^[7] From SBIR grant money, Solar Roadways has built a 12-by-36-foot (3.7 by 11.0 m) parking lot covered with hexagonal glass-covered solar panels sitting on top of a concrete base, which are heated to help remove snow and ice, and also include LEDs to display messages. The hexagonal shape allows for better coverage on curves and hills. According to the Brusaws, the panels can sustain a 250,000 lb (110,000 kg) load. ^[8]

In April 2014, Solar Roadways started a crowdfunding drive at Indiegogo to raise money so they can get the product into production. In May, it was extended by another 30 days. The campaign raised 2.2 million dollars, exceeding its target of 1 million dollars.^[9] The drive became Indiegogo’s most popular campaign ever in terms of the number of backers it has attracted.^[10] The success was attributed in part to a Tweet made by George Takei, who played Sulu on Star Trek, due to his more than 8 million followers.^[11][12] One of the Brusaws’ videos went viral, with nearly 15 million views as of June 2014.^[12]

In 2014, doubt was expressed regarding the political feasibility of the project on a national scale by Jonathan Levine, a professor of urban planning at the University of Michigan. He suggested, however, that a single town might be able to deploy the concept in a limited test case such as a parking lot.^[13]

List of awards and honors

• 2009 EE Times Annual Creativity in Electronics (ACE) Awards "Best Enabler Award for Green Engineering" category finalist.^[14]
• 2010 EE Times Annual Creativity in Electronics (ACE) Awards "Most Promising Renewable Energy Award" category finalist.^[15]
• 2010 General Electric Ecoimagination Community Award of $50,000.^[16]
• 2013 World Technology Award finalist.^[17]
• 2014 Popular Science. One of 7 "Best of What's New" Engineering category.^[18]

Numerical cognition

From Wikipedia, the free encyclopedia

Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics is primarily concerned with empirical questions.

Topics included in the domain of numerical cognition include:

• How do non-human animals process numerosity?
• How do infants acquire an understanding of numbers (and how much is inborn)?
• How do humans associate linguistic symbols with numerical quantities?
• How do these capacities underlie our ability to perform complex calculations?
• What are the neural bases of these abilities, both in humans and in non-humans?
• What metaphorical capacities and processes allow us to extend our numerical understanding into complex domains such as the concept of infinity, the infinitesimal or the concept of the limit in calculus?

Comparative studies

A variety of research has demonstrated that non-human animals, including rats, lions and various species of primates have an approximate sense of number (referred to as "numerosity") (for a review, see Dehaene 1997). For example, when a rat is trained to press a bar 8 or 16 times to receive a food reward, the number of bar presses will approximate a Gaussian or Normal distribution with peak around 8 or 16 bar presses. When rats are more hungry, their bar pressing behavior is more rapid, so by showing that the peak number of bar presses is the same for either well-fed or hungry rats, it is possible to disentangle time and number of bar presses.

Similarly, researchers have set up hidden speakers in the African savannah to test natural (untrained) behavior in lions (McComb, Packer & Pusey 1994). These speakers can play a number of lion calls, from 1 to 5. If a single lioness hears, for example, three calls from unknown lions, she will leave, while if she is with four of her sisters, they will go and explore. This suggests that not only can lions tell when they are "outnumbered" but that they can do this on the basis of signals from different sensory modalities, suggesting that numerosity is a multisensory concept.

Developmental studies

Developmental psychology studies have shown that human infants, like non-human animals, have an approximate sense of number. For example, in one study, infants were repeatedly presented with arrays of (in one block) 16 dots. Careful controls were in place to eliminate information from "non-numerical" parameters such as total surface area, luminance, circumference, and so on. After the infants had been presented with many displays containing 16 items, they habituated, or stopped looking as long at the display. Infants were then presented with a display containing 8 items, and they looked longer at the novel display.

Because of the numerous controls that were in place to rule out non-numerical factors, the experimenters infer that six-month-old infants are sensitive to differences between 8 and 16. Subsequent experiments, using similar methodologies showed that 6-month-old infants can discriminate numbers differing by a 2:1 ratio (8 vs. 16 or 16 vs. 32) but not by a 3:2 ratio (8 vs. 12 or 16 vs. 24). However, 10-month-old infants succeed both at the 2:1 and the 3:2 ratio, suggesting an increased sensitivity to numerosity differences with age (for a review of this literature see Feigenson, Dehaene & Spelke 2004).

In another series of studies, Karen Wynn showed that infants as young as five months are able to do very simple additions (e.g., 1 + 1 = 2) and subtractions (3 - 1 = 2). To demonstrate this, Wynn used a "violation of expectation" paradigm, in which infants were shown (for example) one Mickey Mouse doll going behind a screen, followed by another. If, when the screen was lowered, infants were presented with only one Mickey (the "impossible event") they looked longer than if they were shown two Mickeys (the "possible" event). Further studies by Karen Wynn and Koleen McCrink found that although infants' ability to compute exact outcomes only holds over small numbers, infants can compute approximate outcomes of larger addition and subtraction events (e.g., "5+5" and "10-5" events).

There is debate about how much these infant systems actually contain in terms of number concepts, harkening to the classic nature versus nurture debate. Gelman & Gallistel 1978 suggested that a child innately has the concept of natural number, and only has to map this onto the words used in her language. Carey 2004, Carey 2009 disagreed, saying that these systems can only encode large numbers in an approximate way, where language-based natural numbers can be exact. One promising approach is to see if cultures that lack number words can deal with natural numbers. The results so far are mixed (e.g., Pica et al. 2004); Butterworth & Reeve 2008, Butterworth, Reeve & Lloyd 2008.

Neuroimaging and neurophysiological studies

Human neuroimaging studies have demonstrated that regions of the parietal lobe, including the intraparietal sulcus (IPS) and the inferior parietal lobule (IPL) are activated when subjects are asked to perform calculation tasks. Based on both human neuroimaging and neuropsychology, Stanislas Dehaene and colleagues have suggested that these two parietal structures play complementary roles. The IPS is thought to house the circuitry that is fundamentally involved in numerical estimation (Piazza et al. 2004), number comparison (Pinel et al. 2001; Pinel et al. 2004) and on-line calculation (often tested with subtraction) while the IPL is thought to be involved in overlearned tasks, such as multiplication (see Dehaene 1997). Thus, a patient with a lesion to the IPL may be able to subtract, but not multiply, and vice versa for a patient with a lesion to the IPS. In addition to these parietal regions, regions of the frontal lobe are also active in calculation tasks. These activations overlap with regions involved in language processing such as Broca's area and regions involved in working memory and attention. Future research will be needed to disentangle the complex influences of language, working memory and attention on numerical processes.
Single-unit neurophysiology in monkeys has also found neurons in the frontal cortex and in the intraparietal sulcus that respond to numbers. Andreas Nieder (Nieder 2005; Nieder, Freedman & Miller 2002; Nieder & Miller 2004) trained monkeys to perform a "delayed match-to-sample" task. For example, a monkey might be presented with a field of four dots, and is required to keep that in memory after the display is taken away. Then, after a delay period of several seconds, a second display is presented. If the number on the second display match that from the first, the monkey has to release a lever. If it is different, the monkey has to hold the lever. Neural activity recorded during the delay period showed that neurons in the intraparietal sulcus and the frontal cortex had a "preferred numerosity", exactly as predicted by behavioral studies. That is, a certain number might fire strongly for four, but less strongly for three or five, and even less for two or six. Thus, we say that these neurons were "tuned" for specific quantities. Note that these neuronal responses followed Weber's law, as has been demonstrated for other sensory dimensions, and consistent with the ratio dependence observed for non-human animals' and infants' numerical behavior (Nieder & Miller 2003).

Relations between number and other cognitive processes

There is evidence that numerical cognition is intimately related to other aspects of thought – particularly spatial cognition.^[1] One line of evidence comes from studies performed on number-form synaesthetes.^[2] Such individuals report that numbers are mentally represented with a particular spatial layout; others experience numbers as perceivable objects that can be visually manipulated to facilitate calculation. Behavioral studies further reinforce the connection between numerical and spatial cognition. For instance, participants respond quicker to larger numbers if they are responding on the right side of space, and quicker to smaller numbers when on the left—the so-called "Spatial-Numerical Association of Response Codes" or SNARC effect.^[3] This effect varies across culture and context,^[4] however, and some research has even begun to question whether the SNARC reflects an inherent number-space association,^[5] instead invoking strategic problem solving or a more general cognitive mechanism like conceptual metaphor.^[6][7] Moreover, neuroimaging studies reveal that the association between number and space also shows up in brain activity. Regions of the parietal cortex, for instance, show shared activation for both spatial and numerical processing.^[8] These various lines of research suggest a strong, but flexible, connection between numerical and spatial cognition.

Modification of the usual decimal representation was advocated by John Colson. The sense of complementation, missing in the usual decimal system, is expressed by signed-digit representation.

Ethnolinguistic variance

The numeracy of indigenous peoples is studied to identify universal aspects of numerical cognition in humans. Notable examples include the Pirahã people who have no words for specific numbers and the Munduruku people who only have number words up to five. Pirahã adults are unable to mark an exact number of tallies for a pile of nuts containing fewer than ten items. Anthropologist Napoleon Chagnon spent several decades studying the Yanomami in the field. He concluded that they have no need for counting in their everyday lives. Their hunters keep track of individual arrows with the same mental faculties that they use to recognize their family members. There are no known hunter-gatherer cultures that have a counting system in their language. The mental and lingual capabilities for numeracy are tied to the development of agriculture and with it large numbers of indistinguishable items.^[9]