Asteroseismology studies the internal structure of the Sun and other stars using oscillations. These can be studied by interpreting the temporal frequency spectrum acquired through observations. [1] In the same way, the more extreme neutron stars might be studied and hopefully give us a better understanding of neutron-star interiors, and help in determining the equation of state for matter at nuclear densities. Scientists also hope to prove, or discard, the existence of so-called quark stars, or strange stars, through these studies. [2] Fundamental information can be obtained of the General Relativity Theory by observing the gravitational radiation from oscillating neutron stars. [3]
The modes of oscillations are divided into subgroups, each with different characteristic behavior. First they are divided into toroidal and spherical modes, with the latter further divided into radial and non-radial modes. Spherical modes are oscillations in the radial direction while toroidal modes oscillate horizontally, perpendicular to the radial direction. The radial modes can be considered as a special case of non-radial ones, preserving the shape of the star in the oscillations, while the non-radial do not. Generally, only the spherical modes are considered in studies of stars, as they are the easiest to observe, but the toroidal modes might also be studied.
In the Sun, only three types of modes have been found so far, namely p-, g- and f- modes. Helioseismology studies these modes with periods in the range of minutes, while for neutron stars the periods are much shorter, often seconds or even milliseconds.
The extreme properties of neutron stars permit several others types of modes.
More details on stellar pulsation modes and a comparison with the pulsation modes of black holes can be found in the Living Review by Kokkotas and Schmidt. [12]
Generally, oscillations are caused when a system is perturbed from its dynamical equilibrium, and the system, using a restoration force, tries to return to that equilibrium state. The oscillations in neutron stars are probably weak with small amplitudes, but exciting these oscillations might increase the amplitudes to observable levels. One of the general excitation mechanisms are eagerly awaited outbursts, comparable to how one creates a tone when hitting a bell. The hit adds energy to the system, which excites the amplitudes of the oscillations to greater magnitude, and so is more easily observed. Apart from such outbursts, flares as they are often called, other mechanisms have been proposed to contribute to these excitations: [13]
The oscillations are damped through different processes in the neutron star which are not yet fully understood. The damping time is the time for the amplitude of a mode to decay to e−1. A wide variety of different mechanisms have been found, but the strength of their impact differs among the modes.
So far, most data about neutron-star oscillations come from the blasts of four specific Soft Gamma Repeaters, SGR, especially the event of 27 December 2004 from SGR 1806-20. Because so few events have been observed, little is known for sure about neutron stars and the physics of their oscillations. The outbursts which are vital for analyses only happen sporadically and are relatively brief. Given the limited knowledge, many of the equations surrounding the physics around these objects are parameterized to fit observed data, and where data is not to be found solar values are used instead. However, with more projects capable of observing these kinds of blasts with higher accuracy, and the hopeful development of w-mode studies, the future looks promising for better understanding one of the Universe's most exotic objects.
These oscilations can be observed through a gravitational wave observatories, like LISA. These kind of observations carry important information of the matter content of a neutron star, as well as fundamental information of the very nature of the spacetime itself. [14]
A neutron star is a collapsed core of a massive supergiant star. Stars that collapse into neutron stars have a total mass of between 10 and 25 solar masses (M☉), or possibly more for those that are especially rich in elements heavier than hydrogen and helium. Except for black holes, neutron stars are the smallest and densest known class of stellar objects. Neutron stars have a radius on the order of 10 kilometers (6 mi) and a mass of about 1.4 M☉. They result from the supernova explosion of a massive star, combined with gravitational collapse, that compresses the core past white dwarf star density to that of atomic nuclei.
A magnetar is a type of neutron star with an extremely powerful magnetic field (~109 to 1011 T, ~1013 to 1015 G). The magnetic-field decay powers the emission of high-energy electromagnetic radiation, particularly X-rays and gamma rays.
X-ray bursters are one class of X-ray binary stars exhibiting X-ray bursts, periodic and rapid increases in luminosity that peak in the X-ray region of the electromagnetic spectrum. These astrophysical systems are composed of an accreting neutron star and a main sequence companion 'donor' star. There are two types of X-ray bursts, designated I and II. Type I bursts are caused by thermonuclear runaway, while type II arise from the release of gravitational (potential) energy liberated through accretion. For type I (thermonuclear) bursts, the mass transferred from the donor star accumulates on the surface of the neutron star until it ignites and fuses in a burst, producing X-rays. The behaviour of X-ray bursters is similar to the behaviour of recurrent novae. In the latter case the compact object is a white dwarf that accretes hydrogen that finally undergoes explosive burning.
Asteroseismology is the study of oscillations in stars. Stars have many resonant modes and frequencies, and the path of sound waves passing through a star depends on the speed of sound, which in turn depends on local temperature and chemical composition. Because the resulting oscillation modes are sensitive to different parts of the star, they inform astronomers about the internal structure of the star, which is otherwise not directly possible from overall properties like brightness and surface temperature.
Helioseismology, a term coined by Douglas Gough, is the study of the structure and dynamics of the Sun through its oscillations. These are principally caused by sound waves that are continuously driven and damped by convection near the Sun's surface. It is similar to geoseismology, or asteroseismology, which are respectively the studies of the Earth or stars through their oscillations. While the Sun's oscillations were first detected in the early 1960s, it was only in the mid-1970s that it was realized that the oscillations propagated throughout the Sun and could allow scientists to study the Sun's deep interior. The modern field is separated into global helioseismology, which studies the Sun's resonant modes directly, and local helioseismology, which studies the propagation of the component waves near the Sun's surface.
A stellar black hole is a black hole formed by the gravitational collapse of a star. They have masses ranging from about 5 to several tens of solar masses. They are the remnants of supernova explosions, which may be observed as a type of gamma ray burst. These black holes are also referred to as collapsars.
A pulsar is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. This radiation can be observed only when a beam of emission is pointing toward Earth, and is responsible for the pulsed appearance of emission. Neutron stars are very dense and have short, regular rotational periods. This produces a very precise interval between pulses that ranges from milliseconds to seconds for an individual pulsar. Pulsars are one of the candidates for the source of ultra-high-energy cosmic rays.
A millisecond pulsar (MSP) is a pulsar with a rotational period less than about 10 milliseconds. Millisecond pulsars have been detected in radio, X-ray, and gamma ray portions of the electromagnetic spectrum. The leading hypothesis for the origin of millisecond pulsars is that they are old, rapidly rotating neutron stars that have been spun up or "recycled" through accretion of matter from a companion star in a close binary system. For this reason, millisecond pulsars are sometimes called recycled pulsars.
PSR J0737−3039 is the first known double pulsar. It consists of two neutron stars emitting electromagnetic waves in the radio wavelength in a relativistic binary system. The two pulsars are known as PSR J0737−3039A and PSR J0737−3039B. It was discovered in 2003 at Australia's Parkes Observatory by an international team led by the Italian radio astronomer Marta Burgay during a high-latitude pulsar survey.
The Hulse–Taylor pulsar is a binary star system composed of a neutron star and a pulsar which orbit around their common center of mass. It is the first binary pulsar ever discovered.
A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. Binary pulsars are one of the few objects which allow physicists to test general relativity because of the strong gravitational fields in their vicinities. Although the binary companion to the pulsar is usually difficult or impossible to observe directly, its presence can be deduced from the timing of the pulses from the pulsar itself, which can be measured with extraordinary accuracy by radio telescopes.
The Tolman–Oppenheimer–Volkoff limit is an upper bound to the mass of cold, non-rotating neutron stars, analogous to the Chandrasekhar limit for white dwarf stars. Stars more massive than the TOV limit collapse into a black hole. The original calculation in 1939, which neglected complications such as nuclear forces between neutrons, placed this limit at approximately 0.7 solar masses (M☉). Later, more refined analyses have resulted in larger values.
In X-ray astronomy, quasi-periodic oscillation (QPO) is the manner in which the X-ray light from an astronomical object flickers about certain frequencies. In these situations, the X-rays are emitted near the inner edge of an accretion disk in which gas swirls onto a compact object such as a white dwarf, neutron star, or black hole.
Gravitational waves are waves of the intensity of gravity that are generated by the accelerated masses of binary stars and other motions of gravitating masses, and propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the gravitational equivalent of electromagnetic waves. Gravitational waves are sometimes called gravity waves, but gravity waves typically refer to displacement waves in fluids. In 1916 Albert Einstein demonstrated that gravitational waves result from his general theory of relativity as ripples in spacetime.
Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, or by timing the movements of active features on the surface.
Gamma-ray burst progenitors are the types of celestial objects that can emit gamma-ray bursts (GRBs). GRBs show an extraordinary degree of diversity. They can last anywhere from a fraction of a second to many minutes. Bursts could have a single profile or oscillate wildly up and down in intensity, and their spectra are highly variable unlike other objects in space. The near complete lack of observational constraint led to a profusion of theories, including evaporating black holes, magnetic flares on white dwarfs, accretion of matter onto neutron stars, antimatter accretion, supernovae, hypernovae, and rapid extraction of rotational energy from supermassive black holes, among others.
SGR 1627−41, is a soft gamma repeater (SGR), located in the constellation of Ara. It was discovered June 15, 1998 using the Burst and transient Source Experiment (BATSE) and was the first soft gamma repeater to be discovered since 1979. During a period of 6 weeks, the star bursted approximately 100 times, and then went quiet. The measured bursts lasted an average of 100 milliseconds, but ranged from 25 ms to 1.8 seconds. SGR 1627−41 is a persistent X-ray source. It is located at a distance of 11 kpc in the radio complex CTB 33, a star forming region that includes the supernova remnant G337.0-0.1.
PSR B1937+21 is a pulsar located in the constellation Vulpecula a few degrees in the sky away from the first discovered pulsar, PSR B1919+21. The name PSR B1937+21 is derived from the word "pulsar" and the declination and right ascension at which it is located, with the "B" indicating that the coordinates are for the 1950.0 epoch. PSR B1937+21 was discovered in 1982 by Don Backer, Shri Kulkarni, Carl Heiles, Michael Davis, and Miller Goss.
A pulsar timing array (PTA) is a set of galactic pulsars that is monitored and analyzed to search for correlated signatures in the pulse arrival times on Earth. As such, they are galactic-sized detectors. Although there are many applications for pulsar timing arrays, the best known is the use of an array of millisecond pulsars to detect and analyse long-wavelength gravitational wave background. Such a detection would entail a detailed measurement of a gravitational wave (GW) signature, like the GW-induced quadrupolar correlation between arrival times of pulses emitted by different millisecond pulsar pairings that depends only on the pairings' angular separations in the sky. Larger arrays may be better for GW detection because the quadrupolar spatial correlations induced by GWs can be better sampled by many more pulsar pairings. With such a GW detection, millisecond pulsar timing arrays would open a new low-frequency window in gravitational-wave astronomy to peer into potential ancient astrophysical sources and early Universe processes, inaccessible by any other means.
Valeria Ferrari is an Italian physicist whose research concerns the theoretical modeling of gravitational waves, and the oscillations in black holes and neutron stars that could cause them. She is a professor of theoretical physics at Sapienza University of Rome.
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