Stellar Remnants

There is as yet no comprehensive theory to describe the final stages of evolution of a star: the formation of a white dwarf, the collapse to a neutron star or black hole, or the total disruption of a star by thermonuclear detonation.

… There is no clear and consistent transition from the equilibrium stages of evolution, as described by a stellar evolutionary track on the Hertzsprung-Russell diagram, to the final thermonuclear detonation or collapse of the core…- T. A. Lozinskaya, American Institute of Physics (1992 : 115)White dwarfs, neutron stars, and black holes are born when normal stars dies, that is, when most of their nuclear fuel has been consumed.

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A solar mass star spends about 1010 years on the main sequence, during which time hydrogen fusion (into helium) provides its energy source. Eventually, the amount of H in the core becomes depleted, much of the initial H having been converted into He. As the scale of proton-proton fusion (i.

e., hydrogen burning) diminishes, the equilibrium between the forces of gravity and the radiation pressure within a star is upset and the core contracts under gravity. As gravity takes over, the core temperature rises (Rose 1998).The evolution of stars accelerates when they near the end of their lives as normal stars, with their structure undergoing radical changes. As the core becomes smaller and heats up, the outside of the star cools and expands. During these final stages, a significant fraction of the mass of these stars, enriched with heavy elements generated in their interiors, is dispersed into surrounding space.

The ejected gas, mixed with local interstellar medium can then be recycled to form new stars and planetary systems. Left behind is a compact stellar remnant — a white dwarf, with a radius 100 times smaller than that of the Sun; or a neutron star, with a radius 1,000 times smaller; or a black hole, with an effective radius that is several times smaller yet though its mass is comparable to that of a neutron star. Stellar remnant is thus a collective term used to describe the exotic objects that are left when a high mass star or a low mass star dies: white dwarfs, neutron stars, black holes (Fields et al., 1998).Stellar objects can in fact be more exotic than we know them to be. For instance, most of the mass of any galaxy is dominated by a component concentrated at the center of the galaxy. This nucleus dominates the galaxy’s dynamics throughout, and is known as the dark matter halo. The mysterious dark matter halo is the single largest part of the Galaxy, covering the space between 100,000 light-years to 300,000 light-years from the galactic center.

Scientists often speculate on the possibility of this dark matter being made up of stellar remnants, such as primordial white dwarfs (Silk 1993). On the other hand, Massive Compact Halo Objects, or MACHOs, are surmised to exist in huge numbers in vast halos surrounding galaxies, presumably accounting for much of the missing matter of the galaxies. Stellar remnants are again sometimes considered to be possible candidates for MACHOS (Graff et al, 1999). In short, there are grounds to believe that the mysterious missing matter of universe is at least in part made up of dying stars, although there are growing indications pointing in other directions.Stellar death need not be regarded as the endpoint of a star, most commonly it denotes a very dynamic and intriguing final phase of a star’s life cycle, representing a metamorphosis in which stars that had been powered by nuclear reactions are reborn as “compact objects.” The evolution and eventual fate of stars in the late stages of their lives are critically dependent on the amount of matter they have at birth. Most stars with a mass more than about eight times that of the Sun end their lives in the titanic explosion of a supernova. The stellar remnants are neutron stars or black holes.

Stars less massive than about eight times the mass of the Sun evolve into red giants, so large that at the position of the Sun they would envelop the orbit of Earth. Their distended envelopes, or the planetary nebulae, are ejected soon afterward. The stellar remnants in this case are white dwarfs.

On occasions, white dwarfs themselves can lead to supernova explosions and result in neutron stars.Becoming these small dense spheres of degenerate matter that slowly cool and radiate heat, most stars end their lives. However, these fantastic star remnants have a “pulsating” life of their own. Besides their exceedingly small size, the most fundamental way in which the three species of dead stars or stellar remnants differ from normal stars is that they do not burn nuclear fuel, and cannot support themselves against gravitational collapse by generating thermal pressure. In an ordinary gas, the pressure depends on the density and on the temperature. At very high densities, a mutual repulsion develops between electrons. This repulsion is not due to the classical behavior of their electrical charge: rather, it is due to their quantum mechanical properties.

This repulsion produces an additional pressure, the so-called degenerate pressure, which depends on the density alone, not the temperature. Thus, the material can be heated without expanding, and can be cooled without shrinking. The degenerate pressure halts the gravitational collapse, like the ideal gas pressure, with one significant difference: when material is added, the gravity of the star increases, but the increase in the degenerate pressure is not as high as in ordinary matter.

Therefore, the star shrinks. The higher the mass of a degenerate star, the smaller its volume.White dwarfs are supported by the pressure of degenerate electrons, while neutron stars are supported largely by the pressure of degenerate neutrons. Electrons degenerate when the density equals to 109 kg/m3. Neutrons are degenerate when the density equals to 1018 kg / m3. Black holes, on the other hand, are completely collapsed stars — that is, stars that could not find any means to hold back the inward pull of gravity and therefore collapsed to singularities (Tayler 2004).

White DwarfsMedium-sized stars, such as the sun, eventually consume all of the nuclear fuel available. A star of mass in the range of 1 to 8 solar masses collapses at the core when all the protons in the core have been fused into helium nuclei. The core temperature rises enabling the helium nuclei to fuse into heavier nuclei.

The core keeps shrinking and becoming hotter, while the surface expands. Hydrogen nuclei (i.e., protons) surrounding the core start to fuse and the outer layers of the star expand and cool. The star swells out to become a red giant. In the very last stage of its life as a star, the core collapses into a white dwarf, while the remaining hydrogen drifts away into a shell of gas as a “planetary nebula.” The core contracts until electron degeneracy pressure provides the support against gravity, after which the star does not shrink as it cools.White dwarfs evolve from the central stars of these so-called planetary nebulae, and their final mass depends on the original mass their main-sequence stars.

For a star of one solar mass, the resulting white dwarf is of about 0.6 solar masses, compressed into approximately the volume of the Earth. If the progenitor star was 2-8 MSun, the white dwarf would be 0.7-1.4 MSun. For stars less than twice the sun’s mass, the corresponding white dwarf mass is 0.6-0.7 sun mass.

For stars less than the mass of sun, the final white dwarf mass would be less than 0.6 sun mass.White dwarfs are hot (~10,000 K), low luminosity stars composed mainly of carbon, helium, neon, magnesium and other elements. The stars’ light comes from the trapped residual heat.

The temperatures in the star, however, are not hot enough to have carbon and oxygen burn, as a result no further nuclear reactions occur. The exact chemical composition of the white dwarfs varies from one to another, depending upon the original mass of the progenitor star. A white dwarf is composed chiefly of carbon and oxygen if the progenitor star is approximately of sun’s mass and is therefore unable to ignite carbon fusion. A white dwarf is composed chiefly of oxygen, neon, and magnesium, when the progenitor star is of a few solar masses, and capable of setting off carbon fusion to form magnesium, neon, and smaller amounts of other elements. White dwarfs are very dim.

The luminosities of the central stars of planetary nebulae drop rapidly as they evolve into white-dwarf end-state (Rose 1998). The luminosity of these white dwarfs appears to be particularly low also because their surface is small. Although they are relatively easy to discover, follow-up observations to discover their astrophysical properties require gigantic telescopes (Luyten 1971).The electrons in white dwarfs are degenerate, and therefore the more mass there is in the white dwarf, the smaller the radius. For example, for O.5 MSun, the radius is 1.

5 REarth, and for 1.0 MSun, the radius becomes 0.9 REarth. The largest possible white dwarf mass is 1.4 MSun. This is called the Chandrasekhar limit, and is the most mass that the electron degenerate core can support without collapsing under its own gravity. A white dwarf star is unstable if it exceeds 1.4 MSun.

This upper limit on its mass represents the maximum possible density of matter above which electrons and protons fuse to form neutrons. A white dwarf star of mass below 1.4 MSun might accrete matter due to its intense gravity from the surrounding space or it might draw matter in from it companion if it is a binary star. If this process of accretion causes its mass to reach 1.

4 MSun, an outburst of energy and matter is caused as the star overheats due to the interaction between its electrons and protons. As white dwarf’s mass exceeds the Chandrasekhar limit, the electron degeneracy pressure fails due to electron capture and the star collapses and explodes into a Type I supernova. In the collapse, electrons and protons combine in the core to form neutrons. Nuclei in the outer layers absorb neutrons to form heavier nuclei before the outer layers are thrown off by the collapsing core.

This process would result in the formation of a neutron star (Tayler 2004).Except in the aforementioned scenario, white dwarfs are stable. Once a white dwarf forms, it begins to cool off, but the degenerate pressure inside does not drop and the star does not shrink on cooling. The stability of the white dwarf is the outcome of the inward pull of gravity being balanced by the degeneracy pressure of the star’s electrons.

With no fuel left to burn, the star radiates its remaining heat into space for billions of years. As the star cools, its luminosity decreases, and this process slows over time, so that the dimmer the star gets, the slower it gets dimmer. The correspondence between the luminosity and the age for a 0.

6 MSun white dwarf would  go as follows: 0.1 LSun at 20 million years, 0.01 LSun at 300 million years, 0.001 LSun at 1 billion years and 0.0001 LSun at 6 billion years. At 6 billion years, although the temperature (and therefore the color) of the white dwarf is about the same as the Sun’s surface, the luminosity would be much less, because this star, or rather stellar remnant, is so tiny in size.

The faintest observed white dwarfs are therefore very old (Mestel, Koester  & Salpeter 1992). Eventually white dwarfs would fade off, perhaps becoming part of dark matter.Neutron Stars, Pulsars, and Black HolesA neutron star is the core of a supernova remnant and is a million times denser than the Earth.

Neutron stars rotate rapidly, some of them emitting radio waves in oppositely directed beams that sweep round as the star rotates. Main-sequence stars with mass in the range of 8-25 MSun become supernovae (Type II), lose a lot of their envelope, and leave a degenerate neutron core behind. A supernova is an extremely violent event, producing a colossal outburst of light which decays with a half-life of about 80 days. The star is literally blown apart, leaving a core that may consist of a neutron star or a black hole, or, in some cases it may get blown apart completely leaving nothing behind. Neutron stars and black holes are thus the compact stellar remnants that form from the most massive stars (Wijers et al., 1998). Neutron stars are the extremely dense cores of dead stars composed only of neutrons.

It is estimated that there are 105 active and 108 defunct neutron stars in the Galaxy (Lorimer et al., 1993) Like white dwarfs, neutron stars also get smaller when they are more massive. For example, a 0.7 MSun neutron star has a radius of 10 km. The maximum mass of a neutron star is assumed to be between 1.

5 and 2.7 MSun.Neutron stars collapse from larger stars, and during that collapse, angular momentum must be conserved. Therefore, the stars are rotating very rapidly. Occasionally, a pulsar suddenly increases its rate of rotation, causing its period to jump in a so-called ‘glitch’. This occurs when a pulsar suddenly contract, just as when a spinning ice skater pulls his or her arms in. Pulsars also have large magnetic fields — a trillion times stronger than Earth’s — due to the collapse and compression of the original magnetic field of the star.

The axis of a neutron star’s strong magnetic field is not necessarily the same as the axis of its rotation. Neutron stars become pulsars when the magnetic field axis is not aligned with the rotation axis. A pulsar is a rapidly rotating neutron star, created as the stellar remnant during a Type II supernova explosion of a massive star (Gotthelf, Vasisht 1998). Along the magnetic field lines that come out of the poles of these pulsars are many spiraling charged particles, which emit radiation. Each time the beam sweeps past the Earth, a radio pulse is detected.

The period of a pulsar, or the gap between two pulses, is most commonly less than a second, though it typically ranges from 0.25 to 2 seconds (Sturrock 1971). Each pulse lasts on the order of a few microseconds. A typical pulsar is of the order of less than 100 km in diameter and with a mass of about two suns. All pulsars would gradually slow down. This is evident from the gradual increase of the period of a pulsar.

A supernova event can either lead to a neutron star or a black hole. If the mass of the stellar remnant is very high, no physical process can provide support against the gravitational collapse (Padmanabhan 2000). The neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. Schwarzchild radius is the critical radius at which singularity occurs and for mass M, this radius Rs is given byRs = 2GM/ c2If an object is completely contained within its Schwarzchild radius, a singularity will occur (Kenyon 1990).

 In the case of a massive star, it will form a black hole and is likely to exert a very strong gravitational influence on its surroundings. The mass at which the stellar remnant becomes a black hole is not known with certainty, but is estimated at between 2 and 3 solar masses. Once a black hole has formed, and after all the stellar matter has disappeared into the singularity, the geometry of space-time itself continues to collapse towards the singularity (Luminet 1998). A black hole is, by definition, a region in spacetime in which the gravitational field is so strong that it precludes even light from escaping to infinity. Black holes arise because gravity affects the way light waves travel through space. Einstein’s general relativity both predicted black holes and is employed to the full in the description of black holes.Black holes are objects who properties are absolutely fantastic.

The properties of space and time are changed inside the black hole in a most puzzling manner.The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time. And since the general theory of relativity provides only a single unique family of solutions for their descriptions, they are the simples objects as well.

(Chandrasekhar 1992 : 1)Space and time get coiled into what resembles a funnel, with a boundary deep inside it (event horizon) beyond which both time and space break down into quanta. Black holes are also the most grandiose energy sources of the universe. It is most likely that what we observe in remote quasars and in the exploding nuclei of galaxies are manifestations of black holes. There is considerable evidence for the presence of massive black holes in the center of active galaxies (Collmar & Schonfelder 1998).

Massive black holes in Active Galactic Nuclei (AGNs) accrete matter from their environments, converting gravitational energy to electromagnetic energy. However, the case for massive black holes being present at the center of most galaxies is not yet watertight (Maoz 1998).In the same way as black holes which can be paradoxically regarded as the most complex and yet most simple objects existing in space and time, the stellar remnants that are usually regarded as the dying embers of the fires that were once living stars happen to be some of the most active, dynamic and extreme objects in the known universe. Even if they do not account for the dark matter of the universe, these compact astronomical objects continue to be some of the most mysterious entities imaginable. The study of them has yet to reveal us greater secrets in the years to come.