Neutron stars are final products of stellar evolution. It is widely accepted that they are born in supernova explosions after their presupernova progenitors (giant or supergiant stars) exhaust nuclear fuel in their cores. The cores undergo gravitational collapse into neutron stars (or black holes), while outer presupernova layers are blown away by an expanding shock wave, producing supernova remnants. The whole event is usually referred to as a core-collapse (type II) supernova explosion (see, e.g., Imshennik & Nadyozhin 1988; Arnett 1996, and references therein). The neutron star - supernova connection was suggested by Baade and Zwicky in 1933 as described in § 1.2.
The explosion, which occurs in the presupernova core, triggers a shock wave propagating outward (after bouncing off the dense core). It takes several hours for the shock to travel through extended presupernova outer layers. At this stage the presupernova, observed from outside, looks just as usual, as if nothing happened in its interior. After the shock reaches the surface, it produces a splash of radiation in all bands of electromagnetic spectrum to be observed as a supernova event. In addition, the core collapse itself should be accompanied by a powerful outburst of neutrino emission and, possibly, of gravitational radiation. These events could be detectable by neutrino and gravitational observatories prior to the electromagnetic outburst.
Supernova explosions are accompanied by an enormous energy release, a few times 1053 erg in total (of the order of the gravitational energy of a neutron star, Eq. (1.1)). It is expected that the energy is mostly released in the form of neutrinos. About 1% of the total energy transforms into the kinetic energy of the explosion ejecta, and only a minor part 1049 erg) into electromagnetic radiation; a smaller part can be emitted in the form of gravitational waves.
Theoretical simulations of gravitational collapse are extremely complicated because they should generally involve three-dimensional hydrodynamics with neutrino transport and convection. Many attempts to simulate the collapse (in inevitably restricted formulations) failed to reproduce a neutron star birth accompanied by the formation of a powerful outgoing shock wave (see, e.g., Janka 2004 and references therein). The collapse and supernova explosion can be strongly affected by the combined effect of stellar rotation and magnetic field (see, e.g., Moiseenko et al. 2003, Akiyama et al. 2003, and references therein).
A gravitational collapse of a degenerate stellar core occurs on time scales of 0.1 s. If the shock wave produced by the core bounce is successful in ejecting the outer layers, it should result in the appearance of a protoneutron star with the internal temperature T ~ 1011 K (see, e.g., Pons et al. 2001 and references therein). This protoneutron star is very special. It is hot, opaque to neutrinos, and larger than an ordinary neutron star. It lives for about one minute and transforms then into an ordinary neutron star which is transparent for neutrinos.
Current estimates of supernova explosion rate in the Galaxy are uncertain and give one event per 60-1000 years (e.g., Arzoumanian et al. 2002). Electromagnetic radiation from some of these explosions cannot be observed from the Earth, being hidden by gaseous and dust-grain clouds in the Galactic plane. The total number of neutron stars in the Galaxy is estimated as 108 — 109. Only a very limited fraction of these stars can be observed.
Supernova explosions in the Galaxy were observed by naked eye centuries ago (for recent reviews of such historical supernovae see Green & Stephenson 2002,2003). The most prominent observation is dated back to 1054. It was the birth of the Crab Nebula and the Crab pulsar at its heart. In modern times, it was sinologist Edouard Biot (the son of famous physicist J.-B. Biot) who first paid attention to a "guest star" reported in Chinese chronicles for AD 1054 (Biot, 1846). Other Chinese, Japanese, Arabic, and European historical records were discovered in the 20th century. The extraordinary bright star appeared probably in April,6 remained visible in daylight till August of 1054 and gradually faded away to 1056. Lundmark (1921) listed this star as a "suspected nova," Hubble (1928) noticed that its position was at the center of the Crab Nebula, and Mayall (1939) identified it as a supernova.
Nowadays astronomers detect several tens of type II supernovae per year from distant galaxies (too far away to study collapsars).
Any association of a neutron star with a supernova remnant has a great importance: the age and distance to the star are those of the remnant. Many neutron stars acquire large proper velocities (kicks, § 1.4.7) during their births and leave quickly their parental supernova remnants. Supernova remnants themselves dissolve in ~ 105 years after explosion. Thus, the majority of neutron stars are not related to observable supernova remnants.
A newly born neutron star remains hidden behind an expanding supernova envelope for several years. This prevents direct observation of very young neutron stars.
The most famous supernova detected in the present epoch is the supernova 1987A. It was discovered in the nearby Large Magellanic Cloud on February 23,1987, really close 50 kpc) to us (see, e.g., Imshennik & Nadyozhin 1988; Arnett 1996, and references therein). This is the first (and still the only one) supernova from which the neutrino outburst was observed. All the attempts to find a collapsar (a neutron star or a black hole) in this supernova remnant have failed. Nearby supernova explosions are rare. However, we should be ready to witness a new event.
Let us remark that neutron stars can also be formed via a collapse of accreting white dwarfs in binary systems, after the white dwarf mass exceeds the Chandrasekhar limit. This accretion induced collapse occurs only under specific conditions when electron captures effectively decrease the Chandrasekhar mass limit (Nomoto 1987; Nomoto & Kondo 1991; for a review see Canal 1994). The number of neutron stars formed in this way is expected to be small (Fryer et al., 1999), but it may be the only viable scenario of their formation in some binaries (see, e.g., Nomoto & Kondo 1991; van Paradijs et al. 1997, and references therein). Let us remind that the majority of accreting white dwarfs, whose masses become close to the Chandrasekhar limit, are disrupted by a thermonuclear explosion, producing supernova Ia events (see Nomoto et al. 1994 for a review).
6There were debates about the date of its appearance and about credibility of different records. The most detailed Chinese report indicates July 4, but other historical sources point to earlier dates. For the list of the historical observations, references, and discussion, see Collins et al. (1999) and Polcaro & Martocchia (2006).
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