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Pulsars, Pulsar Wind Nebulae, and Supernova Remnants

The connection between supernovae and radio pulsars was drawn within a year after the discovery of the first radio pulsar in 1967. The Crab pulsar PSR 0531+21 was discovered at the center of the Crab nebula; the birth of the pulsar is attributed to the supernova of 1054 AD observed by Chinese and Japanese astronomers. The discovery of the Crab pulsar was soon followed by the discovery of other pulsars in nebulae, such as the Vela Pulsar PSR 0833−45 in the Vela nebula. This association of pulsars with nebulae, however, does not mean that every pulsar is observationally associated with a nebula, nor does it mean that every supernova nebula contains a pulsar. Systematic searches of supernova nebulae have failed to find pulsars in most nebulae, and of the more than 1600 known radio pulsars, only 34 pulsars are associated with nebulae.1 But pulsars are found in supernova nebulae often enough and reasons why most pulsars should not be in supernova nebulae are strong enough that no astronomer doubts that pulsars are the remnant stars of core-collapse (type II) supernovae.

The pulsars associated with nebulae generally rotate more rapidly than those without this association. The median spin period for pulsars in nebulae is less than 0.2 seconds, compared to about 0.5 seconds for the general pulsar population. More striking, the pulsar associated with a nebula increases its period of rotation by a median value of 2×10-13 seconds per second, versus a median rate of increase for the general pulsar population of 2×10-15 seconds per second. This high spin rate and rapid loss of rotational energy—rapid by astronomical standards—by the pulsars associated with nebulae fits with the idea that these pulsars are young. An older pulsar has time to move far away from the supernova nebula. A pulsar is given a strong kick at birth that propels it with velocities of 400 to 500 km s−1; in several tens of thousands of years, the pulsar emerges from the supernova nebula. This motion can be seen in the Vela pulsar, where the pulsar, which is over 10,000 years old, is far from the center of the supernova remnant. The pulsars with the typical age of 2 million years have outlived their supernova nebulae, which have relatively short lives of 100,000 years. For these reasons, one expects only young pulsars to be in supernova nebulae.

The nebulae associated with supernovae come in two types: thin, hollow shells and twisting, filamented balls. A shell nebula is the supernova remnant created by the debris of a supernova driving into the surrounding gas at high velocity. An example of a shell nebula is the Kepler supernova remnant, which was created by a supernova observed in 1604 by the nebula's namesake, Johannes Kepler. This particular supernova remnant is an example of a supernova nebula without a pulsar. Nebulae of the second type, although they are sometimes called supernova remnants, are not created by supernovae; they are created by young pulsars. These nebulae are pulsar wind nebulae.2 The Crab nebula is the prototype. Often one finds a supernova nebula that is a remnant shell surrounding a pulsar wind nebula and a pulsar. The Vela nebula is an example of this more complex type of nebula. Several observed pulsars generate pulsar wind nebulae despite having exited their supernova remnants.

The difference between the two types of nebula is set by the processes creating each. The supernova shell is characterized by the energy released in a supernova explosion. This energy is massive, of order 1051 ergs, which is 0.06% of the Sun's rest mass energy. Much of this energy goes to driving the outer layers of the exploding star outward at a high velocity. A shell nebula is created when this material drives a shock wave into the ambient gas; the shock wave appears as a shell, because the gas immediately behind the shock wave has been heated to high temperature by the shock wave. The maximum size of a supernova shell depends on its surrounding; a typical radius is 10 parsecs. In contrast, the energy of a pulsar wind nebula is characterized by the energy extracted from a pulsar's spin. The youngest pulsars carry about 1049 ergs of rotational energy, and older pulsars carry much less energy than this. Typically this energy is dissipated over several thousand years as the pulsar expels a wind of electrons and positrons. This wind creates a turbulent cloud of electrons, positrons and magnetic field. The electrons and positrons travel at close to the speed of light, and as they move through the magnetic field, they emit radio wave, visible light, and x-rays in a process called synchrotron emission. This creates a bright nebula that is about 1 parsec in radius.

The Crab nebula is entirely a pulsar wind nebula. No trace of a shell nebula is seen, perhaps because the material expelled in the supernova explosion has not yet had time to drive a shock wave into the surroundings. At visible wavelengths, the nebula has bright, thin filaments, which inspired the nebula's name, and at the center of the nebula is a 14th magnitude star that is the radio pulsar.

Without the continuous input of energy from the pulsar, the Crab nebula would rapidly fade at x-ray and optical energies. The energetic electrons and positrons in the nebula that radiate at x-ray wavelengths lose their energy in less than a year, and the particles emitting visible light lose their energy in less than 1000 years.

For the Crab pulsar, assuming R = 10 km and M = 1.4 solar masses, and setting the period and rate of period change to their observed values of P = 0.033 s and dP/dt = 4.2 × 10−13, which corresponds to a slowing of 37 nanoseconds per 24 hours, one finds that the Crab pulsar loses 3.7 × 1038 erg s−1 from an energy reservoir of 1.8 × 1049 erg. The timescale for dissipating this energy is E/( dE/dt ), or 1,600 years., which is 60% longer than the pulsar's age. This is a tremendous amount of power to dissipate, exceeding the power generated by the Sun by a factor of 105. This power is dumped into the Crab nebula, where it is eventually radiated away as synchrotron radiation in the radio, visible, and x-ray bands . The energy emitted by the nebula is about equal to the rotational energy lost by the pulsar.

The irony of the Crab nebula and the Crab pulsar is that, despite their association with a historic supernova, they do not provide solid evidence for a connection between pulsars and supernovae. The Crab nebula is not a supernova remnant, and the association of the 1054 AD supernova with the Crab pulsar relies on the supernova being in proximity on the sky to the pulsar and the pulsar being about the right age to be created in the supernova. The solid evidence directly linking pulsars to supernovae is provided by the handful of supernova nebulae, such as the Vela supernova remnant, that combine supernova shell nebulae with pulsar wind nebulae and pulsars.

1Manchester, R.N., Hobbs, G.G., Teoh, A., and Hobbs, M. “The Australia Telescope National Facility Pulsar Catalogue.” The Astronomical Journal 129 (April 2005): 1993—2006.

2Gaensler, Bryan M., and Slane, Patrick O. “The Evolution and Structure of Pulsar Wind Nebulae.” In Annual Reviews of Astronomy and Astrophysics, edited by R. Blandford, J. Kormendy, and E. van Dishoeck, vol. 44, 17--47. Palo Alto, California: Annual Reviews, 2006.

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