Key ConceptsMost Type II supernovae leave behindan extremely dense neutron star. A neutron star is a compact object supported bydegenerate-neutron pressure. Rapidly rotating, strongly magnetic neutron starsproduce narrow beams of radiation. (1) Most Type II supernovae leave behind an extremely dense neutron star.Just a reminder: A type II supernova occurs when the iron coreof a supergiant star collapses to the density ofan atomic nucleus (a few hundred million tons percubic centimeter). At such tremendously high densities,protons and electrons are fused together into neutrons.The relevant reaction is this:e- + p -> n + neutrino About 1057 neutrinos are made in theiron core, as the protons (p) are converted to neutrons (n).The billion trillion trillion trillion trillion neutrinoscarry off most of the supernova"s energy (photons are justa minor byproduct of a supernova).After its ``bounce"", the star"s core settles down as asphere of tightly packed neutrons, known as a neutron star.A neutron star can be thought of as a single humongous atomicnucleus (containing roughly 1057 neutrons)with a mass between 1 and 3 solar masses, packed into asphere 5 to 20 kilometers in radius. To put thingsinto perspective, a neutron star is about as big asthe beltway around Columbus.In addition to being amazinglydense, neutron stars have other amazing properties: Rapidly rotating:up to 1000 rotations/second, comparedto 1 rotation/month for the Sun. Strongly magnetized:up to 1 trillion Gauss, compared to an average of1 Gauss for the Sun (and 0.5 Gauss for the Earth). Very hot: initially 1,000,000 Kelvin at the surface,compared to 5800 Kelvin for the Sun.The surface of a neutron star is not anyplace you would want tovisit. The gravitational acceleration is 100 billion g"s (that is,100 billion times the gravitational acceleration at the Earth"s surface). Theescape speed at the surface of a neutron star is half thespeed of light (that is, 150,000 km/sec, versus a paltry 11 km/sec forthe Earth). On the surface of a neutron star, you"d be simultaneouslyvaporized by the intense heat and squashed flat by the intensegravitational force. (2) A neutron star is a compact object supported by degenerate-neutron pressure.Neutrons, like electrons, must follow the laws of quantum mechanics.In particular, they must obey the Pauli exclusion principle, asoutlined in last Thursday"s lecture.The existence of neutron stars was actually first predictedin 1933, only a year after the discovery of the neutron.At a density of 1 ton/cm3, electrons are degenerate,and provide degenerate-electron pressure.At a density of 400 million tons/cm3, neutronsare finally degenerate, and provide degenerate-neutron pressure.The interior structure of a neutron star is fairly uncertain.(We don"t know a lot about how matter behaves at these amazinglyhigh densities.) One proposed model looks like this:
Just as there is an upper limit on the mass of a whitedwarf, there is an upper limit on the mass of a neutron star.White dwarfs can"t have M > 1.4 Msun; abovethis mass, the degenerate-electron pressure is insufficientto prevent collapse. Neutron stars can"t have M > 3 Msun;above this mass, the degenerate-neutron pressure isinsufficient to prevent collapse (the upper mass limitfor neutron stars is fairly uncertain). If a denseobject is too massive to be a white dwarf or a neutronstar, it"s BLACK HOLE TIME (more about black holes next week..)It"s certainly true that the laws of quantum mechanics predictthe existence of neutron stars. However, how can we detectthem, to verify that they actually exist? Well, neutronstars may be tiny, but they are also hot, and hence producea significant amount of blackbody radiation. R = 15 km = 0.00002 Rsun T = 1,000,000 K = 170 Tsun Therefore, L = (0.00002)2 (170)4 Lsun= 0.3 LsunAt a temperature of 1,000,000 Kelvin, the wavelength of maximumemission is at 2.9 nanometers -- in the X-ray range. We canhunt for hot neutron stars by looking for X-ray sources.Although most of the light from neutron stars is emittedat X-ray wavelengths, thenearest neutron star can also be glimpsed at visible wavelengths. (3) Rapidly rotating, strongly magnetic neutron starsemit narrow beams of radiation.Although neutron stars do emit blackbody radiation, theyare not simply boring spherical blackbodies, as stars are.Neutron stars have additional ways of emitting electromagneticradiation. The strong magnetic field and rapidrotation of a neutron star make it a very potentelectrical generator. (Here on Earth,commercial electrical generators workby rotating a series of magnets inside a coilof wires. The essential point is that you needto have a magnetic field in motion.) Theelectric field generated by the rotatingmagnetized neutron star is strong enough torip charged particles (such as electrons) awayfrom the surface of the neutron star.The charged particles follow the magneticfield lines to the north and south magneticpoles of the neutron star. (Remember, whenI discussed the magnetic field of the Sun, I pointedout that charged particles move most readilyalong the magnetic field lines, rather thanperpendicular to them.) The acceleratedparticles produce intense but narrowbeams of radiation,pointing away from the two magnetic poles.We can see one of these beams of lightONLY if it is pointing toward us, justas we see the light from a flashlight onlywhen it is pointing toward us.A complicating factor is that on a neutronstar, just as on Earth, the magneticpoles don"t coincide with therotational poles. Thus,the beams of radiation pointing away fromthe magnetic poles are at an angle tothe rotation axis of the neutron star;as the neutron star rotates, the beamsswing around in a cone. If a beam happensto sweep across our location in space, wesee a brief flash of light. (This is sometimesknown as the ``Lighthouse effect"". If youare down by the shore at night, you seelighthouses emit a blinking light. Thisis not because the lamp in a lighthouse isturned off and on, but because it insidea searchlight which is rotated around andaround.
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As the beam of light from thesearchlight sweeps across your location,you see a brief flash of light.)Neutron stars whose beams of electromagneticradiation happen to sweep across us arecalled pulsars; we"lllearn more about them in tomorrow"s lecture.Prof. Barbara Ryden (ryden