The Lighthouse Model

1. There is a well-defined period that challenges the accuracy of the best atomic clocks.

2. The periods range from about 4.3 seconds down to 0.0016 seconds (that is, 1.6 milliseconds).

3. The period of a pulsar decreases slowly with time. The typical rate of decrease is a few billionths of a second each day, which implies that the frequency of pulsation will drop to zero after about 10 million years.

Possible Explanations

Eclipsing binary stars vary their light output periodically. But by Kepler's third law, for a binary with solar-mass-sized objects to have a very short period the orbital separation must be very small. For a period of less than a second the separation must be no more than several thousand kilometers. This is smaller than the radius of white dwarfs. Neutron stars are smaller than this, but orbiting neutron stars would emit gravitational wave radiation (recall the discussion of the tests of general relativity). This would cause the orbiting stars to spiral together and the period would decrease. But pulsars are observed to have periods increasing with time, not decreasing. Thus, we must rule out eclipsing binaries as the cause of pulsars.

Pulsating variable stars vary their light output periodically. But we saw in discussing pulsating variables that the period for pulsation is inversely proportional to the square root of the density. No regular star, white dwarf, or neutron star has a density that can give the pulsation periods found for pulsars. So pulsars cannot be pulsating normal stars.

A rotating star could appear to pulse if it had some way to emit light in a beam that rotated with the source (just as a lighthouse appears to pulse as the beam sweeps over an observer). But what kind of star could give the required periods? Simple calculations show that only a very dense object could rotate fast enough and not fly apart because of the forces associated with the rapid rotation. A white dwarf is not dense enough. The minimum rotational period for a typical white dwarf would be several seconds; for shorter periods it would fly apart. But a neutron star is so dense that it could rotate more than a thousand times a second and still hold together, so rotating neutron stars could account for the observed periods for pulsars.

Thus, by process of elimination it was concluded that the only explanation for pulsars known that was consistent with the observations was that a pulsar must be a rapidly spinning neutron star. But for this mechanism to be a valid explanation of pulsars, we need a way for a spinning neutron star to beam radiation. The magnetic field of the neutron star offers such a possibility.

Magnetic Fields

A diagram of the magnetic field expected for a spinning neutron star is shown in the above figure. The pulsar mechanism is thought to be associated with this magnetic field through what is usually called the lighthouse mechanism.