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Degenerate Objects

Pulsar Light

Many researchers prefer the term “spin-powered pulsar” to “radio pulsar.” The reason is that many radio pulsars emit more electromagnetic energy in the visible, x-ray, and gamma-ray frequencies than in the radio frequencies, and several spin-power pulsars emit no detectable radio waves, appearing to us only through their x-ray emission. But despite the prominence of the x-rays in carrying away rotational energy, the emission of radio waves is the most prominent characteristic of spin-powered pulsars. Radio waves are detected from 99.8% of them, while x-rays are detected from only 4.4% of them.

The radio emission of a spin-powered pulsar represents about 10-6 of the power lost by the pulsar as inferred from the change in period. Among pulsars detected at x-ray energies, the power in x-rays is typically 10-3, and among young pulsars can be as high as 0.1, of the rotational energy lost by a pulsar. The energy lost as electromagnetic radiation is a small fraction of the total energy lost by a spin-powered pulsar. Most of the rotational energy lost by a pulsar is dumped into electrons and positron, which can reappear as a nebula surrounding the pulsar.

Characteristics of x-ray emitting pulsars

Like the radio pulsars as a whole, the pulsars that emit x-rays fall into two classes: young, isolated pulsars and millisecond pulsars. These two classes are apparent when looking at the rate of spin and the rate of spindown for the pulsars emitting x-rays. The young isolated pulsars have a much longer spin period and a much high rate of spindown than do the millisecond pulsars. While the young, isolated pulsars that emit x-rays rotate more slowly than once every 0.01 seconds, with a median of once per 0.1 seconds, the millisecond pulsars that emit x-rays rotate more rapidly than once every 0.01 seconds, with a median of once per 3 milliseconds. On the other hand, the rotational period of the young, isolated pulsars increases by more than 10−16 seconds per second, with a median value around 10−13, while the rotational period of the millisecond pulsars increase by less than 10−16 seconds per second, with a median value around 10−20 seconds per second.

 

The detection of x-rays from spin-powered pulsar segregates these pulsars from those without detectable x-rays. The fundamental characteristic that causes a radio pulsar to emit x-rays is a rapid rate of rotation. Among the young, isolated pulsars, those with detected x-rays are rotating and spinning down much more rapidly than those that are undetectable. This implies that the pulsars with detected x-rays are the youngest of this class of pulsar. The millisecond pulsars with detected x-rays are the most rapidly rotating of the millisecond pulsars, but they are also the millisecond pulsars with the lowest rate of spin down. This implies that the millisecond pulsars with detected x-rays are the millisecond pulsars with the weakest magnetic fields.

Radio Emission

The radio pulses from a pulsar occur over a very small fraction of the rotational period. Typically the duration of a radio pulse is from 1% to 5% of a pulsar's rotational period. The obvious and often quoted analogy is to a light house, where the lighthouse is dimly visible most of the time, but is very brilliant for the short time that the beam of light from the light house sweeps by us. But this picture is misleading, because the individual radio pulses from a pulsar are not at all regular; instead, the time separation between pulses can vary markedly, as can the shape of each pulse. What is constant is not the individual pulses, but the average pulse profile. Fold together the radio emission from a pulsar for several hundred rotations, and one finds a unique average pulse profile that is unvarying over many years. This invariance of the pulse profile makes pulsars extremely accurate clocks over many years.

The invariance of the radio pulse profile combined with the high frequency of the pulsar's rotation lend support to the basic theory for pulsars of a strongly magnetized and rapidly spinning neutron star. As the star spins, the rotating magnetic field generates a strong electric field that drives an electric current along the magnetic field lines above the magnetic poles of the neutron star. This electric current generates radio waves that travel in the same direction as the current, which is along the magnetic field lines. If the axis for the magnetic field is tilted relative to the rotation axis, as is the case with Earth's magnetic field, then we would see pulsed radio emission as the magnetic poles swept through our line of sight. We see a radio pulse when we are looking along magnetic field lines on which current is flowing. The magnetic field, which is frozen into the neutron star, sets the invariant pulse profile. The positions of the individual pulses, however, are set by where the electrical current is flowing in the magnetic field; clearly the electrical current must change its position within the magnetic field over time for the theory to account for the observations.

X-ray Emission

Like the radio waves, the x-rays can pulsate strongly, but they can also have a steady component. The strongly pulsating x-rays are associated with the electrical current in the magnetosphere of the pulsar, and the steady x-rays are associated with emission from the surface of the neutron star.

In many pulsars, the x-ray pulses are in phase with the radio pulses, which suggest the electrical current creating the radio waves is also creating the x-rays. But this does not hold for all pulsars, and in these pulsars, the pulsed x-rays must come from a different region of the pulsar's magnetosphere than the radio waves.

The steady x-rays are thermal, meaning the x-ray spectrum is characterized by a temperature. A black-body spectrum is associated with light from the photosphere of a star or the surface of a solid body, and similarly the black-body x-rays of a pulsar should be from the neutron star's surface. This radiation does not exhibit the dramatic pulsation of the non-thermal x-rays. The variation is gentle, suggesting that the temperature at the magnetic poles of the star is higher than at the magnetic equator.

Not surprisingly, x-rays from the millisecond pulsars are entirely pulsed, with no thermal component. This reflects the age of these pulsars, where the neutron star has had time to cool and where the amount of energy released by current flowing into the star's surface is much less than for a young pulsar. In contrast, the youngest of the pulsars have a strong thermal component than can exceed the pulsed x-ray emission by factors of 10 or more. Among the young pulsars with strong thermal x-ray emission are the Crab and the Vela pulsars. These two pulsars also emit visible light and gamma-rays.

1Kaspi, V.M., Roberts, M.S., and Harding, A.K. “Isolated Neutron Stars.” In Compact Stellar X-Ray Sources, edited by W.H.G. Lewin and M. van der Klis. Cambridge Astrophysics Series, no.39. Cambridge: Cambridge University Press, 2006.

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