The period changes regularly throughout the 1.7 day cycle. This can be interpreted as a Doppler shift (see Problem 12.7). We can think of the X-rays as a signal being emitted with a period of 1.24 s. When the source is moving away from us the period appears longer, and when the source is coming toward us the period appears shorter. The X-ray source also appears to be eclipsed every 1.7 days.

The mass transfer rate, estimated from the X-ray observations, is about 10—9 M0/yr. The luminosity is about 1037 erg/s. The temperature is estimated to be 108 K. At this temperature, we can estimate the frequency of a photon with energy kT. The frequency, v, is kT/h, or 2 X 1018 Hz. This corresponds to a wavelength of 0.14 nm, clearly in the X-ray part of the spectrum.

Theoreticians have speculated on the future evolution of such a system. The mass transfer rate may become so large that the X-ray emission is quenched. The outgoing X-rays are effectively blocked by the infalling material. This system may eventually end up as two compact objects.

Mass transfer in a system with a neutron star can also explain the existence of pulsars with very short periods, as short as a few milliseconds, known as millisecond pulsars. One of the intriguing features of these objects is that their periods are not decreasing as rapidly as those for normal pulsars. Some of them have values of P/(dP/dt) as large as 1010 per year. That is, in one year, the change in the period is only 10—10 (one-ten-billionth) of the period. This means that they are extraordinarily stable clocks (something which had originally been hoped for normal pulsars until their period changes were observed, as discussed in Chapter 11).

To see how mass transfer can explain millisecond pulsars, remember that if transferred material is not aimed directly at the center of the neutron star, it has a large amount of angular momentum. This explains the formation of an accretion disk, as material goes into orbit rather than falling onto the neutron star surface. As material leaks inward from the accretion disk onto a (normal) pulsar, it transfers a lot of angular momentum to the pulsar, causing a large increase in the rotation rate (decrease in the period). This explains how a normal pulsar can be "spun up" into a millisecond pul-

Binary Pulsar

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