Searches for Planets

In 1991, a group at the Jodrell Bank Radio Observatory published a letter in Nature, claiming that a 10 Earth mass planet was orbiting radio pulsar PSR B1829-10, in a six month orbit (Bailes et al., 1991). The detection relied on the periodic delay and advance of the arrival of the radio pulses from the pulsar at Earth. As the conjectured planet orbited the pulsar, its small but finite mass caused the pulsar to undergo a tiny reflex orbit about the center of mass of the pulsar-planet system. Since the planet orbited at a radius of about a hundred million km, the pulsar orbited the system's center of mass with an orbital radius smaller by a factor equal to the ratio of the mass of the planet to that of the pulsar - a factor of about ten thousand. But the pulsar's motion, over about 10,000 km in radial distance, translated to a periodic delay, and then advance, in radio pulse arrival times, by the time it took for the radio beam to travel the extra distance - a few tens of milliseconds. Since the pulse arrival time was measurable to a precision of a millisecond or so, the periodic change in arrival time was easily measured. Unfortunately, the discovery claim had to be retracted a few months later, in January 1992, at a meeting of the American Astronomical Society. The observed planet was an artefact, caused by an erroneous model for the motion of the Earth within the Solar System. To measure the relative arrival time of the pulses, observers usually subtract the motion of the Earth about the center of mass of the Solar System, but the orbital parameters used in analysing the data on PSR B1829-10 were not precise, and the observations were showing a second harmonic of the Earth's orbit, due to the fact that the Earth's orbit is slightly eccentric. This was not the first claimed discovery of a planet orbiting a pulsar; (Demianski & Proszynski, 1979) had previously found variations in the arrival times of the well-known, bright, 0.714 s pulsar PSR B0329+54, which they suggested were consistent with a planet having a mass less than that of the Earth, but subsequent observations failed to confirm the claim. It seems like that the observed variations in the pulse arrival times for PSR B0329+54 are caused by spin irregularities inherent in this relatively young (~5 x 106 year old) neutron star.

Immediately after the retraction on the candidate planet around PSR B1829-10, came the announcment of the planets around PSR B1257+12, with strong confirmation by further observations following within a couple of years (Wolszczan, 1994).

There are three planets in the PSR B1275+12 system: A is only about twice as massive as Earth's Moon and has an orbital period of 25.26 days; B is about four times as massive as the Earth, with an orbital period of 66.54 days; and C is nearly four times as massive as the Earth, with an orbital period of 98.21 days

Fig. 8.1. Artist's impression of the PSR B1257+12 planet system. (adapted from NASA/Caltech-JPL/R. Hurt (Spitzer Science Center), by permission.)

(Konacki & Wolsczcan, 2003). PSR B1257+12 is different from PSR B1829-10 and PSR B0329+54, because it is a millisecond pulsar, with a spin period of only 6.2 milliseconds. Millisecond pulsars constitute a few percent of the observed pulsar population. As the name indicates, they have spin periods, and hence pulse intervals, measured in milliseconds, rather than seconds. They typically have weaker magnetic fields than regular pulsars (hundreds of millions of gauss fields, compared with trillions of gauss for regular pulsars and a gauss for the Earth). Because of their weaker magnetic fields, and very high rotational kinetic energy, the millisecond pulsars spin-down over periods of billions of years, and therefore can be observed as pulsars for a correspondingly longer time; most of the millisecond pulsars we observe are hundreds of millions to several billion years old. Because of their very high rotational kinetic energy, millisecond pulsars are very stable rotators, and the interval between the arrival of the pulses is stable and measurable to an accuracy of less than a microsecond for a bright millisecond pulsar. The measurements of the pulse arrival times can be done phase coherently over intervals of many years, or even decades, leading to a measurement precision of one part in a thousand trillion or so for the best measured pulsars. This compares with the very best laboratory measurement possible for any physical system, and for some time the limiting factor on pulse timing was the long term precision of clocks in the observatories. The clocks have now got better, although over long periods, an ensemble of millisecond pulsars still provides a more stable clock than laboratory clocks.

Such precision permits measurements of the delay in pulse arrival time of a microsecond or less. Since the speed of light is 300,000 km/sec, this corresponds to a displacement in the pulsar of just 300 meters. The pulsar displacement can be measured even if it occurs over a time interval of many years (corresponding to the orbital motion of a planet). This is equivalent to measuring an orbital speed for the pulsar of less than a millimeter per second. This precision enables the detection of planets of much lower masses or longer orbital periods, than can be measured by any other technique.

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