Orbiting neutron stars

A neutron star is a possible end state of a star. Its nominal mass is ~1.4 MQ and its radius ~10 km. This is an extremely compact object; a mass comparable to the mass of the sun is contained in an object the size of Manhattan. Neutron stars were first discovered in 1967 as radio pulsars. They spin and send out abeam of radiation that sweeps across the earth once each rotation, as does the searchlight beam in a lighthouse. An astronomer thus detects a pulsing radio source. There are ~1500 pulsars now known, most in the Galaxy. They are lighthouses of radio emission.

Most radio pulsars are isolated neutron stars but some are in binary systems with a normal star and a very few are in binary orbits with another neutron star. The latter are called binary pulsars. The first discovered was the H-T pulsar. As the pulsar orbits its companion, the detected radio pulses are delayed or advanced depending on its location in the orbit - farther away or closer to us. In this way the orbit can be tracked with precision. Another view of this technique is that one tracks the line-of-sight velocity through the Doppler shift of the pulse rates.

Hulse-Taylor pulsar The H-T binary pulsar was discovered in 1974; its coordinate name is PSR B1913 + 16 but it often called simply the binary pulsar because for many years it was the only one known. Its pulse (spin) period is P = 59 ms and its orbital period 7.75 h. It is distant about 16 000 LY. The Doppler variation of the pulsing frequency indicates a rather eccentric orbit with eccentricity 0.617. The companion is asecond neutron star which does not pulse and therefore is not directly detected. In fact its gravitational effect on its pulsing companion is a perfectly valid detection.

The short orbital period of only —8 h indicates a small orbit. This and the large measured Doppler velocities mean that the neutron stars are undergoing large accelerations. This acceleration causes them to radiate energy in the form of G waves according to Einstein's theory of general relativity. They lose energy and spiral ever so slowly closer together with increasing angular velocities, just as an artificial satellite spirals toward the earth as it loses energy to atmospheric friction.

The changes in the orbital parameters of the H-T pulsar have been tracked since the 1974 discovery (Fig. 6). They are exactly in accord with the predictions of GR. In particular, the time of periastron (the closest approach of the stars to one another in their mutual eccentric orbits about the center of mass) advanced 26 s from 1975 to 2000, relative to that expected for a constant orbital period. Furthermore, the plot shows that, during the 25-year period, the data points follow very closely the track predicted by GR.

The GR effects allow the inclination of the orbit relative to the line of sight and the two star masses to be individually determined; Newtonian physics yields only a combination of them. The masses of the pulsar and its companion are extremely accurately obtained, 1.442 ± 0.003 M0 and 1.386 ± 0.003 M0 respectively. Another similar pulsar in a binary, PSR B1534 + 12, has been monitored with similar results. A third, PSR 2127+11C resides in the globular cluster M15.

Energy loss rate

This orbital decay is detectable because the very massive neutron stars are whipping around each other in a compact orbit (indicated by the short period). The masses are being highly accelerated and hence they emit sufficient gravitational radiation to bring about a detectable advance in the orbit phase. This detection is equivalent to the discovery of gravitational radiation predicted by the general theory of relativity, even though such radiation has never been detected directly.

Year

Figure 12.6. Decay of the orbit of the Hulse-Taylor binary pulsar, PSR 1913 + 16. By 2000, the phase of the orbit relative to the periastron had advanced by ~26 s from that expected for a constant orbital period at its 1975 value. This indicates the orbital speed has increased ever so slightly as is expected if total energy (kinetic + potential) is being lost; the two neutron stars are spiraling closer together. The decay of the orbital period follows precisely the track expected if gravitational radiation emitted by the rapidly accelerating neutron stars is carrying away the energy. [Provided by J. H. Taylor & J. M. Weisberg, 2000]

Year

Figure 12.6. Decay of the orbit of the Hulse-Taylor binary pulsar, PSR 1913 + 16. By 2000, the phase of the orbit relative to the periastron had advanced by ~26 s from that expected for a constant orbital period at its 1975 value. This indicates the orbital speed has increased ever so slightly as is expected if total energy (kinetic + potential) is being lost; the two neutron stars are spiraling closer together. The decay of the orbital period follows precisely the track expected if gravitational radiation emitted by the rapidly accelerating neutron stars is carrying away the energy. [Provided by J. H. Taylor & J. M. Weisberg, 2000]

The rate of total (kinetic and potential) energy loss dE/dt due to gravitational radiation requires detailed calculations taking into account the eccentricity of the orbits and other effects. The eccentricity makes a large difference because the radiation energy loss is a strong function of the separation of the stars; it varies hugely around an eccentric orbit. The useful value one can calculate is the time average over one orbital period.

With these caveats about its applicability to the H-T pulsar, we write here the energy loss expression for two stars in circular binary orbits. The total mass is

M = m 1 + m2, the reduced mass is x = m 1m2/M, and the separation between the stars is a. The expression is based on a weak field approximation to Einstein's field equations which is applicable if the gravitational fields are not too strong.

—— = - ——;--;— (W; energy loss to dt 5 c5 a5

gravitational radiation; (12.6)

64 Gl (mV circular orbits)

This is the total power lost to the system by radiation. The radiation is not isotropic; it is maximum at the pole of the orbit, but is substantial in the orbital plane. The result here is thus an integration of the radiated energy flux density over all directions. Finally note the strong dependence on separation, a a-5.

Gravitational waves

Gravitational waves may be loosely compared to electromagnetic waves. The latter originate with oscillating electric charges and are detected through their effect on other electric charges, e.g., conduction electrons in an antenna. Similarly, G waves originate in the oscillations of masses and are detected by their effect on other masses. In each case, the waves travel at the speed of light, c = 3 x 108 m/s, and may be described with a frequency and wavelength, according to c = Xv.

Distortion of space

In GR, gravity is considered a distortion of the space-time fabric. Light rays are bent when they pass near a massive object (e.g., the sun). We might be tempted to say that gravity exerts a force on the photons. However, it is more appropriate to say that space is warped, and that light rays define "straight" lines, known as geodesics. When a G wave passes us, space is momentarily distorted.

A ring of test particles in empty space will respond to a passing wave as shown in Fig. 7 where the view is along the propagation direction. In the first polarization (left side), the ring will successively be flattened, circularized, and elongated as shown. In the other polarization, the oscillatory flattening will be rotated at 45° to the first.

The passing wave will produce a strain h in space defined as twice the fractional change in diameter (length) of the ring, h Ml

Ring of test particles in space

Gravitational wave propagates out of (or into) the page.

Telescopes Mastery

Telescopes Mastery

Through this ebook, you are going to learn what you will need to know all about the telescopes that can provide a fun and rewarding hobby for you and your family!

Get My Free Ebook


Post a comment