Orbits for two short-period and two long-period binaries
Even more, the measured orbital decay was in perfect agreement with the predictions of general relativity. Both astronomers were rewarded with the Nobel prize for physics in - the second Nobel prize for pulsar astronomers.
The test performed by Taylor and collaborators is actually more subtle than indicated above. We outline the principle in brief: The orbital decay can be described by a decrease in orbital period, P b , representing one post-Keplerian parameter. Each post-Keplerian parameter can be written as a function of the measured Keplerian parameters and the pulsar mass and companion mass. Measuring one post-Keplerian parameter hence describes a line in a pulsar mass - companion mass diagram blue line in Figure 2 which depends on the assumed theory of gravity.
Measuring a second post-Keplerian parameter provides another line in the mass-mass diagram, which cuts the first line at a certain mass combination.
Assuming that the theory of gravity being used is correct, two post-Keplerian parameters obviously determine the masses of both the pulsar and its companion, enabling the mass determination for neutron stars as summarised in Section 1.
Only for a theory of gravity that describes nature correctly will all three lines meet in one single point. General relativity passed this test with flying colours! Derived pulsar and companion masses m p and m c respectively in solar masses for the measurement of three post-Keplerian parameters of a binary system, each represented by a different line. If the particular theory of gravity used is to be correct the 3 lines must meet at a single point as shown.
Note that any two lines can cross providing a determination of the two masses but only a correct theory will allow all three lines to cross at the same point. The first of the two pulsars, now known as PSR JA , was discovered at the Parkes Radio Telescope in Australia, in a large scale survey at a wavelength of 21 cm see the original letter to Nature.
This pulsar, known as A, has a short spin period of 23 milliseconds, with large Doppler shifts showing it is in a mildly eccentric 2. Relativistic precession of the orbit was soon detected, at the phenomenal rate of 17 degrees per year, over four times greater than that of any other pulsar binary system and , times greater than the relativistic precession of Mercury.
The precession rate is proportional to the sum of the masses of the binary pair, while the two Doppler shifts give the ratio, allowing the masses of A 1.
The companion was almost certainly another neutron star: Several other pulsar-neutron star pairs were already known; this one was distinguished by its orbital period, which was the shortest so far observed. Because the system was obviously so important for observational tests of General Relativity, it seemed worthwhile to explore the possibility that A's companion might also be a pulsar.
As in the other double neutron star binaries, at first nothing was found. A deeper search was proposed, designed to track a periodicity varying as the inverse of A's Doppler shifts, so that a longer integration time could be used. However, before this was done, pulsar B was discovered almost by accident see the original paper in Science.
It turned out that pulsar B is strong but very variable, and it is only detectable for part of the orbit, a part which was not covered by the data analysed during the discovery of A. When the second pulsar was finally discovered, a strong pulsar signal was found with the long spin period of 2. Table 1 summarises the relevant spin and orbital parameters of the system. Parameters of pulsars JA and B - the "double pulsar".
Radio signal from the double pulsar showing pulses from both A and B. Figure 3 shows the radio signal strength in a colour table where blue is weak and white is strong from the two pulsars they are so close together their signals are picked up in the same beam of the radio telescope. The horizontal axis is time folded at the period of pulsar B whilst the vertical axis is time labelled in the orbital phase of the binary system. Hence we can look at a horizontal line through the middle of this diagram and see that the signal from B is initially zero and then a pulse appears in the middle before it falls away to zero again.
Looked at vertically we see that there are strong repeated pulses from B over orbital phases from about to degrees a period of time of about 10 minutes. In fact pulses are only visible from B in this part of the orbit and another section centred on phase 28 degrees.
In the background the much shorter period pulses of A can be seen. The pulse period of A appears to vary relative to that of B resulting in the curvature of the lines in the background because of doppler shifting due to the binary motion. Over the year since discovery the parameters of the system have been measured through timing so that, for example, the masses are increasingly accurately determined - see Figure 4.
The various observables constrain the masses to lie within the small light blue box which is shown magnified in the inset. This figure shows how well the masses were determined in December The observables indicated here are the mass ratio R, the advance of periastron omega-dot , the gravitational redshift and time dilation parameter gamma, the Shapiro parameters r and s. Note in the magnified region each of these parameters is measured to some accuracy which is indicated by a pair of lines - the true value must lie in the intersection of these regions.
Various parameters have been determined to higher accuracy and a new parameter, the orbital decay i. There is also a very remarkable interaction between the radio emissions of the two pulsars, which provides the most striking example of magnetospheric physics apart from the terrestrial magnetosphere itself.
A powerful wind from one pulsar distorts the magnetosphere surrounding the other, forming a comet-like shape closely resembling the terrestrial magnetosheath and with many of its characteristics see Figure 5. The diameter of the orbit, determined through radio timing, is 2. The line of sight to each pulsar therefore passes within km of its partner. Although the radius of a neutron star is only 10 or 11 km, every pulsar is surrounded by a co-rotating ionised and very energetic magnetosphere, which for an isolated pulsar extends to the velocity-of-light cylinder radius at which co-rotation would require a velocity of c.
The magnetosphere of the millisecond pulsar, A, extends to a radius of km, while that of the long-period pulsar, B, should extend to , km, well beyond the line of sight to A at superior conjunction. A should therefore be eclipsed by B for several minutes, and an eclipse is indeed seen in every orbit. But the eclipse lasts only 30 seconds, corresponding to an 18, km movement of the line of sight to A across pulsar B.
This was the first observation of the magnetosphere of any pulsar, but with a radius of only 9, km it was much smaller than expected. We therefore see a strong influence of pulsar A on pulsar B, distorting its magnetosphere and preventing us from seeing its pulses over much of its orbit, while B's distorted magnetosphere obstructs the line of sight to A at superior conjunction. A's magnetosphere is smaller and does not cross the line of sight; it appears to be unaffected by the proximity of B.
This is not surprising; the rapidly rotating A is in fact the more powerful of the two, since its energy loss by spin down is times greater the spin down rate of both pulsars is easily measured.
The detailed mechanism of energy loss from pulsars has been under discussion for many years. Originally it was thought to be simple magnetic dipole radiation at the rotation period, together with an approximately equal energy density in particles flowing out from the magnetic poles.
Observations of energetic nebulae near some pulsars, notably the Crab pulsar, can however only be explained as the result of a pulsar wind streaming out along the rotation axis. The outflow apparently changes character at some distance from the pulsar, but up to now the composition close to the pulsar has been unobservable.
The double pulsar binary offers the first opportunity of observing the outflow close to a pulsar. The geometry shown in Figure 5 might apply equally well with some changes in parameters to the terrestrial magnetosphere and magnetopause. Around the orbit, this cometary tail points away from A, so that our line of sight to B passes through the compressed head when it is furthest away from us, and through the tail when it is closest.
The orbital phases of B at which it is observable are between these two positions, when it is seen from either side of the tail. At the eclipse, pulses from A are blocked by the nose and the front half of the 'comet'.
The front half of the magnetosheath is therefore opaque to radio waves, probably through synchrotron absorption. The shape of the magnetosheath seems to be well represented as a comet, although rotation of B within the magnetosheath distorts the surface, creating cusps similar to those found in the terrestrial magnetosheath, and giving the complex variations of absorption seen during the eclipse of A.
Cartoon not to scale showing the interaction between the relativistic wind from pulsar A and the magnetosphere of pulsar B. The collision of A's wind and B's magnetosphere creates a magnetosheath of hot, magnetized plasma surrounding the magnetosphere of B. Robert Mathieu for being such a wonderful mentor. It is a very rich, concentrated cluster with approximately solar metallicity. The mean radial velocity of the cluster is 2. The highlighted marks represent the binaries for which we have found orbital solutions.
In this study, I was only interested in binaries on the main sequence. Before determining whether or not a star was a binary, we first had to make sure that it was a probable member of this cluster. If an object's radial velocity fell within 3 standard deviations of the cluster mean radial velocity 2.
The next step was to look at the spectra for each variable star and search for spectroscopic binaries. Spectroscopic binaries are found by examining the cross-correlation function for the object and some reference spectrum. In this case, we used the solar spectrum as the reference. For a cross-correlation function, the object spectrum is shifted with respect to the reference spectrum, pixel by pixel, and the strength of the correlation between the two is plotted against pixel shift this is all done in IRAF.
We see a peak where the correlation was the strongest. A Gaussian is then fit to the peak and the center of the Gaussian is the measured radial velocity. Actually, the value of the pixel shift at the center of the Gaussian is converted to a radial velocity. Cross-correlation heights less than 0. If one star in a binary system is much fainter than the other, we will get only one peak in the cross-correlation function.
This is called a single-lined spectroscopic binary, or SB1. If the two stars in the system are of comparable brightnesses, we will see two peaks in the cross-correlation, one for each star. This is known as, you guessed it, a double-lined spectroscopic binary, or SB2.
We can then fit a Gaussian to each of these peaks and get out a radial velocity for each star. The next step was to find an orbital solution for these variable stars. By looking at the radial velocities and corresponding julian dates, we can usually guess an approximate orbital period. If we couldn't get a good estimate, we plotted the velocities against julian dates in IDL. This usually gave us a better idea about the period. Once we had a ballpark figure for the period, we used a program called SB1 to find an orbital solution.
This found solutions for the brighter star in the system the one we have radial velocities for. If we also had data for the fainter star in an SB2 , we could use a second program, called SB2, in addition to SB1, and come out with orbital solutions for both components of the system.
This usually gave us a better idea about the period. Once we had a ballpark figure for the period, we used a program called SB1 to find an orbital solution. This found solutions for the brighter star in the system the one we have radial velocities for. If we also had data for the fainter star in an SB2 , we could use a second program, called SB2, in addition to SB1, and come out with orbital solutions for both components of the system.
SB1 searched for orbital periods within the interval that we input which we estimated based on the velocities and dates. The search gave a best period based on the lowest chi-squared value. The search was repeated several times while narrowing the interval down on the best period found previously. Once an acceptable period was found, the orbit was plotted up along with several orbital parameters listed i.
Here are examples of orbital solutions we found. The first and second are examples of SB1s one eccentric, one circular , and the third is a SB2. The circular orbit above is the shortest-period circular orbit found in NGC with a period of only 1. This corresponds to an orbital radius of 0.
This is shown below:. Notice that there is a lack of long-period circular orbits and relatively few short-period eccentric orbits. This can be explained by tidal circularization. The orbital parameters of a binary system constantly change due to the tidal interactions between the two stars until a stable equilibrium is reached. Although energy is dissipated in this system, the total angular momentum is conserved.
As the stars tidally interact, the rotational angular momentum is transferred to orbital angular momentum. Thus, the eccentricity of the orbit decreases becomes more circular , causing the stars to "spin down," or, rotate at a slower rate.
How exactly does this happen? The tidal interactions cause tidal bulges on the stellar surfaces. When these bulges are misaligned with respect to the line joining the centers of the stars, a torque is produced. As mentioned above, the rotational angular momentum from one star is generally transferred to the orbital angular momentum of the other star.
An increase in orbital angular momentum corresponds to a decrease in eccentricity the orbit becomes more circular. The closer binaries or those with shorter periods will therefore circularize first. So short period binaries will tend to have circular orbits, while those with longer periods will have a distribution of nonzero eccentricities. With time these eccentric binaries will circularize, and the observed circularization period see next paragraph will increase.