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BINARY STAR SYSTEM

4.8 BINARY STAR SYSTEM

Background and actual explanation

Binary systems are important for special theory of relativity for at least two reasons: light constancy argument and absence of abnormal aberration in case of moving source.
Another indirect observation involving the propagation of light was first proposed in 1913 by De Sitter.
More than 50% of all the stars are considered as forming multiple star systems, some of them are near enough to be discerned with powerful telescopes.
De Sitter's basic idea was that if two stars are orbiting each other and we are observing them from the plane of their mutual orbit, the stars will be sometimes moving toward the Earth rapidly, and sometimes away. According to an emission theory this orbital component of velocity should be added to or subtracted from the speed of light. As a result, over long interval of time necessary to the light to reach the Earth, the arrival times of the light from approaching and receding sources would be very different.
When a source of light has a speed of u, say in the direction of the positive x axis - according to the ballistic theory the speed of the light emitted in the same direction is c + u, where c is the speed of light emitted by a resting source. Considering such system and an observer at a great distance D in the plane, light emitted by the star from points A becomes observed, in accordance with the theory of Ritz, after a time D/(c+u) and light emitted from B after the time D/(c-u).
binary1
Figure 4.16 Binary star system


Being T the half orbit time of the star (its path is considered circular), so the time interval between the two observations is T+2uD/c2 .
If the star goes in the second half of its period from B to A, then the observed time interval is T-2uD/c2 .
Now if 2uD/cis of the same order of magnitude as T, then if the ballistic theory were true, it would be impossible to bring the observations into agreement with the Keplerian laws. With all spectroscopic binary stars 2uD/c2 is now indeed not only of the same order of magnitude as T, but probably in most cases even much larger. One takes e.g. u=100 km/sec, T = 8 days, =33 years (i.e. a parallax of 0.1"), then one has approximately T-2uD/c2≈0 . All these dimensions are on an order with the best known spectroscopic binary stars.
The existence of the spectroscopic binary stars and the circumstance, that...in most cases the observed radial velocity completely becomes represented by the Keplerian motion is thus a strong proof for the constancy of the speed of light.
The De Sitter argument predicts the appearance of stellar ghost and the distortion of the orbits of the double stars.
Some new theories point out the modifications of speed light due to the interstellar medium. This medium will act in order to make the speed of light constant for long distance. The effect is related to the light frequency, so for visible light independent on the initial speed, the observer will measure the same speed of light in interplanetary medium.
The experiments made at x-rays and gamma rays (Brecher, 1977), having a extinction distance much greater shows that light speed is ,,independent on the source speed”.

Proposed explanation
The internet is a huge source of information so I will start with one latest news about binary systems: ,,Astronomers at the Mullard Space Science Laboratory (MSSL) together with a colleague in Finland have discovered a stellar binary system in which the two stars are orbiting around each other every 5 minutes. A separate group in Rome also made this discovery independently at the same time. This object sets the record as the fastest known binary and beats the previous record-holder by 5 minutes” .
For any experimented astronomer such period should give some problems of interpretations because it is quite impossible to have such real periods; this will mean a close distance between stars and an orbital speed greater then 10000 km/hour.
As curiosity, it is very strange how visually and close to Earth binary star has periods of revolution in range of tenth of years and far away binary systems (spectroscopic or eclipsing ) presents lower period of revolution, generally periods of few days or even smaller. A statistical study about the subject will reveal something strange. Probability of a star to have a smaller period is direct related to the distance to Earth.
The proposed explanation start from temporal aberration phenomena already explained in the previous chapter. Let’s consider a binary system and let’s see how general example is fitting on this particular case.
In order to simplify the discussion the central star is considered stationary relative to observer situated on Earth and the other components revolves on a circle like in fig 4.17. Supplementary let’s consider that photons are generated on both stars, due to the atomic processes, with the same ,,born” speeds c. The interaction of these photons with interplanetary medium during the trip up to observer is neglected.
binary2
Figure 4.17 Binary star system

In the picture the distance from central star to observer is d and the distance between components of binary system is r.
The only information considered reliable in actual astronomy received from binary system, and on this information, the entire theory was build is related to the period of such binary system.
But represent the measured period of binary system reliable information?
In order to establish the period of binary system let’s consider a clock on the star S and at time t=0 the position of star is aligned relative to observer like in fig 4.18.

binary3
Figure 4.18 Star P eclipse star S

A photon emitted from companion P during the eclipse in the direction of observer (detail case a) will never reach the observer O. This is due to the classical composition of star speed and photon speed, and even the angle is small, the distance d being large (hundreds of year light commonly), the photon will follow another direction and will reach a point somewhere in front of the observer.


In order to be catch by the observer situated in O, the photon from companion must be emitted under an angle greater then π/2 like in case b), and after the classical composition of speeds, the final direction must be parallel with SPO line. The angle of emmision depends on the orbital velocity of star and can be calculated very easy. But such photon will have a modified speed on trajectory (c’) and this speed is less then ,,born” speed (c).
The time necessary for the photon to arrive in point O will be :

binary01

If the observer in the O considers that photon is traveling with speed c, a faulty appreciation of traveling time will be made.
After a half period, the companion arrives in opposite point of orbit and in this case S is eclipsing P.
From a corpuscular point of view, due to the composition of speeds, the eclipse is observed, not when a photon is emitted parallel with PSO direction, but when resultant speed is directed parallel with PS like in fig 4.19-b.
binary4
Figure 4.19 Star S eclipse star P

Until here nothing special seems to appear. But what will be the time necessary for light to travel from P to O in this case? 
For the interval PS (radius of orbit) it will be necessary an time equal with:binary02

But for the interval SO light will travel with speed c, due to the fact that S is stationary to the observer, so there is:

binary03
For the second eclipse, the transfer of information up to observer will be made with a modified and greater speed. The total time of arriving information at observer will be:

binary04

In practice d >> r and consequently a nice effect appear. Because from the second eclipse the information travel faster then from the first eclipse a phenomena of time aberration appear. It is avoided to be used the term ,,time contraction” because there is not such effect. If a clock is going faster or is going slow it does not mean a time contraction or time dilation, it’s only a clock problem. Here there is the same problem; the clock is going irregularly, relative to our expectations. I highlight this aspect, because only the transfer of information up to observer is affected.
If we suppose that real period of companion star is TP, the observer will measure a smaller period TO than the real one. The difference between the real period TP and measured one TP, will increase with the distance to the binary system and also with the relative speed of binary components movement. Therefore, there will not exist visually binary system with period of one hour or minutes, but there will be an appreciable percent of spectroscopic or eclipse binaries with such small periods.
According to proposed model, the period of revolution of stars in binary system must be, generally, on the order of decades and only in special cases can be on the order of years. The measured period from an observer situated at high distance is affected by the speed of transfer on information and does not correspond with reality. All measured periods of binary stars must be corrected in order to obtain the true period of motion.
At extreme case it is possible to have for the second eclipse, a smaller traveling time up to observer in comparison with first eclipse time. But these are special cases.
In real cases there are another two interference factors affecting this time aberration, namely, movement of primary star and interstellar matter. The simultaneous movement of primary star can be easy counted and second factor will be described at Fizeau experiment and in the optic book.
The judgment made by de Sitter is right in principle, but the period of motion is not correct. If in his original example instead of a period of 8 days a period of years or decade is taken into consideration of course there will be no double image or another effect.
This does not mean the observed trajectory of visually binary stars correspond with the real one. Of course it is vague idea to speak about trajectory in case of binary stars. With the must performing telescopes a binary star is seen under an angle of few arc seconds and it is good if the components are separable in visual field. In the same time there is no possibility to observe a star in points indicated by de Sitter calculus, more precisely when a photons emitted by revolving star has maximum or minimum speed relative to Earth. The detailed analysis of binary stars will be made in further study related to astronomy, because it’s more a problem of astronomy and not of relativity.

 

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