Using Radio Astronomy to Improve Variable Star Theory

Robert S. (Bob) Fritzius Shade Tree Physics [email protected]

Abstract

This talk is based on the idea that the constancy of the measured speed of light by all observers is an unresolved issue. I’m investigating Walter Ritz’s (1908) c + v emission theory (in which source velocities are added to the speed of their emitted light; combined with John Fox’s (1965) extinction theorem in which the speed of electromagnetic waves, no matter their original speed, eventually reach a terminal speed “c” with respect to their medium. De Sitter’s (1913) binary star argument against Ritz’s theory is used as a springboard for an alternative interpretation of what are currently considered to be radially pulsating variable stars. If the Ritz/Fox approach is right then most, or all, apparently pulsating stars will turn out to be constant radius spectroscopic binaries (or multiples).

Spectroscopic Binaries

Spectroscopic binary stars (and sometime multiples or even clusters) are stars which orbit a common center of mass but are so far away that we cannot resolve the individual stars with optical telescopes. They are typically identified by measuring periodic shifts in the spectra of the individual stars.

In 1908, Canadian amateur astronomer J. Miller Barr(1) published a study of 30 spectroscopic binaries whose radial velocity curves (where the orbits were assumed to be well behaved Keplarian ellipses) showed that their calculated lines of apsides tended to point toward the earth. Simplified diagram showing the calculated lines of apsides pointing toward earth.

For anybody who thinks that all those orbits actually tend to point toward earth, I’d like to sell you a bridge. Seven of the binaries listed were considered, at the time, to be Cepheid Variables, which are currently thought to be intrinsically pulsating single stars.

One Possible Explanation for the “Earth Friendly” Orbits

Also, in 1908, Swiss Physicist Walter Ritz formulated an emission theory of general electrodynamics(1) in which the velocity of a source is additive with the velocity of the light emitted by it, i.e. the velocity of light is c+v or c’=c+v.

According to Ritz:

“Fictitious particles are constantly emitted in all directions by electric charges; they keep on moving indefinitely in straight lines with constant speed, even through material bodies. The action undergone by a charge depends uniquely on the disposition, velocity, etc., of these particles in its immediate surroundings.” (2) p. 150. “The velocity of light then depends on that possessed by the body that emits it at the instant of emission. From that instant, the velocity of the particles remains invariable, … even when the particles pass through ponderable bodies or electric charges.”

“I said in the introduction that this hypothesis … is only temporary and is contrary to that of action and reaction…” (2) p. 210

Ritz died (age 31) in 1909 and didn’t get to finish the job of bringing his theory [actually he was modeling Maxwell-Lorentz electromagnetic theory] more in line with physical reality.

De Sitter’s Binary Star Argument Against Ritz

In 1913 Dutch astronomer Willem de Sitter, who was championing the Lorentz- Einstein constant speed of light relativity, urged abandoning Ritz’s theory.(3) His argument against Ritz began with the following line of reasoning. de Sitter

“One imagines a binary star, and an observer at a great distance Δ in the plane. Light emitted by the star at points near [point] A become observed, in accordance with the theory of Ritz, after a time Δ/(c+v),

that light emitted from point B after the time Δ/(c-v). We call T the half orbit time of the star (its path, for the sake of simplicity is considered to be a circle) [and the other star of the binary is not shown] so that the time between the two observations is T+2vΔ/c². If the star goes in the second half of its period from B to A, then the observed time interval is T-2vΔ/c². In the customary [constant speed of light] theory both intervals are equal to T.” Derivation of the Delay Expressions

“Now if 2vΔ/c² is on the same order of magnitude as T, then if the Ritz theory were true, it would be impossible to bring the observations into agreement with Keplerian laws. With all spectroscopic binary stars 2vΔ/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., v = 100 km/sec, T = 8 days, Δ/c = 33 years (i.e. a parallax of 0.1”), then one has approximately T-2vΔ/c² = 0. All these dimensions are on an order with the best known spectroscopic binary stars.”

“Maybe Not” according to Freundlich (1913)

A colleague of de Sitter, Irwin Freundlich(4) questioned de Sitter’s handling of the c+v issue.

“Mr. de Sitter’s argument that the measured shift in the lines of a spectroscopic binary star cannot be interpreted by Keplerian motion if the speed of light were to be variable does not apply to the entire field of possible movements. [Circular] orbital movement with a variable speed of light, … [can appear to be] identical to the Keplerian orbital motion of an ellipse whose line of apsides is directed towards us, while the periastron [the fastest part of the orbit] lies on the side pointed away from us.” [Freundlich cited Barr’s 1908 study.] Freundlich showed computed radial velocity curves for (1) a Keplerian elliptical orbit “K” (e = 0.5) with its apsides directed toward us and (2) a circular orbit “S” with similar-in-magnitude c+v effects.

In a follow-up article(5) de Sitter acknowledged Freundlich’s argument but said that he had better statistics, (related to orbit periods and eccentricities) and so dismissed it.

Where c’ = c + kv, k=0 implies that c’ is constant and k=1 represents Ritz’s theory, de Sitter said:

“The spectroscopic binary stars with short periods, thus large velocities, have small or infinitesimal eccentricities, while those with long periods, and the visual binary stars, have generally larger eccentricities. If k had a rather high value, this would have to be the other way around.”

De Sitter provided no data tables or graphs to support his claim so I have appended a plot of eccentricity versus orbit period, derived from the Second Catalogue of Spectroscopic Binary Stars(6) published in 1910. Examination of the plot shows that de Sitter appears to be mistaken about short period binaries having small or infinitesimal eccentricities.

John Fox’s Extinction Theorem

In 1965 John Fox proposed an extinction theorem which says: “When a light wave sets into motion the charges of a medium; these in turn emit new waves whose centers move in vacuum with the velocity of the charges of the medium.”(7) p. 4 Fox’s theorem is actually in consonance with a viewpoint expressed by Ritz in another 1908 paper.

In talking about the speed of Lorentzian (constant speed of light) re-radiated electromagnetic waves, Ritz said:

“When a light ray sets the ions of any given body into vibration they, in their turn emit new waves, the centers of these waves move, not with the velocity of the body (like that wanted by our hypothesis) but with the velocity of the [original] light source.“(8) Emphasis added.

I interpret Ritz’s parenthetical phrase “like that wanted by our hypothesis” to mean that he favored the idea of the new waves traveling at the speed of light with respect to the new radiation sources.

Fox considered this kind of extinction to be a form of repeated forward scattering, and invoked an extinction length  [n= index of refraction] 2(n 1) over which the amplitude of the original light wave exponentially decreases to 1/e times its initial value. After five extinction lengths the original wave has essentially disappeared. He calculated one extinction length in earth’s atmosphere at sea level to be 0.3 mm. (6) p. 5

Based on that short atmospheric extinction length Fox invalidated all of the open-air laboratory tests ever done to check for variations (or non-variations) in the speed of light on or near the earth’s surface or on other celestial sources “such as the sun’s limbs.

Fox reasoned that the common atmospheres of close binary systems [spectroscopic binaries] are large enough to extinguish c+v effects of the orbiting stars.

In the interstellar medium of the galaxy’s spiral arms his extinction length estimate (based on a density of one Hydrogen atom per cm³) was “about one light year.”

According to Fox it would require a high binary-speed and a short orbital period to produce observable c+v effects before extinction occurred. Once extinction occurs, the c+v effects which accrued to that point would persist with no further diminishing.

“One is led to ask whether there are any other data on binaries which might provide evidence on the constancy of the velocity of light. For example, on the Ritz theory the light from a high-velocity, short period binary with insufficient atmosphere for complete extinction might bring us some evidence of its nonconstant velocity even though it is extinguished after about one light year. If no such evidence can be found, that would be support for the assumption of special relativity.”(7) p. 6

Spectroscopic Binaries as Variables?

What follows involves theoretical modeling and is in need of observational material to verify or refute it. There may be new capabilities being developed in radio astronomy spectral analysis that could add to the mix.

Recall that Barr’s 1908 list of 30 spectroscopic binaries, included seven Cepheid variables. These variables are currently considered to be single stars that are periodically varying in diameter (they are considered to be intrinsically pulsating). Even if we remove Cepheid variables from a list of spectroscopic binaries, some ten percent of the remaining binaries are variable (and eclipsing binaries are not in this percentage.) De Sitter did not address periodic brightness variations for spectroscopic binaries.

In 1987, Vladimir Sekerin, of Novosibirsk, Russia, working from de Sitter’s argument against Ritz, realized that if you had a binary star, where the distance L to an observer (L corresponds to de Sitter’s Δ) was such that the faster light (c+v) from one side of a component’s orbit actually catches up with the slower light (c-v) from a half orbit earlier, and that the distance L would be so great that we can not resolve the two images. In this case the total light seen by the remote observer will be twice as bright as either single image.(9)

L (overtaking distance) =Tc²/2v

“[T]he result of adding the absolute speed of light and the speed of its source relative to the observer ought to reveal itself as changes in intensity of the received radiation when compared to the constant intensity of the star S. This is so because at certain moments the "faster" light catches up with the "slower" light and is received simultaneously by the observer. This means that the speed modulation leads to an intensity modulation with simultaneous changes in the ‘observation’ in step with the Doppler effects of the orbit.”

A Problem with the Phasing of Sekerin’s Radial Velocity and Brightness Curves

Figure 3a in Sekerin’s article (reproduced here) is meant to roughly approximate the radial velocity and brightness curves for Cepheid variables. For Cepheids the maximum approaching radial velocity tends to occur almost coincident with the maximum of the brightness curve. Sekerin’s maximum approaching velocity, as drawn, occurs about 90 degrees later than the brightness peak. Radial Velocity (v) and Brightness (B) Curves vs Observer Distance

NOTE 1 - The apparent radial velocity curves lag the brightness curves by 90 degrees. This phasing error, at first glance, seems fatal to Sekerin's brightness variations hypothesis.

NOTE 2 - Recomputed brightness variation curves, furnished by Sekerin's colleague, M.S. Serbulenko, are shown for the second cycle. (Faster-later light overtaking slower- earlier light produces the unorthodox arrival time reversals in 3b and 3c.) Fixing Sekerin’s 90 degrees phasing error

I wrote computer software to model a binary star system with one or both stars visible to a remote observer.(10) At multiple points around the orbit of either star, pretend bursts of energy are emitted toward the remote observer. The enroute speed of those bursts can be set up either for a constant speed of light, “c” or “c+v” for the Ritzian model. The distance between the star and the observer at the time of each burst emission is determined, and the travel time between the star and observer is computed based on how fast the light is traveling. The program keeps track of emission times (t) and arrival times (τ). The fixed interval between emission times is Δt and the interval between burst arrival times at the observer is Δτ. Burst arrival time accumulator bins are used to construct an intensity light curve.

For radial velocity calculations, an arbitrary rest frequency at the source is fs. The observed frequency fo would be calculated as follows.

1 fo = fs –––– Δτ/Δt

For observer distances that are very much less than the Sekerin overtaking distance Lo, the observed frequency fo behaves as though fs is being Doppler shifted.

When the observer distance is in the regime of 0.1 to 0.3 times Lo, the observed frequency fo behaves as though orbital accelerations with respect to the observer are producing the observed frequency shifts.

At greater distances the brightness and radial velocity curves just get “ornery.” You see what look like time reversals in the arrival time sequence. Extinction distance equals one fourth the overtaking distance L

Extinction distance equals half the overtaking distance L

Extinction distance equals the overtaking distance L

Note that in this graph there is line tripling taking place during the times of the double peaks in the light curve. The Crab Pulsar as a Ritzian Binary?

Here is a plot for a binary star with both components visible and a extinction distance equal to 0.4 times the overtaking distance. The program was set up so that the orbit of one of the stars is smaller than the other, with a higher orbit speed. This leads to a sharp higher amplitude peak followed by a broader, lower amplitude peak. \

Note that emission or absorption features of both components can produce measurable radial velocity lines (line doubling). The light curve for this hypothetical object is similar to that of the Crab Pulsar. Light Curve for Crab Pulsar – NP 0532 After R. Lynds, Jan 21, 1969

Rather than the Crab pulsar being a single rapidly rotating neutron star, 30 revolutions per second, with two hot spots, it might be a spectroscopic binary composed of two neutron stars, each with a diameter on the order of 12 -20 km. These stars would each have about 1.4 solar masses. To get an approximate orbit size, I assumed a circular orbit, where each star follows the other’s path, but on opposite sides of the orbit. Such an orbit would have a radius on the order of 109 km. (That’s slightly more than the 95 km distance across Houston Texas.) The components would be doing 30 orbits per second at an orbital speed of 0.069 c.

Those values were calculated by equating centrifugal and gravitational accelerations and using an orbit speed equal to the orbit circumference divided by its period P.

v² GM –– = –––– r (2r)²

2 π r Replace orbit speed v with –––– and solve for r. P

A comparison of the light curves for the Crab pulsar and those of the simulated Ritzian light curves, suggests that the gamma ray extinction distance for the pulsar would be about one half of Sekerin’s overtaking distance for the hypothetical binary.

Sekerin re-arranged de Sitter’s expression T - 2vΔ/c² = 0 to get L=Tc²/2v Plugging the calculated orbit parameters, into Sekerin’s equation for overtaking distance “L” leads to an extinction distance of about five percent of the earth-moon distance.

The First Identified Pulsar was discovered in the radio spectrum

In the report of Jocelyn Bell’s pulsar discovery in 1967(11) it was stated: “The impulsive nature of the recorded signals is caused by the periodic passage of a signal of descending frequency through the 1 MHz pass band of the receiver.” (The receiver’s center frequency was 81.5 MHz.)

References

(1) J. Miller Barr, “The Orbits and “Velocity curves of Spectroscopic Binaries,” Journal of the Royal Astronomical Society of Canada.,2, 70-75 (1908). http://www.datasync.com/~rsf1/barr1908.htm

(2) Ritz, W., “Recherches critiques sur l'Électrodynamique Générale,” (Critical Researches on General Electrodynamics), Ann. de Chim. et de Phys. 13, 145-275 (1908). www.datasync.com/~rsf1/crit/1908a.htm

(3) De Sitter, W., “Ein astronomischer Beweis für die Konstanz der Lichgeshwindigkeit,” (An Astronomical Proof for the Constancy of the Speed of Light), Physik. Zeitschr. 14, 429, (1913). www.datasync.com/~rsf1/desitter/desit-1e.htm

(4) Freundlich, E., “Zur Frage der Konstanz der Lichtgeschwindigkeit,” (On the Question of the Constancy of the Speed of Light), Physik. Zeitschr. 14, 835-838 (1913). www.datasync.com/~rsf1/freund.htm

(5) de Sitter, W., Über die Genauigkeit, innerhalb welcher die Unabhängigkeit der Lichtgeschwindigkeit von der Bewegung der Quelle behauptet werden kann. (About the accuracy within which the independence of the speed of light from the movement of the source can be stated.) Physik. Zeitschr, 14, 1267, (1913). English translation is at: www.datasync.com/~rsf1/desit2-e.htm

(6) Campbell, W.W., “Second Catalogue of Spectroscopic Binary Stars,” Lick Observatory Bulletin, 6, 17, (1910)

(7) Fox, J., “Evidence Against Emission Theories,” Am. J. Phys. 33, 1, (1965)

(8) Ritz, W., “Recherches Critiques sur les Théories Électrodynamiques de Cl. Maxwell et de H.-A. Lorentz” (Critical Researches on the Electrodynamic Theories of Cl. Maxwell and H.A. Lorentz), Archives de Sciences physiques et naturelles, 26, 209- 236, (1908). An English translation of the material mentioned is available online at: http://www.datasync.com/~rsf1/rtz-mir.htm

(9) Sekerin, V.I., “Gnosiological Peculiarities in the Interpretation of Observations (For Example the Observation of Binary Stars,” Contemporary Science and Regularity in Its Development, 4, 119-1923 (1987). www.datasync.com/~rsf1/sekerin.htm

(10) Fritzius, R., BASIC program titled D-CEPHEI.BAS www.datasync.com/~rsf1/bas/d-cephei.exe , www.datasync.com/~rsf1/bas/d-cephei.bas

(11) Hewish, A., Bell, S. J., Pilkington, D. H., Scott, P. F., Collins, R. A., “Observation of a Rapidly Pulsating Radio Source,” Nature, 217, 709-713, (1968). www.ice.csic.es/research/forum/2010-Inaugural_catalan_files/nature-paper-1968.pdf