Paradoxes Resolved, Origins Illuminated - Requiem for Relativity
Paradoxes Resolved, Origins Illuminated
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United Kingdom
1065 Posts

Posted - 02 Jun 2007 :  04:55:55  Show Profile  Reply with Quote
This raises a whole slew of questions. Though, the first one is about the politics of the thing. Talk about it now and it might look as though it's an attempt to fudge the issue of whether we have a brown drawf in our solar system. First we need a couple of very good images of the brute. Then we can look at what the pulsar data tells us.

So, do we talk about the ideas on this board, or just make a note of it for later? Tom must have loads of data on exploding planets but with a pulsar we are talking about an implosion first. Now I think of this aether "atmosphere" as being a sub luminal aether but it will be cantained within, permeated by, the ftl aether. Gravitational collapse must alter the sub light aether, as potential energy becomes kinetic energy.

What happens to this "kick" if a companion "knows," almost instantly, that its partner has imploded? It's orbit must alter hours before the explosion effects hit it.
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Joe Keller

1061 Posts

Posted - 02 Jun 2007 :  14:22:33  Show Profile  Reply with Quote
Barbarossa would torque the angular momentum vectors of J,S,U & apparently somehow Neptune too, as a unit, around Barbarossa's angular momentum vector many times in the life of the solar system. Presumably JSUN began with their average orbital plane as near as possible, in that precession circle, to the sun's equatorial plane (5 deg). Only about 1/12 of the time would JSUN's angular momentum vector be as close to the sun's as it is now (6 deg). Although this is believable, there's another explanation for the near equality of JSUN's plane to the sun's equator.

Companion stars at the distance of, say, Uranus, tend to orbit in the same plane as the primary's equator. Companion stars at the distance of Barbarossa tend to orbit in arbitrary planes. Typically a brown dwarf companion would be, according to the best estimates, somewhat farther away than Barbarossa but also somewhat more massive and at a somewhat steeper inclination, typically giving about the same torque as Barbarossa, overall, and a larger precession circle. Even a stellar companion of 0.7 solar mass at 20 AU would have no more angular momentum than an 0.1 solar mass brown dwarf at 1000 AU. If brown dwarf companions are as common as they seem to be, the correlation of close companion's orbits with the primary's equator might be poorer than it is. So, there might be an unknown mechanism of angular momentum transfer between a star and its planets, which maintains that alignment despite brown dwarf torques.
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Joe Keller

1061 Posts

Posted - 02 Jun 2007 :  17:57:08  Show Profile  Reply with Quote
Requiem for Relativity

Relativity is dead, long live Relativity.

Above, I suggest that there might be a kind of boundary or barrier surrounding the solar system ("ether iceberg"), maybe at 52.6 AU, beyond which the Doppler effect is not orthodoxly relativistic. Suppose a radio signal from Pioneer 10 crosses that barrier and reaches Earth. The redshift might be the sum of the two redshifts produced by: Earth's motion relative to the barrier (i.e., relative to the "iceberg"); and Pioneer 10's motion relative to the interstellar medium. If the barrier is scarcely moving relative to the nearby interstellar medium, then only some small effects, e.g., retardation of Pioneer 10's time dilation (see my 2002 Aircraft Engineering & Aerospace Technology article or its recapitulation on this messageboard) or retardation of stellar aberration (see my discussion of the Kimura phenomenon on this messageboard) remain.

Larger effects are noticed, when the movement of the barrier, relative to the interstellar medium, is not negligible. Pulsar timing fails to detect Earth's gravitational acceleration by Barbarossa, because to first order approximation, Barbarossa equally accelerates the 52.6 AU barrier and everything inside it. Also, interstellar space outside the barrier is so slack over interstellar distances that this term of the redshift doesn't change either. By the same mechanism, pulsar timing fails to detect distant companions of the millisecond pulsars. Above, I argue that the solar system detections around pulsars are better explained by this than by the "kick" theory.

Binary stars sometimes show paradoxical orbital redshifts (AW Irwin et al, Publications of the Astronomical Society of the Pacific 108:580-590, 1996). The binary star 36 Ophiuchus AB shows a supposed mutual Doppler redshift about 30% larger than consistent with any possible celestial mechanics. This might be because the light from one star passes through the dumbbell-shaped (defined, as above, by critical gravitional field intensity) barrier three times.

(About half of my posts on this subject recently disappeared from one of the largest amateur astronomy messageboards in Australia.)
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Joe Keller

1061 Posts

Posted - 03 Jun 2007 :  22:26:31  Show Profile  Reply with Quote
Let's consider a nearby star with a surrounding spherical barrier or boundary (like the barrier or boundary I hypothesize for the sun at 52.6 AU). Maybe the star can achieve an apparent Doppler acceleration toward us, in two ways. One way, is if a distant companion, outside the star's barrier, accelerates the star and its barrier as a unit toward us.

Another way, is if a close companion, inside the star's barrier, accelerates the star relative to the barrier. There is a wavetrain between us and the star. Part of this wavetrain is within the star's barrier: call that part's length, L. If the first time-derivative of L is negative, blueshift may occur.

Let the star have a small distant companion whose distance is twice the barrer radius. If the "barrier" occurs at that surface in space where the magnitude of the gravitational field vector is such-and-such, then a distant companion causes the barrier to be indented, like a "flat tire", a small distance proportional to the mass of the small companion. Let the small companion be seen in inferior conjunction. As the small companion slowly orbits at inferior conjunction, the star and barrier are accelerated toward us. Also, we see the star's light through a part of the "tire" that is less and less indented. The first and second time-derivatives of L (see previous par.) are positive. There is accelerating positive "apparent radial velocity" due to the asphericity of the rotating barrier. The barrier's indentation is proportional to the mass of the small companion. So, the distortion of the barrier commonly could appear to cancel up to about half, of the entire barrier's acceleration toward us.

Now let's consider an equal-mass binary near conjunction, both sunlike, separated by a distance of order 50 AU. The barrier in such a binary might be a dumb-bell or it might be two flattened spheres which are not connected (dumb-bell with no handle). Either way, light from the more distant star passes twice through the barrier of the nearer one. Plausibly, the apparent (from apparent radial velocity, "RV", red/blueshift measurement) acceleration, of the farther partner, inferred from the progessive blueshifting of its light, is the sum of five terms:

1. The acceleration of its own barrier toward us.

2. The acceleration of its partner's barrier away from us (#1 & #2 cancel, because the light passes through both these equal but oppositely accelerated "icebergs").

3. The second time derivative of L1, the length of wavetrain within its own barrier (zero for a spherical barrier).

4A. The second derivative of L2, the length of the farther partner's wavetrain, within the nearer partner's barrier, but only that part due to the shortening at the surface nearest us.

4B. This term is the same as 4A except that it is that part due to shortening at the surface farthest from us, and has sign opposite the sign of 4A. That is, shortening at the surface nearest us simulates movement toward us, and shortening at the surface farthest from us simulates movement away from us.

The orbital elements (see Aitken, "Binary Stars" for clear definitions of these symbols) of 36 Ophiuchus AB (Irwin et al, 1996, op. cit.) make it relatively easy to calculate what the apparent "RV"-based acceleration of the farther partner toward us, should be if the foregoing theory is correct. With a slide rule, trigonometry and careful approximation (considering, to first order, the distortion of the barriers), I found that the "RV"-based apparent acceleration toward us should be 1.64 times the celestial mechanics prediction. Irwin et al found 1.64 times.

"Web of science" (the online Science Citation Index) shows only six papers citing Irwin's. None of these measure binaries like Irwin's. 36 Ophiuchus AB is special because the stars are far enough apart to be outside each other's barriers, yet close enough to conjunction that the farther partner's light must pass through the "barrier" hypothetically surrounding the nearer partner. The nearer partner's hypothetical "barrier" eclipses the farther partner.
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Joe Keller

1061 Posts

Posted - 05 Jun 2007 :  17:08:27  Show Profile  Reply with Quote
Open letter to professional binary star experts:

Dear Dr. Fletcher, Dr. Marcy, Dr. Butler, Dr. Yang, Dr. Campbell, Dr. McArthur & Dr. Cochran:

Alan W. Irwin, et al (Publications of the Astronomical Society of the Pacific 108:580-590, 1996) discovered that the Doppler-derived radial velocity ("RV") of the farther partner in the binary star, 36 Ophiuchus AB, is anomalous by a factor of 1.64. This did not seem to the authors to be plausibly due to any other companion, nor to motion of the star's surface.

Within 1% error, this 36 Ophiuchus AB anomaly in RV, is consistent with my theory of solar system (our solar system and others) light propagation. This theory deviates somewhat from the standard textbook interpretation of Special Relativity, but might nonetheless be valid. No physical theory, much less any standard textbook interpretation, has lasted forever. The evidence for the high accuracy of the standard textbook interpretation of Special Relativity, has been gathered from particle physics experiments and might be not always exactly applicable at solar system distances.

The unexplained Kimura phenomenon (Astronomical Journal, 1902), which is, basically, that the aberration of starlight, corresponds to Earth's velocity retarded by about seven hours, is encompassed by my theory. My theory also encompasses the apparent sinusoidal variation in the Pioneer anomalous acceleration, which sinusoidal variation began at about 53 AU and is plainly discernible on at least one of JD Anderson's graphs published on

I'd like to discuss my theory with any or all of you. It might apply to other binary stars such as gamma Cephei. Please give me a call at **********.

Joseph C. Keller, M. D.
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United Kingdom
1065 Posts

Posted - 06 Jun 2007 :  11:39:54  Show Profile  Reply with Quote
For anyone who wants to put some figures in for doppler shifts, using the contracted form. Note that the square root will alter any assessments of mass.

f = f0 sqrt (1 - v^2 / c^2) c / c + or - v cos theta
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Joe Keller

1061 Posts

Posted - 06 Jun 2007 :  18:38:17  Show Profile  Reply with Quote
Kimura phenomenon.

H Kimura, Astronomical Journal 22(517):107-108, 1902.
SC Chandler, AJ 22(524):164, 1902.

"[Kimura's latitude variation] does not depend upon the longitude...[it] is not due to the wanderings of the pole. ...No plausible explanation of the Kimura term has as yet made its appearance,..."

"...southern hemisphere [observations show variations of the same sign as the northern hemisphere]"

- Frank Schlesinger, Proceedings of the American Philosophical Society 54(220) (available on internet) 1915, p. 357.

Circa 1900 the Astronomical Journal has many papers, often by famous astronomers, about "variation of latitude" and the related problem "aberration of starlight". Usually, the altitude of a star would be measured vs. a plumb line or mercury pool, when the star crossed the meridian. Often, bright stars and smallish refractors were used, day and night, to measure a star throughout the year. The observatories then involved, were in the northern hemisphere, often northern Europe, so to maximize accuracy, almost-circumpolar northern stars were used because these were near the zenith.

Kimura's meta-analysis included many studies. These seem to have been corrected by their authors, for aberration of starlight (neglecting Earth's rotation and orbital eccentricity) and for precession; and by Kimura, for Chandler wobble.

It would seem that the 9" "lunar" term of Earth's nutation also was corrected as part of the authors' "reduction procedure"; its long (18.6 yr) period would be forgiving of small errors, because our interest is in a phenomenon with period one year. The 1.2" "solar" nutation term has period one-half yr, so could contribute negligibly to Kimura's phenomenon, which has period one yr. The 0.1" "fortnightly" nutation has period 15 days, so could be trusted to average out.

Parallax corrections sometimes would be insignificant, and sometimes were significant and made. Their effect is opposite in phase, to the Kimura phenomenon (with my sign presumption; see below).

Chandler said that Kimura's "phenomenon may have an objective existence", perhaps "an annual periodical oscillation" of "earth's center of gravity". Chandler did not propose that nutation was the explanation. Chandler noted two imperfections (both of about the magnitude of Kimura's phenomenon) in the correction for the aberration of light:

1. Chandler indicated that often observations were not timed to the nearest hour, and that the average hour might vary enough, seasonally, to give the Kimura phenomenon. This author calculates an average observation time four hours earlier (!) in winter than summer, to give Kimura's 0.03" amplitude, even assuming usually a sensitively positioned star such as Vega or Zeta Draconis near the ecliptic pole, and assuming observation times seldom were recorded to the hour. This suggestion of Chandler's gives the correct period and phase for Kimura's phenomenon, but cannot give enough amplitude. Also this suggestion reveals that Chandler uses the same phase for the Kimura phenomenon that I do: a reversed phase would imply *later* observations on winter nights than summer, which is absurd.

2. Chandler indicated that stellar aberration wasn't corrected for Earth's orbital eccentricity (correction for Earth's rotation is unneeded for declinations). Chandler doesn't give the period of this term but my own approximations suggest that the period is 1/4 yr; therefore it averages out.

On the other hand, the retardation of stellar aberration, to the time the light crosses the 52.6 AU barrier, agrees with Kimura's phenomenon in period, phase and magnitude. A sensitively positioned star, i.e., +/- 90 ecliptic latitude, e.g. Vega or, better, Zeta Draconis, would move 0.107". A star near the arctic circle and 6h RA, e.g. Capella or, better, Delta Aurigae, would move 0.0765". For a crude estimate, suppose the stars studied are distributed randomly over the northern hemisphere. At ecliptic (lat,long)=(0, 0 or 180), the movement is 0.107 * sin(23.5) = 0.043"; at (0, 90 or 270), it's zero. This averages 0.050", vs. Kimura's amplitude of about 0.03".

A better estimate realizes that the stars used for such studies basically were evenly distributed on the arctic circle. I tallied all variation of latitude studies, and included the (more numerous) aberration of starlight studies, published in the Astronomical Journal 1856-1899. There were 46, excluding one using Polaris. I calculated the exact effect predicted by my theory at 18h, 6h, 0h & 12h; interpolated at 3h, 9h, 15h & 21h using a quarter-wave spline; and weighted by the number of studies using stars nearest those RAs. The resulting predicted amplitude of the Kimura phenomenon, is 0.0304".

Unaccounted stellar parallax (see below) is thought to be up to one-fourth the magnitude of the observed Kimura phenomenon (but opposite in sign, I assume here), which would decrease my prediction by as much as 25%. On the other hand, the calculation above assumes all stars are on the arctic circle; really, few were above the arctic circle; some ranged as far south as Arcturus; usually the latitude of the observatory was preferred, which according to Kimura averaged 42N. Use of the 42nd parallel instead of the arctic circle increases my estimate by 41%. Stars might sometimes have been measured on the far meridian (under the pole); this would subtract from the phenomenon. So, the agreement between theory and observation remains good, when I explain Kimura's phenomenon as a retardation of Earth's effective velocity vector, by 52.6 AU * 8.3 minutes/AU.

Sign confusion in Kimura phenomenon.

Kimura uses "phi" for baseline latitude on p. 108. This suggests that phi minus phi0, essentially Kimura's "xi", is the baseline latitude, minus the latitude measured by the star's altitude on the meridian. That's the sign I used. The correctness of this also is suggested by Kimura's formula in his introduction, which puts his "xi" (sometimes called "Kimura's Z") term on the same side of the equation as what looks like the Chandler pole wobble (hence opposite in sign, to the measured minus baseline latitude).

However, in "Physics of the Earth - II The Figure of the Earth - Bulletin of the National Research Council" (1931)(available on the internet), p. 269:

"...annual parallaxes of the stars...cannot account for greater than one-fourth of the [Kimura phenomenon] effect."

This usage implies that the sign of the Kimura phenomenon is the same as that of stellar parallax, i.e., opposite what I assumed. Then phi would be the latitude measured by the star's altitude, and phi0 the baseline latitude. If so, the phase of Kimura's phenomenon is opposite that expected from retardation of Earth's velocity vector.
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Joe Keller

1061 Posts

Posted - 08 Jun 2007 :  17:57:39  Show Profile  Reply with Quote
Except for a sine function in place of a cosine, an article by SC Chandler, Astronomical Journal 17(400):125-127, 1897, resolves the sign ambiguity of the Kimura phenomenon in favor of my usage and my theory. Furthermore Chandler gives an observed dependence, of catalog declination errors, on right ascension, which might conform to my theory.

The three catalogs considered by Chandler were Russian/French, or German productions. In this era such catalogs typically covered the sky to Decl -30. Catalog declinations typically were measured when a star was on the meridian at midnight.

In 1902 Chandler mentioned that stellar aberration corrections then customarily ignored Earth's orbital eccentricity. (This reflected not so much laziness, as lingering doubt of the true cause of the aberration.) Using Simpson's rule to integrate over the truncated lune from -30 to +90, I find that correction for eccentricity, requires on average that 0.182" be added to declinations of stars at RA 180#, and that as much be subtracted from the declinations of stars at RA 0#.

Let's assume that the correct sign of Kimura's phenomenon, makes it consistent with the theory that Kimura's phenomenon is caused by a seven-hour (i.e., 52.6 AU / c) retardation of Earth's orbital velocity vector. Again using Simpson's rule to integrate over the truncated lune, I find that correction for said retardation, requires on average that 0.0665" be added to declinations of stars at RA 270#, and 0.0755" subtracted from declinations at RA 90#, with declinations 0# & 180# requiring intermediate, small positive, corrections.

The above two corrections together amount to adding approximately:

0.126" * cos( RA + 139 )

to the declinations. Except for the presence of a sine rather than a cosine in Chandler's formula, this agrees perfectly with Chandler's "systematic correction needed by the new Pulkowa declinations":

+0.14 * sin ( RA + 135 )

and with Chandler's correction to the previous 1865 version of the Pulkovo catalog:

+0.09 *sin ( RA + 153 ).

Chandler's correction to declinations in Kuestner's 1890 catalog was:

+0.12 *sin ( RA + 120 ).

With standard error of the mean, the average of the three is:

(+0.117+/- 0.024 ) * sin ( RA + 139+/- 8 ).

The remarkable resemblance of this to my theory, suggests that the replacement of cosine with sine is a transcription error, an error by Chandler, or due to an unknown complication.
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Joe Keller

1061 Posts

Posted - 09 Jun 2007 :  19:00:16  Show Profile  Reply with Quote
If alternatively, an advancement rather than a retardation ( by 52.6 AU / c ) is assumed for Earth's velocity (i.e., other sign convention for Kimura phenomenon) 180+34 --> 180-34 for the axis needing positive correction. That is, RA-214 --> RA-146, giving cos(RA-146) = -sin(RA+124) or rather -sin(RA+117) considering that Earth's perihelion (1889 ephemeris) is 11.5# past the solstice and that most of the effect depends on the former, not the latter. This too is acceptably close to Chandler's values, especially if Kuestner's catalog (which differs only 5% in amplitude and 0.05 radian in phase) is emphasized. The problem now is that the sign is reversed from Chandler's. Maybe there is a misunderstanding about what is being corrected to what. For example, the catalogs might be based on declinations measured on the meridian at all seasons and Chandler's supposed correct values based on midnight declinations.

Wagner's 1861-1872 right ascensions of Polaris (quoted in Chandler AJ 19(444):89-92, 1898) are consistent with advancement rather than retardation of Earth's velocity as it affects stellar aberration. The table on p. 90 gives Wagner's "Observed minus Calculated" values for the RA of Polaris. I used the 1887 (oldest ephemeris in the library) coordinates, with yearly changes given, for Polaris, extrapolating them to 1867. Including along with the velocity advancement also the small effect of parallax, I found an expected excess, of "Obs - Calc", with period one year, and maximum 0.289s (i.e., seconds of RA) when the sun is at ecliptic longitude 108. I averaged Wagner's figures for each month, weighted proportionally to the number of observations, then found the first-order Fourier coefficients. This gave for the "O - C" excess a maximum of 0.066s when the sun is at ecliptic longitude 82, a phase discrepancy of 26#. Wagner's twelve-year study averaged out the effect of the 14-month Chandler wobble, unless the wobble's axes varied much. The text indicates that Wagner sometimes used inferior instead of superior culminations of Polaris; if 3/8 of the time he used the inferior culmination, then the amplitude would be reduced, as it is, to 1/4 of predicted.

Now three studies - Kimura's meta-analysis of latitude determinations, Chandler's analysis of catalog declinatons, and Wagner's right ascensions of Polaris - roughly agree with my theory that for stellar aberration, Earth's velocity is advanced by about seven hours (there is a questionable sign disagreement for Chandler's analysis).
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Joe Keller

1061 Posts

Posted - 12 Jun 2007 :  20:49:06  Show Profile  Reply with Quote
Proposed experiment:

Get a big old refracting telescope, with a dome and stone pier. Refractors are best for this experiment because of their stable alignment. Let the refractor have an eyepiece with two very straight lines crossing at some angle.

Each night, put the crosshairs on a known star that is as close as possible to the pole, record the time, and fix the telescope in that position though the star eventually will move away from the crosshairs. Also at this moment rotate the crosshairs so that each of the four branches has a known visible star slightly clockwise of it.

Due to precession, uncorrected J2000.0 coordinates don't accurately tell us which stars now are closest to the pole, but at epoch 2000.0, two stars with USNO-B "Red 1" magnitudes of +13.4, were < 2.4' from the north pole. So with a big refractor we typically expect to see a +13.4 star 2' from the pole, maybe closer. The billion-star printed & bound "Millenium Catalog" shows two pairs of almost opposite stars, none dimmer than magnitude +10 or +11, 20-30' from the N pole, and the pairs making about a 60# angle with each other (so crosshairs 60# apart would be best).

Four crossings will be timed soon after aiming the telescope, and four more crossings (for these stars) four or eight hours later (the latter precluding summer observation). Opposite pairs of angles will be perfectly equal. The inequality of the times required for the stars to move from one crosshair to the next, will tell how much the crosshair is displaced in that direction, from the pole. So, the position of the pole will be found.

The pole change due to change in Earth's axis (i.e., precession & nutation) can be removed by calculation based on ephemeris data. Chandler wobble doesn't move the pole; it only changes the latitude. Herein lies the superiority of my method, to that of using zenith cameras: daylight prevents 24-hour zenith camera observations, so zenith cameras don't distinguish pole motion (axis change) from Chandler wobble (latitude change). Stellar aberration due to Earth's rotation will not affect the time intervals, so the only effect remaining is stellar aberration due to Earth's orbital motion (and to the sun's motion).

The altitude of observation is constant, but temperature, pressure and humidity also correlate with atmospheric refraction, and these might change in 4-8 hours. Adjustment can be made for these, using the formula in PASP 108(729):1051+, 1996. This formula is said to agree with the empirical Pulkovo tables within 0.01", if the altitude of observation is > 15#.

"Anomalous refraction" limits accuracy. Over several hours, anomalous refraction amounts to 0.05-0.20" (A&A 459(1):283+, 2006). So observations on ~100 nights are needed, not necessarily all from the same observatory.

A book says that one-hour clock-drive exposures sometimes are made unattended. Then a firmly grounded fixed telescope should remain within one arcsecond for eight hours.

Another book says that for typical eyepieces, eyepiece fields of view are 40-50#, and that the observer's actual field of view equals the eyepiece field of view divided by the magnification. So, a one or two degree field of view would correspond to 20-50x magnification, which seems plausible.

Earth's motion may be found by numerical differentiation of the sun's apparent ephemeris position, projected onto Earth's equatorial plane. The difference between the sun's apparent and geometric position might as a first approximation be neglected. Also the sun's motion due to Jupiter might be neglected.

If Kimura's phenomenon is due to a lead or lag in stellar aberration, then the direction of deviation of the pole will lead or lag (the opposite of) the direction of Earth's velocity vector. This will provide another accurate test of Special Relativity over solar system distances.

Dimitroff & Baker, "Telescopes & Accessories", 1948, lists the world's big (15"+) refractors. In the US these include, in order of aperture:

Yerkes (40 inch)
U. of Va.
Wesleyan (Middletown, Conn.)
U. of Denver
Oakland, Cal.
U. of Penn.
Carleton Coll.
U. of Cincinnati
Mt. Lowe
U. of Wisc.
U. of Miss.
Yale (15")

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Joe Keller

1061 Posts

Posted - 16 Jun 2007 :  00:11:04  Show Profile  Reply with Quote
Special Relativity is disproven by double stars. There should be several arcseconds difference in stellar aberration between the primary and the secondary, because their velocities differed by several km/s when their light departed. Therefore stellar aberration is determined by something besides mere relative motion of source and observer.

Red giant variables give a clue. Over many years, the angular diameter of Antares, the brightest red giant that can be occulted by the moon, was measured many times at lunar occultations (Astronomical Journal 62(2):83+, 1957). One of the most precise such diameter measurements, was 0.0413" +/- 0.0001" (41.3 +/- 0.1 mas)(A&A 230(2):355&, 1990; see also Table 2); this and other references (ApJ 242:646&, 1980, Table 5; this article is missing from "Web of Science")(ApJ 463(1):336&, 1996) list 22 determinations of Antares' diameter since 1920; some used visible light and others infrared. Ten were by occultation, eleven by any of three different kinds of interferometry (Michelson, amplitude, and speckle); one used flux curves. Fourteen of the 22 were in the range 40-43 mas inclusive. Only four (35,28,29 & 28 mas) of the 22 were outside the range 39-45 mas inclusive. Yet the Radial Velocity measurements 1905-1909 (op. cit., 1957) showed about 6 km/s "full amplitude" (max minus min) in roughly a sinusoidal pattern with period 6-7 years. The period is somewhat irregular and uncertain (AJ 98:2233+, 1989). No one seems to think that such periods in RV, typical of 25-30% of pulsating asymptotic giant-branch stars (Astrophysical Journal 604:800+, 2004), are due to engulfed companions. An average 6/2*2/pi*1.35("projection factor" to find velocity radial to Antares; because of "limb darkening", the factor is less than 1.5) km/s radial velocity for 6.5 / 4 years, even using Antares' most generous (Hipparcos) distance estimate of 185 parsec, gives +/- 9.5 mas in diameter. If the RV indicates expansion of Antares, and the period 1905-1909 wasn't unusual, then Antares' diameter should vary roughly sinusoidally +/- 9.5 mas. So, the occultation-measured diameters are too tightly clustered near 42 mas.

Antares varies about +/- 0.4 magnitude; possibly as much as +/- 0.15 mag variation (i.e., 15% of power) could occur in a 6 or 7 year cycle (AJ 1989, op. cit.). Maybe the apparent RV change is due to a +/-0.56 AU change in the radius of Antares' "ether iceberg". With about 20x the sun's mass, the radius of this "iceberg" might be 52.6*sqrt(20)=236 AU, so, the change is +/- 0.2%. Antares, like other stars of its type, expels about 0.000002 solar mass per year as wind (ApJ 275:704+, 1983). Even if the boundary or barrier at the edge of Antares' "iceberg" is mainly a gravitational phenomenon, the barrier's position yet might be affected slightly by strong solar wind.

Polaris is the nearest Cepheid variable. How fortunate that the nearest Cepheid variable is placed so prominently! Cepheids are yellow giants, smaller than Antares; only recently have their diameters begun to be measured accurately and directly. So far, only one report (Nature 407(6803):485&, 2000) seems to confirm, even roughly, for a Cepheid (Zeta Geminorum), the diameter periodicity implied by RVs.

There are two more reasons for doubting that there is any real periodic diameter change in Cepheids. The periodic time plot of RV often is grossly nonsinusoidal yet almost identical, except for sign and magnitude, to that for luminosity: e.g., Delta Cephei (Inglis, "Planets, Stars & Galaxies", 3rd ed., Fig. 11-2)(M. Petit, "Variable Stars", 1987, Fig. 4; includes temperature and radius plots). Yet luminosity is supposed to be due to temperature and radius, not RV. The luminosity waveform should resemble the temperature waveform most and the RV waveform least.

If luminosity causes apparent RV by affecting the "ether iceberg" boundary (at distance 52.6 * sqrt(M) A.U.) then the geometric midrange classical (i.e., Population I) Cepheid (Strohmeier, "Variable Stars", 1972, Table 42)(for the period, I used the geometric mean of the luminosity range, and an 0.8-slope log-log period-luminosity relation, with period the abscissa, and through the data point for Delta Cephei) should have (negative) RV lagging luminosity by 7.7% of one period or thereabouts. Indeed the lag is 7% (Carnegie Inst. Yearbook, 36:164, 1937).
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Joe Keller

1061 Posts

Posted - 20 Jun 2007 :  20:47:08  Show Profile  Reply with Quote
Elsewhere on Dr. Van Flandern's messageboard, I've remarked that stability at temperatures proportional to (Z-0.5)^4, involving Special Relativity violations by innermost-shell electrons, might determine, for Hydrogen, the CMB temperature (2.726K); for He, the far CIRB temperature (i.e., about 2.726*1.5^4=13.8K); and for O, the temperature of the main sequence/Cepheid trough intersection. Likewise these temperatures might determine, for Ne, the least-luminous temperature of the beta Cepheids (a.k.a. beta Canis Majoris stars); for O, the least-luminous temperature of the delta Cepheids (aka Population I Cepheids) and/or Pop. II Cepheids; and for C, the least-luminous temperature of the long-period (Mira) variables.

Cepheids range from 5400-6900K according to Strohmeier (op. cit., 1972) but from 6000-8000K according to Dr. Koji Mukai ("Ask an Astrophysicist" website, 1998). The least luminous tend to be hottest (chart in Inglis, 3rd ed., op. cit.). My theoretical oxygen stability temperature is 8625K.

Beta Cepheids (a.k.a. beta Canis Majoris stars) are said on various websites to range B0 - B2 or B3 in spectral type, i.e. 18,700 or 22,000 - 30,000K. Beta Can Maj itself is said to be 22,000 or 25,000K. For these, the least luminous tend to be coolest (Inglis, op. cit.). My neon stability temperature is 22,200K.

Dyck & van Belle, AJ 112(1):294&, p. 299, quote an article then submitted to the AJ by van Belle, stating that Mira variables average 2700K. My carbon stability temperature is 2490K. Dyck & van Belle also find that "carbon stars" (kin to the Mira variables) average 3000K. The coolest "carbon star" was TW Oph at 2150K. The least luminous tend to be coolest (Inglis, op. cit.).

A delta Cepheid might have a beta Canis Majoris star inside it; and a long-period variable, a Cepheid inside it. The law relating Cepheid period to stellar density, resembles Kepler's for orbital periods. Strohmeier (op. cit., Table 42) gives P(days) = Q /sqrt(density/solar density), where 0.037 < Q < 0.066 days. That is, P = Q / sqrt(M in solar masses) * sqrt(4*pi/3)*(R in solar radii)^1.5. If almost all the star's mass is in a tiny central core, and something orbits between this core and the outer surface, its period is found when Q = 0.041 days. If something orbits between the oxygen-temperature (2.726*7.5^4=8625K) surface and a fluorine-temperature (14,230K) surface beneath that, the ratio of the radii is (7.5/8.5)^(4*2) = 0.367; the period is found when Q = 0.066 d. The periods of variable stars might be orbital periods between one stable surface and another, in the near-vacuum of a giant star's interior. The Q values given by Strohmeier for classic (i.e., delta) Cepheids are the same as the theoretical Q values given for beta Cepheids by Lesch & Aizenman A&A 34:203&, if the 0.066 comes from tripling their 0.022 given for the "second harmonic" (also there are "first harmonic" & "fundamental" modes); their Table 4 shows observational Q values ranging from 0.018 to 0.033 for 12 beta Cepheids.

The Blazhko effect "...occurs among all types of pulsating variables, but...mainly those of short period." [i.e., the RR Lyrae stars, which merge into the low-luminosity side of the Population II Cepheid distribution] (M Petit, "Variable Stars"). The Blazhko effect is, that the amplitude and waveform of a variable star's lightcurve changes grossly, while its period remains nearly constant. The explanation might be that the amount and phase distribution of matter orbiting within the star might vary though the Keplerian period doesn't. More luminous variables, being more fully developed structurally, would tend to approach a mathematical limit whereby the period is longer, the lightcurve more sinusoidal, and the Blazhko effect less.

The three (3/22) anomalously small values for Antares' diameter (0.029", 0.028", 0.028"; see previous post) might be glimpses of the next inner, perhaps N-based, surface. One of these small values was obtained at lunar occultation, observing at 1.04 microns. At this wavelength, the inner surface might be especially visible, with less scattering (long wavelength) yet denser emission from the hotter inner surface than from the outer surface (wavelength not too long).

Two of the small Antares diam values were from the longer (50 ft) Michelson interferometer; as we would expect, Pease noted difficulty from ambiguous readings. If the N-surface were detected on one side only (radius = (5.5/6.5)^8=0.263x the carbon surface), then the angular diameter found should have been 0.0413" * 1.263/2 = 0.026".

The small 1986 occultation value for Antares' diam, was followed by two normal 1987 occultation values (41 & 45 mas). Likewise Pease's small 1934 and 1936 Michelson interferometer values were preceded by a normal (41 mas) 1932 value by Pease with the same interferometer. Such a diameter dip in one year would require (0.041-0.028)"/2*1.35(cosine correction with limb darkening) * 185parsec = 1.6 AU/yr = 7.7 km/s average net positive RV, twice the extreme RV observed during the extensive early 20th century observations. The anomalous small diameters were partial detections of an inner surface. Nor do the RVs indicate real diameter changes.
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Joe Keller

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Posted - 22 Jun 2007 :  17:43:59  Show Profile  Reply with Quote
The Hertzsprung-Russell luminosity diagram in, inter alia, Inglis (3rd ed., op. cit.) suggests that, because of similar luminosities, long-period (Mira) variables might have Pop. II Cepheids inside, and Pop. I (classical, delta Cephei) Cepheids might have beta Cepheids (beta Canis Majoris stars) inside. Though the period vs. density formula in Strohmeier (op. cit., see previous post) gives "Q" values for classical Cepheids (for which Eddington originally devised the formula) the formula also is thought to apply to Pop. II Cepheids, though maybe with somewhat different Q values.

Thus variable stars seem to release energy via a kind of variable convection with period suspiciously similar to the Keplerian. At the simplest, a huge, repeating solar flare in a sun-grazing elliptical orbit cyclicly delivers energy to some outer surface which hides the flare. If the flare quickly cools to equilibrium temperature with solar radiation, then maximum luminosity occurs only slightly after perihelion because the orbit is so elliptical. The Blazhko effect occurs because the period is much more invariant than are the other cyclical features of the event.

Electrons sometimes disobey Special Relativity. As Thompson theorized a few years ago, electrons are agitated by Lorentz contraction. In several posts above, I quantified this energy, showing that there is a large latent heat for innermost-orbital electron pairs, analogous to melting, released at "electron melting temperatures" of thousands of degrees K for elements such as C, O, and Ne. In variable stars, it is efficient that each idealized flare (see previous par.) cross one of the surfaces at which solar radiation equilibrium temperature equals electron melting temperature for some common chemical element. Thus also this large latent heat can be carried away with the flare.

For the least luminous stars, the physical outer envelope surface, the aphelion of the flare, and the electon melting surface for some element, all are the same. When the outer melting surface is that of neon or carbon, the latent heat is a minor consideration: the surface tends to be a bit closer (hotter) for more luminous Beta Canis Majoris or Mira type stars, so the flare doesn't have to travel so far. On the other hand, oxygen is so abundant and its latent heat per atom so large, that its latent heat is a major consideration: the surface tends to be a bit farther (cooler) for more luminous Cepheids, so more latent heat can be extracted.

Generally, Ne < Ne' < O < O' < C < C', where Ne, etc., are the radii at which inner-orbital electrons of each element melt, and Ne', etc., are the aphelia of successive stages or stories of flares. For increasingly luminous stars, the primed quantities increase fastest, overtaking the next unprimed (except for C' or Ne' if outermost). This explains the classical Cepheids' Hertzsprung progression (Hertzsprung, BAstronINeth 3:115, 1926; Petersen et al, A&A 134:319-327, 1984, p. 319). As Ne' increases for more luminous classical Cepheids, the "bump" at which oxygen's electronic latent heat is released, moves "backward" (i.e., to the left on the time graph) from an almost 0.5 cycle (observationally, 0.4 cycle) "lead" (i.e., position to the right of the peak), into synchrony with the luminosity peak, and then even "behind" (i.e., left of) the peak, before becoming hidden by the Ne' surface itself. A disproportionate increase in Ne' might also make the waveform less sawtooth and more sinusoidal.
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Joe Keller

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Posted - 02 Jul 2007 :  15:56:15  Show Profile  Reply with Quote
Let's combine some well-known variable star relations:

(1) deltaR / R = 0.25 deltaL / L

(Inglis, op. cit.). Here L is absolute, not logarithmic. This relationship is claimed only to be a rough average. R is inferred from the spectral line shift. This fits within about a factor of two (Delta Cephei, for example, misses by about a factor of 1.6). For classical Cepheids, the so-called RV curve, with peak "V0", is more sawtooth than sinusoidal. So,

(2) deltaR = V0 / 2 * Period / 4 * 1.35. (The last factor would be 1.5 geometrically, but is about 1.35 for visible light, due to "limb darkening". If the RV curve is sinusoidal, the "2" becomes "pi/2".)

(3) Q = Period * sqrt(density / solar density)

This is the theoretical Eddington relation. Empirically, it fits not only classical (Delta) Cepheids but also Beta Cepheids. Both types have Q typically 0.037 days within about a factor of two.

Combining these,

(4) deltaL / L = 1.91 * V0 / sqrt(2*M*G/R).

If the RV curve is sinusoidal instead of sawtooth, the 1.91 becomes 2.43. So, the variable star's power output is proportional to (Vesc + V0*cos(t) )^2.
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Joe Keller

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Posted - 14 Jul 2007 :  21:54:21  Show Profile  Reply with Quote
Thesis. Cassiopeia A exploded twice, causing both the Spoerer & Maunder sunspot minima.

Sunspots. Many main-sequence stars in the sun's neighborhood, show evidence of starspot cycles of 4 to 20 yrs (vs. 11.1 yrs for the sun). When starspots are big enough, measurable luminosity changes due to stellar rotation, indicate a sunlike differential rotation and butterfly diagram (IY Alekseev, Solar Physics journal, 2004). If starspots are too small to detect, chromospheric activity, especially CaII emission, still often reveals the cycle (P Wilson, Cambridge Astrophysics Series #24, pp. 109, 114-118).

Jupiter's 11.86 yr period is only slightly greater than the 11.1 yr Schwabe sunspot cycle; Uranus' 84 yr period only slightly greater than the 82.2 yr (according to H. Kimura) Wolf (1862) cycle which Gleissberg found also in auroras (see Gleissberg's aurora article in: J. Schove, ed., "Sunspot Cycles"). Yet if the planets cause the cycles, then why does Saturn lack effect, and why do other stars generally have roughly the same (primary) starspot cycle length as the sun? Maybe the planets' periods and the sunspot cycles have, or originally had, a common cause.

Sedimentary rocks, inter alia, 680 million yr old, show cycles of from 8 to 15, or even 22 (!) yr, though now it is thought that some or all of these cycles are associated with lunar tides, not sun-caused weather (RY Anderson, NY Acad Sci Annals, 1961; in: Schove, op. cit.)(George Williams, 1980s, mentioned in: Brody, "Enigma of Sunspots", p. 163). Maybe the exact sunspot cycle length is determined by, say, the total mass of the solar system, but sunspot activity is maintained in disequilibrium despite damping, by an interstellar wave which limits the cycle length to a narrower range than would be expected from the diversity of stellar masses and planetary configurations.

From sunspot numbers (inter alia, the chart in Branley's Astronomy) and from the corroborating aurora records gathered by Agnes Clerk (see John Eddy, 1976, in: Schove, op. cit.) the Maunder sunspot minimum (discovered by Spoerer in 1887) occurred from about 1645 to 1715. There also is a Spoerer sunspot minimum from about 1480 to 1520; both the Maunder and Spoerer minima are confirmed by high (presumably due to lessened protection from cosmic rays) C14 levels in tree rings (Eddy, op. cit.).

Cassiopeia A. Cassiopeia A has the greatest apparent (not absolute) power (i.e., radio magnitude) of any radio source outside the solar system. At galactic coords. 111.7, -2.1, it lies near the galactic plane, only about 22 degrees away from the sun's presumed direction of travel around the galaxy (Tycho's supernova is at galactic coords. 120.1, +1.4). Cassiopeia A is thought to have been an exploding Wolf-Rayet star 11,000 lt yr away.

Flamsteed recorded a now-gone star, probably 6th mag, in 1680 near the location of Cas A. Flamsteed was a great astronomer and recorded his date of observation for this star. It's thought that a dust envelope might have caused its relative faintness vs. Tycho's or Kepler's supernovae. The most recent motion studies support the 1680 date: 1681 +/- 19 (Astrophysical Journal 645:283+, 2006); or 1671 +/- 1 if without deceleration of ejecta, a few (maybe 10) years later if with deceleration (Astronomical Journal 122:297+, 2001).

Two other recent motion studies support the date, c. 1505. These found 1539 +/- 30 (Aqueros & Green, MNRAS 305:957, 1999) and 1495 +/- 15 (Astronomy & Astrophysics, 339:201, 1998).

Discussion. Maybe two major explosions occurred at Cas A, c. 1505 and in 1680 (minus light travel time). These would have followed the beginnings of the Spoerer & Maunder sunspot minima by about 25 & 35 yr, resp., almost obliterating the sunspot cycle for 40 & 70 yr, resp., if the sunspot effect could arrive c. 30 yr prior to the light.

The supernova might send out a superluminal wave which disrupts a segment of the track of the underlying, lightspeed, interstellar wave regulating the sunspot cycle. If this track passes through Cas A, then the sunspot cycle disruption would be observed at the same time as the supernova, and plus or minus "X" yrs, depending on the size of the disruption. Indeed this occurred: [1480-1520] equals [1500-20, 1500+20]; [1645,1715] equals [1680-35, 1680+35].
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Posted - 15 Jul 2007 :  18:05:55  Show Profile  Visit cosmicsurfer's Homepage  Send cosmicsurfer a Yahoo! Message  Reply with Quote
Hi Joe,

Excellent data comparisons that show possible synchronicity between solar sunspot cycles, supernova and superluminal waves. I think you are on to something that has most definitely been overlooked by main stream science. Fluctuations in superluminal wave pressures may exist that have periodicity due to large scale interactions that change "windows" of polarity with in regions of space. Hence, polar magnetic field reversals act like a butterfly effect with 'lines of force migrations'[following lines of force of fluctuating wave patterns of greater universe] occuring on sun's surface creating super magnetic storms or sunspots that are actually aligned with superluminal wave/current interaction migrations [polar to equator migrations tip scale to a polarity reversal-butterfly effect] within our scale.

Just thought of something that really just blew my mind. What if these system wide fluctuations on sun spot migrations are revealing axis differentials of superluminal lines of force that 'are' the overall major axis centers moving around our point of reference with in our MEGA SCALE. Look at torque values of such a switching effect and measure scale probability by co-factoring other center migrations then measuring difference between to juxtaposition large scale structure rate of motion.

Just some thoughts.


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Joe Keller

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Posted - 15 Jul 2007 :  18:12:51  Show Profile  Reply with Quote

There's a wealth of ideas here. Thanks for your thoughts.

- JK
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Joe Keller

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Posted - 16 Jul 2007 :  13:51:10  Show Profile  Reply with Quote
J Eddy's C14 tree ring data (see previous post) confirm ~40+70=~110 years of Maunder minima in the sun's latest 950 yrs. Measuring CaII line strengths has allowed about 2000 nearby sunlike stars to be checked to see if they are actively cycling, or in a Maunder minimum. Instead of the expected ~230, approximately none of these stars are in a Maunder minimum ("Do We Know of Any Maunder Minimum Stars?", JT Wright, AJ 128:1273+, 2004).

Type IV subgiants have different CaII measurements than do Type V dwarfs; in early surveys, subgiants comprised a large distinct minority: fictitious Maunder minimum stars. When subgiants were excluded, < 10 Maunder minimum "candidates" were found in collections of ~1000 solar-metallicity Type V dwarf stars, i.e., sunlike stars (Wright, op. cit.; Gray, AJ 126:2048+, 2003). These candidates have borderline measurements, do not form a bimodal peak, and might be merely a statistical tail.

Binary star companions affect starspot distributions; Jovian planets might affect sunspot cycles. This can't explain the absence of Maunder minima, because maybe 1/4 of sunlike stars, both lack binary companions and have Jovian planets. Either the sun or solar system has a rare unknown property causing Maunder minima, or the occurrence of Maunder minima in the sun and in nearby sunlike stars is synchronized.

The 1645-1715 Maunder minimum might be found, in measurement epochs c. 1995, in sunlike stars 43-54pc distant opposite Cassiopeia A (see previous post). Distance cutoffs in the above star collections, were 40-60pc (Wright op. cit.; Gray op. cit.; Henry et al, AJ 111:439+, 1996). Henry (op. cit.) also usually used an apparent magnitude cutoff of +9.00, which, he noted, corresponds to our sun at 50pc. Hipparcos gave distances for the 9 stars which Gray deemed his elite northern Maunder minimum candidates (Gray, op. cit., Table 6, p. 2057): the farthest was 30pc. The middle page, of Henry's list of southern observed stars (Henry, op. cit., p. 450) happened to show only 3/90 stars with apparent magnitudes dimmer than +8.674, which I infer to be our sun's magnitude at 43pc on Henry's scale.

The hypothetical locus for manifestation of the Maunder minimum is bounded by two very eccentric prolate spheroids, approximately paraboloids. The paraboloid through 43pc, passes beyond 60pc when 52deg away from the point opposite Cass A; this cap covers 19% of the sphere. Roughly, the fraction of sample stars, that are within the Maunder minimum locus, is then 3/90*19%*1/2 = 0.3%; i.e., 2000*0.3% = 6 stars. As sunlike stars near 50pc, these would be near Henry's magnitude limit. Instead of expecting 230 stars having good data, we expect 6 relatively distant, southern, mostly circumpolar (low altitude of observation) stars having poor data. The distance and magnitude limits of present studies might just barely fail to reach the stars that would be at Maunder minimum.
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Joe Keller

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Posted - 16 Jul 2007 :  22:27:28  Show Profile  Reply with Quote
The sun's best lookalike, 18 Sco, has a 7 yr cycle (Astronomical Journal 133:2206+, 2007). Baliunas (op. cit., p. 284) states that all clearly detected cycles in his ~100 star sample, are at least 7 yrs long; also, our sun's shortest cycles, over the last 250 yr, are 7 yrs. This is further evidence of overriding interstellar regulatory control: the most similar, and - almost - the least similar stars, all cycle with the same range of periods.

Baliunas et al, Astrophysical Journal 438:269+, 1995, report three possible Maunder-minimum Type V stars. One of these, HD (Henry Draper catalog) 9562, really might be Type IV (i.e., subgiant & "evolved", hence disqualified - see previous post) according to their footnote; indeed the ARICNS catalog classifies it G2IV.

Another, Tau Ceti, spectral type G8Vpeculiar, absolute magnitude 5.7 (0.2 mag dimmer than the main sequence norm) was noncycling but seemed to be starting to cycle slightly beginning in 1990 (Baliunas, op. cit.; also Frick, ApJ 483:426+, 1997). However, true Maunder minimum includes more than mere absence of cycling (Hall & Lockwood, ApJ 614:942, 2004).

Baliunas' best Maunder-minimum candidate was HD 3651 (Flamsteed designation: 54 Pisces), spectral type K0V, absolute magnitude 5.8 (near the main sequence norm). It showed a cycle of 13.8 +/- 0.4 yr, peaking in 1966 or slightly earlier, again in 1978, and then with a much smaller peak in 1989, consistent with Maunder minimum beginning sometime between 1980 & 1989 (Baliunas, 1995). Subsequently HD 3651 has remained photometrically stable at < 0.1% variation (ApJ 590:1081+, 2003). This would be small photometric variation, for a cycling sunlike star; our sun's cycling-associated photometric variation is 0.1%, which is very small for a vigorously cycling star such as our sun. HD 3651, with 0.79 solar mass, has an extrasolar planet smaller than Saturn, with major axis 0.3 AU and eccentricity 0.6 (Ibid.). HD 3651 also has a faint, cool Type T brown dwarf companion at 480 AU projected separation (MNRAS 373:L31+, 2006).

HD 3651 might be giving early warning of another event at Cassiopeia A which is causing Maunder minimum for stars in this quadrant of the galaxy. Both Vostok and South Polar ice cores show increased nitrate levels (presumably due to increased atmospheric cosmic rays) simultaneous with Tycho's and Kepler's supernovae, to within a few months' accuracy (Dreschhoff & Laird, Advances in Space Research, 2006, on internet 2004). However a similar nitrate spike is shown in 1667, not 1680 when Flamsteed recorded a star, now gone, at the location of Cas A. This, and the beginning of the Maunder (resp. Spoerer) minima c. 1645 (resp. c. 1480), not 1680 (resp. c. 1505), suggest superluminal processes associated with Cas A events.

At first, Flamsteed named Cas A "supra Tau Cassiopeiae" (Thorstensen et al, AJ 122:297+, 2001, Introduction)(the real Tau Cassiopeia is 3deg east both from Flamsteed's recorded star location, and from today's Cas A at RA 23h23.4m Decl +58deg50'); this suggests that Flamsteed saw a large nebulosity, perhaps aimed toward Tau Cassiopeia. Then Flamsteed changed the name to 3 Cassiopeiae; maybe the nebulosity subsided and Flamsteed decided it must have been a cloud. The low Flamsteed number suggests that Flamsteed's star was bright: Bayer designations are twice as common among the top half of Cassiopeia's Flamsteed numbers as among the bottom half; the top three Flamsteed numbers in Cepheus and the top ten in Ophiuchus (site of Kepler's supernova) all have Bayer designations. However, Flamsteed's map shows the star of the faintest brightness; he "recorded [it] of 6th magnitude" on Aug. 16, 1680 (Nature 285:132, 1980).

Van den Bergh & Dodd (ApJ 162:485, 1970, pp. 491-492) used the amount of neutral hydrogen along the line of sight, to estimate the rather large amount of dust along the line of sight, thus estimating the peak magnitude of a typical supernova at the position of Cas A, as +2, even without any special dust cloud around it; they also found that almost all regular +2 novae went unrecorded either by European astronomers of that era, or by Asian astronomers. Though Flamsteed's position differs 15' from today's (the diameter of Cas A's main broken shell is only 4', and its extreme diameter only 5.4') it's thought that much or all of the error might be attributable to Flamsteed's usual errors including sextant corrections & atmospheric refraction (Nature, ibid.). Alternatively, Cas A's proper motion might have decreased from an earlier average of 3"/yr (16% the speed of light).

It's thought that maybe Cas A was an exploding Wolf-Rayet star, but it is uncommonly placed, for a W-R star (see heliocentric galactic coordinate plot of all ~60 W-R stars then known within 3 kpc, in Conti, "O Stars & Wolf-Rayet Stars", 1988, Fig. 2-10, p. 107). The short lifespan of W-R, O & B stars, would prevent a W-R star from pacing the 8 to 15 yr sedimentary cycles of Earth hundreds of millions of years ago (see posts above). If these sedimentary cycles were due to sunspots, and if now there is interstellar pacing of sunspots by Cas A, then either Cas A is not a W-R star, or long ago other W-R stars provided a similar pace.

Cassiopeia A is complicated and asymmetrical. HD 3651 (54 Pisces) is 11pc (36 lt yr) from us, making a 42 degree angle with Cas A, thus 7.5 arcminutes from us as viewed from Cas A. HD 3651 might have begun its Maunder minimum especially early so that we observed it c. 1985 despite the 9 years longer lightpath. The other stars in that direction won't begin their Maunder minima until nearer the time that our sun does; half the stars in that direction won't be observed to have entered their Maunder minima until after the sun does.

Hall et al, AJ 133:862+, 2007, p. 879, found two sunlike stars, HD 43587 & HD 140538 (Bayer designation: Psi Serpens), whose cycles seem to be entering or leaving Maunder minimum, but these cycles aren't very clearly detected. Hall notes (op. cit., Sec. 5.4.2) that Baliunas (op. cit., 1995) called HD 43587 "Flat?" even during the allegedly un-flat era in Hall's data. Hall says (op. cit., Sec. 6, Conclusions) that his "most significant example of a clear transition" between noncycling & cycling states, is HD 140538.

The ARICNS catalog absolute magnitudes of +4.05 & +4.42, resp., make HD 43587, 0.35 mags, & HD 140538, 0.68 mags (thus HD 140538 fails Wright's subgiant rejection criterion; see below) brighter than normal for their Sky Catalog 2000.0 (and Hipparcos) spectral classifications, G0 (G0.5Vb in Hipparcos) or G5, resp., if they are "V" dwarfs (Jaschek, "The Classification of Stars", 1987, Table 12.5). The ARICNS catalog classifies HD 43587 as F9V, which is 0.2 mag brighter than G0V (by interpolation in Jaschek, op. cit., Tables 12.5 & 11.5). This would make HD 43587 only 0.15 mag brighter than the main sequence norm; furthermore, use of the Hipparcos parallaxes instead of the ground-based, and the slightly different Hipparcos visual magnitudes, puts both these stars on the main sequence norm, within 0.1 mag. (The absolute magnitude of HD 140538 in the Sky Catalog 2000.0 seems to be erroneously faint; both these stars are listed there as spectral type "dGx" rather than "GxV"; in the old Harvard classification, "d" denoted either V or IV, as there was no subgiant designation.) If its ground-based parallax distance, 19pc, is too large by twice the standard error published by ARICNS, then HD 140538 (Psi Ser) likely is a star that has been observed emerging from Maunder minimum.

Gray's nine elite Maunder minimum candidates (Gray, op. cit., Table 6) were critiqued by Wright (op. cit., p. 1275). Two he discarded as showing only modest changes in CaII lines, consistent with mere cycle minima rather than Maunder minima. Three he discarded as > 0.6 mag above the main sequence norm at their spectral type, i.e., as subgiants.
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Joe Keller

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Posted - 18 Jul 2007 :  22:00:41  Show Profile  Reply with Quote
Wright (op. cit., 2004) found three Maunder minimum candidates of his own, in addition to Gray's. One, GJ 561, is listed in the VizieR catalog as having absolute magnitude, visual magnitude and parallax of a subdwarf, 2.4 mag below the main-sequence norm for its spectral type, K0; so, maybe this was an error in Wright's data. Another, HD 186427, not only was found, by the rival Lowell Observatory survey, to fail Wright's own CaII line strength criterion (Wright op. cit.) but also now is listed by VizieR as a double star (two G dwarfs with projected separation of 90 AU), thus excludable because of the effects of companion stars on stellar cycles.

Wright's third candidate persists: HD 233641 is spectral type G0, with Hipparcos parallax implying 97 pc distance and absolute magnitude either +4.0 or +4.3 depending which of the two online visual magnitudes is believed. This is only 0.4 or 0.1 mag brighter than the norm for its spectral type. Its coordinates are RA 9h31m Decl +53, about 60deg from Cassiopeia A. Unless disqualified by magnitude variability, HD 233641 is a fifth apparent Maunder minimum star, and fits the pattern of the four listed in the previous post, except for its spectral type.

I manually rechecked the published "Phoenix" list of nearby southern sunlike stars (Henry, AJ v. 111 op. cit., 1996). Excluding binaries, 71 stars had logR'HK <= -5.10 (the usual criterion). Thirteen of these were listed as Type IV or IV/V (i.e., subgiant or borderline subgiant) in the online Heidelberg ARICNS or Hipparcos catalogs; another 44 were more than 1.0 mag too bright for their Hipparcos distance and spectral type; eight were 0.7 to 1.0 mag too bright; HD 57062 (type G5V) & HD 59741 (type G3/5V) had conflicting visual magnitudes according to which they were either 1.4 or 0.5 mag too bright (variable stars?); HD 67581 isn't in the Hipparcos catalog (distant subgiant?); HD 3795 possibly has acceptable absolute magnitude but is a well-documented "evolved" (-2.0 < [Fe/H] < -0.75; Li, Be, B depleted) star (Astrophysics & Space Science 265:67, 1999; Astronomy & Astrophysics 343:545, 1999).

The two best "Phoenix" candidates in 1996 were HD 56972 (G5V, 0.51 mag too bright, 69pc distant per Hipparcos, RA 7h18m Decl -32, 48deg from the antipode of Cassiopeia A) & HD 179699 (F8/G0V, 0.63 mag too bright, 80pc distant per Hipparcos, RA 19h 15m Decl -40, 69deg from the antipode of Cas A). Both these stars are within that relatively distant locus, where stars would appear to be in Maunder minimum, if that minimum is caused by a lightspeed signal from Cas A which also caused our sun's Maunder minimum. On the other hand, at this distance the sample covers declinations < -25, and most of the stars at this distance brighter than the +9 magitude cutoff are subgiants. So, many subgiants in the sample would be expected to be found within this locus.

The abovementioned five northern hemisphere candidates (three from Gray, one from Baliunas & one from Wright) would require supraluminal communication of the next Maunder minimum inducing event from Cas A. Let phi be the angle seen from Earth, between Cas A & the star, and "d" the distance by which the star is nearer to the (practically infinitely distant) Cas A. The extra lightpath length is d*(sec(phi)-1). For small phi, the supraluminal excess, varying randomly (like Brownian motion) with the direction of flow outward from Cas A, might be k0*sqrt(d*tan(phi)), so:

(1) d*(sec(phi)-1) = k0*sqrt(d)*sqrt(tan(phi)).

At large phi, k0, in units in which c=1, might be replaced by a randomly varying k = K*sqrt(d), so:

(2) sec(phi)-1 = K*sqrt(tan(phi)).

The surface, on certain azimuths of which, a star might be now seen to be entering Maunder minumum, would resemble a paraboloidal nosecone fired from Cas A and about to reach the sun, except that, letting phi --> 0 in the first equation, there would be a narrow tubular central stem reaching upward from the sun toward Cas A. Letting K --> 1 in the second equation, shows that the asymptotic flanks of the surface would be sloped at phi = 66.63deg from vertical, instead of vertical as for a paraboloid. Letting d --> 0 in the first equation, shows that the front of the nosecone, connecting the flanks & stem, would be sloped at 90deg (i.e., a surface perpendicular to the line to Cas A, then deflecting toward Cas A before intersecting our solar system).

The angles phi for the five northern hemisphere candidates, are 1, 37, 42, 63 & 66.1 degrees. The farthest star is at 66.1 deg. If the coming Maunder minimum is again 50 yrs (15pc), the stars showing early warning of it should be near the inner side of the above-described surface, especially on the flanks and central stem. This is so.

Four stars among those discussed above, make about 90 degree angles to Cas A:

HD 10700 (Tau Ceti) (Baliunas' candidate for emergence, in 1990, from Maunder minimum) (type G8Vp; [Fe/H] = -0.50; 3.6pc parallax distance; 80deg angle "phi" to Cas A)

HD 57901 (GL 2057) (of Gray's nine, one of the four which survived Wright's cull) (type variously listed as K3V, K2, or G5; [M/H] = 0.00, i.e., solar-metallicity; 25pc Hipparcos distance; phi = 93.5deg)

HD 140538 (Psi Serpentis Aa; a multiple star, with a small companion, 0.2 solar mass according to its magnitude, at 60 AU projected distance; and three midsize to giant companions at 2500-5000 AU projected distance) (Hall's candidate for emergence from Maunder minimum, starting 4-yr cycles in 2000) (type G2.5-5V; 14.7pc Hipparcos distance, which is more than the ground-based distance, 19.4pc, by > 2 std error of the latter - perhaps due to its binary orbit; phi = 99.9deg)

HD 43587 (Hall's statistically weaker transition candidate: possible entrance into Maunder minimum in 2002) (type G0.5Vb; 19.6pc Hipparcos distance; phi = 92.6deg)

So, these four stars range from 80-100 degrees from Cas A. The two stars at phi = 93deg are only 0.2 radian apart in RA and 20% different in distance.
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