Paradoxes Resolved, Origins Illuminated - Requiem for Relativity
Paradoxes Resolved, Origins Illuminated
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Joe Keller

1093 Posts

Posted - 06 Apr 2008 :  20:58:56  Show Profile  Reply with Quote
The Mar. 19, 2008 Bradford photo is upside down (South at the top, West at the right). I see two additional disappearing dots on it, but the green dot you noted seems approximately consistent with Frey's position. It's brighter than expected (the magnitude limit seems too low to detect the objects seen on the sky surveys) but still it could be Frey.
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United Kingdom
1088 Posts

Posted - 07 Apr 2008 :  04:06:44  Show Profile  Reply with Quote
Hi Joe, the digital sky survey image is also upside down then. I blame the Australian astronomers that took it.

As I've said, hold down the mouse key on those images and download them. In photoshop, or paintshop pro open the sky survey image, then open the bradford nem4b image (the better one) Then do a "select all." This can be found in the top menu, or "apple a" "command a", on p.c. and a dotted line will appear round the image. Then do a "copy" command, which is again on the menu, or "apple c", "command c" on p.c.

Then select the sky survey image, by just clicking on its border, to bring it to the front. Then do a "paste" command, which is again from the menu, or apple v", "command v". This pastes a new layer over and above the sky survey.

In the layers palette on the right, you can adjust the transparency of that layer. Knock it down about 30% Make sure that the "move tool" from the tools palette, on the left; that's the one with arrows, top right button of the tools palette; is selected.

Drag the bradford image up to line up with those yellow lines. Then blink the images. There's a little eye symbol on the layers palette, click it on and off.

You'll see that there's a good line up on some stars but others have large proper motions. Zoom in on some of the fainter objects that show on both plates. Then use the arrow keys on your keypad to "nudge" the top plate into line up with them. A couple of galaxies look good for that, no proper motion.

Then, once you're happy that the two plates are lined up nicely, slide the transparency slider back to 100% Do another set of blinks, to see the things which look as though they are moving back and forth, or are not on both plates. There are a number of things to look at then.

Maybe you should ask some of the people doing the stuff on Mars images here, to help out with this. They know their photoshop inside out
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United Kingdom
1088 Posts

Posted - 07 Apr 2008 :  05:07:44  Show Profile  Reply with Quote
Oops Flip the bradford image horizontally. I must have forget that I'd done that.
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United Kingdom
1088 Posts

Posted - 07 Apr 2008 :  07:52:39  Show Profile  Reply with Quote
If I've even got the images lined up correctly, and that's something of an if, as bright stars show up as rather red and dim on the bradford image. Plus there's proper motions. And one bright star seems to have vanished from the face of the earth (excuse the lousey pun)

Anyway, Go almost straight up, about 5'(a third of the bradford image) from that green dot. Then across to the left, past the whitish star to an orange red star. That might be a possible.

If one wants to just look at it on the board, remember that it needs to be flipped, so look across to the right.
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Joe Keller

1093 Posts

Posted - 07 Apr 2008 :  15:32:26  Show Profile  Reply with Quote
Initial Analysis of Robert Turner's March 19, 2008 Photo of Frey

This is the only photo taken so far in 2008, of the Barbarossa/Frey system. It is the only color photo (not counting Red filtered sky surveys) ever taken of the Barbarossa/Frey system. It shows Frey as a bright green dot in the NE quadrant of the frame. (As this photo is shown here on Dr. Van Flandern's messageboard, S is up and W is to the right, so, the frame is upside down, but not reversed; the usual presentation is, N up and W right.) It was taken with a 14-inch reflector on Tenerife, remote-controlled under the direction of amateur astronomer Robert Turner of England, observing at my predicted coordinates for the Barbarossa/Frey center of mass.

I haven't rechecked my calculation yet, but to the best of my ability to calculate Frey's position based on Joan Genebriera's 2007 Barbarossa photo, Barbarossa's 1954 and 1986 positions, and my theory of Frey's precessing orbit, the position of the bright green dot noted by Turner in his photo, differs only 16" from expectation. This could be caused by a plausible, 3% error in my estimate of Frey's orbit. The theoretical position of Barbarossa, is off the photo, slightly E of the margin. I knew of four Barbarossa/Frey candidates on the photo before calculating the position; the random chance that one or more of these four would have been within 16" of Frey's theoretical position (Barbarossa's theoretical position is off the frame) is 4 * (pi*16"^2) / (17.1' * 17.6'), i.e., p = 0.003.

After Turner found the first disappearing dot, I found, basically, three more in the photo. These are not near the theoretical positions of Barbarossa, Frey or Freya. Near the S edge, is a medium-bright disappearing green dot (i.e., not found on the 1987 SERC-ER survey); this is W of a disappearing double red dot. In the SW quadrant is a faint disappearing red dot; its faintness, its color, and its starlike broad smooth intensity contour, make it especially likely to be a real astronomical object.

As I noted on Steve Riley's photos last year, these electronic photos, near their detection limit, give highly variable images. Stars confirmed on sky surveys, of brightness near the electronic photo's detection limit, can have a classic appearance, or a small bright or irregular appearance, or be totally absent; all on the same photo. An unusual photon distribution should be especially likely to have an unusual appearance, especially near the detection limit.

Barbarossa and Frey theoretically have about 1" diameters. A star might be approximated as a point source hopping randomly on a 1" disk, staying in each place for ~ 1/30 sec. The light from Barbarossa or Frey, composed of many point sources more-or-less evenly distributed on a 1" disk, presents the electronic camera with a drastically different object, for which light intensities over the blur circle are much more constant. This involves the subject of "reciprocity" of photographic film. Characteristics of electronic detectors, loosely analogous to reciprocity, seem little investigated. I'm wary of dismissive, unsupported claims about how an image of Barbarossa (especially, near the detection limit) should appear.

Another factor, is the now known (see my posts above) transient generalized extinction (dimming) of stars within a few degrees of the Barbarossa/Frey system. Such an interposed cloud would further alter these light sources, further vitiating any assumptions about the appearance of Barbarossa/Frey images.
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Joe Keller

1093 Posts

Posted - 08 Apr 2008 :  15:49:37  Show Profile  Reply with Quote
The paired blink photos (posted by "marsrocks" on another thread of this messageboard) do show the abovementioned bright green disappearing dot (not in color)(in the lower left, i.e., NE corner, above & left of a small equilateral triangle of stars) disappearing as expected. The background lightness of the other photo almost obscures a nearby star of similar brightness. The blink pair might give more false positives, than comparing Turner's March 19, 2008 photo to a sky survey, without blink. Still, the blink pair gives us a dramatic demonstration.
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Joe Keller

1093 Posts

Posted - 09 Apr 2008 :  16:58:42  Show Profile  Reply with Quote
Requiem for Relativity

Such a large mass as Barbarossa, so close to the positive "Cosmic" Microwave Background dipole, would refute the theory that the dipole is a Doppler effect. It also would refute the theory that the "Cosmic" Microwave Background is cosmic.

Likely, the CMB would be found to originate from the sun's gravitational field, and the dipole from Barbarossa's gravitational field. This would demolish present relativistic ideas about gravity and light.

That is why Barbarossa is in the thread entitled "Requiem for Relativity".
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Joe Keller

1093 Posts

Posted - 09 Apr 2008 :  19:06:04  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part IV)

The Other Hubble Relation

Hubble, ApJ 56:162+, 400+, 1922, discovered that with a 60 or 100 inch telescope, the apparent photographic size of stellar "reflection nebulae" is what would be expected assuming total scattering of the central star's light at the outermost detectable edge of the nebula, where the nebula is just barely detectably brighter than background (p. 410). Hubble's empirical relation (p. 411, eq. (8)) is:

apparent magnitude + 4.90 * log10 (radius in arcmin) = 11.0.

If all light is scattered at the effective surface of the nebula, then the star itself should be invisible. Yet Hubble was able to use the apparent magnitude of the star, to estimate how much light was available for scattering at the surface of the nebula. There's twice too much light in his model. Hubble (p. 401) even cites Hertzsprung's finding (Astronomische Nachrichten 195:449, 1913) that the effective nebular surface scatters only 1-2% of the light.

In Hubble's model, wouldn't the cloud of nebular material often be bigger than given by Hubble's relation, and continue to scatter 100% of the light? If so, then the contrast at the edge of the nebula, would be too low to detect. Suppose this were the case for many stars (after all, most stars lack detectable nebulae). Then, likely also for many stars, the cloud would be smaller than Hubble's relation, giving a smaller reflection nebula. Yet, according to Hubble's Fig. 2, p. 411, this seldom occurs.

Maybe the radius of the cloud of nebular material coincidentally (but not accidentally) happens to be proportional to (stellar mass)^1.5. For stars from 1 to 30 times solar mass (MNRAS 382:1073+, 2007, Table 6, p. 1078) there is an accurate quadratic polynomial for log(luminosity) as a function of log(mass). Using Wikipedia's 18 solar mass figure for Type B stars (more accurate would be to average Hubble's spectral type sample) the luminosity-mass relation becomes a power law with exponent 2.91. That is, Hubble's relation for the typical Type B star, is equivalent to:

nebula radius = const. * (stellar mass)^(2.91/(4.90/2.500)) = (stellar mass)^1.48

with such proportionality constant as to give that radius at which the total luminance of the star, divided by the surface area of the nebula, just exceeds background intensity.

Hubble's nebulae almost all were around stars of Spectral Type B (though one of the 33 listed in his Table III, p. 181, was K8). Other, presumably older spectral types, seem generally to lack such nebulae. Maybe a failed cold brown dwarf also would have such a cloud, never completely expelled by radiation pressure.

Assuming luminosity were proportional to mass^2.91 (typical in the Type B range), the Barbarossa system's absolute magnitude, if it could behave as a Type B star, would be roughly 4.83 - 2.5 * log(20,000 * (0.0103/18)^2.91) = +17.67. At 10pc, Barbarossa's nebula would, according to Hubble's relation, subtend a radius of 0.0435'. At Barbarossa's actual distance, that's 454' = 26 AU. This predicted angular diameter of Barbarossa's cloud, 15 deg, agrees well with the observations of transient dimming in sky surveys, discussed in Parts (II) and (III) above.
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Joe Keller

1093 Posts

Posted - 10 Apr 2008 :  01:00:43  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part V)

According to Skuppin et al, A&A 177:228+, 1987, absorption lines in the spectra of fast-rotating Type B stars, are one of the best ways to quantitate local interstellar matter. They discuss three such stars, one of which is Theta Crateris. The data for Theta Crt and for one of the other stars, were obtained by the Intl. UV Explorer (IUV) satellite, Jan. 1985.

The density of interstellar material between us and Theta Crt, measured by spectral lines of four different elements, was consistently greater than for either of the other two stars; the factor generally was ~10. Also, only Theta Crt lacked the MgI line; this signifies that only Theta Crt lacked hot gas along the line of sight. So, Theta Crt has more intervening material, but in contrast to the other two stars, all the intervening material is cold.

Theta Crt is 66pc distant, so having 10x the interstellar material, gives extra Visual extinction equivalent to 600pc, i.e. roughly 0.6 mag using the usual approximate 1 mag / kpc value. If the distribution of UV extinction resembles that of Blue extinction in Part (III), then Theta Crt is where the extinction was, in 1985, increasing fastest, as the front of Barbarossa's cloud moved in. Where its derivative is greatest, the normal distribution is at 0.6 times its peak. So, the peak extinction of Barbarossa's cloud is roughly 1 mag in Visual.

According to Skillen et al, MNRAS 265:301+, 1993, the RR (type RRab) Lyrae star, W Crt (RA 11:26:30, Decl -17:55)(near Gamma Crt) underwent dimming of a portion of its V and B light curves, between 1986 & 1988. The authors say they have "no explanation for the discrepancy" (p. 303). Their variable star light curves were, as usual, calibrated against nearby reference stars. If the light of W Crt becomes polarized during this phase of its cycle, and the Barbarossa cloud preferentially extinguishes light of that polarization, the dimming might be explained. Strohmeier's text, "Variable Stars", says some stars of another variable class, the semiregular variables (Type M) do show weak polarization of their visible light.
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Joe Keller

1093 Posts

Posted - 10 Apr 2008 :  19:26:52  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part VI)

Fruscione et al, ApJSupp 94:127+, 1994, Table 1, list 594 stars toward which the ("integrated") column density of neutral hydrogen, log( N (H I) ) has been determined, either by direct measurement, or by estimation from the logN determined for other atom(s). Only two of these 594 really rival Theta Crater, as evidence of nearby high extinction.

Almost 1/3, i.e. almost 200, of Fruscione's stars are <= 100pc distant (Theta Crt is 66pc). Of these, only four exceed Theta Crt's value log(N(HI)) = 20.50 +/- 0.10 (a few stars had ambiguous values such as " < 21.00"). One of these four exceeds Theta Crt slightly, but because its distance is greater, the average HI density along the path to it is less, though the sum, i.e. ("integrated") column density, is more.

The values of all four of these rivals, are less reliable than Theta Crt's. Theta Crt's value was estimated from more than one (four) other kinds of atoms. One of the others, 34 Cygni, was measured directly from LymanAlpha, which normally would be the gold standard, except that only "earlier than B2-B3" spectral types are suitable for this method (Fruscione, p. 128) and Fruscione lists 34 Cyg as B2. The other three rivals all were estimated from NaI alone; this can overestimate HI by 0.5 log units (p. 129).

Thus the only two stars (among the almost 200 at distance <= 100pc) toward which average HI density seems really higher than toward Theta Crt, are 34 Cyg and Lambda Per. 34 Cyg lies before "a heavily obscured region of the galaxy" (Burnham); it's less than a degree from the open cluster M29 (5 to 8' diam.). Lambda Per, according to Norton's Atlas, lies between an open cluster and a diffuse nebula, a degree to either side of it. Theta Crt, by contrast, lies in an almost empty field (only a small galaxy, almost 3 deg away).

Another of Barbarossa's champions is 69 Leonis (RA 168, Decl 0, distance 80pc). Welsh et al, ApJ 437:638+, 1994, Tables 2 & 4, reporting a study of interstellar NaI density, list, inter alia, 28 other stars at distances 70 to 90pc inclusive. Six of the 28 exceed 69 Leonis' value of log(N(NaI)) (none were ambiguous). Three of these six were toward the galactic center; these three also were by an investigator who performed only 19 of the 167 total determinations used. All eleven of Welsh et. al.'s own determinations, in that distance range, were at least 1.15 log units less, than for 69 Leo.

Welsh cites Albert, ApJ 272:509+, 1983, as his source for 69 Leo. Albert tested only three stars at distance <= 100pc. For TiII and NaI absorption, differences between the three, corrected for path length, did not exceed error bars. However 69 Leonis, at 80pc, showed log(N(CaII)) = 3.0 +/- 0.5, vs. (1.1 or 1.0) +/- (0.6 or 0.4) for the other two stars, at 100pc or 90pc, resp. Correction for distance, gives 4.5x the average density, along the path to 69 Leonis.
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Joe Keller

1093 Posts

Posted - 11 Apr 2008 :  14:43:11  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part VII)

Above, I very roughly estimated a Visual extinction of 1.0 mag for passage through the full thickness of Barbarossa's cloud; a more accurate version of this estimate (see below) is 0.3 mag. This would of course be due to the dust component. What about the gas?

The column of hydrogen atoms amounts to a layer of dissociated neutral hydrogen at standard temperature and pressure, 12cm thick; add another 1cm for the helium. This is 1/60,000 the number of gas molecules in a column of Earth's atmosphere, so, Visual extinction, due to the gas, would be negligible. These molecules are illuminated only 1/197.7^2 = 1/40,000 as intensely by the sun. The regional sky brightening seen from Earth's surface, due to sunlight scattered by the gas atoms of Barbarossa's cloud, would be somewhat less than the sky brightening, due to starlight scattered by Earth's atmosphere.

Let Barbarossa's cloud be a homogeneous oblate spheroid with a=26AU, b/a=0.5. Let the path to Theta Crt transect a chord 0.6 * 2 * a. Then the mass of the cloud, assuming 75% H by weight and that 90% of Fruscione's N(H) is within the cloud, would be 0.028 Earth masses (1/120,000 the mass of the Barbarossa system). Because estimates from metal atom abundances can overestimate H abundance by 0.5 log unit (Fruscione, 1994, p. 129), a lower bound for the mass would be 0.01 Earth masses. (In interstellar matter, dust averages only 0.7% the mass of gas.) There would be 740,000 gas atoms (helium or dissociated hydrogen) per cubic cm; this is 100x the density of the Martian exosphere as measured by Mars Express (Wurz et al, Geophysical Research Abstracts, Vol. 8, 01954, 2006). The equivalent altitude on Earth is below that at which aurorae begin to manifest, so, if Barbarossa has a magnetic field, the sun should cause aurorae in Barbarossa's cloud.

What about sky brightening due to sunlight scattered by the dust of Barbarossa's cloud? If the densest part of Barbarossa's cloud intercepts (i.e., extinguishes, either by absorption or scattering) ~30% of starlight (0.3 mag extinction)(Bohlin's 1978 empirical formula relating N(H) to extinction, cited by Draine, AnnuRevAstronAstrophys 2003, 41:241+, p. 244, sec. 2.1.2, eq. (2), gives 0.25 mag), then it also intercepts 30% of sunlight.

I follow Endrik Kruegel's text, "The Physics of Interstellar Dust" (ch. 4, "Case Studies of Mie Calculus"). For a spherical particle which is a "strong absorber" (sec. 4.1.3)(optically not very different from amorphous carbon, which is discussed in detail in sec. 4.1.5), define x = circumference/wavelength. For the "typical" interstellar dust grain, diam = 0.1mu (Kruegel, sec., wavelength = 0.6mu for visible light, so x = 1. For x < 0.5, the ratio of scattering to extinction is proportional to x^3, and for x=0.5, is (Fig. 4.3) about 1/3 * 0.5^3 = 1/24. For x > 2, the ratio of scattering to extinction is about 1/2 overall, but "g", the average cosine of the scattering angle, is about 0.8, which implies that backscattering can't possibly be more than 1/5 of the amount found when there is isotropic scattering; so, the ratio of backscattering to extinction is < 1/10. For x = 1, the situation is intermediate. So, a fair estimate of backscattering to extinction, is 1/24.

More precisely, I could for x < 0.5, neglect scattering, and for extinction (which in this domain is proportional to x times the geometric cross section), integrate the often assumed a^(-3.5) power law for particle size distribution (JE Dyson, "The Physics of the Interstellar Medium", p. 53), assuming (as Draine suggests) the law holds at least halfway down to molecular sizes; and assuming it achieves the geometric cross section, when x = 1. The ratio of scattering to extinction is maximum at the "typical" (maybe this is why it's considered typical) diameter 0.1mu; again I could use the power law to integrate scattering between x = 0.5 & x = 2 (using a constant scattering efficiency ~1/6 seen near x = 1, from Kruegel's Fig. 4.3); Simpson's rule (based again on Fig. 4.3) to get from the scattering, the extinction due to this domain; using "g" = ave(cos(theta)) = 0.2 at x = 1, and a first-order spherical harmonic, I can estimate the relative backscattering efficiency as 40% in this domain. This more precise calculation merely changed the estimate to 1/25 from 1/24.

The effective albedo of Barbarossa's cloud then would be at least 70% (a lower bound for the fraction of light which escapes a second interception) * 30% * 1/24 / 2 (because of isotropy) = 0.44%, ~1/30 that of Luna. The cloud's surface would be 1/(30*40,000) as bright as Luna's; it would be Vmag -12.7+15.2 = +2.5 on a 0.52deg diam disk, i.e. +0.8 on a sq. deg. The brightest part of the northern Milky Way (Zavarzin, Astrophysics 23:647+, Table 1) has brightness +4.05 on a sq. deg.

So, if the ~0.3 mag extinction (much less than that, hardly would be consistent with the observed relative dimness of R2 & B2 in the region) is due to "typical" dust grains, the Barbarossa cloud would be too bright. However, the extinction can be achieved with arbitrarily little scattering, if these "strong absorber" grains are small enough. Diameter 0.01mu, gives scattering/extinction = ~ 1/3 * (1/10)^3 = 1/3000, 3000/24 = 5.2mag less, i.e., sky brightness a plausible +6.0 on a sq. deg. Alternatively, the physical properties of the "dust" might be different than presently believed.
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Joe Keller

1093 Posts

Posted - 14 Apr 2008 :  15:15:40  Show Profile  Reply with Quote

To: organizers of 2nd (Sept. 2008) Crisis in Cosmology Conference

Dear sirs:

The link didn't work for me, so here is my application.

Joseph C. Keller

Presentation Type: Oral Presentation

Paper Title:
Brown Dwarf, Barbarossa, Causes "Cosmic" Microwave Background Dipole

Author & Affiliation: Joseph C. Keller (B. A., Harvard)

Primary contact: Joseph C. Keller

Contact email: *******

Short Abstract:

A cold brown dwarf, Barbarossa, causes the "Cosmic" Microwave Background dipole. Barbarossa+Frey+Freya, with a dark nebula, lie at the (+) CMB dipole.

Full Abstract (slightly < 2500 character count):

A cold brown dwarf, Barbarossa, causes the "Cosmic" Microwave Background dipole. Barbarossa+Frey+Freya, with a dark nebula, lie at the (+) CMB dipole.

Exclusively near there, red & blue USNO-B magnitudes dim between c.1954 and c.1985; likewise, Johnson's bright star photometry c.1964 vs. Harvard magnitude as published mostly in 1908. Barbarossa's nebular size, is given by extrapolating Hubble's nebular size relation. Interstellar absorption lines before the two studied nearby stars in this direction, are exceedingly strong.

My original finding was that automated USNO-B R1 & R2 magnitudes, differing enough to be misidentifications of wanderers, outlined an orbital path there. Dots of magnitude ~ +18, though not of typical starlike appearance, on all relevant red and infrared survey plates, and on prospective photos by Joan Genebriera, Steve Riley, and Robert Turner, lie within arcseconds of an e < 0.1, 198 AU orbit slightly leading the (+) CMB dipole. Frey has a 3-yr, e = 0.65 orbit around Barbarossa with retrograde apsis precession in 24 yr. Freya (not yet identified) is inferred to orbit in 6 yr. perpendicular to the ecliptic, causing Frey's precession, and lateral deviation of the Barbarossa-Frey c.o.m. The projection of Barbarossa's orbit onto Jupiter's, follows the mean position of a Jupiter/Saturn conjunction resonance.

Claimed COBE & WMAP error bars rule out such a near orbit. However, only a cause within the solar system, explains the correlation, of the Maxwellian moments of the CMB anisotropy, with the plane of the ecliptic.

My theory of CMB production by gravitational fields (electrons boiling from the surface of the sun's, 52.6 AU radius, ether island, detected by anomalies in Pioneer10's transmission there), and, a Newtonian theory of nodal regression resonances in the outer solar system, give equal estimates of Barbarossa's mass. Subtraction of Barbarossa's gravity makes the Pioneer Anomaly consistent with gravitation by a smoothly decreasing mass density.

I have ~100 references in major refereed journals and other authoritative sources. See my posts to the messageboard of Dr. Van Flandern's website.
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Joe Keller

1093 Posts

Posted - 14 Apr 2008 :  16:34:36  Show Profile  Reply with Quote
Earth's atmospheric twinkling is said to be a phenomenon of timescale ~ 1/30 sec. A lightning flash on Barbarossa might make a pointlike image almost as though Earth's atmosphere did not exist. This would amount to "active optics". Previously on this messageboard I estimated the likely brightness of lightning on such a giant planet (or cold brown dwarf), and found it competitive with reflected sunlight.
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Joe Keller

1093 Posts

Posted - 16 Apr 2008 :  14:27:52  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part VIII)

Three Articles from the Annual Review of Astronomy & Astrophysics

1. Salpeter, "Formation & Destruction of Dust Grains", 1977. In Sec. 5.1, Salpeter cites observations by Zappala, of a circumstellar dust shell which is basically a solid sphere (inner diam. << outer diam.), though this is around a presumed mass-losing giant star. In Sec. 4.1, Salpeter says that the almost constant ratio of blue to red extinction, suggests that interstellar dust grain size distribution is about the same almost everywhere in the galaxy. On the contrary, the formulas and graphs of Kruegel's text say that for realistic "strong absorber" grains in the domain x < 0.5 (i.e., grain circumference < 0.5 * wavelength) extinction is proportional to grain cross-section times x; therefore the ratio of blue to red extinction = 0.55/0.44 = 1.25 is the same for any grain size distribution whatever, if only the extinction is mainly by small grains ( < 0.05 micron).

2. Aannestad & Purcell, "Interstellar Grains", 1973. In Sec. 3, p. 325, eqs. (6) & (7) (the "rho-g" factor of eq. (7) is a misprint), the authors say that (basically because of the "x" proportionality discussed above) extinction is proportional to the volume, hence mass, of dust whatever its grain size. Their lower bound of 0.5% dust::gas, agrees with the refined estimate of 0.8% in recent texts, and with the estimate 0.7% based on element abundances. They say, "This result applies equally well to grain mixtures. It can be applied with only slight modifications to 'grains' that are nothing but large molecules...".

3. McCray & Snow, "The Violent Interstellar Medium", 1979. In Sec. III.B, p. 228, the authors cite Shull's calculation that sputtering from high-velocity interstellar shocks, can reduce grain size to ~ 0.02 micron.

So, grains mainly moderately smaller than usually supposed, are quite possible. In (VII) above, I used formulas and graphs in Kruegel's text to show that such grains would reduce the apparent brightness of Barbaross'a nebula, to plausible levels.
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Joe Keller

1093 Posts

Posted - 17 Apr 2008 :  13:41:10  Show Profile  Reply with Quote
Why GPS does not disprove the ether theory, and why this is relevant to Barbarossa.

(To the best of my knowledge and belief, this ether drift calculation essentially first was made by James Clerk Maxwell. It also paraphrases an earlier post of mine to this messageboard.)

Let all velocities be measured in a frame of reference centered on Earth. Suppose Earth sits in an ether drift of speed v << 1 (choose units so c = 1). Let an orbiting satellite have speed u << 1 parallel to the drift, and speed w << 1 perpendicular to it. The satellite's clock is slowed by a fraction:

0.5*((u-v)^2 + w^2) = 0.5*(u^2+w^2+v^2) - u*v

The clock on Earth is slowed by a fraction:


The difference between the clock rates is a fraction:

0.5*(u^2 + w^2) - u*v

Suppose Jim is a physicist who believes in textbook relativity. Jim will correct for what Jim thinks the difference between the clock rates is:

0.5*(u^2 + w^2) (i.e., half the square of the velocity vector relative to Earth)

Now let the satellite move along any path whatever, so that it is now more downstream in the ether, by a distance d. Jim doesn't know about the u*v term. That is, the clock is faster than Jim thinks it is, by a fraction u*v. The satellite clock now is ahead of what Jim thinks it says, by

integral(u*v*deltat) = v*d (because u*deltat is the distance, d, that the satellite moved downstream)

Now for simplicity suppose that the satellite's path was, to move from Earth, to a distance d straight downstream from Earth in the ether. The time really required for light to move from the satellite, to Earth, is d/(1 - v) = d * (1 + v) to first order in v. Jim thinks the satellite clock is v*d behind what it really says, so Jim thinks the time interval was d * (1 + v) - v*d = d. Jim might think this disproves the ether theory. Really, all it proves is that, even for a one-way test, the ether theory differs from textbook relativity, only to second order in v.

What GPS can do, is essentially repeat the Dayton Miller round-trip experiment (Miller found an ether drift, though somewhat smaller than expected; anyone who looks at the graph in Michelson & Morley's original paper can see that Michelson & Morley got roughly the same result as Miller; yes, a significant, positive result, though somewhat smaller than expected. I dare anyone to look at the original Michelson & Morley paper and say he doesn't see that. Recently Yuri Galaev in Kharkov, using two different, novel interferometric schemes considerably different from Michelson's, quantitatively confirmed Miller's result, at least to within an order of magnitude.) The discrepancy a 10 km/s ether drift would cause in a round-trip geostationary GPS time is equivalent to only 30,000km * 2 * 0.5 * (10/300,000)^2 = 3cm.

If the ether exists, it's likely to be related to the sun's gravitational field. Then, it's also likely to be related to the gravitational field of a fundamental particle. The distance from the sun, at which the sun's field becomes weaker, than that produced inside the most compressed possible proton (Gaussian distribution of deBroglie waves, following Merzbacher or other quantum mechanics texts) is 52.6 AU. Pioneer10 showed transient abnormal signals at this distance (JD Anderson's best explanation was a gravitational encounter with Edgeworth-Kuiper belt objects there, but quantitatively the frequency shifts were too big, for too long, to be due to acceleration from any plausible such encounter).

It so happens that the gravitational escape energy of electrons at this distance from the sun, is roughly their mean thermal kinetic energy at the "Cosmic" Background temperature. Depending on the details of the mechanism, various factors of order unity might be involved. The "Cosmic" Background temperature, is basically the gravitational potential of an electron at the surface at which the sun's gravitational primacy ends.

Primordial pinheads aside, the only known object big enough and symmetrical enough to explain the "Cosmic" Microwave Background, is the sun with its fields. The first (dipole) and some higher Maxwellian moments of the CMB distribution, are significantly correlated with the plane of the ecliptic. Only solar system influence, by three or more bodies, can explain this. Planets distort that mathematical surface at which the macroscopic gravitational field becomes equal to some small critical value; thus the gravitational potential of an electron at this surface also varies, due both to the gravitational potential of the planet, and to the distortion of the mathematical surface, due to the gravitational field of the planet. A brown dwarf outside the surface is best for causing a dipole; planetesimals near the surface best for local variations.

Please don't ignore the data merely because they lack an explanation consistent with textbook relativity theory. Here's another synopsis I've been providing to inquiring scientists:

"The 'ether' is like an approximately spherical pot of water. The sun is in the center of this 'water'. The boundary of this 'water' is at 52.6 AU. There's some activity on this boundary, on this distant 'movie screen' all around the sun. We call this activity the 'Cosmic' Microwave Background. (Someday we might be able to detect a 'CMB'-radiating surface around Sirius. The radius of the 'movie screen' sphere goes as sqrt(M), the 'CMB' temperature as sqrt(M), the absolute magnitude of the 'CMB' thus as M^3, but the absolute magnitude of the star as M^(3 or 4), so the easiest case is a bright nearby star, of mass enough greater than the sun's, that its 'CMB' curve is distinguishable.) The position or 'locus' of the 'screen' is determined by some critical value of the macroscopic gravitational field strength vis-a-vis the internal gravitational fields of fundamental particles. This critical equation allows unknown processes of some kind to occur. The screen isn't quite a perfect sphere, nor is the 'activity' on it everywhere exactly equal. But it's close to perfect, because the sun has almost all the mass in the solar system, so the gravitational field is almost perfectly symmetrical. Maybe the sun provides the CMB energy. Maybe something else does. But the sun does define the locus of the activity, except for small asymmetries caused by smaller gravitating solar system bodies."
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Joe Keller

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Posted - 17 Apr 2008 :  20:03:45  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part IX)

The Johnson (c.1964) vs. Harvard (c.1908) magnitudes near Barbarossa's 1964 position

As detailed above, in regions near Barbarossa, USNO-B blue magnitudes were dimmer c.1983 than c.1954, and USNO-B red magnitudes dimmer c.1987 than c.1954 (these years can't be exact, because several overlapping plates were available to compute magnitudes). Interpolating between tested regions, the greatest blue dimming occurred about 3 deg ahead of Barbarossa and the greatest red dimming about 3 deg behind, along Barbarossa's track. During the time interval, Barbarossa moved 4 deg. So, the fastest increase in extinction, seems to be about 3 + 4/2 = 5 deg ahead of Barbarossa for blue, and about -3 + 4/2 = a degree behind Barbarossa, for red.

One explanation, would be that Barbarossa's cloud is nonhomogeneous: the most red-extinguishing material lags behind the most blue-extinguishing. The real explanation may be even stranger. Historical photometry shows that Barbarossa's cloud has no effect on the magnitude of stars of approx. Type G0. However, exclusively in the region of Barbarossa, bluer stars are dimmed, and redder stars are brightened, by amounts an order of magnitude greater than can be explained by error in zenith angle correction. The red dimming following Barbarossa, might be due to replacement of Barbarossa's cloud by some complementary medium which extinguishes red more than blue.

Methods. VizieR's online documentation of Harvard's Henry Draper catalog, gives its vintage as 1918-1924, but to secure data even older and of more certain vintage, I used the Harvard magnitudes listed, to 0.1 mag precision, for the stars on pp. A413-A415 (RA 10:26:15 to RA 11:40:43, B1900) of the USNO "Catalogue 4526 Stars" (Publications of the USNO, 2nd ser., vol. 9, pt. 1, published 1920 but dated 1917). The listed Harvard magnitudes mostly were from "Annals of the Astronomical Observatory of Harvard Coll." vol. 50, 1908, or vol. 54; many magnitudes were personal communications, from Prof. Pickering of Harvard, to the USNO. So, no magnitudes were later than 1917; many were earlier than 1908. An even older USNO publication (House Misc. Docs., 2nd ser., v. 2672, 1884) contained the USNO "Catalog of Stars 1845-1877"; I eschewed these because they took their magnitudes from various European catalogs, and often differed > 1.0 magnitude from later measurements. Only one difference between the Harvard magnitudes, and the Johnson (1966) online photometry catalog magnitudes, was truly a non-normal statistical outlier; this printed Harvard magnitude also differed from the online Draper catalog, so I used the Draper value, which was more plausible. I checked several other magnitudes whose differences from Johnson were greatest; only one more, which happened to be the magnitude with the second biggest difference from Johnson, differed from Draper (listed to 0.01 mag) by more than rounding error; likewise I adopted the Draper value here. I noticed several Boss (1928) "San Luis Catalogue" magnitudes, which Boss said were taken from Harvard, did agree exactly with the corresponding Harvard magnitudes printed.

Those stars on the three pages, which also were in HL Johnson's online "UBV Photometry of Bright Stars" (1966) catalog, numbered 61, and comprised my study. Johnson's observations (Comm. of the Lunar & Planetary Lab. vol. 4, pt. 3, #63) were dated approx. 1964.0 +/- ~ 1 yr and were taken at 32deg N lat in Arizona. He also used Cape, South Africa, observations by others; the text indicates these were taken in 1963 or 1964, and that no use was made of any observations from prior to 1955.

Spectral types were taken from the online Jaschek catalog when found (most); otherwise from the recent online Kharchenko catalog (many). All the Kharchenko spectral types were checked against Draper; all agreed within the 1/2 color rounding of Draper.

I found five of the 61, listed as variable in the "Bright Star Catalog 2000.0", vol. 2. Information given on these five, suggested amplitudes not big enough to require expulsion from my study.

Results. The magnitude changes, c.1908 to c.1964, within each color type, B through M, were fitted by exhaustive computer search, to a function of the star's Declination difference from Barbarossa's orbit. Barbarossa's orbit was approximated by a Mercator projection line through the (B1900) 1954 and 1986 center-of-mass positions. The function used, consisted of a constant term, plus a normal curve centered on Barbarossa's Declination for that star's RA. The three adjustable parameters giving the least-squares fit are:

magnitude change, Type B: -0.20 + 0.47 * exp(-deltaDecl^2/12^2) n=3
magnitude change, Type A: -0.10 + 0.10 * exp(-deltaDecl^2/11^2) n=12
magnitude change, Type F: -0.09 + 0.04 * exp(-deltaDecl^2/16^2) n=6
magnitude change, Type G: -0.12 - 0.04 * exp(-deltaDecl^2/23^2) n=14
magnitude change, Type K: -0.14 - 0.12 * exp(-deltaDecl^2/6^2) n=21
magnitude change, Type M: -0.11 - 0.19 * exp(-deltaDecl^2/14^2) n=4
(for Type M, one outlier was discarded)

Note that the denominators, 12^2, etc., imply that the standard deviation of the normal curve, in degrees of Decl, is 12/sqrt(2), etc. The weighted mean standard deviation is 9.1deg.

A Type M star near the N pole, with a moderately big magnitude change, tended to force a very large standard deviation (100deg) for best fit. So I decided the exclusion of this outlier would give a more representative result.

The linear variation of the coefficient of the bell curve term, proves the statistical significance of this result. The magnitude change, Johnson vs. Harvard, was different in the neighborhood of Barbarossa. Along this section of its track about 20 deg long, the "track effect" averages about 18 deg wide. By interpolation (using average number types for each color), there is no "track effect" for type G0; that is, no effect for starlight of the composition of sunlight. Blue undergoes extinction here relative to other parts of the sky, but red undergoes what amounts to "negative extinction": red stars brighten more here, than in other parts of the sky.

This is not due to Barbarossa's track acting as a proxy for the equator and revealing errors in zenith angle correction. Boss, in his 1928 catalog, gives 0.25 * (sec(z) - 1) for this, noting that this value also applies to the "northern Harvard measures". (Boss also gives the useful figure of +/- 0.08 mag error for one visual magnitude observation as done by his team 1909-1911; he says at least two, sometimes three, observations were made even for his hurried program.) With access to Cape observations, surely no Harvard magnitudes are based on observations lower than the traditional limit of z = 45. Even such observations would be extinguished only 0.10 mag for yellow light.

The difference between B and V band extinction would be only 0.024 mag, using the standard 4.16:1 ratio. The difference between Type A Visual and Type G Visual extinction can be estimated from the lambda^(-1) law, by replacing the Visual sensitivity window with the Type G spectrum as a proxy, considering the Type A0 spectrum to be the same as Type G2 but transformed to 9500K from 5800K (temperatures used by Johnson, Comm. Lunar & Planetary Lab vol. 3, #53, p. 73+, 1965), and expanding both factors of the convolution's integrand as Maclaurin series. For small changes in star temperature, the extinction is proportional to sqrt(temperature). This approximation says there's 28% more extinction in V for Type A0, than for Type G2. Again using the average type numbers in my sample's colors, this implies only 0.027mag more extinction for my Type A than my Type G, even at 45deg zenith angle. Likely, Johnson corrected for color differences in extinction, and Harvard (like Boss in 1928) didn't. This would brighten Johnson's Type A,
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Joe Keller

1093 Posts

Posted - 19 Apr 2008 :  17:26:10  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part X)

Using error bars for all colors, for the 31-star control sample in Part IX above, shows that the maximum-likelihood linear interpolation (roughly, this passes through the lower ends of the error bars for Types B, F & K, the upper ends for A & M, and the center of G), is roughly the "extreme choice" discussed in the last paragraph; it has half the slope of that found in Barbarossa's region. About half the control stars lie near Barbarossa's orbit (though not near Barbarossa); about half lie well away from the orbit. The sample is too small to say much about how these two halves differ, but there is a hint that the stars well away from Barbarossa's orbit, show mainly the negative magnitude change, and not so much the change with color type. So, the anomalous negative magnitude change seen for redder Types at this Declination, might be mainly due to Cape calibration c. 1908. The increasingly positive magnitude change with bluer spectral type, at this Declination, might be mainly due to fortuitous time changes in dust density along Barbarossa's orbit, not necessarily near Barbarossa.

From the Harvard-Johnson magnitude change, the extinction due to the center of Barbarossa's cloud, can be estimated as (0.10 - (-0.12))/(1.23 - 0.86) (from the extinction for Type A vs. K, according to my calculus estimate described previously) * pi/2 (assuming a spherical cloud just filling the 20 deg track investigated) = 0.9 mag. Maybe half this is near Barbarossa and the other half spread out along its orbit.

However, for such large extinction to be present, it would have to be canceled by a large Declination effect, but the part of the control group, far from Barbarossa's track, shows that the Declination effect (on Johnson minus Harvard) is ~ -0.1 mag. This suggests that there is a new kind of extinction here. Ordinary extinction dims all colors, but dims blue a little more. This new kind of extinction somehow dims blue while perhaps brightening red.

Let's turn away from the complications of dynamic tests such as the USNO-B R1 vs. R2 or B1 vs. B2, or the Harvard vs. Johnson magnitudes. Evidence of changing extinction, near Barbarossa's new position, is compelling, but complicated by unknown calibrations.

Let's instead perform another static test. Above, we found that the two stars studied near Barbarossa, 69 Leonis & Theta Crateris, have 3-10x stronger than normal interstellar spectral absorption lines, for such nearby stars; Theta Crateris arguably has the strongest well-measured absorption lines in an entire ~200 star sample < 100pc. Today I find that Hipparcos V & B mags, near Barbarossa, are abnormally dim, for white stars, and abnormally bright, for orange ones. This is the same abnormality which arises (see above) in the V magnitudes, Johnson vs. Harvard.

Methods. The online Hipparcos catalog lists V & B magnitudes, and parallaxes, recorded by the Hipparcos satellite 1991 +/- 2 yr. I considered all Hipparcos stars brighter than V = +10.00, nearer than 50pc, and within 10deg of RA11:20:00, Decl -8:00:00 (the approx. location of Barbarossa in 1991). The number of such Hipparcos stars here, per magnitude interval, began decreasing at about magnitude +10. My magnitude cutoff, +10.00, should lessen selection bias, give more accurate photometry, and exclude subdwarfs. I used only Draper (i.e., Annie Cannon) spectral types; this early typing, all by one research group, would be methodologically consistent, almost free of any possible influence by Barbarossa, nor would there be any influence of presumed absolute magnitude. There was one Type A; the rest were F, G, or K. Judging by absolute magnitudes, all the stars were class V (dwarf) except two G stars that were class IV (subgiant). I avoided the question of subgiant outliers, by considering only F and K. To get more stars, I arbitrarily annexed another disk centered 2deg farther N. In all there were 38 Hipparcos stars; 32 were in Draper (and had spectral types listed).

Results. First, I compared absolute V magnitudes ("MsubV") of near and far (from Barbarossa) members of the exact same letter-number spectral type, when available. Thirteen stars were such.

Type F5. Far from Barbarossa (>= 9.7deg): MsubV = 3.44 (SEM 0.20, n=2).
Near Barbarossa (2.4deg): MsubV = 3.56 (n=1).

Type K0. Far from Barbarossa (one at 7.8deg, five > 10deg): MsubV = 5.72 (SEM 0.23, n=6).
Near Barbarossa (<= 3.0deg): MsubV = 5.59 (SEM 0.01, n=2).

Type K2. Far from Barbarossa (7.7deg): MsubV = 7.07 (n=1).
Near Barbarossa (4.4deg): MsubV = 6.60 (n=1).

Second, I compared "B-V" near and far, for the same thirteen stars.

Type F5. Far from Barbarossa: B-V = 0.483 (SEM 0.003, n=2).
Near Barbarossa: B-V = 0.541 (n=1).

Type K0. Far from Barbarossa: B-V = 0.848 (SEM 0.042, n=6).
Near Barbarossa: B-V = 0.780 (SEM 0.048, n=2).

Type K2. Far from Barbarossa: B-V = 1.126 (n=1).
Near Barbarossa: B-V = 0.971 (n=1).

Though none of these six far-near differences reached statistical significance standing alone, walking together they are significant whatever their error bars. Using nonparametric statistics, the chance is only p = 1 / 2^6 = 0.02 that the change near Barbarossa, for both MsubV and B-V, would be positive for F5, negative for K0, and even more negative for K2.

The Johnson-minus-Harvard magnitude study above, predicts this very change near Barbarossa for absolute V magnitude, MsubV. Because most known forms of scattering affect B more than V, B-V should show the same behavior as MsubV, and it does.

The accidental inclusion of slightly brighter, bluer stars (e.g., a G9 star among the K0) would give a change in B-V only ~ 1/7 as big as the change in MsubV (Vega & the sun differ 4.2 in MsubV but only 0.63 in B-V). Ordinary dust extinction gives a change in B-V ~ 1/4 as big as in MsubV, but both changes would be positive through a nebula. Not only are both changes negative near Barbarossa for orange stars, but the change in B-V is ~ 1/2 as big as for MsubV. Autocollimated stimulated emission, through a nebula pumped with sunlight, would tend to move all stellar spectra toward that of the sun, i.e., B-V increase for white stars and decrease for orange stars. Also, MsubV might be increased for all colors, but especially for redder colors, because redder photons, with less energy apiece, might stimulate more emission per unit energy input.
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Joe Keller

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Posted - 23 Apr 2008 :  00:07:19  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part XI)

Barbarossa's Nebula Imaged via B-V Magnitudes of K0 Stars < 100pc

Motivation. Ideally, a large number of nearby stars, all with the same intrinsic B-V magnitudes, would allow mapping of the extinction near Barbarossa, according to varying B-V. For reasons given in the previous post, I best could realize this ideal, with Draper/Cannon K0 stars measured by Hipparcos, lying within 10deg of Barbarossa, within 100pc of the sun, and brighter than V = +10.00.

Calibrating the stars. The Draper/Cannon spectral types are given only to the nearest 1/2 or perhaps 1/5 color, that is, to the nearest 5 or perhaps 2 numbered steps; e.g., oftenest G0, G5, K0, less often K2, etc. So, some "K0" stars will fit a Planck curve closer to that of a G9 or K1, perhaps a G8 or K2, or, with errors other than rounding, an even further spectral type. Accuracy might improve, by assuming all stars are exactly on the main sequence, and correcting B-V according to Mv (the absolute magnitude in V). Using Mv and B-V for Vega (A0) and the sun (G2), we find that the change in B-V is 15% of the change in Mv. However, the sample K0 stars usually differ much more in Mv, than can be explained by a few color steps. Especially beyond 50pc, there are, judging by Mv, many borderline subgiants, subgiants, and giants. The effect of size class is much more important, than that of a few color steps. Surprisingly, size can be corrected in just the same way as color.

Materials. The raw sample consists of the 20 Hipparcos stars < 100pc, within 10deg of RA11:20:00, Decl -8:00:00 (approx. Barbarossa's 1991 position), with V < +10.00, and Draper/Cannon spectral type K0. (The stars < 50pc, in a 10deg circle centered 2deg N, which had been annexed for the earlier study above, were retained.) Two stars, both class V, seem to be an apparent double, separated by 30" of arc at 20pc, but by 0.4pc in depth according to their Hipparcos parallaxes. In retrospect, the B-V values of these two, were the most abnormal of any sample stars in size class V, suggesting mutual contamination. So, I averaged their Mv & B-V values, weighted by luminosity, and considered them one star. This reduced the sample size to 19. Extrapolating from Vega and the sun (using color steps as the abscissa), the Mv of a K0V star is +6.36. Twelve stars of the (modified) sample had Mv >= +4.55 (and <= +6.23), so these were considered class V, i.e., dwarf, i.e., main sequence. Seven stars had Mv from +2.92 to -0.32; these were considered class IV or III. Snow's "Dynamic Universe" college astronomy text lists Pollux (Mv = +0.95) and Dubhe (Mv = -0.7) as K0III.

Results. The 12 K0V stars were calibrated by adding to their B-V, 15% of the difference between +6.36 (taken as standard for a K0V) and their measured Mv. Also, by extrapolation from Vega and the sun, the B-V of a K0V star is +0.86. The result is, that the calibrated B-V is a smooth function of angular separation from Barbarossa. It equals the expected value, for K0V, at 0deg and at 10deg, from Barbarossa. In between, it increases linearly to about +1.10 = +0.86 + 0.24, at 8.4deg, then drops sharply. The corresponding V extinction would be 0.24 * 4.16 = 1.00mag. For the 13 (effectively 12) K0V stars:

(angular separation from Barbarossa, calibrated B-V for dwarfs)
(11.14,0.964) (composite of two; apparent double)

This function is consistent with a nebula densest in an outer shell near 8.35deg from Barbarossa. For the first through 8th points, the correlation coeff. is r = +0.762, p = 0.03; for the 8th through 12th, r = -0.961, p = 0.009 (two-tailed).

Though the color and spectral lines of these stars are consistent with a photosphere at the usually assumed temperature, B-V is not. B-V is consistent with the temperature of an "inner photosphere" appropriate to an exact main-sequence star of Mv equal to that of the given K0V or K0IV/V star. This calibration removes variance from the data, and renders them consistent with, or at worst, smoothly deviant from, standard K0V values. Earlier on this messageboard, I used the inner shell or inner photosphere concept to explain features of variable stars.

An "inner photosphere" concept also seems to apply to the K0 giants (IV and V). For a giant, divide the luminosity by the reciprocal fine structure constant, 137 (i.e., add 5.35mag). Then assume an inner main sequence photosphere as above. The results again are consistent with K0:

(angular separation from Barbarossa, calibrated B-V for giants)

Four of the seven giants are consistent to within 0.01mag. The two least consistent, are the extreme brightest and dimmest.
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Joe Keller

1093 Posts

Posted - 23 Apr 2008 :  17:12:31  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part XII)

Barbarossa's Nebula Imaged via B-V Magnitudes of F5 & Bluer Stars < 100pc

This study differs from that in Part XI, only by using Draper catalog Type F5 & bluer, instead of K0. Instead of calibrating B-V to Type K0V, I calibrated it to Vega (Type A0Va). That calibration is of course routine for this sample, because they are almost all dwarfs, whose Mv differs mainly because they are spread out along the main sequence. The raw sample included 28 stars: one B9, six A, and 21 F0-F5. Judging by Mv, only one star was definitely class IV; this star also had the only outlier value for the corrected B-V; so, I excluded it.

Of the 27 remaining stars, the most significant break occurred at 6.96deg from Barbarossa. These bluish stars mirrored the K0 case of Part XI. That is, they started (ave. of initial three: corrected B-V = +0.029) near the normal value, decreased, then increased. The correlation coeffs. of the decreasing & increasing legs were -0.399 & +0.560 with p = 0.20 & 0.024, resp. (two-tailed).
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Joe Keller

1093 Posts

Posted - 25 Apr 2008 :  14:09:48  Show Profile  Reply with Quote
In Barbarossa's Cavern There Are No Stars (Part XIII)

Now let's return to the first evidence I discovered (besides the abnormal faintness of Barbarossa & Frey), of Barbarossa's moving nebula: the differing R1 & R2 USNO-B magnitudes measured on sky survey plates. Yesterday I searched the USNO-B catalog in a 30deg wide x 18deg tall region, centered slightly west of Barbarossa's 1987 position (the R2 magnitudes were measured on plates dated a few years either way from 1987). In disks one degree in diameter (30' radius) I found the number of stars for which R1 was between +15.00 & +16.00 and R2 between +16.00 & +17.00, and the number for which this held with R1 & R2 switched. The ratio of these numbers, will be denoted "q". In most of the region, I spaced the disks 2deg apart in each direction, but near Barbarossa, 1 deg apart.

I don't know the details, but R1 & R2 were estimated somehow from overlapping sky survey plates. More plates were available for R2 than for R1. So, the sky is divided into orthogonally oriented (i.e., EW by NS) "partition rectangles" of various sizes and shapes, but never bigger than 6.5deg (the size of the survey plates). Each partition rectangle has a different set of plates available for magnitude measurement. Also, each plate has a narrow, roughly rectangular strip along each edge, where the image is grossly fainter; if this part is used at all, magnitude calibration must be different there, so this amounts basically to a separate plate. If magnitude calibration is imperfect, the ratio "q" will be more uniform within one (up to 6.5 deg long, but usually narrow) "partition rectangle", than between rectangles. That is, my entire map of "q" should show scattered horizontal and vertical strips up to 6deg long, where q is consistently high or low, purely as measurement artifact. This predicted tendency, is indeed seen on inspection.

Only one area differs obviously from the above pattern. It is roughly trapezoidal (boat shaped), 8deg long (definitely bigger than one plate) and almost as wide, centered on Barbarossa, and inclined ~30deg NW to SE (i.e., along Barbarossa's orbit). Here "q" is consistently big, i.e., R2 is consistently dim.

One might expect a double image, a congruent region of small q, parallel to this region and lying 4deg NW by W, due to Barbarossa's orbital motion. On the overlap, the effect might cancel, giving roughly average q. Even allowing for scattered strips of measurement artifact in q, I don't see this.

The unequal roles of R1 & R2 might result from the different far-red sensitivities of the the emulsion/filter combinations used. According to the DSS "plate finder", the 1950s survey used "xx103aE + plexi [red plexiglass, i.e., RP2444, equivalent to approx. Wratten 29]", and the 1980s survey used "IIIaF + OG590". According to, these equate to photographic passbands "E", and "R59F" [equivalent to "Fpg"], resp.

The galaxy is only ~300pc thick here, so at this high galactic latitude, almost all stars are within 200pc. Since they all have red magnitude approx. +16, their absolute red magnitudes are > +16 - 6.5 = +9.5. So, these are Type MV stars.

The Hipparcos data suggest that the nebula has roughly a spherical shell shape, and that its material somehow dims the V magnitude of red stars, while brightening blue stars in V. The controlled study of Johnson vs. early Harvard photometry, might have indicated the reverse, only because I fitted the data to a bell curve (e.g., up in the middle and down at the sides) instead of a shell (e.g., down in the middle and up at the sides). If so, then Barbarossa's nebula should strongly extinguish red. The 1980s sky surveys, if their red passband is narrower, so that the R2 magnitude depends mainly on the most extinguished wavelengths, might show an effect on q, next to which the 1950s effect would be unnoticeable.

Indeed, photographic passband "E" is approx. the same as passband "Rc", in the range 0.3 < B-Rc < 2.6 (Spagna, A&A 311:758+, 1996, Table 3, citing Evans' 1988 Cambridge Ph.D. thesis). This range doesn't include red dwarfs like the M5.5 Proxima Centauri (B-Rc = 3.5), but for lack of better information, I returned to MS Bessel's PASP 98:1303+, 1986, article, Fig. 1. Bessel says (p. 1305), " the late-M stars the main contribution to the light measured in Rc comes from wavelengths not seen by R<subF>. ...gross deviations occur only for the M stars...". Not only is Rc's turnoff at much longer wavelength than R59F's turnoff; Rc's 50% turnon is at 285A shorter wavelength than R59F's. Either the turnon or the turnoff difference, might explain why, unlike R2, R1 seems little affected by Barbarossa's proximity.

On the W half of my region, sampling over a 2deg mesh, I found average q = approx. sqrt(6). If R2-R1 is normally distributed, this corresponds to a tail area 1/(1+sqrt(6)), and a displacement of ~ 0.5 std. dev. Throughout the region, many disks had q < 1 (corresponding tail area for q=1, is 0.5, i.e. ~ 0 std. dev.) and many had q > 6 (tail area for q=6, is 1/(1+6), i.e. ~ 1.0 std. dev.). So, the displacement of the magnitude (i.e., the extinction) is proportional roughly to log(q).
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