Requiem for Relativity

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.

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)
(2.15,0.942)
(2.96,0.849)
(4.34,0.9195)
(5.10,0.9925)
(5.81,0.981)
(6.56,1.0495)
(7.85,0.967)
(8.35,1.0965)
(10.52,0.9645)
(11.14,0.964) (composite of two; apparent double)
(11.32,0.888)
(11.66,0.8885)

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)
(3.33,0.7635)
(5.29,1.0055)
(6.78,1.3115)
(8.15,1.0415)
(8.33,1.043)
(9.65,1.0415)
(9.86,1.041)

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

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).

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 www.nofs.navy.mil , 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), "...in 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).

In Barbarossa's Cavern There Are No Stars (Part XIV)

The figures below are the Briggs logarithms x 1000 (i.e., divide by 1000 to get the base-10 log) of "q" (see Part XIII) on 30' radius disks centered at, 1st row, (11h40m,-3deg30'), (11h36m,-3deg30'),...,(10h52m,-3deg30'); 2nd row, same but Decl -4deg30'; etc.; last row, same but Decl -11deg30'. This region is 13deg EW by 9deg NS. It is roughly centered on Barbarossa's 1987 position (approx. 11h18m,-8deg), which is near a "four corners" where degree squares circumscribed around four of the disks, marked by (*), touch. At this Declination, 4m is 0.98deg, so I treat 4m as 1 deg.

-778,-929,-1315,-796,-1431,-559,-393,63,-324,201,653,457,166
987,507,-332,462,664,549,542,740,772,789,1239,752,201
750,488,000,607,627,580,441,1097,966,733,751,787,426
487,833,38,637,745,648,554,903,903,1088,644,727,488
-628,-526,346,525,641,602*,1024*,1124,970,1103,1058,625,675
-204,-556,867,833,862,1003*,1146*,1103,869,566,765,766,534
280,211,655,826,1465,1610,1542,765,804,673,548,258,611
-140,-18,556,622,680,773,987,140,311,-204,-275,-643,372
-84,182,463,160,229,753,708,261,79,577,-186,-204,470

These numbers could undergo a suitable arbitrary linear transformation a*x + b, to give a grayscale optical density, to make a 9x13 pixel grayscale picture. A refinement would be to interpolate at corners (average of 4) and at midpoints of edges (average of 2) to make a 17x25 grayscale picture.

In Barbarossa's Cavern There Are No Stars (Part XV)

The USNO-B catalog hardly could correct for the difference between the spectral sensitivity curves, "E" (for the plates used to determine R1)(E is approx. the same as "Rc") and R59F (for the plates used to determine R2). This correction depends drastically on spectral type; most USNO-B stars have only Red magnitudes known, hence nothing known about spectral type.

The long-wavelength tail of the Rc sensitivity curve, which, MS Bessell remarked, is important for Type M stars' magnitudes, lies roughly halfway between the R59F and IsubN sensitivity curves (see MS Bessel's Fig. 1). Optical infrared ("I") magnitude could be substituted for R2 magnitude, and the calculations of Parts XIII & XIV repeated to find another matrix. Because the R2 (R59F) & I (IsubN) sensitivity curves might effectively differ (for Type M stars) from the R1 (E or Rc) curve by equal amounts in opposite directions, averaging the two matrices might find the result that would have been found if R1, R2, and I all had the same sensitivity curve.

I did this. The average matrix is below. In the region described by the matrix, the dates of the most important "I" plates, are approx. 1995.2 & 1997.2. The dates of the most important "R2" plates are approx. 1986.2 & 1987.2. So the effective date of the second measurement is approx. 1991.45 (and of the first, approx. 1954.2).

In this region, 20% more stars list I & R2, than list I & R1. Using I & R2 (instead of I & R1) also lessens the chance of misidentification due to proper motion or long-term variability; because, the plate dates are much closer. So, I compared R2 vs. I as I had compared R2 vs. R1. Averaging was effected by subtracting half the new log(q) for R2 & I, from the log(q) found for R2 & R1. For R2 vs. I, I further increased sample sizes (to about triple those of the R2 vs. R1 study) and hence significance, by using +17 instead of +16 as the dividing line, and by using semi-infinite intervals instead of intervals of length 1 mag.

The matrix entry, corresponding to the degree square containing the 1991.45 c.o.m. Barbarossa/Frey heliocentric position, is marked (**). The three next-closest degree squares are marked (*).

-1140,-1265,-1420,-969,-1519,-608,-421,-162,-686,-186,332,149,-34
507,245,-469,483,728,687,640,576,518,403,844,477,-45
296,231,18,709,684,731,514,913,648,393,461,541,192
64,504,-33,746,818,682,644,706,572,697,316,471,368
-996,-724,214,628,741,636*,1027*,905,683,812,695,368,531
-535,-758,587,546,631,736**,881*,754,500,288,491,598,389
-152,-148,365,394,925,1099,1116,517,499,355,369,137,481
-1180,-395,249,246,288,200,579,-110,-68,-71,-16,-637,329
-498,-213,211,-225,-220,186,329,-118,-274,285,-375,-129,421