Requiem for Relativity

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. One of the subgiants has metallicity indicating that it is slightly less "evolved" than the sun; the other four rejects have metallicities indicating that they are slightly more "evolved" than our sun, which Wright associates with subgiantism and gives as another reason for rejection.

Gray's four elite candidates surviving Wright's culling, all have metallicities exactly equal to our sun's. All are also 0.2 to 0.6 absolute magnitude brighter than the main sequence norm for their spectral type, as calculated by Wright using Hipparcos distances, so are suspect of subgiantism (Wright, op. cit.). Three of the four would be 0.2 to 0.4 mag dimmer in absolute magnitude if ground-based parallaxes (see Heidelberg ARICNS, "upper part") were used instead of Hipparcos; but ground-based parallax measurements brighten HD 221354 by 0.2 mag.

HD 57901 (Wright transposes digits in the name)(Gliese designation: GL 2057) is called spectral type K3 by Gray, K2 by the Heidelberg ARICNS near star catalog, but G5 by the Henry Draper catalog. The USNO-B1 catalog lists its B1, B2, R1, R2, & I mags as +9.35, 8.71, 7.65, 7.59, & 7.13, resp. The USNO-B blue magnitude search option is malfunctioning, but scanning its lists of stars near HD 57901, shows that this blue discrepancy is slightly uncommon for such bright and equal red magnitudes. So, I'll discard HD 57901 as a possible unusual variable.

HD 12051, HD 164922, and HD 221354 remain. Of Gray's original nine, these three are closest to Cas A: 60 degrees or less. As mentioned above, use of ground-based measurements would brighten the magnitude of HD 221354 by 0.2 mag, putting it at least 0.4 mag above the main sequence norm; but this star also is closest to Cas A: only 1.1deg away, which is a remarkable coincidence, so I'll keep it. HD 221354 also is, of the nine, closest to Earth: only 16.9pc (Hipparcos) or 18.6 +/- 1.5pc (ground-based); it has "Vega-like" 60micron-band (~50Kelvin) infrared emission (presumably a dust ring; and stars with dust rings tend not to have large inner planets)(Jura et al, ArXiv.org, May 31, 2004; Chen et al, ArXiv.org, May 10, 2006; Greaves et al, MNRAS 348:1097, 2004).

Approximating both Gray's and Baliunas' samples as Decl -15 to +90, that all four qualifying Maunder-minimum candidates (Gray's three + Baliunas' one) would be within 60deg of Cassiopeia A (RA 23h 23m, Decl +60) is significant at p = ((1/4)/(5/)^4 < 3%. Assuming uniform directional distribution of these nearby stars, that one of the four would be within 1.1deg of Cas A, is significant at p = 4*pi*1.1^2 / (5/8*41,000) < 0.06%. Gray's three stars corroborate the supraluminal signal detected by Baliunas' HD 3651 (see above). Though the spectral types assigned these four apparent Maunder-minimum stars vary as much as two grades, between authorities, the current majority opinion seems to be that all four (Baliunas' HD 3651 and Gray's HD 12051, 164922 & 221354) are G9V or K0V.

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.

Suggestion for small-telescope observation:

The eleven stars which, it seems from my above review of the literature, might be in, or might recently have entered, or might recently have exited, Maunder minimum, are:

HD 3651 (54 Pisces)
HD 10700 (Tau Ceti)
HD 12051
HD 43587
HD 56972
HD 57901
HD 140538 (Psi Serpentis Aa)
HD 164922
HD 179699
HD 221354
HD 233641.

Some of these are visible with the naked eye, under good conditions; all of them are visible with binoculars, under good conditions. All are sunlike, G or "early K" spectral type. All are "dwarf" stars (i.e., on the "main sequence"). According to my theory, four of these stars lie near an envelope, where that envelope is tangent to our line of sight:

HD 43587
HD 57901
HD 221354
HD 233641.

Generally, I expect the envelope to be tangent to our line of sight when we look in one of these three directions:

Cassiopeia A
66.63deg away from Cassiopeia A
90deg away from Cassiopeia A.

My suggestion is to look for anything at all unusual about the appearance (e.g., magnitude, color) or apparent location (angular distance from nearby stars) of these eleven stars, with special attention to the four stars theoretically near the envelope. Also one might observe any and all stars near the envelope (i.e., near Cas A or near the two circles around it, at ~66.63 and ~90deg).

This program is ideal year-round for northern hemisphere amateur astronomers with small telescopes. All these stars are included in robust professional observing programs (Mt. Wilson, Lowell and/or Phoenix projects) but observations are only intermittent. Transient nonatmospheric phenomena, involving either the stars themselves or the intervening space, could be missed.

Rho Cassiopeiae and NGC 7789 both lie 1/2 or 2/3 of the way from us to Cassiopeia A, within 5 deg of the line to Cas A. Several different indirect estimates have been made of all these distances; probably rho Cas is farther than NGC 7789. Cas A, rho Cas, NGC 7789 and ourselves are almost collinear.

Rho Cas is the nearest yellow (type recently given as G2Ia0e, but varies from F8Ia, probably its normal status, to K and sometimes even M) hypergiant star; as of 1999 only 12 hypergiants of whatever color were known in our galaxy (ApJ 523:L145, 1999). Usually, roughly every 50 years (1893?, 1946, 1986, 2000) rho Cas seems to eject a shell of gas, causing its apparent surface to dim and cool, with typically -25 km/s (blue)shifted emission lines (not absorption lines as with ordinary photospheric pulsations - PASP 98:914 & 99:272), complete with molecular TiO bands (Sargent, ApJ 134:142, 1961; Beardsley, ApJSupp 5:381, 1961; Lobel et al, ApJ 583:923, 2003). It also varies with sometimes a 300 day and sometimes an 800 day period, but only by 0.2 or 0.3 mag (A&A 325:714, 1997; PASP 112:363, 2000, Fig. 1).

The approximate dates on which rho Cas reached major magnitude bottoms are:

December 1893, 0.6 mag drop (Beardsley, op. cit., Table 2, p. 500)
July 1946, 1.3 mag drop (Beardsley, op. cit.)
March 1986, 0.4 mag drop (Lobel, op. cit., Fig. 13)
September 2000, 0.8 mag drop (Ibid.)

(The last three bottoms were accompanied by spectral changes consistent with an ejected shell; such data might exist for the first bottom also.)

The dates of eruption of Cas A are:

August 1680 (Flamsteed records 6th mag star)(likely peak, +2, likely in April)
1667 (Dreschhoff & Laird, ice cores 1 mo. after Tarumi volcano; so far I haven't found the date, of this volcanic eruption in Japan)

If the 1680 Cas A eruption initialized a 53.4 yr cycle, the 1893 minimum would be four cycles later; the next cycle lengths (to 1946 & 2000) would be 52.6 & 54.2, which average to 53.4. If the 1667 supraluminal early event, initialized a 40 yr cycle, 1986 would be eight cycles later; the two cycles could coincide in 1946, giving a summed effect, and the observed longer bottom. (There was an Astronomische Nachricten article in 1934, available to me only by interlibrary loan or photocopy service, which would reveal whether the 40-yr cycle manifested in 1906.)

Nova 1592C (FR Stephenson, Quarterly Journal of the Royal Astronomical Society London 12:10-38, 1971, Sec. 4, pp. 21, 34) was noted in Korean annals, stationary near beta Cas (Caph) from Nov. 30, 1592 until March 4, 1593. Probably the nova had peak mag +2 or +3, as it "escaped the vigilance of...the West, ...[and of] the Chinese & Japanese..." (Stephenson, op. cit.). Probably Cas A is too far from Caph (Stephenson, op. cit.) but the nova might have been a flareup of rho Cas, only 2.5deg away from Caph. No other easily visible star is nearer to Caph than is rho Cas; this might be the meaning of the oft-used oriental description translated as "within" the reference star. Such a flareup of rho Cas happened in Nov. 1950, though only 0.6 mag (Beardsley, op. cit.).

Burnham, vol. 1, p. 495, says, "Trigonometric parallaxes have been measured [with the large refractors] at Allegheny, McCormick, & Mt. Wilson, and agree in giving a distance of about 200 lt yrs [ = 16mas][to rho Cas]." Allegheny parallaxes c. 1950 (resp. c. 1920) had probable errors of 4.9 (resp. 8.6) mas (AJ 55:185). A McCormick parallax for rho Cas was 8+/-6 mas (AJ 62:276, 1957). Not only the absolute magnitude as estimated from the spectrum, but also the small Hipparcos parallax (0.3+/-0.6 mas), the small proper motion (near zero after correction for galactic rotation), the large radial velocity (Oort's law) and the distances of objects in the presumably equidistant "Cas IV association", suggest a true distance 35x larger than Burnham's parallax figure, or 17x larger than the 1957 McCormick parallax figure: namely, 7000 lt yr. (ApJ 134:142). With a 200 lt yr distance, the detour from Cas A to rho Cas to us is negligible, but a 2kpc distance foils the rho Cas cycle convergences at 1680 & 1667.

Increasing the interstellar speed of light about 270x, rescues the cycle convergence for rho Cas. It also harmonizes the cycles of P Cygni (34 Cygni) and eta Carinae.

Using typical recent distance estimates, P Cygni is the peak of an isosceles triangle. The base angle is 30deg, the sides are 2kpc and the base is 3.4kpc. The other vertices are the sun & Cas A. Extending the base 2.3kpc beyond the sun, reaches eta Carinae. The extra lightpath for P Cygni is 2*2*(sec(30) - 1) = 0.62 kpc. The extra lightpath for eta Car is 2*2.3 = 4.6kpc, 7.4 times more than for P Cyg. The actual observed delays are 56 yr & 7.7 yr (56/7.7=7.3) for eta Car & P Cyg, resp. The ratio is as expected but it is as if the interstellar speed of light is 270x (maybe 137*2; the "fine structure constant" is 1/137) times greater.

Eta Car's outburst peaked 1843 = 1680 + 2*53.4 + 56. If the 53.4 & 40 yr cycles, seen with rho Cas, are initialized in 1680 & 1667, resp., for eta Car also, then their 1843 coincidence (2 & 3 cycles, resp.) would make an unusually big event, analogous to the 1946 event for rho Cas. Because eta Car & P Cyg are "luminous blue variables" (i.e., blue hypergiants) whereas rho Cas is a yellow hypergiant, the former have an outburst where the latter has a dimming. Indeed P Cyg (type B2Ia) is an "S Doradus variable" having blueshifted absorption lines, not blueshifted emission lines as does rho Cas. At 270x lightspeed, the 2.3kpc roundtrip to eta Car requires only 56 yr.

P Cygni suddenly reached +3, then was discovered by Blaeu on August 18, 1600 (Israelian & DeGroot, Space Science Reviews 90:493, 1999). Presumably under the influence of an earlier initialization by Cas A, rho Cas (Nova 1592C) had burst out 7.7 yrs earlier and was discovered in Korea. P Cygni reappeared in 1654, 54 yrs later: the same cycle length as rho Cas.

Cas A also might somehow affect the location of the "blue stragglers", the main-sequence blue stars found within clusters of much yellower stars. NGC 7789 usually is called an open cluster though some call it a transitional object between open and globular cluster; its color-magnitude array resembles that of a globular cluster (MNRAS 114:583). It includes a delta Scuti variable (A&A 366:178) and probably a Mira variable, WY Cas (PASP 72:48).

NGC 7789 is "very rich in blue stragglers", still counted as ~25 in 1995 (A&A 366:490). Already in 1980 (McNamara, 92:682, 1980; Fig. 3, p. 686) 29 were plotted. On the average, the blue stragglers are displaced a few arcminutes toward Cas A. The positional angle of the center of the blue stragglers, relative to the center of the cluster, is 50+/-10deg depending on the weighting used. The position angle of Cas A relative to the cluster center is 53deg.

Blue straggler catalogs of the other, smaller, open clusters near Cas A (NGC 7380, 7419, 7510, 7654=M52, and the overlapping 7788 & 7790) seem to be absent from the literature. "In general, the blue stragglers show a remarkable degree of central concentration [i.e., they tend to be well within the cluster]." (A&ASuppl, 109:375, 1995, Abstract). Blue stragglers have spectral type late B or early A (A&A 366:490, 2001). One could follow the precedent of professional astronomers, who identified stars appearing to be within the cluster and which had "B minus V" magnitude typical of spectral types bluer ("earlier") than about A5. Then those not having proper motion (or radial velocity or light polarization) typical of the cluster would be eliminated, because presumably they are accidentally superposed on the cluster.

Luminous blue variable (hypergiant) HD 160529 (V905 Sco)(assigned spectral types range from B8 to A4 Iae, sometimes even to F0)(Stahl et al, ArXiv.org 20 Dec 2002)(Sterken et al, A&A 247:383, 1991)(also online article by AW Fullerton & F Najarro) erupted in 1992 with a blueshifted ejected shell and a magnitude peak (Gaeng, Leitherer et al, display #80.02, 1995 - see internet). Maybe this is analogous to the rho Cassiopeiae eruption of 1946. The 1992-1946=46 yr delay is due to a signal traveling the extra distance from Cas A to V905 Sco & thence to us. For eta Carinae, 2*2.3kpc apparently caused a 56 yr delay (see above). The galactic longitudes of V905 Sco & Cas A are about 0 & 110, resp., so the law of cosines gives 2.4kpc for the distance from us to V905 Sco. Stahl (op. cit.) adopts Sterken's (op. cit., p. 390) estimate of 2.5kpc; Stahl notes upper and lower bounds of 1.9 & 3.5kpc.

In Huygens' construction for light propagation, let the small wavelet circles be 1/137 the radius of the large wavefront circle, or in general 1/137 the radius of curvature, R, of the wavefront. Let r = R/137. If photons move perpendicular to the wavefront, they advance by a distance r. If photons move tangent to the wavefront, they advance by sqrt(R^2+r^2)-R, which is smaller by a factor 2*137=274. The latter might be the usual speed of light; and the former, the faster signal which operates in interstellar space.

The seemingly fairly accurate ground-based parallax of rho Cas, cited by Burnham (see above) is 35x (maybe 17x) too large. The difference between ground- and space-based parallax might be due to different modes of light propagation in matter & vacuum.

I found another star with, like rho Cas, Yale parallax catalog ground-based parallax ~20mas with error 8mas, yet Hipparcos parallax much less. This star is Antares. For Betelgeuse the two catalogs are in good agreement. Yet for rho Cas & Antares, the Hipparcos parallaxes are 70x and 4x less, resp., both more than two standard errors lower.

Through Strasbourg's "VizieR", I searched the (ground-based) Yale parallax catalog (4th ed., 1995)(9000 stars) for stars with visual mag < 6.00, 15 < ground-based parallax < 30mas, and given error "sigma" of ground-based parallax < 10.6mas. Then I considered 2 or 2.5 sigma difference from Hipparcos parallax (also requiring Hipparcos parallax < 7.5mas as a labor-saving screen). For convenience I considered only the 375 (3/4 of the Yale stars) for which Bayer or Flamsteed designations were given.

The expected number with Hipparcos, 2.5 sigma or more, less than Yale, is a little less than 375*0.6% = 2.2. Instead I found 4 stars:

rho Cas
55 Cam
beta Sct
36 Aql

The 7.5mas Hipparcos cutoff is about two sigma less than Yale, for the median Yale parallax (21.7mas) and Yale error (7.3mas) of the nine stars eventually found (see below). So here in the tail of the bell curve, almost half of stars for which Hipparcos is 2 sigma or more less than Yale, would have Hipparcos parallax >7.5mas and be excluded. Thus here the expected number of stars with Hipparcos 2 sigma or more less than Yale, is a little more than 375*2.3%*0.5 = 4.3. Instead I found 9:

rho Cas
55 Cam
theta UMi
nu1 Boo
52 Ori
beta Sct
36 Aql
alpha Sco (Antares)
chi Sco

Their positions correlate with the positions of the five SN remant - like radio/X-ray nebulae:

Sgr A
Cas A
M1 (Crab nebula)
Tycho's supernova
Kepler's supernova

Five of the nine stars are within about 15deg of one of these nebulae. Rho Cas has the most extreme parallax discrepancy (2.8 sigma) and is closest of the nine stars, to any of these nebulae (Cas A is 4.3 deg away); 55 Cam has the third most extreme parallax discrepancy (2.5 sigma) and is second closest (~20deg) to Cas A. Also 55 Cas and chi Sco are about 10deg from Tycho's SN and Sgr A, resp.; 52 Ori and Antares are about 15deg from M1 and Sgr A, resp.

Because stars with parallax 4.7mas (median Hipparcos value for the nine above) are 695 lt yr away, comparable to the galactic disk "scale height in the solar neighborhood" of 800 lt yr (ApJ 596:204, 2003), Hipparcos stars with <7.5mas parallax are almost twice as likely as random, to lie within 10 deg of the galactic equator. Even so, the binomial test for 5 or more of 9 stars to lie within 15deg of one of the five nebulae, gives p < 0.5% (the 15deg radius disks for Tycho's SN and for Cas A considerably overlap).

Summarizing this thesis so far: Huygens' construction, together with the ubiquity of the fine structure constant, suggests an alternative lightspeed of 274*c. This lightspeed synchronizes almost all hypergiant star eruptions in this quadrant of the galaxy, on a 53.4 yr cycle initialized by Flamsteed's supernova (Cas A). The "blue stragglers" of Caroline Herschel's cluster NGC 7789 are displaced toward the line of sight to Cas A. Discrepancies between ground- and space-based parallaxes occur for giant stars near lines of sight to SN-like nebulae, especially Cas A. Also, the distribution of sunlike Maunder minimum candidate stars, is consistent with a lightspeed, or slightly greater than lightspeed, initiating signal from Cas A. In particular, the sun's two Maunder minima (c. 1500 & c. 1680) correspond to the two main recent reverse calculations of Cas A's explosion date(s).