Quantized redshift anomaly

“... Lorentz, in order to justify his transformation equations, saw the necessity of postulating a physical effect of interaction between moving matter and æther, to give the mathematics meaning. Physics still had de jure authority over mathematics: it was Einstein, who had no qualms about abolishing the æther and still retaining light waves whose properties were expressed by formulae that were meaningless without it, who was the first to discard physics altogether and propose a wholly mathematical theory...” Herbert Dingle, Science at the Cross-Roads.

Tommy,

(That's a mighty low frequency stutter you have developed)

Newton explicitly ducked the physical side of gravity in his theory. I'm not sure if anyone preceded Newton in this, but Dr E. was not the first.

Curiously, the lack of a physical explanation for both men's theory is seldom discussed in college classes. Many technologists with formal training never think in these terms until they hear someone else talk about it.

It seems important to me, but most just shrug it off. After all, their professors didn't think it was important ...

LB

Removing an apex-to-antapex lune from the celestial sphere, changes neither the RV-based nor the PM-based apparent solar apex speeds. If the apparent stellar motion is slower within the cylindrical Orion arm (the sun is somewhat outside this cylinder, which is roughly parallel to the solar apex motion) this will reduce the RV- and PM-based speeds.

The maximal reduction of PM-based speed, occurs over a sphere cutting through most of the cylinder. The intersection patch then resembles a lune. So, it is the Fehrenbach/Hipparcos ratio, 0.77, near Hipparcos' stationary point wrt. distance (see above) that is closest to the theoretical 0.800.

As mentioned above, a drag equal to the Pioneer probe acceleration, 8.1*10^(- cm/s^2, explains the power output of white dwarf stars. Because masses and diameters of white dwarfs vary little, the surface temperature should tend to be inversely proportional to the fourth root of the rotational period. The radius of a white dwarf is, theoretically and empirically, roughly inversely proportional to its mass, so the temperature is also proportional to the square root of the mass. The available data, on ten magnetic white dwarfs (mwd's), confirm my theory.

Over 10% of white dwarfs are magnetic (fields exceeding one megagauss); observational bias must be considered because the coolest, dimmest dwarfs are oftenest magnetic (J Liebert et al, AJ 125:348, 2003). Very accurate rotation periods are known for some mwd's. Moderately accurate surface temperatures are known for some. My literature search today at ISU's Parks Library, found five mwd's for which rotation period, temperature and mass are accurately known, and five more for which the mass is unknown (DT Wickramasinghe & L Ferrario, Publications Astr Soc Pac 112:873-924, 2000, review article, Table 1, pp. 885,886).

The mass of PG 1015+014 (a.k.a. PG 1015+015) was found in a later table which is practically a subset of the above (Astrophysics 47:324, 2004). Also, the review article's table gives the temperature of this star as 10 kK, but the cited source says 14 kK (Wickramasinghe et al, MNRAS 235:1451-1465, 1988, p. 1460).

The review article's table gives the temperature of EUVE J0317-853 as 40-50 kK (apparently from Ferrario's introduction) but I adopted the original source value of 50 kK (actually relied upon by Ferrario) and given by the review article's cited source, Barstow (L Ferrario et al, MNRAS 292:205-217, 1997, pp. 205,211)(MA Barstow et al, MNRAS, 1995).

The review article's original source gives the temperature of KUV 813-14 as 10,700 +/- 350 K (J Liebert et al, PubAstrSocPac 97:158-164, 1985, p. 159). I also included the recently discovered WD 1953-011 (CS Brinkworth et al, MNRAS 357:333-337, 2005). Here are the data:

PG 1031+234
3.4h 15,000 K 0.93 solar masses 1.0 Earth radius

EUVE J0317-855 (aka EUVE J0317-85)
725s 50,000 K 1.35 s.m. 0.55 E.r.

PG 1015+014 (aka PG 1015+015)
98.7m 14,000 K 1.15 s.m. 0.7 E.r.

Feige 7
2.2h 23,000 K (but equiv. to 19,000 in power) 0.6 s.m. 1.3 E.r.

WD 1953-011
1.442d 7920 +/- 200 K 0.74 s.m. 1.2 E.r.

G 195-19
1.3d 8000 K

HE 1211-1707
110m 23,000 K

KUV 813-14 (aka WD 2316+123)
17.9d 10,700 +/- 350 K

KPD 0253-5052
3.79h 15,000 K

PG 1312+098
5.43h 15,000 K


Given the mass, the radius is estimated (SD Provencal et al, "Testing the White Dwarf Mass-Radius Relation with Hipparcos", conference poster, 1998, on internet, Fig. 2). If the mass is unknown, then 0.9 solar mass, the median in the review article's table, is assumed (and 1.0 Earth radius). The mwd's are assumed to be homogeneous spheres.

To predict surface temperature, I applied the blackbody Stefan-Boltzmann law to my previous, planetary, power output formula, sans the fine structure constant factor. The power is assumed to be the absolute value of the projection of the rotational velocity on the galactocentric line, times the magnitude of the Pioneer probe acceleration force. I assume that the rotational axis differs 60 degrees from the galactocentric line (i.e., the median expectation). Even a 30 degree angle (13th percentile expectation) gives a temperature only 16% less than does a right angle.

Results:

PG 1031+234
predicted temp 15,300 K
observed temp 15,000 K

EUVE J0317-855 (aka EUVE J0317-85)
pred temp 39,500
obs temp 50,000
Prevalent opinion is that maybe obs temp is as low as 40 kK.

PG 1015+014 (aka PG 1015+015)
pred 21,200
obs 14,000
A small axis-galactocentric angle, 9.5 degrees, which happens 1% of the time, would cause such a temperature. There are ten objects here, so one such would happen, 10% of the time. This object's rotation axis is at i=70 to our line of sight (Wickramasinghe, op. cit., 1988), so its galactic coordinates are consistent with this possibility.

Feige 7
pred 14,300
obs 19,000 (blackbody equiv., rough est.)
This is much higher than my model allows. Although Feige 7 has a spectrum resembling 23 kK, its radius (estimated from its mass) and distance (roughly estimated from proper motion) imply that its power output is equivalent to 19 kK, less than half of blackbody (Greenstein & Oke, ApJ 252:285-295, 1982, p. 288). A true distance 57% of Greenstein's estimate would reduce the observed power to 14.3 kK equiv., with an albedo of 15%. Feige 7 has been found to have a banded surface and is the only object of this sample listed as "pulsating" by SIMBAD. The explanation offered for KUV 813-14 doesn't apply, because i=60 for Feige 7 (Achilleos, ApJ, 1992).

WD 1953-011
pred 7730
obs 7920 +/- 200

G 195-19
pred 9000
obs 8000

HE 1211-1707
pred 18,200
obs 23,000
This could be explained by a mass of 1.3 s.m. with an axis-galactocentric angle of 90.

KUV 813-14
pred 4650
obs 10,700 +/- 350
This is much higher than my model allows. As far as I know this is the only mwd in this sample, which is viewed nearly end-on: the best fit to the data is i < 10 (or perhaps 20) degrees (Achilleos et al, ApJ 346:444-453, 1989, p. 451). Perhaps the apparent rotation frequency is (sin(i))^2 times the actual. Then i=10 implies pred=11,200 K. On average, only about 1/8 of mwd's should have i<30. (Sin(45))^(-0.5)=1.19; multiplication of predicted T by this much or less, would not much worsen the fit to observation, and might improve it. The polarimetry data for this object (Schmidt & Norsworthy, ApJ v. 366) are too few, or over too long a time, to give the stated period accurately. Using the 11 data falling in daily or almost daily runs of 3 or 4 each, my analysis, optimally adjusting the phase anew for each run (they are separated by three or ten months) suggests a period of 35 hours superposed on a long period. Such a period would predict T=8700 K.

KPD 0253-5052
pred 15,200
obs 15,000

PG 1312+098
pred 13,900
obs 15,000

Six of ten are perfectly consistent with my theory (one of these is consistent only because the observed temperature is uncertain). Two more are consistent if their mass, or axis angle, are appropriate. Feige 7 might be consistent by virtue of its unusually low albedo. The end-on mwd might be consistent, if the rotation frequency observed by polarimetry, is related to the true rotation frequency by a sin^2 law, or if the period is simply incorrect due to sparse data.

The above, isolated, white dwarfs have not been discovered to have increasing periods. The Ulysses probe analysis of J. D. Anderson (see above) suggests that the anomalous probe deceleration acts antiparallel to the velocity of an object relative to some frame such as the infalling frame of the sun. Thus the attempt to fit the Ulysses data to a simple sunward acceleration, gave a somewhat too-large figure, with large error bars. For isolated white dwarfs, the relevant frame might be that infalling to the galactic center, as seems to be the relevant frame for Uranus (see above). For wd's in binary systems, it might be the frame infalling to the companion star. Either way, the Pioneer probe deceleration acts mainly to generate heat, because its direction, nearly constant in space, rotates relative to the structural elements of the rotating object.

The speed of the infalling galactic frame might be sqrt(2)*250=350 km/s, or without dark matter, perhaps 350/sqrt(4.5)=150 km/s. The circular 9.88h orbit of the "intermediate polar" ("IP") wd AE Aquarii about its red dwarf companion is about 100 km/s. Anyway, the equatorial rotational speed of the wd, with radius, perhaps, 3700 km and rotational period 33.08 sec, is 700 km/s, which implies that the Pioneer probe deceleration, for this object, acts mainly to brake it, rather than to generate internal heat.

Assuming the Pioneer deceleration is always antiparallel to the rotational velocity of the mass element, the spin-down dP/dt=5.64*10^(-14)sec/sec is consistent with a radius of 3700 km (0.0053 solar radii). For an iron wd, this implies 0.97 solar masses from the theoretical line on the abovementioned mass-radius chart, or perhaps 1.02 solar masses from the empirical line drawn through Procyon B. For an iron wd, the polar flattening would be only 1.8%, vs. 7% for a helium wd.

Making no assumptions about the companion's mass, Welsh estimated 0.89 +/- 0.23 solar masses for the wd. Reinsch called the companion spectral type K5V, assumed 0.70 solar masses from the main sequence average for that type, and from the mass ratio, estimated 0.91 +/- 0.04 solar masses for the wd. Welsh found that K3V and K5V fit the companion spectral type about equally well; with newer data, Casares found K4V fit best. From the Hipparcos standard lists of K3V and K5V stars, I estimated that the former spectral type is 15% more massive (assuming L=M^3.7), which would give 1.05 (for a K3V companion) or, interpolating, 0.98 (for a K4V companion) solar masses for the wd.

Casares found Doppler evidence that the companion nearly fills its Roche lobe, so that asymmetric rotational speed required upward adjustment of its orbital speed; his assumption-free estimate of the wd mass became 0.79 +/- 0.16. This might be incorrect. The asymmetry widened the band only 10%; the speed correction, and ensuing mass correction, should be higher-order effects, not 10%. Also, Casares indicates no (compensatory) correction for the increased gravitation due to the asymmetry.

Such lobe-filling requires an unusually large, bright, K4V star. Indeed, assuming a 100 pc distance, its absolute visual magnitude (from SIMBAD) is greater by 1.3 than the K4V average I interpolated from the Hipparcos standard lists. This would imply a rare "evolved" star that had departed the main sequence.

By Simpson's rule we can consider a midradius point as typical. Here the cosine of the angle between element velocity and Pioneer10 force (assuming that the 350 km/s infalling galactic frame is the relevant one) varies from 1 to cos(45), so the heat-generating power is (1-0.7)/(1+0.7)=18% of the spin-down power; that is, equal to the system's bolometric luminosity. So, maybe the companion is really an average main sequence star, or a white or black dwarf. A gaseous disk, at 4500 K like the presumed red dwarf companion, could radiate this energy. It also could explain the unusual shape of Casares' graph of apparent rotational speed.

Although Poincare (see, e.g., Lamb) found rotational instability for self-gravitating spheroids flattened (a-b)/a=42%, the flattest such spheroid observed empirically, Saturn, is flattened only 10%, and Altair, one of the fastest-spinning stars, theoretically only 12% (A & A, Nov. 2005). Such objects have the advantage of a denser, less flattened core. Modeling Saturn as a homogeneous core surrounded by a massless mantle, implies a core (0.4/0.21)^1.5 = 2.6x denser than the planet overall; this core would be flattened only about 10/2.6=3.8%. If this is the true limit of stability, the mass of the iron wd in AE Aquarii must be greater than 0.97/(3.8%/1.8%)^0.25 = 0.80. Also, it must be less than 1.2, the Chandrasekhar limit for an iron wd (Weinberg, 1972).

Because the polar temperature (26 kK, vs. millions) of this IP wd is so low, it probably isn't accreting enough mass from its companion, to explain its spin-down. This unusual poorly accreting but rapidly rotating IP wd allows accurate measurement of the Pioneer10 deceleration.

The median "normal" pulsar, roughly P=0.5s, and (by my estimate from Lorimer & Kramer's plot) P'=2*10^(-15)s/s, has equatorial speed 14km*2*pi*2=170km/s, half the speed of the infalling galactic frame. Reduction of the Pioneer10 deceleration by a factor of 170/350 to account for this, gives agreement of predicted with observed spin-down, assuming a pole-on presentation to the galactic center. If the presentation is side-on, the spin-down is half as much, which agrees with the typical P' of Lorimer & Kramer's discussion.

P (resp. P') for normal pulsars has a standard deviation of about 0.3 (resp. 1) log unit. Millisecond (a.k.a. recycled or binary) pulsars are too interactive to expect intrinsic forces to dominate. Accurate n = omega" * omega /(omega')^2 values of four "normal" pulsars ranged from 2.2 to 2.9, mean 2.6. The young Vela pulsar, a supernova remnant (SNR), has n=1.4. The oblique magnetic dipole radiation / kinetic energy spin-down theory partially fails, because it predicts n=3. It also partially fails, because there is no log(P')=-log(P)+C trough (see the plot in Lorimer & Kramer; their appendix has the omega and P formulas).

Suppose that during its collapse a neutron star briefly resembles a typical isolated rotating mwd. If angular momentum and magnetic dipole are conserved during the final collapse, then the new neutron star's magnetic field energy will be more or less than, but usually of about the same order of magnitude as, its kinetic energy. Maybe this huge field energy mostly becomes electrostatic energy confined to the corotating orbital radius, i.e., energy proportional to omega^(2/3) for constant charge. The dipole might tend to be proportional to the square root of this field energy. If kinetic energy predominates, the time derivative side of the pulsar evolution equation is the traditional omega*omega'. If field energy predominates, the time derivative side is omega^(2/3 - 1)*omega'.

For the traditional oblique rotating magnet, the power side of the evolution equation is omega^4. For the Pioneer probe deceleration, it is omega. The four possibilities in which one term dominates on each side of the equation, give n=0,1.33,3.33,4.67. The Vela SNR (n=1.4) conforms to the depletion of field energy by the Pioneer probe deceleration. Most normal pulsars have n about halfway between this option and the n=3.33 (oblique magnetic dipole spin-down) option.

Thus a pulsar's evolution on the log(P')vs.log(P) plot can have slope 2-n = 2, 0.67, -1.33, -2.67. Often both terms on both sides of the equation are significant, so the instantaneous slope is an intermediate number. Hence the plot, excluding binary pulsars, is amorphous, though with some hints of these fundamental slopes.

Refs.

NR Ikhsanov et al, Astronomy & Astrophysics 385:152-155, 2002; "Can the 33 sec...", A & A 374:1030-1034, 2001; A & A 358:201-207, 2000.

VS Geroyannis, ArXiv.org, 2001.

J Casares et al, MNRAS 282:182-190, 1996.

WF Welsh et al, MNRAS 275:649-670, 1995, pp. 654-655, 659.

K Reinsch et al, A & A 282:493-502, 1994, p. 501.

Lamb, Hydrodynamics, 6th ed., ch. 12, sec. 374, p. 703.

RX Xu & GJ Qiao, ArXiv.org, 14Sept.2001 "draft version 6/3/05", internet.

Lorimer & Kramer, Handbook of Pulsar Astronomy, 2005.

It seems to me simpler to explain the frequency shifts by the same effect: the thermodynamically allowed transfers of energy between light beams refracted by a gas containing excited atomic hydrogen, these transfers of energy producing frequency shifts without any change in the geometry of the beams.

Two blueshifts are observed by a transfer of energy from the solar light to the radiowaves in the excited atomic hydrogen provided by the cooling of the solar wind beyond 5-10 AU: the "acceleration" of the Pioneer 10 and 11 probes and the observation that a part of the anisotropy of the "CMB" is bound to the ecliptic (evidently the wind is bound to the sun through the corona).

The anomalous redshifts of the light are observed each time the light crosses a gas containing excited atomic hydrogen obtained generally by a Lyman alpha absorption in atomic hydrogen. They are so many examples that it is impossible to be precise. Two examples :
- In the observation of Arp's alignements of a galaxy and quasars, the redshift is lower for the galaxy because the hydrogen is more excited (by the quasar far UV radiation) close to the quasar, therefore on the path from the quasar.
- The periodicities observed by a lot of authors are a simple result of the propagation of light in atomic hydrogen; it is trivial physics!

The CREIL is a magic stick : look for neutral atomic hydrogen in states 2S or 2P, you will find anomalous frequency shifts (or, vice-versas).