Requiem for Relativity

My excuse is... I used to be Sisyphus in a past life []

Hobson's text on Spherical Harmonics is a good reference on multipoles. In my theory of the origin of the CMB, its temperature is essentially the escape energy of an electron, at a barrier approx. 52.6 AU distant, where the internal gravity of a proton just exceeds the sun's gravity. Small masses near this barrier cause small fluctuations in its position, hence small localized fluctuations in the CMB temperature. These small fluctuations add up to small multipoles of the temperature distribution. Above, I showed that the quadrupole due to Neptune is small enough to be consistent with observation.

Apparently the CMB dipole has moved about 0.27 degree west, parallel to the ecliptic, in 11 years between COBE & WMAP. The change in the known giant planets' positions predicts that it should have moved 0.31 deg east; so, the actual movement might be 0.58 deg west. This would imply an object at 360 AU, revolving backwards. With 0.019 solar masses, it would create a CMB dipole equal to that observed; but, the next few higher multipoles would be too large.

An object of 0.019 solar masses would be a smallish brown dwarf, with 20x Jupiter's mass but about the same radius due to "degeneracy pressure" (BR Oppenheimer et al, "Brown Dwarfs", in "Protostars & Planets IV", V Mannings et al, eds., 2000). Such a brown dwarf would experience no hydrogen fusion and only evanescent deuterium fusion. In a five billion year life, it might have cooled too much to have been observed. My estimate of the angular motion, hence distance, might be inaccurate: if the mass is less than 0.013 solar masses, then it is a planet and never experienced any nuclear fusion reactions at all.

I propose that the higher multipoles of the CMB are removed by ellipticity of orbits in the Kuiper belt, induced by the brown dwarf (or distant giant planet). The elliptical orbits would not induce dipole, because that is proportional to 1/r^2 in my theory (because it is mediated throught the effect on the barrier distance) and, so is the angular velocity along the orbit. Only higher multipoles would be induced by the elliptical orbits of the Kuiper belt objects; these might cancel the multipoles induced by the brown dwarf. The quadrupole of the brown dwarf would be roughly 53/360=15% of the dipole; all but 0.3% of this would need to be cancelled. The n=4 multipole would be about the magnitude of the observed quadrupole.

The CMB multipoles are aligned for n < 6 (K Land & J Magueijo, PhysRevLett, 12 Aug 2005, "95,071301"). This might be because for n > about 5, the multipoles due to different regions of the Kuiper belt, no longer would add constructively. Also, the multipoles induced by the brown dwarf begin to be tiny after n=4.

I just had a look through an old book, and I found a scrap of paper where I had jotted down some stuff on the famous "Nemesis." I put down 10 thousand a.u. for the perihelion and 1.2 light years for aphelion. No idea how I arrived at these figures, as the paper is years old. I think everyone has whiled away a few hours looking for our brown dwarf but the problem comes down to the fact that it should show up. In fact, that I suspect, is why I gave it such an large elliptical orbit.

360 a.u. is very close, and I would like to hear something further on your ideas regarding the reason for its retrograde orbit.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Stoat</i>
<br />I just had a look through an old book, and I found a scrap of paper where I had jotted down some stuff on the famous "Nemesis." I put down 10 thousand a.u. for the perihelion and 1.2 light years for aphelion. No idea how I arrived at these figures, as the paper is years old. I think everyone has whiled away a few hours looking for our brown dwarf but the problem comes down to the fact that it should show up. In fact, that I suspect, is why I gave it such an large elliptical orbit.

360 a.u. is very close, and I would like to hear something further on your ideas regarding the reason for its retrograde orbit.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Thanks for this important information! See my next posts!

The first observations of brown dwarfs were in 1995. There is extreme observational bias in favor of relatively hot dwarfs.

The usual theory is, that for a small brown dwarf such as the above, only deuterium fusion would occur, and that, only "evanescently". If the deuterium has been "burning" at a constant rate from 4.5 billion years ago until now, and has almost run out, then the temperature would be about 4000K and the dwarf would be the third brightest object in the sky. If some or all of the deuterium burned quickly, maintaining the dwarf at 40,000K (the temperature of the hottest white dwarfs) until it stopped burning, thereafter the dwarf cooled at constant radius (with perfect convective mixing, and specific heat 0.2) as a blackbody radiator, it would be 0.07K now (if space were absolute zero temperature). So the brown dwarf might essentially be a planet by now; sunlight would maintain it at 15K.

A planet the diameter of Jupiter with the albedo of Uranus (57%), at 360 AU, would have magnitude +16.0. It's said that the limit of Tombaugh's wide ecliptic search was magnitude 17 except for a small region, presumably the galactic equator, where it was 16. Commonly, albedos are 1/10 that of Uranus, implying magnitude +18.5. So, the brown dwarf might have been slightly too dim to be found by Tombaugh. On the other hand, the (2001) automated search, by RL Allen et al, of 1.3 sq deg of the Kuiper belt, extended to mag +25. It wouldn't be too expensive to find a +18.5 object whose position (i.e., the CMB dipole) is known to 0.1 deg.

Above, I say that two simple equations involving gravity and fundamental physical constants, determine the CMB temperature emanating from a surface at about 52.6 AU. The more accurate of the two equations is, that the macroscopic gravitational force must equal the maximum self-gravitational force within a proton, contracted (Heisenberg uncertainty principle) to a Gaussian radius of hbar/(2*Mproton*c); this gives a barrier at 52.63 AU. The less accurate equation, involving the gravitational constant G and the CMB temperature T, is, that the mean(Vx^1.5), where Vx is one velocity component, e.g., along a magnetic field line, for an electron, equals Vescape^1.5; this gives 52.60 AU. This 52.63 - 52.60 difference, lies within the uncertainty of G and/or T.

Thereby mainly the sun's gravitational field determines the CMB temperature, which becomes a sensitive detector for gravitating objects in the outer solar system. The CMB dipole is caused by the sun's retrograde, small cool brown dwarf, 0.019 solar mass, mag +18 companion at 360 AU distance in the positive dipole direction.

The dwarf's gravity elongates the orbits of Kuiper belt or Oort cloud objects, which does not affect the CMB dipole (due to cancellation of factors) but which does, observationally, neutralize all but 1/50, of the quadrupole due to the dwarf (which otherwise would equal 1/6 of the dipole). The total mass of highly eccentric comets required, near their perihelion (opposite the dwarf) somewhat outside the 53 AU barrier, at any given time, would be 0.019 * 333,000 * (52.6/360)^3 = 20 Earth masses. Theoretical models estimate the mass of inner + outer Oort cloud comets as considerably greater than 1 Earth mass, but this estimate includes only comets exceeding 2.3 km diam (L Dones et al, in MC Festou et al, "Comets II", 2004, p. 170 "Summary"). For 142 comets with semimajor axes greater than 500 AU, the dominant high density of aphelia is near ecliptic longitude 210, ecliptic latitude +15 (JA Fernandez, "Comets", 2005, Fig. 6.9, p. 154).

The Kuiper belt mass observed by Allen et al was 0.37 Earth masses if extrapolated to all sky within 30 degrees of the ecliptic, assuming a body density of 2 grams/ml. If N=1/M, then because Allen et al observed objects 50km-500km diam, the contributions of other decades of size down to 0.15 micron diam (below which solar radiation pressure often would sweep the objects away), would multiply this mass by 12.5, to 4.6 Earth masses. If this mass were just inside the 53 AU barrier when in conjunction with the dwarf, and far inside the barrier when in opposition to it, then it would be as effective as 4.6 Earth masses of the above-mentioned comets.

Indeed the distribution of (almost 100 known) Trans-Neptunian Objects (a.k.a. Kuiper belt objects) as of 1998, is shifted about 5.9 A.U. toward 182deg ecliptic longitude (A Fitzsimmons, 1998-2000, "Surveys of the Distant Solar System", Fig. 2 in: Fitzsimmons et al, eds., "Minor Bodies in the Outer Solar System", 2000, p. 91). (I divided Fitzsimmons' chart into 20 sectors and based my calculation on the number and median radius in each sector; replacing median with mean in one of the twenty, whose median was importantly different from the mean.) So, the mass of Kuiper belt objects, supplemented by comets, is plausibly high enough to neutralize the CMB quadrupole. Both types of objects show a preference for perihelia that do so: perihelia near the 53 AU barrier opposite the brown dwarf and from above, for the comets; aphelia near the barrier adjacent to the dwarf and from below, for the TNO's.