Astronomy / - a 5-dimensional model tested on the planet system and other data -
Stars. galaxies...
2. Stars


In the proposed view on levels in preceding file, as connected d-degree steps in a dimension chain, stars appear in the middle step 3 - 2.

The FA-force outwards from 0-pole of d-degree 5, the FG-force from 00-pole inwards, the other way around: Disintegration outwards, polarizing steps inwards.
   The internal development and differentiation of stars should be imagined as along a new coordinate axis z - or as a fractal level development within step 3-2.

Three first notes:

a) On the underlying level of physical properties in this dimension model Mass has been assumed as 3-dimensional when analysed in relation to vector fields as 4-dimensional and Charge as 2-dimensional. This could be compared with the fact that for stars on the main sequence mass is proportional to (~) the cube of the radius.
   For white dwarfs this relation is inverted, with mass inversely related to the cube of radius:
Here it's suggested that such an inversion may be an expression for the opposite directions of the chain above, the structure of the loop model.
   The double directions in the middle step may be regarded as illustrated on the atomic level in the process:

n ↔ p + e + anti-ν

Neutrons n representing uncharged mass, protons and electrons the polarization in charges. (Cf. too the p/e-quotient.)

Range of variations in some elementary properties in 10-powers from spectral classes O- to M-stars: 10-powers coincide rather well with the d-degrees 3- 2-1 of the properties:

Masses*                       ~103
Circumferences            ~102
Rotation velocity          ~ 101
and temperature of the surfaces ~101.

*From 1/20 to ~70 times mass of our sun.
(Velocity in this model assumed as a property in step 1-0, represented in each d-degree step.)

Spectral classes of stars on main sequence in order of surface temperature from hottest to cool:

O-B-A-F-G-K-M, with 10 subclasses of each kind.

Temperatures from ~ 40.000° to 2.400°. (Range widened through later observations of new stars.)

Magnitudes are by scientists divided in 5 steps, the 5th root of 100 = 2,512 as factor. It give the number chain:

100 - 39,81 - 15,85. - 6,31 - 2,51 - 1.

It can be observed that middle 4 numbers also approximates surface temperature steps for stars on the main sequence above divided in 3 steps with quotient 5/2 = 2,5 (the middle also in d-degrees in the dimension chain.):
   O5 → B5, B5 → G0, G0 → M-8.
The numbers becomes in pairs inversions of each other:

39,8 /\ 2,51,     15,85 /\ 6,3. (x10-2),

also reflecting the complementary and polarity principle of the loop model?. (More about spectral classes below.)

5 phases in life time of stars:

A common description defines 5 main phases:

  1. Contraction in dense areas of clouds, aggregation of matter until density and heat through gravitational pressure starts first fusion process, the birth of a star.
  2. Fusion of H to He: stars on the "main sequence" .
  3. Contraction of the core, expansion of the outer regions (shell): the star becomes a "red giant".
  4. Fusion of He in the core to heavier elements. Further H-combustion in the shell.
  5. Eventual "superfluous" material thrown out, new contraction of the core to a white dwarf or neutron star or a black hole, depending on mass of the core.

Hence, astronomers count on 2 main different phases of fusion, of H to He and of He to heavier elements, and 3 main phases of contraction from birth to death.

A first addition: Also in the very first step there is a polarization observed between denser, cooler areas in the clouds and hotter thinner areas. (Curiously contradicting thermodynamic laws as it seems.) Gravitational energy in the denser area is then self-strengening and transformed to heat according to common descriptions. (What happens with the hotter, peripheral area of clouds?)
   This change from the property Density coupled with Cold to Density connected with Heat, is it really fully understood?
   In the dimension model the properties Density and Heat are connected with opposite steps of the dimension chain, assumed as the physical quantities defined in steps 5→4 and 1→0/00 respectively. May the loops shed light upon the "transformation"?

Fusion need both a certain degree of density and of high temperature.
   The problem, if one, returns when synthesis of elements are connected with spectral types of stars (see below).

In any case life time phases of stars may be described in 3 main steps along the Time axes:

  • 3 polarizations, type core - "shell" (a centre - anticentre structure, c-ac), with increasing strength: a) clouds dense ↔ thin b) red giants: core ↔ shell, c) dwarfs, n-stars ↔ nebulae,
  • 3 contraction phases: a) dense area of clouds, b) of core after H-combustion in red giants, c) collapses,
  • 3 "divergence" phases of increasing outward "detached" matter: a) outer hotter cloud, b) giant shell expanding, c) thrown out material as nebulae.

3 alternatives for collapses too, mass-depending: a) black holes, b) neutron stars, c) white dwarfs.

An attempt to illustrate the 3 stages in a dimension chain:
The loop model and the reinterpretation to 3 levels of polarizations "vertically":

   5" → 3 ↔ 2
5'  → 4 ↔ 1
5  → 0 ↔ 00.

The figures below are built on following aspects:

- The relation core - shell as a relation c-ac, 0 and 00-poles, also higher d-degrees in relation to lower ones.

- The two different parts of contractions: a) for fusion, b) for collapses, related to the border in middle step 3-2: mass polarized into charges, n —> p + e + ν. Mass - Charge properties a relation d-degree 3 to 2 in the dimension model.

- Associations with d-degrees in the figures built on the 2x2-chain, x = 5 - 0,where intervals mark electron orbitals s - p - d..., in connection with synthesized elements in these orbitals: See figure 8, figure 9, figure 11 below.
   Fusion of elements (up to about Fe/Ni, "endogen", will come to represent only "half" of the way for contractions through gravitation, the inward directed force, from the 00-pole.

- The ambiguous relation between density and temperature: demanded increasing temperature in the core for fusion of heavier elements, connected with decreasing surface temperature. Density and Temperature properties primarily dined in opposite ends of the dimension chain.

To the life time stages above it has to be added that very massive stars also can undergo series of smaller development phases during fusion of heavier elements.

a) Life time, fusion:
Contractions horizontally: synthesis of elements in right part of the figure:

- Centres here in the middle step: cores with decreasing size vertically upwards.
- Fusion steps corresponding to contractions leading to new decreasing polarizations core ↑ —> shell: diagonal arrows. (Illustrated as of "90° " !?) Which impact do the higher stages of density, left diagonal arrows, have in these polarizations? If any ?

- Released energy: steps from radiation toward more closed "circles" as convection in denser cores.
    (From more of gravitational "radiation" at H→He-synthesis (?) to more of electromagnetic radiation, to convection streams of matter in rotational motion. Cf. dimension chain of forces: step 4-3 FA / FG ; step 3-2 FE / FM. And rotational motions of matter in d-degree 3. Radiation as waves in lower steps →2 →1 → 0/00.)

- Gravitation - or this force as inward direction - is also, according to the model, originally a polarizing force, here perhaps responsible for separation of p and e as a condition for fusion of nuclei?

One question concerns the polarizations in the 3 processes, diagonal arrows, in physical interpretation. To take the apparently best known of these, when stars at the end of the phase on main sequence transform to red giants: Why do their cores "suddenly" contract, why do their shells blow up ?
   It's vaguely said that it occurs when all hydrogen has been fused to He, - but the shells still contain H. for further He-fusion. The same question may be asked about why so called "superfluous" matter are thrown out.
   Are there really any good explanations for these quantified "jumps" in gravitation and the connected polarizations core - shell / thrown out matter?

One suggestion here is to interpret these "polarizations" as effects of the FA -force (Vdiv): in d-degree 4 "anti-parallel" to gravitation FG , but in d-degree 3-2 perpendicular as poles circular versus radial according to assumptions about angle steps in the model.
   As such a force for divergence, from 0-pole of polarized d-degree 5, FA also represent the primary integration force (in opposition to "gravitation" as primarily a polarizing force), and FA would - as such - be an essential factor in the fusion process (!?).
   The FA -force (the outward acceleration vector field) as the basis for, or root to, Vacant Space as pole of d-degree 3 is closest related to the FE -force in d-degree 3, and among materialized particles to electrons, (neutrinos here disregarded). Compare the statement about a high density of electrons in the centre of our sun.
   It would be the "vacant space" as such that is pressed out at certain levels, when certain degrees of mass density is reach: a new level of the polarization mass - space.
Appearance of the FA -force in different d-degrees:
   Step 5 - 4:  0-pole:   Integrating;
   Step 4 - 3: 4b-pole:  Vdiv, "polarizing", separating,
   Step 3 - 2: 3b-pole:  Vacant space

Presumably the same view is or may be described in other more scientifically established terms by astronomers. However, only "radiation pressure" or similar expressions shouldn't be enough to explain these "jumps" in the processes. (?)

b) End of fusion:
Here polarizations horizontally, contractions vertically: a"pole exchange".
(Regarded in the model as result in the very last step 0/00, equivalent 5', expression for the 5-dimensional motion in d-degree 0 of structure.)

Collapses of charge in step 3-2 on the left side of the middle

Left side of the border n <—|—> p + e + ν (anti-ν:
The mass depending steps for collapses should perhaps be regarded as smaller:

- White dwarfs (dw): degeneration of the charge polarity p - e. ("3-2,5")
- Neutron stars (n): polarity p+ <—> e- replaced by neutrons. ("3")
- Black holes (bl.h.): property of mass disappearing. ("3,5" - "4")

- Degeneration pressure is proportional to the density, obviously in two different steps 5/3  → 4/3:
At a density 1035 u/m3 the degeneration pressure is proportional to the density5/3,
At still higher density it's proportional to the density4/3, hence lower (!).
It sounds as if a certain border has to be passed, revealing such a border, - through stepwise released energy?

The polarizations horizontally: as through the FA -force.

What should here diagonals represent and vertical steps, the "relations"?
The logic seems to demand that diagonal arrows here point downwards, representing contractions. The FG -force in the illustration along the vertical axis.

- Hence, first suggestion is that they represent attraction forces around black holes and neutron stars, also then around white dwarfs (?). Cf. for instance that the rotational energy of neutron stars as pulsars is transmitted to their whole nebula, indicating such attraction bonds.

- Secondly they may mark the circular structures between centre and anticentre in d-degree step 3-2 of galaxies and solar systems. (From the perpendicular relation FG /FA .)

- Pointing to the unpolarized 5 - 5' - 5" levels, they could eventually also be defining new centres for aggregations of matter ? (And "corridors" of thrown out matter for new phases of contraction and fusion "the other way around", for solar systems, planets - star clusters - galaxies (galaxy clusters ?),
   If so, there should be such connections as between black holes and first phase of synthesis, H-He, between neutron stars and the second phase, between white dwarfs and third phase of synthesis?
   Cf. M-stars (below), coolest stars with heavy elements and molecules in spectral lines, also found near our galaxy centre, probably a black hole according to one theory.
   Vertical lines as number of steps 1-2-3: downwards: expression for sizes of these levels, (in last step to the right depending of depth of black holes).  

- Finally the diagonals in both life time and end figures could illustrate the combination of high density and high temperature created in the cores of stars, the combination of the opposite properties. It obviously have to imply a transformation of gravity to temperature "through work", in opposition to temperature as high kinetic energy. Or more adequate to high temperature as high spread of velocities? One example would be "M-sigma"-relations between high "mass" of black holes and spread of star velocities around them (stars corresponding to particles, see file Temperature)?
   (Cf. Big Bang: infinite density to pure kinetic energy, highest temperature.)

Generally in the figure there are more of structure and mass as structure in higher degrees, left side of the dimension chain, more of motions and kinetic energy in lower degrees, right half of the figure (thrown out matter), according to the model. A in our own solar system the sun represents most of the mass (~ left side of figure above), planets most of the impulse moment, i.g. most of kinetic energy.

An older figure:

Synthesis of elements in the periodic system - first 2 - 3 steps:

A series 2x2 , (x= 5-0) defines the number for electrons in orbitals s-p-d-f and additions for whole shells in the periodic system.

- 1st synthesis in stars H → He concerns elements in orbital s1,
- 2nd synthesis elements as C-N-O in orbital p1,
- 3rd and following steps of syntheses goes on up to Fe/Ni, elements at about the middle of orbital d1.

(These steps regard "endogen", "exothermic" reactions, with terms from biology and chemistry, which release energy and don't need energy from outside.)

1st synthesis is by astronomers assumed as the only one occurring in stars on the main sequence (first generation?). 2nd, 3rd and following syntheses in the phase as red giants.

The orbital elements as corresponding to illustration of phases above:

The numbers 4 x 1 = H → He in 1st synthesis could be noted.
There is, simplified, at least 4 stages of synthesis up to element Fe, 56 u, as exothermic, endogen, not demanding external energy. Examples of elements below:

Steps of synthesis as multiplications: 1 u x 4 →x 3 →x 2 → x 2:

1st phase x 4 4He s1
2nd phase x 3 12C (→14N →16O p1
3rd phase x 2 -24 Mg - 28Si - 32S s3-p2
4th phase x 2 56Fe (~ 2 x 28Si) d1

(Cf. "A-Z"-number chain below.)

A general statement connects synthesis of the heavier elements here to the sub-phases of smaller contractions in cores of "variables", circa 1/3 of red giants.

A suggestion is that the 3rd and 4th steps of fusion above could include features corresponding to spx- and spdx-hybridizations on the molecular level.

Spectral lines of elements from spectral classes of stars on the main sequence O →M:
(Simplified data from an older source, of course incomplete, but mainly in agreement with data from Wikipedia.)

The series implies a spectral development roughly from
s1 to p1 elements in O→B-types, to
d1-elements in A→F-types, stepwise towards more neutral elements
and molecular bands appearing from first p1+s1 type (CH) in G-stars to p2+d1 types (as TiO) in K- to M-stars.

5 → 3 - 2

5 → 4 - 1

5 → 0 - 00

The star series from O to M on the main sequence corresponds to decreasing masses according to the Hertzsprung-Russel diagram (HR). From hotter massive stars to cooler in the middle. K-stars on the main sequence are orange dwarfs, M-stars red dwarfs.
   Cf. white dwarfs as collapsed stars with minor mass on the other side of the middle.

Principle of mass dependence along diagonals, decreasing towards middle of the chain.
Compare mass dependence at collapses, figure "End of fusion..." above, left part of that illustration.

- H→He synthesis continues also in the shell of red giants.
- It's said to be a mystery that no red dwarfs (~ M-stars) are found without elements heavier than H, He. Why a mystery? Seems natural with proposed illustrations.
- The more massive the stars (with highest luminosity), the more of the whole scale for surface temperature they seem to involve in the phase as red giants. Also varying in periods and sub-periods.
   About "curious" B-stars with spectral lines from Mn (55 u) and Hg (~200 u) and other curiosities among the "Ap-stars" above, see below.

It seems to be a contradiction between the astronomers' statements that stars on the main series only synthesize H → He, and that all the spectral classes but the very first part of O-B-stars include spectral lines from increasingly heavier elements. The most accepted answer seems to be that all the following spectral classes are later generations of stars from clouds already containing matter thrown out from earlier red giants.
   It sounds however rather strange actually that an even series of stars roughly connected with increasingly heavy elements (and decreasing mass) should represent generations in Universe: lately born stars as mostly dwarfs? With still most matter in macrocosm as hydrogen H and helium He?
   A certain vagueness in the statements could make it allowed to ask if it really is impossible to imagine heavier elements also synthesized in deeper levels of cores in original stars? Unrecognized levels perhaps in most massive stars? With reference to the figure above? Are really newborn stars on the main sequence, if of a second (or 3rd?) generation, from clouds including many heavier elements, unable to synthezie still heavier elements from these?

Our sun is a G-star surrounded by inner planets containing heavy elements, in fact nearly all, even Uranium. It's assumed that the sun is a later generation of an earlier one, explaining these heavy inner planets, but why then in exactly the same place ? Couldn't the inner planets and the outer ones of light elements reflect inversely thrown out material from deeper levels of the same sun in older times?
   Observe G-stars at or near the middle in the figure above, related to d1-orbital elements as Fe and Ni, and the series of lighter elements towards the right, p and s-orbital elements:
   It seems illustrating the opposition between inner small planets dominated by Fe and Ni, and outer planets with dominating light elements.

It's in any case an accepted proposition that not only H→He synthesis but also the CNO-cycle does occur in our sun.

Three first synthesis:

   1. H → He. - s1-orbital
   2. CNO-cycle - p1-orbital elements (also producing He)
   3. Triple-alpha synthesis of C, carbon.

It could be observed that they also are 3 in number.

"A-Z-number chain", illustrating processes 1 and 2:
With the loop model the d-degrees 5(or 0) → 4 → 3 are defined simultaneously with d-degrees 2 ← 1 ← 0/00 (or 00), steps for s- and p-orbitals. Hence, in following illustration we may see the first three processes in a complete chain:

First two processes may be illustrated by the "A-Z" number chain, 2 ways to synthesize He, both in our sun on the main sequence. (From Chemical elements):
   If we take a dimension chain with superposed odd figure level and add 2-figure numbers vertically downwards, we get numbers as "A-Z"-numbers of primary elements:
   Exemplified: 94+74 = 168, 74 + 73 = 147, 73+52 = 126 etc.

Right half: scientists imagine a process:
1H12D13He2, x 2 (potentially 6Li3) → 4He2 + 2 x 1H1.)
Left half: CNO-cycle: (O)-N.C; intermediate steps as 13C etc. here excluded.

The figure illustrates a clear division of the two processes as between first and second half part of the chain.
   B, Boron, Be, Beryllium and Li, Lithium are elements that seldom are observed in star spectra, mostly found in interstellar "radiation". They are said to disintegrate ("decay") again towards He + n x p. Also in the CNO-cycle disintegration appears as 16O →12C + alpha (He): "A-Z"-numbers at steps 4 → 3 + 1 in the figure.

Hence, 2 cyclic processes is given for synthesis and disintegration for He-production; steps 4-3 and 2-1 corresponding to each other in the loop model. Polarizations outwards, as "decay", aggregations inwards, expressions for the complementary, opposite forces.

The fact that middle number for B is mostly found in interstellar space (and Be, 8-4, Li 6-3 as well, "numbers depending" directly and indirectly on B) may support the loop model. Lower steps possible to regard as debranched from higher degrees "meeting the other way around". (What about O (16-8) and N (14-7) in interstellar space - for symmetry?
   Left half C-N-O-(OH) gives the foundation for life structures.

- A special mystery, which the "A-Z"-figure eventually could shed some light upon, is the appearance of double OH-lines in spectrum from cool M-stars and in H+-clouds. (They should curiously correspond to two different velocities of the objects.)
   In the "A-Z"-chain we have suggested first number 18-9 from step 5 → 4 as corresponding to H20-OH (Z-number ionized), where one H goes the other way around, step 1 ← 0/00 . Spectral lines of H+ dominate from hottest O-B-stars, M-stars represent the coolest. Hence the mystery derives at it seems from opposite ends of the chain for stars with respect to temperature. The double spectral lines could reveal this connection between opposite objects?

(A correspondence to photolysis in macrocosm?)

Cf. the polarization already in big Hx-clouds between hot, thinner and cool, denser areas!

3rd process, triple-alpha:
It has been a problem for astronomers how carbon C have been created for the CNO-cycle in the sun, which presupposes C.
   In later years a hypothesis (by Hoyle) seems to be more or less proved that this creation is a result of "resonance" with scientists' term.
   The "energy" of one 8Be4 plus one 4He2 happens to be the same as the energy of one excited 12C6 .
   (The synthesis would depend on Be-production rapid enough to give time for its use in C-synthesis before Be disintegrated into He.)

In "A-Z"-number terms we get this 3rd process called "triple-alpha" in the middle of the chain, in step 3 - 2.
   Each whole step in the dimension chain (1 d-degree) corresponds to one alpha or He, number 42 as intervals (168 - 126 - 84 - 42 ).
   Sum of Be 84 + He 42 in A-Z-numbers = 126 = C.

The term "resonance" sounds as it could support the loop model with original polarizing steps towards middle of the chain and "border" in this step. "Energies" perhaps only equal in this step 5 → 3-2 ? Resonance as balance between acting polarizing-synthesizing forces (FG / FA) on underlying level).
   However, also C + He (alpha) have the same energy together as O, oxygen, (A-Z-numbers 126 + 42 = 168), which is said to explain the production of stable oxygen, in opposition to the CNO-cycle where oxygen disintegrates: O → C + alpha. The He-part of stable oxygen could perhaps derive from half Be (for symmetry), just be another alpha!


Elements heavier than Fe/Ni:
It has at least earlier been regarded as a problem by astronomers how these heavier elements are created, since their synthesis demands energy from some outer source. (Reactions could be called "exogen", "endothermic".)
   A simple answer to the question seems to be that stars for these synthesis uses own released energy from the fusion of lighter elements. Why not? That would be in accordance with polarities in the loop model of a dimension chain. Energy transport should follow as through "underground tunnels" inwards higher d-degrees:

The scientists' explanation today is that the heavier elements originate from "neutron capture" of lighter elements (slow or rapid as indicating a border between two types).
Returning to the figure of spectral types in the loop model:

With the properties Mass and Charge related as d-degrees 3 to 2, it may be seen as expressed in the reactions n <—> p + e (+ ν, anti-ν.
   Hence, "neutron capture" seems generally as one way to interpret the heavier elements.

(But from where all these neutrons in solar plasma?)

An additional view, suggested here, would be to interpret the neutron capture as an expression for the involvment of left part in the chain above: imagine the masses of heavier elements as defined, more or less indirectly (through "resonances"?), in left part of the chain through the steps in the right part where we have the "endogen" fusion of lighter elements. In accordance with the loop model.

Cf. perhaps inversions: all elements down to "about 150" u are said to undergo fission processes, the inversion 150 /\ 67. (10x), 67 a bit higher than highest stable isotope of Ni 60, end of right side fusion processes. 60 /\ 167 u (x 10x).

Ap-stars, temperature windows and the loop model:
It's observed that within a certain temperature interval, called a "temperature window", between B-5 and F-5, from stars objects called Ap-stars, there is odd concentrations of spectral lines from for instance lantanides, that's from elements in the f1-orbital, also from e.g. Hg in d3-orbital, hence really heavy elements (Eu ~152 u, Ho ~185 u, Hg ~ 200 u).
   "Chemically peculiar B-type stars" (B7-B9) have spectral lines of Mn, 55 u and Hg, 200 u.
   (There are also, in totally other contexts, talk about "windows" on the scale of electromagnetic waves. And something similar for sound waves, special frequencies giving resonances for different human organs in the body.)

With reference to views in the paragraph above and to the mentioned mysterious double spectral bands of OH, it seems possible to interpret the curious Ap-stars in a similar way, expressions for the loop connections between higher and lower steps in the dimension chain?
   With the figure illustrating connections of d-degree steps with the chain of orbitals, we have the f-orbitals in step 4-3, in the loop model connected with step 2-1, that of the p–orbital.

The supposed view however doesn't appear so simple as in the figure:
There is no fixed borders between the spectral classes with all subclasses, and it needs more data to find an eventual more precise connection, if one, between orbital elements on the right and left side of the picture. d1-orbital elements is mentioned first in A-F-stars but late B-stars B7-B9 shows spectral lines from Hg, a d3-element. And spectral class for stars showing much of f1-orbitals as lantanides isn't mentioned in that source.
Also for the fusion of heavier elements than Fe/Ni we can associate to "sp(d)-hybridizations" on the moleclar level, imagining similar kinds of additions for syntheses of those elements: s+p+d in numbers 2 + 6 + 10 = 18, highest orbital x (not in Nature), 8 (as 2 + 6) + orbital 6 in the figure below = 14, also the number of the f-orbital on the higher d-degree side of the middle...

Uranium - Hydrogen:
Cf. the relations between lightest and heaviest element in Nature, H and U, H 1 u and uranium 238 u: (from files Chemical elements):

The two halves of the dimension chain as triplets:

Here it should also be observed that taking the quotient between the two superposed numbers as representing opposite direction in the chain we get:

975 / 531 (x102) ≈ 2 x 92, Z-number of Uranium,

531 / 975 (x102)≈ 2 x 27, Z-number middle of Fe 26 Z and Ni 28 Z.

(Number 54 not only the surplus of neutrons in Uranium but also the "endogen" fusion.)

(To Chemical Elements here.)




© Åsa Wohlin
Free to distribute if the source is mentioned.
Texts are mostly extractions from a booklet series, made publicly available in year 2000


Synthesis of elements
and Spectral classes

1. Planet distances in AE - Exponent 3/2

2. Planet distances
- variation
of Bode's formula - 1/98

3. Planet distances out of a

4. A graph for planet distances in AE

Masses in Earth units

0. Planet masses
from the Exponent series

1. Masses of planets
from 1/98

2. Masses of planets from
a chain 2x2

3. Masses of planets from
simple triplet chains with exponent 9/4, [3/2]2


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