The stability of stars is a function of
the equilibrium condition, which balances the inward pull of gravity with the outward pressure of the thermodynamic energy
or enthalpy of the star (H=PV+U). The Jeans Mass MJ
and the Jeans Length RJ a used to describe the stability conditions for collapsing molecular hydrogen clouds to
form stars say, are well known in the scientific data base, say in formulations such as:
MJ=3kTR/2Gm
for a Jeans Length of:
RJ=√{15kT/(4πρGm)}=RJ =√(kT/Gnm²).
Now the Ideal Gas
(IG)-Law of basic thermodynamics states that the internal pressure P and Volume of such an ideal gas are given by
PV=nRIGT=NkT
for
n moles of substance being the Number N of molecules (say) divided by Avogadro's Constant L in n=N/L .
Since the Ideal Gas Constant RIG divided by Avogadro's
Constant L and defines Boltzmann's Constant k=RIG/L.
Now the statistical analysis of kinetic
energy KE of particles in motion in a gas (say) gives a root-mean-square velocity (rms) and the familiar 2.KE=mv²(rms)
from the distribution of individual velocities v in such a system.
It is found that PV=(2/3)N.KE as a total system described
by the v(rms).
Now set the KE equal to the Gravitational PE=GMm/R for a spherical gas cloud and you get the Jeans
Mass.
(3/2N).(NkT)=GMm/R with m the mass of a nucleon or Hydrogen atom and M=MJ=3kTR/2Gm as stated.
The Jeans'
Length is the critical radius of a cloud (typically a cloud of interstellar dust) where thermal energy, which causes the cloud
to expand, is counteracted by gravity, which causes the cloud to collapse. It is named after the British astronomer Sir James Jeans, who first derived the quantity; where k is Boltzmann's constant, T is the temperature of the cloud, r
is the radius of the cloud, μ is the mass per particle in the cloud, G
is the Gravitational Constant and ρ is the cloud's mass density (i.e.
the cloud's mass divided by the cloud's volume).
Now following
the Big Bang, there were of course no gas clouds in the early expanding universe and the Jeans formulations are not applicable
to the mass seedling Mo; in the manner of the Jeans formulations as given.
However, the universe's dynamics is in the form of the expansion parameter of GR and so the
R(n)=R max(n/(n+1)) scalefactor of Quantum Relativity.
So
we can certainly analyse this expansion in the form of the Jeans Radius of the first protostars, which so obey the equilibrium
conditions and equations of state of the much later gas clouds, for which the Jeans formulations then apply on a say
molecular level.
This analysis so defines the ylemic neutron stars
as protostars and the first stars in the cosmogenesis and the universe.
Let the thermal internal energy or ITE=H be the outward pressure in equilibrium with the gravitational potential
energy of GPE=Ω.
The Nuclear Density in terms of the superbrane parameter is ρcritical =mcritical
/Vcritical with mc the base nucleonic or ylemic neutronmass.
Vcritical
=(4π/3)Re 3 as the volume of the ylemic neutron as given by the classical electron radius
for superbrane quantisation/magnification Re=1010.λw /360=e*/2c2.
H=(molarity)kT
for molar volume in N=(R/Re)3 for dH=3kTR2/Re3.
Ω(R)= -∫GMdm/R = -{3Gmc²/(Re3)²}∫R4.dR=
-3Gmc².R5/Re6 for
dm/dR=d(ρV)/dR=4πρ.R²
and for ρ=3mc/4πRe³.
So dΩ(R)=-3Gmc2R4/(Re5)2=-16π²ρ²G.R4/3.
For equilibrium, the condition is that dH=dΩ as the minimum condition dH+dΩ=0. This gives: dH+dΩ=3kTR2/Re5-16Gπ2ρ2R4/3=0
and the ylemic radius as:
Rylem = √(kT.Re³/Gomc²).
as the Jeans Length precursor and progenitor.
The ylemic Jeans-Radii are all independent of the mass of the protostar
as a function of its nuclear generated temperature. Applied to the protostars of the neutronic ylem matter, those radii are
all neutron critical with respect to gravitational collapse, due to electron degeneracy as defined in the Chandrasekhar
white dwarf limit of 1.5 solar masses.
This spans from the 'First three minutes'-scenario of the (Weinberg cosmogenesis)
to 1.1 million seconds or about 13 days and encompasses the ordinary beta-minus decay of the common neutron - underpinning
radiaoactivity of the elements.
The upper limit defines a trillion degree temperature and a radius of over 40 km:
the typical Schwarzschild solution gives a typical ylem radius of so 7.4 km and the lower limit specifies the 'mysterious'
planetesimal limit of 1.8 km.
For long a cosmological conundrum, it could not be modelled just how the molecular
and electromagnetic forces applicable to conglomerate matter particles (say hydrogen gas as dust) on the quantum scale of
molecules could become strong enough to form say mass agglomerations so 1 km across and required for ordinary gravity to assume
interactive control.
The ylemic lower limit so indicates that it is indeed an ylemic temperature of then 1.2 Billion
Kelvin, which is responsible under the auspices of the Ylem-Jeans formulation; which subsequently becomes applicable to the
normal collapse of hydrogenic atoms in summation and the evolutionary scenarios of stars.
The stellar evolution from the ylemic(dineutronic) templates is well established in QR and confirms
most of the Standard Model's ideas of nucleosynthesis and the general Temperature cosmology. The standard model is correct
in the temperature assignment, but is amiss in the corresponding 'size-scales' for the cosmic expansion.
The Big Bang cosmogenesis describes the universe as a Planck-Black Body Radiator,
which sets the Cosmic-Microwave-Black Body Background Radiation Spectrum (CMBBR) as a function of n as T4=18.2(n+1)²/n³
and derived from the Stefan-Boltzmann-Law and the related statistical frequency distributions.
We have the GR metric for Schwarzschild-Black Hole Evolution as RS=2GM/c²
as a function of the star's Black Hole's mass M and we have the ylemic Radius as a function of temperature only as
Rylem=√(kT.Re³/Gomc²).
The nucleonic mass-seed mc=Planck-Mass(mP).Alpha9 and
Gomc² is constant in the partitioned n-evolution of mc(n)=Yn.mc
and G(n)=Go.Xn.
Identifying the ylemic Radius
with the Schwarzschild Radius then indicates a specific mass a specific temperature and a specific radius.
Those we call the Chandrasekhar Parameters:
MChandra=1.5 solar Masses=3x1030 kg and RChandra=2GoMChandra/c²
or 7407.40704..metres, which is the typical neutron star radius inferred today.
TChandra=RChandra 2.Gomc2/kRe3
=1.985x1010 K for Electron Radius Re and Boltzmann's Constant k.
Those Chandrasekhar parameters then define a typical neutron star with a uniform temperature of 20
billion K at the white dwarf limit of ordinary stellar nucleosynthetic evolution (Hertzsprung-Russell or HR-diagram).
The Radius for the massparametric Universe is given in R(n)=Rmax(1-n/(n+1))
correlating the ylemic temperatures as the 'uniform' CMBBR-background and we can follow the evolution of the ylemic
radius via the approximation:
Rylem=0.05258..√T=(0.0753).[(n+1)2/n3](1/8)
Rylem(npresent=1.1324..)=0.0868
m* for a Tylem(npresent)=2.73 K for the present time
tpresent=npresent/Ho.
What is nChandra?
This would describe the size of the universe as the uniform temperature CMBBR today manifesting
as the largest stars, mapped however onto the ylemic neutron star evolution as the protostars
(say as nChandra'),
defined not in manifested mass (say neutron conglomerations), but as a quark-strange plasma, (defined in QR as the Vortex-Potential-Energy
or VPE).
R(nChandra')=Rmax(nChandra'
/(nChandra'+1))=7407.40741.. for nChandra'=4.64x10-23 and so a time of tChandra'=n
Chandra'/Ho=nChandra'/1.88x10-18=2.47x10-5 seconds.
QR defines the Weyl-Temperature limit for Bosonic Unification as 1.9 nanoseconds at a
temperature of 1.4x1020 Kelvin and the weak-electromagnetic unification at 1/365 seconds at T=3.4x1015
K.
So we place the first ylemic protostar after the bosonic unification
(before which the plenum was defined as undifferentiated 'bosonic plasma'), but before the electro-weak unification,
which defined the Higgs-Bosonic restmass induction via the weak interaction vector-bosons and allowing the dineutrons to be
born.
The universe was so 15 km across,
when its ylemic 'concentrated' VPE-Temperature was so 20 Billion K and we find the CMBBR in the Stefan-Boltzmann-Law
as T4=18.20(n+1)2/n3 =1.16x1017 Kelvin. So the thermodynamic
temperature for the expanding universe was so 5.85 Million times greater than the ylemic VPE-Temperature; and implying that
no individual ylem stars could yet form from the mass seedling Mo. The universe's expansion however cooled
the CMBBR background and we to calculate the scale of the universe corresponding to this ylemic scenario; we simply calculate
the 'size' for the universe at TChandra=20 Billion K for TChandra4 and we then find nChandra=4.89x10-14
and so for
tChandra=26,065 seconds or so 7.24 hours.
The Radius R(nChandra)=7.81x1012 metres or 7.24 lighthours.
This is about 52 Astronomical Units and an indicator for the largest possible star in
terms of radial extent and the 'size' of a typical solar system, encompassed by supergiants on the HR-diagram.
We so know that the ylemic temperature decreases in direct proportion to the square
of the ylemic radius and one hitherto enigmatic aspect in cosmology relates to this in the planetesimal limit. Briefly,
a temperature of so 1.2 billion degrees defines an ylemic radius of 1.8 km as the dineutronic limit for proto-neutron stars
contracting from so 80 km down to this size just 1.1 million seconds or so 13 days after the Big Bang.
This then 'explains' why chunks of matter can conglomerate via molecular
and other adhesive interactions towards this size, where then the accepted gravity is strong enough to build planets and moons.
It works, because the ylemic template is defined in subatomic parameters reflecting the mesonic-inner and leptonic
outer ring boundaries, the planetesimal limit being the leptonic mapping. So neutrino- and quark blueprints micromacro
dance their basic definition as the holographic projections of the spacetime quanta.
Now because the Electron Radius is directly proportional to the linearised wormhole perimeter and then
the Compton Radius via Alpha in Re=1010 λW/360=e*/2c2=Alpha.RC
, the characteristic Chandrasekhar White Dwarf Limit should be doubled to reflect the protonic diameter mirrored in the classical
electron radius.
Hence any star experiencing
electron degeneracy is actually becoming YLEMIC or DINEUTRONIC, the boundary for this process being the Chandrasekhar
mass. This represents the subatomic mapping of the first Bohr orbit collapsing onto the leptonic outer ring in the
quarkian wave-geometry.
But this represents the Electron
Radius as a Protonic Diameter and the Protonic Radius must then indicate the limit for the scale where proton degeneracy would
have to enter the scenario. As the proton cannot degenerate in that way, the neutron star must enter Black Hole phasetransition
at the
Re/2 scale, corresponding to a mass of 8MChandra=24x1030 kg* or 12 solar
masses.
The maximum ylemic radius so is found from the
constant density proportion ρ=M/V:
(Rylemmax/Re)³=MChandra/mc
for Rylemmax=40.1635 km.
The corresponding ylemic
temperature is 583.5 Billion K for a CMBBR-time of 287 seconds or so 4.8 minutes from a n=5.4x10^-16, when the universe
had a diameter of so 173 Million km.
But for a maximum nuclear
compressibility for the protonic radius, we find:
(Rylemmax/Re)³=8MChandra/mc
for Rylemmax=80.327 km, a ylemic temperature of 2,334 Billion K for a n-cycletime of 8.5x10-17
and a CMBBR-time of so 45 seconds and when the universe had a radius of 13.6 Million km or was so 27 Million km
across.
The first ylemic protostar vortex was at that time
manifested as the ancestor for all neutron star generations to follow. This vortex is described in a cosmic string encircling
a spherical region so 160 km across and within a greater universe of diameter 27 Million km which carried a thermodynamic
temperature of so 2.33 Trillion Kelvin at that point in the cosmogenesis.
This vortex manifested as a VPE concentration after the expanding universe had cooled to allow the universe
to become transparent from its hitherto defining state of opaqueness and a time known as the decoupling of matter (in the
form of the Mo seedling partitioned in mc's) from the radiation pressure of the CMBBR photons.
The temperature for the decoupling is found in the galactic scale-limit modular
dual to the wormhole geodesic as λW=1022 metres or so 1.06 Million ly and its luminosity
attenuation in the 1/e proportionality for then 388,879 lightyears as a decoupling time ndc. A maximum galactic
halo limit is modulated in 2πλW metres in the linearisation of the Planck-length encountered
before in an earlier discussion.
R(ndc)=Rmax(ndc/(ndc+1))=1022
metres for ndc=6.26x10-5 and so for a CMBBR-Temperature of about T=2935 K for a galactic protocore
then attenuated in so 37% for ndcmin=1.0x10-6 for R=λW/2π and
ndcmax=3.9x10-4 for R=2πλW and for temperatures of so
65,316 K and 744 K respectively, and descriptive of the temperature modulations between the galactic cores and the
galactic halos.
So a CMBBR-temperature of so 65,316
K at a time of so 532 Billion seconds or 17,000 years defined the initialisation of the VPE and the birth of the first ylemic
protostars as a decoupling minimum. The ylemic mass currents were purely monopolic and known as superconductive cosmic
strings, consisting of nucleonic neutrons, each of mass mc.
If we assign this timeframe to the maximised ylemic radius and assign our planetesimal limit of fusion temperature
1.2 Billion K as a corresponding minimum; then this planetesimal limit representing the onset of stellar fusion in a
characteristic temperature, should indicate the first protostars at a temperature of the CMBBR of about 744 Kelvin.
The universe had a tremperature of 744 K for ndcmax=3.9x10-4
for R=2πλW and this brings us to a curvature radius of so 6.6 Million lightyears and an 'ignition-time'
for the first physical ylemic neutron stars as first generation protostars of so 7 Million years after the Big Bang.
The important cosmological consideration is that
of distance-scale modulation.
The Black Hole Schwarzschild metric
is the inverse of the galactic scale metric.
The linearisation
of the Planck-String as the Weyl-Geodesic and so the wormhole radius in the curvature radius R(n) is modular dual
and mirrored in inversion in the manifestation of galactic structure with a nonluminous halo a luminous attenuated diameter-bulge
and a superluminous (quasar or White Hole Core).
The core-bulge
ratio will so reflect the eigenenergy quantum of the wormhole as heterotic Planck-Boson-String or as the magnetocharge
as 1/500, being the mapping of the Planck-Length-Bounce as e=lP.c²√Alpha onto the electron
radius in e*=2Re.c².
From Tony
B. www.tonyb.freeyellow.com
