Section VII

VII. PHYSICS IN EACH WINTER PER CYCLE

The familiar laws of physics that govern both red and blue summer evolution have processes that go in only one direction. Nuclear fusion (nucleosynthesis) steadily changes the universal mixture of nuclides, Kelvin contraction causes canister MDGOs to steadily shrink, etc. To have a viable (eternal) cyclic cosmology, it is necessary to have unfamiliar laws of physics during each winter that undo some of the results of evolution during the other seasons.
The most important winter task is to return the universal mixture of nuclides (averaged over suitably large volumes) to the same initial state at the beginning of each red and blue spring—reverse nucleosynthesis (RN). This section will examine various topics that will define the difference between winter and summer physics.

A. Particle census

As a prelude to a discussion of RN, it is useful to consider a simple model for the most important material constituents of the universe (proton, neutron, electron, and the electron-flavor neutrino and antineutrino). Furthermore, the model will consider only two weak-interaction red and blue summer processes: \[\begin{array}{l}{p^ + } \to {n^0} + {e^ + } + \nu (e){\rm~{ (fusion),}}\\{n^0} \to {p^ + } + {e^ – } + \bar v(e){\rm~{ (beta~decay)}}{\rm{.}}\end{array}\tag{7.1}\] Next, define mean densities (number of particles per unit volume averaged over sufficiently large volumes of space) which will depend only on time. Eq. (7.1) and electrical charge conservation require the following constraints: \[\begin{array}{c}{N_p}\left( \tau \right) + {N_n}\left( \tau \right) = {N_{RN}}{\rm{,}}\\{N_n}\left( \tau \right) – {N_\nu }\left( \tau \right) + {N_{\bar v}}\left( \tau \right) = {\vartheta _{RN}}{N_{RN}}{\rm{,}}\\{N_p}\left( \tau \right) = {N_e}\left( \tau \right){\rm{.}}\end{array}\tag{7.2}\] For NCNG, \({N_{RN}}\) and \({\vartheta _{RN}}\) are universal constants. Let \(\tau = 0\) correspond to the start of the red or blue spring transition. I have chosen \({N_\nu }\left( 0 \right)\) and \({N_{\bar v}}\left( 0 \right)\) to be very small. It is thought that our early universe (start of red summer) consisted of about seven protons per neutron, in which case \({\vartheta _{RN}} = 0.125\). It is also thought that\({N_{RN}} = 0.25/{m^3}\) based on LCDM (now suspect). These values represent the desired initial state of each half-cycle. During summers \(d{N_\nu }\left( \tau \right)/d\tau > 0\) and \(d{N_{\bar \nu }}\left( \tau \right)/d\tau > 0\). Winter requires \(d{N_\nu }\left( \tau \right)/d\tau < 0\) and \(d{N_{\bar \nu }}\left( \tau \right)/d\tau < 0\).

B. Winter changes

The task of returning the winter universe to its initial state does not require changing the winter strong and electromagnetic forces from their summer version—these forces are independent of season. Only the weak interactions and gravitation will change. In winter, fusion must be stopped. One way to stop fusion is the elimination of high temperatures and pressures needed—turn off local gravity. Another way to stop the processes of Eq. (7.1) is to favor a reverse, \[\begin{array}{l}\bar v(e) + {p^ + } \to {n^0} + {e^ + }{\rm{,}}\\\nu \left( e \right) + {n^0} \to {p^ + } + {e^ – }{\rm{.}}\end{array}\tag{7.3}\] Eq. (7.3) requires a winter change in the weak interactions.
I believe the following changes in the winter version of the weak interactions will be sufficient: (1) The PMNS matrix (\({U_{FM}}\)) will be diagonalized. (2) The electron-flavor neutrino mass will be increased. (3) The W boson mass will be decreased. (4) The weak coupling-constant, \({g_W}\), (W-fermion vertex) will be increased. (5) The Z boson coupling-constant and mass will retain their summer values. These changes are summarized: \[\begin{array}{c}{U_{FM}} = U_{FM}^S\left( {1 – {K_W}({\phi _{ep}})} \right) + {\delta _{FM}}{K_W}({\phi _{ep}}){\rm{,}}\\{m_{\nu e}} = m_{\nu e}^S\left( {1 – {K_W}({\phi _{ep}})} \right) + m_{\nu e}^W{K_W}({\phi _{ep}}){\rm{,}}\\{m_W} = m_W^S\left( {1 – {K_W}({\phi _{ep}})} \right) + m_W^W{K_W}({\phi _{ep}}),\\{m_Z} = m_Z^S,\\{g_W} = g_W^S\left( {1 – {K_W}({\phi _{ep}})} \right) + g_W^W{K_W}({\phi _{ep}}){\rm{,}}\\{g_Z} = g_Z^S,\\{K_W}({\phi _{ep}}) = 0.5\left( {1 – \tanh \{ {\Gamma _W}[E({\phi _{ep}}) – {E_W}]\} } \right),\end{array}\tag{7.4}\] where \({\Gamma _W}\) and \({E_W}\) are universal constants (tabulated in Appendix Z) that govern when and how rapidly the weak interaction values change between winter and summer.
It is important to understand that Eq. (7.4) represents a list of what is necessary for RN, not how the goal is achieved. The weak interactions are radically different in winter compared to the existing theory for summer. An entire reformulation of the weak interactions is necessary,
The S superscript is the summer value and W superscript is for winter. The winter electron-flavor neutrino mass is chosen to be \(m_{\nu e}^W = 30{\rm{ Mev}}\). The tiny \(m_{\nu e}^S\) will be neglected in what follows. The winter W boson mass (\(m_W^W\)) and the winter coupling-constant (\(g_W^W\)) are chosen so that the universal neutron conversion processes of Eq. (7.3) can proceed at a rate sufficient to return the universe to the desired initial state during the physical time allotted to winter. The rationale for these choices will be clarified below.
Note that there are 2856 nuclides (\( \le \) Pu245) that have been studied theoretically or observed by experiment, of which 273 are stable against all decay mechanisms in all seasons. All 2856 can be in play during winter. The attenuation process must leave significant amounts of only four nuclides (H1, H2, He3, He4) at the end of winter and only infinitesimal amounts of the other nuclides—the desired initial state of the universe.
I will explain choice (1). The summer universe is filled with electron-flavor neutrinos, but the second and third generation neutrinos are rare. During winter, a \(\nu \left( e \right)\) inflight cannot initiate the attenuating process of Eq. (7.3) all the time if \({U_{FM}}\) is not diagonal, thus requiring a longer winter. (2): The choice of 30 Mev makes \(\nu \left( e \right)\) heavy enough so that none of the 2856 nuclides can undergo either positron decay or beta decay during winter—only the processes of Eq. (7.3) can occur: (3) and (4). These changes make the cross section for the processes that can occur many orders of magnitude larger in winter—shorter physical time to arrive at the initial state. (5): The Z interaction causes scattering events that drain needed energy from any \(\nu \left( e \right)\) inflight during winter—keep the Z cross section weakly small. I have chosen the following gravitational changes in winter including five new universal constants (\({Q_{GC}}(q,1)\)) tabulated in Appendix Z: \[\begin{array}{l}{Q_{GC}}[1,E({\phi _{ep}})] = [1 – {K_G}({\phi _{ep}})] + {K_G}({\phi _{ep}}){Q_{GC}}(1,1),\\{Q_{GC}}[2,E({\phi _{ep}})] = [1 – {K_G}({\phi _{ep}})] + {K_G}({\phi _{ep}}){Q_{GC}}(2,1),\\{Q_{GC}}[3,E({\phi _{ep}})] = [1 – {K_G}({\phi _{ep}})] + {K_G}({\phi _{ep}}){Q_{GC}}(3,1),\\{Q_{GC}}[4,E({\phi _{ep}})] = [1 – {K_G}({\phi _{ep}})] + {K_G}({\phi _{ep}}){Q_{GC}}(4,1),\\{Q_{GC}}[5,E({\phi _{ep}})] = [1 – {K_G}({\phi _{ep}})] + {K_G}({\phi _{ep}}){Q_{GC}}(5,1),\\{K_G}({\phi _{ep}}) = 0.5\left( {1 – \tanh \{ {\Gamma _G}[E({\phi _{ep}}) – {E_G}]\} } \right),\end{array}\tag{7.5}\] where \(E({\phi _{ep}})\) is developed leading to Eq. (2.17), Note that I have chosen to provide the possibility of a slightly different time and rate for gravity changes versus the weak interactions.
The timing and order of Eq. (7.4) and Eq. (7.5) have been chosen to marginalize the effects of the bubble era. In both cases, the value of constants of interest are nearly the same on both sides of the bubble wall.

C. Reverse nucleosynthesis

RN is extremely complex—so much so that a simplified model is necessary. During winter, the stable nuclides and free neutrons present at the start of winter must be converted by the end of winter into H1, He4, relic amounts of H2 and He3, and very tiny amounts of heavier nuclides. Furthermore, electron flavor neutrinos, and antineutrinos must be attenuated into relic amounts. The heavier nuclides are eliminated at the beginning of winter. The remainder of winter is devoted to converting He4 into H1.
The strong interactions will be unchanged in winter, so nuclear physics and the properties of the nuclides will be important. A good source is the website for the Brookhaven National Nuclear Data Center (NNDC), which has an interactive chart of all 2856 studied nuclides. The details of RN will be outlined in the following sub sections.

1. Attenuation model

The rate of attenuation of nuclear species in winter requires knowledge of the neutrino and antineutrino densities (#/cubic meter), their energy spectrums, and the densities of each of the 2856 nuclides that could exist during the process everywhere in space. This requirement overwhelms us from the start. Only the crudest estimates of these factors are available at present, and one has no idea about their values 42 billion years in the future when winter will begin. Also needed are 2856 neutrino-initiated reaction cross sections, of which only a few have been calculated (for summer). A precise evolution of the attenuation process will require super-computer computations and many years of research. Simplifying assumptions are needed now.
First, neglect antineutrinos and free neutrons. Those densities are likely small compared to others, and their neglect will halve the number of nuclides in play. The determination of relic H2 will be lost in this approximation. Next, construct an initial abundance of stable nuclei for the start of winter, which mimics present day estimates but with a bias toward more neutrons. Then neglect many of the smaller entries. Figure 6 illustrates the start of winter abundance that will be used. The model will have 54 stable species instead of 273, and 406 nuclides in play. Furthermore, all these model nuclides will be assumed to reside within canisters.

Figure 6.Log10 of the number of nuclides per cubic meter versus proton number, Z, at the start of winter.

It is important that attenuation is not influenced significantly by the random distribution of canisters in space. That result can be obtained by having the attenuation process take place over a sufficiently long physical time. In that case, even the slowest heavy neutrino can travel through a collection of neutron rich canisters. I have chosen 300 billion years for each winter per cycle for this model. A major simplification results—the densities will only depend on physical time.
A winter neutrino will travel at the slowest velocity outside of canisters and then speed up considerably in transit across an intercepted canister. All the neutron rich canister mass is concentrated within or near the MDGO at the center of the canister (a radius of roughly 2 million light-years). The transiting neutrino will follow an orbit within the canister that has a nearest approach to the center. Attenuation may only occur when the nearest approach is within the central MDGO—a specific range of impact parameters. Even then, attenuation may not occur. If attenuation does not occur the neutrino will exit the canister at a deflected angle without loss of kinetic energy. Thus, the path of a winter neutrino is a random walk through a density of randomly situated canisters until it is absorbed. I believe that the random walk justifies the attenuation model of uniform nuclide density, which then implies uniform winter neutrino flux.
The universal constants of Eq. (7.2) can be used, e.g., the initial neutron density associated with Figure 6 is \(0.385{N_{RN}}\), and the initial neutrino density for this model must be \(0.260{N_{RN}}\). The proton/neutron ratio of Figure 6 is 1.597 (end of red or blue fall) compared to 7.0 (start of red or blue spring).

2. Neutrino model

The electron-flavor neutrino spectral-densities can be approximated by a series of delta functions as in the following profile: \[\begin{array}{c}{n_\nu }\left( {{E_\nu },\tau } \right) = {N_{RN}}\sum\limits_{k = 1}^K {{{\rm P}_k}(\tau )\,} \delta \left( {{E_\nu } – {E_{\nu k}}} \right){\rm{,}}\\{N_\nu }(\tau ) = {N_{RN}}\sum\limits_{k = 1}^K {{{\rm P}_k}(\tau )} {\rm{,}}\end{array}\tag{7.6}\] where \({E_{\nu k}} = k\Delta {E_\nu }\), \(\Delta {E_\nu } = (20.0/K){\rm{ Mev}}\)in summer, and \({N_{RN}}\) is the universal constant of Eq. (7.2). I have assumed that a neutrino in-flight during summer will have the same momentum in winter—the mass change will alter only the energy. Therefore, the winter values of neutrino energy will be \({E_{\nu k}} = {[{(k\Delta {E_\nu })^2} + {(m_{\nu e}^W{c^2})^2}]^{1/2}}\). \({{\rm P}_k}(\tau )\) is dimensionless and continuous across red or blue spring or fall transitions. The start of winter corresponds to \(\tau = 0\), and \({N_\nu }\left( 0 \right)/{N_{RN}} = 0.260\) as described above. A suitable model would have \(K = 500\), and \({{\rm P}_k}(0)\) would rise to a peak at \(k = 10,\) (approximating the pp branch for solar neutrinos) followed by an exponential decline \( \propto \exp ( – \chi k)\) thereafter. The attenuation model uses \(\chi = 0.018\), and Figure 7 shows \({\log _{10}}{{\rm P}_k}(\tau )\) at the start and end of winter. The higher energy neutrinos are exhausted to a much greater extent due to the energy dependence of the reaction cross section for He4.

Figure 7.Log10 of the dimensionless neutrino spectral density defined in Eq. (7.6) versus the total winter neutrino energy. The blue curve is at the start of winter and red is at the end of winter.

3. Neutrino initiated processes

A general electron-flavor neutrino-initiated process (NIP) can be represented as follows: \[\begin{array}{l}\nu \left( e \right) + {[A,Z]_0} \to \\{[A – a,Z – z + 1]_j} + \{ a,z\} + {e^ – }\end{array}\tag{7.7}\] where [..] are nuclides, the subscript 0 is the ground state, and \(j \ge 1\) would be an exited state. The ejected state {..} in what follows can be nothing (\(a = z = 0\)), one or more protons, or He4 (alpha particle). The high energy of the winter neutrino makes the probability of the electron in Eq. (7.7) being captured negligible.
The reaction cross section for Eq. (7.7) is important for RN, but it has only been calculated for a few NIPs [11], otherwise the calculations are extremely difficult. There will be an important NIP, \(\nu \left( e \right) + {\rm{He4}} \to {\rm{He3 + }}{p^ + } + {e^ – }\), that illustrates the problem. This NIP is the inverse of the theoretical hep process, one branch of the proton cycle in stars. Two decades of theoretical work were required to get a convergent estimate for the hep process [12], but this research is not useful for RN.
There is a subset of Eq. (7.7) that can be calculated with reasonable accuracy, the case where {} = 0. If the positron decay half-life in summer of the final state is known—the inverse of the NIP, \({[A,Z + 1]_j} \to {[A,Z]_0} + {e^ + } + {\nu _e}\)—then the corresponding NIP (\({\nu _e} + {[A,Z]_0} \to {[A,Z + 1]_j} + {e^ – }\) ) is known. The underlying assumption is that the nuclear matrix elements are independent of energy and are the same for NIP and inverse NIP, and that the probabilities and energy dependence of transitions are dominated by the density of final states. See the first half of Appendix I for more details about NIPs.

4. General attenuation

Dimensionless nuclide densities can be defined, \({Y_j}(\tau ) = N(j,\tau )/{N_{RN}}\), where j corresponds to an entry in a table of the 2856 nuclides having positive binding energy. There is a specific atomic number, \({A_j}\), and proton number, \({Z_j}\), for each entry. The second half of Appendix I has details about the physical time evolution of the \({Y_j}(\tau )\) set. The figures below are based on the following requirements, \[\begin{array}{l}{N_\nu }\left( {{\rm{winter – end}}} \right)/{N_\nu }\left( {{\rm{winter – start}}} \right) = {10^{ – 4}},\\\left( {g_W^Wm_W^S/g_W^Sm_W^W} \right) = 4.3404{\rm{x}}{10^5}.\end{array}\tag{7.8}\] Figure 8 shows the number of nuclides having \(Y > {10^{ – 20}}\) as a function of time. This number quickly grows to 404 as nuclides start moving down their attenuation chains, but they must funnel through an ever-smaller set of recipient nuclides. All must pass through C10, and then after 819 million years only H1, He3, and He4 are left along with an extremely tiny amount of relic nuclides heavier than He4. That phase represents only 0.27% of winter.

Figure 8.Number of nuclides undergoing attenuation versus time.

Figure 9 shows details for three important nuclides—C10, C12, and O16. C12 and O16 are stable and plentiful at the start of winter but are eliminated very quickly. C10 has a smaller reaction cross section than C12, and it serves as the last storehouse for heavier nuclides before they are converted to He4.

Figure 9.Dimensionless density functions, Y (defined before Eq. (I.5)), for three nuclides versus time. C10 is the red curve, O16 is blue, and C12 is green.

Figure 10 shows the slow attenuation of He4 and neutrinos over the entire winter. Throughout the later part of this period \(Y\left( {{\rm{He3}}} \right)/Y\left( {{\rm{He4}}} \right) = 6.07 \times {10^{ – 5}}\). The relic density of He3 depends on the relative size of the reaction cross sections for both He3 and He4. For this model He4 was estimated and He3 was chosen to give the asymptotic ratio above. The actual ratio is poorly known, but it is thought to be of the order shown. The asymptotic density of He4 corresponds to a proton/neutron ratio of seven at the end of winter as required for this model.

Figure 10.Dimensionless density functions, Y, for He4 (blue) and neutrinos (red) versus time.

Every aspect of reverse nucleosynthesis in this model is governed by the assumption that the reaction cross section for He4 is significantly smaller than those of the nuclides that have high neutrino-energy thresholds for their NIPs. The estimation process of Sec. VII(C3) bears out this assumption for those few nuclides that are well known.

D. Distribution of matter during winter

The model of subsection C above has been simplified by treating matter as being distributed uniformly in winter. That model served a useful purpose, how much time is required to return the universe to the desired early summer state? One has discovered that almost all of winter is used to convert helium into hydrogen—both widely distributed. However, some nuclides are distributed in a lumpy fashion during summer (and winter as well), e.g., iron. What is their fate during winter? Section VII (C.1) justifies using the average flux of winter neutrinos to study the fate of specific lumps of nuclides.
NCNG has a new sequestration of matter featuring canisters on the largest scale. A ghostly MDGO accounts for a significant portion of the canister mass. I have no clue what the average mass density is for the universe. The number I have used (Appendix Z) is unreliable (based on LCDM). Worse yet, the currently concordant universal abundance of nuclides is unreliable as well. In the next subsection, the fate of stars and stellar cinders will be studied. This subsection will study the winter fate of lumpy relics from summer (subject to the uncertainties of unreliable constants).
What are lumpy summer objects? They are planets, planetary cinders, asteroids, and small objects that I will call rocks. When a star dies, its planets can be gasified if close enough. If farther away, only the core of the planet may survive (planetary cinders). Asteroids seem to be big rock piles weakly held-together by local gravity in summer. Summer rocks are distantly associated with stars, but when the star dies, the rocks will eventually disperse. All these summer types will be distributed throughout inter-stellar space.
The second event in the fall transition is turning off local gravity. Any stellar systems created late in summer will disassemble after the transition, and their planets will disassemble and cool as well. Asteroids will disperse as rocks. An early winter galaxy will consist of a vast amount of gas, a sparse collection of large planetary core parts, and a vast collection of rocks, and dust (molecular size rocks). The first event in the fall transition is changing the weak interactions—RN gets a slight head start before winter starts.
The fate of lumpy galactic constituents in winter is extremely complex. An example will clarify the process. Imagine an iron (Fe56) sphere of radius \({R_{LUMP}}\) at the start of winter. The properties of metallic iron will hold the lump together despite the lack of gravitational binding. This lump will be bombarded by a uniform (very faint) flux of heavy neutrinos (\({\nu _e}\)) for billions of years—RN in progress. Each \({\nu _e}\) will initiate a NIP within the lump. The mean free path for the most common winter neutrino that collides with the iron ball immediately after the second transition is only 6 millimeters. Furthermore, the reaction of this winter neutrino will leave behind an Fe55 nuclide, a proton, and an energetic electron. The energetic electron will heat the locale and eventually join the proton to form a hydrogen atom in the locale. The incident neutrino can strike the ball surface from any angle, so the average penetration would be less than 6 millimeters. A scenario emerges.
The fate of a winter lump is determined by the NIPs generated in a thin zone at the surface of the lump. The probability that a \({\nu _e}\) will be absorbed is a decreasing function of distance from the surface (depth). Thus, each lump will have a profile of nuclide constituents versus depth that is time dependent. The profile consists of nuclides that are on the attenuation chain for the material at that depth at the start of winter. The nuclide at the surface will move lower in the attenuation chain (toward C10) with time, whereas the nuclide at the depth of the zone remains unchanged. When the surface nuclide reaches a point where the surface lump structure will disassemble into gas and dust, the surface will start moving inward. That point (lower than or equal to A40) is inevitable since there are many lower nuclides that are gaseous. Furthermore, hydrogen trapped in the lump would weaken the structural integrity of the lump material.
The fate of lumps clearly depends on size. Planetary core parts will survive winter almost intact. Small rocks will be converted to gas and dust. Larger rocks will shrink but survive winter depending on their initial size and composition.
Rocks play an important role in NCNG. The MDGO in every canister generates Xray radiation in all seasons (Appendix F). The energy of the Xray photons is of order 1000 ev and they form a universal Xray background. The only way a background Xray photon can be destroyed is by being stopped in matter of sufficient thickness. There must be an equilibrium between the endless creation of canister Xray photons and the endless destruction of these photons by matter. The luminosity of the background is faint, so the destruction must use matter efficiently. A large lump is overkill. A tiny lump will not stop the Xray. A rock of sufficient size is best, and there must be a significant numerical density of them throughout the universe.

E. The fate of boundary and stellar-cinder objects in early winter

All galactic stars are created during the period extending from turning on local gravity (at the end of winter) to turning off local gravity (at the beginning of winter). During that period a star can die and create three types of stellar cinders (WD, CCNS, CCBO) and gas. That topic was discussed in section VI(E). At the beginning of that duration, a single CCBO near the galactic center will grow during the duration to become a MBO at the center of the galaxy. That topic was discussed in section VI(G). During the summer, light-weight lumpy objects can form, and their fate during winter is discussed in section VII(D).
In this subsection, the fate of major objects existing when local gravity is turned off will be discussed (star, CCBO, CCNS, WD, and MBO). Recall that fusion is turned off just before the end of the duration.
Any star that exists at the off local gravity transition will disperse into a diffuse gas in winter—star evaporates. In what follows, evaporation means that the constituents of the object are dispersed sufficiently so that the constituent matter is efficiently recycled by RN into hydrogen during winter. The information about the object does not survive winter.
A WD cinder consists of electron degenerate matter (EDM) which retains the identity of the constituent elements that formed it since the nuclides remain intact. The off local gravity transition for a WD will disperse diffuse constituent gases (largely carbon and oxygen)—WD evaporates.
A CCNS is a mixture of EDM (iron) and denser neutron-soup. The mixture has EDM (iron) on the surface, soup at the center, and a combination between. The soup has lost the identity of the matter that formed it. The local gravity transition for a CCNS will disperse into iron and a diffuse neutron gas. During winter, neutrons are efficiently recycled into hydrogen. The mixture of iron and neutrons depends on the mass of the CCNS. Heavier objects will have less iron and this iron will likely be diffuse. Light objects will have fewer neutrons, and the iron could be somewhat chunky rather than diffuse. In either case, little iron will survive RN during the winter, so the object-information is lost—CCNS evaporates.
The source of a recently created CCBO is similar to a CCNS in composition— EDM on the surface, neutron soup at the center, and a combination between. However, the mixture is the reverse of the CCNS object. The lightest CCBO has the least iron, and the iron content increases with mass. The boundary disappears at the end of the off local gravity transition, so the fate of a CCBO is much the same as a CCNS—CCBO evaporates.
The fate of a MBO is extremely complex. Section VI(G) describes the MW MBO composition at the end of summer. I will use that model as a guide to the fate of MBOs in general in this section.
The off local gravity transition lasts about a thousand years—practically instantaneous. The boundary and the hydrostatic pressure that holds the MBO source together will vanish at once, but the radiation pressure will not. The radiation pressure is only significant in the iron zone. The reduced pressure cannot support EDM material.
Suddenly, the MBO source (several hundred thousand km in radius) becomes a ball of hot static material. The ball has two parts. The inner part is the iron zone which consists of an iron supercritical fluid. The outer part consists of all the other zones and phases. The outer part will eventually disperse into a gas that will be efficiently recycled by RN.
The evolution of this system can only be expansion and cooling. The expansion will be driven by iron zone radiation pressure until cooling favors thermodynamic expansion. The thermodynamic expansion will be adiabatic, and the work done will be the increase of kinetic energy of all the expanding material.
What will be the final state of the MBO in winter, and will it be efficiently recycled by RN? There is no problem for the layer gases (hydrogen, helium, oxygen, carbon) since they will eventually disperse completely into an ultra-diffuse state.
The fate of the iron zone material is important but not obvious. The pressure, density, and temperature (PDT) of the iron zone material will all decline toward zero during the expansion. However, the PDT must not intersect a change of phase during the expansion to a sufficiently diffuse final state (a very cold and very diffuse atomic-iron perfect gas). An intersection would lead to large blobs of solid iron in the final state (not efficiently recycled). The expansion of the iron zone can be divided into three eras. The first era is the radiation expansion (RE), the second era is the thermodynamic supercritical expansion (TSE), and the final era is the thermodynamic gas expansion (TGE).
The RE era starts when local gravity is turned off and ends when the partial pressure of the radiation can be neglected relative to the partial pressure of the iron supercritical fluid (\({P_{ISF}}\)), e.g., \({P_{Rad}} > 0.01{P_{ISF}}\). The pressures follow: \[\begin{array}{l}{P_{Rad}} = (4/3)\sigma {c^{ – 1}}{T^4},\\{P_{ISF}} = f({\rho _{ISF}},T),\end{array}\tag{7.9}\] where \(\sigma = 5.6686\,{\rm{x}}{10^{ – 8}}\) and T is the temperature (MKS and degree kelvin units). \({\rho _{ISF}}\) is the MKS density of the iron supercritical fluid. For the RE and TSE eras, the properties and thermodynamics of iron supercritical fluid are unknown (the function f is not known). Even the iron critical pressure and density are not well established.
The TSE era starts when RE ends, and Eq. (7.9) represents an initial condition for TSE. The TSE era must end when the pressure (\({P_{iron}}\)) is small enough so that the supercritical iron fluid is well approximated by a perfect atomic iron gas, \[{P_{iron}}({\rm{TSE end}}) = \alpha {P_{critical}}{\rm{ ,}}\tag{7.10}\] where alpha is small, and it is thought that \({P_{critical}} = 8.750\,{\rm{x}}{10^8}{\rm{ mks }} \pm {\rm{13\% }}\).
The TGE era starts when TSE ends. TGE ends at the final state, e.g., \({T_{final}} = 5{\rm{ K}}\). During the TGE era the iron zone will undergo adiabatic expansion of a perfect monatomic gas. Eq. (7.10) provides a constraint on the initial condition, \[k{N_{TGS}}{T_{TGS}} = \alpha {P_{critical}}{\rm{ }}.\tag{7.11}\] The expansion relation, \(N = {N_{final}}{(T/{T_{final}})^{(\gamma – 1)}}^{^{ – 1}}\) (where \(\gamma = 1.67\)), gives the final density as a function of the temperature at the beginning of the TGE era as follows, \[{N_{final}} = \alpha {P_{critcal}}{k^{ – 1}}{T_{final}}^{ – 1}{({T_{TGE}}/{T_{final}})^{ – 2.4525}}.\tag{7.12}\] The resulting final density is best illustrated by a ratio (\(\chi = {N_{final}}/{N_{lab}}\) ), where \({N_{lab}} = 8.476\,{\rm{x}}{10^{28}}{\rm{ meter}}{{\rm{s}}^{ – 3}}\) is the density of iron in my laboratory. If \(\chi < < 1\), then one should expect that the probability of a large lump of iron surviving winter (observable in the following summer) is negligible. As an example, if \(\alpha = 0.01\), \({T_{final}} = 5{\rm{ K}}\), and \({T_{TGE}} = {10^5}{\rm{ K}}\). Then \(\chi = 2.85\,{\rm{x}}{10^{ - 11}}\).
The development of a MBO fate so far has served to establish a plausible initial temperature profile and a plausible distribution of nuclides and their thermodynamic state (supercritical fluids). An actual calculation of the evolution would produce a specific value of \(\chi \) for a specific model. However, the uncertain properties of the supercritical fluids prevent such a calculation.
Any type of debris from the expansion would eventually end up with a substantial radial velocity. Lacking any local gravity, the constituents of the expansion would move apart until their radial velocity is stopped. I believe that fact alone is sufficient to prevent the MBO debris forming any observable iron lumps that would survive winter.