APPENDIX L: ENVIRONMENT OF THE MILKY WAY MASSIVE BOUNDARY OBJECT
This Appendix reviews the information necessary to calculate the evolution model in VI(G). An important topic is the distribution and identity of local matter in the vicinity of the MW MBO (massive boundary object)—the environment. The local matter consists of stars, stellar cinders, and gas. The local matter and the MBO are the source of the local gravitational field, and the MBO grows by ingesting local matter through collisions of local matter with the MBO boundary—described in VI(G).
At the start (local gravity turned on), there is no MBO or cinders, just stars and gas. I believe the following model defines the environment at the start:
\[\rho (r) = {\rho _0}{\rm~{ if }}~r < {R_{ENV}}~{\rm{ else = }}{\rho _1}(r),\tag{L.1}\]
where \({R_{ENV}} = 20{\rm{ LY}}\) and \({\rho _1}({R_{ENV}})\) is small compared to \({\rho _0}\). Furthermore, \({\rho _1}(r)\) trends to zero as r increases. The environment is all the matter within \({R_{ENV}}\).
The rational for Eq. (L.1) comes from the fact that the orbits of stars within the environment all have the same period. Thus, one finds that the mixing time of randomly moving stars can be very brief (several thousand years) if \({\rho _0}\) is large enough—excellent mixing inside the environment and poor mixing outside. A star at a specific position in the environment could have come from anywhere within the environment a short time ago. Furthermore, there is little matter moving across the edge of the environment. The mass of matter within the environment is very large compared to the mass of the MBO at the end of summer. Thus, one should assume that the mass of the environment is independent of physical time. Evolution is just the change of the populations of different types of local matter within the environment.
There is scant information about the environment and the MBO. \({M_{MBO}}({\tau _{TODAY}}) = 4.1 \times 10^6\) solar and an estimate [16], \({\rho _{Stars}}({\tau _{TODAY}}) = 2.6\,{\rm{x1}}{{\rm{0}}^7}\) solar per cubic parsec. The density of cinders and gas today is unknown—not observable. The census today of star types and masses within the environment is poorly understood.
An evolution model must start with a census of (Kelvin contraction) stars of different masses and an average gas density (hydrogen and helium) shortly after the on transition of local gravity. After fusion is turned on, the census will include oxygen and carbon (gasses) and cinders of all types and masses. One will know the various initial censuses are correct only if the two (today) numbers above are produced—a very weak constraint.
The Newtonian gravitational potential within the environment is well approximated by the following:
\[V(r,\tau ) = – {M_{MGO}}(\tau )\,G\,{r^{ – 1}} + 2\pi \,G{\rho _0}\,{r^2} + {\rm{ constant}}{\rm{.}}\tag{L.2}\]
Eq. (L.2) is used to define the partial orbits of stars and cinders between random gravitational deflections (when they pass close by other objects). As the MBO grows, the partial orbits of projectiles near the MBO will change so that the probability of the projectiles having tiny angular momentum (necessary for a collision with the MBO boundary) is reduced. This detail is important because a model that neglects the MBO term of Eq. (L,2) always ends up with all the mass of the environment in the MBO a billion years after today—no stars of cinders left.
The most important evolution factor for stars is their lifetime (a function of the mass of the star). Every star will eventually suffer a spectacular transition into a cinder and gas. The gas will be recycled into (a smaller number of) new stars. During summer, the environment object census will have a growing population of (unobservable) cinders and a shrinking population of stars. The rate of growth of the MBO is different for cinders versus stars. Thus, the changing populations will directly influence the growth of the MW MBO.
This information does not make the model of VI(G) easier to achieve, but it does tell us which topics need the most study.