by  J. M. McCANNEY
Copyright 2 May, 1980

Abstract: A new theory for galactic arm formation shows the arms to be continually emanating from the galactic nucleus due to a continual influx of cosmic dust. In the neighborhood of the nucleus the problem is treated as a fluid flow and a simple solution is given using conservation of momentum. when rotational dynamics are included the spinning arm system is the result. This solution resolves the problem of the 'missing mass', accounts for warped disk galaxies and gives a probable source for the gravity waves measured by Weber which emanate from our galactic center. Reversal of arm direction is demonstrated and examples of such reversals are cited. An approximate theoretical estimate of the age of our Sun is found to be in good agreement with radio isotope dating. A general result shows why twin star systems are in such great abundance in a galaxy. It gives a model of galactic evolution which begins with only a single massive nucleus with the collapsing gas clouds forming the arms.

1. Galactic Arm Formation
Figure 1 illustrates a homogeneous cloud of cosmic dust and gasses as it collapses around a hemisphere which represents a half model of a galactic nucleus, The matter is considered to be in a fluid state in the vicinity of the nucleus. Viscosity between the fluid and the nucleus is neglected at this point but evidence will be presented later which indicates that the angular momentum of the nucleus is instrumental in maintaining the galactic plane. The flow problem is divided
 Fig1. Flow of gas clouds collapsing around 
a half-model of the galactic nucleus
into three distinct areas: (1) cloud influx, (2) fluid flow in the vicinity of the nucleus, and (3) a 'shotgun' effect as the matter is sprayed outwards from the nucleus and condenses into new stars. The analysis of the shotgun effect in producing many stars in an infinite variety of sizes will show why twin star systems are in such abundance. The hot stellar matter sprays outward in Keplerian elliptical orbits (e = 0.75 used in this article) shown in Figure 2. 
Due to the back pressure caused by the constant inflow of matter, a single out-flowing arm of circular cross-section will result which moves perpendicular to the base of the hemisphere. This circular cross-section allows the least amount of surface area between inflow and outflow (i.e., lowest surface viscosity). The same quantity must flow out as flows inward. It can easily be shown that if two outflowing arms resulted, the resistive viscosity between the two arms and the inflow would be the square root of 2 times greater than the case of one flow. (In general total viscosity is proportional to the square of n where n is the number of out- flows.) The arm will choose the path of least resistance. Therefore, a single arm of circular cross-section is forced out of the galactic nucleus. It will be perpendicular to the plane of the base of the hemisphere. As a thin hemispherical shell of dust falls onto the hemisphere the galactic nucleus will be forced to recoiI perpendicular to the base of the hemisphere using conservation of momentum. Thus, the arm must emanate in the opposite direction being also perpendicular to the base of the hemisphere. Putting two such hemispheres together gives a model for the arm generating process. In the real galaxy the faint gas clouds which are continually falling inwards are not homogeneous and will fall to the nucleus with a certain angular momentum, thus defining the plane of the Galaxy. This is the cause of the spinning arm system. The matter in the arm is thrown outwards in elliptical orbits with high eccentricity. The total energy is designated by initial conditions. This article assumes the following parameters but they are not meant to typify any particular galaxy. 
(The model can, however, be used to duplicate the past movements of a galaxy and tell much of its history of encounters with Magellanic clouds.A few examples are presented in this article but a complete analysis should be done. Most galaxies show tremendous symmetries even to very small detail when viewed by this model.)
Fig 2. The orbit of a single star in the Galaxy.
   It is assumed that about one-third of the galactic mass is in the nuclear region and that the angular velocity of the nucleus is a constant. This idealized case is illustrated in Figure 3.
Fig 3. The present positions of stars are plotted. Ellipses rotate backwards in time to plot the spiral arm shape. 

The ellipses are rotated backwards in time to locate where the stars are that left the nucleus at that time in history. This has been done numerically and a typical spiral arm shape is duplicated (see Figure 3). In this example the galactic nucleus rotates 200 degrees in the time it takes a single star to move from the surface of the nucleus (Pi divided by 2) to 'aphelion' which is 45 million years. The ratio between these two times is the 'spiral constant' and varies from between near zero to as much as 5 in real galaxies. A value of 5 is a galaxy whose visible arms wind five times around the nucleus. This value also changes with time in real galaxies, depending on the angular momentum of the infalling cosmic clouds. 

From Kepler's second law, it follows that:

for the total ellipse or any triangular subdivision with the galactic nucleus at one focus. The differential form gives
where T is the total time for a star to from the surface of the galactic nucleus to S (a is a dummy) and Ttot, is time to pass from the galactic nucleus to aphelion. Since the galactic nucleus has rotated at a constant angular velocityw  throughout this time, 
where wT gives the angle backwards in time that the ellipse must rotate a particular star in its present position. Two equations can be solved numerically to give the absolute coordinates of the spiral arm curve at a given paint in time.
  The quantity S ranges from where the star leaves the nuclear surface to where it returns billions of years later after completing its elliptical orbit The perihelion of the orbit lies within the galactic nucleus thus the star never traverses this portion of the orbit. Figure 3 illustrates one arm of a galaxy in which a particular star moves only 90degrees in its elliptical orbit while the nucleus rotates 200degrees. Figure 4 shows two spirals ((a) and (b)) with different spiral const. and a reversal (c). The stars normally burn out during their millions of years drifting near their aphelion points and are not visible their return trip to the nucleus.
Fig 4. Spiral arms with spiral constant 2.0 (a) 
       and 1.0 (b). Part (c) illustrates a reversal.
2. Conceptual Results of Model
The newly formed arm initially has higher angular velocity than the nucleus giving the appearance that the arm is preceding the point on the nucleus where the arm emanates. This area is rarely visible due to the glow of the clouds in the area. In this area are forming giant blue stars and evidently the entire Main Sequence. It seems possible that very small stars may form also and can burn H2 for a short time as the star is forming in the gravitational field of the galactic nucleus, and not solely by its own mass. 

Since the visible galaxy is about 45 million years old, it must regenerate one 45 millionth of this each year. If the Galaxy contains 10 to the tenth stars then it is producing about 200 stars per year or at a rate of approximately one per day. By the same reasoning, approximately one star per day is returning to the galactic nucleus and it is the collapse of these old stars as they fall onto the nucleus that is a probable cause of the gravity waves being detected by Dr Weber of Maryland. For galaxies with spiral constant greater than a half, the old stars will fall in over the newly forming stars in the arm. This crossing over also occurs in galaxies which have reversed their directions of arm propagation such as in NGC 2523 which is a barred galaxy. The barred galaxies derive their form from an arm which stopped rotating and began propagating with no angular velocity. The arm falls back into itself. Most barred galaxies show a gap at the ends of the bar. 

So only about 200M of dust clouds fall on the galactic nucleus per year. The globular galaxies seem to be receiving great influxes of clouds which scatter light rendering the entire galaxy invisible. These will be expected to develop massive bright arm systems. 

The time-scale on which a galaxy works is seen by the estimate of w(=3x 10-6 deg yr-1) and the time for a star to pass the first one percent of its distance to aphelion (~30,000 years). In the present crude example, time TTot (45 million years) is close to the estimated age of our solar system. Slight adjustments in orbital parameters will account for this.

Fusion of the heavy radio-isotopes will occur in the intense star-like environment of the galactic core. This must have important consequences in the future development of solar systems in the Galaxy. The energy which supports this fusion comes from the difference in kinetic energy between the infalling clouds and the outward moving arm (i.e, arms do not flow back to infinity).

Warped disc galaxies (Wright, 1979) can be explained by assuming that the galactic nucleus maintains a substantial angular momentum and does interact with the collapsing cloud flow. The randomly approaching gas clouds will introduce random changes in total angular momentum. If the nucleus contributed no angular momentum, new arms could develop at large angles to old arms. Instead it is observed that only slight changes occur in the plane of the generating arms, causing the disc to 'warp'. Elliptical galaxies appear to be new galaxies in the initial state of formation with some beginning to develop arms whereas the exploding galaxy marks the end of the organized existence of the Galaxy.

The problem of the missing mass (Salpeter, 1977) is also resolved in the present theory. The original galactic theories predicted circular Keplerian orbits. Figure 5(a) shows the predicted orbital velocities. Figure 5(b) shows the v  versus r  graph for the 'wave theory' which claims the arms to be continually rotating about the nucleus. Figure 5(c) shows the predicted orbital velocities of the present theory as seen by a red-shift observer who sees only the receding component of the arm velocity.

In support of the present theory, a summary of current observations of the  Milky Way is given (Geballe, 1979; Wynn-Williams, 1979):
-There are tremendous quantities of radio signals emitted by the Milky Way's nucleus.
-The immediate environment surrounding many hot blue stars.
-Novae and Supernovae art frequent.
-Observation of supergiant stars of short life times indicates that stars are being formed in the galactic center.
-There is also an abundance of old stars near the galactic center.
-The nucleus is an extended object emitting intense radio noise and is about 16 AU in size.
-Gravitational waves are detected emanating from our galactic center at the rate of about one per day.

The twin star system is the result of the shotgun effect as the condensing stars of all sizes are thrown out at approximately the same velocities. Two stars can begin orbiting one another as they leave the gravitational dominance of the galactic nucleus and can remain as a pair until they return to the galactic nucleus billions of years later. Jupiter and the Sun are such a pair and it should be considered that in conjunction with the few stars that are not in twin systems there will most likely reside an unlit companion. It is easy to see how a twin star forms in this way, but why should there be mainly twin star systems and not systems of three or four more stars? Only rarely are even triple star systems observed. Alpha-Centuri is a triple star for example, and has two close orbiting central stars with a smaller relatively distant star orbiting these two. The first two are little affected by the third and the third sees the other two as one. So it behaves much like a double star. The answer is that the shotgun problem introduces only unstable stellar systems into the galactic arm, As a massive newly formed star begins to control the smaller condensed objects around it, they will be distributed on all sides and will take orbits of random eccentricities and orbital planes. Within the first orbit there is a great many encounters with the smallest bodies leaving the system and only the most massive, which generally has an eccentric orbit, remains. Studies have been undertaken to determine the stability of systems with such random initial conditions (Szebehely. 1974). Results indicate that: (1) randomly selected initial conditions and masses lead to eventual disruption of the many bodied system with the smaller bodies being ejected, leaving in most cases, the two largest to orbit one another. (2) Triple systems are inherently unstable and are therefore rare. Higher order systems are possible but are exceedingly rare. Observation that 72% of the stars exist in double star systems with another 24.9% residing alone, is proof of this statement. As mentioned before, the lone stars will be in most cases accompanied by an unlit companion.

A number of difficulties arise in presently accepted theories of solar system evolution which are not compatible with this concept of galactic evolution. One is that an entire solar system of nine planets and over 30 moons is not the result of a solitary gas cloud evolving on its own but in fact, no more than the Sun and Jupiter could have been in the original system. The other 40 bodies could only have been the object of subsequent captures by this twin star system. Secondly, there is no chance that comets made of condensed ices could form in the heated environment of the galactic nucleus. It is generally accepted in the plasma theories of solar system evolution that the comets were an original part of the solar system (Delsemme, 1972). Two possibilities exist: (1) comets were not an  original part of the solar system or, (2) comets are not icy balls or both.

I have proposed (McCanney, 1979a, b, c) a complete theory for comet  behavior and solar system evolution based on a new model for the comet which shows it to be a hot radioactive nuclear conglomerate. These papers were not  accepted for publication as they did not fit into the accepted theoretical scheme of solar system evolution. This paper lays a firmer foundation for those papers.

3. Conclusion

A new model for galactic evolution was given which predicts the spiral arm shape. Stars are found to be in highly elliptical orbits after being thrown out of the nucleus. The theory correlates heretofore anomalous data and answers the question of 'where is the missing mass'. The most important result is that presently accepted theories of solar system evolution are not compatible with this model.


Delsemme, A.H.: 1972 in H. Reeves (ed.). The Origin of the Solar System, CNRS, Paris.  Geballe, T. R.: 1979. Sci. Am.  241, 52.
McCanney, J. M.: 1979a.'Comet Nuclei: An Explanation and Predicted Effects'. unpublished.
McCanney, J. M.: 1979b,'The Role of Comets and Selection Ruler in the Formation of Solar Systems', unpublished.
McCanney, J. M.: 1979c, 'A New Self-Consistent Theory of Solar System Evolution', unpublished
Salpeter, E. E.: 1977. Ann. N.Y. Acad. Sci. 302, 681.
Szebehely, V.: 1974. L. N. Mavridis (ed.), in Stars and the Milky Way System, Vol.2, Springer-Verlag, Berlin, p. 273.
Wright, M. C. H.: 1979, Astrophys. J. 233, 35.
Wynn-Williams, C. G.: 1979. Mercury-J. Astrophys. Soc. Pacific 8, 97.