Download Galaxy Spiral Arms

Galaxy Spiral Arms Gravitational Stability
Gravitational Kinematics, Dynamics, Structure and Persistence
Simple Newtonian gravitation is sufficient to explain the entire existence and behavior of
Galaxy Spiral Arms, including their long-term stability. The well-known Keplerian
centripetal force effect certainly dominates even though Isaac Newton downplayed its
importance, but a tapering-shaped Spiral Arm also has complex internal mutual gravitation,
which has surprisingly strong local effects!
Some really obvious logical errors exist in the understanding of the structure of our Milky Way
Galaxy. For example, there is much evidence that the Sun and Earth are currently about 250
light years “above” the centerline of our Galaxy, and for more than 200 years, we have known
that the Sun and Earth are currently traveling “upward at an angle” toward a spot in the sky we
call the Apex of the Sun’s Way. We know that the Galaxy is very “thin”, less than onehundredth as thick as it is in diameter. Prior to the math presented below, no one seemed to
notice that at the rate we are moving “upward” we now can expect to entirely leave the Galaxy in
only around 9 million years. Which means that our understanding is extremely wrong when the
Sun and Earth are certainly 500 times older than that. This current reasoning establishes and
mathematically proves that the Sun and Earth oscillate up and down in our Galaxy, likely around
150 complete cycles so far. This reasoning also establishes and mathematically proves that the
Sun and Earth also oscillate radially in our (Orion) Arm, apparently doing around 100 complete
radial cycles so far. This radial cycling has resulted in the Solar System having passed through a
very crowded region of our Arm’s Centerline about every 26 million years, where we may have
been intensely pounded by many massive asteroids on a regular basis.
It is not necessary to speculate about “Gravity Waves” or “Dark Matter” or bizarre patterns of
invisible structure within the Galaxy to fully explain all of the details of Galaxy Spiral Arms, in
full compliance with all the Conservation Laws of science.
The stability of galaxy spiral arms has long
troubled the Astrophysics community. It has
always been assumed that only a Keplerian
(centripetal) central force was acting, as
suggested in the (partial) drawing here. The
orange dot represents the current location of
the Sun, within the blue-outlined Orion Arm
that we happen to be in. We are currently
fairly near the inner edge of that Arm. For
local gravitational reasons, the tapering shape
of the Arm turns out to be very important. The
rest of the Galaxy was left out of this drawing. Traditionally we make the usual assumption that
the Sun is revolving in the Milky Way Galaxy with a tangential velocity of around 250 km/sec,
and that the Sun is currently around 28,000 light years from the center of the Galaxy (the black
arrow represents that radius vector). It is then easy to calculate that a centripetal (Keplerian)
acceleration MUST exist of a = v2/r or 2.36 * 10-10 meters/second2. This acceleration must also
equal G * Mgalaxy/r2 which tells us that the effective Keplerian mass of the Galaxy must be
around 125 billion solar masses. This is only true given the assumption that only a Keplerian
central force is causing the Sun to have its revolution motion.
However, Isaac Newton made very clear that such a basic assumption is absolutely wrong.
When Newton analyzed Kepler's Laws, he quickly realized that the Kepler Laws are all
approximate. Newton derived the exact formulations of Kepler's Laws, but even then, only for
within our Solar System. Kepler had (incorrectly) assumed that only the Sun's mass applied, and
it acted at the exact center of the Sun, and the Gravitational attraction between the Sun and Earth
would therefore be given by:
Force = G * MSun * mEarth / r2
Newton discovered that the sum of the mass of both of the objects must be used, that is:
Force = G * (MSun + mEarth) * mEarth / r2.
It was later determined that the Sun has a mass which is 330,000 times greater than the Earth,
which makes these two equations virtually identical. However, the first is approximate and the
second is far more precise. Newton also used the Calculus (Fluxions) which he invented, to
discover another important fact. When a mass such as the Sun has its entire mass Integrated
regarding gravitational effect (for any location outside the Sun itself) the gravitational effect is as
though the entire mass of the Sun is gravitationally acting as though it is all at a point at the exact
center of the Sun. This is only true if the object is symmetric regarding density, and this is a
basic problem given to beginning Physics students to solve as homework! In the case of the
Solar System, this caused very minor differences, entirely because the Sun is so massive, that is,
that virtually all of the mass in the Solar System resides in the Sun. The results of using Kepler's
Laws, within the Solar System, therefore always gave wonderfully useful results.
But Newton therefore knew that Kepler's Laws only (approximately) apply for a point source
mass such as the Sun. Our Milky Way Galaxy has distributed mass, where hundreds of billions
of individual stars all contribute to the total mass of the Galaxy. On a gross scale, that mass is
relatively symmetrical, so for our gravitational effect on any other galaxy, yes, our entire Galaxy
acts as though it is a point mass (as Kepler might have assumed). But for locations inside our
Galaxy, both of these assumptions which are embedded in Kepler's Laws happen to be very
wrong.
Having overlooked this obvious fact, modern Astrophysics has felt it necessary to create
countless unsupported speculations to try to explain how and why our Galaxy can rotate as it
does and still not quickly fly apart. So they have come up with Dark Matter, Hidden Matter,
Gravity Waves, massive numbers of Neutrinos and many other wild assumptions and
speculations. If they had recognized, as Newton did, that Kepler's Laws only apply for pointsource masses like the Sun, and they certainly do not apply for distributed masses like a galaxy,
they might have seen that standard Newtonian gravitation was the only explanation which is
necessary.
Specifically, the local irregularities regarding where stars are, is extremely significant. If our
Galaxy were a uniform distribution of stars and other mass, the usage of Kepler's Laws would
not be too terribly wrong. But our Sun and Earth happen to be near the (inner) edge of one of the
tapering Spiral Arms of our Galaxy. That is, radially inward from where we are, there are
very few nearby stars (for several thousand Light Years distance). In contrast with that,
radially outward from where we are, there are many millions of stars within that same
several thousand Light Years distance. In other words, the uniformity of mass density upon
which Kepler's Law must be based, is not remotely valid.
It would have been great if the tremendous simplification of using Kepler's Laws would apply
for our Galaxy, but it certainly is not true. So, to do a proper analysis of our Galaxy, we need to
set aside Kepler's Laws and instead use Newton's Gravitation, where we need to mathematically
Integrate the gravitational effects on the Sun of ALL of the individual stars and debris in the
Milky Way.
This is actually the same Gravitation that Newton had quantified, but it is an entirely different
perspective. Think of any galaxy spiral arm as a very large and massive “open cluster” of
stars. We all accept that open clusters have a structural integrity due to mutual gravitation, even
while revolving with the galaxy as a whole. We all believe that the Pleiades Cluster stays
together due to mutual gravitation between the component stars and gases.
We can make some decent estimates of characteristics of this very large, tapering and somewhat
cone-shaped, open cluster that we all call our Orion Spiral Arm.
If we consider a galaxy to primarily have two (symmetric) main spiral arms, it seems reasonable
to estimate that the total mass of each of those arms is around 1/10 of the mass of the entire
galaxy (leaving 80% of the mass as being in the Core). In the case of the Milky Way Galaxy,
that would be around 12.5 billion solar masses in each of two major Arms.
We can immediately apply some simplifications. We can assume that the Core of the Galaxy is
far enough away and uniform enough that Kepler's Laws do apply, specifically because we are
outside that mass of Core stars. In addition, the Spiral Arm opposite our Arm is on the other side
of the Galaxy, where again we can treat the contents of that Arm as complying with Kepler's
Laws. Therefore, we specifically need to focus on nearby stars, that is, the stars that share our
Orion Spiral Arm with us. The fact that gravitation is an inverse second-power dependence,
these nearby stars have far more gravitational effect on the Sun than the many similar
stars that are farther away from us have.
Specifically, we immediately have a rather simple estimate that is available. Treat the 90% of
the Galaxy's mass as Kepler's Laws would do. They are far enough away where the assumptions
are generally minimal. But then realize that we have nearby neighbor stars, which are currently
essentially all outward of where we are. With very few nearby stars inward from us (that is, not
in any Spiral Arm) we can create a simple estimate of the gravitational effect of the 10% of the
Galaxy's mass which is near us and outward of us. (A full Calculus Numerical Integration is
really needed for a more precise calculation.)
Given the known dimensions of the Galaxy, reasonable estimates of the dimensions of an Arm
are 15,000 light years wide at the start, with a uniform taper to end 60,000 light years away. If
the Spiral Arm is estimated to have a uniform thickness of 1000 light years, this results in
credible mass density figures, as discussed below.
If the mass of the Spiral Arm is assumed to be uniformly distributed over this volume (as 450
million discrete equal masses), a numerical integration of the trillions of mutual
gravitational attractions can be done, which results in two new consequences, as noted in this
drawing. There is a rather strong gravitational “restoring force” acting on the
Sun to transversely keep it within our Arm, and there is also a “forward
boost” acceleration which aids the Sun in “keeping up” with the more massive
portions of the Arm that are forward and inward of it. The first exists because
nearly all the nearby masses are currently pulling us outward, since gravitation is an inversesquare force law. The second exists because the part of the Arm that is ahead of us is much
fatter, meaning that there are far more massive objects in front of is than behind us.
It is important to note that the scales of these accelerations are comparable to that due to
the Keplerian central force. They exist because the assumption of “symmetric mass
distribution of the Galaxy” on which the Keplerian formulas are based, is not true, because
of the presence and massiveness of the Spiral Arm structure, and our proximity to the massive
objects in the Arm we are in. That is, galaxy spiral arm dynamics is primarily a combination
of this “intra-arm” self-gravitation and the traditional Keplerian central force effect. Both
are simple applications of standard Newtonian gravitation.
As a clear indication of this, the discussion below shows that there is an “intra-Arm gravitational
restoring force” currently acting on the Sun [and on everything else within the Arm] (toward the
centerline of our Arm) which currently causes an Arm-lateral acceleration on the Sun of around
8.62 * 10-10 m/s2 outward. This varies with the distance from the centerline of the Arm but is
currently over three times the acceleration the Sun experiences due to the Keplerian central force
in revolving around the Galaxy. The point here is that this intra-Arm effect is significant, on the
same order of magnitude as the effects of the universally accepted Keplerian central force. This
Arm-restoring acceleration is large enough to keep the Sun forever within the Arm,
meaning the persistence of the Arm Structure. All other objects also experience restoring
accelerations toward the center-line of the Arm, such that nearly all are kept within the region of
the Arm.
This top-view graphic of the flattened Arm shows the net long-term effect on all the objects that
are within an Arm, each constantly weaving back and forth across the width of the Arm, the Sun
being represented by the yellow dot.
Note also that there is a significant net forward acceleration imparted on the Sun (not shown in
the graphic above), because of the greater amount of mass in front of the Sun than behind it.
(The current forward boost due to material in front of us is actually around 5.43 * 10-10 m/s2 and
the rearward drag due to material behind us is actually around -3.67 * 10-10 m/s2, so the net
(forward) acceleration is the 1.76 * 10-10 value shown above). This forward effect enables the
Sun to revolve around the Galaxy more quickly than suggested by Kepler alone. This effect
is actually enhanced by the fact that the Arm centerline is angled in toward the Core, which
causes this effect to not only be "forward" but also to have a component that adds to the
Keplerian central force acceleration.
If the Arm centerline were inward at a 30-degree angle, then there would be an inward (radial)
component of this 1.76 * 10-10 m/s2 of about 0.88 * 10-10 m/s2. If so, that would imply that the
ACTUAL Kepler central acceleration would only need to be 1.48 * 10-10 m/s2. THAT would
imply a far lower total mass of the Galaxy!
The subject of the Galaxy Spiral Arm Stability has long been the cause of massive research and
countless speculations and theories. There seem to be a couple solidly established facts which
cannot be ignored, but for some reason, nearly always are!
(1) Our Milky Way Galaxy, like millions of other galaxies, has “spiral arms”, which tend to be
relatively symmetric. We have good experimental evidence that suggests that our Galaxy has
rotated around 60 times already, which suggests that the Spiral Arms are also a persistent
characteristic. The fact that there are millions of other galaxies that have spiral arms seems to
suggest that the arm structures are either stable or meta-stable in nature.
(1b) This being the case, consider a child's pinwheel. Because it is of stable structure, it rotates
as a unit. Therefore the actual velocity of rotation of any point on it is proportional to the radius
of the location of that point; points farther out have to have higher velocity to rotate with the
whole structure.
(2) There is strong empirical evidence that our Sun is currently moving (locally) toward a point
in the direction of mu Herculis, which is around 26° degrees UPWARD of the Plane of our very
thin Galaxy. The upward (Z-direction) velocity we have would cause us to entirely leave the
Galaxy in only around 9 million years, barely a moment in the lifetime of most stars or a
Galaxy.
Virtually all of the currently popular theories seem to ignore both of these established facts! The
concept presented here shows how those facts, and all others, are easily explainable, without
violating any established principle of Physics, by simple Newtonian gravitation.
Globular Star
Cluster
(Centaurus)
Nebula
(Orion)
Open Star Cluster
(Pleiades)
Spiral Arm
(M100)
Spiral Arm
(NCG 1566)
Which of these Galaxy components do NOT have gravitational self-cohesion?
They ALL do!
The Milky Way has countless star clusters, gas clouds, and many nebulae.
They certainly all revolve with everything else around the Galaxy center. But everyone accepts
that clusters, nebulae and gas clouds maintain their structures due to mutual gravitational
attraction, due to their relative nearness to each other and the inverse square nature of
gravitation. They all certainly revolve around with the Galaxy, but their individual structures
persist.
The same situation must be true for a Spiral Arm structure.
The billions of stars and countless other masses within a Spiral Arm certainly have mutual
gravitational attraction. There is a “relative nearness” of the component parts, as there are in
those smaller structures. The claim here is that a Spiral Arm should also have a gravitational
integrity. In fact, the total amount of mass involved is far greater than in any nebulae or cluster,
and so a meta-stable shape-persistence must occur.
The complexity of a galaxy is such that BOTH the principles of Keplerian revolution AND this
gravitational Arm self-cohesiveness must apply. The great size and mass of a spiral arm
structure requires additional consideration, but the situation is essentially that of a normal star
cluster or nebula. This combination then explains all the observed evidence.
Current Thinking
It seems that virtually every researcher regarding the Galaxy starts off with the assumption that
Keplerian calculations are the absolute starting point, and then they find various ways, such as
there being an extremely massive but invisible halo of dark matter surrounding the Galaxy, to
explain the observed data. Since this is the case, essentially all Papers start off by assuming
either of two pre-conditions, that stars that are farther from the Galaxy Core revolve more slowly
(per Keplerian thinking) OR that stars might revolve at the same velocity at any radii.
It is hard to see why this would be believed, except for an absolute reliance on Kepler's
approach! We know that spiral galaxies are numbered in the millions, so the configuration is not
a fluke. We believe that ours has probably already rotated at least 60 revolutions, which implies
that there is some sort of stability or meta-stability. Doesn't this imply something similar to the
rotation of a "rigid toy pinwheel"? The critical point is that the local rotational velocity of any
point on such a pinwheel is directly proportional to radius? Larger radius should therefore imply
proportionately larger revolutionary velocity, at least in the Spiral Arms, in our Galaxy.
This reasoning is based on the far larger relative size of the Sun's velocity of revolution (roughly
200 kps) than the local recognized velocity of around 1/10 that. Those individual small
velocities are just too small to account for the velocities required to keep up with the revolution
of the Galaxy or its Spiral Arm.
Available data regarding differential velocity rates at different radii inside of other galaxies tend
to have rather large error factors. We are primarily interested here in that the error factors
presented are often comparable in size to the variations of the data itself.
Unfortunately, the existing error factors in determining rotational speeds in galaxies, or in our
own Galaxy, are great enough as to not even provide us whether the galaxy rotation velocity
curve increases, decreases, or stays constant with increasing distance from the center. This
situation seems to be true for all the data that appears to yet be available.
The data regarding the rotation of our own Galaxy also has many unavoidable large error factors,
which again can be interpreted as supporting any of the general concepts. The individual motions
of each of the stars are often large enough to mask the effects of localized differential rotation.
Around 80 years ago, Eddington, Oort, Lindblad and others developed generalized descriptions
of apparently systematic patterns of star movements, which are essentially still the data we rely
on today.
Solid Evidence that Current Theories are Incorrect!
By about 1783, it was already known that the Sun appears to be moving toward a spot that
Herschel called the Apex of the Sun's Way, in the Constellation of Hercules. This motion is
implied by the examination of proper motions of thousands of other nearby stars, so the Sun is
definitely moving toward that direction, in a "local" sense.
However, Stromberg, Kapteyn, Eddington, Oort, Lindblad, and many others noted what
Eddington referred to as "Star Drifts A and B". Large-scale patterns of movements in two
opposite directions were noticed in the proper motions of stars, which was realized as being
generally tangential to the Galaxy. The analysis was that, given that the Galaxy is revolving with
the Sun as part of it, then the Galaxy must be rotating at different velocities at different distances
from the Core. Lindblad and others devised formulas to associate Galactic radius with these
Drift velocities.
More recent and more accurate research has confirmed these differential velocity effects, which
even then implied that we are revolving in the Galaxy toward a point that we might refer to as a
Tangent, which is along the Galaxy Plane but 90° from the direction of the Galaxy Core. A
Polaris.net star chart has been provided here that shows the exact locations of the Galaxy Plane
(yellow line) along with small green dots to indicate the locations of the Galaxy Tangent (which
we are certainly moving toward at over 200 km/sec) and the Galaxy Core (the center of our
revolution motion). On the same star map is another green dot which shows the location of the
Apex of the Sun's Way.
Note that the 20 km/sec locally identified motion of the Sun toward a spot in the constellation of
Hercules (approximately at R.A.18h02m Dec. +29.2°) is generally toward the Tangent direction
(at R.A. 21h12.0m Dec. +48°19') but is also aimed around 26° above the Galaxy Plane, as well
as about 37° inward from that Tangent direction. These are significant facts.
Given that our local motion is believed to be around 20 km/sec toward the Apex, this means that
the Sun has a Z-axis (vertical) component velocity of around 8.7 km/sec upward relative to the
Galaxy Plane (toward the North Galactic Pole). It also has a radially-inward (toward the Core)
component velocity component of around 12.0 km/sec. The bulk of this local motion is the third
component, along the direction of the revolution motion of the Sun around the Galaxy, with that
component being around 16.0 km/sec.
This is in general agreement with currently accepted figures:
(found in Wiedenhoff) “the galactic circular velocity components, which give [for the Sun] U = 9 km/sec, V = +12 km/sec, and W = +7 km/sec.” where “Space motions comprise a threedimensional determination of stellar motion. They may be divided into a set of components
related to directions in the Galaxy: U, directed away from the galactic centre; V, in the direction
of galactic rotation; and W, toward the north galactic pole.”
We have long known that the Galaxy where we are is roughly 1,000 light years thick. We also
see that a great-circle for us is actually around 1.6° above the center of the distribution of the
components of the Milky Way Galaxy. Therefore, it has long been universally accepted that we
are currently ABOVE the Plane of the Galaxy, at a Z-distance that seems to be around 250 light
years. This means that there is only around 250 light-years of Galaxy currently above us. We
are moving upward, as noted above. It is easy to calculate that, at the rate we are currently
moving upward, we would entirely escape the Galaxy in under 9 million years! Another
similar calculation regarding the fact that we are near the inner edge of the Arm that we are in,
and we are moving inward, shows that we would escape the inner edge of the Arm in roughly 13
million years. These are very brief intervals of time, considering that a single revolution of the
Galaxy is believed to take around 200 million years.
None of the current popular theories regarding the Galaxy seem to account for these wellestablished facts. It seems that such theories would not have much of a Galaxy to work with,
after even 50 million years if a majority of all the stars had exited toward the Galactic Poles!
This current presentation insists that each Spiral Arm have gravitational self-cohesion.
This results in the component stars and other objects being decelerated when moving away from
the Galactic Plane, by the billions of solar-masses “behind” it collectively providing that
deceleration. In fact, the result certainly is that all such stars and other objects must be
oscillating in the Arm (vertically) along the Z-axis. In the case of the Sun, the current “upward”
velocity would therefore be slowing, eventually stopping and reversing, at or before the upper
limit of the Galaxy. Then it will proceed “downward” through the thickness of the Galaxy to
eventually approach the bottom limit of the Galaxy. After some “period” of this oscillation
(probably around 12 million years), we will again be at about the Z-position and Z-velocity that
is currently true.
Incidentally, this concept helps explain the previously unexplained "waviness" seen in many
spiral galaxies, as being short-term, local gravitational, effects, which will self-correct within a
few million years.
The exact same effect must certainly be happening for every component of a Spiral Arm, along a
radial direction. The current radially-inward velocity of the Sun must “soon” stop and reverse,
such that the Sun remains part of this Arm. Otherwise, there could be no recognizable structure
in a spiral galaxy! The Sun must therefore weave back and forth across the width of our Arm.
In our case, it appears that we must oscillate across nearly the entire width of the Arm that we are
in. My calculations of Newton’s Gravitational Calculus suggests that a full oscillation must take
about 52 million years. This means that we must have passed through a very crowded region
near the Arm centerline about 13 million, 39 million, 65 million, 91 million, 117 million years,
etc, ago. It might also provide an explanation for why the Moon, Mercury and other planets and
moons have massive impact craters in their southern hemisphere, IF the Solar System’s leading
side 13 million years ago was that hemisphere.
A popular common idea is to attribute elliptical galactic orbits to many stars, while others have
relatively circular orbits in their paths around the Galaxy. (That approach has some real
problems when the Z-axis velocities are considered, due to the extreme small dimension of the
thickness of the Galaxy!) This new approach shows the same net effect, of arm-transverse
velocities, but attributes them to a different cause, that of a constant weaving back and forth
across the Arm. It results in rather different calculations, though, because the elliptical orbit
hypothesis requires a period of that of the rotation of the Galaxy (~200 million years) while the
intra-Arm weaving can have an independent period, which appears to be ~50 million years.
If this new reasoning is valid, and it seems to be, then the situation is actually a little different
than it first appears. Yes, we may be currently moving upward, but it seems logical that a
significant number of stars in our vicinity are actually currently moving downward. This would
result in an apparent value for our upward velocity that is larger than is actually true. With
certain reasonable assumptions, we might conclude that the ACTUAL upward velocity of the
Sun might be around half of what we observe. This might be a better value to use in
gravitational acceleration calculations regarding the nearly harmonic motion due to the Zrestraining force of gravitation.
These matters are discussed a little more below, and in the web-page calculations of this
(referenced below), it appears that the likely period of such a radial, cross-Arm oscillation is
around 50 million years.
Arm-Longitudinal Effects
We will use the following estimates here: The total mass of the Milky Way Galaxy is 125 billion
Suns. The bulk of that mass is in the Core area, but a pair of major spiral arms can realistically
each be expected to have a total Arm mass of 1/10 of this, around 12.5 billion Suns. If the Arm
were straightened it would extend for 60,000 light years in length, with a taper from a maximum
of 15,000 ly width to zero at the tail. The thickness is assumed to be a uniform 1000 light years.
These assumptions have a volume of 450 billion cubic light years. With the assumed mass of
12.5 billion Suns, that represents an average mass density of one Solar mass in every 36 cubic
light years. In our immediate vicinity, it is believed that the mass density is around 1/20 of that,
around one solar mass in every 700 cubic light years. This has a reasonable explanation,
regarding the following discussion and the fact that we are currently near the inner edge of the
Arm that we are in. The reasoning below suggests that it is quite possible that the mass density
may easily be twenty times as great along the Arm centerline region.
This suggests that our mass and dimensions, of 1/10 the Galaxy mass in each of two major,
relatively symmetric arms, are credible estimates. When a numerical integration is done
regarding a UNIFORM distribution of the mass in the Arm, we get the following results:
Consider a random distribution of masses in a tapered wedge region as indicated here, as
representing a Spiral Arm. Consider the yellow star indicated. We note that geometrically, there
is three times the area to the right of it as to the left. Forward of it (to the right) there are
9,300,000,000 solar masses of material. Behind it (to the left) there are 3,100,000,000 solar
masses of material. The summation of gravitational attractions certainly is a net force to the
right (forward). For the current situation of the Sun, with the above estimates in
numerical integration, we get a forward acceleration of around 1.76 * 10-10 m/s2. As noted
above, the Keplerian central force from the entire mass of the 125 billion Suns of the Galaxy
causes a radially inward acceleration of around 2.36 * 10-10 m/s2. This "forward boost" is
therefore very significant.
This must certainly be true for every star and object in the pattern. All the component objects
would therefore receive a (forward) incremental acceleration. In a Spiral Arm, this is a
forward- and somewhat inward- directed (due to the angle of the Arm's centerline to the Galaxy)
acceleration, for all components. All objects in the Arm therefore revolve FASTER than
they would if the (tapered) Spiral Arm structure was not present. Numerical integrations for
an object at the very end of the tail of the Arm describe above would receive a forward boost of
8.0 * 10-10 m/s2. This acceleration is around four times the magnitude of the Keplerian central
force acceleration for that object, a strong evidence that this indicates why such trailing materials
are able to keep up with the Arm.
Angle of Taper is Important
If the taper is broad, the differential masses of stars are physically closer, more masses are at
nearer distances for gravitational effect and so the effect is stronger. If the taper is narrow and
long, the differential masses are physically farther away, and so the effect is weaker. The angle
of taper of the Arm is very important regarding the meta-stability of the Arm structure.
Even though this yellow star is not along the centerline of the pattern, there is certainly still the
effect of a net gravitational attraction toward the right (forward) side.
An analysis of current data suggests that the Sun is currently getting this "forward boost"
which results in about 1/4 of the effect of the Keplerian Central Force. This therefore
causes the Sun to revolve at a rate around 20% FASTER than it would if the Spiral Arm
was not present. This differential acceleration enables the different parts of a Spiral Arm
to "keep up" with the revolution rate of inner portions of it.
One effect of this is that the Keplerian calculated total mass of the Galaxy is therefore
much less than previously thought. If only Keplerian effects were present, the period of
revolution of the Sun would therefore be about 5/4 what we believe it to actually be. By Kepler,
the Galaxy mass would therefore be 25/16 as great, more than 3/2 of what we now believe it to
be.
Arm-Transverse Effects
Stars and material that are not along the centerline of the Arm must also be accelerated
toward the centerline of the pattern. Therefore all stars and materials must constantly
weave back and forth across the width of the Spiral Arm. Using the Arm specifications
given above, numerical Integration gives a current "Arm restoring acceleration" for the Sun to be
about 8.62 * 10-10 m/s2. Again, this is several times stronger than the Keplerian acceleration that
also acts on the Sun, keeping the Sun securely part of this Arm.
The acceleration that the Sun is subjected to decreases as the Sun passes some of the attracting
mass and approaches the Arm centerline, where it becomes zero and the Sun is moving
transversely across the Arm at the highest velocity. If we have a net average of 4 * 10-10 m/s2,
using standard Newtonian equations, we find that the Sun should be traveling at around 170
km/sec as it crosses the Arm centerline. Those standard Newtonian calculations indicate that
the Sun should "fall" to the Arm centerline in around 13 million years. This would result in a
full cycle of oscillation across the Arm and back in around 52 million years. The Sun must
therefore weave back and forth across the width of our Arm around four times for each
revolution around the Galaxy.
After the Sun crosses the centerline, there is obviously no further acceleration, and with the bulk
of the Arm mass then behind it, from then on the effects are in deceleration. The differential
mass density within the Arm affects the value of this acceleration, so until better mass density
distributions are known, this value must be considered to have a high error factor.
The motion then resembles a periodic sinusoidal motion across the Arm, but it is actually more
complicated, having variable acceleration along its motion. But the gravitational restorative
force must certainly exist, and it is of significant amplitude, probably around 8.62 * 10-10 m/s2.
For comparison, if we accept the distance of the Sun from the center of the Galaxy to be 28,000
light years, and the total mass of the Galaxy to be 125 billion Suns, by Kepler we get a central
acceleration of 2.36 * 10-10 m/s2. These are not to be compared literally, due to the many
possible inaccuracies in the data within the Arm, but it is clear that the effects are on the same
order of magnitude. The Intra-Arm gravitational effects are strong enough to enable Arm
Stability and Persistence. In fact, they are strong enough to enable Arm-genesis.
Possible Implications
Due to collisions and the effects of near passes, it seems logical that the local density of material
would become greater near the centerline of the Arm, as compared to near the inner edge of it
where we currently are. Such a differential may even indicate the age that an Arm has had to
evolve. As noted above, the local mass density near the centerline may be twenty times what it
is around us now. That may be an indication that the Spiral Arms of the Milky Way Galaxy have
persisted for a long time. We calculated above that the Sun is likely to pass through that
congested area at extremely high transverse velocity, around 170 km/sec.
This might suggest that the Sun and Earth passed through a region of far more debris
approximately 13 million, 39 million, 65 million, 91 million, 117 million, etc, years ago.
Paleobiologists seem to have found some evidence for repetitive mass extinctions of species
at around those pseudo-periodic dates. The Sun would pass through that cluttered region at
extremely high (Arm-transverse) speed, while other debris would simultaneously be passing
through at equally high speed going the opposite direction. It therefore seems that a possible
astronomical explanation of such mass extinction periodicity might exist.
If such an object would hit the Earth head-on, the relative speed could be over ten times as fast as
any Solar System meteorite could impact the Earth. This would therefore involve over 100 times
the kinetic energy to cause destruction, such as the speculated K-T boundary event meteorite.
Actual Physical Evidence
There may be actual physical evidence for this. The orientation of the plane of the Solar System
is such that the southern hemisphere would have been in front as the Sun and planets passed
through that cluttered Arm centerline region, roughly 13 million years ago. (The Northern
hemisphere of each Solar System object would lead on the return path across that region (such as
13 million years in the future).
It has long been noted that the Moon has many more large impact craters in its southern
hemisphere than in the northern. The same has been found true of the planet Mercury.
Possibly even for Mars and some satellites. This new approach may provide a logical
explanation for that long-known asymmetry, that the (leading) south side of the Moon,
Earth, Mercury, Mars, etc, would have been susceptible to far more damaging collision
impacts than would be true of the trailing side. We note the same effect every night in that
evening meteors tend to be less brilliant than early morning meteors, because of being on the
trailing/leading sides of the Earth in its orbital motion.
This also implies that the many meteorite craters we see on the Moon's surface may NOT be four
and a half billion years old, but instead only about 13 million years old!
There is another possibility as well as the brute force impact.
Such an impacting object would have come from well outside our Solar System, quite possibly
carrying simple molecules or even amino acids that are not present in the Earth's or the Solar
System's environment.
This might provide a biological source for mass extinctions, and/or rapid bursts of new
biological species.
The unexplained bursts of biological diversity might therefore have an astronomical explanation.
The cratering of the Moon might also therefore occur primarily in cycles of around 26 million
years.
Many of the craters visible on the Moon might be from a barrage around 13 million years ago
rather than at the dawn of the Solar System.
Stars and material near the very tail of a Spiral Arm would have virtually all of the locally
attracting mass forward of it. We already calculated this boost acceleration as 8.0 * 10-10 m/s2.
This would have the effect of enhancing the forward- and inward-acceleration imparted on
materials in that region. This effect creates a meta-stable "adhesion" of such materials to the
main body of the Spiral Arm. This provides an explanation of how Spiral Arms can be stable for
extended periods of time, and without the Arms spiraling themselves around the Core as is often
suggested. The summed accelerations caused by the relative nearness of billions of solar masses
ahead of it are significant enough to have large effects.
Yes, a star near the end of the tail of a Spiral Arm is affected by the Keplerian Central Force of
maybe 100 billion solar masses, but it is also attracted by maybe 12 billion solar masses within
its own Arm, which are generally closer to it and therefore more gravitationally effective.
Our discussion above has assumed a constant mass density distribution throughout the length and
breadth of the Arm. We have already mentioned that it seems likely that the local mass density
near the Arm centerline may be 20 times our local mass density. It seems highly likely that due
to "forward migration" the local mass density will be greater nearer the Core (forward of us)
(where it is thought to be as high as 1.0 solar masses per cubic light year, around 700 times as
great as in our vicinity (Zielek p. 352)) and lower farther out in the Arm. If these situations are
true, the Arm-longitudinal effect described here becomes far greater yet.
Around 1998, I did extensive computer simulations regarding this concept. NO assumptions
were made, and only simple Newtonian gravitation was calculated, between each and all of the
component stars. The available computer had limited speed, so my simulations used 1000 equal
mass mega-stars, with a total mass approximating that of an entire Spiral Arm. In the
simulations, those 1000 objects were given initial random positions within a two-dimensional
tapering triangle shaped area, (indicated above) approximating the shape of a Spiral Arm.
A single iteration therefore involved approximately a million gravitational attractions of megastar to mega-star, which essentially devolved to determining the actual distance between the two,
to quad precision. Some simulations ran for weeks! The pattern was seen to gradually change
along the length of the Arm, with the objects tending to migrate together toward the wider
(forward) end of the pattern. There were also transverse bunchings near the centerline, mostly
due to close passes of the objects to each other, where some transverse velocity was sometimes
altered into longitudinal velocity. I interpret these things as indicating a self-sustaining
structure where the taper of the Spiral Arm actively maintained itself. All the individual
components continually weaved / danced back and forth across the width of the pattern.
Additional simulations were done where an additional mega-star was given
an initial location outside of the triangular region. The exact position and
initial velocity were critical, as sometimes it would be drawn into the Arm
pattern and sometimes it would drift away. It also occasionally happened that
one of the included mega-stars became severely perturbed by a close pass of
another mega-star and then exited the pattern area. Further study in this area
indicated that there is a meta-stability rather than a true stability, and that
there are some conditions where objects can break away.
The whorl of M51 that appears to have broken away from a now shortened
Arm is potentially an example of this.
There are also z-axis effects and oscillations for all components in the
Spiral Arm. Since the thickness of the Galaxy is rather small, these
effects seem to be somewhat irrelevant, and their shorter time periods of
oscillation seem to be unimportant. In the case of the Sun, the period of
this Z-axis oscillation may be around 12 million years. The current Solar
velocity toward the North Galactic Pole seems to be such that it will stop
around 400,000 years from now, only a few light years above where we
are now. This effect appears to provide an explanation for the "waviness"
of the Galaxy's Plane, where no other explanation seems to have been
presented.
This photo of NGC 891 shows a slight waviness in its plane.
Note that since all spiral arms have centerlines that angle inward toward
the front, the resulting acceleration not only acts to instantaneously
increase the orbital speed but also acts to add an incremental Central
Force to the existing Keplerian Central Force. The results of these two effects are different, but
they both act to inspire self-formation of spiral arms and also persistence of existing arms.
This general effect is somewhat similar to ice
skaters holding hands and circling in a "crackthe-whip" action. The image here is meant to
show an aerial view of a skating rink with
seven people standing still in a line. The lines
between the seven are meant to suggest their
arms as they are holding hands with each
other. The small lumps are to represent their
hands gripping each other.
They have now started to skate SLOWLY
around the one (larger) person who represents
a pivot point. Notice that the inner people are
hardly moving while the people farther out are
skating fairly quickly, in order to keep the line
straight. They each must skate at a speed that
is exactly proportional to the radius of the
circle they are following.
There is NO significant tension in the hand-tohand grips, and they are essentially only
needed to keep them all aligned in a row.
Here they have picked up rotary speed. The
inner skaters still have no trouble skating fast
enough to keep up, but the outer skaters are
now unable to skate fast enough to keep up.
They are only able to because of the additional
forward (and inward) thrust they receive from
the hand-to-hand connection with the next
person in.
The outermost skaters are now in a meta-stable
situation, where they are actually revolving
faster than they could otherwise skate! The are
receiving an additional force / acceleration
from the hand-to-hand pulling of the person
just inside them. That hand-to-hand
force/acceleration is both forward and inward
to create that effect. Notice that the angle of
that effect changes with the radius /speed
involved. In this particular example, the
outermost person is hardly any farther out than the next person in, and is pulled nearly directly
forward by the hand-to-hand tension.
That effect is meta-stable, as when any hand-to-hand grip slips, one or more outer skaters shoot
off radially outward! Therefore, in any large such skater formations, except at very low
rotational speed, the outermost skaters tend to be somewhat behind a desired straight line, which
makes the somewhat logarithmic curve pattern which is essentially the same as the observed
curvatures in all galaxy spiral arms.
At MODERATE rotation speed, most of the inner people can generally maintain the original
straight line formation, where only the outermost skaters cannot keep up and are pulled forward.
This is extremely similar to the pattern of the Barred-Spiral galaxies, which have rarely been
decently explained otherwise.
The currently popular density-wave concepts do not adequately explain several things. There
seems no provision for keeping most of the component stars from quickly escaping along the Zaxis. The universal logarithmic curvature/convexity seen in the shape of spiral arms would not
be a consequence of any (planar) density wave concept. In addition, no one seems to have
considered that an incoming planar gravity wave would have had to have come from some initial
direction, and there would therefore NOT be any "spiral pattern" of a shock or density wave at
all, but instead a rather planar wave which would pass through the region of a galaxy, allegedly
causing starbursts. There is no conceivable way that would cause a pattern of stars "lighting up"
that were ALWAYS in a spiral pattern! And a generally symmetric one at that! So the common
claims of a fairly uniform actual (but invisible) distribution of a disk mass, with the alleged
density waves causing localized ignition, cannot be causing spiral arm patterns. In addition,
many existing theories do not seem to properly consider Keplerian considerations as they
describe them.
There are claims that enormous amounts of invisible mass must exist, as in a giant massive halo
around the galaxy, but such claims seem to never have contemplates where that mass would have
to be! In some such theories, a super-massive halo is supposed to exist OUTSIDE the Galaxy,
but Newton showed us that such external mass would have no gravitational effects interior to it.
In some such theories, a very massive torus of invisible material (dark matter, hidden matter,
neutrinos) would have to exist around the rim of the Core, and additional peculiar distributions of
that mass would have to exist, in order to cause the non-Keplerian fast revolving of the Spiral
Arms. The alleged distribution is often simply referred to as an invisible halo! Such a structure
would not be stable or even meta-stable.
The alleged invisible matter could not be uniformly distributed, but it would have to be arranged
in a very unstable pattern. Such an unstable arrangement would have to exist in all of the many
observed spiral galaxies.
There are people who make a popular claim that 90% or 99% of all the mass of the entire
Universe is actually neutrinos. It is a rather silly idea, I think! Consider the known source of
neutrinos. A neutrino is emitted when a neutron breaks apart into a proton and electron, and is
needed back when they re-combine to form a neutron again. That seems to me to indicate a
pretty solid limitation that there are not likely to be more neutrinos in existence than there are
neutrons. Yet those very speculative theories claim that there are billions or trillions of times as
many neutrinos than neutrons or protons. If there actually were such an astounding number of
them, then someone should explain where they all originally came from! The claims seem to
force a conclusion where all those neutrinos were created at the start of the Universe, with no
actual function or purpose, just somehow existing to account for a lot of mass that people think is
needed! Sounds pretty funny to me!
Calculations and an extended presentation are presented in a web-site at
http://mb-soft.com/public/galaxy.html Explaining Galaxy Arm Stability / Apparent Rotation
Inconsistencies
Also: http://mb-soft.com/public/galaxyzz.html
References
Michael Zeilek Astronomy: The Evolving Universe
First Developed, Nov 1997,
First Published on the Web: Aug 16, 1998