SPIRAL GALAXIES AND no-no DARK MATTER
Everybody is fascinated with a beauty of spiral galaxies with bright spiral arms. Their shape is very stable and lasts for billions of years and rotates very slowly compared to the stars rotating through the arms again and again. Milky Way — our home galaxy is a spiral galaxy too, and our Sun and Earth are in Orion Spur of the Sagittarius Arm at the moment, but we’ll get out of the arm in a few million years. There is one long standing problem — when astronomers (Vera Rubin especially) measured velocity of some stars near the perimeter of spiral galaxies, they found it was too high — stars should have flown away from the galaxy if stars’ trajectories were circular. To explain how these stars are retained in their galaxies some scientists suggested that galaxy itself is in some ball-shaped cloud of Dark Matter, which provides additional gravitation pull to retain the stars. No such Dark Matter was “measured” or “discovered” so far. And when more data about stars’ trajectories was collected — the theory collapsed.
How stars move in Spiral Galaxies? You can find computer animations that were built of the measurements and see that stars move like a fish school — often changing direction and velocity, amazingly synchronous, and without collisions. Dark Matter ball cannot do such schooling — it can drive stars in circular orbits only. You can say “Programmers got it all wrong”. But in 2010 very precise measurements from our galaxy came, let me quote https://phys.org/news/2010-11-milky-stars-mysterious-ways.html:
“… by an international team including several researchers from the Strasbourg Astronomical Observatory: near the Earth, stars move towards the exterior of the Galaxy at an average speed of around 10 kilometers per second, which is considerably faster than previously thought… The researchers were thus able to ascertain that the average speed of stars towards the exterior of the Galaxy increases with their distance from the Sun in the direction of the Galactic center, reaching 10 kilometers per second at a distance of 6,000 light years from us (in other words, 19,000 light years from the Galactic center).”
Let me describe this observation in other words: while looking from Earth down into Milky Way center astronomers noticed some stars rush from their low orbit to a higher orbit. That is known as “Hohmann transfer orbit” — when a satellite is given a thrust to get to a higher orbit:
For such satellite to stay on a higher orbit, another thrust is required when the higher orbit reached. Otherwise, the satellite continues down by its elliptic orbit, fluctuating between two “heights”. And in reverse — if task is to lower a satellite from a higher circular orbit to a lower circular orbit: one thrust in the opposite to the movement direction first, then another thrust in the opposite to the movement direction when the lower orbit is touched. Without the second thrust, the satellite will continue by its elliptic orbit, oscillating between two “heights”. Later we’ll see that for a star in a spiral galaxy, its velocity is boosted when the star exits a spiral arm, and its velocity is reduced when the star enters another spiral arm. Now we have to find what gives such thrust to the stars in spiral galaxies, and the value of it.
Let’s return to the Doppler redshift and time dilation. (If not familiar with these, please check TIME DILATION = REDSHIFT, and no-no Big Bang). Let’s look at simple imaginary task of calculating velocity of a ball falling of a moving platform:
Now let’s look at the same task when the reason for blueshift between two timezones is not because of Doppler effect, but because of time running differently in the white (at the left of the drawing below) and in the grey (at the right of the drawing below) zones. Let Z’ be blueshift observed by someone staying in the grey zone and looking to the white zone and Z is redshift observed by someone staying at the white zone looking at the grey zone. Z and Z’ are related by Z’=-Z/(1+Z) formula, so for small Z:
Z’ = — Z almost.
From “redshift” perspective this drawing is equivalent to the previous drawing. If two cases are the same from redshift perspective — then the impact on trajectories and velocities is the same — why? Basically, it is known since Einstein’s General Theory of Relativity, but was stated in other than redshift terms. It is because time changes cause geodesic changes of space, and light follows altered geodesic layout by taking new fastest path. Redshift (wavelength change) causes refraction by the same reason — light follows the fastest path. Change in geodesic layout impacts all object trajectories. In a sense, this observation is close to mass equivalency by Einstein — gravitational and inertial: the cause of gravity is not some force but in geodesy. So, we can just reuse math from the previous drawing: V’ = V — Z’ * c. And since Z’ = — Z we get the following relation between velocities of the object when it crosses timezone border:
V’ = V + Z * c
The above formula is for non-relativistic velocities V and Z * c — when redshift Z is close to 0. For relativistic velocities, we are to use another formula that I put at the end of this chapter, and add velocities using Einstein’s formula for velocity addition.
Coming back to the Spiral Galaxy problem — the solution is in timezones: time in spiral arms runs faster than outside the arms (in grey areas). Or time in grey areas is slower than in spiral arms.
Here are several facts confirming time difference between arms and non-arms:
1) Arms are brighter — because time runs faster, stars burn faster, highlighting the area of the faster time.
2) “White and blue” stars are more common in the arms and “yellow and reddish” stars are more common in the grey area — it is because arm / not arm areas are blueshifted / redshifted to each other.
3) There is an impression that new stars being born when entering the arms, and an impression that some stars die when leaving the arms. The actual reason is different and it is good to discuss it here. Some stars of Spiral Galaxies are on the edge of a critical mass, their burner is either flickering, or goes on and off. By now we understand when time speeds up the probability of certain events goes up, in this case — the probability of Hydrogen atom collisions in a star. That ignites a star that was off, and was on the edge of a critical mass — when such star enters an arm where time runs faster. And when such star exits an arm, its burner goes off again — so for an external observer star dies on exiting the arm.
Why or how come that time is faster in spiral arms - read in BURNING TIME IN LABS AND IN GALAXIES later.
And even more. Why stars move in a fish school manner we already explained using “Hohmann transfer orbit” and by the formula V’ = V + Z * c (velocity boost happens when star exits an arm — enters a grey area, and velocity is reduced by Z*c when star enters an arm). Why stars do not collide on such maneuver? Two reasons for this:
All stars’ velocities change by the same value Z*c (and they try to follow changed geodesic lines);
Another reason, and it was recently confirmed for the stars at the center of Milky Way, stars are saved from the collisions by their magnetic field pushing them away when they come close. They are repelled like the same polarity’s magnets when coming close to each other. See screenshots from a video posted on Youtube that shows two stars on the collision course and how they bounce off each other:
And now coming back to Vera Rubin’s paradox, when she plotted observed maximum velocities of stars by distance R from the center of a galaxy, she received velocities like that:
VERA RUBIN’s DELTA + Const * R⁻⁰·⁵ + Fluctuations
Apart from Const*R⁻⁰·⁵ that comes from the gravitational pull, the rest we already figured out in this chapter:
· Fluctuations come from “Hohmann transfer orbit” and non-circular orbits
· The puzzling constant VERA RUBIN’S DELTA is Z*c constant of the boost!
From VERA RUBIN’S DELTA of a specific spiral galaxy we can find redshift between arms and grey areas of this galaxy:
Z = VERA RUBIN’s DELTA / c
Please take a moment to appreciate that a small redshift ~1/c has a profound effect on the galactic processes: it switches stars on and off and messes up all orbits. Vera Rubin measured velocity at the perimeter of five dozen galaxies, results were at 100–300 km/sec range, half of them around 300 km/sec. That gives Z around 0.001. What a big impact should be anticipated for larger redshift values. Meaning, what a profound effect should be anticipated when time differences are big. When we were calculating the boost value S, we rounded formula
1+ Z = (1+S/c)⁰·⁵ / (1-S/c)⁰·⁵
for small values of redshift Z. Let’s do exact calculations for Z>>0:
(1+ Z)² = (1+S/c) / (1-S/c) => (1+ Z)² * (1-S/c) = 1+S/c =>
(1+ Z)² — (1+ Z)² * S/c = 1+S/c => (1+ Z)² — 1= (1+ Z)² * S/c+S/c =>
2Z + Z² = (2+2Z+Z²) * S/c => S/c = (2Z+Z²)/(2+2Z+Z²) =>
S = (2Z+Z²)/(2+2Z+Z²)*c
That gives us formula for relativistic boost
(2Z+Z²)/(2+2Z+Z²)*c
and it is comparable to speed of light c when Z>1.
P.S. Check Time Energy Potential = 0.5 c²/D² with a different approach for boost estimation.
