# Missing Matter Problem and Galactic Flows

1. Mar 5, 2015

The standard example of the Missing Mass Problem comes from the rotational profiles of galaxies. By counting up the visible matter, we extrapolate a mass profile for a galaxy. We then apply Kepler's laws (the enclosed mass of a stable orbit can be modeled as a point mass) to calculate the expected velocity:

$f(v) = \sqrt{\frac{GM}{r}}$
Where G is the gravitational constant, M is the enclosed mass of an elliptical orbit, r is the radius of the orbit. But this formula assumes a closed, elliptical orbit. I'm sure the data exists, but I haven't been able to find it. How do we know that the Earth, for instance, is not falling towards or away from the center of the Milky Way. That is, when we apply the rules of Keplar's orbits, what information do we have that the orbits of the observed galactic bodies describe a closed ellipse and not a spiral in or out (which would change the amount of missing mass considerably)?

Last edited: Mar 5, 2015
2. Mar 5, 2015

### Drakkith

Staff Emeritus
We can measure our velocity relative to other stars in the galaxy. We happen to be sitting right in the middle, faster than some and slower than others. Our relative velocity is taking us around the galaxy, not towards or away from the center. We do drift around some thanks to interactions with nearby stars, but overall we're in a stable orbit around the center. Also, orbits do not spiral inward unless the orbiting body has a way of losing kinetic energy.

3. Mar 5, 2015

The tangential velocity is well understood and measured (I've found numerous papers on the subject) at roughly 235 km/s. What appears to be less well understood is the radial component of that velocity. You say we're in a stable orbit, but I can't find any definitive papers on the subject. Would you mind sending me the reference that you're using?

Yes, and stars are supposed to get slower as you get further away from the galactic center, but they don't. If the disk is the result of a galactic collision, then the disk could be the result of the ejecta and be spiraling out or in. I'm looking for a kinematic study that supports the assumption of a closed, elliptical orbit.

4. Mar 5, 2015

### Staff: Mentor

The orbital period of such an orbit, at our distance from galactic center, is about 250 million years; that's the relevant dynamic time scale. If the solar system were not in such an orbit, it would not have remained stable for a time 18 times longer than that time scale.

5. Mar 5, 2015

Whoa! That's the part I'm missing. How do you know we've been stable for 18 times 250 million years? We could have been spiraling outward (at roughly 0.5 km/s by my calculations) or spiraling in (again, as ejecta as the result of a collision). Would you please point me in the direction of the reference you use?

Last edited: Mar 5, 2015
6. Mar 5, 2015

### Chalnoth

This is largely down to the way gravity works.

Gravity, in the Newtonian approximation (which is good enough for the orbits of most stars in our galaxy), is a force that conserves energy. For an orbit to spiral inward or outward would require a loss or gain of energy. So the question arises: where would the energy be coming from or going to?

A close pass between our Sun and another star might transfer some energy between the two stars, but stars rarely pass that close to one another. For the most part, the Sun's orbital energy remains pretty constant. There's a little bit of friction from the interstellar gas, but that's a pretty small effect.

7. Mar 5, 2015

Where is the energy lost or gained: Collision with a dwarf galaxy could either add or remove energy/mass from the Milky Way. For all we know, our local group of stars could be the remnants of a galaxy that was merged billions of years ago. Most spirals are believed to have been formed from mergers. There's substantial evidence of large streams of matter in our halo from previous collisions. So can we move on to the question of whether we're falling in, falling out or in a stable orbit?

8. Mar 5, 2015

### Chalnoth

The energy transfer only occurs during the collision. The collision (or close pass) changes the orbit. The orbit immediately after the interaction that changes the energy of the orbit is a stable orbit (until a new interaction occurs).

9. Mar 5, 2015

I can't figure out what you are talking about. When exactly did the collision between the proto-galaxies stop?
(OK, the moon was a bad example, but the collision between proto-galaxies will be felt for hundreds of millions, perhaps billions of years. There will be ebbs and flows and ejecta from the collision).

Last edited: Mar 5, 2015
10. Mar 5, 2015

### Drakkith

Staff Emeritus
If two galaxies collide, the collision is over with once the two galaxies are separated again. If they don't separate, then the collision just rolls into a complicated merging process. Collisions of galaxies are more like long-term processes anyways, not single events, since the relevant interactions take place over the course of hundreds of millions of years.

The Moon gets further away because of the transfer of rotational energy from the Earth to the Moon. This slows down the Earth's rotation and accelerates the Moon, resulting in a larger orbit.
http://en.wikipedia.org/wiki/Tidal_acceleration

11. Mar 5, 2015

### Chalnoth

That's a very different effect. The Moon's orbit is slowly increasing because of tidal effects: the fact that the Earth's rotational period is different from the Moon's orbital period transfers energy from the Earth's rotation to the Moon's orbit. This effect is only significant for objects that are very close to one another.

The solar system itself is more than 3 light years from any other star. There just aren't any collisions/close passes going on at the moment. Nor are there likely to be any time soon.

12. Mar 6, 2015

Where is the energy lost or gained: Collision with a dwarf galaxy could either add or remove energy/mass from the Milky Way. For all we know, our local group of stars could be the remnants of a galaxy that was merged billions of years ago. Most spirals are believed to have been formed from mergers. There's substantial evidence of large streams of matter in our halo from previous collisions. If you've ever watched a simulation of galaxy collisions, it's not immediately obvious what parts fall back in and what parts are ejected (into the halo). Can we move on to the question of whether we're falling in, falling out or in a stable orbit, please?

13. Mar 6, 2015

### Chalnoth

That question has been answered, a few times. Our solar system's orbit is relatively stable until the Sun experiences a close pass with another star.

14. Mar 6, 2015

You've expressed your opinion. I asked for references. I would like to read up on the data used and the method employed to determine that the orbit is closed. I'm assuming you must have read something also to have such a strong belief in the subject, so please share with me how you came upon this information.

15. Mar 6, 2015

### Bandersnatch

For an orbit not to be closed the mass inside the radius of the orbit would need to be changing. With constant central mass all orbits are closed. For the proof of this statement look towards Newtons Principia, or read on central force motion.
Galactic mergers can only be relevant while in progress, as has been mentioned already. You can't have a spiral for an orbit if there's no mass currently being added. Past mergers affected past orbits. Current orbits have to be stable closed ones (perturbations notwithstanding), as there are no on-going mergers.

16. Mar 6, 2015

### Drakkith

Staff Emeritus
Here you are: Radial Migration of the Sun in the Milky Way: a Statistical Study

ABSTRACT The determination of the birth radius of the Sun is important to understand the evolution and consequent disruption of the Sun’s birth cluster in the Galaxy. Motivated by this fact, we study the motion of the Sun in the Milky Way during the last 4.6 Gyr in order to find its birth radius. We carried out orbit integrations backward in time using an analytical model of the Galaxy which includes the contribution of spiral arms and a central bar. We took into account the uncertainty in the parameters of the Milky Way potential as well as the uncertainty in the present day position and velocity of the Sun. We find that in general the Sun has not migrated from its birth place to its current position in the Galaxy (R). However, significant radial migration of the Sun is possible when: 1) The 2 : 1 Outer Lindblad resonance of the bar is separated from the corrotation resonance of spiral arms by a distance ∼ 1 kpc. 2) When these two resonances are at the same Galactocentric position and further than the solar radius. In both cases the migration of the Sun is from outer regions of the Galactic disk to R, placing the Sun’s birth radius at around 11 kpc. We find that in general it is unlikely that the Sun has migrated significantly from the inner regions of the Galactic disk to R.

17. Mar 6, 2015

### Tanelorn

18. Mar 7, 2015

### Chronos

The Hulse-Taylor study closed the book on kinetic energy loss due to gravitational waves, as predicted by Einstein. It appears consistent with the figure offered by PeterDonis.

19. Mar 8, 2015

Correct me if I'm wrong, but this paper appears to be the results of a simulation, not a kinematic study. Am I missing something?

20. Mar 8, 2015