Galaxy rotation curve

[ccwebb]

This still just baffles me and I was hoping it can be explained better. How do we know that an entire spiral galaxy is spinning at the same speed? I mean, we (solar system) haven't even made it one lap around the milky way yet. How can we tell that other galaxies are spinning at all?

 

For simplicity, I was reading on Wikipedia:

"...a new sensitive spectrograph that could measure the velocity curve of edge-on spiral galaxies to a greater degree of accuracy than had ever before been achieved. Together with fellow staff-member Kent Ford, Rubin announced at a 1975 meeting of the American Astronomical Society the discovery that most stars in spiral galaxies orbit at roughly the same speed."

 

Roughly? Obviously this have been proven, but it surprised me when I learned that so much study was placed on on observation conducted within a decade. Pluto hasn't even made it a full orbit around the sun since it was discovered, yet we can see how fast a spiral galaxy is spinning?

 

Thank you in advance for the education I so obviously need...

Edited March 24, 2014 by ccwebb

[Greg H.]

As far as I know, you don't have to measure the entire orbit of an object to determine its orbital velocity as long as the orbit is assumed to be stable. If, for example, I determine that it takes the earth 3 months to cover rougly a quarter of its orbit, then I can feel reasonably certain it would take 12 months to cover the whole thing. Combined with the distance from the center of gravity, I can determine the orbital velocity with a reasonable amount of error. The math isn't that hard - you just need measurements precise enough to be useful.

 

In fact, all you really need to compute it is a fairly accurate measurement of the masses of the two objects and the distance between them to compute the orbital velocity:

 

[math] v_o = \sqrt{\frac{G (m_1 + m_2)}{r}}[/math]

 

See: http://en.wikipedia.org/wiki/Orbital_speed

[ccwebb]

Greg, I understand what you are saying. That makes complete sense on the planetary level. However, on the galaxy level, everything is said to move at the same orbital speed. How is that possible with systems of different masses, distances and so on?

 

(I know this eventually leads into other threads about dark matter, so I want to make sure I am clarifying my question.)

 

How can other galaxies orbital speed be measured when there is practically no rotation during our life time? The formula above proves that if the masses or distance are different, then there should be different speeds. Yet is has been proven they entirety of a spiral galaxies (maybe others?) orbits at one speed.

[J.C.MacSwell]

As far as I know, you don't have to measure the entire orbit of an object to determine its orbital velocity as long as the orbit is assumed to be stable. If, for example, I determine that it takes the earth 3 months to cover rougly a quarter of its orbit, then I can feel reasonably certain it would take 12 months to cover the whole thing. Combined with the distance from the center of gravity, I can determine the orbital velocity with a reasonable amount of error. The math isn't that hard - you just need measurements precise enough to be useful.

 

In fact, all you really need to compute it is a fairly accurate measurement of the masses of the two objects and the distance between them to compute the orbital velocity:

 

[math] v_o = \sqrt{\frac{G (m_1 + m_2)}{r}}[/math]

 

See: http://en.wikipedia.org/wiki/Orbital_speed

The galaxy problem lies in the fact that the assumptions used to produce that formula, taking into account all the apparent mass in the galaxies, don't seem to hold true. (so Newton's law of gravitation wasn't matching the evidence)

This still just baffles me and I was hoping it can be explained better. How do we know that an entire spiral galaxy is spinning at the same speed? I mean, we (solar system) haven't even made it one lap around the milky way yet. How can we tell that other galaxies are spinning at all?

 

For simplicity, I was reading on Wikipedia:

"...a new sensitive spectrograph that could measure the velocity curve of edge-on spiral galaxies to a greater degree of accuracy than had ever before been achieved. Together with fellow staff-member Kent Ford, Rubin announced at a 1975 meeting of the American Astronomical Society the discovery that most stars in spiral galaxies orbit at roughly the same speed."

 

Roughly? Obviously this have been proven, but it surprised me when I learned that so much study was placed on on observation conducted within a decade. Pluto hasn't even made it a full orbit around the sun since it was discovered, yet we can see how fast a spiral galaxy is spinning?

 

Thank you in advance for the education I so obviously need...

The speeds of rotation were calculated from the difference in the redshift (generally) relative to that of the galaxy as a whole. So one "snapshot" could provide a lot of information given the right set of assumptions and measurements. I don't believe they were noting any displacements over time to get the data.

Edited March 24, 2014 by J.C.MacSwell

[michel123456]

IIRC orbital speed goes less and less as the distance from the center increases. Laws of planetary motion do not give a same orbital speed for all objects.

 

from http://en.wikipedia.org/wiki/Orbital_speed#Transverse_orbital_speed

 

Transverse orbital speed

The transverse orbital speed is inversely proportional to the distance to the central body because of the law of conservation of angular momentum, or equivalently, Kepler's second law. This states that as a body moves around its orbit during a fixed amount of time, the line from the barycenter to the body sweeps a constant area of the orbital plane, regardless of which part of its orbit the body traces during that period of time. This law is usually stated as "equal areas in equal time."^{[citation needed]}

This law implies that the body moves faster near its periapsis than near its apoapsis, because at the smaller distance it needs to trace a greater arc to cover the same area.

 

Edited March 25, 2014 by michel123456

[swansont]

 

IIRC orbital speed goes less and less as the distance from the center increases. Laws of planetary motion do not give a same orbital speed for all objects.

 

 

For a large central mass. Which is why dark matter was hypothesized — if the mass also increases with distance, the speed increases relative to the prediction without the dark matter.

[michel123456]

 

For a large central mass. Which is why dark matter was hypothesized — if the mass also increases with distance, the speed increases relative to the prediction without the dark matter.

But the spiral shape corresponds to the predictions of laws of motion without dark matter.

No?

[swansont]

But the spiral shape corresponds to the predictions of laws of motion without dark matter.

No?

 

No. As you point out, the basic model has a speed that depends on the distance from the center, which is a problem for a permanent spiral. This is known as the winding problem.

[michel123456]

 

No. As you point out, the basic model has a speed that depends on the distance from the center, which is a problem for a permanent spiral. This is known as the winding problem.

I thought it was established that in a spiral galaxy, the objects do not go towards the center but simply orbit the galaxy round and round.

Just like objects in the solar system orbit the Sun, objects in a galaxy orbit the center of the galaxy.

Edited March 25, 2014 by michel123456

[swansont]

I thought it was established that in a spiral galaxy, the objects do not go towards the center but simply orbit the galaxy round and round.

 

Yes. But if they orbited as expected without dark matter, there would not be a simple spiral. The inner part of the arms should have revolved much more than the outer part, i.e. it should be more "wound up" than we see.

[michel123456]

 

Yes. But if they orbited as expected without dark matter, there would not be a simple spiral. The inner part of the arms should have revolved much more than the outer part, i.e. it should be more "wound up" than we see.

Oh, I see.

But in this case, dark matter should be "in" the objects. I mean, the observed objects should be more massive than expected. Not that there should exist dark matter around them.

[swansont]

Oh, I see.

But in this case, dark matter should be "in" the objects. I mean, the observed objects should be more massive than expected. Not that there should exist dark matter around them.

 

Dark matter around them would have an effect on the rotation speed, so I'm not seeing why this is true.

[Janus]

Oh, I see.

But in this case, dark matter should be "in" the objects. I mean, the observed objects should be more massive than expected. Not that there should exist dark matter around them.

 

That would effect the orbital speeds, but not the relative distribution of the speeds.

 

Here's the gist of it: You look at that galaxy and see how its visible mass is distributed (A central bulge and disk.) You then calculate what the orbital speeds should be at different distances from the center of the galaxy given this distribution of mass and you plot a curve of orbital speed vs distance. You look at how fast stars at different distances actually orbit. This will tell you how much mass is actually inside the orbit of each star. and plot the orbital speed vs distance curve.

 

Now the first curve is based on the guess of how much matter there is, but as long as as the mass is actually distributed as it visibly appears to be, the two curves should be a simular shape. There may be more or less actually mass than your guess, but this only leads to a difference of scale in the curves.

 

However, what we do see is that the two curves look nothing like each other. The first curve is what we would expect if the mass distribution matches what we see of the galaxy. The second matches what we would expect if there was mass distributed above and below the visible part of the galaxy, mass that we do not see.

[michel123456]

That would effect the orbital speeds, but not the relative distribution of the speeds.

 

Here's the gist of it: You look at that galaxy and see how its visible mass is distributed (A central bulge and disk.) You then calculate what the orbital speeds should be at different distances from the center of the galaxy given this distribution of mass and you plot a curve of orbital speed vs distance.

O.K. based on the laws of planetary motion, you get a speed decreasing with distance.

You look at how fast stars at different distances actually orbit. This will tell you how much mass is actually inside the orbit of each star. and plot the orbital speed vs distance curve.

I don't understand why does that give you "how much mass is actually inside the orbit of each star". Do you mean as if the "how-much-mass' was concentrated in the centre?

 

Now the first curve is based on the guess of how much matter there is, but as long as as the mass is actually distributed as it visibly appears to be, the two curves should be a simular shape. There may be more or less actually mass than your guess, but this only leads to a difference of scale in the curves.

 

However, what we do see is that the two curves look nothing like each other. The first curve is what we would expect if the mass distribution matches what we see of the galaxy. The second matches what we would expect if there was mass distributed above and below the visible part of the galaxy, mass that we do not see.

I really don't understand. If the law predicts that speed must decrease with distance, and we are observing that it is not the case, how is it possible to correct the situation by increasing the mass inside the orbit?

[ccwebb]

The galaxy problem lies in the fact that the assumptions used to produce that formula, taking into account all the apparent mass in the galaxies, don't seem to hold true. (so Newton's law of gravitation wasn't matching the evidence)

The speeds of rotation were calculated from the difference in the redshift (generally) relative to that of the galaxy as a whole. So one "snapshot" could provide a lot of information given the right set of assumptions and measurements. I don't believe they were noting any displacements over time to get the data.

 

Ooohh... I see. Red shift of the light is used. Thank you.

 

 

O.K. based on the laws of planetary motion, you get a speed decreasing with distance.

I don't understand why does that give you "how much mass is actually inside the orbit of each star". Do you mean as if the "how-much-mass' was concentrated in the centre?

 

I really don't understand. If the law predicts that speed must decrease with distance, and we are observing that it is not the case, how is it possible to correct the situation by increasing the mass inside the orbit?

 

In addition to your question (in which I was going to ask as well) Why does the inner parts (systems) act differently than the whole? Why would the galaxy spin/rotate different than the planets orbiting the stars inside itself?

[Strange]

O.K. based on the laws of planetary motion, you get a speed decreasing with distance.

I don't understand why does that give you "how much mass is actually inside the orbit of each star". Do you mean as if the "how-much-mass' was concentrated in the centre?

 

I really don't understand. If the law predicts that speed must decrease with distance, and we are observing that it is not the case, how is it possible to correct the situation by increasing the mass inside the orbit?

 

Take the solar system as an example. Pretty much all the mass is in the Sun and so you get a the expected change in orbital speed, dependent only on distance. That is because the mass inside the orbit is the same for all planets (it is the mass of the Sun).

 

However, if there was significant mass distributed throughout the solar system, then the further out you went, the more mass there would be within the the orbit. And so velocities wouldn't fall off as expected. (It is important to note that only mass inside the orbit has any effect.)

 

The latter is what we observe with galaxies (and galaxy clusters) meaning that the mass isn't concentrated in the most visbily massive bulge in the middle.

[swansont]

I don't understand why does that give you "how much mass is actually inside the orbit of each star". Do you mean as if the "how-much-mass' was concentrated in the centre?

 

I really don't understand. If the law predicts that speed must decrease with distance, and we are observing that it is not the case, how is it possible to correct the situation by increasing the mass inside the orbit?

 

Speed decreasing with distance assumes the bulk of the mass is at the center. If the mass is distributed, the speed behavior changes.

[Cosmobrain]

Their shapes wouldn't be possible if they weren't spinning

[LaurieAG]

I posted the following thread about what the apparent light paths from sources rotating around a center of mass would look like geometrically.

 

http://www.scienceforums.net/topic/75390-apparent-red-shift-in-a-discrete-newtonian-frame/

 

It is well known that Newton worked out all of his proofs geometrically first before identifying the underlying mathematics and Einsteins papers progress from geometric considerations as well. When did this method become passe?