How Does Dark Matter Influence the Spin of Galaxies Compared to Solar Systems?

[nhmllr]

Okay, so I understand that galaxies spin more like a frisbee than the solar system, and that there is evidence for a lot of non-light-emitting mass (such as gravitational lensing) but how would dark matter account for the difference in the spin of galaxies? Gravity still decreases inverse to the square of the distance, right? And also, why wouldn't dark matter have an effect on the solar system, where pluto would orbit in one Earth year?

 

[Ken G]

Okay, so I understand that galaxies spin more like a frisbee than the solar system, and that there is evidence for a lot of non-light-emitting mass (such as gravitational lensing) but how would dark matter account for the difference in the spin of galaxies?

Actually, spiral galaxies don't spin like frisbees either. The solar system orbits such that farther planets from the center are slower, and frisbees spin such that farther places from the center are faster. Galaxies spin with nearly constant speed everywhere-- so the analogy there might be joggers on a circular track, assuming people generally jog at a similar speed.

Gravity still decreases inverse to the square of the distance, right?

Yes, the difference is not in the nature of the gravity, it is in the nature of the mass distribution. When we have gravity that falls like distance squared for an entire mass distribution, it means the mass distribution is highly centrally concentrated, almost like a point of mass at the center. But if the mass distribution is very spread out, such that a lot of the mass is actually at larger radius than the point in question, then only the mass interior to the point in question contributes to the gravity there (the rest canceling if it is a spherically symmetric distribution). So as you go farther out in the galaxy, more of the dark matter mass contributes, because the dark matter is very spread out (unlike the stars, which are centrally concentrated). That's the key to allowing the orbital speeds to stay the same-- more mass contributing to holding them in, as you go farther out.

And also, why wouldn't dark matter have an effect on the solar system, where pluto would orbit in one Earth year?

Because dark matter is relatively low density, regions where the regular matter is concentrated, like solar systems, can ignore it.

 

[nhmllr]

Ah, I see. But then why wouldn't the dark matter just fall into the centers of galaxies?

 

[Ken G]

It is falling all the time-- but it can't lose energy, so it cannot shrink. It just falls right on past and keeps on going-- like an orbit. Exactly like an orbit.

 

[nhmllr]

It is falling all the time-- but it can't lose energy, so it cannot shrink. It just falls right on past and keeps on going-- like an orbit. Exactly like an orbit.

Oh, like a pendulum. Makes sense, thank you!

 

[Chronos]

Dark matter is collionless. It falls in, but, without collisions to slow it down, it just shoots right back out again. IOW - what Ken said.