Dark Matter Halo: Exploring Dynamics & Time Scales

[oldGhost1]

From other threads here I’ve gained a rough understanding of why Dark Matter forms into a halo around galaxies. It makes sense, since DM doesn’t interact and doesn’t clump together, that when a DM particle falls from the halo towards the gravitational centre of the galaxy it gradually accelerates all the way up to very high speeds near the galactic centre. Once it has passed through this central region it then decelerates on the way out again and returns back to the halo with very little momentum, where eventually it will start to fall towards the galaxy centre again. And in order for the halo to exist to the extent it does, each DM particle must spend more time in the halo than traveling across the galaxy.

I’m not sure I’ve got the last bit right though since 1) our galaxy is 100,000+ light-years across, 2) the halo is said to be far outside this limit and 3) the DM particle will only be traveling at a sizeable fraction of light speed for a small percentage of its journey. With these factors in mind I’d expect a DM particle to take several 100,000s (if not millions) of years between leaving and returning to the halo. So is it correct that it spends more time in the halo than out, and what are the current best estimates for the time scales of these oscillations?

Also, on a more local scale, DM is said to be all around us, with roughly uniform distribution but at low density. I’m just wondering if this local DM consists entirely of that which is traveling across our galaxy or whether some of the DM has been permanently trapped by our sun’s local gravity well?

I ask because I could imagine that by the time a DM particle gets to our solar system it has built up enough momentum to escape the ‘pull’ of the sun. If that is the case, are there any stars that DM particle encounter before they have gained ‘escape momentum’ (i.e. large stars, close to the galaxy rim) around which we might expect to find miniature DM halos?

 

[phinds]

The speed of travel at the various points in its journey, and the absolute time it spends in various locations, is irrelevant to the halo formation as long as the speed is enough to overcome the gravitational pull of the center of the galaxy and not so much that it exceeds escape velocity. Another way of saying this is that a sine wave with a high amplitude is exactly the same shape as a sine wave of a lower amplitude other that a scale factor. If you include the scale factor in the Y axis then the two look the same. If you then draw a line at, say, 50% of the height and see how much time points spend above that line vs below that line, you'll see why the halo exists.

 

[oldGhost1]

The speed of travel at the various points in its journey, and the absolute time it spends in various locations, is irrelevant to the halo formation as long as the speed is enough to overcome the gravitational pull of the center of the galaxy and not so much that it exceeds escape velocity. Another way of saying this is that a sine wave with a high amplitude is exactly the same shape as a sine wave of a lower amplitude other that a scale factor.

Thanks. Yes I hadn't really considered a population of particles with varying speeds, but of course those particles from the outer edge of the halo have a longer journey and so will build up more speed than those which only make it as far as the inner edge of the halo. So these latter DM particles spend most of there time traveling across the galaxy and little time in the halo, whilst faster moving particles make it to the outer rim and spend a high proportion of their time within the halo. So overall, the average DM particle spends more time in the halo than out.

 

[phyzguy]

From other threads here I’ve gained a rough understanding of why Dark Matter forms into a halo around galaxies. It makes sense, since DM doesn’t interact and doesn’t clump together, that when a DM particle falls from the halo towards the gravitational centre of the galaxy it gradually accelerates all the way up to very high speeds near the galactic centre. Once it has passed through this central region it then decelerates on the way out again and returns back to the halo with very little momentum, where eventually it will start to fall towards the galaxy centre again. And in order for the halo to exist to the extent it does, each DM particle must spend more time in the halo than traveling across the galaxy.

I’m not sure I’ve got the last bit right though since 1) our galaxy is 100,000+ light-years across, 2) the halo is said to be far outside this limit and 3) the DM particle will only be traveling at a sizeable fraction of light speed for a small percentage of its journey. With these factors in mind I’d expect a DM particle to take several 100,000s (if not millions) of years between leaving and returning to the halo. So is it correct that it spends more time in the halo than out, and what are the current best estimates for the time scales of these oscillations?

Also, on a more local scale, DM is said to be all around us, with roughly uniform distribution but at low density. I’m just wondering if this local DM consists entirely of that which is traveling across our galaxy or whether some of the DM has been permanently trapped by our sun’s local gravity well?

I ask because I could imagine that by the time a DM particle gets to our solar system it has built up enough momentum to escape the ‘pull’ of the sun. If that is the case, are there any stars that DM particle encounter before they have gained ‘escape momentum’ (i.e. large stars, close to the galaxy rim) around which we might expect to find miniature DM halos?

(1) We don't believe that the DM particles are traveling anywhere near light speed. This is the meaning of the "Cold" in calling it Cold Dark Matter (as in Lambda-CDM). For the DM in our galactic halo, we think the particle velocities are on the order of 100's of km/sec, so the orbital time scales are on the order of 100's of millions of years. Much faster than this, and the DM particles would exceed the escape velocity from the galaxy and simply escape.

(2) We don't think there is a significant quantity of dark matter trapped by stars, because there is no way for it to get trapped. In order to get trapped, it has to somehow interact and lose energy.
Otherwise it simply falls into the star's potential well and flies on out again. However, there is some small probability that a DM particle could interact with an atom in the star's core and get trapped. There are proposals to look for annihilation of these particles which might have been trapped in the sun's core through interactions over the sun's lifetime, but so far no confirmed signal has been seen.

 

[oldGhost1]

For the DM in our galactic halo, we think the particle velocities are on the order of 100's of km/sec, so the orbital time scales are on the order of 100's of millions of years. Much faster than this, and the DM particles would exceed the escape velocity from the galaxy and simply escape.

Just to be clear, does this speed refer to the particles in the halo or those falling towards the galaxy centre? (I would expect the latter to be significantly faster than the former)

We don't think there is a significant quantity of dark matter trapped by stars, because there is no way for it to get trapped. In order to get trapped, it has to somehow interact and lose energy.

I wasn't really thinking of it being trapped by somehow impacting on something. I was wondering why it wouldn't/couldn't fall into a stable orbit around a star. Is it just that the chances of a particle happening upon the exact path that produces a stable orbit are so vanishingly small that it hasn't happened often enough for a detectable amount of DM to accumulate? (or is there a more fundamental reason why this couldn't happen that I've overlooked?)

 

[phyzguy]

Just to be clear, does this speed refer to the particles in the halo or those falling towards the galaxy centre? (I would expect the latter to be significantly faster than the former)

Well, a particle falling from the outer halo into the center will gain on the order of a few hundred km/sec. So, while the ones in the center are going faster than the ones in the halo, the velocities are still "on the order of" 100's of km/sec.

I wasn't really thinking of it being trapped by somehow impacting on something. I was wondering why it wouldn't/couldn't fall into a stable orbit around a star. Is it just that the chances of a particle happening upon the exact path that produces a stable orbit are so vanishingly small that it hasn't happened often enough for a detectable amount of DM to accumulate? (or is there a more fundamental reason why this couldn't happen that I've overlooked?)

A mass orbiting a star has a negative total energy relative to the star, since its negative gravitational potential energy is greater than its positive kinetic energy. So it is bound to the star or trapped by the star. If a mass approaches a star from a very large distance, it has a positive total energy, since its gravitational potential energy is basically zero, and it has some positive kinetic energy. So it is unbound relative to the star. The only way it can become bound to the star in a state of negative total energy is to somehow lose energy, which requires some type of collision or interaction. Otherwise, like I said before, it comes in and goes right back out.

 

[oldGhost1]

Thanks phyz. Think that rounds off this thread nicely.
Good work both of you.