Effect of Dark Matter on fast moving bodies

[Thomas Sturm]

TL;DR Summary

Consider a fast moving (relative to its galactic neighborhood) star: would its gain in mass due to dark matter have measurable consequences?

Given the fact that our galaxy consists mostly of dark matter (accounting for roughly 70% of its mass) we know astonishingly little about the stuff. Admittedly, if I could give you a lump of dark matter, you would propably be totally underwhelmed by the "experience". First of all, you wouldn't see it. Dark matter isn't "dark" but completely and utterly invisible. It simply doesn't interact with electromagnetic forces.

It does interact with gravity, though, so you would propably anticipate being given a lump of "nothing" and feeling its weight in the palm of your hand. Only, as far as we know, it doesn't interact with your hand either, so it would pass right through you and follow the call of gravitiy towards the center of the earth. In fact it would go right through and swing backwards and forwards through the planet around its center of gravity until kingdom comes. At least, according to our "knowledge" of dark matter, this should be what happens.

If it was made out of particles - which we don't know - those particles would be moved backwards and forwards each time the lump passes the centre of the earth. In other words: the lump would "warm up", losing its kinetic energy and eventually settling down. But we don't know even that. It would, however, add to the mass of our planet, one way or another. As would any other lump of dark matter our planet ever encounters.

This wouldn't amount to much given the fact that dark matter, being gravity bound, moves around the center of the milky way just like our solar system does: so from our point of view, the whole ghostly soup should remain relatively static. This is entirely different for the few rogue stars that we find in every galaxy. Since their velocity relative to the dark matter that makes up the bulk of the mass of their host galaxy is quite high (i.e. 1200 km/s in case of "US 708"), it should "gobble up" quite a sizeable amount of dark matter over time - and this should have observable consequences. It should shrink, for starters. The fact it is getting heavier all the time should also affect its trajectory.

So my question is: have I taken a wrong turn somewhere or should it not be possible to learn something about the nature of dark matter by observing hyper-velocity stars?

 

[PeroK]

Dark matter does not interact with ordinary matter, regardless of whether that ordinary matter is "fast moving" or not.

 

[Thomas Sturm]

Wrong. It interacts gravitationally.

 

[Vanadium 50]

Another person comes to PF with intent to school the experts. <sigh>

OK, what exactly do you think would be learned? Please use equations.

 

[Ibix]

In other words: the lump would "warm up", losing its kinetic energy and eventually settling down.

A key point about dark matter is that this doesn't happen. The frictional processes that lead to heating and clumping of normal matter are primarily electromagnetic in nature. As you note, dark matter doesn't interact electromagnetically. So you don't get "lumps" of dark matter to start with, and it doesn't heat up beyond what heat it has to start with.

Thus, your reasoning is incorrect. Dark matter that isn't already bound to a mass won't become bound to it - it'll just swing through on an open orbit and leave (edit: exception: black holes, but the volume they sweep clean of matter is tiny). You can see effects of the dark matter distribution on the velocities of stars (that's how we learned about the stuff in the first place), but not due to it accumulating.

 

[Thomas Sturm]

Ok, let's leave the "thermodynamics" of dark matter aside as that was not the actual point (of my post). And yes, I am fully aware that temperature is a concept which can not be applied to dark matter - as this would imply particles, for starters.
Let F(g) ~ (m1*m2)/r^2 be the gravitational force F(g) between two masses m1 and m2 distanced r apart from each other. One thing to note is that F(g) is a vector of equal length but opposite direction for both m1 and m2 pointing to the pivot point between the centre of the masses m1 and m2 spaced r apart. Both masses will experience the same force pulling them towards their pivot point. Entities with the property "mass", if left undisturbed, will form what, if I found it in my soup, would call a "lump".
Dark matter has "mass", because that is the single property we need it for, and lumps of it "look" like this:

This "picture" is from the wikipedia article briefly detailing (one of) the reasons why we came up with the idea of dark matter in the first place. In a nutshell: mass at the edge of galaxies is moving too fast to stay put. It needs to rotate around the centre of gravity of a galaxy with an angular speed roughly proportional to 1/r^2 - because it is subjected to F(g). This seems to work neatly in any planetary system but apparently not on a (much) larger scale. In fact, the angular speed we measure is (very roughly) close to 1/r, which means we should see galaxies shedding mass at their edges like nobody's business. This is not what we observe (and in fact we wouldn't be able to observe anything if this was the case), so we need additional mass to keep it all together. So it seems.

There are other options. Maybe you scoffed about F(g) ~ (m1*m2)/r^2 being the experts that you are (sorry, but after the first 2 posts...) but things might be not that simple. While I have some objections to this book, they are of philosophical nature and shouldn't concern us here. As far as modified Newton dynamics (MOND) is concerned, it makes an interesting read.

Talking of Philosophy: my post was a figure of what is called a "thought experiment". Somewhat flippant, I admit, and at some point fundamentally wrong. But not at any point you picked up.

So. If we can agree that dark matter is not distributed evenly across space (by definition), and dark matter has a mass (by definition) but no other properties we know of (otherwise we would know of it - sorry for the pun, but we have made considerable unsuccessfull efforts to determine any other property of it): what would happen, if we "placed" an entity of dark matter onto the surface of the earth?
This is a thought experiment. I know full well this will not happen, thank you.
Since it has mass - and nothing else - it would accelerate towards the center of the earth. At a rate of more-or-less 9.81 m/s^2. It would do so for roughly 6371 km (depending on its mass) because that's the distance from the surface of our planet to its center. Note: this contains the assumption that m(dark matter) << m(earth), otherwise the distance would be less. Given the fact that people seem uncomfortable with the idea of a massive lump of dark matter, let's settle for "really not much". v = sqrt(2a*r) I hear you thinking which would make for an impressive 11180 m/s at which our dark matter would pass the center of the earth. After which it would decelerate for the same stretch at the same rate only to arrive at the surface on the "other side". If it has mass, it has inertia, whatever it is. So it would arrive at the other side of our beloved planet, whatever its shape, mass or colour at exactly v=0. How it would "just swing through on an open orbit and leave" is beyond me, though. Having said that, this situation (a perfect pendulum) leaves me rather uneasy as well.

Nonetheless, dark matter wasn't my idea, and if all you attribute to it is mass, you have to live with the consequences. Like, you have to apply physics. For a star, which moves at a certain speed through the galactic halo, you have to assume it exerts a force on the mass it passes by. Forget about dark matter for a moment, but a star which moves relative to the galactic merry-go-round will pick up matter. Mostly Hydrogen. Which you can "see". As long as the star moves slower in relation to the galactic rotation plus its own escape velocity it will gather mass. If it is faster, mass will simply pass it by, as it can not reach the star quick enough before other sources of gravity (like the bulk of the galaxy) will take over. I say "mass", because this holds true for dark matter as well.
My quoted case of US 708 thus was a bad example; its speed relative to the galactic movement (1200 km/s) is far to fast to pick up much mass whatever its shape. It will even leave our galaxy. The reason is simply: by the time m1 (whatever) is moving towards m2 (the star), m2 is beyond "catching up".
There are plenty of HVS Stars which fit the bill, however, with a realtive velocity lower than their escape velocity, that will pick up mass which they can not burn.
If this only affects their trajectory (if they pick up mass, then the force between them and the centre of mass of the galaxy will get stronger), only some of this change will be accountable.
If it would only be (mostly) Hydrogen, this star would encounter, it wouldn't have much of an impact. Hydrogen is what stars burn. However, dark matter picked up along the way would add to the star's mass, but not to its energy output.
What can be learned? - whether "dark matter" is actually anything behaving like (or actually deserving the term) "matter" at all. Isn't that something?

 

[PeterDonis]

As long as the star moves slower in relation to the galactic rotation plus its own escape velocity it will gather mass.

You mean, as long as velocities of other mass near the star relative to the star is less than the star's own escape velocity, that other mass will become bound to the star.

While this is technically true, I think you are greatly overestimating its applicability. Consider the neighborhood of our solar system. To a first approximation, all the mass in this neighborhood that can be bound to our solar system, already is bound to our solar system. There is no reservoir of "mass" out there waiting to be captured; it either already has been, or it can't be. To a first approximation, we expect relative velocities of any piece of matter that comes near our solar system now to be larger than the escape velocity from our solar system at the distance that matter is.

For ordinary matter, there is one other possibility: by non-gravitational interactions (such as emitting radiation), that matter can lose energy relative to our solar system and become bound when it wasn't before. To some extent this happens, but I don't think it's very significant. In any case, the real point for this discussion is that this other possibility is not there for dark matter, because dark matter has no non-gravitational interactions.

So to a first approximation we should not expect any dark matter in the vicinity of our solar system that isn't already bound to it, to become so. And similar remarks would apply to other stars, in our galaxy and other galaxies.

 

[PeterDonis]

How it would "just swing through on an open orbit and leave" is beyond me

That remark was about a different scenario--one that, unlike yours, could actually happen (you admit yours can't). In the scenario @Ibix was using in that remark, the dark matter isn't magically "placed" at rest at the Earth's surface; it is passing by the Earth with whatever relative velocity it already had. Which, as I noted in my previous post just now, is expected to be larger than the Earth's escape velocity. (In fact, as I noted, it's expected to be larger than the escape velocity from the solar system as a whole.) In that scenario, the dark matter will indeed swing through on an open orbit--a hyperbolic, non-bound trajectory--and leave.

 

[Ibix]

Entities with the property "mass", if left undisturbed, will form what, if I found it in my soup, would call a "lump".

So you'd regard a comet and the Sun orbiting hundreds of AU apart as just one "lump" of matter? That seems like an unusual definition to me, but ok.

How it would "just swing through on an open orbit and leave" is beyond me, though.

It wouldn't. What I said was that any dark matter not already bound to a mass would just swing through on an open orbit and leave. You are here descrbing dark matter that is already bound.

My point is that this is irrelevant to your original question, which was about hyper-velocity stars. Any dark matter that isn't already bound to a star must be moving fairly slowly with respect to the galaxy - otherwise it would not be bound to the galaxy either and would escape, not form a halo. Thus the dark matter is going very fast relative to a fast-moving star and will be unbound as far as the star is concerned.

Having said that, this situation (a perfect pendulum) leaves me rather uneasy as well.

Why? If there are no dissipative processes, why would it be a problem? As Peter notes, there are in fact dissipative processes such as gravitational radiation, but the energy loss from these is utterly negligible on timescales as short as the current age of the universe.

As long as the star moves slower in relation to the galactic rotation plus its own escape velocity it will gather mass.

Remember that escape velocity isn't a single number, but rather a function of distance. Earth's escape velocity from the surface is about 11km/s. But its escape velocity from the moon's orbit is a bit over 1km/s. Escape velocity starting at 1AU is only 150m/s. At three light days it's a bare 1m/s. That means that anything more than three light days from Earth has escape velocity if it's doing 1m/s relative to Earth. You can repeat the calculation relative to the Sun if you wish.

Probably the easiest way to think accurately about the relationship between fast moving stars and a dark matter medium is to look at it from the star's rest frame. In this frame, the star is at rest and the dark matter has whatever velocity you would normally attribute to the star. Clearly any dark matter that wasn't initially bound to the star flows through on open trajectories, accelerating towards the star and decelerating away from it, but always above the local escape velocity.

The problem with your thinking seems to be that you think initially fast moving matter (normal or dark) will somehow become bound to a star just because it moves near. That is possible for normal matter because it can interact electromagnetically (i.e. collide with the star or some other bit of matter), which dissipates energy, slows the matter, and can cause it to become bound, although I suspect that's only a relatively small effect. But dark matter is pretty much collisionless, so it doesn't slow down even if it passes dead center through the star. So it doesn't accrete.

 

[Thomas Sturm]

Well, thank you all for this discussion, as it helped me getting a bit wiser.

The problem with your thinking seems to be that you think initially fast moving matter (normal or dark) will somehow become bound to a star just because it moves near.

This sums it up neatly. I made "half a step" with my "perfect pendulum" thought without going all the way - so even a star going right perpendicular through the halo of our galaxy might pick up a few tons of ordinary matter per second (in other words: next to nothing) - but even if it encountered roughly six times more dark matter, practically none of it would "stick".

So first of all I would like to thank you very much for taking the time to put me right: this is very much appreciated and I hope this discussion might be (have been) interesting for others, too, as I think it sums up neatly just how elusive this stuff is.

Lessons learned:
a) If you come up with a thought experiment to simplify a situation, when you go out into the real world, think about how applicable your simplifications are in the first place.
b) "Shut up and calculate" - however roughly. Take the density of the intergalactic medium of one atom (H+) per cm r^3 = 6*10^-23g. A (very roughly) sun sized star (1*10^6 km = 1*10^11 cm) "cruises" exactly perpendicular to the galactic halo (so we don't have to take it's angular speed into account because we're lazy) at 600 km/s = 6*10^7 cm/s. So it gets hit directly by (d^2*Pi/4) (3/4*10^11)^2*(6*10^7)*(6*10^-23) = 20250000 g/s (oops!) ~ 20 t/s (of Hydrogen). Um. Ok, it would have an effective radius of a lot more than its actual radius for ordinary matter - but 20 t/s is actually nothing.
c) Do step (b) before being carried away by "what would happen if a star picked up mass that was actually inertial even to it's fusion processes? If one watched it for years and years, could one deduce anything about the properties of this matter" - as step (b) gives a clear answer: this is orders of magnitude away from the 4*10^6 t/s a star "very roughly" the size of our sun burns. The answer is "nada".
d) Even if you come up with stupid ideas like this, there are people knowledgeable and kind enough to put you right. You will inevitably learn a lot from this. Be grateful and don't test their patience.

 

[Thomas Sturm]

Regarding the distribution of dark matter in the Universe, there has just been an article in Nature about the most comprehensive WIMP simulation to date: Universal structure of dark matter haloes over a mass range of 20 orders of magnitude. It contains the following, fascinating picture:

(Courtesy of astronews.com)
The image shows a part of the entire simulation with a side length of roughly 2 billion Lj. The lumps on this scale are about the size of galaxy clusters (~10^17 m(sol)). The first enlargement covers about 700 kLj while the last one is about 600 Lj each side, with the smallest lumps about 10^-3 m(sol).
If you would present this picture to a neurologist telling them it was a flourescence enhanced section of the cortex, they wouldn't bat an eyelid.