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Quick explanation: A galaxy (elliptic, or spiral) is made out of billions of stars, like our sun. These stars rotate around the center of the galaxy (very slo

by Maro 2y ago

Quick explanation: A galaxy (elliptic, or spiral) is made out of billions of stars, like our sun. These stars rotate around the center of the galaxy (very slowly, think millions of years for 1 rotation). A rotation curve measures the velocity of stars as a function of distance from the center of the galaxy. Newtonian physics (or Einstein's GR) says that the rotation curve should decay with distance, ie. with greater distance the stars' velocity should go down --- assuming the matter in the galaxy is the visible matter that we see, ie. the stars (which shine light). The problem is, there is a rich set of observational data, from many different experiments, telescopes, and methodologies that show that the rotational curve is in fact flat, it does not decay. There are 2 big competing theories to explain this discrepancy: 1. Assume that there is a lot of unseen, non-shining, ie. Dark Matter (DM) in the galaxies (also ours). If you put the appropriate amount of dark matter in there, with the right distribution, you can reproduce the observed rotational curve. There are also other places is astrophysics/cosmology where having dark matter (specifically Cold Dark Matter, CDM, where cold just means "slowly moving") is useful. The biggest example is to explain the history of the Universe and the observed Hubble-constant. In fact the standard model of cosmology is called λCDM, CDM for Cold Dark Matter (λ for the cosmological constant, currently modeled as Dark Energy, not relevant for this discussion). 2. Assume that Newton was wrong and gravity is not exactly 1/r^2 --- this is called MOND, Modified Newtonian Dynamics. This way you can also reproduce the observed rotation curves. This is much less popular, because: (i) physicsts don't want to give up the beautiful and geometric simplicity of 1/r^2 (ii) Dark Matter is also useful for solving other discrepancies in astrophysics/cosmology. What this article is saying is that, even in the first Dark Matter model, per the model DM distributions inside galaxies that also work with all the other places where DM is used to explain something (eg. in cosmology), at some distance from the center, the dark matter bubble has an edge and stops --- and then the velocities should finally break down. However, these latest observations are showing that the velocities remain constant even beyond the modeled/assumed DM bubbles. This is an additional ε argument in favor of MOND, and science proceeds.

merek 2y ago
Fantastic explanation, thank you. For a more detailed description of the Milky Way's rotation curve, this is a brief segment from David Butler's How Far Away Is It video series (which I highly recommend): https://youtu.be/uVxrsJ5lZlQ?si=ZwpBDpAvTV8AALke&t=1890 https://youtu.be/uVxrsJ5lZlQ?si=ZwpBDpAvTV8AALke&t=1890
xeonmc 2y ago
What falloff function will create an exactly flat curve? G ~ 1/r instead of 1/r^2 ? What if gravity has non-scalar components?
- canjobear 2y ago
  https://en.m.wikipedia.org/wiki/Tensor%E2%80%93vector%E2%80%93scalar_gravity https://en.m.wikipedia.org/wiki/Tensor%E2%80%93vector%E2%80%... The extra components would have energy and function as Dark Matter.
jprete 2y ago
I'm not a physicist but 1/r^2 strikes me as conceptually very important, because it's the relative contribution of any fixed area of spherical surface to the total area of that surface. So the total strength of gravitational field emanating from a particular object, at a given distance from that object, is a constant. It's somewhat weird to think of the total gravitational "force field" _increasing_ in magnitude with distance. Decreasing, sure. Increasing? That makes no sense. Certainly not at a large enough function of distance for the rotational curve to be _flat_. That's got to be some kind of wonky power term over distance which implies potential energy from the field goes up with distance as well. As above, I'm not a physicist, but a linear rotational curve breaks every intuition I've ever gleaned from physics about the nature of what's really going on with relativity, particle mediation of forces, or even the concept of a field. Maybe it means spacetime curvature is way higher than we think.
- throwawaymaths 2y ago
  > spacetime curvature is way higher than we think. You mean way weirder. Remember 1/r^2 does not work quite right for, e.g. mercury.
- Avshalom 2y ago
  Well the general solution is to invent a field with force mediating particles that have the exact same properties as dark matter but insist it's not dark matter.
- empath75 2y ago
  The strong force increases with distance, fwiw.
  - nh23423fefe 2y ago
    I'd thought that was because gluons are color charged. Unlike neutral photons
- PuffinBlue 2y ago
  Maybe not so weird if gravity isn't the curvature of spacetime but a symptom of there being either more or less of it, and mass creates spacetime. Replace the highly curved spacetime region close to a blackhole with the idea that huge amount of spacetime is being created by the mass of the blackhole, so there is more spacetime near the blackhole. The more spacetime being created and 'flowing outwards' away from the mass, the faster the apparent 'velocity' of an object through that region of spacetime ner the blackhole (and have this work out that the spacial component handles the physical motion and time slows down to compensate - just like it does in highly curved spacetime), and consequently the slower it moves relative to an external observer. Areas further from mass see much more 'dilute' spacetime (whatever the heck that means) and travel with relative slower spacial velocity but faster in time, so it appears to be travelling faster up. This would be doubly obvious at the scale of galaxies. I think this ridiculousness would rely on the relativity of simultaneity in rather a large way! The other interesting thing is, if mass does create spacetime then pockets of mass like galaxies should move away from each other faster and faster as they make more of it in between themselves. (NOTE - this is just a silly thought experiment, don't take it seriously)
ryandrake 2y ago
> (i) physicsts don't want to give up the beautiful and geometric simplicity of 1/r^2 Not a physicist here, so maybe this is a naive question: but is this really something that they care about? Why does a formula describing some physical principle have to beautiful and simple? Aren't we supposed to observe reality and then come up with the math? Rather than start with a "known true" equation and add factors and parameters it as more and more observations call the equation into question? Who's in charge of the direction physics proceeds? The observing scientists or the mathematicians?
- xeonmc 2y ago
  1/r^2 directly comes from how much area an object spans your field of view vs how far away it is. To a paraxial approximation, of course.
- wyager 2y ago
  A general principle of science is that simpler explanations are more likely. Rule-of-thumb described by Occam's razor, formalized by concepts like Solomonoff induction. Rules like 1/r^2, being simple, are assigned a higher prior probability. This makes sense because otherwise you waste a bunch of time on overfitted theories.
- jlokier 2y ago
  It's not about the formula. The formula comes from the geometry. 1/r^2 falls out as the formula, starting from the geometry of "flux" and "field lines", along with "conservation of flux", in 3d space. That's the idea that the force acts like something that's radiated in all directions, that doesn't fade with distance, instead it just spreads out so it seems weaker at individual points. The amount of spreading out, if it's uniform in 3d, turns out to be exactly 1/r^2. You get the same 1/r^2 if you measure the flow of water in a 3d volume with a point source of water in the centre, or electric current in a 3d block of metal with a point source of electric current in the centre. (In both cases, presumably through a thin pipe or cable to the centre). In 2d space, you get a different formula from the geometry, 1/r. If you see a force, or flow, reducing by 1/r^2 in a system you thought was 2d, you might ask "is there a third dimension involved here which I haven't accounted for?" In 1d, the force or flow doesn't reduce with distance. For example, current in an electrical wire is the same all along the wire. And if you see 1/r^3 in 3d, you might speculate about a hidden fourth dimension to explain it.
dameyawn 2y ago
Are you aware of any visuals that show what the density distribution of DM looks like to fix the expected the rotation curves for some example galaxies?
- Maro 2y ago
  Google images: dark matter halo
- naasking 2y ago
  DM distribution is different for every single galaxy, and so can only be fit to the galaxy's rotation curve after observing it. In contrast, MOND successfully predicts rotation curves a priori using only the visible matter.
joshjje 2y ago
For 1/r^2, wouldn't curved spacetime mess that up? Not sure how you would calculate say a moon or other things in between.
- hwc 2y ago
  it _does_ mess it up, but near the gravitational source, not way out like the problems with the galactic gravity.
yongjik 2y ago
> physicsts don't want to give up the beautiful and geometric simplicity of 1/r^2 Eh, just like MOND proponents don't want to give up the beautiful simplicity of "If something is attracting me gravitationally I'd better see it!" When you think about it, there's no a priori reason why a particle with mass should interact with any other force. We'd just like to assume it because it seems "simpler" that way.
- Filligree 2y ago
  Nor that there should be just one family of interconnected fields. We’ve got, what, two dozen or so? Some affect each other, some don’t. You can create a graph from that, and you get one that’s dense in places but have some nearly disconnected regions. Why not a graph with actual disjoint subgraphs? We’d only be able to tell through gravity.
infogulch 2y ago
It has to drop off at some point otherwise it would affect other galaxies...
Supermancho 2y ago
> If you put the appropriate amount of dark matter in there, with the right distribution, you can reproduce the observed rotational curve. What is the "right distribution"? If it's not roughly uniform, it's unlikely to result in a uniform flatness of rotation curves, across the distances in the galaxy. This seems almost impossible when accounting for clustering within the galaxy. I would believe such a uniform distribution of DM would be possible, if Dark Matter is something that exists/acts differently than matter. For example, if there were space-time bumps that form. Small bubbled/hilled spacetime is created in reaction to masses traversing it? ie the classic ball on a sheet, except it behaves more like a liquid than a sheet. This feels like a blow to Dark Matter theories, regardless.

by Maro 2y ago

merek 2y ago

Fantastic explanation, thank you. For a more detailed description of the Milky Way's rotation curve, this is a brief segment from David Butler's How Far Away Is It video series (which I highly recommend): https://youtu.be/uVxrsJ5lZlQ?si=ZwpBDpAvTV8AALke&t=1890 https://youtu.be/uVxrsJ5lZlQ?si=ZwpBDpAvTV8AALke&t=1890

xeonmc 2y ago

What falloff function will create an exactly flat curve? G ~ 1/r instead of 1/r^2 ? What if gravity has non-scalar components?

canjobear 2y ago
https://en.m.wikipedia.org/wiki/Tensor%E2%80%93vector%E2%80%93scalar_gravity https://en.m.wikipedia.org/wiki/Tensor%E2%80%93vector%E2%80%... The extra components would have energy and function as Dark Matter.

jprete 2y ago

I'm not a physicist but 1/r^2 strikes me as conceptually very important, because it's the relative contribution of any fixed area of spherical surface to the total area of that surface. So the total strength of gravitational field emanating from a particular object, at a given distance from that object, is a constant. It's somewhat weird to think of the total gravitational "force field" _increasing_ in magnitude with distance. Decreasing, sure. Increasing? That makes no sense. Certainly not at a large enough function of distance for the rotational curve to be _flat_. That's got to be some kind of wonky power term over distance which implies potential energy from the field goes up with distance as well. As above, I'm not a physicist, but a linear rotational curve breaks every intuition I've ever gleaned from physics about the nature of what's really going on with relativity, particle mediation of forces, or even the concept of a field. Maybe it means spacetime curvature is way higher than we think.

throwawaymaths 2y ago
> spacetime curvature is way higher than we think. You mean way weirder. Remember 1/r^2 does not work quite right for, e.g. mercury.
Avshalom 2y ago
Well the general solution is to invent a field with force mediating particles that have the exact same properties as dark matter but insist it's not dark matter.
empath75 2y ago
The strong force increases with distance, fwiw.
- nh23423fefe 2y ago
  I'd thought that was because gluons are color charged. Unlike neutral photons
PuffinBlue 2y ago
Maybe not so weird if gravity isn't the curvature of spacetime but a symptom of there being either more or less of it, and mass creates spacetime. Replace the highly curved spacetime region close to a blackhole with the idea that huge amount of spacetime is being created by the mass of the blackhole, so there is more spacetime near the blackhole. The more spacetime being created and 'flowing outwards' away from the mass, the faster the apparent 'velocity' of an object through that region of spacetime ner the blackhole (and have this work out that the spacial component handles the physical motion and time slows down to compensate - just like it does in highly curved spacetime), and consequently the slower it moves relative to an external observer. Areas further from mass see much more 'dilute' spacetime (whatever the heck that means) and travel with relative slower spacial velocity but faster in time, so it appears to be travelling faster up. This would be doubly obvious at the scale of galaxies. I think this ridiculousness would rely on the relativity of simultaneity in rather a large way! The other interesting thing is, if mass does create spacetime then pockets of mass like galaxies should move away from each other faster and faster as they make more of it in between themselves. (NOTE - this is just a silly thought experiment, don't take it seriously)

ryandrake 2y ago

> (i) physicsts don't want to give up the beautiful and geometric simplicity of 1/r^2 Not a physicist here, so maybe this is a naive question: but is this really something that they care about? Why does a formula describing some physical principle have to beautiful and simple? Aren't we supposed to observe reality and then come up with the math? Rather than start with a "known true" equation and add factors and parameters it as more and more observations call the equation into question? Who's in charge of the direction physics proceeds? The observing scientists or the mathematicians?

xeonmc 2y ago
1/r^2 directly comes from how much area an object spans your field of view vs how far away it is. To a paraxial approximation, of course.
wyager 2y ago
A general principle of science is that simpler explanations are more likely. Rule-of-thumb described by Occam's razor, formalized by concepts like Solomonoff induction. Rules like 1/r^2, being simple, are assigned a higher prior probability. This makes sense because otherwise you waste a bunch of time on overfitted theories.
jlokier 2y ago
It's not about the formula. The formula comes from the geometry. 1/r^2 falls out as the formula, starting from the geometry of "flux" and "field lines", along with "conservation of flux", in 3d space. That's the idea that the force acts like something that's radiated in all directions, that doesn't fade with distance, instead it just spreads out so it seems weaker at individual points. The amount of spreading out, if it's uniform in 3d, turns out to be exactly 1/r^2. You get the same 1/r^2 if you measure the flow of water in a 3d volume with a point source of water in the centre, or electric current in a 3d block of metal with a point source of electric current in the centre. (In both cases, presumably through a thin pipe or cable to the centre). In 2d space, you get a different formula from the geometry, 1/r. If you see a force, or flow, reducing by 1/r^2 in a system you thought was 2d, you might ask "is there a third dimension involved here which I haven't accounted for?" In 1d, the force or flow doesn't reduce with distance. For example, current in an electrical wire is the same all along the wire. And if you see 1/r^3 in 3d, you might speculate about a hidden fourth dimension to explain it.

dameyawn 2y ago

Are you aware of any visuals that show what the density distribution of DM looks like to fix the expected the rotation curves for some example galaxies?

Maro 2y ago
Google images: dark matter halo
naasking 2y ago
DM distribution is different for every single galaxy, and so can only be fit to the galaxy's rotation curve after observing it. In contrast, MOND successfully predicts rotation curves a priori using only the visible matter.

joshjje 2y ago

For 1/r^2, wouldn't curved spacetime mess that up? Not sure how you would calculate say a moon or other things in between.

hwc 2y ago
it _does_ mess it up, but near the gravitational source, not way out like the problems with the galactic gravity.

yongjik 2y ago

> physicsts don't want to give up the beautiful and geometric simplicity of 1/r^2 Eh, just like MOND proponents don't want to give up the beautiful simplicity of "If something is attracting me gravitationally I'd better see it!" When you think about it, there's no a priori reason why a particle with mass should interact with any other force. We'd just like to assume it because it seems "simpler" that way.

Filligree 2y ago
Nor that there should be just one family of interconnected fields. We’ve got, what, two dozen or so? Some affect each other, some don’t. You can create a graph from that, and you get one that’s dense in places but have some nearly disconnected regions. Why not a graph with actual disjoint subgraphs? We’d only be able to tell through gravity.

infogulch 2y ago

It has to drop off at some point otherwise it would affect other galaxies...

Supermancho 2y ago

> If you put the appropriate amount of dark matter in there, with the right distribution, you can reproduce the observed rotational curve. What is the "right distribution"? If it's not roughly uniform, it's unlikely to result in a uniform flatness of rotation curves, across the distances in the galaxy. This seems almost impossible when accounting for clustering within the galaxy. I would believe such a uniform distribution of DM would be possible, if Dark Matter is something that exists/acts differently than matter. For example, if there were space-time bumps that form. Small bubbled/hilled spacetime is created in reaction to masses traversing it? ie the classic ball on a sheet, except it behaves more like a liquid than a sheet. This feels like a blow to Dark Matter theories, regardless.