
A Natural Law for Rotating Galaxies: What Does This Mean for Dark Matter? - altstar
http://www.physicscentral.com/buzz/blog/index.cfm?postid=5308541299875990673
======
gh1
First we had Newton's laws of gravity. It worked quite well in the solar
system scale and everyone was happy. Then Einstein formulated the special
theory of relativity and Newtonian gravity was found to be incompatible with
that. So Einstein formulated the General Theory of Relativity (Einsteinian
Gravity) which solves that problem. As a bonus, his theory could also explain
the eccentric behavior of Mercury's orbits, which Newtonian Gravity couldn't.
It also predicted that galaxies should be able to bend light (lensing) and
this was confirmed by Arthur Eddington. However, for many galaxies, the amount
of lensing is way off from what the Einsteinian theory predicts. Similarly,
rotational velocities of stars in a galaxy are also way off from what is
predicted by both Einsteinian and Newtonian theory. In addition, when you
apply the Einsteinian theory to the entire universe, you can't explain the
observable geometry of the universe. That is also way off. Dark matter and
Dark Energy are just a very clever way of saying "we have no idea what's going
on with gravity in the large scale (beyond solar system scales)". No one has
ever observed any dark matter or dark energy so far. It is entirely possible
that Einsteinian theory of Gravity is just an approximation that works well
for small scales and that we need a new theory of gravity at the galactic
scale or the scale of the universe. It is also entirely possible that Dark
Matter and Energy don't actually exist.

~~~
aaron695
Einstein made a small improvement to Newton.

People seem think think this allows our current theories to be wrong.....

Perhaps there might be small issues with Einstein theories, personally I doubt
it, but, to me, I really don't think small fixes to the theory will explain
this stuff away.

~~~
madaxe_again
It's not actually clear that there is _any_ problem with current theory - it
may just be that our understanding and application of it is incorrect. You can
have a perfect mathematical model, but if just one of your premises is
incorrect, the output can be nonsensical.

I am a physicist (well, I studied as one, before going technology
entrepreneur), and have always sat in the "dark matter is bullshit" camp - so
my opinion is likely tainted.

I think a far more likely explanation, as this paper could suggest, is that
something far more mundane is happening.

For instance, we already understand tidal forces - that bodies can become
tidally locked, that there is an inertial frame shear that drags bodies along
around a rotating centre of mass, and exchanges energy between an orbiting
body and the centre.... So why is it infeasible that galaxies are tidally
locked, and the lack of fall-off in radial velocity is down to the
gravitational shear from the galactic core being far more intense than we
anticipate, causing the behaviour we see. It doesn't require a rewrite of
relativity, "just" of galactic evolution.

Either that, or galaxies are sprites, and lazily rendered ones, at that.

~~~
kmm
> For instance, we already understand tidal forces - that bodies can become
> tidally locked, that there is an inertial frame shear that drags bodies
> along around a rotating centre of mass, and exchanges energy between an
> orbiting body and the centre.... So why is it infeasible that galaxies are
> tidally locked, and the lack of fall-off in radial velocity is down to the
> gravitational shear from the galactic core being far more intense than we
> anticipate, causing the behaviour we see. It doesn't require a rewrite of
> relativity, "just" of galactic evolution.

Because someone has indubitably already ran the numbers. The tidal force only
has a non central, orbit changing influence on spatially extended bodies, and
its effects even on objects as large as our solar system are completely
negligible, as it doesn't seem to have a measurable effect on the orbits of
the planets. The rotation curves are way off, which is a huge chunk of excess
angular momentum that no tidal force can conjure. Where would it even come
from, the rotational angular momentum of component stars?

~~~
madaxe_again
You're aware that mercury is tidally locked, as is our moon, mars' moons, and
others? I would call those real, physical effects, not negligible.

As to running the numbers - agreed - but one can get an answer which is
correct but incorrect if your premises are incorrect.

At a galactic scale the perturbations are likely tiny, but a tiny force
applied over enough time adds up.

Anyway. It's a poor example that's almost certainly wrong but my point was
more about how a single incorrect assumption can wreck a model.

------
michaelrccurtis
It always depresses me (as an astrophysicist) how poor the communication is on
dark matter, and this leads people to unfair conclusions. We have known for
some time about the limitations of our understanding of gravitational dynamics
in extreme environments - the issue is not that "our theories must be right",
it's that we have to square General Relativity (which is phenomenally well
tested in other regimes) with the results we see. There are broadly 2
different ways of doing this: you can postulate that not all particles
interact with electromagnetic radiation (after all, why should they?) or you
can come how add extra terms into your gravitational laws.

Both of these have been tried, but there are many reasons why the majority of
astrophysicists prefer the dark matter approach. Firstly, there are
observations which suggest large regions of mass that are not aligned with the
visible mass (e.g. the bullet cluster). Secondly, dark matter can explain the
statistical properties of the Cosmic Microwave Background radiation in a way
that can not be achieved with ordinary matter alone. Thirdly, when we include
dark matter in simulations, we get results that are a very good match for the
universe as we observe it. etc. etc. If that weren't enough, we know that
there are plenty of types of matter that are dark - e.g. neutrinos, early
black holes etc. Whilst none of these have yet satisfied the conditions for
dark matter as we understand it, it's perfectly possible that we have already
identified some of the constituent parts, and there is a list of potential
candidates as long as my arm that the particle physicists are working their
way through.

Finally, the biggest annoyance is the intimation that we are all just one big
cabal. Let me put it like this: if you could provide indisputable evidence
that dark matter was wrong, you would be a superstar in our field and everyone
would be phenomenally excited, because it would demand the hunt for new
physics. Scientists are a rational bunch, however, so any evidence must be
weighed against the existing evidence already observed (which, as above, is
substantial).

Dark energy is slightly different. No one know's what this is, but models with
a dark energy component do very well at modelling the universe. The question
is, why? No one is pretending that this is a solved question, but what we do
know is that whatever is driving the universe's accelerated expansion has
properties that are very similar to what dark energy is.

tldr: There are loads of great reasons for thinking dark matter exists,
contrary to many posters here, and it is well accepted that dark energy is a
mathematical term that represents something of unknown physical origin.

~~~
phkahler
I keep seeing a couple problems in this whole discussion.

Number one is the continued references to Keplers laws. Kepler only applies to
2-body systems where the mass of one is dramatically larger than the other.
This works well for the solar system, where the sun is huge compared to the
planets and the planets have little effect on each other. But do note that
some planets were predicted to exist based on their effect on the orbits of
other planets, so even in this sparse system the effects do make a difference.
My point is that Kepler has no place in galactic dynamics but is often
referenced - if that were the model that doesn't match observation then DUH!
But the physicists are smarter than that.

Second, I occasionally see mis-application of the divergence theorem and/or
gauss's law. Some folks seem to treat a portion of a galaxy out to a radius R
as a point mass by using this theorem. The problem of course is that to make
that leap you must have a uniform spherical distribution of matter inside the
spherical boundary. In other words, a disk-like distribution of matter does
not have a uniform gravitational pull at all points of distance R from its
center. You'll find it is stronger near the edge of the disk than at the same
distance perpendicular to it.

Third, this particular article keeps making reference to the "radial velocity"
or speed of stars where I believe they are actually talking about the orbital
or tangential velocity.

And lastly, if the dark matter obeys the same laws of gravitation, there must
be a reason for its distribution to be different than the other matter. At
that point, I don't see any need for "strange dark matter" or new particles or
physics. You really can't have it both ways - it's fundamentally different,
yet it obeys the same rules. Having said that, I could see how exploding stars
would spread non-visible matter (remnant material) in a way that might be very
different from the stars themselves.

~~~
Keysh
_In other words, a disk-like distribution of matter does not have a uniform
gravitational pull at all points of distance R from its center. You 'll find
it is stronger near the edge of the disk than at the same distance
perpendicular to it._

But stars (and gas clouds) orbiting in a disk are essentially always "near the
edge" of the disk (that is, the disk defined as matter interior to the orbit
in question), so the approximation is usually pretty good.

 _reference to the "radial velocity" or speed of stars where I believe they
are actually talking about the orbital or tangential velocity._

The (understandable!) confusion originates because "radial" and "tangential"
refer, in an observational sense, to velocities along or perpendicular to the
line-of-sight vector. To simplify a bit: for observations of astronomical
objects, velocities along the line of sight from you to the object (detectable
from Doppler shifts in its light) are "radial", while velocities perpendicular
to the line of sight (which require that you wait long enough to see things
change position on the sky) are "tangential". For edge-on spiral galaxies, the
orbital motions that we can observe are those producing Doppler shifts along
the line of sight (which are, in the frame of the galaxy, "orbital or
tangential", as you suggest).

 _And lastly, if the dark matter obeys the same laws of gravitation, there
must be a reason for its distribution to be different than the other matter._

The usual argument is that dark matter is "non-dissipative" \-- that is, it
can't lose orbital energy via things like radiation, the way ordinary matter
in the form of gas can. (And, unlike gas, it doesn't feel pressure forces.)
_Stars_ are also non-dissipative, but stars form out of gas, so their
distribution reflects the effects of dissipation in ways that dark matter
can't.

~~~
phkahler
>> But stars (and gas clouds) orbiting in a disk are essentially always "near
the edge" of the disk (that is, the disk defined as matter interior to the
orbit in question), so the approximation is usually pretty good.

Not sure we're on the same page. For a star orbiting at radius r on a disk of
radius R, some folks will lump all mass inside r into a point and apply
keplers laws. They will reject all the mass between r and R because of the
same surface integral theorems. The problem is that neither of those
assumptions are anywhere near correct. The pull from the interior <r mass is
not the same as though it were a point, and the pull from the outer mass >r is
very much non-zero. For an example using electric charge instead of gravity:

[http://www.phys.uri.edu/gerhard/PHY204/tsl34.pdf](http://www.phys.uri.edu/gerhard/PHY204/tsl34.pdf)

Note that the field is non-zero at most places inside the ring, however it
would be zero over the entire volume if it were a spherical distribution.

~~~
Keysh
Ah, I thought you were making some special argument about stars orbiting with
very tilted orbits or something like that.

Yes, the orbits within the inner part of a galaxy don't follow a Keplerian
curve. However, at large radii most of the visible matter is _well inside_ the
orbit and very little is outside (galaxies are quite centrally concentrated),
so the rotation curve _should_ approach the Keplerian limit as you go to
larger and larger radii. The fact that it doesn't is one of the primary pieces
of evidence for dark matter in galaxies (though not the only one).

(I'm not sure why you linked to that slide, since it's not calculating the
field in the plane of the ring, nor is it dealing with a continuous charge
distribution. Regardless, you'll note that E_x goes to 1/x^2 for x >> a, which
is a "Keplerian" limit.)

~~~
phkahler
>> so the rotation curve should approach the Keplerian limit...

I don't agree. If we treat the galaxy as a bunch of concentric rings, many of
them are nowhere near far enough away to reach that "Keplerian" limit.

As an experiment I modeled a flat disk of uniformly distributed stars. Without
doing a dynamic simulation one can do the n-body calculation to determine the
total pull on each star and determine what its orbital velocity must be to go
in a circular orbit. You find that the "galactic rotation curve" will have a
velocity that actually increases all the way to the edge. Of course a uniform
distribution is not what a real galaxy looks like, but I think we can all
agree reality is somewhere between the uniform flat disk and the highly
concentrated central mass. And the actual rotation curves are somewhere
between Keplers and mine. I'd expect people to work backward from the rotation
curves to determine the mass distribution and then try to understand why that
isn't what is observed. I suppose that's just a different way to get at the
same mystery.

------
tjic
I remember being in fifth grade science class (in the early 1980s) and hearing
first about Kepler's law and that planets further out circle the sun less
quickly than those closer in, and then next hearing that we had spiral
galaxies.

I raised my hand and asked "how do the galaxies maintain their spiral shape?
Shouldn't the inner stars rotate much more quickly than the outer ones?"

The teacher didn't understand my question (this was one of my first inklings
that teachers didn't tend to be that bright).

The last 10-15 years with headlines in the popular press about dark matter,
MOND, etc. are quite satisfying - 10 year old me is thrilled that my question
is mainstream now!

~~~
wcoenen
It's a good question, but that is not the same issue as the one the article is
about.

The spiral arms maintain their shape not because of an anomaly in orbital
velocities, but because they are density waves[1]. Kepler doesn't work because
the arms themselves and the rest of the disk exerts significant gravity.

[1]
[https://en.wikipedia.org/wiki/Density_wave_theory](https://en.wikipedia.org/wiki/Density_wave_theory)

------
conistonwater
[https://arxiv.org/abs/1609.05917](https://arxiv.org/abs/1609.05917)

------
josephagoss
I thought that Dark Matter and Dark Energy are simply placeholders for our
lack of explanation of observed phenomenon?

In which case these types of discoveries are to be expected as we fill in the
missing blanks.

If so then I am happy to see progress being made.

If I am wrong about my assumptions about Dark Matter and Dark Energy I
wouldn't mind some starters :) Thanks!

~~~
conistonwater
My understanding is that the difference between observed and predicted galaxy
rotation rates is real, and the thing that is thought to cause it is given the
name of dark matter. But that doesn't make it a placeholder! Any more, for
example, than when people detected the effects of Mercury or Neptune on the
orbits of other planets in the solar system, before they could see those
planets directly, they could give them a name without being able to see them:
yet those weren't placeholders, rather their effects on orbits was evidence of
their existence.

OTOH, maybe _everything_ in science is a kind of a placeholder, but that sort
of thing can get unpleasantly philosophical.

~~~
hanoz
It seems to me there's a big difference between an explanation of an
expected/obsevered mismatch which says there must be another massive object
involved - and here's where to point your telescopes to look for it, and one
which says well there must be some other mass of some form somewhere.

~~~
conistonwater
For a pretty long time, for both those planets, they _didn 't_ know where to
point their telescopes. This was also true for the outer planets, and Pluto
too. A similar sort of thing, to a different/lesser extent, used to be the
case with gravitational waves not having been directly observed despite other
evidence. There were similar problems with the early discussions of atomic
nuclei, electrons, neutrinos, neutrons, where all kinds of things were posited
based on their effects only. I know it's quite a bit more difficult, and less
direct, with dark matter, but still.

(Really, I was objecting to the use of the word _placeholder_ , because I
found it unfair.)

------
joe_the_user
I am not sure why this isn't MOND, Modified Newtonian Dynamics in different
garb [1] - instead of modifying Newton's equations, just modify the
predictions of those equation - ie, the laws of planetary motion.

And MOND is an interesting theory that's been explored but hasn't gone
anywhere.

[1]
[https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics](https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics)

------
infectoid
I'm a bit simple, but is this saying that dark matter (at least at a galactic
scale) is in some way proportional to visible matter and that this is
something that had not been tested for until now?

~~~
Avshalom
Yeah. There's no obvious reason it should be but this data says it is.

The actual paper also says that but then ignores the fact that they just said
it so they can suggest MOND.

------
peter303
Dark matter is used to explain other observations - the accelerated movement
of galaxy clusters, lensing of objects behind galaxies, the spatial frequency
off the background radiation.

~~~
Avshalom
The authors have for some reason decided to leave "the amount of visible
matter [is] directly related to the amount of dark matter" out of their list
of possible conclusions but I suspect that if their data/methods are
legitimate than that is exactly the conclusion we're going to end up with.

~~~
nshepperd
That isn't on the list because two of them items on their list are possible
explanations for _why_ the visible matter would be directly related to the
dark matter. The fact that visible and dark matter are related is not much of
a conclusion by itself.

------
Animats
The observation that the visible galaxies all behave similarly, as if they
have a dark matter halo, clashes with the observation that our galaxy doesn't
have any detectable dark matter in the neighborhood.[1]

[1] [http://www.space.com/15333-dark-matter-missing-
sun.html](http://www.space.com/15333-dark-matter-missing-sun.html)

~~~
vorg
According to that article (2012), you'd better clarify that as "...our galaxy
doesn't have any detectable dark matter in the neighborhood _of our sun_."

Perhaps the phenomenon is the result of new _relativistic_ dynamical laws
instead of dark matter, e.g. "All large-scale rotating structures appear to be
indistinguishable from a single rotating object when viewed from any
observer's frame of reference" for some definition of "large-scale".

------
bawana
Does the presence of dark matter and dark energy imply other 'dark'
properties. Consider 'dark' intelligence - I think our presidential candidates
qualify as vast repositories of this - you can't observe any intelligent
speech but you know there must have been some - otherwise how could they get
to where they are today?

------
slicktux
[http://blogs.scientificamerican.com/critical-
opalescence/is-...](http://blogs.scientificamerican.com/critical-
opalescence/is-dark-matter-a-glimpse-of-a-deeper-level-of-reality/)

------
mgalka
Unusual to see a new physics discovery that you don't need a PhD to understand

------
nonbel
One thing that bugs me about dark matter is that all the assumptions being
made do not seem to have been fully investigated before "accepting" the idea
as mainstream:

"The Duhem–Quine thesis, also called the Duhem–Quine problem, after Pierre
Duhem and Willard Van Orman Quine, is that it is impossible to test a
scientific hypothesis in isolation, because an empirical test of the
hypothesis requires one or more background assumptions (also called auxiliary
assumptions or auxiliary hypotheses). In recent decades the set of associated
assumptions supporting a thesis sometimes is called a bundle of hypotheses."
[https://en.wikipedia.org/wiki/Duhem%E2%80%93Quine_thesis](https://en.wikipedia.org/wiki/Duhem%E2%80%93Quine_thesis)

For example, when predicting the rotation curves you can instead assume the
mass is log-normally distributed and get the flat curves:

"The generation of the 37 galaxy velocity profiles presented in this paper
assumed that most of the galactic mass is in the disk, and gravity is
Newtonian. A best-fit algorithm was used to generate the curves of Figures 1
and 3 – 38 using a truncated log-normal surface density distribution function.
The log-normal models closely matched the shape of observational rotation
velocities, and the predicted masses for these curves fitted a baryonic Tully-
Fisher relation reasonably well over a wide range of galaxy sizes, from LSB
galaxies to massive high-luminosity disks."
[https://arxiv.org/abs/1502.02949](https://arxiv.org/abs/1502.02949)

It isn't that I think that must be the correct solution, but why was no one
publishing the results of investigating that assumption until 2015?

~~~
FrozenVoid
see [https://arxiv.org/abs/astro-ph/0612434](https://arxiv.org/abs/astro-
ph/0612434)

~~~
nonbel
>"The stars in spiral galaxies are settled thin disks with an exponential
surface mass distribution"

Can you expand on that post? The paper you linked appears to assume the very
thing being questioned here...

~~~
FrozenVoid
Its explained on the next page(it a simplification) In fact, by relaxing some
of the assumptions made above, we have the more general relationship: L ∝ V
2/(+s+q−t) opt (here s, q and t can be band- dependent) that can be even more
complex and non-linear when the scaling laws (2), (3), (4) are not just power
laws. As a matter of fact, in several different large samples of galaxies it
has been found that the TF has different slope and scatter in different bands:
a I ≃ 10, s I ∼ 0.4mag, while a B ≃ 7.7, s B ∼ 0.5mag (Pierce & Tully 1992),
(Salucci et al. 1993). Moreover, a non linearity in the TF is often found at
low rotation velocities (Aaronson et al. 1982).

~~~
nonbel
Thanks, I will take a closer look.

------
hzhou321
This is good.

Dark matter has always in my eye so similar to the God hypothesis that we
conjure something that is mysterious with undefined but whatever necessary to
explain _away_ the discrepancy or mystery.

Acknowledging that we don't know -- not even assume it is _matter_ that fits
our current understanding -- is the start of understanding.

Now it appears we do know it fits some mathematical equation ...

PS: the God hypothesis could well be correct, but that should be the last
resort -- It is not really an explanation, so it is not necessary until the
explanation is needed for reasons of other than explaining.

~~~
pharrington
If that's what bugs you, then just call dark matter "Fred" instead. Its
functionally equivalent.

e: I'm agreeing with you that putting "matter" in its name is fairly
misleading. Fortunately, that doesn't confuse physicists.

~~~
ab5tract
I'm sorry, but scientists rarely talk about dark anything as if it is an
unknown. They use it all of the time as a central component of their
explanations.

It's as baseless as the ether of the 19th century and as ubiquitous in its
invocation.

But mention this and get downvoted.

~~~
ifdefdebug
That's not entirely fair, because treating it as "matter" gives a quite good
mathematical fit for current observations so far, while the first experimental
observation of light speed ever made immediately falsified the ether
hypothesis.

~~~
hzhou321
It took a while even after the experiment was repeated a couple times. And
even after the experiment only very few could abandon the idea of ether, and
only after abandon the idea of ether, they see the new physics. Now with dark
matter, we have no experimental idea and it is out-of-reach. It is there to
protect the consistency (cover up the inconsistency) of our current
understanding -- familiar?

