Question about MOND and gravity

twofish-quant

Not quite. The thing about dark matter is that you wave that magic wand once and lots of seemingly unrelated things make sense. For example, there seems to be more deuterium than you would expect if the universe were all "normal matter" and you can calculate the "lumpiness factor" of the universe.

Galaxy rotation curves are only one "weird thing", and frankly, if galaxy rotation curves were the only "weird thing" that we see, then MOND would make more sense to me than dark matter.

Also the possibility exists that both are correct (i.e. that there is dark matter and gravity doesn't behave the way we think it does).

twofish-quant

I was misremembering something that you seem to have remembered correctly.....

When people saw that this was like *wow* there might be something here. It's this particular observation that gave MOND quite a bit of credibility for a time.

Yup. The trouble is that the more "tweaking" you have to do to get things to work, the less strong the theory is. Both dark matter and modified gravity require tweaking to get the right fit with observations, but at this point dark matter seems to require a lot less tweaking than modified gravity, but this is one of those things that could change quickly.

One other thing about arguments toward elegance is that different people can weight things differently. If someone looks at the data that modified gravity requires less tweaking than dark matter, it can be hard to argue otherwise because these are somewhat subjective.

twofish-quant

The other problem is that Krupa seems to misunderstand the applicability of LCDM. The idea behind LCDM is that the big bang produced large scale clumps and that these clumps influences where galaxies form. How galaxies actually form is outside of the theory, so LCDM really says nothing about things at small scales.

No one has been able to reproduce the cosmological observations with only modified gravity (lots of people have tried). Once you assume that some dark matter is necessary, then it becomes easier to assume (unless you have some reason otherwise) that it's all dark matter.

Jonathan Scott

MOND has a different gravitational acceleration rule for cases where the gravitational acceleration is of the order of a0 or weaker. If this rule were just treated as additional to Newtonian gravity, it appears that corrections due to MOND would already have been necessary to match solar system experiments (although it's not completely conclusive, because MOND accelerations don't add up in the same way as Newtonian gravity). For this reason, MOND assumes an interpolation function which means that the acceleration of an object in a very weak field obeys the MOND rule but in a stronger field it obeys Newtonian rules (or GR where that level of accuracy is necessary).

A star on the edge of a galaxy is treated by MOND as being very weakly accelerated as a whole by the galaxy, so the MOND rule applies. However, if you consider the component atoms of the star, they are all within the gravitational field of the star itself, so the overall gravitational acceleration on those atoms would be expected to be much greater than a0, which means they would obey Newtonian gravitation and be "immune" to MOND. It is difficult to see how the atoms of a star can accelerate in one way but the star as a whole accelerate in a different way.

Similarly, a system of masses such as a binary star or a star and planets at the edge of the galaxy is also treated by MOND as a single object in the low-acceleration regime, even though the components are clearly subject to higher accelerations from each other.

Note however that the MOND force is quite tricky to work with anyway, in particular because it is not linear in the source mass.

mesa

How is the formula set up for the dark matter halo? Can we work out an example? Perhaps predict the velocity of a star using basic Newtonian Mechanics vs DMT vs MOND

So there is a great deal more to the predictions of these systems than star velocity alone. Is star velocity the predominating area or are there other aspects of equal or greater importance? I would like to put some chalk to a board on star velocities unless you feel there is a better place to start, can we work out an example?

Okay, I understand what you were saying now.

mesa

I was looking at the MOND equation, it looks like the adjustment is 'hidden' at smaller scales allowing newtonian mechanics to work on our scale as the function brings it's value to 1 while adjusting to increased values for 'a' as the effects of gravity would become weaker as distance 'r' is increased.

I can not figure out how the function μ(a/a0) actually works except that a0 becomes more significant with respect to an increase in the value for 'r' as it reduces 'a' to a lesser value than a0 = 1^-9m/s^2, a very tiny value.

So the equation has terms in it I am unfamiliar with:
∇ - ???
ρ - this is a function for the spread of mass in a galaxy is it not? If so how does it work?
I don't see the symbol to the right for gravitational potential as written in the function

Any thoughts?

Jonathan Scott

The symbol ∇ or "nabla" is used as the mathematical operator called "Del" which is the vector differential operator, used as a short notation for the differential operators grad, div and curl (depending on whether it is applied to a scalar, or to a vector via dot product, or to a vector via cross product). If you don't know about those, it's probably beyond the scope of this forum to explain. Technically, it is equivalent to a sort of vector with the following partial derivative operator components:
$$
\left ( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right )
$$
For example, if you apply the gradient operator to the gravitational potential, you get the vector field describing the gravitational acceleration.

The symbol ρ in the MOND article is simply the local density of mass (in mass per unit volume).

mesa

Lets give it a shot. Where would you like to start?

123 mark

Sorry if I'm in the wrong section to ask this question.

I'm trying to find out when astronomers discovered that the solar system oscillates through the galactic plane. I just can't imagine the Mayans having the ability to determine that it actually occurs on a 26,000 (or whatever) year period.

Thanks for the consideration

123 mark

twofish-quant

Let me just sketch out the problem.

You have a function X. You have a set of rules to convert that function into another function Y.

The problem is here is that learning what those rules are is a one semester course in calculus. Look at 18.02 on MIT OCW.

mesa

So lets start with the basics and go from there, how do they calculate for ρ? Do they just take the average for the mass of the entire galaxy or is it based on what is inside the area swept by a star?

With DMT I was told by an astrophysicist that the dark matter is put into the model and essentially is an adjustment to the mass to have the stars match newtons gravitation formula. Is that right? Is Gm/r^2 modified in any way?

Jonathan Scott

The local density of matter in the form of stars or gas is estimated from the luminosity of that part of the galaxy in various parts of the spectrum.

The Newtonian acceleration is then calculated in the usual way by integration (summing the effect of all the mass). With spherical symmetry, Newtonian gravity would simplify to being equivalent to having all the mass inside a given orbit concentrated at the center, but for galaxies the shape is more complicated. The MOND acceleration can then be calculated in terms of the Newtonian acceleration.
Yes, Dark Matter simply adds additional invisible source mass obeying the standard Newtonian gravitational formula (as an approximation to GR).

A very weird feature of the MOND rule is that for a wide range of galaxies it correctly predicts the velocity distribution based only on the distribution of visible matter. If dark matter is the real explanation, this suggests that the distribution of the dark matter in galaxies must somehow be strongly linked with the distribution of the visible matter in such a way as to reproduce the MOND result, but so far there is no theoretical explanation for this.

mesa

Sorry it took a few days to get back to you, had finals last couple days.

I'm a little surprised that would work, how is the integretion setup? Is it a function of the gravity of each sun and it's affect on the next by putting together an artificail layout based on average distances apart or is it simply the sum of all the masses thrown into the center for the swept area of the galaxy by a particular star?

I was told by an astrophysicist that it has only been recently that papers were published changing the model from a spherical density to a more disc like shape, I found this surprising as well.

That's very interesting, so MOND at least is able to show a possible correlation between matter and dark matter (that is if DMT is correct).

Jonathan Scott

I don't know the practical details. For a simple case, I guess one could assume one could treat the mass as a series of rings of varying density surrounding a spherical nucleus. In a more complex cases one could use numerical methods to sum the effects of mass density over a modelled shape of the galaxy consistent with the observations. There's certainly no need to model the individual stars, because from sufficient distance the gravitational effect is essentially the same as that of a continuous medium with an appropriate average density.

mesa

Where do you think would be a good place to start to find the actual formulas used for these calculations? I looked online and came up with very little. Are there members on the board that would be helpful?

I am going to quiz the proffesors at school again and see if I can get a more complete answer. I was told by one it was basically the same as you stated originally; the mass is essentially summed and put into the center and then calculated.

That seems overly simplified and frankly I don't see how that could calculate anything properly.