Galaxy mass distribution without DM

[Jeon]

I've searched for a formula of galaxy mass Distribution formula along the radius, often the papers say:
ρ∝e^x
( ρ is the surface density, x is distance from the Center of the galaxy). is it correct without DM?
Or is there any other correct formula?

 

[mfb]

What do you mean by "correct without DM"? Without DM, the galaxies as we know them would not exist.

 

[Jeon]

I'd like to know the mass distribution without dark matter, estimated by only visible mass.

 

[mfb]

If the paper is talking about a surface density, I would expect that to be limited to the visible mass contribution. Dark matter doesn't form a nice disk.

The exponential shape is odd, by the way, it has to have a limited range.

 

[Jeon]

That means the surface density is only about the visible mass contribution.
I should have a look again. Thanks!

 

[ohwilleke]

There shouldn't be just one formula. The mass distribution in galaxies differs materially between, for example, elliptical galaxies, disk galaxies with bulges, disk galaxies without bulges, dwarf galaxies, etc.

 

[v4theory]

There are 2 methods for calculating the mass distribution using only "visible mass". One inaccurate way is to count the stars themselves by closely counting visible stars, dust, and gas as determined by infrared observations in a convenient representative area of a galaxy, and extrapolating that result to the rest of the comparable areas of a galaxy. The other far more accurate and widely used method is to calculate the mass distribution by using the rotation curve. We calculate the mass inside a series of concentric rings and subtract the mass obtained from the calculation for the mass enclosed inside the inner rings from the mass calculated enclosed inside the outer rings. This give a mass value for a specific ring. Divide this ring mass by its area i.e. area inside of outer circle of the ring minus area of inner circle of the ring gives area of ring. Divide the mass calculated for the ring by the area of the ring gives the mass per unit area (mpua) of the ring. We can then graph the mpua of the outer rings to the mass per unit area of the inner rings. What we find using this method is an mpua that is closely consistent with a disk distribution. For example when we drill a hole of a specific size in a record album near the edge (equator) and another the same size near the center (pole) we find the mass from the holes to be equal. That shows the mass from the holes per unit area of the holes to be consistent with coming from a disk. In the bulge or spherical galaxy the mpua from the equator to the pole increases consistent with a bulge or sphere.

The mpua derived from the star, dust, gas counting method, while consistent with a disk distribution, is vastly lower than the mpua derived from rotation curves. We recognize this to mean that there is a vast amount of non stellar, non dust, and non gas mass in galaxies. Some call this mass dark matter. But dark matter just means unseen with no other assumed attributes. Some give it attributes not supported by any observation, and which are inconsistent with observation, such as saying it's non baryonic (not normal matter). Non baryonic matter models are inconsistent with the disk shape because there are no interaction attributes of non baryonic matter that allow for accretion to a disk. There are non baryonic models with ad hoc assumption of weakly interacting attributes. But none fit the observed disk distribution as well as fully interacting normal baryonic matter.

Some pursue a modification of Newtonian dynamics (mond) as an explanation. But they are fringe ideas and not supportable mathematically, or by physics.

The question remains, what is the unseen matter if not stars, dust, gas, or non baryonic? A conservative assumption would be that it is composed of compact sub stellar objects. Sub stellar objects include gas giant planets, terrestrial planets, asteroids, Kyper belt, and Ort cloud objects. There is a problem with nomenclature however. Recalling the Pluto nomenclature squabble. What is an object not orbiting a star? A rogue planet? What if they are super Jovians with terrestrial satellites? What about rogue asteroids? What about rogue terrestrials?

 

[Chronos]

Whatever dark matter may be, we are more acquainted with what it is not - namely, detectable by any known particle or EM emissions. That leaves a pretty broad parameter space for unexpolored detection methods. The most traditionally human reaction to such a failure is to appeal to the paranormal.

 

[v4theory]

Well, not detectable by those means at this distance. Even if there were 4 times more mass in the space between centarus and us, even if it emits a lot of EM, it is obviously not enough to detect at this distance. Such bodies would at minimum be at least, on average, 2 light years away from any given star. Even if it's very large and very bright it can still be undetectable this far away.

 

[JMz]

Back to the OP: A typical formula for the Milky Way would have a density ~ 1/(1+x^2) radially, and exp(-b*x) "vertically" (i.e., perpendicular to the disk) for some constant "b".

A typical scale would have x measured in units of perhaps 10,000 LY (that is, x = radial distance/1e4 LY), and b ~ 0.1 or less (so the vertical fall-off distance is 1000 LY or less).

Note that these are not really statements about the Milky Way. They are statements about approximate models of the MW that have just 1 or 2 parameters, so they are easy to think about, easy to fit to data, and easy to work with. They are particularly bad models in the central bulge -- really, b should depend on radius, or the whole model should have a separate component for the central bulge (and additional components for additional structure, such as the halo).