What is the Meaning of Scale Radius in Spiral Galaxies?

[minase]

What is "scale radius"

I've tried posting this on the Cosmolgy and astronomy forum but got no reponses yet.* Of course it only been a few days but I'm impatient...

*I've been researching dark matter lately.* Evidence for it in spiral galaxies is the fact that the stars revolve about the center of a galaxy in a strange way: they all travel at the same speed.* When one graphs "rotation curves", orbit speed vs. distance from the center, the velocity curve rises (in the central bulge) then flattens in the disk.* When one plots curves based on the matter in the bulge and disk and sums them, the curve isn't flat.* Therefore, there must be invisible matter in the form of a sphere, or halo, enveloping the galaxy.

My problem is that I can't reproduce those curves.* When I look at curves from actual galaxies my curves for the bulge and the central black hole are similar, but the curves for the disk and dark matter halo aren't.* I've downloaded explanations of the mass distrubution in spiral galaxies, which should solve my problem, but they always talk about "scale radius" and use that value in their formulae --- but I don't know what that means. It seems to mean a number compared to some arbitrary value, what what is that value?* One article mentions a "scale radius" for the disk of the Milky way of 3.5.* Can't be megaparsecs, since the MW disk is about 16 Mpc in radius.

*So, I'm stuck.* Can anybody help me understand this stuff?

 

[ohwilleke]

This link illustrates the calculation and gives you a unit for scale length (h=3.5 kpc) for the Milky Way. http://burro.astr.cwru.edu/JavaLab/RotcurveWeb/back_DM.html

Some detailed calculations at the nuts and bolts level here: http://www.cv.nrao.edu/~jhibbard/students/CMendelowitz/caylin.html

More discussion here: http://www.ifa.hawaii.edu/faculty/barnes/ast626_05/dmdg.pdf

Here: http://www.atnf.csiro.au/pasa/14_1/sackett/paper/node1.html it says:

Scale lengths of the disk and bulge are typically measured from photometry, with assumptions for the flattening of the bulge and the scale height of the stellar disk. The flattening of the dark halo is also fixed by assumption (generally to be spherical). Such a procedure produces ``best-fit'' halo parameters, or -- if the mass-to-light ratios are fixed by the maximum disk hypothesis (van Albada & Sancisi 1986) -- ``maximum disk'' halo parameters.

This source www.physto.se/~ingemar/Moskva.ps[/URL] (post-script) says:

[QUOTE] For an exponential disk we have a natural length scale available. Astronomers also use r 83, which is the radius containing 83% of the light. For an exponential disk r 83 corresponds to 3.2 scale lengths r0. [/QUOTE]

See also: http://www.ingentaconnect.com/content/bsc/mnr/2004/00000353/00000002/art00001

[QUOTE]We investigate in detail the mass distribution obtained by means of high-resolution rotation curves of 25 galaxies of different morphological types. The dark matter contribution to the circular rotation velocity is well-described by resorting to a dark component, the density of which shows an inner core, i.e. a central constant density region. We find a very strong correlation between the core radius size RC and the stellar exponential scalelength RD: RC 13 [RD/(5 kpc)]1.05 kpc , and between RC and the galaxy dynamical mass at this distance, Mdyn(RC) . These relationships would not be expected if the core radii were the product of an incorrect decomposition procedure, or the biased result of wrong or misunderstood observational data. The very strong correlation between the dark and luminous scalelengths found here seems to hold also for different Hubble types and opens new scenarios for the nature of the dark matter in galaxies. [/QUOTE]

The powerpoint presentation here, gives you your answer:
[PLAIN]http://www.mso.anu.edu.au/newcosmology/lectures/Freeman_DM1.ppt

Scale length is the value of a constant needed to fit an exponential luminosity curve to the observed luminosity distribution. See slide 11. The formula is I(R)=Io*e^(-R/h) where h is the scale factor (about 4 kpc for the Milky Way). Optical rotation curves typically extend to R=3h.

 

[minase]

Wow!* That's a lot of information.* Thank you very much.* I've been digging for this stuff for several weeks,* rephrasing my* search parameters for Google, etc., etc.* I'll check this out right away.

This just shows how complicated the answer to a simple question can be.

Wanna try this one?* Do DM halos form around stars?* Could a spinning DM mass form a disk?

Thanks again for the wonderful information.

 

[ohwilleke]

Do DM halos form around stars?

There isn't any evidence to support this. But, this is partially a lack of data problem. Dynamical analysis requires you to see luminous objections moving towards you and away from you so that you can infer system dynamics. Stars are not surrounded by luminous objects, and binaries are generally too close to each other for a halo to have a discernable effect. Hence, there is no room for detection.

Could a spinning DM mass form a disk?

Inferred dark matter distributions have not been disklike. The more useful question is, why do we not observe DM disks? If there is DM, what would it have to be like to prevent disklike formations?