I’m trying to better understand the dark matter issue and have a question.

I don’t understand this picture from this site (http://www.owlnet.rice.edu/~spac250/elio/spac.html):
http://www.owlnet.rice.edu/~spac250/elio/expected

Doesn’t the chart assume there’s negligible mass beyond the central bulge? If the mass beyond the bulge instead dropped off percentage-wise as the radius increased, wouldn’t the chart flatline as in the following actual rotation curve (from here ( http://astron.berkeley.edu/~mwhite/darkmatter/rotcurve.html)) at R = 10?:
http://astron.berkeley.edu/~mwhite/darkmatter/rotation.gif

In a spreadsheet I forced the mass to fit each point in the actual rotation curve above. A plot of the mass showed nothing unusual. It was nearly linear with respect to the radius, meaning that it drops off percentage-wise as the radius increases. So why invoke dark matter to explain the actual rotation curve above, when we can just invoke a slightly different mass distribution than we visually see?

(One of the best sites about dark matter I’ve found is this one ( http://www.astro.queensu.ca/~dursi/dm-tutorial/dm0.html), which has some excellent educational applets like here ( http://www.astro.queensu.ca/~dursi/dm-tutorial/rot-vel.html) about rotation velocity.)

If you measure mass by simply counting the flux of photons from each different part of the galaxy (which makes the assumption that all matter of the same density is similarly luminous), then you get the rotation curve as shown in your first figure.

If you measure velocity of the stars in the outer edges of the galaxy, you'll discover that the velocity does NOT descrease as it would if the mass distribution is just the trivial distribution derived from the flux measurements. Instead, the mass distribution is quite different, which leads to the flat rotation curve. The notion of dark matter (which isn't a spooky term at all, necessarily -- it's just matter that isn't glowing) is invoked to explain many situations in astrophysics. The rotation curve is one good example.

- Warren

Originally posted by zanket
In a spreadsheet I forced the mass to fit each point in the actual rotation curve above. A plot of the mass showed nothing unusual. It was nearly linear with respect to the radius, meaning that it drops off percentage-wise as the radius increases. So why invoke dark matter to explain the actual rotation curve above, when we can just invoke a slightly different mass distribution than we visually see?
Looks you like fudged your calculations then. A linear mass vs. radius distribution will certainly not result in a flat rotation curve.

- Warren

That’s good info, thanks. The mass vs. radius distribution sure looks nearly linear in the attached (simple) spreadsheet.

Excuse me, I fudged.

v²/r = G M(r) / r²

where v is the linear velocity, r is the distance from the center of the galaxy, and M(r) is the mass enclosed at r.

If v is constant, M(r) is linear in r. Woops! I'm sorry.

The problem, zanket, is that photometric measurements of luminosity are NOT linear in r -- the luminosity falls off much faster than r, but the velocity doesn't.

- Warren

Originally posted by chroot
If v is constant, M(r) is linear in r.

Note to self: I need only look at the math. I need not chart the data.

The problem, zanket, is that photometric measurements of luminosity are NOT linear in r -- the luminosity falls off much faster than r, but the velocity doesn't.

The mass is cumulative as r increases (that is, each r includes all the mass between 0 and r), but I wouldn't expect a luminosity measurement to be cumulative, so neither would I expect it to be linear in r. Do you mean the luminosity is not linear in r when the luminosity is cumulative?

If yes, I understand that, thanks. Couldn’t the assumption that all matter of the same density is similarly luminous be easily wrong? For example, if the core of the galaxy were a black hole, wouldn’t the tidal forces there be ripping apart stars to make matter of the same density more luminous?

Also, I’m curious why none of my sources mention the seeming oddity of how the rotation curves sink towards zero velocity at the center, without shooting up to velocities expected of matter orbiting a black hole, like, say, 10,000 km/s. Why is that?