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Grey
2005-Feb-23, 09:31 PM
Can someone give me a decent explanation of exactly what is or is not isotropic when referring to this parameter [beta] for an elliptical galaxy's rotation? The specific paper I'm looking at is this one (http://www.arxiv.org/abs/astro-ph/0501622), and I can find plenty of references to this parameter in other papers, but I'm having a hard time understanding its precise significance. There's a definition, which seems to suggest that for an isotropic orbit the radial and angular velocity dispersions are equal, so that would be a particular shape of elliptical orbit. But is there something special about that shape, other than the equality of the velocity dispersions? If the stars in the elliptical tend to have this kind of orbit, does that say something about the mass distribution?

dgruss23
2005-Feb-23, 11:17 PM
Can someone give me a decent explanation of exactly what is or is not isotropic when referring to this parameter [beta] for an elliptical galaxy's rotation? The specific paper I'm looking at is this one (http://www.arxiv.org/abs/astro-ph/0501622), and I can find plenty of references to this parameter in other papers, but I'm having a hard time understanding its precise significance. There's a definition, which seems to suggest that for an isotropic orbit the radial and angular velocity dispersions are equal, so that would be a particular shape of elliptical orbit.

If I'm reading this correctly, the Velocity Aniosotropy parameter (Beta) is a measure of the velocity anisotropy of the radial orbits relative to the tangential orbits:

Beta = 1 - sigma^2(tan)/sigma^2(r)

where sigma(r) is the radial velocity dispersion and sigma(tan) is the tangential velocity dispersion.

According to the above equation for circular orbits Beta is -infinity which implies sigma (r) is zero. For isotropic orbits, beta is zero because sigma tan = sigma(r) which gives a ratio of 1 in the above equation. So 1-1 = 0 (even in the new math - right? :lol: ) Finally if sigma tan = zero, then Beta = 1 with the above equation because the sigma(tan)/sigma (r) ratio equals zero.

Now according to equation 2 in the paper as Beta increases the projected velocity dispersion decreases - an observational effect for the stellar component of the galaxy.


But is there something special about that shape, other than the equality of the velocity dispersions? If the stars in the elliptical tend to have this kind of orbit, does that say something about the mass distribution?

It looks like what they're saying it affects the observed velocity dispersion of the stellar component. If the Beta value is ~0.5 to 0.75 then they claim they can match the observed profiles of Romanowski et al which claim evidence for a dearth of DM.

But the key for this is that the DM particles and the Stellar component (which is what Romanowski et al observed via Planetary Nebula) must not share the same velocity dispersion aniosotropy. According to their simulations the DM particles still have very close to isotropic distribution (Beta = ~0.1). But the merger process gives the stellar component an anisotropic velocity dispersion.

Well, I'm not sure if all I've done here is re-state what you already got from the article. :o :)

Grey
2005-Feb-23, 11:34 PM
Well, I'm not sure if all I've done here is re-state what you already got from the article. :o :)
I'm afraid so. :D I was hoping to know whether there's any relation between the anisotropy parameter and the mass distribution, or whether there are other parameters that relate to it. If it's just the typical orbital eccentricity, more or less, why call it that? Any of our resident astronomers want to weigh in?

dgruss23
2005-Feb-24, 12:03 AM
Well, I'm not sure if all I've done here is re-state what you already got from the article. :o :)
I'm afraid so. :D I was hoping to know whether there's any relation between the anisotropy parameter and the mass distribution, or whether there are other parameters that relate to it. If it's just the typical orbital eccentricity, more or less, why call it that? Any of our resident astronomers want to weigh in?

It seems it is unrelated to the mass distribution of the DM because the DM simulations predict Beta=0.1 whereas they get Beta=0.5 to 0.75 for the stars. So the anisotropy parameter could only speak to the distribution of the stellar mass.

But that discrepancy is at odds with recent results for spiral galaxies which indicate a coupling (http://xxx.lanl.gov/abs/astro-ph/0403206) between luminous and DM. Why would the DM be coupled to the luminous mass in spirals, but not so in ellipticals?

Grey
2005-Feb-24, 01:26 AM
It seems it is unrelated to the mass distribution of the DM because the DM simulations predict Beta=0.1 whereas they get Beta=0.5 to 0.75 for the stars. So the anisotropy parameter could only speak to the distribution of the stellar mass.
I just feel like I'm missing something, but perhaps I'm thinking too deeply.


But that discrepancy is at odds with recent results for spiral galaxies which indicate a coupling (http://xxx.lanl.gov/abs/astro-ph/0403206) between luminous and DM. Why would the DM be coupled to the luminous mass in spirals, but not so in ellipticals?
To be fair, it's a response to this entertainingly titled paper (http://xxx.arxiv.cornell.edu/abs/astro-ph/0310874), so it's not necessarily claiming that the observed velocity profiles demonstrate the existence of dark matter, merely that they don't rule it out.

dgruss23
2005-Feb-24, 02:56 AM
To be fair, it's a response to this entertainingly titled paper (http://xxx.arxiv.cornell.edu/abs/astro-ph/0310874), so it's not necessarily claiming that the observed velocity profiles demonstrate the existence of dark matter, merely that they don't rule it out.

That seems to be the important conclusion from the paper. Speaking of entertaining titles, I thought this one (http://xxx.lanl.gov/abs/astro-ph/0502237) was pretty funny. Although you could argue that to characterize an observational result as "evil" seems a bit dramatic. :)

Grey
2005-Feb-24, 03:10 AM
Speaking of entertaining titles, I thought this one (http://xxx.lanl.gov/abs/astro-ph/0502237) was pretty funny. Although you could argue that to characterize an observational result as "evil" seems a bit dramatic. :)
Very nice. A few of us were discussing this the other day, and noting for future reference that it greatly increases the chance that people will actually read your paper if you come up with a suitably amusing title.

dgruss23
2005-Feb-24, 03:27 AM
Speaking of entertaining titles, I thought this one (http://xxx.lanl.gov/abs/astro-ph/0502237) was pretty funny. Although you could argue that to characterize an observational result as "evil" seems a bit dramatic. :)
Very nice. A few of us were discussing this the other day, and noting for future reference that it greatly increases the chance that people will actually read your paper if you come up with a suitably amusing title.

You're probably right. This is probably worth another thread, but here was another one that has stuck in the back of my mind which plays off the Lord of the Rings Trilogy (http://xxx.lanl.gov/abs/astro-ph/0301067) or this one (http://xxx.lanl.gov/abs/astro-ph/0310368) by a researcher with some alternative views. Unfortunately for the second author, its a pretty good way to alienate oneself - even if he's made valid points about the research process.

Grey
2005-Feb-24, 03:31 AM
...or this one (http://xxx.lanl.gov/abs/astro-ph/0310368) by a researcher with some alternative views.
Oh, my!

ngc3314
2005-Feb-24, 03:41 AM
Can someone give me a decent explanation of exactly what is or is not isotropic when referring to this parameter [beta] for an elliptical galaxy's rotation? The specific paper I'm looking at is this one (http://www.arxiv.org/abs/astro-ph/0501622), and I can find plenty of references to this parameter in other papers, but I'm having a hard time understanding its precise significance. There's a definition, which seems to suggest that for an isotropic orbit the radial and angular velocity dispersions are equal, so that would be a particular shape of elliptical orbit. But is there something special about that shape, other than the equality of the velocity dispersions? If the stars in the elliptical tend to have this kind of orbit, does that say something about the mass distribution?

It's a property of an ensemble of orbits. If they are (along the line of sight one is measuring) not only of a particular eccentricity but spatially in phase, the anisotropy parameter is large (i.e. there is net tangential motion). In the case that the orbits are largely in the same direction, the jargon is that the system is "rotationally supported" - that is the shape of the stellar distribution is sort of a figure of equlibrium. If not, you have orbits going in all tangential directions at each point, and you have the opposite - "pressure supported". These are properties not only of the mass distribution, but the dynamical history of the stars. There are eliptical galaxies, with the same apparent shape, for example, but different ratios of random to systematic velocity, so that some have net rotation while others (nearly) don't. In at leats one definition, beta is the ratio of random (velocity dispersion) motion to net mean (rotational) motion evaluated along a particular line of sight. There are about four chapters in the Binney and Tremaine book on galaxy dynamics that go into this stuff in much more detail than I (at least) ever imagined wanting to see.

Grey
2005-Feb-24, 05:00 AM
Thanks! That's exactly what I was looking for.