NET Angular Momentum of Globular cluster of stars

Is the NET angular momentum of a globular cluster of stars, zero?

e.g. Omega Centauri or M13 for example.

Is the NET angular momentum of an elliptical galaxy and or the
central bulge of a spiral, zero or close to zero..........oblate
spheroids might have a net angular momentum if the oblate geometry
is due to rotation in a single direction. But if it's due to net
rotation 50 / 50 in two opposite directions, again, there would be
no net angular momentum, right?

rt

[[Mod. note -- I think the answers are Yes (or very close to zero),
Yes, and Yes (respectively). -- jt]]

On 16/03/2017 16:46, wrote:
Is the NET angular momentum of a globular cluster of stars, zero?

e.g. Omega Centauri or M13 for example.

Is the NET angular momentum of an elliptical galaxy and or the
central bulge of a spiral, zero or close to zero..........oblate
spheroids might have a net angular momentum if the oblate geometry
is due to rotation in a single direction. But if it's due to net
rotation 50 / 50 in two opposite directions, again, there would be
no net angular momentum, right?

The latter is a rather unlikely scenario since there would inevitably be
sufficient close stellar encounters to thermalise the velocity
distribution over time (ie shift stellar orbits by 90 degrees).

rt

[[Mod. note -- I think the answers are Yes (or very close to zero),
Yes, and Yes (respectively). -- jt]]

Indeed.

A reasonable treatment of the evolution of gravitationally bound
clusters of stars is online at Caltech minus a few diagrams:

http://www.astro.caltech.edu/~george...y20-Lec15x.pdf

It might help clear up some of the OP's misconceptions.

--
Regards,
Martin Brown

In article , Martin Brown
writes:

Is the NET angular momentum of an elliptical galaxy and or the
central bulge of a spiral, zero or close to zero..........oblate
spheroids might have a net angular momentum if the oblate geometry
is due to rotation in a single direction.

[[Mod. note -- I think the answers are Yes (or very close to zero),
Yes, and Yes (respectively). -- jt]]

Indeed.

A reasonable treatment of the evolution of gravitationally bound
clusters of stars is online at Caltech minus a few diagrams:

http://www.astro.caltech.edu/~george...y20-Lec15x.pdf

I'm no expert in this field, but I think that it might be a bit more
complicated. Look up "fast rotator" and "slow rotator" in the context
of elliptical galaxies. This might be a place to start:

http://www-astro.physics.ox.ac.uk/~b...rly-types.html

OK, so far great, close to zero net angular momentum in a globular or
elliptical. Please keep in mind I'm attempting to march down a Gedanken
path, and am not proposing anything that is likely.

Now, if I have an elliptical with zero angular momentum, this is not to
say there is no momentum. Clearly there is a lot of momentum and each
star contributes an angular momentum vector to the total sum, which is
zero.

If I establish a coordinate system X,Y,Z, then I can sum the angular
momentum about each axis with a SMBH at coordinate 0,0,0 at the origin
as a reference position.

As this has been decades since I've crunched these equations, perhaps my
terms need updating so please feel free to change my variables. I'll
use L for angular momentum. I can sum angular momentum about each of
the principle axis'.

For each axis, I get some number of objects moving around the axis with
one orientation, and another number of objects moving in the reverse
sense. So, I can sum them as total angular momentum L

L = aL_x + (-bL_x) + cL_y + (-dL_y) + eL_z + (-fL_z) = 0

So, a=b, c=d, and e=f.

And for a typical elliptical or globular, without oblateness, we can
probably go further and say that a=b=c=d=e=f.

In other words, objects are moving about the origin in all possible
orientations, they are thermalized, and there is no net angular
momentum.

But this does not mean there is no angular momentum. The stars possess
a lot of momentum, it's just all randomized.

[Moderator's note: This is not necessarily the case. It is also
possible---probable?---that each individual star has zero angular
momentum with respect to the SBH at the center, i.e. executes a
back-and-forth motion, passing through the centre of the galaxy. Stars
are few and far between, so this is possible without an appreciable
number of collisions. -P.H.]

If this seems about correct, then I'll move forward to the next step in
the Gedanken path, working with a galaxy that starts off with only

L = aL_x and with all of the rest of the components initially zero.

Have I made a mistake so far?

rt

On Thursday, March 16, 2017 at 12:46:59 PM UTC-4, wrote:
Is the NET angular momentum of a globular cluster of stars, zero?

e.g. Omega Centauri or M13 for example.
....
[[Mod. note -- I think the answers are Yes (or very close to zero),
Yes, and Yes (respectively). -- jt]]

I'm not sure that's the case. Searching for "globular cluster
rotational flattening" gives a lot of papers that discuss the rotational
dynamics of globulars. I would say the consensus is, there is
significant angular momentum in some globulars.

In article ,
writes:
Is the NET angular momentum of a globular cluster of stars, zero?

I think that's the case for most clusters, but I vaguely remember
that there are a tiny number that show rotation. I might be mistaken
on either part of this.

Is the NET angular momentum of an elliptical galaxy and or the
central bulge of a spiral, zero or close to zero

For elliptical galaxies, a quick web search turned up
https://academic-oup-com/mnras/artic...6.2011.18496.x

The authors claim 86% of early type galaxies are "fast rotators." I
haven't studied the paper to find out what that means or what sample
they defined.

I expect there are many more works on this subject; as I say, it was
a very quick search.

There are also lots of theory papers simulating major mergers, from
which elliptical galaxies are supposed to form. The simulation
results must include a final angular momentum.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

Steve Willner wrote:
In article ,
writes:
Is the NET angular momentum of a globular cluster of stars, zero?

I think that's the case for most clusters, but I vaguely remember
that there are a tiny number that show rotation. I might be mistaken
on either part of this.

As I recall dimly from either reading or hearing talks about this, Omega Cen
appears slightly oblate, although I do not know what if any radial velocity
observations confirm that this is due to rotation. And it may be the core
of a small galaxy captured by the MWG long ago, rather than being a
"classical" globular.

Mike Dworetsky


Is the NET angular momentum of an elliptical galaxy and or the
central bulge of a spiral, zero or close to zero

For elliptical galaxies, a quick web search turned up
https://academic-oup-com/mnras/artic...6.2011.18496.x

The authors claim 86% of early type galaxies are "fast rotators." I
haven't studied the paper to find out what that means or what sample
they defined.

I expect there are many more works on this subject; as I say, it was
a very quick search.

There are also lots of theory papers simulating major mergers, from
which elliptical galaxies are supposed to form. The simulation
results must include a final angular momentum.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

On 04/04/2017 05:29, Mike Dworetsky wrote:
Steve Willner wrote:
In article ,
writes:
Is the NET angular momentum of a globular cluster of stars, zero?

I think that's the case for most clusters, but I vaguely remember
that there are a tiny number that show rotation. I might be mistaken
on either part of this.

As I recall dimly from either reading or hearing talks about this, Omega Cen
appears slightly oblate, although I do not know what if any radial velocity
observations confirm that this is due to rotation. And it may be the core
of a small galaxy captured by the MWG long ago, rather than being a
"classical" globular.

There was something in ApJ early stellar dynamics measurements mid
1990's showing that the luminosity oblateness varies with radius more or
less spherical near the middle and far out but oblate in between.

https://arxiv.org/pdf/astro-ph/9612184.pdf

They credit someone else in 1983 as having first measured the isophotes
in 1983 and claim mean 0.121 minimum 0 up to 2', maximum 0.25 at 10' and
then becoming rounder as you go further out. (see p6)

--
Regards,
Martin Brown

On Thu, 16 Mar 2017 12:46:58 EDT, wrote:
Is the NET angular momentum of a globular cluster of stars, zero?
... Is the NET angular momentum of an elliptical galaxy and or the
central bulge of a spiral, zero or close to zero

I think the current status of thinking is long on theory and short on
observations. I don't think there's been a single comprehensive
survey of the actual stellar movements in any globular cluster. I'm
not aware of any done for an elliptical galaxy either.

Not long ago there was an idea of "tri-axial" rotation for these which
implied that individual star orbits could be decomposed into 3 axial
components which would somehow serve to keep the stars from plunging
into the core. That doesn't seem to be de rigueur anymore.

Also there was speculation some decades ago that globular cluster
stars simply fell through the cluster cores in a sort of mass yo-yo
action. Also not popular of late, I don't think.

I had a notion which I publicized on these forums some years ago, that
there's a gravitational scalar, as yet unmodelled, which allowed stars
to freely float in such environments. I plead guilty for hand-waving
on this, but it seems an elegant concept. Ugly facts begone!

I mention all this because it looks to me that other answers on this
thread are muddying up the distinction between theory and observation.
If there've been cogent observations made recently on actual stellar
orbits in globular clusters or ellipticals, I'd be glad to be directed
to them.

On 23/03/2017 22:23, Eric Flesch wrote:
On Thu, 16 Mar 2017 12:46:58 EDT, wrote:
Is the NET angular momentum of a globular cluster of stars, zero?
... Is the NET angular momentum of an elliptical galaxy and or the
central bulge of a spiral, zero or close to zero

I think the current status of thinking is long on theory and short on
observations. I don't think there's been a single comprehensive
survey of the actual stellar movements in any globular cluster. I'm
not aware of any done for an elliptical galaxy either.

I'm no expert in this apart from having known a few of the early
practitioners of computational stellar dynamics but I think there are
now some precision observations of stars in local globular clusters like
Omega Centuri which show that things are never simple.

http://www.aanda.org/articles/aa/pdf.../aa3061-05.pdf

and

https://www.astro.umd.edu/~richard/A...ergy_equip.pdf

There are plenty of velocity dispersion and luminosity measurements
along lines of sight through various of the brighter Messier globular
clusters dating from way back. eg M15

http://articles.adsabs.harvard.edu//...00251.000.html

Not long ago there was an idea of "tri-axial" rotation for these which
implied that individual star orbits could be decomposed into 3 axial
components which would somehow serve to keep the stars from plunging
into the core. That doesn't seem to be de rigueur anymore.

Also there was speculation some decades ago that globular cluster
stars simply fell through the cluster cores in a sort of mass yo-yo
action. Also not popular of late, I don't think.

I'm sure I have seen somewhere a claim that stars out on the fringes of
clusters tend to be in very elongated orbits rather than circular ones.
Certainly the eye tends to pick out spiky rays in for example M13 around
the edges of the core.

I had a notion which I publicized on these forums some years ago, that
there's a gravitational scalar, as yet unmodelled, which allowed stars
to freely float in such environments. I plead guilty for hand-waving
on this, but it seems an elegant concept. Ugly facts begone!

At a handwaving level a single test particle in an evolved spherically
symmetric globular cluster moves in a gravitational potential that far
out is roughly 1/r^2 but closer in becomes weaker and in the dense core
becomes almost linear. This implies that a test particle will no longer
follow an ellipse around the centre of mass but will instead trace out a
somewhat more circular petal shape staying further away from the core.

Self consistent models in phase space seem to be one interesting way of
approaching it using maximum entropy or some other computational
heuristic to create the most non-committal distribution of matter in
consistent with a given mass M, energy E and angular moment L.

Going through the core must increase the possibility of a three body
close encounter from time to time resulting in ejection of stars and the
condensation of the rest.

I mention all this because it looks to me that other answers on this
thread are muddying up the distinction between theory and observation.
If there've been cogent observations made recently on actual stellar
orbits in globular clusters or ellipticals, I'd be glad to be directed
to them.

On the simulation early evolution of star clusters this was published
fairly recently, but I don't know enough to comment on its veracity.

http://rsta.royalsocietypublishing.o...t/368/1913/829

--
Regards,
Martin Brown