NET Angular Momentum of Globular cluster of stars

[r***@gmail.com]

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]]

[Martin Brown]

Post by r***@gmail.com
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).

Post by r***@gmail.com
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/ay20/Ay20-Lec15x.pdf

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

[Phillip Helbig (undress to reply)]

Post by Martin Brown

Post by r***@gmail.com
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
http://www.astro.caltech.edu/~george/ay20/Ay20-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/~bureau/early-types.html

[r***@gmail.com]

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

[Craig Markwardt]

Post by r***@gmail.com
Is the NET angular momentum of a globular cluster of stars, zero?
e.g. Omega Centauri or M13 for example.

...

Post by r***@gmail.com
[[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.

[Steve Willner]

Post by r***@gmail.com
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.

Post by r***@gmail.com
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/article-lookup/doi/10.1111/j.1365-2966.2011.18496.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]

Post by Steve Willner

Post by r***@gmail.com
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

Post by Steve Willner

Post by r***@gmail.com
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/article-lookup/doi/10.1111/j.1365-2966.2011.18496.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.

[Martin Brown]

Post by Mike Dworetsky

Post by Steve Willner

Post by r***@gmail.com
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)

[r***@gmail.com]

Post by r***@gmail.com
Is the NET angular momentum of a globular cluster of stars, zero?

OK, it can be difficult to communicate in words rather than pictures and
sketches.............trying again:

I'm just trying to get us on board for a qualitative exploration. Sure,
with ellipticals, as with globulars, there is a range of oblatness to
the spherical geometry. A flattened structure may (and may not) have
net angular momentum, it depends on whether there are stars rotating in
a preferred (or in counter rotational

e.g. the spiral ngc4138 is counter rotating, so it's possible for stars
in ellipticals to also have this feature
https://en.wikipedia.org/wiki/NGC_4138)

directions about the flattened plane's normal axis. ie, we have E0
through E5 ellipticals.

BUT,

COMPARED TO.... a simple spiral disk, with no central bulge, with all
stars moving around a center in the SAME direction..........like
Saturn's rings. ........... an elliptical and or a globular have

ESSENTIALLY, ZERO angular momentum .

In other words, can we agree that if I have the same number of stars,
and the same orbital radii, ellipticity etc. for every star, with the
sole exception that the globular has stars that appear as spherical
morphology, where as a flat spiral has purely single angular momentum
axis.............

The globular will be nearly zero compared to the flat spiral.

Agreed? If so then I can move on.

rt

[Phillip Helbig (undress to reply)]

[[Mod. note -- I apologise to readers for the delay in processing this
article, which the author submitted on 2017-03-23. Unfortunately there
were some garbled characters in one of the article headers that took a
bit of time to straighten out.
-- jt]]

Post by r***@gmail.com

Post by r***@gmail.com
Is the NET angular momentum of a globular cluster of stars, zero?

OK, it can be difficult to communicate in words rather than pictures and
I'm just trying to get us on board for a qualitative exploration.

While a qualitative understanding is necessary, it is not sufficient. As
Lord Kelvin said, "I often say that when you can measure what you are
speaking about, and express it in numbers, you know something about it;
but when you cannot measure it, when you cannot express it in numbers,
your knowledge is of a meagre and unsatisfactory kind."

Post by r***@gmail.com
Sure,
with ellipticals, as with globulars, there is a range of oblatness to
the spherical geometry. A flattened structure may (and may not) have
net angular momentum, it depends on whether there are stars rotating in
a preferred (or in counter rotational
e.g. the spiral ngc4138 is counter rotating, so it's possible for stars
in ellipticals to also have this feature
https://en.wikipedia.org/wiki/NGC_4138)
directions about the flattened plane's normal axis. ie, we have E0
through E5 ellipticals.

Note that this refers only to the appearance. So if we look at
something cigar-shaped along the major access, or something shaped like
a disk along the minor axis, we see E0 in both cases.

Post by r***@gmail.com
BUT,
COMPARED TO.... a simple spiral disk, with no central bulge, with all
stars moving around a center in the SAME direction..........like
Saturn's rings. ........... an elliptical and or a globular have
ESSENTIALLY, ZERO angular momentum .

As has been noted here, this doesn't seem to be the case, based on
current observations. There seems to be an appreciable number of
"fast-rotating" ellipticals.

Post by r***@gmail.com
In other words, can we agree that if I have the same number of stars,
and the same orbital radii, ellipticity etc. for every star, with the
sole exception that the globular has stars that appear as spherical
morphology, where as a flat spiral has purely single angular momentum
axis.............
The globular will be nearly zero compared to the flat spiral.
Agreed? If so then I can move on.
rt

[Eric Flesch]

Post by r***@gmail.com
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.

[Martin Brown]

Post by Eric Flesch

Post by r***@gmail.com
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/2006/02/aa3061-05.pdf

and

https://www.astro.umd.edu/~richard/ASTRO620/glob_clust_energy_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//full/1989ApJ...347..251P/0000251.000.html

Post by Eric Flesch
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.

Post by Eric Flesch
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.

Post by Eric Flesch
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.org/content/368/1913/829

[Eric Flesch]

Post by Martin Brown
http://www.aanda.org/articles/aa/pdf/2006/02/aa3061-05.pdf
https://www.astro.umd.edu/~richard/ASTRO620/glob_clust_energy_equip.pdf
... 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 ...

Thanks for the references -- the measurements of proper motion are a
great step forward, but the authors go on to calculate orbitals (or
fractions thereof) using certain standard assumptions. Stars shooting
out of the globular cluster are assumed to have highly eccentric
elliptical orbits, etc. The notion of orbits is a given.

I'm realizing nowadays that my old notion of "gravitational scalar"
really is just the same as today's notion of "dark matter". If dark
matter resides throughout an elliptical galaxy or globular cluster (or
the Galactic halo) then it could raise the ambient background
gravitational level to where a resident star no longer feels the
gravitational effect from its neighbours or from the system centre.
Instead, the star would follow thre contours (potentials) of the dark
matter structure. So stars would just mingle throughout without
following orbits as such. Thus my concern about the current narrative
which puts all star motions in a framework of orbits.

cheers.

[Steve Willner]

If dark matter resides throughout an elliptical galaxy or
globular cluster (or the Galactic halo) then it could raise the
ambient background gravitational level to where a resident star no
longer feels the gravitational effect from its neighbours or from
the system centre. Instead, the star would follow thre contours
(potentials) of the dark matter structure. So stars would just
mingle throughout without following orbits as such.

What distribution of dark matter are you postulating? If the
distribution is uniform, then the dark matter has no effect
regardless of how much of it there is. If the distribution is
spherically symmetric, then we have the familiar case where each
object responds to the amount of matter interior to that object's
position relative to the center of the dark matter distribution. If
the distribution is more complicated, then so are the effects, but in
any case, stars are affected in the usual way by other stars. I
suppose if you have clumps of dark matter (say tens or hundreds of
solar masses each) whizzing around randomly, the overall effects
could look random, but it's hard to see how such dark matter clumps
could form or be held together or why they should inhabit elliptical
but not spiral galaxies.

A nice calculator for galactic rotation curves is at
http://burro.astr.cwru.edu/JavaLab/RotcurveWeb/main.html
but it didn't work when I tried it just now. (I suspect some kind of
Java compatibility problem.)

[Eric Flesch]

Post by Steve Willner

the system centre. Instead, the star would follow thre contours
(potentials) of the dark matter structure. So stars would just
mingle throughout without following orbits as such.

What distribution of dark matter are you postulating? If the
distribution is uniform, then the dark matter has no effect

My point is that "dark matter" could be gravitationally opaque even as
it gravitates. We know it has different qualities than baryonic
matter, but we're not yet at the point where "we know what we don't
know". So it could act to muffle the gravitational environs of
ellipticals (etc) while responding to those environs in ways that
creates contours from it. Gravitational permeability & permittivity,
anyone? From outside the system its gravitational effect would be
indistinguishable from baryonic matter.

[[Mod. note -- The notion of "gravitationally opaque" doesn't exist
in general relativity, so if you want this then you need to come up
with a new theory of gravity.
-- jt]]

[Eric Flesch]

Post by Eric Flesch
My point is that "dark matter" could be gravitationally opaque even as
it gravitates. We know it has different qualities than baryonic ...
[[Mod. note -- The notion of "gravitationally opaque" doesn't exist
in general relativity, so if you want this then you need to come up
with a new theory of gravity.
-- jt]]

I'm pretty sure that general relativity is not a theory of gravity.

[Moderator's note: I've kept this bit in because the rest of the post
might prompt some interesting discussion. I don't think that this is
the place to debate whether GR is a theory of gravity. -P.H.]

Post by Eric Flesch
I

can however rephrase my point, Think of dark matter as a medium.
Compare stars in a dark matter environment to fish in a lake. Fish
don't fall because they are buoyant in the water. In a dark matter
lake, stars would similarly have some gravitational buoyancy. The
gravitational medium would modify or nullify the inverse square law.
How could it not? And that's pretty much all of my point.

[Phillip Helbig (undress to reply)]

I can however rephrase my point, Think of dark matter as a medium.
Compare stars in a dark matter environment to fish in a lake. Fish
don't fall because they are buoyant in the water. In a dark matter
lake, stars would similarly have some gravitational buoyancy. The
gravitational medium would modify or nullify the inverse square law.
How could it not? And that's pretty much all of my point.

The analogy doesn't work because with buoyancy, there is a force working
in the direction opposite to gravity, and this is possible because of
non-gravitational interaction between the object and the surrounding
medium. But the kind of dark matter we are talking about has little if
any interaction with baryonic matter.

I also don't think that it would work quantitatively. Can you show that
this idea (even neglecting the point I mentioned above) results in the
very simple MOND law?

[Eric Flesch]

Post by Eric Flesch
gravitational medium would modify or nullify the inverse square law.
How could it not? And that's pretty much all of my point.

... But the kind of dark matter we are talking about has little if
any interaction with baryonic matter.

Um, sorry Phil, but dark matter is supposed to account for (1) spiral
galaxy rotational profiles, and (2) "great attractors". Given the
existence of dark matter (for this argument), it definitely interacts
with baryonic matter. And if it does so, it must have a major effect
on the dynamics of galactic haloes, elliptical galaxies and globular
clusters. Maybe fish-in-water isn't the right analogy, but the
presence of a gravitational scalar diminishes (or nullifies) the
gravitational influence of near neighbours. So the boundary of our
solar system may simply be where our Sun's gravitational influence is
supplanted by that of the "dark matter" medium, with neighbouring
stars not in the equation. That's the idea, anyway.

I also don't think that it would work quantitatively. Can you show that
this idea (even neglecting the point I mentioned above) results in the
very simple MOND law?

I'm not up with MOND. Is it simple? Simple is good but not
sufficient. I expect that MOND is a "top down" system designed to
best account for observed behaviour, as opposed to a "bottom up"
system which builds on known physical law. A top-down system must, of
human necessity, be simple, else nobody will pay attention.

thanks, Eric


[[Mod. note --
1. I think Phillip Helbig was referring to dark matter having little if
any *non-gravitational* interaction with baryonic matter.

2. There's an extensive history of people studying what the consequences
of a gravitational scalar field might be. See, for example, section
5.3 of Clifford M Will, "Theory and Experiment in Gravitational Physics"
(Cambridge University Press, 1981, 1985), or section 3.3.2 of Will's
review paper "The Confrontation between General Relativity and
Experiment" (open-access at http://www.livingreviews.org/lrr-2014-4 ).
To summarize, compatability with various solar-system experiments
constrains the free parameters in these theories so as to give
results almost identical to general relativity.
-- jt]]

[Eric Flesch]

Post by r***@gmail.com
[[Mod. note --
2. There's an extensive history of people studying what the consequences
of a gravitational scalar field might be. See, for example, section
5.3 of Clifford M Will, "Theory and Experiment in Gravitational Physics"
(Cambridge University Press, 1981, 1985), or section 3.3.2 of Will's
review paper "The Confrontation between General Relativity and
Experiment" (open-access at http://www.livingreviews.org/lrr-2014-4 ).

Thank you for this outstanding reference which I'll be reading for
days. I wasn't aware of Clifford Will's work.

[[Mod. note -- Will is also the author of the excellent popular book
"Was Einstein Right?" (Basic Books, paperback 2nd Edition 1993) on
experimental tests of general relativity.
-- jt]]

[Phillip Helbig (undress to reply)]

Post by Eric Flesch

Post by Eric Flesch
gravitational medium would modify or nullify the inverse square law.
How could it not? And that's pretty much all of my point.

... But the kind of dark matter we are talking about has little if
any interaction with baryonic matter.

Um, sorry Phil, but dark matter is supposed to account for (1) spiral
galaxy rotational profiles, and (2) "great attractors". Given the
existence of dark matter (for this argument), it definitely interacts
with baryonic matter.

Sorry: it has little if any interaction with baryonic matter OTHER THAN
GRAVITATIONAL INTERACTION. Thus, the buoyancy analogy doesn't work.

Post by Eric Flesch
I'm not up with MOND. Is it simple?

Phenomenologically? Yes.

Post by Eric Flesch
1. I think Phillip Helbig was referring to dark matter having little if
any *non-gravitational* interaction with baryonic matter.

Indeed.

[Richard D. Saam]

Post by r***@gmail.com
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

The paper:
https://arxiv.org/abs/1704.02005
provides some interesting insight and more questions as to
this general problem.
In as much as hydrogen alpha
is an indicator of the Milky Way galactic halo,
it remains fixed relative to the galaxy rotating within.
RDS