Galaxies without dark matter halos?

John Chandler wrote in message
...
greywolf42 wrote:


: The inclination of the orbit is one of those things that it is very
: difficult to determine in astronomy. We can't tell -- just by
: looking -- whether we're looking nearly edge-on or straight
: down onto the plane of the orbit.

Actually, Kepler gave us more than the elliptical shape of orbits.
He also discovered that the body treated as "at rest" occupies one
focus of the ellipse and that the angular velocity varies inversely
with the radial distance.

Historically, the latter is Newton, not Kepler. Kepler discovered that
planets sweep out equal areas in equal time. Similar, but not the same.

Using those two additional properties of
orbits allows us to tell what the inclination is.

The problem is that we don't know the 'angular velocity' of the orbit. We
can only directly measure the radial portion of the speed projected in our
direction.

greywolf42
ubi dubium ibi libertas

greywolf42 wrote:
: The problem is that we don't know the 'angular velocity' of the orbit. We
: can only directly measure the radial portion of the speed projected in our
: direction.

Not so. Nowhere in the discussion was there any stipulation that
astrometric data would be somehow excluded from consideration. With a
combination of radial velocity and astrometry, the 3-D orbit can be
determined directly. Indeed, the astrometry can do the job all by
itself, without the help of radial velocities. (This is in the
context of Keplerian motion, where the eccentricities are "proper"
instead of caused by outside perturbations.) Of course, it's a
different matter to determine the inclination of a disk galaxy. To
put it mildly, it's very tedious to watch a galaxy long enough to map
out the orbits astrometrically, and most graduate students are
unwilling to take on a research project that will last millions of
years (heh, heh). Nonetheless, it's possible to substitute finesse for
brute force -- high-precision proper motions will do the job, too.
The real problem is that it's so easy to measure the aspect ratio of
a disk galaxy that it hardly seems worthwhile to determine the
inclination independently.

--
John F. Chandler

greywolf42 wrote:
: The problem is that we don't know the 'angular velocity' of the orbit. We
: can only directly measure the radial portion of the speed projected in our
: direction.

Not so. Nowhere in the discussion was there any stipulation that
astrometric data would be somehow excluded from consideration. With a
combination of radial velocity and astrometry, the 3-D orbit can be
determined directly. Indeed, the astrometry can do the job all by
itself, without the help of radial velocities. (This is in the
context of Keplerian motion, where the eccentricities are "proper"
instead of caused by outside perturbations.) Of course, it's a
different matter to determine the inclination of a disk galaxy. To
put it mildly, it's very tedious to watch a galaxy long enough to map
out the orbits astrometrically, and most graduate students are
unwilling to take on a research project that will last millions of
years (heh, heh). Nonetheless, it's possible to substitute finesse for
brute force -- high-precision proper motions will do the job, too.
The real problem is that it's so easy to measure the aspect ratio of
a disk galaxy that it hardly seems worthwhile to determine the
inclination independently.

--
John F. Chandler

John Chandler wrote in message
...
greywolf42 wrote:

: The problem is that we don't know the 'angular velocity' of the orbit.
We
: can only directly measure the radial portion of the speed projected in
our
: direction.

Not so. Nowhere in the discussion was there any stipulation that
astrometric data would be somehow excluded from consideration.

The angular velocity is calculated -- not observed.

With a
combination of radial velocity and astrometry, the 3-D orbit can be
determined directly. Indeed, the astrometry can do the job all by
itself, without the help of radial velocities. (This is in the
context of Keplerian motion, where the eccentricities are "proper"
instead of caused by outside perturbations.)

One cannot determine inclination of a stellar orbit just from astrometry --
even in the rare cases where you can watch and measure the describing of a
full ellipse by the orbiting body. The projection of an ellipse is still an
ellipse. You can get an upper bound to the central mass -- but not a
measurement of the central mass.

Using both doppler and astrometry of a full (or significant fraction of
full) ellipse description, one can determine the inclination of the orbit to
our line-of-sight. Either alone is insufficient.

Of course, it's a
different matter to determine the inclination of a disk galaxy. To
put it mildly, it's very tedious to watch a galaxy long enough to map
out the orbits astrometrically, and most graduate students are
unwilling to take on a research project that will last millions of
years (heh, heh).

For galaxies, we usually 'cheat,' and assume that the profile of a spiral
galaxy is always circular. Then our measurement of the major and minor axes
gives us a direct calculation for inclination.

Nonetheless, it's possible to substitute finesse for
brute force -- high-precision proper motions will do the job, too.

Do we have any such things? I thought all the measurements of proper
motions inside other galaxies had been discredited.

The real problem is that it's so easy to measure the aspect ratio of
a disk galaxy that it hardly seems worthwhile to determine the
inclination independently.

I agree. However, the main question at hand is the use theoretical
statistical corrections to data on the motions of individual stars.

greywolf42
ubi dubium ibi libertas

John Chandler wrote in message
...
greywolf42 wrote:

: The problem is that we don't know the 'angular velocity' of the orbit.
We
: can only directly measure the radial portion of the speed projected in
our
: direction.

Not so. Nowhere in the discussion was there any stipulation that
astrometric data would be somehow excluded from consideration.

The angular velocity is calculated -- not observed.

With a
combination of radial velocity and astrometry, the 3-D orbit can be
determined directly. Indeed, the astrometry can do the job all by
itself, without the help of radial velocities. (This is in the
context of Keplerian motion, where the eccentricities are "proper"
instead of caused by outside perturbations.)

One cannot determine inclination of a stellar orbit just from astrometry --
even in the rare cases where you can watch and measure the describing of a
full ellipse by the orbiting body. The projection of an ellipse is still an
ellipse. You can get an upper bound to the central mass -- but not a
measurement of the central mass.

Using both doppler and astrometry of a full (or significant fraction of
full) ellipse description, one can determine the inclination of the orbit to
our line-of-sight. Either alone is insufficient.

Of course, it's a
different matter to determine the inclination of a disk galaxy. To
put it mildly, it's very tedious to watch a galaxy long enough to map
out the orbits astrometrically, and most graduate students are
unwilling to take on a research project that will last millions of
years (heh, heh).

For galaxies, we usually 'cheat,' and assume that the profile of a spiral
galaxy is always circular. Then our measurement of the major and minor axes
gives us a direct calculation for inclination.

Nonetheless, it's possible to substitute finesse for
brute force -- high-precision proper motions will do the job, too.

Do we have any such things? I thought all the measurements of proper
motions inside other galaxies had been discredited.

The real problem is that it's so easy to measure the aspect ratio of
a disk galaxy that it hardly seems worthwhile to determine the
inclination independently.

I agree. However, the main question at hand is the use theoretical
statistical corrections to data on the motions of individual stars.

greywolf42
ubi dubium ibi libertas

greywolf42 wrote:

: The angular velocity is calculated -- not observed.

What's observed astrometrically is the projected angular velocity.
That's adequate for the purpose of determining the 3-D orbit, except
for a reflection ambiguity about the plane of the sky. Needless to
say, that ambiguity is resolved if Doppler data are included.

: One cannot determine inclination of a stellar orbit just from astrometry --
: even in the rare cases where you can watch and measure the describing of a
: full ellipse by the orbiting body. The projection of an ellipse is still an
: ellipse. You can get an upper bound to the central mass -- but not a
: measurement of the central mass.

You're confusing two very different problems: determining the mass of
the system and determining the orbit. They are not the same.

--
John F. Chandler

greywolf42 wrote:

: The angular velocity is calculated -- not observed.

What's observed astrometrically is the projected angular velocity.
That's adequate for the purpose of determining the 3-D orbit, except
for a reflection ambiguity about the plane of the sky. Needless to
say, that ambiguity is resolved if Doppler data are included.

: One cannot determine inclination of a stellar orbit just from astrometry --
: even in the rare cases where you can watch and measure the describing of a
: full ellipse by the orbiting body. The projection of an ellipse is still an
: ellipse. You can get an upper bound to the central mass -- but not a
: measurement of the central mass.

You're confusing two very different problems: determining the mass of
the system and determining the orbit. They are not the same.

--
John F. Chandler

John Chandler wrote in message
...
greywolf42 wrote:

: The angular velocity is calculated -- not observed.

What's observed astrometrically is the projected angular velocity.

We observe a series of astrometric positions on the celestial sphere over
time. Not the transverse speed.

That's adequate for the purpose of determining the 3-D orbit, except
for a reflection ambiguity about the plane of the sky. Needless to
say, that ambiguity is resolved if Doppler data are included.

From "The Cosmological Distance Ladder," p. 42, 1985, Michael Rowan-Robinson
(used earlier in this thread by Ulf Torkelsson):

M1 + M2 = P(V1 sin i + V2 sin i)^3 (1 - e^2)^3/2 / (2 pi G sin^3 i)

Note that i is the inclination of the orbital axis to our line-of-sight.
And we cannot determine this from either just projected (transverse) speed
or from just doppler speed. It's not just a "reflection ambiguity." We
don't know the value of *i* at all, without both transverse and radial data.

: One cannot determine inclination of a stellar orbit just from
astrometry --
: even in the rare cases where you can watch and measure the describing of
a
: full ellipse by the orbiting body. The projection of an ellipse is
still an
: ellipse. You can get an upper bound to the central mass -- but not a
: measurement of the central mass.

You're confusing two very different problems: determining the mass of
the system and determining the orbit. They are not the same.

You are specifically contradicting every reference I've ever seen on the
subject. Perhaps you could provide us with a way of determining mass
without first determining the orbital inclination.

greywolf42
ubi dubium ibi libertas

John Chandler wrote in message
...
greywolf42 wrote:

: The angular velocity is calculated -- not observed.

What's observed astrometrically is the projected angular velocity.

We observe a series of astrometric positions on the celestial sphere over
time. Not the transverse speed.

That's adequate for the purpose of determining the 3-D orbit, except
for a reflection ambiguity about the plane of the sky. Needless to
say, that ambiguity is resolved if Doppler data are included.

From "The Cosmological Distance Ladder," p. 42, 1985, Michael Rowan-Robinson
(used earlier in this thread by Ulf Torkelsson):

M1 + M2 = P(V1 sin i + V2 sin i)^3 (1 - e^2)^3/2 / (2 pi G sin^3 i)

Note that i is the inclination of the orbital axis to our line-of-sight.
And we cannot determine this from either just projected (transverse) speed
or from just doppler speed. It's not just a "reflection ambiguity." We
don't know the value of *i* at all, without both transverse and radial data.

: One cannot determine inclination of a stellar orbit just from
astrometry --
: even in the rare cases where you can watch and measure the describing of
a
: full ellipse by the orbiting body. The projection of an ellipse is
still an
: ellipse. You can get an upper bound to the central mass -- but not a
: measurement of the central mass.

You're confusing two very different problems: determining the mass of
the system and determining the orbit. They are not the same.

You are specifically contradicting every reference I've ever seen on the
subject. Perhaps you could provide us with a way of determining mass
without first determining the orbital inclination.

greywolf42
ubi dubium ibi libertas

John Chandler wrote in message
...
greywolf42 wrote:
: We observe a series of astrometric positions on the celestial sphere
over
: time. Not the transverse speed.

Are you asserting that the tabulated positions as a function of time
represent a non-differentiable function?

No.

If not, then your attempt to
distinguish between what is "observed" and what is "merely calculated"
is pointless quibbling.

Differentiating between observations and theoretical calculation is never
"quibbling." In this case, I was alluding to the fact that we do not get
orbital speeds from astrometry (observation) until we include a theoretical
calculation of distance (calculation).

The astrometric positions themselves are of
course calculated in turn from the filar micrometer readings, plate
measurements, and other "actual" observations.

Your statement, to which I was replying was: "What's observed
astrometrically is the projected angular velocity." We actually observe an
angular velocity (not projected) on the celestial sphere. WE then include
the assumption or calculation of distance, to convert angular motions into
projected angular velocity -- of the orbit. I assumed the last three words,
since we were discussing determinations of orbital parameters.

The key here is that we can't determine the true *orbital* angular velocity
from observation (which I thought was your original claim). Because we
don't know the inclination of the orbit.

:From "The Cosmological Distance Ladder," p. 42, 1985, Michael
: Rowan-Robinson (used earlier in this thread by Ulf Torkelsson):
:
: M1 + M2 = P(V1 sin i + V2 sin i)^3 (1 - e^2)^3/2 / (2 pi G sin^3 i)
:
: Note that i is the inclination of the orbital axis to our line-of-sight.
: And we cannot determine this from either just projected (transverse)
: speed or from just doppler speed. It's not just a "reflection
: ambiguity." We don't know the value of *i* at all, without both
: transverse and radial data.

As I've explained at least twice before, the astrometry determines the
orbit all by itself.

You've provided no explanations, but only unsupported claims. I belive you
are incorrect. However, I'll be happy to listen to an explanation. How
does the astrometry give you the orbital inclination? Give equations,
please.

The formula you have carefully copied here is for
radial velocity, not for astrometry.

The same equation applies to astrometry (transverse velocity) as for radial
velocity. You cannot determine the orbital inclination from a projected
velocity alone. You have either radial velocity in doppler alone, or
transverse velocity in astrometry alone (leaving aside the issue of
converting angular plate motions into tangential velocities with calculated
theoretical distances).

: You are specifically contradicting every reference I've ever seen on the
: subject. Perhaps you could provide us with a way of determining mass
: without first determining the orbital inclination.

Who said anything about wanting to determine the mass? Certainly not
I.

That is the prime point of this thread. Once we have determined an orbit,
we have determined the central mass. If we cannot determine mass, it is
because we cannot resolve the orbit.

We were talking about determining the orbit using astrometry
(which is possible), not determining the mass using radial velocity
curves (which is not).

This thread is about determining the mass of a central object. The equation
I provided is used for radial velocities. But it also holds for transverse
velocities. There is no fundamental difference between the two.

on 10/10, the discussion of stars was:
====================
You:
With a combination of radial velocity and astrometry, the 3-D orbit can be
determined directly. Indeed, the astrometry can do the job all by itself,
without the help of radial velocities. (This is in the context of Keplerian
motion, where the eccentricities are "proper" instead of caused by outside
perturbations.)

Me:
One cannot determine inclination of a stellar orbit just from astrometry --
even in the rare cases where you can watch and measure the describing of a
full ellipse by the orbiting body. The projection of an ellipse is still an
ellipse. You can get an upper bound to the central mass -- but not a
measurement of the central mass.

Using both doppler and astrometry of a full (or significant fraction of
full) ellipse description, one can determine the inclination of the orbit to
our line-of-sight. Either alone is insufficient.
====================

As I pointed out, you have confused the two problems.

And as I have now pointed out, I haven't confused the problems. The problem
of mass is trivial -- once we know the orbit. It is finding the orbit that
is the hard part.

You even trotted out that formula for computing the binary
mass and seemed to think it was relevant. Just let go of the mass
and focus on one thing at a time.

Determining the mass(es) by determining the orbit is what *I've* been
talking about, all along.

May I suggest that you provide some equations (from a similar reference to
mine, above) wherein you can determine the orbital inclination of an
arbitrary elliptical orbit solely from astrometry measurements. I'll even
spot you the calculation of distance to the star (presuming that it is
within parallax range) so that you can convert those plate positions into
speeds around a focus mass.

greywolf42
ubi dubium ibi libertas