Disk Stability versus Dark Matter.

Accordingly to book "Galactic Dynamics" half of all the disk
galaxies contain bars (page 399).
What I first try to understand are galaxies without a bar.
A typical case is Sb galaxy NGC 2841 (page 392) and
M31 (page 19) Andromeda Galaxy
Accordingly to theory each of those galaxies contains a
massive dark matter halo. This is explained because
without this dark matter they would be unstable.
I do not understand why dark matter is a prerequisite
and a must, in order to make spiral galaxies stable.
To state this different why cannot disks be stable without
dark matter.
In par 2.8 and 6.3 N body simulations are discussed.
(As a side comment at page 372 , 373 a simulation of
a spiral disc is shown. Only around t = 10 for a small
period the simulation shows a bar which then disappears.
is that not strange ?)
I have also performed N body simulations.
My initial configuration are N body situated in r concentric
circles each with the same number of stars n. n*r = N
The masses of the stars are selected such that all the N bodies
are in equilibrium and that the speed of all the stars is identical.
= flat rotation curve. However a different rotation
curve is also possible.
My simulation resembles the pictures of the galaxy in fig 6-25
at page 395.
My simulation does not include dark matter and is IMO stable.
In reality the simulation is not stable but that is clearly
an accuracy issue.
(there is also a second cause when N is small)
My question is what is wrong with my simulation.

I could have added an halo of dark matter but such a
configuration would also be unstable, again only
as a result of the accuracy issue.

My question is how do you explain that dark matter in the
form of an halo changes the disk stable from unstable
to stable (while your initial condition is stable i.e. in equilibrium)

For an explanation of the program and technical details
see: http://users.pandora.be/nicvroom/progrm14.htm

Nicolaas Vroom
http://users.pandora.be/nicvroom/

In my previous posting I raised the question if
it is possible to simulate flat Galaxy rotation
curves using Newton's Law.
My answer is possitive.
What is also interesting that no dark matter is required.

A similar question can be raised related to MOND.
For a copy of a program that simulates Galaxy Rotation
curves using MOND See:
http://users.pandora.be/nicvroom/prgmond.htm
For a general discussion See:
http://users.pandora.be/nicvroom/mond.htm

Newton's Law is = G*M/r^2
MOND uses : a^2/a0 = G*M/r^2

One of the most striking results of Galaxy simulations
using MOND is that they are much more stable than
equivalent simulations using MOND.

On the other hand in simulations strictly based on MOND
no stars are ejected which is contrary to observations.
Of course those simulations are wrong because at small
distances Newton's Law should be used.
This immediate raises some objections against MOND:
At small scales Newton's Law applies and and large distances MOND
with a certain range where a little bit of both can be used.
This makes the whole MOND concept rather speculative.

However there are more objections against MOND.
Many rotation curves are flat
or the speed decreases at larger distances.
It is not possible to make such simulations using MOND.
With MOND the speed increases or stays flat.
(In the extreme case we have a BH in the center.
The result is a complete flat rotation curve)

Galaxy simulations should be based around the same
baryonic mass.
The problem is that the shape of such rotation curves
are quite different.
If you compare a galaxy with a flat rotation curve
with a speed of 200 km/sec based on Newton's Law
with a galaxy with the same mass distribution based on MOND
than the speed increases from roughly 300 to 1500 km/sec.

One solution is to decrease the universal constant a0.
When you do that the shape of the rotation curve stays
the same but speeds involved decrease.
Again this makes the whole concept rather speculative.

Ofcourse my simulations could be wrong.

See also the discussion topic:
"Barred galaxies mass distribution" in this newsgroup.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

"Nicolaas Vroom" wrote:

I have also performed N body simulations.

My initial configuration are N body situated in r
concentric circles each with the same number of
stars n. n*r = N The masses of the stars are
selected such that all the N bodies are in
equilibrium and that the speed of all the stars is
identical. = flat rotation curve. However a
different rotation curve is also possible.

My simulation does not include dark matter and is
IMO stable.

In reality the simulation is not stable but that
is clearly an accuracy issue.

(there is also a second cause when N is small)

My question is what is wrong with my simulation.

Well, first off you've created an artificial
stability by making everything perfectly
symmetrical. Make the masses vary randomly by 50%,
the initial momentum vectors vary randomly by pi/50
in spherical coordinates, and the initial positions
vary in 3 space by 5% of the radius, from the setup
you have now, and see how long your simulation
remains stable. You should soon be ejecting stars
early and often.

We know the existing galaxies eject stars, so we
know that "stable" isn't an appropriate description
of their _current_ conditions in any case. "Stable"
is therefore the wrong thing to simulate if you want
to investigate reality.

Your simulation is likely to be unstable even _with_
a symmetric starting condition, not because of
accuracy issues with 128 bit arithmetic, but because
gravitational resonances of the various stars in the
differently spinning adjacent orbits quickly push
and pull stars out of circular alignment [but in
your case only in the plane where they all commonly
orbit because that's how you've started them going,
so that there are no forces perpendicular to that
orbital plane to perturb them from that plane].

Second off, you've ignored the whole reason dark
matter is being posited: the stars in their existing
orbits are _not_ in equilibrium, but without lots
more mass holding them toward the center of the
galaxy than is seen, would be flying outward until
they found some stable orbit or else departed the
galaxy.

Third, the part I don't understand well, that
proposed dark matter is described as a _halo_ rather
than as an invisible point mass at the galaxy
center, because it is only by being embedded inside
part of the total dark matter mass, that the
distribution of close to same speed orbits that we
see, could exist.

Quantum valeat.

xanthian.

Third, the part I don't understand well, that
proposed dark matter is described as a _halo_ rather
than as an invisible point mass at the galaxy
center, because it is only by being embedded inside
part of the total dark matter mass, that the
distribution of close to same speed orbits that we
see, could exist.

The reason astronomers postulate a roughly spherical halo
of dark matter, rather than a thin disk of dark matter or a
point mass of dark matter, is that thin, self-gravitating disks
are unstable to perturbations. We would see many more
"kinked" and "twisted" disks if the material were concentrated
in a plane, rather than spread out in a roughly spherical form.

"Kent Paul Dolan" schreef in bericht
...
"Nicolaas Vroom" wrote:

I have also performed N body simulations.

My initial configuration are N body situated in r
concentric circles each with the same number of
stars n. n*r = N The masses of the stars are
selected such that all the N bodies are in
equilibrium and that the speed of all the stars is
identical. = flat rotation curve. However a
different rotation curve is also possible.

My simulation does not include dark matter and is
IMO stable.

In reality the simulation is not stable but that
is clearly an accuracy issue.

(there is also a second cause when N is small)

My question is what is wrong with my simulation.

Well, first off you've created an artificial
stability by making everything perfectly
symmetrical. Make the masses vary randomly by 50%,
the initial momentum vectors vary randomly by pi/50
in spherical coordinates, and the initial positions
vary in 3 space by 5% of the radius, from the setup
you have now, and see how long your simulation
remains stable. You should soon be ejecting stars
early and often.

There are two issues:
Is the galaxy stable versus
Are there stars ejected.

The fact that single stars are ejected does not mean
that the galaxy as a whole is unstable.

Yes it is true that the galaxy is symmetrical.
This is inconflict with reality.

But that is not so much an issue.
The purpose of the exercise is to create in a simple
manner stable galaxies starting with a given rotation curve.
The result are mass values for each ring.
Using those values in a the simulation I will observe that
my galaxy maintains its shape.
For example with 5 rings and 50 stars after an angle
of 20 degrees the inner ring is still at a distance of 5800
and the speed is 200. No stars are ejected

Now suppose that at the beginning of the simulation
I keep the position and and the speed as calculated
but I multiply each mass with 0.8
My simulation stays symmetric but after 20 degrees
the distance of the inner has increased to 6205 and
the speed decreased to 190. No stars are ejected.
The important lesson is that this is not a stable galaxy.

We know the existing galaxies eject stars, so we
know that "stable" isn't an appropriate description
of their _current_ conditions in any case. "Stable"
is therefore the wrong thing to simulate if you want
to investigate reality.

The only thing I want to calculate what the total mass
should be in each area of the galaxy, based on a given
rotation curve. In a galaxy with
5 rings and 50 stars there are 250 of those areas.
If the total mass in each area differs from this
calculated value your galaxy for sure is unstable
even when there are no ejections.

Your simulation is likely to be unstable even _with_
a symmetric starting condition, not because of
accuracy issues with 128 bit arithmetic, but because
gravitational resonances of the various stars in the
differently spinning adjacent orbits quickly push
and pull stars out of circular alignment [but in
your case only in the plane where they all commonly
orbit because that's how you've started them going,
so that there are no forces perpendicular to that
orbital plane to perturb them from that plane].

The initial position is symmetric.
Generally speaking each star in each ring should
feel the same force and move in the same direction
and the result should be a new symmetrical situation.
This does not happen.
The reason is accuracy with 128 bit arithmatic.

(If you study MOND that is much less of an issue)

Second off, you've ignored the whole reason dark
matter is being posited: the stars in their existing
orbits are _not_ in equilibrium, but without lots
more mass holding them toward the center of the
galaxy than is seen, would be flying outward until
they found some stable orbit or else departed the
galaxy.

I have not ignored that.
Starting point is a measured galaxy rotation curve GRC
You also should tell me what based on measured light density
and based on the M/L function what the calculated Mass
distribution is and what total mass MtotC is.
The object of the program is to calculate based on the GRC
the total mass of the galaxy MtotS that is stable.
If MtotL is smaller that MtotS than you know for sure
that there is not enough visible mass to have a stable galaxy.

The solution is to predict Dark Matter
A different solution is MOND.
IMO the difference between MtotS and MtotC is small.
Are we sure that we cannot solve this discrapency
by introducing Pluto sized objects in the disc?

Third, the part I don't understand well, that
proposed dark matter is described as a _halo_ rather
than as an invisible point mass at the galaxy
center, because it is only by being embedded inside
part of the total dark matter mass, that the
distribution of close to same speed orbits that we
see, could exist.

Which such a point mass in the center i.e a hugh black hole
you cannot solve the discrepancy between MtotC and MtotS
i.e. you cannot make the rotation curve flat.

Quantum valeat.

xanthian.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

"Nicolaas Vroom" schreef in bericht
...


A similar question can be raised related to MOND.
For a copy of a program that simulates Galaxy Rotation
curves using MOND See:
http://users.pandora.be/nicvroom/prgmond.htm
For a general discussion See:
http://users.pandora.be/nicvroom/mond.htm

Newton's Law is = G*M/r^2
MOND uses : a^2/a0 = G*M/r^2

One of the most striking results of Galaxy simulations
using MOND is that they are much more stable than
equivalent simulations using MOND.

I would like remark that this are simulations with MOND
only. If Newton is added over small distances than the picture
changes.

On the other hand in simulations strictly based on MOND
no stars are ejected which is contrary to observations.
Of course those simulations are wrong because at small
distances Newton's Law should be used.
This immediate raises some objections against MOND:
At small scales Newton's Law applies and and large distances MOND
with a certain range where a little bit of both can be used.
This makes the whole MOND concept rather speculative.

However there are more objections against MOND.
Many rotation curves are flat
or the speed decreases at larger distances.
It is not possible to make such simulations using MOND.
With MOND the speed increases or stays flat.
(In the extreme case we have a BH in the center.
The result is a complete flat rotation curve)

ppt # 9 at the following url
http://www.slac.stanford.edu/exp/gla...y_mar16_06.ppt
shows 30 rotation curves
ppt # 11 shows an 15 rotation curves.

At some of those at larger distances the speed is decreasing.
IMO which MOND such simulations are not possible.

Galaxy simulations should be based around the same
baryonic mass.
The problem is that the shape of such rotation curves
are quite different.
If you compare a galaxy with a flat rotation curve
with a speed of 200 km/sec based on Newton's Law
with a galaxy with the same mass distribution based on MOND
than the speed increases from roughly 300 to 1500 km/sec.

This is also a problem with the above mentioned 45 rotation
curves.
The amount of baryonic mass is missing for each.
Only with that data you can verify the claims made with MOND.

One solution is to decrease the universal constant a0.
When you do that the shape of the rotation curve stays
the same but speeds involved decrease.
Again this makes the whole concept rather speculative.

Ofcourse my simulations could be wrong.

A comparison with Newton versus MOND
often starts with a rotation curve.
With the aid of my program you can calculate
with for example 10 rings and 50 stars (500)
the mass involved to support a stable galaxy.
The results show that the amount with MOND
is smaller than with Newton.
Perform the same simulation but now with 50
rings and 80 stars (4000).
The results show is that the amount of mass
with Newton stays approximate the same
but with MOND decreases roughly with a factor 10.

If you make the simulation based on star sized
particles than the differences are almost gargantuan.

This same problem is also discussed in the article by
Chris Mihos:
http://www.astro.umd.edu/~ssm/mond/mondnbody.ps

IMO this is a serious issue.

I would like to know how the people responsible
for the 45 rotation curves coped with that issue.

See also the discussion topic:
"Barred galaxies mass distribution" in this newsgroup.


Nicolaas Vroom
http://users.pandora.be/nicvroom/