Hubble makes 3D dark matter map

Hans Aberg wrote:

One idea that comes to my mind is that very young,
nearby galaxies are very hard to observe for two
reasons: they are faint, and quickly gets absorbed
into larger galaxies.

Why would any even exist? Surely after ~14 billion
years, most of the easily accumulated intergalactic
gas has long ago gathered into galaxies, and the
remaining cases gathering more recently would be so
thinly scattered throughout the universe that the
chance of even one being "nearby" for useful
meanings of that vague term would be "slender to
none"?

FWIW

xanthian.

ebunn=40lfa221051.richmond.edu wrote:
[Mod. note: quoted text deleted. The text below is MIME-damaged.
I don't have time to fix it. Please post only in ASCII. -- mjh]

Looking a bit more at Ted's calculations,
it unclear what fraction of 7 x 10=5E=7B-25=7D g/cm=5E3
is considered dark matter.

the wiki page
http://en.wikipedia.org/wiki/Milky_Way
provides the relevant parameters of the Milky Way

Solar mass 1.99E+33 g
Milky Way mass 5.80E+11 solar masses
Milky Way mass 1.15E+45 g
Milky Way diameter 100,000 light years
Milky Way diameter (D) 9.46E+22 cm
Milky Way diameter (R) 4.73E+22 cm
Milky Way thickness .01*D 9.46E+20 cm
Milky Way rotation velocity 2.00E+07 cm/sec (200 km/sec)
Milky Way age 13.4 billion years
Newtonian G 6.67E-08 cm=5E3 / (g sec)

v is constant with R at 200 km/sec
which implies as Ted says:

dM =3D (v=5E2/G) dR

which implies dM =3D K dR

but here is the point and correct me if I am wrong:
The relationship dM =3D K dR does not have to be in a sphere
for the derivation to be valid.
Observations indicate that the Milky Way is essentially a disc.

then paraphrasing Ted here

The incremental volume of the Milky Way disc is 2 pi thickness R dR,
so the local density is

rho =3D v=5E2 / (2 pi thickness G R)
=3D (2.00E+07)=5E2 / (2*pi*(9.46E+20)*(6.67E-08)*(4.73E+22))
=3D 2.13E-23 g/cm=5E3

this value of density (rho) at R says nothing
about the nature of the matter
whether it is dark matter or other.
It is an average value of all stars, dust, gas, dark matter, etc at R.

the wiki page
http://en.wikipedia.org/wiki/Milky_Way
indicates that:
'The distance from the Sun to the galactic center
is estimated at 26,000 =B1 1400 light-years=22

so the local (rho) density at our solar system would be:

rho (local) =3D 2.13E-23 * 50,000/26,000 =3D 4.1E-23 g/cm=5E3

but this value again is an average value
of all stars, dust, gas, dark matter, etc at R (local).

The key question is how after 13.4 billion years
does the Milky Way galaxy have a distribution of mass
which is proportional to R or (dM =3D K dR).

Calculations indicate that a persistent and continuous force
over 13.4 billion years
related to universe critical density (6E-30 g/cm=5E3)
as applied to galactic mass will result in (dM =3D K dR).

Richard

In article , "Kent Paul Dolan"
wrote:

One idea that comes to my mind is that very young,
nearby galaxies are very hard to observe for two
reasons: they are faint, and quickly gets absorbed
into larger galaxies.

Why would any even exist?

One problem, from the point of view of theory, is that they have been
observed. :-)

Surely after ~14 billion
years, most of the easily accumulated intergalactic
gas has long ago gathered into galaxies, and the
remaining cases gathering more recently would be so
thinly scattered throughout the universe that the
chance of even one being "nearby" for useful
meanings of that vague term would be "slender to
none"?

Big Bangists must explain it in terms of the Big Bang. :-)

I suggested it might come from tunneling of matter out of black holes,
which in fact leads to a complicated model in order to work, but can in
principle be tested. It was discussed here before. That is in part I am
asking these questions. If there one is looking for a*situation where QM
and GR closely interact, that is either the early universe (if there was
one), or black holes; I do not know of any other situation.

--
Hans Aberg

In article ,
wrote:

I don't know the term "infancy matter," but it sounds like it means
stuff that includes a lot of hydrogen gas.*

It should probably be the composition of matter that the nearby, very
young galaxies, that one has observed, have been formed of.

Yet another suggestion for dark matter, that comes to my mind, is dark
planetary systems, that is, essentially a star system before the star has
ignited. Is that possible or impossible by current theoretical knowledge?
Normally, I think, one thinks of the planetary system being formed after
the star has been ignited. But with the other way around at hand, perhaps
lower fundamentals could be sucked into the formation of the star, while
some of the heavier*fundamentals might go into the formation of the
planets. I have no idea why such a thing might take place, though. Perhaps
if particles collide, they might be sorted out in layers, like when one is
shaking a box with some stuff in it.

--
Hans Aberg

ebunn=40lfa221051.richmond.edu wrote:

In article mt2.0-23776-1168506825=40hercules.herts.ac.uk,
Richard Saam rdsaam=40att.net wrote:


If the density of dark matter
is anywhere close to critical density =7E10=5E-30 g/cc,
its influence on planetary orbits would be negligible



That's right. In fact, the density of dark matter in the neighborhood=

of the solar system is considerably larger than the critical density, =
but
it's still far too small to have a measurable effect on solar system d=
ynamics.
Working out why is a nice exercise.

The orbital speed of objects in our Galaxy is approximately v=3D200 km=
/s
over quite a range of orbital radii, including the Sun's orbital radiu=
s.
Assuming the Galaxy's mass distribution can be approximated as a spher=
ical
halo, the mass Mwithin a radius R obeys

GM/R=5E2 =3D v=5E2/R,

so M =3D v=5E2 R / G.

Since v is roughly constant as a function of R, the mass in a thin
spherical shell is dM =3D (v2/G) dR. The volume of the shell is 4 pi =
R2 dR,
so the local density is

rho =3D v=5E2 / (4 pi G R=5E2).

At the Sun's orbital radius, this works out to 7 x 10=5E=7B-25=7D g/cm=
3.

If you don't assume a spherical halo, then the numbers change somewhat=
,
but the order of magnitude doesn't.

Suppose you filled the solar system with material at this density.
The amount of stuff within Pluto's orbit would be equal to this densit=
y
times the volume of a sphere of radius equal to Pluto's orbit. That w=
orks
out to 6 x 10=5E=7B17=7D kg, or less than a trillionth of a solar mass=
...

-Ted

Looking a bit more at Ted's calculations,
it unclear what fraction of 7 x 10=5E=7B-25=7D g/cm3
is considered dark matter.

the wiki page
http://en.wikipedia.org/wiki/Milky_Way
provides the relevant parameters of the Milky Way

Solar mass 1.99E+33 g
Milky Way mass 5.80E+11 solar masses
Milky Way mass 1.15E+45 g
Milky Way diameter 100,000 light years
Milky Way diameter (D) 9.46E+22 cm
Milky Way diameter (R) 4.73E+22 cm
Milky Way thickness .01*D 9.46E+20 cm
Milky Way rotation velocity 2.00E+07 cm/sec (200 km/sec)
Milky Way age 13.4 billion years
Newtonian G 6.67E-08 cm3 / (g sec)

v is constant with R at 200 km/sec
which implies as Ted says:

dM =3D (v=5E2 / G) dR

which implies dM =3D K dR

but here is the point and correct me if I am wrong:
The relationship dM =3D K dR does not have to be in a sphere
for the derivation to be valid.
Observations indicate that the Milky Way is essentially a disc.

then paraphrasing Ted here

The incremental volume of the Milky Way disc is 2 pi thickness R dR,
so the local density is

rho =3D v=5E2 / (2 pi thickness G R)
=3D (2.00E+07)=5E2 / (2*pi*(9.46E+20)*(6.67E-08)*(4.73E+22))
=3D 2.13E-23 g/cm=5E3

this value of density (rho) at R says nothing
about the nature of the matter
whether it is dark matter or other.
It is an average value of all stars, dust, gas, dark matter, etc at R.

the wiki page
http://en.wikipedia.org/wiki/Milky_Way
indicates that:
'The distance from the Sun to the galactic center
is estimated at 26,000 =B1 1400 light-years=22

so the local (rho) density at our solar system would be:

rho (local) =3D 2.13E-23 * 50,000/26,000 =3D 4.1E-23 g/cm3

but this value again is an average value
of all stars, dust, gas, dark matter, etc at R (local).

The key question is how after 13.4 billion years
does the Milky Way galaxy have a distribution of mass
which is proportional to R or (dM =3D K dR).

Calculations indicate that a persistent and continuous force
over 13.4 billion years
related to universe critical density (6E-30 g/cm3)
as applied to galactic mass will result in (dM =3D K dR).

Richard

In article ,
Hans Aberg wrote:
In article ,
wrote:

Yet another suggestion for dark matter, that comes to my mind, is dark
planetary systems, that is, essentially a star system before the star has
ignited. Is that possible or impossible by current theoretical knowledge?

Well, the planets are a bit of a red herring he the star completely
dominates the mass of a star system, so what you're asking is whether
protostars can be the dark matter. The answer is no for any number of reasons.
First, protostars are observable, especially in the infrared, so we
have quite a good idea of how many there are. Second, a protostar
remains a protostar for only a limited time before becoming a star.
So the number of stars we see sets a good limit on the number of
protostars.

The subject of when planetary systems form and what they look like
as they do is quite an interesting one. It's been getting a lot
of attention in recent years as infrared observations have gotten
better. It ends up having nothing at all to do with the dark matter,
but it's a lot of fun in its own right.

-Ted


--
[E-mail me at , as opposed to .]

wrote:

In article ,
Richard Saam wrote:


If the density of dark matter
is anywhere close to critical density ~10^-30 g/cc,
its influence on planetary orbits would be negligible


That's right. In fact, the density of dark matter in the neighborhood
of the solar system is considerably larger than the critical density, but
it's still far too small to have a measurable effect on solar system dynamics.
Working out why is a nice exercise.

The orbital speed of objects in our Galaxy is approximately v=200 km/s
over quite a range of orbital radii, including the Sun's orbital radius.
Assuming the Galaxy's mass distribution can be approximated as a spherical
halo, the mass Mwithin a radius R obeys

GM/R^2 = v^2/R,

so M = v^2 R / G.

Since v is roughly constant as a function of R, the mass in a thin
spherical shell is dM = (v^2/G) dR. The volume of the shell is 4 pi R^2 dR,
so the local density is

rho = v^2 / (4 pi G R^2).

At the Sun's orbital radius, this works out to 7 x 10^{-25} g/cm^3.

If you don't assume a spherical halo, then the numbers change somewhat,
but the order of magnitude doesn't.

Suppose you filled the solar system with material at this density.
The amount of stuff within Pluto's orbit would be equal to this density
times the volume of a sphere of radius equal to Pluto's orbit. That works
out to 6 x 10^{17} kg, or less than a trillionth of a solar mass.

-Ted

Looking a bit more at Ted's calculations,
it is unclear what fraction of 7E-25 g/cm^3
is considered dark matter.

The wiki page
http://wikipedia.org/wiki/Milky_Way
provides some of the relevant parameters of our Milky Way Galaxy

Solar Mass 1.99E33 g
Milky Way Mass 5.8E11 solar mass
Milky Way Mass (M) 1.15E45 g
Milky Way diameter 100,000 light years
Milky Way diameter (D) 9.46E22 cm
Milky Way radius (R) 4.73E22 cm
Milky Way thickness .01 D 9.46E20 cm
Milky Way rotation velocity (v) 2.0E7 cm/sec (200 km/sec)
Milky Way age 13.4 billion years
Newtonian (G) 6.67E-8 cm^3 / (g sec)

rotational velocity (v) is constant with R at 200 km/sec
which implies as Ted says:

dM = (v^2 / G) dR

which implies dm = K dR (where K is constant)

but here is a divergent point from Ted:
The relationship dM = K dR does not have to be in a sphere
for the derivation to be valid.
Observation indicates that the Milky Way is essentially a disc.

then paraphrasing Ted he

The incremental volume of the Milky Way is 2 pi thickness R dR
so the local density (rho) is:

rho = v^2 / (2 pi thickness G R)
= (2.0E7)^2 / (2*pi*(9.46E20)*(6.67E-8)*(4.73E22))
= 2.13E-23 g/cm^3

this value of density (rho) at R says nothing
about the nature of the matter
whether it is dark matter or other.
It is an average value of all stars, dust, gas, dark matter, etc at R.

The wiki page:
http://wikipedia.org/wiki/Milky_Way
indicates that:
'The distance from the Sun to the galactic center
is estimated at 26,000 +/- 1400 light years.

So the local (rho) density at our solar system would be:

rho = 2.13E-23 g/cm^3 * 50,000 / 26,000 = 4.1E-23 g/cm^3

but this value again is an average value
of all stars, dust, gas, dark matter, etc at R (local).

The key question is how after 13.4 billion years
does the Milky Way galaxy have a distribution of mass
which is proportional to R or (dM = K dR).

Calculations indicate that a persistent and continuous force
over 13.4 billion years
related to the universe critical density (6E-30 g/cm^3)
as applied to galactic mass
results in (dM = K dR)
and consistent with the Milky Way Mass of 1.15E45 g.

Richard

In article ,
Richard Saam wrote:
wrote:

Looking a bit more at Ted's calculations,
it is unclear what fraction of 7E-25 g/cm^3
is considered dark matter.

It depends on where you are and over what size scale you're willing to
average. What we think we know observationally is the average density
of all stuff (visible and dark), averaged over largish volumes of
space. To decide how much of that stuff is dark matter, you'd want to
subtract off the mass of all the stuff you can see.

The number that I gave is an estimate of the density averaged over
pretty large volumes -- in particular, over volumes that extend
significantly above and below the scale height of the visible disc
of the Galaxy. Over that sort of volume, most of the mass is due
to dark matter: the visible stuff is only, maybe, 1/3 or 1/4 of the
total. On the other hand, right in the disc of the Galaxy, the density
of visible stuff (stars, etc.) is quite a bit higher, so right in the
solar neighborhood the fraction of all the matter that's dark is probably
smaller.

We think that the dark matter is pretty smoothly distributed over these
sort of scales, so within a factor of a few (which is all I cared about)
the above number should be about equal to the local dark matter density.
I don't think we can say anything more precise than that.

rotational velocity (v) is constant with R at 200 km/sec
which implies as Ted says:

dM = (v^2 / G) dR

which implies dm = K dR (where K is constant)

but here is a divergent point from Ted:
The relationship dM = K dR does not have to be in a sphere
for the derivation to be valid.

Yes, it does. The rule it's derived from,

M = v^2 R / G,

which is essentially Kepler's third law, is derived based on a spherically
symmetric distribution of matter.


Observation indicates that the Milky Way is essentially a disc.

The visible stuff is. The overall density is not. That's really part
of the point: the distribution of mass as inferred by its gravitational
effects does not match the distribution of visible matter.

From observations of only things in the disc of the Galaxy, you can't
tell whether the overall density distribution in the Galaxy is disc-like
or spherical, but from observations out of the plane you can: the
orbits of things significantly above or below the disc will be different
depending on whether the bulk of the mass in the Galaxy lies in the
disc or is spread out in a more three-dimensional way. Observations
of such objects show that the bulk of the mass of the Galaxy is indeed
spread out in a three-dimensional volume, as opposed to being
confined to a disc, although the exact shape is debated. I'm not an
expert on the details of this stuff, but here's a sample article
that discusses some observational constraints:

http://arxiv.org/abs/astro-ph/0107248

-Ted

--
[E-mail me at , as opposed to .]

Thus spake
We think that the dark matter is pretty smoothly distributed over these
sort of scales, so within a factor of a few (which is all I cared
about) the above number should be about equal to the local dark matter
density. I don't think we can say anything more precise than that.


I think the rotation curves of globular clusters, as analysed by
Riccardo Scarpa, Gianni Marconi, Roberto Gilmozzi, Giovanni Carraro,
astro-ph/0611504 (accepted in A&A), astro-ph/0601581 throw something of
a spanner in the works with your calculation. If there is so smooth a
density of dark matter, there would also be relatively little in a
globular cluster. Yet globular cluster exhibit flat rotation curves,
similar to Low Surface Brightness Galaxies. Of course one may take this
as evidence for MOND, but MOND is not without inconsistency either.



Regards

--
Charles Francis
substitute charles for NotI to email

Oh No wrote:
Thus spake

We think that the dark matter is pretty smoothly distributed over these
sort of scales, so within a factor of a few (which is all I cared
about) the above number should be about equal to the local dark matter
density. I don't think we can say anything more precise than that.



I think the rotation curves of globular clusters, as analysed by
Riccardo Scarpa, Gianni Marconi, Roberto Gilmozzi, Giovanni Carraro,
astro-ph/0611504 (accepted in A&A), astro-ph/0601581 throw something of
a spanner in the works with your calculation. If there is so smooth a
density of dark matter, there would also be relatively little in a
globular cluster. Yet globular cluster exhibit flat rotation curves,
similar to Low Surface Brightness Galaxies. Of course one may take this
as evidence for MOND, but MOND is not without inconsistency either.



Regards

The reference indicates that globular cluster NGC 7099
contained in Milky Way system
exhibits flat rotation curve (v = constant with R)
at ~200 km/sec
similar to the Milky Way.

The globular cluster NGC 7099 has a radius of 30 pc or about 100 light years.
This compares to Milky Way radius of 50,000 light years.

Why would this ~common velocity be?

If it were a chemistry or fluid problem,
this possibly could be explained by an equipartition of energy
between rotational and translational modes
with particles (stars) in a fluid.

Richard