Black hole mass-sigma correlation

A BBC Horizon program described the correlation found between the galaxy
hub black hole mass and the "sigma", the speed of the stars in the outer
regions of the galaxy.

One thing that confuses me, would not the speed of the stars in a galaxy
also follow a distance from center relation as that of planets around a
star?

Hans Aberg * Anti-spam: remove "remove." from email address.
* Email: Hans Aberg
* Home Page: http://www.math.su.se/~haberg/
* AMS member listing: http://www.ams.org/cml/

In message , Hans Aberg
writes
A BBC Horizon program described the correlation found between the galaxy
hub black hole mass and the "sigma", the speed of the stars in the outer
regions of the galaxy.

One thing that confuses me, would not the speed of the stars in a galaxy
also follow a distance from center relation as that of planets around a
star?

In "Wrinkles in Time" George Smoot writes that Vera Rubin and Kent Ford
published a paper in 1978 showing that galaxies _don't_ obey Kepler's
third law - beyond a certain distance, the rotational velocity of stars
is almost constant. That's when dark matter became fashionable, though
apparently it "should" have happened much earlier.
--
"Roads in space for rockets to travel....four-dimensional roads, curving with
relativity"
Mail to jsilverlight AT merseia.fsnet.co.uk is welcome.
Or visit Jonathan's Space Site http://www.merseia.fsnet.co.uk

In message , Hans Aberg
writes
A BBC Horizon program described the correlation found between the galaxy
hub black hole mass and the "sigma", the speed of the stars in the outer
regions of the galaxy.

One thing that confuses me, would not the speed of the stars in a galaxy
also follow a distance from center relation as that of planets around a
star?

In "Wrinkles in Time" George Smoot writes that Vera Rubin and Kent Ford
published a paper in 1978 showing that galaxies _don't_ obey Kepler's
third law - beyond a certain distance, the rotational velocity of stars
is almost constant. That's when dark matter became fashionable, though
apparently it "should" have happened much earlier.
--
"Roads in space for rockets to travel....four-dimensional roads, curving with
relativity"
Mail to jsilverlight AT merseia.fsnet.co.uk is welcome.
Or visit Jonathan's Space Site http://www.merseia.fsnet.co.uk

(Hans Aberg) wrote in message ...
A BBC Horizon program described the correlation found between the galaxy
hub black hole mass and the "sigma", the speed of the stars in the outer
regions of the galaxy.

Yes, the relation is very roughly

Msmbh varies as sigma^4 ,

where Msmbh is the supermassive bh mass...thus if galaxy A has
a central bh whose Msmbh is 16 times that of galaxy B, galaxy A
will show a sigma (velocity dispersion, actually) of about twice that of
galaxy B.

One thing that confuses me, would not the speed of the stars in a galaxy
also follow a distance from center relation as that of planets around a
star?

No, because the fairly pure Keplerian curve we see with, say our solar
system, is overwhelmingly generated by the huge concentrated mass
of the sun, while the masses of the planets only contribute little to the
overall mass distribution of the solar system as a whole [no offense to
jupiter ;-) ]. However, in a typical galaxy, the mass distribution is not
concentrated in some central object. Instead, the stars and gas/dust
clouds ever farther out contribute significantly to the overall local g-field.
The result would then be an altered and complex, but still recognizably
Kepler curve, were it not for the still mysterious dark matter g-field poten-
tial which 'lays on top of' the normal stellar/gas/dust g-field, as it were,
and thus results in a quite flattened velocity curve for all objects as far
out as we can see.

But whatever the nature of the dark matter source, a solar system like
ours does not make a closed elliptical curve in its ~2 * 10^8 yr. orbit.
Instead, it follows an open rather springlike orbit, whose perihelion
changes by a large angle each orbit (maybe 100 degrees or so?)

Gene

(Hans Aberg) wrote in message ...
A BBC Horizon program described the correlation found between the galaxy
hub black hole mass and the "sigma", the speed of the stars in the outer
regions of the galaxy.

Yes, the relation is very roughly

Msmbh varies as sigma^4 ,

where Msmbh is the supermassive bh mass...thus if galaxy A has
a central bh whose Msmbh is 16 times that of galaxy B, galaxy A
will show a sigma (velocity dispersion, actually) of about twice that of
galaxy B.

One thing that confuses me, would not the speed of the stars in a galaxy
also follow a distance from center relation as that of planets around a
star?

No, because the fairly pure Keplerian curve we see with, say our solar
system, is overwhelmingly generated by the huge concentrated mass
of the sun, while the masses of the planets only contribute little to the
overall mass distribution of the solar system as a whole [no offense to
jupiter ;-) ]. However, in a typical galaxy, the mass distribution is not
concentrated in some central object. Instead, the stars and gas/dust
clouds ever farther out contribute significantly to the overall local g-field.
The result would then be an altered and complex, but still recognizably
Kepler curve, were it not for the still mysterious dark matter g-field poten-
tial which 'lays on top of' the normal stellar/gas/dust g-field, as it were,
and thus results in a quite flattened velocity curve for all objects as far
out as we can see.

But whatever the nature of the dark matter source, a solar system like
ours does not make a closed elliptical curve in its ~2 * 10^8 yr. orbit.
Instead, it follows an open rather springlike orbit, whose perihelion
changes by a large angle each orbit (maybe 100 degrees or so?)

Gene

Thanks for the replies. I suspected that the galaxy mass might have
something to do with the its stars not obeying the Kepler law.

But if the outer galaxy stars do not do that, what are their movements,
generally faster or slower than the Kepler law? Or perhaps there are some
stars in the outer regions that do not move in circular orbit around the
galaxy center at all?

Hans Aberg * Anti-spam: remove "remove." from email address.
* Email: Hans Aberg
* Home Page: http://www.math.su.se/~haberg/
* AMS member listing: http://www.ams.org/cml/

Thanks for the replies. I suspected that the galaxy mass might have
something to do with the its stars not obeying the Kepler law.

But if the outer galaxy stars do not do that, what are their movements,
generally faster or slower than the Kepler law? Or perhaps there are some
stars in the outer regions that do not move in circular orbit around the
galaxy center at all?

Hans Aberg * Anti-spam: remove "remove." from email address.
* Email: Hans Aberg
* Home Page: http://www.math.su.se/~haberg/
* AMS member listing: http://www.ams.org/cml/

In article ,
(Gene Partlow) wrote:

Thanks for the replies. I suspected that the galaxy mass might have
something to do with the its stars not obeying the Kepler law.

Well, to be clear, it's the -distributrion- of the galaxy mass that is
important here.

Right.

All orbiting stars must follow the inverse square force law,
regardless of their distance from the galaxy center...

Only approximately, as there is a GR correction showing that they will in
fact slowly drop into the center (due to emission of "gravity waves").
This is also why this development is so exiting:

As GR, unlike Newtonian physics, predicts that the galaxy mass should drop
into the center, one would think that the belief that there are black
holes at the centers of the galaxies should have come along very early,
but in fact it took a long time. Now there are even formulas for telling
the size of that black hole mass.

Another thought comes to my mind: My very own idea is that what goes into
a black hole might also be able to leave it via tunneling. Roughly, this
would happen because the GR classical sharp event horizon in a combined
GRQM would be merely a QM "fuzzy" energy barrier, so that particles inside
the black hole, when nearing this barrier, would in reality have a state
both inside and outside the corresponding GR classical sharp event
horizon. Thus, they escape the event horizon by not engaging gravity at
all. In my mind, I think of this process as that all particles entering
the black hole are crushed into smithereens, but certain physical
invariants are preserved. I wrote a paper that shows that the particle
intrinsic spin will be preserved in that way in a certain Lorentz manifold
intrinsic model. (The intrinsic spin ends up in the differential bundle,
and it is known that the Levi-Civita connection, which communicates
gravity in GR, acts trivially on that.) What comes out of the black hole
would then be the stable particles composed of the physical invariants
preserved in this process.

What now strikes me is that an old galaxy should have continued to feed on
the galaxy mass, in view of the GR prediction. If there is no mass leaving
the black hole at all, then this black hole should be more massive than if
mass can leave it by tunneling.

Might one perhaps devise observational experiments determining that?

Hans Aberg * Anti-spam: remove "remove." from email address.
* Email: Hans Aberg
* Home Page: http://www.math.su.se/~haberg/
* AMS member listing: http://www.ams.org/cml/

In article ,
(Gene Partlow) wrote:

Thanks for the replies. I suspected that the galaxy mass might have
something to do with the its stars not obeying the Kepler law.

Well, to be clear, it's the -distributrion- of the galaxy mass that is
important here.

Right.

All orbiting stars must follow the inverse square force law,
regardless of their distance from the galaxy center...

Only approximately, as there is a GR correction showing that they will in
fact slowly drop into the center (due to emission of "gravity waves").
This is also why this development is so exiting:

As GR, unlike Newtonian physics, predicts that the galaxy mass should drop
into the center, one would think that the belief that there are black
holes at the centers of the galaxies should have come along very early,
but in fact it took a long time. Now there are even formulas for telling
the size of that black hole mass.

Another thought comes to my mind: My very own idea is that what goes into
a black hole might also be able to leave it via tunneling. Roughly, this
would happen because the GR classical sharp event horizon in a combined
GRQM would be merely a QM "fuzzy" energy barrier, so that particles inside
the black hole, when nearing this barrier, would in reality have a state
both inside and outside the corresponding GR classical sharp event
horizon. Thus, they escape the event horizon by not engaging gravity at
all. In my mind, I think of this process as that all particles entering
the black hole are crushed into smithereens, but certain physical
invariants are preserved. I wrote a paper that shows that the particle
intrinsic spin will be preserved in that way in a certain Lorentz manifold
intrinsic model. (The intrinsic spin ends up in the differential bundle,
and it is known that the Levi-Civita connection, which communicates
gravity in GR, acts trivially on that.) What comes out of the black hole
would then be the stable particles composed of the physical invariants
preserved in this process.

What now strikes me is that an old galaxy should have continued to feed on
the galaxy mass, in view of the GR prediction. If there is no mass leaving
the black hole at all, then this black hole should be more massive than if
mass can leave it by tunneling.

Might one perhaps devise observational experiments determining that?

Hans Aberg * Anti-spam: remove "remove." from email address.
* Email: Hans Aberg
* Home Page: http://www.math.su.se/~haberg/
* AMS member listing: http://www.ams.org/cml/

Hans Aberg wrote:

Only approximately, as there is a GR correction showing that they will in
fact slowly drop into the center (due to emission of "gravity waves").
This is also why this development is so exiting:

As GR, unlike Newtonian physics, predicts that the galaxy mass should drop
into the center, one would think that the belief that there are black
holes at the centers of the galaxies should have come along very early,
but in fact it took a long time. Now there are even formulas for telling
the size of that black hole mass.



This effect should be completely negligible compared to other
effects taking place in a galaxy, such as the transport of angular
momentum by the spiral arms, which may let some of the material in the
galactic disc drift inwards while angular momentum is transported
outwards, and the scattering of stars against giant molecular clouds.
There may be even more dramatic effects taking place during the
formation of a galaxy, and as far as we can tell today the black holes
at the centers of the galaxies form early in the life of the galaxies.

Angular momentum loss through the emission of gravitational waves can be
important in the evolution of close binaries though, and provides a perfect
explanation for the timings of the double pulsar PSR 1916+13.

Ulf Torkelsson

[Mod. note: reformatted to 80 characters per line -- mjh]