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

(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/

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

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/