We now turn our attention to the other end
of the Hubble sequence, the elliptical
galaxies.
In Hubble's definition, ellipticals were
old, boring systems containing just old
stars with no star formation, no dust, no
gas.
And the first theories of their formation
whether they form through a single
monolithic collapse of giant protogalaxy
where all the stars are made.
Turns out all of these are incorrect.
The modern view is that ellipticals are
actually fairly complex systems.
They do contain lots of gas except most of
it is X-ray gas, sometimes they have star
formation.
Sometimes they have dust mites, and they
probably form through hierarchical merging
of smaller pieces, although, dissimilitude
collapse was probably also involved.
They're also not simple systems, they have
subsystems just like spiral galaxies do.
Some ellipticals seem to show weak disks,
some have special decoupled cores in the
middle.
Most of them have super massive black
holes in the centers.
One important distinction between
ellipticals and spirals is that, whereas,
spirals have contained most of their
kinetic energy in the ordered rotational
motion, in the elliptical galaxies most of
the kinetic energy is in the form of
random motions, so we call them pressure
supported stars moving like molecules in
gas.
And here is a blatant example of dust in a
elliptical galaxies.
This is an elliptical galaxy NGC 1316
which is in the center of the nearby
Fornax Cluster.
The reason why it has all this dust is
that it gobbled up a spiral galaxy which
had plenty of dust in its disks, and so
that's still being digested Somehow.
We do see the signature of mergers in
ellipticals and a particularly interesting
one is so called, shells.
If you turn the contrast up in some of the
elliptical galaxies, you'll see these
shell like structures of the radii and now
we think we know where they come from.
If you have a largely 2-dimensional
stellar components, such as this galaxy,
and then you merge it into an elliptical
galaxy, the stars will still stay on sort
of 2-dimensional surface until sometime
later.
And so what we see our diluted stretched
curved pieces of former galactic disks
that be now wrapped around the elliptical
galaxy as they are being merged in.
This is being seen in numerical
simulations and starts on the
observations.
The way we quantify structure for
elliptical galaxies, is through surface
photometry.
We measure brightness as a function of the
radius and the azimuth.
And where this is light, we can then try
to convert that into mass through
kinematic measurements.
The way we quantify structure of
elliptical galaxies is first by measuring
their radial brightness profiles, so
called surface brightness profiles.
And there are a number of formulae
proposed to account for the shape of these
brightness profiles.
The most popular of them is so called the
Vaucouleurs profile, it was invented by
Gerard de Vaucouleurs and sub purely
empirical formula.
And it says that the log of the surface
brightness which is luminosity per unit
area, behaves as the radius to the 1
quarter power, it's proportional to radius
to minus 1 quarter power, and it was
something called to the 1 quarteral.
There is a parameter because it's an
exponential involved, and that is called
the effective radius.
And if you tweak the constant multiplying
that parallel that radius can be made so
that it contains exactly one half of all
projected light.
So it's sometimes called an effective
radius, or a half-light radius.
And typically, for elliptical galaxies,
it's value is the order of a few
kiloparsec, not too different from say,
typical scaling lengths of spiraling
galaxy disks.
So here are some plots of surface
brightness for a thousand elliptical
galaxies.
What's show here is a logarithm of the
surface brightness and y axis measured in
magnitudes per square, second versus
radius to the 1 quarter power.
And the Vaucouleurs profile looks like a
straight line in those coordinates.
Indeed for some galaxies it seems to fit
remarkable well in at least some part of
the radial range but in the others it does
not, and so these deviation are also of
some interest.
Other profiles have been suggested, and
the one that's currently most popular is
so called, Sersic profile.
Which is a generalization of the
Vaucouleurs profile, that log of a surface
brightness goes as the radius to the minus
1 over n.
Where n is some number, and in case of the
Vaucouleurs profile, n is equal 4.
So it's proportional to the radius to the
minus 1 quarter.
In case of this galaxy n is 1.
So then you have just traditional old
declining exponential.
This formula turns out to actually to work
remarkably well for elliptical galaxies as
well as dark holes which is a very
interesting thing.
Its physical origin is not really well
understood, it is also purely an empirical
formula.
Hubble himself proposed a different
profile, this was essentially a parallel
with surface brightness going as 1 over
the radius squared, except in the middle
where it's softened.
So there is a parameter called, core
radius.
And within that core radius, profile is
more or less flat and then it turns around
and goes into the parallel.
Now one profile, problem with Hubble's
profile are originally envisioned, is that
it diverges.
If you integrate the surface brightness
profile in radius, you'll reach infinite
total luminosity at infinite radius and
that clearly can't work.
So, Hubble profile has to truncate at some
point.
So, it's actually quite remarkable that
the ellipticals can be fit by the same
family of profiles that have, say just two
parameters, in case of the Vaucouleurs
it's the effective radius that scales the
radial coordinate and effective surface
brightness that scales the vertical
coordinate.
In case of Sersic profile, there is that
shape parameter, little n for which
Vaucouleurs is fixed.
And if it were always fixed then
ellipticals would be a homologous family
of objects, one could be scaled into
another.
Turns out, that's pretty close but that's
not exactly true.
And the deviations of that, from that, are
actually quite important.
One deviation that we already talked about
before is the diffuse envelopes of cD
galaxies and clusters, but you may recall
that those are really stars that belong to
the cluster itself, just cospatial with
the galaxy itself.
Nonetheless, if you obtain a surface
brightness profile of the many, many
ellipticals and then if you fit Sersic law
to all of them and plot the value of the
Sersic parameter.
And which in this plot on the left is
confusingly labeled as M by the authors of
the paper, you find out that the shape
parameter, Sersic parameter, depends on
the size of the galaxy, and by the same
token on the luminosity of the galaxy.
And goes in the sense that galaxies with
larger radii or larger luminosities have
shallower profiles.
A more direct way to see this is to simply
bin together profiles of many ellipticals
average them up, and plot prolific
response to certain bin of luminosity and
that's shown in the lower right done by
Jim Schombert.
And again you can see that the more
luminous ellipticals seem to have
shallower profiles.
On the other hand, near the centers of
galaxies, very interesting things
happening.
In Hubble's days, seeing an angular
resolution simply were not good enough to
actually tell what's happening in the
inner arc second or so, and now a days
with Hubble space telescope we can probe
the inner portions of the elliptical
galaxies, and interesting things are
happening there.
In some cases, there are corse flat
density distributions, sort of like Hubble
envisioned.
In other cases, their density cusps,
density goes as a parallel all the way in,
as far as we can tell.
And those may be related to the presence
of super massive black holes.
And carrying on with what happens at
larger radii, you see that more luminous
ellipticals tend to be those that have
flat cores and small ellipticals tends to
be those with cusps.
So, here is just a collection of surface
brightness profiles from Hubble, and they
have been divided empirically into those
that show a core, which are shown as solid
lines here and those that look like
parallel cusps, not impure parallels.
Maybe slightly curved, but nevertheless
the cusps and those are shown as dash
lines.
So the shape of the surface brightness
profile changes at smaller radii.
And so, people who study this have come up
with a broken power law or nuker profile,
that has one parallels synthetically
smaller radii.
And a different parallel, synthetically at
large radii, and there is some transition
radius between them where one bends into
the other.
And so here are the examples what those
profiles look like.
On the left, you see what happens as we
change the inner slope.
Whereas, the outer ones remain more or
less fixed on the right it's the opposite.
We keep the inner slope, but change the
outer slope.
Galaxies seem to fit all over this
particular family of profiles.
So next, we will talk about two
dimensional and three dimensional shapes
of ellipticals.