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.