Let us now turn to the internal motions inside elliptical galaxies.
This turns out to be really the key to their nature and understanding.
So the stars in elliptical galaxies have largely random motions.
And so therefore, their kinetic energy can be characterized by a velocity dispersion.
You can think of the distribution as being pretty close to Gaussian, because they're
supported by random motions rather than rotation, they're called pressure
supported systems. And the way we usually measure this is
through Doppler broadening of their absorption lines as I'm sure you know,
spectra of galaxies composed of stars, have many different absorption lines those
are different elements. And, each of these lines is pretty sharp
when it originates. But, because there are many, many
different stars moving at random velocities, the total observed Line will
be a weighted sum of those and it's shape will reflect the overall Doppler
broadening by the velocity distribution. So by deconvolving an unmeasured line, say
from templates. Spectral stars that are like those that
make elliptical convolved with say Gaussian distribution of Doppler shifts.
We can infer what is the underlying velocity dispersion of the elliptical
galaxy. Note that whereas, we measure rotation by
simple shift of the line, the red or blue. Here, the line is not shifted it's just
broadened. And here are some velocity profiles of
elliptical galaxies. The velocity dispersion up top, rotational
speed on the bottom. In some cases, there is actually a
rotational component, those tend to be this elliptical, because in other cases
there is no net overall rotation, but there is a lot of velocity dispersion.
Generally speaking, velocity dispersions tend to be higher near the center of the
galaxy but, by and large they remain nearly flat by analogy with flat rotation
curves of spiral galaxies. A nice new way to measure this is so
called integral field spectroscopy. Here a spectrograph is composed of many
different entrance aperture, usually it's done with optical fibers and then spectrum
taken of each one of those. So you're getting a spectroscopically
resolved picture in the sky. And from that you can reconstruct what
Doppler shifts and broadening are anywhere across the face of the galaxy.
It can also add up all the light and then you have surface brightness distribution.
So here are some examples from group, an instrument called Sauron of several
elliptical galaxies as indicated here. The top row shows their surface brightness
distribution, just adding up the light. The middle row shows the rotational
velocity component and it's coded into two fashion, red ones going away from us, blue
ones approaching us. And you can see that there is definitely
some rotation present in some cases. Actually, in all cases in this particular
set, which is not chosen randomly. And the bottom shows the distribution of
velocity dispersion. There, you can see there is generally a
tendency to be a little higher in the middle, but otherwise, it doesn't not seem
to show have much of a shape distribution. So when velocity dispersions and
rotational speeds were measured for elliptical, to everybody's surprise back
then, it was found out that shapes are not due to the rotational velocity.
And you can compute from simple dynamical models that for a given ellipsoid that's
supported largely by rotation and has a commensurate amount of random motions,
viewed from different angles, what should be the ratio between maximum rotational
speed and velocity dispersion. And you can divide the two and so for
purely rotationally supported oblate ellipsoids, that's a line in the diagram
that shows the ratio of velocity to the rotational speed to velocity dispersion as
a function of [unknown]. As it turns out, the elliptical do go up
to that line, but most of them are below. Meaning that they have too little
rotational speed for their ellipticity and their radial velocity component.
And so, that also means that they cannot be supported entirely by rotation, that
could be that sort of the upper envelope. There can be none of the rotation that
will be the zero point on this diagram. But they're somewhere in between and so a
great majority of elliptical galaxies are supported by velocity anisotropy.
And it can take that the ratio of maximum rotational speed to velocity dispersion.
And align for perfect oblate rotationally supported ellipsoid and normalized by that
line. So that rotationally supported oblate
ellipsoid will have the normalized value of exactly one and lower than one, means
more anisotropy. So now we can plot this normalized
quantity. The relative importance of velocity
anisotropy as a function of say galaxy luminosity.
And it was found that more luminous galaxies are more anisotropic.
This can be understood as a consequence of random merging.
You may remember that disks have to involve dissipative formation.
You have to dissipate energy, not the angular momentum get a disk, then make
stars. Whereas, random merging does not preserve
rotation. It scrambles up any rotation and just
creates pressure supported systems. So if you indeed you build up ellipticals
through random merging then you would expect the more luminous ones to be more
anisotropic and that's exactly what we see.
As we measure spectra we can tell about chemical composition of stars, not just
their velocities. And so we can measure strengths of
absorption lines of elements such as iron or magnesium, which are fairly common and
use that as an indicator of the chemical evolution history of the galaxy.
So the, it was found that elliptical galaxies are more metal rich near the
middle than on the outside skirts. There is, there was a more recycling of
interstellar material through subsequent actions of star formations in the central
portions. Now you cannot do this through merging.
In fact, merging will scramble any such arrangement.
So there has to be a dissipative self-enrichment component to the formation
of ellipticals that then reflects itself through this dependence of stellar
population as in the function of red shift.
Now spectra are hard to obtin because they require long observation times.
A much easier thing to measure are colors, which are ratios of [unknown] to different
filter. Now it turns out that more metal rich
stellar populations have more absorption lines in the blue part of the spectrum,
removing some blue light. So the more metal rich populations will
have a redder color. And you can measure colors fairly easily,
you use them as a proxy for the metallicity of galaxies.
And it turns out that more luminous ones are redder, they're more metal rich.
And you may recall that there's a picture whereby supernova ejecta, which is where
metals come from into the new generation of stars, can escape from low mass
galaxies. But are still bound to the higher mass
host galaxies where it can be recycled into new stars.
So it makes sense that subsequent episodes of star formation in deeper potential
levels in more luminous galaxies, more massive galaxies would result after a
little while in a more metal rich stellar population.
So we see that both within individual galaxies, more metal rich stuff near the
middle and between different galaxies, the more luminous or more massive ones
retaining more of their metals. Likewise, you can use velocity dispersion
instead of luminosity and find out that those which have higher velocity
dispersions, which are really kinetic energy per unit mass, therefore reflecting
in a very equilibrium the depth of potential oil.
Also have higher metallicities deeper potential wells, more recycling of the
metals. We already talked about gas in elliptical
galaxies so whereas spiral galaxies have plenty of interstellar medium, cold one,
hydrogen mostly. In elliptical galaxies there is hardly any
cold gas. Only if its been recently secreted, but
there is plenty of gas all cold and that gas comes largely as a product of stellar
evolution. But somehow it's secreted from the
outside, and it's heated to millions of degrees, which is a very equilibrium
temperature for the corresponding potential wells in elliptical galaxies.
Now that we can measure kinematics of ellipticals, reflecting their potential
wells, we can fit dynamical models and find what their masses are so here is from
a large survey of gal-, of particular galaxies by a group called Spider
[unknown] and Carvalho [unknown] collaborators.
Plot of stellar masses and directly from integration of visible light versus the
nominal masses, which are now inferred. From kinematics velocities of stars
reflecting total mass not just the visible component.
And they're proportional, right? But there is trend the more massive
galaxies tend to have a larger component of dark matter, or I should say more
masses in form of the dark component. So the moss galaxy is on this band where
one envelope is that there is no dark matter, there is just stars.
The other envelope is that the anomical mass is about 6 times the amount of
visible mass in stars. Interestingly enough, that corresponds to
the riot of omega matter to the omega of variance in [unknown] at large.
If you can think of stellar masses for luminosity then that means that mass to
light ratios will be higher for the more massive galaxies.
And that's indeed what's seen through a number of other pieces of evidence.
So fitting dynamical models in detail to galaxies we can figure out exactly what
their masses are, and you can plot masses to light ratio versus luminosity or
reduced mass, and here they are. The more massive or more luminous galaxies
have higher mass to light ratios, which [unknown] need not specify the amount of
dark matter. It could be the invisible variance, but
there are good reasons to believe that in fact most of this is due to the relative
abundance or relative amounts of dark luminous matter within the regions where
we measure this. Now, notice that qualifier.
We, remember that we already talked how in galaxies baryionic component is more
condensate than dark matter. Dark matter halos are fluffier and
dominate more at large radii. This is certainly true in elliptical
galaxies as well. So if you're measuring velocity
dispersions and what not in the luminous parts of the galaxies, you're liable to be
finding mostly luminous bariartic mass. In the ratio of distribution of dark and
luminous matter changes is a function of mass.
So that halo distributions are more extended but the light distributions tend
to be more condensed for smaller galaxies as is indeed the case if you remember how
surface brightness profiles the pen in luminosity.
Well, then you would expect to see just this.
So it's not 100% clear at this point how much of this effect is due to a different
distribution of luminous and dark matter. Or is this different amounts of luminous
and dark matter? It's probably a combination of both a
gravitational lensing provides a completely different way of measuring
masses, independent of all the schematics and so this was done, for sample galaxies
using galaxies themselves as, as lenses. And what's plotted here, confusingly in
the same diagram, is the mass to light ratios for the total mass that's sort of
the tilted component and for the luminous mass alone, which is a kind of flat
component. And we find out that for the luminous mass
alone, mass to light ratio doesn't change through the function of mass.
Meaning, ellipticals of all different masses have the same stellar populations.
And, consistent from what we expect from stellar evolution laws.
But there is always total mass, so higher total mass the light ration and more so t
higher mass end which is exactly what you've seen in for previous diagrams but
this time measured in a completely different way.
Thus, giving us some confidence that this is in fact correct.
Yet another independent way of assessing this is through.
Their X-ray profiles just like we use X-ray measurements to constrain masses
inside clusters of galaxies you can do the same thing inside elliptical galaxies, and
there again you find out using X-ray gases dust particles that the ratio of total, or
non luminous mass to the luminous ones, increases as a function of radius.
And next time we'll talk about supermassive black holes in galactic
centers and something that's completely unrelated dwarf galaxies.