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Now let's continue our inquiry into
scaling relations for galaxies.

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I already introduced the fundamental plane
of elliptical galaxies.

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It is a set of bivariate correlations
between many of their different

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properties, always unified in a way that
any one of them can be expressed as a

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logarithmic combination of two others.
And so usually, it's expressed as scaling

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a relation between radius, surface
brightness, and velocity dispersion.

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Because that's a very useful way of,
taking it but, it could be any other.

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And what's shown here is the plot of what
it looks like.

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Almost face-on, or you don't see much
correlation at all, or essentially

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edge-on, where the only thickness is due
to measurement errors.

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I mentioned that you can use different
quantities indeed, you can.

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So for example, you can substitute
luminosity for Radius, and so this, you

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can think of as the improved version of
tally fissure relation, but it's really

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fundamental plane projection, slightly
differently.

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And you can also use galaxy metallicity
expressed as strains of indices like

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magnesium or iron, where, which implies a
couple interesting things.

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That history of star formation and
ellipticals therefore their chemical

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enrichment, is tightly coupled to their
structure of dynamical parameters.

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And that in itself is a very important
fact.

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It really tells us how dynamical and
stellar evolution history of galaxies must

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be, Be connected in a very tight fashion
which is, I would say, still not perfectly

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well understood.
You will recall from our hand waving

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derivation of the scaling relations that
if you take a very old theorem which

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connects three variables, say radius, mass
and characteristic velocity scale, or

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radius density in characteristic velocity
scale.

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Therefore it implies there is a plane in
the parameter space of these three

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quantities which we can call virial plane.
And then we make some assumptions

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about[UNKNOWN], that all galaxy kill
versions of each other and about mass to

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light ratios that say.
You can substiture mass directly for

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luminosity.
That should lead into the observable thing

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like fundamental plane.
Now any differences in the slope of the

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observed versus virial plane are telling
us something about our assumptions.

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And in fact you can show that.
If you can express mass to light ratio as

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some power of mass or luminosity, and
allow for scaling those at roughly 1 5th

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power then you can account for the
difference in the tilt of the observed

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plane to the virial theory.
So you can achieve this in various ways,

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there could be a different mix of dark to
luminous matter as we discussed earlier.

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There can be different amounts of dark to
luminous matter, or there can be different

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stellar populations.
But, in any case, they have to be very

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tightly correlated with the galaxy mass
itself.

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And that is not an obvious thing to
arrange.

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Now that we can measure masses of
ellipticals using either virial theorem

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estimates or better yet, gravitational
lensing, which does not depend on any

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assumptions of an isotopry and what not.
We can now form mass equivalent

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fundamental plane using mass instead of
luminosity or mass density instead of

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luminosity density or surface brightness.
And here it is, and it's, it looks very

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close to the observed 1, the slope now is
more or less within the errors exactly

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what you'd expect from Virial Theorem.
Which indeed suggest that some assumptions

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about mass to light ratios, and homology
are probably what's wrong.

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You will remember that both Tally-Fisher
and fundamental plane have been used as

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the distance indicate inter relations.
And those are crucial in determining

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peculiar velocities of galaxies.
So the question then is: Are those

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relations universal?
Are they same everywhere, in all

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environment?
Because if the reflect different

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evolutionary histories.
Say formation, or galaxies, evolution and

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galaxies and dense cluster may be
different, then in the field.

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Then you might expect to see differences
in correlations.

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And it turns out, yes, there are some
dependencies.

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This one is from the study by the spider
group.

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La Barbera et al that I've shown you
earlier.

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And it shows dependence of the intercept
on the projected galaxy density.

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Around the galaxy in question as well as
projected slope, and I can see there are

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small but significant trends.
They can measure these only because they

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had in excess of 10,000 galaxies, so they
can put lot of galaxies in each bin.

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So the effects are there, we know them,
and we can measure them, but they are very

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subtle.
Essentially, with these subtle effects say

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that our assumptions were almost right.
Elliptical galaxies do form a very well

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regulated family.
Where in, in, mass light ratio changes as

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a function of, of luminosity.
But at any given mass there is so little

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scatter that it's truly amazing.
It could be consistent with zero.

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Just measurement errors.
So this is an outstanding puzzle that all

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elliptical galaxies in all enviroments
everywhere, independent of the size, mass

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or anything else.
Just two numbers determine at least a

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dozen, of fundamental quantities, that
describe the galaxies having to do with

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their masses, densities, kinetic
temperatures, luminosities, star formation

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histories, and so on.
Just two numbers.

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And we can come up with any number of
scenarios why this shouldn't be the case.

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Why, even if you started with pure Virial
Theorem impact relation, you're going to

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scramble up by different evolutionary
paths.

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And yet that doesn't happen even though
processes of galaxy formation are fairly

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sarcastic in terms of random merging and
so on.

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Somehow, in the end, galaxies always end
up following this correlations.

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Note also that there are quantities that
do not participate in these correlations.

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Usually those are quantities that
describes, shape of the light

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distribution.
So how can this possibly be?

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Now we can turn to numerical simulations
of structured galaxy formation, and it

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turns out that if you do this very
carefully you can make synthetic

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ellipticals in computer.
They too follow fundamental plane, just as

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observed.
There was no new physics put in, there is

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nothing magical, same old gravity
dissipation and so on, and somehow this

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correlation emerges in the end.
We can reproduce this correlation in, in

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computer, but that doesn't mean we
understand it.

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So the tilt is relatively easily
understood by changing comology and mass

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light ratio assumptions.
The thickness is not.

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Why the thickness is so small is truly an
out-, outstanding mystery.

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Same thing for[INAUDIBLE] fissure
relation.

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So you can look at this in a more general
way.

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You can think of the galaxies as families
of objects form two dimesional sequences

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in a three dimensional space or ten
dimensional space if you want, but at

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least three and fundamental plane would be
one them.

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This is my knowledge with stars in HR
diagram which is a parameter space of

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stellar luminosity and stellar temperature
and their stars of different families.

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...form linear sequences in that space,
whether it's main sequence,[UNKNOWN]

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branch,[UNKNOWN] branch and so on.
So here we have, for galaxies,

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two-dimensional sequences in
three-dimensional parameter space.

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So this is just like H-R diagram for
galaxies.

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And like we used H-R diagram...
(End of transcription.) to understand and

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probe[UNKNOWN] structured evolution we can
do the same for galaxies in this galaxy

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parameter space.
And further lets look at dark halos, can

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we look at there scaling relation at first
it sounds ridiculous but in fact we could

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This is important because we know already
that many galaxian properties seem to be

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driven by the properties of their halos
because that's where most of the mass is.

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Now in numberical simulations we can see
what dark halos look like.

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We can plot their density profiles and.
Several have been suggested.

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One is this one called Navarro, Frenk, and
White profile.

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But Sersic profile works just as well.
And just as it describes distribution of

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light in the galaxies, so it seems to
distribute, describe distribution of dark

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matter, at least in model galaxies.
What about observations?

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So here is just a set of dark matter
density profiles derived from simulations

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and the lines going through them are the
fit of the Navarro-Frenk-White profile.

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Well, that's the theory.
What about the observations?

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Dark matter is kind of hard to observe.
But we can infer something about this

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distribution from observable things in, in
galaxies like this is how we do rotation

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curves.
And indeed, with some care and delicacy

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Kormendy and Freeman have done this for a
whole lot of different galaxies,

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estimating their central halo densities.
Their core radii halo distributional

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characteristic radii halo mass
distribution, as well as their effective

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velocity dispersion.
The kinetic energy per unit mass that they

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have to have in order to balance their own
self-gravity.

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And so after doing this, they found out
that there are scaling relations for dark

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halos and here they are.
The quantities like core radius, central

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density, kinetic energy, they're
proportional to some shallow power of

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galaxy luminosity and therefore galaxy
mass.

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00:10:52,079 --> 00:10:57,647
So it was quite remarkable that we can
actually measure scaling relations for

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galaxy halos which might be actually the
root of existence of those that we see for

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visible light.
And that concludes our study of galaxian

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properties as such.
Next, we will start talking about galaxy

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evolution and galaxy formation.