Now let's continue our inquiry into
scaling relations for galaxies.
I already introduced the fundamental plane
of elliptical galaxies.
It is a set of bivariate correlations
between many of their different
properties, always unified in a way that
any one of them can be expressed as a
logarithmic combination of two others.
And so usually, it's expressed as scaling
a relation between radius, surface
brightness, and velocity dispersion.
Because that's a very useful way of,
taking it but, it could be any other.
And what's shown here is the plot of what
it looks like.
Almost face-on, or you don't see much
correlation at all, or essentially
edge-on, where the only thickness is due
to measurement errors.
I mentioned that you can use different
quantities indeed, you can.
So for example, you can substitute
luminosity for Radius, and so this, you
can think of as the improved version of
tally fissure relation, but it's really
fundamental plane projection, slightly
differently.
And you can also use galaxy metallicity
expressed as strains of indices like
magnesium or iron, where, which implies a
couple interesting things.
That history of star formation and
ellipticals therefore their chemical
enrichment, is tightly coupled to their
structure of dynamical parameters.
And that in itself is a very important
fact.
It really tells us how dynamical and
stellar evolution history of galaxies must
be, Be connected in a very tight fashion
which is, I would say, still not perfectly
well understood.
You will recall from our hand waving
derivation of the scaling relations that
if you take a very old theorem which
connects three variables, say radius, mass
and characteristic velocity scale, or
radius density in characteristic velocity
scale.
Therefore it implies there is a plane in
the parameter space of these three
quantities which we can call virial plane.
And then we make some assumptions
about[UNKNOWN], that all galaxy kill
versions of each other and about mass to
light ratios that say.
You can substiture mass directly for
luminosity.
That should lead into the observable thing
like fundamental plane.
Now any differences in the slope of the
observed versus virial plane are telling
us something about our assumptions.
And in fact you can show that.
If you can express mass to light ratio as
some power of mass or luminosity, and
allow for scaling those at roughly 1 5th
power then you can account for the
difference in the tilt of the observed
plane to the virial theory.
So you can achieve this in various ways,
there could be a different mix of dark to
luminous matter as we discussed earlier.
There can be different amounts of dark to
luminous matter, or there can be different
stellar populations.
But, in any case, they have to be very
tightly correlated with the galaxy mass
itself.
And that is not an obvious thing to
arrange.
Now that we can measure masses of
ellipticals using either virial theorem
estimates or better yet, gravitational
lensing, which does not depend on any
assumptions of an isotopry and what not.
We can now form mass equivalent
fundamental plane using mass instead of
luminosity or mass density instead of
luminosity density or surface brightness.
And here it is, and it's, it looks very
close to the observed 1, the slope now is
more or less within the errors exactly
what you'd expect from Virial Theorem.
Which indeed suggest that some assumptions
about mass to light ratios, and homology
are probably what's wrong.
You will remember that both Tally-Fisher
and fundamental plane have been used as
the distance indicate inter relations.
And those are crucial in determining
peculiar velocities of galaxies.
So the question then is: Are those
relations universal?
Are they same everywhere, in all
environment?
Because if the reflect different
evolutionary histories.
Say formation, or galaxies, evolution and
galaxies and dense cluster may be
different, then in the field.
Then you might expect to see differences
in correlations.
And it turns out, yes, there are some
dependencies.
This one is from the study by the spider
group.
La Barbera et al that I've shown you
earlier.
And it shows dependence of the intercept
on the projected galaxy density.
Around the galaxy in question as well as
projected slope, and I can see there are
small but significant trends.
They can measure these only because they
had in excess of 10,000 galaxies, so they
can put lot of galaxies in each bin.
So the effects are there, we know them,
and we can measure them, but they are very
subtle.
Essentially, with these subtle effects say
that our assumptions were almost right.
Elliptical galaxies do form a very well
regulated family.
Where in, in, mass light ratio changes as
a function of, of luminosity.
But at any given mass there is so little
scatter that it's truly amazing.
It could be consistent with zero.
Just measurement errors.
So this is an outstanding puzzle that all
elliptical galaxies in all enviroments
everywhere, independent of the size, mass
or anything else.
Just two numbers determine at least a
dozen, of fundamental quantities, that
describe the galaxies having to do with
their masses, densities, kinetic
temperatures, luminosities, star formation
histories, and so on.
Just two numbers.
And we can come up with any number of
scenarios why this shouldn't be the case.
Why, even if you started with pure Virial
Theorem impact relation, you're going to
scramble up by different evolutionary
paths.
And yet that doesn't happen even though
processes of galaxy formation are fairly
sarcastic in terms of random merging and
so on.
Somehow, in the end, galaxies always end
up following this correlations.
Note also that there are quantities that
do not participate in these correlations.
Usually those are quantities that
describes, shape of the light
distribution.
So how can this possibly be?
Now we can turn to numerical simulations
of structured galaxy formation, and it
turns out that if you do this very
carefully you can make synthetic
ellipticals in computer.
They too follow fundamental plane, just as
observed.
There was no new physics put in, there is
nothing magical, same old gravity
dissipation and so on, and somehow this
correlation emerges in the end.
We can reproduce this correlation in, in
computer, but that doesn't mean we
understand it.
So the tilt is relatively easily
understood by changing comology and mass
light ratio assumptions.
The thickness is not.
Why the thickness is so small is truly an
out-, outstanding mystery.
Same thing for[INAUDIBLE] fissure
relation.
So you can look at this in a more general
way.
You can think of the galaxies as families
of objects form two dimesional sequences
in a three dimensional space or ten
dimensional space if you want, but at
least three and fundamental plane would be
one them.
This is my knowledge with stars in HR
diagram which is a parameter space of
stellar luminosity and stellar temperature
and their stars of different families.
...form linear sequences in that space,
whether it's main sequence,[UNKNOWN]
branch,[UNKNOWN] branch and so on.
So here we have, for galaxies,
two-dimensional sequences in
three-dimensional parameter space.
So this is just like H-R diagram for
galaxies.
And like we used H-R diagram...
(End of transcription.) to understand and
probe[UNKNOWN] structured evolution we can
do the same for galaxies in this galaxy
parameter space.
And further lets look at dark halos, can
we look at there scaling relation at first
it sounds ridiculous but in fact we could
This is important because we know already
that many galaxian properties seem to be
driven by the properties of their halos
because that's where most of the mass is.
Now in numberical simulations we can see
what dark halos look like.
We can plot their density profiles and.
Several have been suggested.
One is this one called Navarro, Frenk, and
White profile.
But Sersic profile works just as well.
And just as it describes distribution of
light in the galaxies, so it seems to
distribute, describe distribution of dark
matter, at least in model galaxies.
What about observations?
So here is just a set of dark matter
density profiles derived from simulations
and the lines going through them are the
fit of the Navarro-Frenk-White profile.
Well, that's the theory.
What about the observations?
Dark matter is kind of hard to observe.
But we can infer something about this
distribution from observable things in, in
galaxies like this is how we do rotation
curves.
And indeed, with some care and delicacy
Kormendy and Freeman have done this for a
whole lot of different galaxies,
estimating their central halo densities.
Their core radii halo distributional
characteristic radii halo mass
distribution, as well as their effective
velocity dispersion.
The kinetic energy per unit mass that they
have to have in order to balance their own
self-gravity.
And so after doing this, they found out
that there are scaling relations for dark
halos and here they are.
The quantities like core radius, central
density, kinetic energy, they're
proportional to some shallow power of
galaxy luminosity and therefore galaxy
mass.
So it was quite remarkable that we can
actually measure scaling relations for
galaxy halos which might be actually the
root of existence of those that we see for
visible light.
And that concludes our study of galaxian
properties as such.
Next, we will start talking about galaxy
evolution and galaxy formation.