You will recall that, value of Hubble's constant, was fairly unsettled all the
way through 1980s. The reason for this, is that, these
measurements are difficult. There are so many different relations,
then one has to be calibrated against the other, and there are many opportunities
for errors. And systematic errors in particular.
And that resulted in the values of Hubble constants scattering by a factor of 2,
which means that distances will be also uncertain by a factor 2 and things like
luminosity by a factor of 4 and that, clearly, was not a satisfactory
situation. So when the Hubble space telescope was
launched, measuring Hubble constant was seen as one of it's key goals and it was
a subject of a so called distance scale or Hubble Constant key project.
This took ten years of very diligent measurements using Hubble space
telescope. And even today Hubble space telescope
continues to be used for this purpose, improving the results.
The idea here was to observe Cepheids in a number of nearby spiral galaxies, and
the reason why Hubble was needed is that these stars are faint, and they're in
crowded fields, so the superb resolving power of HST was needed in order to
actually measure their brightness and populate their light curves.
Then, using the locally calibrated Cepheid relation, understand the distance
to these galaxies and then use those to calibrate other things such as
supernovae. A choice was made to use the distance to
the Large Magellanic Cloud to establish The zero point to the Cepheid period
luminosity relation. You recall that, that was the original
discovered period luminosity relation by Henrietta Leavitt, and it still plays a
role. And so any uncertainties in the distance
to the Large Magellanic Cloud would then map directly into the inserted piece in
the Hubble. Constant.
Now not only did this team perform wonderful measurements, but they're also
very careful about their analysis, and they tried to honestly account for every
source of error they can think of. And the final result is shown here.
Hubble constant turned out to be right in the middle of the disputed interval
between 50 and 100 kilometers per second per megaparsec.
It's 72 + or - 3 in just random errors, but also + or - 7 kilometers per second
per megaparsec plus potential systematic errors and that's an honest result.
In fact this is still perfectly consistent with all of the more modern
measurements, Note, however, that there is still dependance, on the assumed to
the [UNKNOWN] clouds. And that is osmething that people
continue to improve. So here is a sample image of what they
were looking at. The picture on the left, is 1 of the
spiral galaxies used in their study, and superimposed on that, is an outline of
the field of view of the camera, of a space telescope, that was used.
This was the original White field Blanthery camera, and has the strange B2
bumper shape. The picture on the right, shows a zoom
in, on one of those images, with some of the candidates Cepheid's circled.
As you can see, this would be a very hard thing to do from the ground.
Some of these Cepheid's, occur in star-forming regions, so there may well
be other bright stars that are blended with them and that has to be taken care
of. And here are some light curves of
cepheids discovered by the key project. These represent many measurements of
different times that we folded together into the best fit period.
And you can see that those really look like those of nearby cepheids.
So here are some Hubble diagrams they obtain in the end.
The bottom left one shows only that one. For galaxies, whose distance was derived
from Cepheid's. The one on the right includes all
possible calibration sources they could come up with.
And here is a table that accounts for different sources of uncertainty in their
measurement. I'm just showing for information only,
and you can see how many things they can think of And here is their final error
probability distribution around hubble constant This is actually a good
scientific way of presenting result. It's not a number, it's a probability
distribution for that number The peak value is the one that's quoted and the
width of that distribution is indicative of that uncertainty.
People continued, to try to determine Hubble constant, using any 1 of the
number of methods and combinations of different indicators and callibrators,
and here is again, a table of those. Not there for you to remember all of it,
but just to see how, much the different measurements, scatter around each other.
Most of them are certainly within the error bars of the value determined by
Hubble key project. Now recall that the basis for the whole
thing was distance to the Large Magellanic Cloud which is about 50 kpc
from the Milky Way. So the uncertainty of this distance maps
directly onto the uncertainty on Hubble Constant.
And the distance to The Magellanic Cloud was measured many different ways by many
different authors. That alone, has a spread of + or - 10%.
There is maybe about, 10 different methods, by which this was attempted, and
here is the table that shows some of the results.
Again, not there for you to remember all of it, but just to see the, roughly, the
spread of the numbers, and the accuracies that are involved.
A more important Check, which is actually becoming a very powerful new method is,
as follows: in the neclei, of many, large spiral galaxies, there is a massive black
hole. Which, for all practical purposes, is
like a point mass, just like, essentially, all of the mass in the solar
system is in the sun. Now, if we have test particles moving
around that black hole. From measuring their orbits, we can find
out how far the galaxy is. The orbits can be well-assumed to be
Keplerian. And the suitable test particles are
so-called interstellar masers. These are interstellar clouds that have
very sharp line due to the coherent emission, and as they're moving around,
the center of this galaxy, they can be used to measure the central mass, But
also they can be used to measure the semi-major axes of these orbits.
This was the first case in which this was done, since then there have been more,
and the distance to this particular galaxy was found to be consistent with
that one determined by the Cepheids. Now wouldn't it be nice, if we can bypass
all this messy distance scale ladder climbing from one to another and so on,
and go directly into the tuple flow. Well, there're 2 methods by which death
can be accomplished, that do not require any other calibration.
They're both based on physical reasoning. The first one is gravitational lens time
delay and the second one is so-called Senile of Gorbachev effect.
Whereas these are based on physics, they're still very much model-dependent.
Initially, at least, we are producing values that were somewhat lower than that
when measured by the Hubble Key Project, but since then, they have converged a
little more. Any of these small discrepancies can be
understood in terms of systematic errors. So firstly, gravitational lens time
delays. Assuming that we understand the geometry
of the lensing, and I'll show this in a moment, we can in principal derive the
distance between the lens and the lensed object using the measured time delay.
Modeling the lens geometry is the key uncertainty here.
Because masses responsible for gravitational lensing are not always
perfectly straightly symmetric and there can be combination of many potential
wells of say galaxies in a cluster or group.
So here is how it works,.Here's a schematic diagram showing what
gravitational source might be. There is a background source, say a
quasar, There is a foreground which could be a galaxy or a cluster.
It bends the lights rays coming from the original source and One usually sees
mulitple images, on the sky. Each of these images correspond to
particular path of light rays that came around the gravitational lens and there
will generally difference in length. The difference in length would translate
itself in to a difference in arrival times.
So we are going to see in our ability in the place are we will first see it in one
image And then some time later in the other.
These time delays are typically in the range of weeks or months.
The path difference between different rays, assuming that you know, know the
geometry will scale directly with everything else, every other length in
the system. And the ratio of this path difference to
the, distance to the lens or the source. Is also something that the model will
tell you. So by measuring the time delay,
multiplying by the speed of light, we directly measure the difference in the
path length. And if we knew the lens model, we can
then use it to infer the distance to the lens, or the lensed object.
Synyaev-Zeldovich Effect is something entirely different.
Clusters of galaxies contain galaxies, dark matter.
But also a lot of hot gas. Gas that was expelled from galaxies or
accreted by the cluster. And since that gas is in a potential well
of a cluster, the speed of individual particles.
Protons. Electrons has to be such that the kinetic
energy balances the potential energy. It turns out that [UNKNOWN] responds to
temperatures of millions or tens of millions of degrees, which means that the
gas will emit in the X-rays. Now we're looking at the cosmic microwave
background [UNKNOWN] cluster Cluster. The photons of the micro background will
come through, and some of them will scatter off these hot energetic
electrons. In the cases of forward scattering this
will generally result in an increased energy of the photon.
The energy's been gained from the electrons in the cluster.Of course there
is equal amounts going out from the other side.
So essentially what you see on the micro background sky is there's going to be a
bump that corresponds to this X-ray cloud.
And the entire spectrum of the cosmic micro background will be shifted towards
a somewhat higher energies. By measuring that shift We can find out,
how long was the path? Because the longer the path along the line of sight, more
chances the photons have to be scattered. Therefore, we can, derive from this
measurement directly, physical we can measure the apparent size of the cluster
on the sky. In an average, we expect the cluster will
have the size in radial direction or orthogonal to it.
So since we have observed apparant angular size of the cluster in the sky.
And we know how much that is in physical units, the cluster's red shift.
We can derive the angular diameter distance Now, any given cluster is not
likely to be spherically symmetric, but the whole ensemble, on average, will
probably work out. A beautiful thing about this method, is
that it does not depend, on the distance to the cluster itself.
The source that's observed, is cosmic microwave background.
Cluster could be near by, or it could be very far away.
So the method can work over a very broad range of redshift's.
There are uncertainties in modelling the process because the gas could be clumpy,
there are some density gradients, all of that has to be accounted for before we
can derive the actual diameter of a cluster that photon goes through.
Next we will talk about measurements of the age of the universe.