So welcome back to the second day of a busy week for this lecture. So yesterday we essentially

talked about how we measure distances all over the universe. We are lacking one method

which we will talk about today. Then we will determine H0 and look at how galaxies are

distributed around us and then we will create the universe. So it's kind of a busy evening.

So yesterday we were talking about most of the methods really used for distance determination,

but for time reasons we didn't manage to talk about the last one, which is one that you

all already know, the total official relationship. That's the relationship that we already discussed

I think end of November, early December when we were talking about how the width of the

21 centimeter line of hydrogen is correlated with the luminosity of the mass. And here

are three correlations for total official from one of the calibration papers that show

you how well the correlation works between the logarithm of the line width and the absolute

magnitude in these bands. So you see there is a really tight correlation. And obviously

now if you have a way to determine the absolute luminosity based on another observable like

the width of the 21 centimeter, you can also measure its luminosity and therefore you have

a standard candle. And the basis for this is well understood because we know that it

is related to the total amount of mass in the overall system. So we all know the basis

of this. There is one caveat in there in that spiral galaxies rotate like a disk and so

one of the big problems when looking at these galaxies is always that you have to de-project

the measured width. This is the sine I factor here which is just the sine of the inclination

and that is something that sometimes is a problem especially if you can't have a good

image of the galaxy. So for sources that are far away, if you can't really image the spiral

galaxy and measure the projected, the shape of the projected ellipse on the sky then obviously

you have a problem in correcting for inclination. There are also other issues for example there

might be a contributing component to the line broadening caused by turbulent motion and

there is also trends along the, for different types of spiral galaxies as As and Bs have

different types, have different luminosities than the As. So there are issues but often

essentially if you have a spiral galaxy and nothing else in it before you don't have a

distance at all using Tully-Fisher is a better distance and determinator than the other methods.

And the same is obviously also true for elliptical galaxies and we also already looked at these

systems and that was the so called favor Jackson law where you have a correlation between the

luminosity and the fourth power of the velocity dispersion of stars in there and because there

is little gas in these systems, right, you can't use 21 centimeters so you really have

to do optical spectroscopy. And we already spoke about the d sigma relation in the context

of galaxies so I'll just jump over this. So now we know how to measure distances both

in our galaxy and the local group and out to the total, into the total universe. So

in order to determine age zero from that you need to do two things, you need to measure

a distance, we know how to do that, and you need to measure a redshift, we know how to

do that, right. Doing the redshift is easy, distance now that we know what methods there

are is also easy. So the problem is really to measure enough distances to objects that

are far away and that's something where major projects happened over the last 30 years roughly

starting really with the Hubble Space Telescope key project on the extra galactic distance

scale that was pushed by Friedman and others in the 90s that finished first in 2001 and

then got an update with further deeper observations that led to another really important paper

in 2010. So what they did essentially is they said okay let's start with really the best

type of standard candles for primary distance indicators, that means let's calibrate the

cepheid distances, then go with the cepheids out to the Virgo cluster because that's the

nearby largest collection of galaxies so it contains enough sources that have secondary

calibrators and we spoke about the fourth, effectively what they use is Tully Fisher

and type 1a, surface brightness fluctuations and the fundamental plane for ellipticals.

And then go from there really into the deep universe. And since you have multiple methods