TELESCOPES

M JUDY

little maybe

OK. So welcome.

The last time we were talking about exponential disks and

about the distribution of mass in spiral galaxies.

And we found.

using a fairly long discussion that in the end we can approximately we can

approximately connect the mass that's connected within the radius to the

observed rotational velocity according to this equation which you would derive

using simple Keplerian Kepler's laws and simple mechanics or using this more

complex discussion here.

And what we found there is that if you then invert this

equation, you find that unfortunately if we assume that

light traces mass and if we assume that the mass to

luminosity ratio is constant, which are both assumptions

that so far I think everybody would have said we would agree

on, the rotational curves imply that the mass inside radius is

rather constant. It is not constant because of the flat

rotation curves. And that means that if you then look at the

components that make up the mass, mainly the disk and the

bulge and the gas distribution, if we just use these

distributions, we cannot explain the observed rotational

curves of spiral galaxies. So in order to reconcile the

rotation curves and the mass distribution, we have to posit

a unseen population of mass, so-called dark matter, that is

located in a massive halo that has this type of a

distribution. This is important, right? The massive halo

density distribution that you see here just depends on the

radius, so it is a spherical thing that contains a lot of

mass with a density profile that fairly slowly falls, which is

very different to the distributions from the

distributions that we saw for the stars, which were

exponential distributions. Okay, so there's a big difference

in the distribution of dark matter and of stars. And these

things are called dark matter halos, and they're observed

essentially around each spiral galaxy. And later, we'll see

that we can indeed build spiral galaxies using a dark matter

model where dark matter first collapses, forms this halo, and

where then normal material falls into this halo, variants fall

into this halo, and then form the spiral galaxy that we

observe. And as a result, the mass to luminosity ratio of

spiral galaxies is on the order of between 5 and 25. Since for

normal stars, the mass to luminosity ratio in solar units

is 1. This means that 80% up to, well, whatever 24, 25th is of a

galaxy consists of dark matter and not of stars and gas. Okay,

so dark matter is really, really important. Now, irrespective of

what exactly the dark matter is, what is important is that for

spiral galaxies, there is again a kind of constant mass to

luminosity ratio. And that can be used to derive a very