 Greetings and welcome to the introduction to astronomy. In this lecture we are going to continue talking about galaxies and specifically look at the properties and distances of galaxies. How do we measure those distances? So let's start out with some of the basic properties. So what about the mass of a galaxy? How do we determine the mass? So remember in astronomy all we can do is look at an object. All we do is see its light and we have to be able to determine the mass using just the light. And that is done from Kepler's third law as modified by Isaac Newton where we measure the rotation of the, we look at the rotation of objects in the galaxy. So we can look at two different things. We can either look at the rotation of objects such as stars in the galaxy as we see here for a rotation curve for a spiral galaxy or we can look at the broadening of spectral lines for an elliptical galaxy. Remember elliptical galaxies don't have quite the coherent rotation that a spiral galaxy does. When we measure these masses we have a problem. The problem is that there is far more mass in the galaxies than what we can see. And we've talked about dark matter before. This is where dark matter comes in. We expect based on what we see the curve to follow the lower line but it follows the upper line and increases meaning that there has to be a lot more mass out beyond the edge of the galaxy here. There has to be a lot more mass all around it. Now when we look at galaxies we can look at the ranges and we find that elliptical galaxies have a big range in mass. They can go from 10 to the 5th solar masses the smallest dwarf ellipticals to 10 to the 13th the giant ellipticals much larger, 10 times larger than the largest spirals. So big, big range here whereas the spirals and ellipticals and irregulars are a much narrower range. Diameters are the same. Big, big range in diameters big range in luminosity. And we see that irregulars tend to be smaller than the spirals so ellipticals and spirals are among the bigger two galaxies irregulars tend to be a little bit smaller in terms of the mass and the diameter. Now when we look at the stellar populations again we looked at this previously ellipticals are all old populations they have no gas and dust that's why they're old populations they are not forming stars and we will come back and look at mass to light ratios again in a second here. So what do we mean by a mass to light ratio? Well we compare the mass of the object in solar masses to the luminosity of the object in solar luminosities and we divide these two and that gives us what we call the mass to light ratio. Let's look at an example for the Sun. The Sun has a mass of one solar mass and a luminosity of one solar luminosity that's how those are defined. So one divided by one gives us one for the mass to light ratio of the Sun and anything else would then be compared to that so something that gives off a lot more light with less mass would then have a much smaller mass to light ratio it's giving a lot more luminosity something that has a lot of mass and is dark would have a very high mass to light ratio. Now how does this apply? Well low mass stars contribute a lot of mass but very little light they may be low mass stars but they give off very little light relative to their mass so they have a large mass to light ratio. High mass stars give a lot of light relative to their mass and therefore have a small mass to light ratio. So that ratio is really just added up from all the objects that is composed of so very young galaxies with lots of very hot bright stars would have a low mass to light ratio maybe in the order of 1 to 10. An old galaxy without those hot young stars would have a mass to light ratio in the range of say 20 to 30. Now how about dark matter? Well these ratios are applied to what we see in the inner parts of the galaxy but most of that matter is invisible dark matter stuff that we cannot see it has a lot of mass and no light meaning it is an extremely high mass to light ratio all galaxies have some amount of dark matter so we see some of these galaxies can have mass to light ratios in excess of 100 so they have a lot more mass as compared to the amount of light that they give off and understanding this dark matter is going to be very important for understanding galaxies and the universe. Now how about distances? How do we determine distances? Well distances are very difficult how do we figure out the distance to a galaxy? Well what we can do is we need to get these accurate so how can we do this? We cannot use parallax so no parallax for galaxies only the closest galaxies can we resolve the individual stars so things like variable stars and cepheids do work but only for the nearest galaxies this is how we determined that Andromeda was actually another galaxy so if we find a cepheid the period luminosity relationship can be used to give us the distance then but you have to be able to resolve those stars and you can't see them once you get outside the local neighborhood of galaxies so we have to use other things some things we use are what we call standard bulbs or candles so something that is a standard brightness standard bulb is an object with the same luminosity so that any differences in the apparent brightness only depend on the distance they're all just as bright so if something is very faint it must be further away if it's very bright it must be close so once the object is identified we know the luminosity we've got that and we measure the apparent brightness which means we can then determine the distance to these now one of the most prominent standard bulbs that we use are the type 1A supernovae these are a good standard bulb why? if you recall a type 1A supernova are all made from the same type of object a 1.4 solar mass white dwarf star in a binary system they're all exactly the same objects that explode they should theoretically reach the same peak luminosity meaning that when we see something like a supernova go off in one of these galaxies as we see here an image is taken in March and then in July of 2012 from this small distant galaxy we can detect them we can then determine we know it's a type 1 way identify it as a type 1 supernova so we know it's peak brightness in luminosity we measure its peak brightness in apparent luminosity and therefore we can get the distance to this star to the gal at the star which gives us the distance to the galaxy that contains it this works out to 8 billion light years that's a good fraction out toward the edge of the universe considering the universe is about 13 to 14 billion light years outward so this is very important for determining distances and understanding the evolution of the universe now let's look at some other methods that are used to determine distances for disk galaxies we use the Tully-Fisher relationship which says that the luminosity of a spiral galaxy is related to its rotation rate more luminous spiral will spin faster so we can measure this rotation speed through the 21 centimeter hydrogen line use this to determine the luminosity from our chart so we measure the rotation and then we can determine from that what the magnitude would be so we can then determine that magnitude brightness of luminosity once we know a luminosity and then we can see it then we can determine its apparent and its absolute magnitudes and that gives us the distance however it is limited to spiral galaxies so we cannot use this method for ellipticals now let's look at our distance ladder overall and we're not quite done with this yet we still have one more method to go but different methods will work to various distances and remember that we need to use one method to calibrate the others and those errors build as we move out so we can use things like Cepheid variables for certain galaxies out to about 100 million light years the Tully-Fisher relationship to 300 million light years this type 1 supernovae getting much further out and then finally Hubble's law which we will talk about later out to the edge of the universe as long as we are able to view that galaxy we can then determine its distance and remember that this builds on things the Cepheid variables builds on things that we looked at previously with spectroscopic parallax and with parallax itself as other ways of determining those distances so each one builds on our knowledge of the previous measurements so let's go ahead and finish up here with our summary and what we've looked at is that masses of galaxies can be determined using Kepler's Thurs law as modified by Newton we looked at the mass to light ratio as a way of comparing the amount of mass an object contains to the amount of light it emits for the sun this is one and we looked at some of the ways of determining distances to galaxies using Cepheid variables or for more distant galaxies type 1a supernovae so that concludes this lecture on galaxies, properties and distances we'll be back again next time for another topic in astronomy so until then have a great day everyone and I will see you in class