 Greetings and welcome to the Introduction to Astronomy. In this lecture, we are going to talk about stars and specifically look at their brightness and colors that we see for stars. So when we talk about the brightness of a star, we have two different ways to look at this. We have the absolute brightness and the apparent brightness. The absolute brightness is the luminosity. This is the amount of energy being emitted at all wavelengths by a star every single second in all directions. This is a measure of how truly bright a star is. So if you want to compare two stars, you want to look at their luminosities. The units for this are in terms of the luminosity of the sun, which is L with the little sun symbol below it. So we can compare other stars and find out that they may be a hundred or a thousand times more luminous than the sun, or they might be one-tenth or one-one-hundredth as luminous as the sun, but we use that as the sun as our comparison. When we talk about apparent brightness, this is how bright a star appears from Earth and depends on the distance. So a star that is very far away will naturally appear fainter than if that same star were close. It also depends on the presence of dust, something that could cause the star to dim. The question is, is a faint star really faint, or is it far away? So we don't know. If we just look at a star out in the sky, we don't know whether it's a faint star or if it is a really bright star but very, very far away. So that is something that requires other measurements to make. Dust will make stars appear fainter than they otherwise would. So the dust makes them appear fainter by absorbing some of their light and we'll look at dust later on. Now, brightnesses are measured in magnitudes and we use stellar magnitudes which were developed by Hipparchus back in 150 BC or so. And what he did was to group stars in categories by brightness. So the brightest stars were stars of the first magnitude. They were the brightest and the faintest stars that could be seen were stars of the sixth magnitude. So he had classifications one, two, three, four, five, and six with the bright stars being on this end and the faint stars being on this end. Now what that means is that this system is backwards from what we're used to doing. This system is backwards numerically. A larger number is a fainter star. Now that's different than most other measurements that we use. Temperatures, a higher number means something is hotter. Distances, a larger number means something is farther away. So it's a difference backwards scale because of the way it was set up. Also, this system is not linear. And what that means is that a second magnitude star, while it's fainter than a first magnitude star, it's not twice as faint. It's about two and a half times fainter. And we'll look at that a little bit more detail here coming up on the next slide. But normally, if something is 10 meters away and something else is 5 meters away, then something is twice as far. It is a non-linear scale. It's similar to what is used for the Richter scale for earthquake intensities, that each little bit of intensity can make a big difference in the amount of the earthquake. So let's look about a little bit how this got expanded into the 1800s. As I said, we now know that each magnitude is a factor of two and a half in brightness. So every magnitude doesn't matter if magnitude 1 and 2 or magnitude 31 and 32, they represent a factor of two and a half in brightness. Now, that means that if you multiply two and a half by itself five times, that five magnitudes will be a factor of 100 in brightness. So a star of magnitude 1 will be 100 times brighter than a star of magnitude 6. So they are five magnitudes apart. That is a factor of 100. And telescopes have expanded this scale. So whereas Hipparchus gave us things in the order of 1 through 6, we've now expanded that with binoculars and telescopes, going all the way down into the low 30 magnitudes. And remember, multiply by two and a half each time, and that is the difference in magnitude. So each of these fives would be a factor of 100. So 10 of them would be a factor of 10,000. 3 going from here would be a factor of a million in brightness. So it's a very big difference even though the magnitude scale numbers are actually relatively small. We also expand it to the other direction to quantify this and that there are objects that are brighter. So objects with negative magnitudes would be among the brightest things. The sun and the full moon there as examples. So how about other wavelengths? This talks about visible light. This observations at other wavelengths tend to use luminosity. So radio astronomers, gamma ray astronomers use luminosities and not magnitudes, although sometimes some of the infrared and ultraviolet also use magnitudes as a way of measuring the brightness of those stars. So that's a little bit about brightness of stars. What about colors? Well the color of a star is related to its surface temperature. So the temperature that we see on this surface, a hot star will appear blue, a cool star will appear red. Remember this is Wien's law that we've talked about, that the higher the temperature, the shorter the peak wavelength and therefore will look very short wavelengths will be the hotter stars. Note that the color of a star does not depend on the distance. So even at great distances we can see the color of a star. But it can be affected by interstellar dust. Remember the Doppler shift, does that cause a color change? Well for stars no. It does not cause a change. Remember that the shift is very minor. It's a very small amount of a shift. So it's not going to shift near enough to change colors. However we will look when we get out to the edge of the universe and we have objects and galaxies receding at very very fast rates, then we can get lines shifted way across the spectrum. Now how do we measure this? So here we get a general qualitative idea of how hot the star is, but how can we actually measure that? We can use what we call the color index. And there are a number of different color indices that astronomers use. It's a better way to be able to determine the temperature. And what we do is you measure the brightness, the magnitude of the star, through two different filters. One common set is the U, B and V filters. That's the ultraviolet, blue, and visual bands. So how much light comes through in each of those. And then you measure those magnitudes and you take, for example, a common color index is B minus V. So you take the diff, subtract the two magnitudes and that gives you the color index and that tells you the temperatures. So a negative value, if it's a very small number, that means that V is much bigger than B. That's going to tell you it's a hotter star. Remember, if V is very big, it's very faint in the visual and relatively bright in the blue. It's giving off more blue than yellowish visible light and therefore is a hotter star. A larger positive value means a cooler star. So in that case, B is going to be bigger and V is going to be smaller. You're taking a big number minus a small number and therefore you're going to get a large positive number and that's because in a cool star, B is going to be a lesser magnitude than V. So getting this and quantitatively measuring B minus V can then be correlated directly with the temperature. So we can use this to directly measure the temperature, not just say that something is hotter or cooler. So let's go ahead and finish up with our summary and what we looked at is we looked at the absolute and apparent brightnesses of the stars. We talked about the magnitude scale and how it is numerically backward and nonlinear, making it a little more difficult to deal with than other scales we use. The color of the star will tell us about the temperature and we can use things like the color index to determine the temperature of a star. So that concludes this lecture on brightness and colors of stars. 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.