 Greetings and welcome to the Introduction to Astronomy. In this video we are going to talk about stars, and specifically we are going to look at the brightnesses and the colors of stars and how we go about measuring those and what they tell us. So let's go ahead and get started. And the first thing we want to look at is talking about the brightnesses of the stars. Now when we talk about the brightness of a star there are two specific things we want to look at. One is the apparent brightness of a star and the other is the absolute brightness. Now these two are quite different. Let's start off with the absolute brightness and that is what we also astronomers will call the luminosity of a star. So the luminosity is the amount of energy being emitted at all wavelengths by a star every second in all directions. So it is a real measure of the amount of energy a star is emitting at all times. So it doesn't count just the amount of energy for example of the sun heading towards us here at Earth but it would count that heading out elsewhere in the solar system and that elsewhere into space. And it would look at all of the wavelengths not just visible light but would count all of the energy. Now for a star like the sun most of the energy is being emitted at visible light wavelengths. Some is in the infrared and some is in the ultraviolet but the vast majority is in the visible. Now what kind of measurement units do we use for this? Well we can give it specific units and astronomers sometimes do but for most cases it's much better to refer it to the luminosity of the sun. So what we say is that the sun has a luminosity of one solar luminosity and for the sun we use a circle with a dot at the center. So that is the luminosity of the sun so a very faint star might have a tenth or one one hundredth the luminosity of the sun. Very bright stars might have hundreds or thousands or even more times the luminosity of the sun but it is all compared to the sun as a convenient measure. Now that's the absolute brightness that is how much energy a star is actually putting out. However when we look at the stars at night we don't see the absolute brightness. We see only the apparent brightness or how bright they appear to be from the earth. Now that depends on a lot of different things. It can depend on the distance from the star the further away a star is the fainter it is going to appear it can depend on whether there is dust in the way dust could be making the star appear fainter than it otherwise would be. So the luminosity is what is actually being emitted from the surface of the star the apparent brightness is what we actually see from the earth and since it does depend on these things there are some questions. Is a faint star really faint or is it a bright star that is just very very far away? Well that is something that we have to consider and that we will use later on. Also dust will make stars appear fainter than they would otherwise appear. So in some ways dust can then make a star look further away by making it look fainter we could think it is further away than it actually is if we did not understand that there is the dust in the way. Now in order to measure the brightness astronomers use the system of stellar magnitudes. These were started by the Greek astronomy Hipparchus astronomer Hipparchus back in the 2nd century BC. What he did was to group stars into categories by brightness so he put his brightness stars in the first category here these were the brightest stars and then he had category 2, 3, 4, 5 and 6 and 6 were the faintest stars that were visible. Now that would be what would have been visible with the naked eye as we are long before the time of the telescopes. So he did those into 6 categories and the brightest stars being stars of the first magnitude and the faintest stars being stars of the 6th magnitude. Now this was based on naked eye observations so there were no telescopes or binoculars or any other devices to help you observe at the time so all that could be done was to look at them with your eye and what that does is because this carries over to what astronomers use today it gives us two difficulties that can often confuse people learning the magnitude system. First of all the system is backwards numerically a larger number means that a star is fainter that's not how we measure most things if we measure the height of an object the higher the number the taller the object if we measure the mass of an object the bigger the number the more mass it has if we measure temperatures the higher the number the hotter it is. However in magnitudes the bigger the number the fainter the star. The second is that the system is what we would call non-linear and that simply means that typically if we look at two objects and one is one meter long and the other is two meters long we know that the two meter long object is twice as long as the other so we can easily tell comparative distances if we have two temperatures and if it's 40 degrees versus 80 degrees 80 degrees is twice as hot as something at 40 degrees so those would be examples of linear scales non-linear scales like this means that there are not a sixth magnitude star even though we know that it's fainter it's not six times fainter than the brighter star this is actually 100 times fainter so the five magnitudes in between first and sixth would be 100 times fainter so those are two of the things that can cause difficulty as you're learning the magnitude system now let's look at how this was expanded and over time astronomers expanded this scale but they still built on what Hipparchus did so in the 1800s it was expanded and now ranges much further remember that Hipparchus only gave us this range from about first magnitude here to about sixth magnitude here and what we found as we've been able to make more detailed measurements and develop more technology that binocular objects if you look at an object with binoculars you can actually see much fainter you can get down to tenth magnitude a one meter telescope gets you down to about 18th or 19th magnitude four meter telescopes get you down to about 26th magnitude and the Hubble telescope can get you down to 30 or even 31st magnitude for the very largest telescopes so they've been able to expand the scale but remember when we're looking at magnitudes in the 20s and 30s these are extremely faint objects even though they are the largest numbers numerically now we've also some things that were not considered as Hipparchus was only looking at stars there are some objects that are actually brighter so Jupiter and Mars would actually then have negative magnitudes Jupiter, Mars, Venus can all have negative magnitudes the full moon has a magnitude of about negative 12 the sun has a magnitude of about negative 26 again very small numbers mean very bright objects now the way it was expanded and the way it has finally been formalized based on what Hipparchus had originally done is that each magnitude represents a factor of two and a half in brightness so if you have a first magnitude star and a second magnitude star the first magnitude star is two and a half times brighter than the second magnitude star and if you go to a third magnitude star that would be another two and a half times so two and a half times so the third magnitude star the second magnitude star would be two and a half times brighter than that the first magnitude star would be another two and a half times brighter meaning that between the first and third magnitude it would be 2.5 times 2.5 or 6.25, 6 and 1 quarter times brighter now we don't need to go into all the details of this here but one of the important things to know is that the difference in the magnitudes is two and a half times and that five magnitudes if you multiply two and a half times two and a half and you do that five times you will find that five magnitudes is a factor of 100 in brightness so this is what Hipparchus found between his brightest stars of first magnitude and his faintest stars at sixth magnitude there was about a factor of 100 in the brightness and this is what we still use today so we still use this scale and everything is converted to this if we are measuring magnitudes with the Hubble Space Telescope it still uses the scale that was originally developed by Hipparchus so how about other wavelengths how else can we measure these well typically other wavelengths radio waves, gamma rays use luminosity instead of magnitudes magnitude scale is used for ultraviolet and infrared wavelengths in some cases especially when those are very close to visible so there are some cases where we use the magnitude scale radio astronomers, gamma ray astronomers x-ray astronomers do not convert things to magnitudes but instead use measures of luminosity or at least of apparent luminosity again how bright the objects appear to be from the Earth now the other thing we wanted to look at in this section is the colors of the stars when we look at images like this we note that there are very distinct color variations in the stars there are some stars like these that appear very red there are other stars appear that appear very blue that is very that tells us something about the surface temperature of the star and what we find is that hot stars appear blue cool stars appear red now if you remember back Wien's law told us this Wien's law told us that the peak of the radiation depends on the temperature of an object so a very hot object is going to emit more blue and ultraviolet light a very cool object is going to emit more red and infrared light so just by looking at images like this we can tell where the hotter and the cooler stars are all the red stars you see are relatively cool all the blue stars you see are relatively hot however it does not give us a way of measuring the temperatures directly we need to get more detailed measurements to be able to determine that we find that the color does not depend on the distance so it helps us learn about the stars regardless of distance however it is affected by dust dust is very good at absorbing short wavelengths of light so it can absorb the bluer light and if a star's light is coming through a lot of dust it can look significantly redder than it otherwise would be so a red star could be a bluer star with the light coming through lots of dust on the way to Earth in the case of a cluster like this that is unlikely because all of the dust would not just block out one star but would likely block out all of them but it is something that astronomers have to consider when making measurements of individual stars one of the other color changes that we sometimes talk about is due to the Doppler shift and this was originally thought maybe this was one of the reasons for these changes that if something is moving towards you or you are moving towards it that the colors will be shifted towards shorter wavelengths or bluer colors and if something is moving away from you or you are moving away from it the colors would be shifted towards longer wavelengths but will we know that that cannot be the case because in order to actually shift something from say red to blue you would have to be moving at a significant fraction of the speed of light in order for the Doppler shift to cause that kind of change and with the cases of stars within our galaxy that does not happen however out further in the universe when we start talking about the expansion of the universe certainly when we look at quasars we do see in very distant galaxies we can see some that are moving so far and so fast that light that was emitted in the ultraviolet part of the spectrum ends up being shifted in to the visible so let's take a look at what astronomers call the color index and the color index is a measurement that is used to get a better idea of the temperature I've told you how the color can give you a vague idea of whether something is hotter or cooler but we can use the color indices to be able to measure the brightness through three different filters now the most common of those are the U, B and V filter U for ultraviolet, blue for blue and V for visual now what that means is that they're filters so this lets through just a certain range of ultraviolet light this one just a certain range of blue light and this one the V or visual lets through actually some yellow light and what we do is we make a color index so we measure the magnitudes and the most common one is B minus V so we measure the magnitude in the B we measure the magnitude in the V so we essentially take a picture of the star through the blue filter measure the brightness, the apparent brightness we take a picture of the star through the visual filter measure the brightness again calculate those magnitudes and then subtract them that determines the temperature very specifically and in fact a negative or very small value when you subtract, take B and subtract V means a very hot star a positive value, larger values mean a cooler star so we can use the B minus V values by taking pictures of stars through these various filters determining the magnitudes we can then use that to determine the temperatures of the stars not just say one is hotter or cooler but we can use those exact numbers to really be able to determine precise temperatures so let's finish up here with our summary and what we find is that we looked at two different measures, the absolute and the apparent brightness of stars this is what we see from Earth the apparent brightness this is what the star is really putting out the magnitude scale that astronomers use has two problems and two confusions one it's numerically backwards and the second is that it's not linear and those are two things that can cause confusion for new learners the color of a star would tell us something about this temperature the bluer star being hot hotter a redder star being cooler but we need to use the color index to determine the exact temperature and make more detailed measurements so that concludes our lecture on the 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