If you'd like to know whether Mars is like the Earth, perhaps one of the first things that you'd like to figure out is what is the temperature on the surface of Mars? Let's think about how you figure out the temperature of something from far away. These days we know just how to do it. Could buy one of these things, this is a Infrared IR Laser Thermometer Temperature Sensor Non-Contact Digital LCD Display. So you point at the location that you would like to know the answer to. You pull this trigger right here, and it reads the temperature right through there. Back in the middle of last century, they didn't have one of these. But they used essentially the same principles that this devices used to try to figure out what the surface temperature of Mars was. Let's think about how this works and then we can apply that to Mars. We know that a solid object, when it's heated up, emits radiation. We see this in things like glowing incandescent light bulbs which glow because they're heated. The glowing coils of a toaster, if you've ever had the fun of seeing an active lava flow, you see the glowing lava. All of these things are glowing because of how hot they are. And in fact as we know, everything regardless of the temperature is glowing in some amount. This glow is of course, called black body radiation and there are two important properties that we're going to care about right now. One is that when temperature goes up, the wavelength of the peak of emission goes down. We have limited personal experience with this, but we know when things heat up they are red hot. Red is the longest wavelength of visible light. As you heat them even more, we think of them as blue hot, white hot or blue hot, that's shorter wavelength. The temperature is going up, the peak of that emission is going down in wavelength. But the other important thing is that as the temperature goes up, the energy emitted at every wavelength increases. Let's look at how this looks on a plot. If I show you three three black body curves, one for temperature of 3,000 degrees, hotter than anything we have on the Earth. 4,000 even hotter, 5,000 these are more like temperatures of stars, but it's a good example of what you see. And first thing you see is that the peak of the emission is indeed going down in wavelength. Most of the time in this class when I talk about wavelengths of light, I will use this unit micrometers, microns I'll often call it. And it will be important to remember in general where the visible part of the spectrum is. It's about a half a micron, really between about 0.4 and 0.7 microns is the part of the spectrum that our eyes can see. Beyond 0.7 is the infrared, shortward of 0.4 is the ultraviolet. And much, much longer we have things like microwave emission, radio emission, and even long wave length emission. Now notice as I said, the two important points is that as the temperature increases from 3,000 to 4,000 to 5,000 the peak of emission goes down in wavelength. But also notice the other thing, as the temperature increases, the emission at every wavelength is higher. At 5,000 degrees, yes, the peak is here closer to 0.5 microns. But 5,000 degrees is brighter even over here than 3,000 degrees is. This is a useful property, because it allows you do something very simple and very powerful which is if I am staring at a, let's say rock, a glowing rock. And I measure how much energy is coming off that rock. And let's look at the units over here, spectral radiance kilowatts, so that's kilowatts is energy. Per steradian, that means how much of an angular area you're looking at per meters squared. That's how big your detector or eye is in this case. Per nanometer, that means per every unit wave length. If I'm staring at this rock and I measure how much energy is coming off of it. I can tell you the temperature, that's because if I find an energy equal to this, it's 3,000. If I find an energy here it's 4, energy here it's 5. Higher energy, it's higher. Lower energy, it's lower. This is the principle of the device that you can buy now. The very simple device that you just point at a surface and you measure the temperature of that surface. The device has a little detector which isolates the light from one particular wavelength region like this. Measures how much energy is coming off the surface and says, okay, that's the temperature. It's an interesting question to ask yourself, okay, I can use one of these little devices to measure a grill which is close by. But how does it work if I'm trying to measure Mars which is much further away? Well imagine this, imagine your grill is right here. And you have your device that points here, measures a swath of grill this big, calculates the temperature. How would it work if the grill were over here instead? Well as long as you pointed at it, it would measure a swath of grill that was this big. The amount of emission in watts per meter squared is the same. But notice that the area of the grill that you're looking at is greater at this point. In fact, the area that you're looking at in your cone that's going out of your little device is proportional to the distance squared. Where the further away your grill is, the more of the grill that you see in the field of you of your little detector. The other thing you know of course is that as the photons are traveling from you, the energy is traveling from you from the grill. They are also spreading out, instead of going down, the number of photons goes down as one over the distance squared, and these two things cancel out. This is why the grill thermometer works. You can hold the grill thermometer really close to the grill. And measure a tiny, tiny spot and get the temperature. You can hold it really far away. And as long as the grill is still filling the whole field of view, you still get the same temperature, if it's uniform temperature in there. Your grill thermometer does not care how far away the grill is. Same thing happens with Mars, but actually look what happens with Mars. Mars is so far away that the field of u continues to expand as we get to Mars, and Mars is tiny compared to this field of u. So suddenly, yes, you're measuring photons coming off of Mars, but you're also measuring a lot of just empty sky. What's the solution? The solution is a telescope. In the 1950s, when this was first done. The solution was the 200 inch telescope at Palomar Observatory. The new telescope that was the biggest telescope in the world. A fantastic achievement, and it's a testament to how important these questions were that these were some of the first observations done in that first decade of operation of this telescope. With the telescope, you can focus in on a tiny, tiny region of the sky and make your swath of light that you're looking at, in fact even smaller than Mars itself. So you're looking at only a small portion of Mars. But your entire detector is being filled with thermal emission from that one swath on Mars. So just like the hand held detector that you can point and shoot at, if you can isolate that thermal emission and you are looking at the right wavelength. Then you know how much energy is coming to you from that wavelength, you can figure out the temperature of Mars. One other question to ask yourself is, what's the right wavelength to look at? There are three things to worry about when trying to think about what wavelength to observe Mars to try to determine its surface temperature, to detect that thermal emission. Now you might just say, it shouldn't matter at all, we can observe at any wavelength and when we measure that thermal emission, we have gotten the temperature. And you would be right, if we measure thermal emission of any wavelength, we can figure out what the temperature is. But there's some wavelengths where it's really hard to measure thermal emission. And the reason is because Mars at some wavelengths is not dominated by thermal emission but by reflected sunlight. So if I look at Mars and I went from, let's say, the start of the UV all the way out to, I'm going to go say maybe 20 microns. You would see something look sort of like this. You would see reflected sunlight which is black body emission from the sun reflected off of Mars and that would look something like this. I'm going to draw it in this way, this form is because I'm doing it on a log scale in this way. And when you do it on a log scale, you get these nice straight lines in here instead of the more peaky curves that we saw before. So when I draw things I tend to draw Without even really thinking about it on a log scale like this. So this is the reflected sunlight. And the sun is something like 6,000 degrees Kelvin. We use units of, temperature units of Kelvin here. And the peak of sunlight is something like 0.6 micron Mars is much cooler than the sun, not surprisingly. And so it will have a peak of thermal emission at a much longer wavelength. The Earth's thermal emission peaks at about 10 microns. If we assume that Mars is similar to the Earth then we'll get a spectrum that looks something like this. And here is 10 microns, which would correspond to a temperature of something like 300 degrees Kelvin. Now something funny just happened, I told you that thermal emission is always higher for a higher temperature. And yet I've drawn you a 300 degree Kelvin curve right here that is above a 6,000 degree Kelvin curve. Why is what? That's because this is not thermal emission, this is reflected sunlight. You could imagine if I just have a mirror sitting right here and I'm reflecting the sun. Well it looks like 6,000 degree radiation because that's what the sun. But I could heat the mirror up a lot and have thermal emission coming off of the mirror that's much stronger than the reflected sunlight from the sun. So don't get confused between the reflected part and the immediate part of mass. Immediate part of mass at 300 degree Kelvin does indeed peak over here and it dominates over the reflected part somewhere out here. We don't know exactly where, but somewhere there is a crossover where if you look at Mars. If you look at Mars with your eye, you just see reflected sunlight, you don't see thermo emission. If you looked at Mars at something like 10 microns you would see pretty much all thermo emission and no reflected sunlight. If we want to measure the thermo emission to figure out what the temperature is we had better be measuring out through here. But in fact because the Earth is similar temperature, well in fact we made this the temperature here, and the sunlight at the Earth is similar. I suspect that these point and shoot grill guns better be operating somewhere around 10 microns. Otherwise, if you pointed it at a mirror that was looking at the sun or something just sort of bright and shiny, you'll get a high temperature, even though the temperature is not very high. But if the grill gun is working at 10 microns, there's very little sunlight down here at 10 microns, but a lot of thermal emission at 10 microns. So we don't have to be in 10 microns, we could be anywhere out through here where the Mars thermal emission dominates over the sunlight. Of course, being close to the peak of where Mars might be seems like a good idea. Because that's where most of the light is coming from, most of the energy is coming from. And there's one other consideration that is the final critical one. Which is how are we going to observe Mars? Well we're going to use a telescope. That telescope is sitting on the surface of the Earth. That means we have to look through the Earth's atmosphere. The Earth's atmosphere where we're used to thinking of it as transparent. We look up in the sky and unless there's clouds in the way, we can see anything out there. But that's only because our eyes, which operate at visible wavelengths, sort of by definition. Our eyes are at a region of the spectrum where the atmosphere does not absorb any light. It's really not a surprise that our eyes evolve that way. It's also convenient that our eyes evolve to be sensitive to the peak of solar radiation right in here too. But it's also a region that's very transparent in the Earth's atmosphere. Most regions in the Earth's atmosphere by region, I mean wavelength region. Most wavelength regions of the Earth's atmosphere are not nearly as transparent and some of them are totally opaque. If our eyes worked at something like six microns, we would look up at the sky and wouldn't see any stars or the sun or the moon. Because all of the light that was coming in from those objects would be absorbed by the atmosphere. And we would just see something like looking into a fog where the distance just faded away. And the distance we could see was much smaller than our own atmosphere. This is an empirical plot of the Earth's atmosphere's transmission from about 1 to around 25 microns. I'm not actually plotting the visible part because it's pretty boring, it's pretty flat. There's some choppiness in through here, flat in through here where eyes can see. And then finally, when it gets down to the ultraviolet, it drops back down to zero. No ultraviolet light gets through, which is good because otherwise we would all be sunburned to death a long time ago. This is a pretty complicated looking spectrum, but most of the stuff in through here is caused by a few molecules that are responsible for the absorptions. Much of it is due to water vapor. In fact, all of these in the shorter wave length range are generally water vapor lines. There is another water vapor line, then this sort of strong one here is due to carbon dioxide. And then you can see why I was picking on 6 micron a minute ago. This whole region between about five and a half and maybe eight is almost entirely absorbed in the atmosphere. No photons from above the sky get through to us almost. So now theres CO2 line, right here and also very close to an O2 absorbtion feature. A couple of small water and CO2 lines in through here and then this really big one right here is CO2. In fact, this is what I should have picked on, I should have picked on 15 microns. 15 microns, the CO2 absorption is so strong that nat a single photon gets through in a pretty wide swath. Remember that I told you that the peak of emission of the Earth is somewhere around 10 microns. So that means that most of the heat that is generated by the Earth gets to escape to space in these regions where the atmosphere is pretty transparent. When the atmosphere is not transparent, when the Earth is emitting radiation, it goes up into the atmosphere and it's absorbed in the atmosphere. So the atmosphere heats up and reheats the Earth that is the greenhouse effect. You can see why things like CO2 are important greenhouse gases. If you add more CO2 and you broaden these lines in through here. This is right where the peak of emission of the Earth's black body is and so more heat will be absorb in the atmosphere. It will have more of a greenhouse effect. This also tells you the sweet spot for observing Mars. And it's pretty obvious if you look at it, it is in through here. Mars and the Earth are peaking somewhere around these wavelengths. Mars is further away, so presumably colder. So the peak will be even a little bit past 10 microns, presumably. And this is a region where we can actually see it. So this is the region that astronomers in the 1950s decided to concentrate on to try to detect the thermal imaging from Mars. And even better, they succeeded, there's this beautiful paper by Sinton and Strong. Published in the Astrophysical Journal and it is 1960, which is an amazing thing too. Volume 131, 1960, the Astronomical Journal has been around for quite a long time. In this paper they describe their observations using the 200 inch telescope at Palomar. And I have to say, reading this paper makes me feel lazy. Astronomers today actually can do a lot of really amazing things fairly easily with a really good technology we have. Sinton and Strong to measure Mars had to build their own instrument. They have to bolt them to the back of the Palomar Observatory. They had to figure out how to calibrate them is a pretty amazing read. I recommend going and taking a look at it if you're interested in this sort of historical astronomy. But let me show you a couple of the key figures from this paper. This shows you a couple of the scans they did across the face of Mars. Their aperture, their field of view, the amount of Mars they were looking at one point in time that they're measuring the temperature of is the size of this little circle right here. And they would point the telescope at a particular spot in the sky and let Mars go past and measure at different times these different swaths across Mars. And then they did it a few times where they would manually make the telescope to a north and south to get the swaths in that direction. And they would watch the emission from that 10 micron region increase. Here is the raw plot of the emission increasing and decreasing, increasing and decreasing, increasing and decreasing. What is this telling you? It's telling you that it's hottest here at noon, noon means right down here at the center. It's hottest at noon or perhaps a little bit after noon. I say after noon because remember, Mars is rotating this way so objects that are over here have already experienced noon and that peak is after noon. Sounds a little bit Earth like. These pictures come from simultaneous photographs that were taken, so they knew where on Mars they were looking. And as far as I can tell, they were looking at the region with the sea monster and the porpoise and the sting ray. And yet we think Mars has no oceans. We took those raw measurements and converted them into actual temperatures. How did they do that? They took a plate with a controlled temperature and stuck it directly in front of the instrument and measure the thermal emission from that plate. Again, knowing that the energy emitted from the surface of Mars directly corresponds to the temperature on Mars. They could calibrate that temperature that Mars actually was. Here, they're actual data points. Look at the actual points, don't worry about the curves just yet. These are the points that I was just showing you a minute ago after they have turned them into real temperatures. Here are the real temperatures. This is 0, this is degrees Celsius, so 0 is freezing. This is noon, the coldest temperatures they measured were something like 60 degrees below 0 Celsius, that's pretty cool. Not somewhere I would really want to live. Ice temperatures were more like 20 degrees Celsius. That actually doesn't sound so bad, it's a huge variation in temperature. And the sort of variation although even more extreme of the sort that you can imagine if you are in some sort of a desert location on the aErth where you have very hot days and very cold nights. Why is it happening to desert? Well that happens in the desert because there's very little water vapor in the atmosphere in the desert to reabsorb that heat coming from the Earth at night and retransmit it back and keep the Earth warm at night. This is again, looking like Mars is quite a desert location. But it's interesting, it is at some points during the day, it is certainly warm enough that you could imagine liquid water being there. So I said, we'll worry about the curves here in the middle bit. These curves were some very simple calculations that Sinton and Strong did to sort of guess at what the temperature of Mars should be. And they got something that looks about like their measurements. In an upcoming lecture, we will actually do this in more detail and calculate our own curves of what the temperature of Mars should be and implications for things like water and frozen CO2 on the surface.
