Whats up universe? This is Mike, the other Mike, the third and final graduate student TA for the science of the solar system. One of my primary research interests is Titan, Saturn's largest moon. Which you've already been introduced to by Professor Brown. Titan's really interesting to me because it's one of the most similar objects in the solar system to Earth. Both Titan and Earth share many characteristics, their surfaces are sculpted by wind and rain, volcanism and tectonics. And they both have relatively young and dynamic surfaces. Titan is the only celestial body known to have stable seas of liquid on it's surface. And it is sheathed by the only other thick, nitrogen dominated atmosphere in the solar system. By all accounts, Titan is an active place, though not as quite active as Earth. On Earth, we have a biological factor, you and me, that is capable of and does influence wide scale climate change. For the past few decades indeed, the hottest topic in Earth science has been that of anthropogenic climate change or usually known as global warming. But despite all of our efforts to induce this global warming, we can perhaps take a smidgen of solace in the fact that we will never be able to influence Earth's climate in as a dramatic way as other natural forces. One of the main causes for Earth's climate variation, is its ever revolving dance around the sun. Earlier in this course we've been introduced to the Milankovitch cycles and how changes in the Earth's eccentricity and axial tilt and orbital parameters like that can have influence on Earth's climate in the long term over tens of thousands and hundreds of thousands of years. But a much quicker, and much more familiar, kind of climate variation is that of seasons. And seasons occur simply because the earth has an axial tilt or an obliquity. Basically that's defined as the angle between the earth's spin axis and the normal vector to its orbital plane around the sun. Now Earth has an obliquity or axial tilt of about 23.4 degrees. Saturn has an axial tilt something very similar, 26.7 degrees. Now, Titan, moon of Saturn, which is going around Saturn has an obliquity with respect to its orbit around Saturn of zero. So it inherits its obliquity with respect to the orbit around the sun, so the result of an axial tilt is time varying differential heating across a planets surface. So in this case we have Titan, you see in southern winter here or in northern summer the solar light is more direct over the northern hemisphere and less direct over the southern hemisphere. At equinox both hemispheres receive the same amount of solar light or insolation, not to be confused with insulation. And in the southern summer the southern hemisphere's bathed with much more direct sunlight than in the north. Because warm air rises, and cold air sinks, this differential heating creates wind patterns, namely a circulation cell. So in southern summer, this hot region will begin to advect wind upwards and will travel to the cold northern winter hemisphere. So you can think of an atmosphere as basically a dump truck, it's a thing that distributes energy from a place with excess energy to a place with a deficiency in energy. Now Titan rotates on is axis slower than Earth does, Titan rotates once every 16 Earth days. Rotation is important to circulation patterns, because it determines the Coriolis force, which is parameterized by the Coriolis parameter. So the Coriolis parameter I've defined as f = 2 times the rotation rate multiplied by the sine of the latitude, the location you are on the planet. The rotation rate omega equals 2 pi radians divided by the rotation period, which I have denoted as T here. The rotation period would be 24 hours for a planet like Earth, and 16 days for a planet or a moon like Titan. So this Coriolis effect deflects north and south moving air, these rising and sinking circulation cells to either the east or the west. Now on Titan, which has a long rotation period or a slow rotation rate, the Coriolis parameter is small so the Coriolis effect is minimal. Circulation between the two hemispheres can reach from pole to pole without ever being deflected in the east west direction. But on Earth, which rotate a lot faster, the Coriolis effect is larger. The Coriolis parameter is also larger and so the Coriolis effect is able to deflect the north and south bound winds in east, west direction. And so these winds are deflected and they start to cool down and sink before they make it from pole to pole or from equator to pole. And so as a result Earth has six circulation cells, three in each hemisphere. And you'll see an image like this in any elementary Earth science text book. Now for one more point of comparison, let's look at Jupiter, Jupiter rotates once every nine hours, its super-fast. And as a result, no circulation cell has any chance of making it from one pole to the other, it gets deflected far to wildly and they sink and create a myriad of circulations cells that result in the many bands, you see in Jupiter’s atmosphere. Now on Titan, we can observe the effect of this pole to pole circulation through various tracer molecules. When exposed to sunlight, methane, CH4, is broken down and the pieces recombine into higher order hydrocarbons, C2H2, C2H4, C2H6, so on. During southern summer, for instance, the strong sunlight in the southern hemisphere creates more photo products. Without wind, you would expect that the concentration of higher order, hydrocarbons and nitriles would be the greatest in the southern hemisphere during southern summer. And decrease as it move northward, however, this pole to pole circulation that Titan has, moves the hydrocarbons from their provenance in the southern hemisphere towards the north. And we can observe this effect, here is data from the Cassini mission, which is currently active in the Saturn system, and Voyager's encounter with Saturn and Titan in 1980. So these plots show the volume mixing ratios, or concentrations for various species in Titan's atmosphere, with respect to latitude. So positive 90 degrees would be the north pole, and negative 90 degrees would be the south pole. Now these Cassini measurements come during the southern summertime, the Voyager measurements are closer to vernal equinox, or spring equinox, but they still show the effects of the summer circulation cell. So as you can see almost every single species on these plots have increasing trend towards the northern hemisphere. So they're the smallest where they're actually produced in the southern hemisphere and they increase towards the northern hemisphere where they're not preferentially produced. And this is all because of the wind, so we can gain a better, more exact understand of what is happening in a planet's atmosphere. Titan's atmosphere in particular through the art of photochemical modeling. The point of photochemical modeling is to simulate the composition of a planet's atmosphere by applying the fundamentals of physics and chemistry to a very complex system. And so most photochemical models are done using computers, all photochemical models work this way. You start out with a best guess, an educated guess, an initial atmosphere. You give it a temperature profile, a pressure profile, and some initial chemical abundances. Then you throw it all in your box, how do they interact with each other? Well you need to know the reaction rate coefficients that are empirically derived in labs. Photolysis cross sections that's how your molecules will interact with sunlight and the energy deposition. How much sunlight, how much of other energetic particles that could potentially destroy your molecules are incoming in your atmosphere. That's really all you need, and after that, you sit back, relax, and let physics and chemistry take over. So we move to step two, the model calculations, this is where the physics and chemistry really take hold. This equation here has d number of X by dt, this is a derivative. In words all it means is the change in number of molecules of a certain species X over an infinitesimal time dt. And so the change in abundance of any molecule will be equal to it's chemical production, so minus its chemical loss plus any transport between adjacent grid boxes of your atmosphere. So certain chemical reactions will produce the molecule you're interested in, X. Certain chemical reactions will take X and break it down or turn it into something else. And then, there's this transport term, and what goes in the transport term? Well, there are two major contributors, one is diffusion, and diffusion works like this. If you have an overabundance of molecules in a certain grid box of yours. Given enough time they will random walk themselves, because they have thermal energy and they're influenced by small eddies, into the adjacent grid boxes. So over time your molecules will spread out like this and like that. Until, this is diffusion, this is how diffusion works, the other mode of transport, of course, is the wind. And so if you have a certain wind pattern, for instance, a pole to pole circulation like on Titan, the wind will add vect or basically carry a bulk chunk of air and have it circulate around the planet following the wind. So the winds will carry your molecules from grid box to grid box. And this is really all there is to it, in a photochemical model. You've got chemistry, you've got physics, and you can simulate what's going on in your atmosphere, and what's in your atmosphere, what's produced and what's lost, and if you run your photochemical model for a sufficient amount of time, your abundances should reach a sort of equilibrium value. And that's your answer, that's what's in the atmosphere, so you end up getting abundance profiles for chemical species in your model and you want to compare this to observations. If your model's results match observations of a planet's atmosphere then you can pretty confidently say you've captured all the inner workings of this atmosphere. If your model results don't compare very well to the actual abundances in the planet's atmosphere, then you have to go back and tweak your model. Maybe your temperature was too hot, maybe your winds were to strong. Maybe you started off with wild initial chemical abundances, something like that. So you've got to go and fix something and learn more about exactly what is going on in your atmosphere. We're almost done here but let me show you how a photochemical model can be used to give us insight into a past climate state of Titan. And by doing so I'll hopefully tie everything we've learned together. So we started talking about climate change in this lecture, and seasonal cycles are one extremely short term and subtle climate variation. Milankovitch cycles are a longer term and more dramatic climate variation, they've caused earth to undergo several ice ages in the past. And global warming is of course a man mad climate change that could dramatically alter our way of life. Yet I believe Titan's atmosphere may have undergone something far more drastic than anything Earth has ever experienced, here's why. So nothing is destroyed at a staggering rate on Titan without resupply. The present abundance of methane in the atmosphere of Titan should be irreversibly destroyed by photolysis by UV light from the sun. And converted into higher order hydrocarbons within a few tens of millions of years. Now, that may seem like eternity to human lifespans but geologically speaking compared to the 4.5 billion years of solar system evolution, that's merely the blink of an eye. It Titan's atmosphere somehow sustained its present amount of methane throughout it's 4 billion year history. One would expect to find a huge global ocean of hydrocarbons on Titan, a global ocean. Maybe a kilometer deep, covering the entire surface of Titan. This global ocean would serve to resupply the atmospheric methane throughout the billions of years and also be a catchment for all of the photoproducts of the intense photochemistry going on on Titan right now that would've been sustained for billions of years. But when Cassini arrived on Titan, we found something different on the surface. We didn't find the entire surface completely covered in a global ocean. We found, yes, lakes and seas, but nothing compared to the global ocean we anticipated. This suggests that most of the time, Titan might've existed without a lot of methane in its atmosphere. Furthermore, Titan's atmosphere might return to such a methane depleted state in the future. Where did all of Titan's current atmospheric methane come from? Well, the jury's still out, it's an unsolved problem, but one of the leading hypotheses is that it is periodically injected into Titan's atmosphere from the interior. The abundance or presence of atmospheric methane has a huge implication on Titan's climate. Recall that methane is one of the root molecules in all of Titan's photochemistry. This wild web of photochemistry that is actually simplified in this figure here from Atreya et al. All starts with the photolysis of methane on one side and molecular nitrogen on the other side. But without methane all of this stuff, really, disappears, the haze that shields Titan from our eyes would be gone. And the ability for Titan's atmosphere to be warm and puffy would be profoundly diminished. Also it would make Titan not such a good hiding place, okay, so as part of my research, I ran a photochemical model to simulate an ancient Titan atmosphere with less methane, and see what happens. So what changes between a normal Titan photochemical model and a photochemical model of this ancient atmosphere, well two things change only. First of all is your temperature, it's a colder atmosphere so you have to reduce the temperature. And also the initial chemical abundance of methane is going to be less, much more depleted. Everything else really just stays the same, your reaction rates, all the physics and chemistry that goes on in here, completely the same. It has to be the same or else, we have a pretty big problem on our hands. What do we find when we run our photochemical model of ancient Titan? Well, we can look at the downward carbon mass flux or basically, the stuff that is raining down from the atmosphere, raining or snowing down from Titan's atmosphere. And we have a pie chart here for the present day Titan with a break down of its constituents, and another pie chart representing the stuff raining down out of ancient Titan's atmosphere. I want you to notice to notice two things, one is that present-day Titan's pie chart is about ten times bigger than ancient Titan. That's because more stuff is being produced and more stuff is coming down simply because there's more methane in the atmosphere. But also look at the ratio between orange which denotes hydrocarbons, molecules made up of Cs and Hs only. And the green stuff, which are nitriles, molecules that contain the CN group. In present-day Titan, hydrocarbons dominate almost all the photochemistry, and are responsible for basically everything that is coming down out of Titan's atmosphere. On this ancient Titan, which we've modeled, there's a much greater abundance of nitriles. In fact, nitriles produce 75% of the downward carbon mass flux. Why is this the case? Well basically imagine you are a methane molecule and you're photodissociated in Titan's atmosphere. And you want to buddy up with something, one of your bonds has been broken, and you want to go and bond with something else. On present day time, there's plenty other methane radicals to connect with and buddy up with. But on ancient time, because the amount of methane is severely depleted, you're much more likely to go and react with a nitrogen atom. And nitrogen is, of course, the most abandoned molecule on Titan's atmosphere. So this offers us a testable production. If future missions and studies find that the ratio of nitriles to hydrocarbons on Titan's surface is similar to the pie chart on the right here, of ancient Titan, then this is another strong indication that Titan existed throughout most of its history with less methane in its atmosphere than at present. So I hope you've learned something about Titan today. I hope you've learned that climates do in fact change, on both short and long time scales, in both subtle and profound ways. I hope you've learned the basics of photochemical modeling, and how it helps us understand the processes that go on in planetary atmospheres, thank you.
