1. INTRODUCTION Open Access

My family moved around a lot while I was growing up. My father worked as an engineer for General Electric (GE), which was at that time quite a big company. GE would get a contract somewhere and move people in, then they would lose that contract and move them out. It was almost like being in the military. I was born in Schenectady, New York, in 1953. We immediately moved to Cincinnati, Ohio, then back to Schenectady eight years later. Two years after that, when I was halfway through 5^th grade, we moved to Huntsville, Alabama. My mother, who had grown up in Milwaukee, was initially horrified. How could we be moving to the Deep South? Weren’t people down there hopelessly different from people up North? Would we really fit into Huntsville society?

Moving to Huntsville, it turns out, was the best thing that happened to any of us in my family. Years later, long after we had moved away, my mother would regularly assert that Huntsville was the nicest place she ever lived. And for me, it was a life altering experience. GE was subcontracting for NASA down there, and NASA was fully engaged in the Apollo programme to put astronauts on the Moon. Marshall Space Flight Center, just outside of Huntsville, was where they designed and tested the big rocket engines needed for that programme. First came the Saturn 1B; then, a few years later, the Saturn V (see Fig. 1.1). The Saturn V was 363 ft (111 m) high – roughly twice the height of the Space Shuttle launch system. NASA’s new Artemis rocket that will soon take astronauts back to the Moon is also shorter than this (325 ft). These Saturn rockets did not launch from Marshall; they launched from Cape Canaveral in northeast Florida. But engineers at Marshall would bolt the rockets securely to the ground, then fire the main engines for about 2–3 minutes. The test pad was only about 3 miles from downtown, so the whole town would shake when they did so. Windows occasionally shattered. The head of NASA’s Apollo programme, Wernher von Braun, would appear on the evening news and explain what had gone on that day. Von Braun and many of his team of German rocket scientists lived up on Monte Sano, just outside of town. For the most part, they kept to themselves. It was possible to live in Huntsville and never encounter them. But one could not miss the rocket testing! Huntsville was at the very forefront of the space age, and every kid who grew up there was aware of it.

We left Huntsville in 1970, before the Apollo programme had ended. (Apollo Moon missions were launched from December 1968 to December 1972.) GE had lost another contract, so my father moved on to design refrigerator shelves at GE’s Appliance Park in Louisville, Kentucky. But the memories of Huntsville and of the space programme have stuck with me for the rest of my life. One remembrance stands out: In 1967, during the preparation for the first Apollo mission, three astronauts were killed in a space capsule fire while the capsule was being tested at NASA’s Johnson Space Flight Center. That is where the astronauts did, and still do, train. This happened in Houston, not in Huntsville, but we felt the impact just the same. Two years later, three new schools opened in rapidly growing Huntsville. They were named after the three astronauts who perished in the fire: Ed White, Gus Grissom, and Roger Chaffee. Figure 1.2 shows them training just prior to the tragic accident. I attended Gus Grissom High School for one year just before we moved out of town.

The loss of these astronauts was a tragedy akin to the Space Shuttle accidents that happened decades later: the Challenger in 1986 and the Columbia in 2003. The Challenger blew up 73 seconds into its ascent when two O-rings in a joint in one of the solid booster rocket engines failed, allowing hot flames to escape and eventually ignite the hydrogen in the main fuel tank. The Columbia disintegrated during reentry when the heat shield on the left wing (which had been damaged during launch) failed catastrophically. NASA learned from all these fatal accidents, though. Before the Apollo 1 fire, NASA filled its space capsules with pure oxygen. Because air is 21 % O₂ and 78 % N₂ (and 1 % ⁴⁰Ar), and because people need only the O₂ to breathe, NASA could keep the air pressure down inside their space capsules by including only O₂, thereby placing less stress on the spacecraft hull. But the downside of doing so is that a fire, once lit, burns ferociously in pure O₂. The physics behind this observation is simple: Imagine a candle burning in normal air. The heat from the candle flame causes convection, which carries heat away from the flame, but it also brings in O₂, which helps it burn. When inert gases like N₂ and Ar make up ~80 % of the air, the cooling from convection keeps the flame under control. When the N₂ is removed, however, the flame burns faster, more O₂ is sucked in, causing the flame to burn even faster. A systems engineer, or a geoscientist working on the Earth’s climate system, would recognise that as a positive feedback loop. In the case of Apollo 1, that feedback loop proved fatal.

There is a lesson here for planets, as well, which is why I tell the story. Planets that have atmospheres containing O₂, but no noncombustible gas such as N₂, are probably not habitable. Indeed, this property has been used to estimate an approximate upper limit of 35 % for Earth’s O₂ mixing ratio during the last 400 Myr (Watson et al., 1978). (The term mixing ratio will come up frequently in this book, as it is common parlance for atmospheric chemists. Another scientific term that means the same thing is ‘mole fraction’. When I use the more common term ‘concentration’, the meaning is the same.) The more or less continuous record of charcoal deposition during that time suggests that the atmosphere contained enough O₂ to support combustion (~13 %) but not so much that the forests burned down entirely. So, N₂ is good for plants, as well as people. A biogeochemist would remind us that N₂ can also be split apart to make fixed nitrogen, which is an important nutrient. Lack of N₂ is considered to be a major impediment to terraforming Mars, as some of my NASA colleagues and I pointed out in a paper many years later (McKay et al., 1991).

Another major factor got me interested in science was reading science fiction. This may or may not have been related to living in Huntsville, but I read a lot of sci-fi in middle school and high school. My two favourite authors were Isaac Asimov and Robert Heinlein. Asimov was a bonafide genius who published over 300 books! Some of his early ones may have been his best. These included ‘The Foundation Trilogy’ and the robot series (‘I, Robot; The Caves of Steel’; ‘The Naked Sun’; etc.). ‘Foundation’ has now spawned a television series that is currently streaming on Apple TV. Warning: the TV series has been adapted quite liberally from the trilogy, so if you want to know what Asimov really wrote, be sure to read the books first! As for the robot series, who can ever forget positronic brains and the Three Laws of Robotics embedded within them.

• 1) A robot may not injure a human being, or by inaction, allow a human being to come to harm.

• 2) A robot must obey the orders given it by human beings except where such orders would conflict with the First Law.

• 3) A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.

So, by design, robots were always good. But, of course, in the stories that Asimov wrote, the robots were always doing something they should not, and the challenge was to figure out how they did so without violating the Three Laws. Asimov was quite clever, so he always had a good answer. I was reminded of these stories in July 2022 when a chess playing robot grabbed the hand of its 7 year old human opponent at a tournament in Moscow, breaking his finger. Tournament officials said the child violated safety rules by taking his turn too quickly. Evidently, Russian chess robots may need some redesign work on their non-positronic brains.

Intelligent robots, or computer systems, were also the theme in Stanley Kubrick’s classic movie, ‘2001 A Space Odyssey’, and in the Arnold Schwarzenegger film, ‘Terminator’. In these films, the robots were dangerous, or even evil. Who can forget HAL’s response to astronaut Dave Bowman in 2001 when Dave asks him to open a pod bay door: “I’m sorry, Dave, I’m afraid I can’t do that.” Or Arnold as The Terminator saying, “I’ll be back”. Robots were still in the realm of science fiction when these movies first came out, but they are now much closer to becoming reality, as evidenced by the recent explosive growth in the field of artificial intelligence, or AI. AI may be able to improve our lives in many ways, but it is also widely recognised as being potentially dangerous; indeed, the philosopher Toby Ord at the University of Oxford has identified it as a serious ‘existential risk’ that could conceivably threaten humanity’s future (Ord, 2020). I hope that AI developers have Asimov’s robot series on their required reading lists. They, if anyone, need to be aware of the Three Laws.

I also read lots of early Heinlein, e.g., ‘The Puppet Masters’, ‘The Door Into Summer’, ‘Stranger in a Strange Land’. My favourite was ‘The Door Into Summer’. The protagonist, Dan Davis, was an inventor who came up with all sorts of useful household gadgets, one of which was a vacuum sweeper that went around cleaning rooms all by itself. You can now buy one of these machines from any number of companies. In fact, my wife bought one this spring, and it can frequently be seen rolling around our house. But in 1956, when the book first came up, this was the stuff of homemaker dreams. The book takes its title from the pet cat that Davis takes with him wherever he goes. Davis’ house has seven doors, and the cat wanders from door to door during the wintertime looking for the door into summer. I’ve lived with cats most of my life, and Heinlein’s insights into feline intelligence, or lack thereof, have always struck a chord with me. Heinlein was a libertarian, and his protagonists were often young, resourceful men who succeeded against great odds. I always felt this was something to which to aspire. Heinlein’s later books, though, strayed further and further in this direction, and I don’t recommend them.

I have left out many other sci-fi authors who hooked me on science and further broadened my horizons. Frank Herbert’s ‘Dune’ is perhaps the best single sci-fi novel ever written, and there is finally a new movie series, directed by Denis Villeneuve, that captures a lot of it. Previous efforts had fallen well short. Philip K. Dick’s short story, ‘Do Androids Dream of Electric Sheep’, led to the superb sci-fi flick, ‘Blade Runner’. A. E. van Vogt wrote ‘Slan’ and ‘The Voyage of the Space Beagle’. ‘Slan’, in which a subgroup of humanity evolves tendrils and the ability to communicate telepathically, is also a good introduction to the concepts of discrimination and human diversity. ‘Space Beagle’ contained four novelettes, one of which was the apparent basis for the blockbuster, ‘Alien’, although this was contested in a lawsuit. The hero aboard the Space Beagle was not the captain nor his lieutenant, as in Star Trek, but rather the resident Nexialist, Dr. Elliot Grosvenor. Nexialists are scientists who are generalists, not specialists. They get hooked up to learning machines during their training, which allows them to absorb different disciplines while they sleep. Wouldn’t that be neat! There is a parallel here with the modern field of astrobiology, a term that encompasses many of my own scientific interests. Astrobiology is formally defined as the search for life off the Earth. In practice, it combines elements of astronomy and biology, as its name suggests, but it also draws on geosciences, planetary science, and meteorology. We work on problems that are less imperative than battling the alien, Ixtl, but we all have a little bit of Elliot Grosvenor in us as we attempt to work across multiple scientific disciplines.

I could continue in this vein, but I hope you see my point. I knew I was going to be a scientist long before I started studying science. And I was enthralled by the fabulous worlds that science fiction authors created out of thin air. As I grew older, that interest evolved into fascination with the fabulous worlds that we may one day discover around other stars, as well as our own remarkable world, Planet Earth.

I completed my senior year in high school in Louisville, Kentucky, then went on to Harvard. Once there, I started out in chemistry, then switched to chemistry and physics. I found I liked physics because one can prove mathematically that certain propositions are correct, assuming that we understand the underlying laws. I also had a wonderful introductory physics professor, Edward Purcell, who shared the Nobel Prize in Physics in 1952 for his work on Nuclear Magnetic Resonance, or NMR. The technique was renamed when it was applied to medicine, as most people did not want anything ‘nuclear’ interacting with their body. You may recognise it under its more familiar acronym, MRI, for Magnetic Resonance Imaging. My neck and right shoulder have both been surgically repaired over the years following detailed MRI scans. So, along with many others, I have personally benefited from this amazing technology, brought to us courtesy of nuclear physics.

I also found I didn’t really like chemistry labs. It wasn’t that they were particularly hard. It was more that I am just not a good ‘tinkerer’. My father was a tinkerer; my oldest son, Jeff, is also a tinkerer. I am more like my mother – better at sifting through abstract ideas than at performing hands on tasks. My mother, Martha, majored in chemistry at Wellesley, where she graduated Phi Beta Kappa. She worked for GE for a while after that, where she met my father, then took several years off to start a family. The family got off to a quick start: I have an identical twin brother, Jerry, so there were two infants to manage simultaneously. Little sister, Sandy, came along about five years later. My mom was restless staying at home, however, so by the time Sandy was in kindergarten, she was back taking math classes at University of Alabama, Huntsville. UAH had an excellent math department, partly staffed by German rocket scientists who had come to town along with von Braun. We later moved to Louisville, Kentucky, and Mom taught calculus classes at the University of Louisville for many years after that. She never got her Ph.D., though – U of L didn’t have a Ph.D. programme in mathematics, and she didn’t have the time to commute to the University of Kentucky in Lexington – so she never made it onto the tenure track faculty. She would complain about this later in life. If she had been born a generation later, I’m sure my mother would have stayed in academia and had a fruitful career in one field or another. She was very bright.

There was another reason I didn’t like chemistry labs: my 4 hr freshman chem lab on Tuesday afternoons that caused me to miss wrestling practice once every week. This didn’t matter too much to our coach, as I was only a JV wrestler. (My 4 yr suitemate, Carl Biello, by contrast, was varsity and was quite good.) But I liked wrestling because it was a sport in which someone my size – I’m about 5’6” – could compete on an equal footing. Since joining the faculty at Penn State 34 years ago, I’ve enjoyed watching the outstanding wrestlers we train right here. Penn State wrestlers have won 11 national championships in the past 14 years under head coach Cael Sanderson. Olympic hopefuls come here from all over the country to train with the Penn State Wrestling Club, which operates synergistically with the team. Kyle Snyder, the 2016 Olympic gold medalist at 97 kg, trains here even though he wrestled in college for arch-rival Ohio State.

My father, Dick, was a wrestler, too – I shouldn’t neglect to mention that. (Dad turned 101 this year and is still going strong!) Dad wrestled in college for Purdue University. Like me, he was only JV, so we are hardly a great wrestling family. But when I was in 9^th grade in Huntsville, my dad took off from work early during the winter to help the local middle school coach start a wrestling team, and he enlisted my brother and me to join it. His goal, I think, was to toughen us up. It worked. Not only do you get physically stronger from wrestling, but it also encourages you to become self reliant. When you are out there on the mat, your teammates and coaches may be cheering you on, but it is just you against an opponent whose goal is to flip you over on your back and leave you staring up at the overhead lights. Since then, I’ve always felt that any other type of pressure that I’ve faced is mild by comparison.

Two things happened to me at Harvard that influenced my later career. First, in my senior year, I took an introductory astronomy class. I should have been taking upper level chemistry or physics classes, but I had always been interested in astronomy and wanted to get some actual background in the field. That background proved to be valuable later in my career when I found myself working on direct imaging space telescopes. I will say more about them in Section 6, which is devoted to unsolved problems or, in this case, unfinished business.

I also read a book while at Harvard entitled ‘Intelligent Life in the Universe’ by I.S. Shklovskii and Carl Sagan (1966). I had pretty much given up reading science fiction in college, simply for lack of time, but I found time to read this book. Shklovskii was a prominent Russian astrophysicist who had written a book in Russian about the search for life in the cosmos. Sagan had it translated into English, then annotated it with his own thoughts. Each author’s words were printed in a different colour, so it was like following a conversation between the two of them. To me, this book was inspiring. It was one of the first books about astrobiology, although the authors did not use that term. Sagan was following up on a now famous 1961 meeting at Green Bank Radio Observatory in West Virginia in which he and Frank Drake proposed what is now often called the Drake equation. (Carl himself is said to have preferred the name, Sagan-Drake equation. I can’t remember where I heard that, but it is kind of amusing and has stuck with me.) The equation can be used to calculate the number of intelligent, communicating civilisations in the galaxy as a product of seven terms. Only the first few terms in the equation can be evaluated numerically, but it offers a useful framework for thinking about the factors that might lead to technologically advanced civilisations like our own.

I had the good fortune just a few years ago (July 2019) of attending a SETI workshop at the Green Bank Observatory. SETI, of course, stands for the Search for Extraterrestrial Intelligence. Frank Drake was there, along with Jill Tartar, who became director of the SETI Institute after Drake retired. Drake passed away in 2022 at the age of 92 – he will be missed. Tartar, who is still very much alive, is the character portrayed by Jodie Foster in the movie ‘Contact’, adapted from Sagan’s book by the same name. The original Green Bank radio telescope blew down in a windstorm in 1988, but it has been replaced by an even better one (see Fig. 1.3). It’s still the largest steerable radio telescope in the world, and part of its time is devoted to SETI searches. Be careful to bring a roadmap, though, if you decide to visit. I drove down to the meeting with a colleague from Penn State. The observatory is buried deep within the western foothills of the Appalachians in West Virginia, so one must follow several windy roads to get there. My cellphone GPS got me there with no trouble because it had downloaded the map on the way down from State College. When we left a few days later, though, the GPS map was gone. There is no cell phone service within 30–40 miles of Green Bank, because that would interfere with the radio telescope observations. So, we ended up driving way too far west before finally getting a cellphone connection that alerted us to our mistake. I’ll hopefully remember that next time I visit a radio telescope facility.

During my senior year in college, I asked friends back in Huntsville who I should attempt to study with after that. My junior and senior high school friend, Hunter Waite, had a father (Jack) who had served as a programme manager on Skylab and on Marshall Space Flight Center’s task force on Atmospheric, Magnetospheric, and Plasmas in Space. Jack was well connected with scientists in this field, and they collectively recommended Peter Banks. Peter was an ionospheric/magnetospheric physicist at the University of California, San Diego. UCSD, as it is called, is actually located in La Jolla, just north of San Diego proper. It’s an idyllic location, replete with beautiful beaches, including Black’s Beach where people can sunbathe in the nude. That beach was mostly populated by older people, along with a few tattooed sailors from the naval base down in the city, so there was really not much to see on the beach itself. I loved to watch the hangliders, though, taking off from the 300 ft cliff right behind it. They could soar back and forth all day long, taking advantage of the lift generated when the daytime sea breeze hits the cliffs and is forced upwards. Don’t try this, though, unless you know what you are doing. An expert pilot’s license is required to launch from there, as the consequences of a miscalculation could be catastrophic.

On my first day of school in the fall of 1975, I walked into Peter’s office, and he relayed some bad news. His department, which was part of the School of Applied Physics and Information Science, was going to be shut down at the end of the year. Evidently, it overlapped too much with the Colleges of Science and Engineering, and the university was trying to cut costs. Peter would land on his feet, though, as he had already accepted a position at Utah State University in Logan, Utah.

Peter was still around that academic year, and we developed a good relationship. We were both former tennis players – me at the high school level and Peter at the college level at Stanford. I actually won a set off Peter, I think, the first time we played, as he was out of practice. My initial success didn’t last long, though. After a time or two out, Peter started to regain his old form, and I found myself entirely outclassed.

Peter didn’t know exactly what to do with me scientifically, as I was just a first year student learning the ropes. I certainly didn’t know enough physics to help him with what he did. He had a sabbatical visitor from University of Michigan, though, Paul Hays, who was working in his lab. Paul was the principal investigator for an instrument called the Visual Aurora Experiment (VAE) on a satellite called Atmospheric Explorer that was performing a multi-year survey of Earth’s ionosphere. So, Peter assigned me to work with Paul analysing VAE data. The scientific paper that came out of that collaboration, my first, was a comparison between auroral emissions observed by VAE and precipitating electrons observed by another instrument on the satellite.

At the end of that academic year, I was offered an opportunity to stay at UCSD and transfer to the Physics department. However, the work would not have been NASA-related, and I wanted to stay in the general field of space science. So, I followed Paul back to Michigan – not so much because I was enamoured of working on ionospheric data but, rather, because I thought that the social life would be better in Ann Arbor than in Logan, which is located in a dry county. These days, I would probably choose Logan, as I understand it is beautiful out there, and my goals for social interaction are more limited.

Besides learning more math and physics at UCSD, I also had the good fortune of taking a class from the radio astronomer, Jules Fejer. His class was largely about plasma physics – a subject that was interesting but that I would never come close to mastering. Fejer was a generalist, though, so he allowed us to do a term paper on a topic of our own choice. I wrote mine on the rise of oxygen in Earth’s atmosphere. I can’t remember exactly how I stumbled onto the topic, nor can I locate the paper itself. But I remember the general gist of it. I had come across papers on the rise of O₂ by Lloyd Berkner and L.C. Marshall. Berkner was a famous ionospheric physicist and engineer who had done ground breaking research on the nature of Earth’s ionosphere (see, e.g., Berkner and Wells, 1934). Professor Fejer presumably knew of his work, so that may be how I learned about him.

Berkner later got interested in planetary and atmospheric evolution. He and Marshall wrote a series of papers (Berkner and Marshall, 1964, 1965a,b, 1966) that focused on the history of atmospheric oxygen. They were particularly interested in prebiotic O₂ levels, as that is something that atmospheric scientists ought to be able to compute. Berkner and Marshall were aware that O₂ can be produced when water vapour (H₂O) is photolysed by solar ultraviolet radiation. The reaction sequence (one of several, actually) is;

The O₂ accumulates in the atmosphere while some of the H atoms escape to space. Berkner and Marshall did not worry too much about hydrogen escape, even though that factor turns out to be critical, as discussed later in this section. But they realised that O₂ can shield H₂O from photolysis, as O₂ absorbs UV radiation strongly out to ~240 nm, whereas the effective H₂O cutoff is below 220 nm. (See Fig. 1.4, which is an updated version of one of their figures.) This shielding works effectively because most H₂O is concentrated in the troposphere, while O₂ (in their model, at least) was distributed throughout the atmosphere. Their hypothesis, then, was that O₂ should have accumulated in the prebiotic atmosphere until its concentration became high enough to shield H₂O from photolysis. Going through the relevant atmospheric physics, they calculated that O₂ should have accumulated to a level of between 10^-4 and 10^-3 PAL (see Fig. 1.5). Here, ‘PAL’ stands for ‘times the Present Atmospheric Level’. The present atmosphere has a surface pressure of about 1 bar and an O₂ mixing ratio of 21 % by volume, so this amounts to (2-20) × 10^-5 bar. I will argue in the next section that this value is not only much too high but is also misleading because O₂ should not have been well mixed. It sounded pretty good when I first read it, though, and these papers got me started working on a problem that has remained near and dear to me throughout my career.

Figure 1.5 shows Berkner and Marshall’s postulated evolution of atmospheric O₂ up to the present day. They were aware of pioneering work on this topic by Alexander MacGregor (1927, 1940), Dick Holland (1962, 1964), and Preston Cloud (1965). The existence of a Great Oxidation Event, or GOE, at ~2.4 Ga had not yet been proposed. (‘Ga’ stands for ‘Giga-aeons’, meaning billions of years before present.) That, as we will we see later, is now viewed as the initial rise of atmospheric O₂. They were also aware of the so-called Pasteur point at ~0.01 PAL of O₂. This is the oxygen level at which some facultative anaerobes (e.g., yeast) switch from fermentation to respiration as a metabolic energy source. (The term ‘facultative’ means that they can live either aerobically, using O₂, or anaerobically.) Berkner and Marshall associated this O₂ level with the Cambrian explosion at 543 Ma (Mega-aeons), when shelly animal fossils first appear in the geologic record. They proposed that a second critical level of 0.1 PAL O₂ was reached in the Late Silurian, about 400 Ma, when vascular plants made their first appearance on land. Berkner and Marshall associated this evolutionary event with the rise of atmospheric ozone and the development of an effective screen against solar UV radiation. Although neither of these O₂ critical levels are accepted by modern geobiologists, I was impressed with both their logic and their attempt to link atmospheric science with biological evolution. Indeed, I have spent a good portion of my own career trying to do just that.

So it was that I followed Paul Hays back to Ann Arbor when he returned there at the end of the spring term. But I did not follow him into ionospheric physics. Paul was an instrument designer and a data gatherer, and he was very good at what he did. I was already realising that I was more of a theoretician, and I had gotten interested in the rise of oxygen before even arriving at the U of M. It turned out that what Paul really needed to complement his satellite measurements of the aurorae were observations made looking upwards from Earth’s surface. In particular, he needed someone who was willing to be a scientific crew member on an icebreaker ship whose mission was to allow itself to be locked into the sea ice pack somewhere in the far north Atlantic and rotate underneath the aurorae for three months during the polar night. As I have said, part of my reason for going to Michigan was to have a social life, so this offer did not sound that attractive. Fortunately, Paul found another graduate student in our department who was better suited to this task, and together they made excellent progress in understanding the causes of the aurorae.

Already during my first year at Michigan, 1976–77, I was fixated on the problem of the rise of O₂. Before we parted ways scientifically, Paul did me a huge favour by introducing me to Jim Walker. Jim was a fellow ionospheric physicist who was working at the time at the Arecibo Radio Observatory in Puerto Rico. Arecibo, for those who don’t know about it, was for many years the largest radio telescope in the world. It was not steerable like the Green Bank telescope. Instead, its 305 m dish was dug into a sinkhole in the karst terrain of Puerto Rico. I visited there twice in the early 2000’s, so I saw the telescope while it was still operative. The telescope suffered irreparable damage during Hurricane Maria in 2017 when a cable became unhooked and its 900 ton science platform fell 450 feet onto the radio dish. Even if you were not privileged to see this telescope in person, you may have seen it in the movies, as it was featured both in the James Bond flick GoldenEye and in the movie Contact, mentioned earlier. The scene in GoldenEye was particularly memorable because the dish is (apparently) filled with water and looks like a lake when it is first seen. The water then drains out, revealing the huge dish, which was supposedly being used as an anti-satellite weapon in the movie. Bond and the villain, Secret Agent 006, fight it out on the telescope receiver, with Bond winning the battle and Agent 006 falling to his death just as the entire facility explodes. Bond is helicoptered out just in time by his current love interest, Natalya. As you can see, I never really lost my interest in science fiction, and I haven’t missed many James Bond movies, either.

Back to real science. As I mentioned earlier, I had become interested in the history of atmospheric O₂ from reading papers by Berkner and Marshall. This was an atmospheric science problem but working on it also required understanding something about Earth’s long term history, and this in turn required learning some geology. My knowledge of geologic history was poor, as I had never taken a geology class in my life. So, I xeroxed a copy of the geologic time scale and taped it on the wall above my office desk, as a start towards learning this new field. I contacted Jim Walker and explained what I wanted to do, which was to test Berkner and Marshall’s ideas about prebiotic O₂ levels using an up to date photochemical model. In response, Jim sent me an advance copy – a typewritten manuscript – of his book, ‘Evolution of the Atmosphere’, which was scheduled to come out later in 1977 (Walker, 1977). This book was a goldmine of ideas, which provided the basis for my Ph.D. thesis, as well as introducing related scientific problems that have occupied me during much of my career.

Like Berkner and Marshall, Walker was an ionospheric physicist who had become interested in Earth history, particularly the rise of atmospheric O₂. Walker had the advantage of coming to this topic a decade or more later than Berkner and Marshall. During the interim, Don Hunten had published two landmark papers dealing with the escape of hydrogen from planetary atmospheres (Hunten, 1973a,b). The first paper dealt with hydrogen escape from Saturn’s moon, Titan. Titan has a cold, dense, N₂-CH₄ atmosphere. The CH₄ is continually broken apart by solar UV radiation and charged particles precipitating from Saturn’s magnetosphere. Molecular hydrogen, H₂, is formed by this process. Because hydrogen is light and Titan’s gravity is small, H₂ escapes to space despite the cold temperatures. Indeed, Hunten demonstrated that, because escape from the top of Titan’s atmosphere is relatively easy, the escape rate is limited by the rate of upward diffusion of H₂ through Titan’s homopause. (The homopause is the altitude at which the vertical ‘eddy’ diffusion coefficient is equal to the molecular diffusion coefficient. Eddy diffusion is how aeronomers – researchers who study planetary upper atmospheres – parameterise various forms of vertical atmospheric transport.) Hunten called this diffusion limited escape rate the limiting flux, and that term remains in common usage.

In a second paper, Hunten (1973b) applied this limiting flux concept to other planetary atmospheres, including Earth’s. On Earth, the problem is more complicated because hydrogen is present in several different chemical forms. Figure 1.6 shows how the chemical form of hydrogen changes as one goes up in the atmosphere. Near the top of the troposphere, around 10 km at mid-latitudes, most of Earth’s hydrogen is in the form of H₂O and CH₄. Their mixing ratios are approximately 3–5 ppmv and 1.6 ppmv, respectively. Above this level (in the lower stratosphere), CH₄ is oxidised to CO₂ + 2 H₂O. At still higher altitudes, H₂O is photolysed, producing H₂ and H. But because hydrogen itself is neither created nor lost, the total hydrogen mixing ratio, f_T(H) is conserved. Here

i.e. it is the sum of the mixing ratios of all hydrogen containing species, weighted by the number of H atoms they contain. The diffusion limited flux may then be written (approximately) as

Here, b_i (= D_i/n) is the molecular diffusion coefficient of hydrogen at the homopause, D_i (weighted between H and H₂) divided by the total number density at that altitude, n. Using the higher value of 5 ppmv for the H₂O mixing ratio at the tropopause, the escape rate comes out to be ~4 × 10⁸ molecules cm^-2s^-1 – a value that agrees well with observations. Total hydrogen is not conserved in the troposphere because H₂O rains out, causing f_T(H) to decrease rapidly with altitude.

Why is all this important? Remember that oxygen is produced when H₂O is photolysed and H escapes to space (reactions in Eq. 1.1). Berkner and Marshall totally neglected hydrogen escape in their papers. A later study by Brinkmann (1969) did consider hydrogen escape, along with consumption of O₂ by crustal weathering. But Brinkmann assumed that precisely one half of the H atoms produced by H₂O photolysis escaped to space. Using this assumption, he concluded that Earth’s O₂ level could have been >0.25 PAL over 99 % of geologic time. He pointed out, rather proudly, that this was over 250 times the upper limit predicted by Berkner and Marshall.

Jim Walker knew better because he had read Hunten’s papers and knew how to estimate the escape rate of hydrogen. He also assumed, correctly, that at low pO₂ the dominant sink for O₂ would be reaction with reduced volcanic gases, not crustal oxidation. Walker had read papers on volcanic outgassing by Dick Holland and others, so he knew how to estimate the reduced gas sink. Holland (1964) did this by using estimates for the modern outgassing rates of H₂O and CO₂ and then assuming thermodynamic equilibrium at 1200 ^oC (the approximate temperature of molten lava) to deduce outgassing rates for H₂ and CO. For H₂O, the relevant reaction is

From this reaction, one can easily show that

Here, pH₂ and pH₂O are the partial pressures of the two gases, K_eq is the equilibrium constant, and fO₂ is the oxygen fugacity, which is determined by the oxidation state of the magma from which the gases are released. For those not familiar with the term ‘fugacity’, one may think of it as the effective O₂ partial pressure in equilibrium with a mineral assemblage or with a collection of such assemblages that are found within a rock. Both Holland and Walker knew that Earth’s upper mantle today has an oxygen fugacity near the quartz-fayalite-magnetite (QFM; SiO₂-Fe₂SiO₄-Fe₃O₄) buffer, so pH₂/pH₂O ≅ 0.01. Unlike Holland, Walker assumed that the mantle fO₂ has always been near its present value. Holland, by contrast, had assumed that metallic iron was present in the upper mantle for the first ~500 Myr of Earth’s history, prior to core formation. (Researchers at that time thought that Earth accreted from small planetesimals and that its interior remained cool until it was warmed by heat released from radioactive decay.) If so, the mantle fO₂ should have been close to the iron-wüstite (IW; Fe-FeO) buffer, which at high temperatures is about 4 log units below QFM. The ratio, pH₂/pH₂O, is closer to 0.5 at this value of fO₂. We now think (see, e.g., Stevenson, 1983) that the accretion process involved very large planetesimals. Thus, Earth’s interior was initially hot, the core formed simultaneously with the planet, and metallic iron would have been absent from the mantle once the main accretion period ended. Walker did not yet know this, but he assumed that Earth accreted inhomogeneously, with metallic iron coming in early and more oxidised material being added later. The ‘true’ (or at least current) story is more complicated, as the mantle probably was more reduced during the main accretion period, but it self oxidised as a consequence of ferrous iron disproportionation in the lower mantle, followed by segregation of metallic iron into the core (Wade and Wood, 2005; Frost and McCammon, 2008). One can write this chemically as: 3 FeO ➝ Fe₂O₃ + Fe. Here, FeO represents ferrous iron (Fe⁺²), Fe₂O₃ represents ferric iron (Fe⁺³), and Fe represents elemental, or metallic, iron (Fe⁰). In the mantle, ferrous and ferric iron are included within more complicated iron bearing minerals. Hydrogen escape may have played a role, as well, as we shall see in Section 3. So, Walker may have made the right assumption for the wrong reason, but this does not invalidate his calculation.

In any case, Walker put all of these thoughts together in his book. He outlined some atmospheric chemistry that included the O₂ formation reaction sequence shown in Eqs. 1.1., along with a catalytic reaction sequence that would have destroyed O₂.

The H and OH radicals in this reaction sequence come from photolysis of water vapour. The H₂ concentration, f(H₂) = 10^-3, comes from balancing the outgassing flux of H₂ from volcanoes with the diffusion-limited H₂ escape rate calculated from Eq. 1.3. Using this chemistry, along with an (admittedly crude) estimate for the rate of H₂O photolysis, Walker calculated a tropospheric average O₂ number density of ~2 × 10⁴ cm^-3. (Here, I have omitted ‘molecules’ from the units, following standard atmospheric chemistry nomenclature.) The present ground level O₂ number density is about 5.7 × 10¹⁸ cm^-3, so this amounts to less than 10^-14 PAL. Evidently, all previous authors had overestimated the amount of abiotically produced O₂ by a factor of 10¹⁰, or more. We shall see in the next section that Walker’s result is essentially correct, even when more elaborate models are used to calculate O₂. If the early mantle was more reduced than today, then the H₂ content of the atmosphere would have been higher than he assumed, and the predicted prebiotic O₂ concentration would have been even lower.

I was aware of all this thinking about abiotic O₂ levels, or at least learning about it, as I was working on my Ph.D. thesis at Michigan. Since Walker seemed to have solved the problem, you might ask what remained for me to do. My answer would be that Walker’s calculation was essentially a BOTEC (back of the envelope calculation). Walker himself realised that the O₂ concentration should vary with altitude and that one could do this calculation more accurately with an atmospheric photochemical model designed to capture that variation. That was my goal for my thesis. I was again fortunate to find someone (two researchers, actually) at Michigan who could help me with that problem. The first was my next, and thankfully final, Ph.D. advisor, Tom Donahue. Donahue was a widely respected upper atmosphere researcher whose interests extended to planetary atmospheres. At the time, he was a team member on the Voyager missions to the outer planets. He had funding for students to work on those data, but he was also willing and able to support my project. Even more importantly, he had a research associate, Shaw Liu, who had such a 1-D photochemical model. Such models are termed ‘one dimensional’, or 1-D, because they resolve the vertical structure of the atmosphere, while averaging over the horizontal variations. Shaw Liu had developed his model from scratch, and he and Donahue were using it to test Hunten’s theories of diffusion-limited hydrogen escape from Earth’s atmosphere, described earlier (Liu and Donahue, 1974a,b,c).

My story about the rise of atmospheric O₂ continues from here, but I will defer the rest of it to the next two sections because this is where I started working on the problem myself, rather than just learning about it from others.