Wednesday, June 19, 2013

Everything is Solar (or stellar!) Powered*

Everything around that moves, emits light or sound, or generates heat is, in some fashion, solar powered. This includes all machines, electronics, industrial process, the entire biosphere, and all the weather on the planet.

Do you believe me?

Let’s back up a bit. I suppose the first thing we think of when we hear “power” or “energy” is the generation of electricity. The direct production of electricity from solar photovoltaic panels is a small contributor to the worldwide energy mix, so I’m not going to discuss it in detail.

Human civilization is primarily dependent on the use of fossil fuels like coal and oil to run our cars and power plants. But what are fossil fuels and where do they come from?

Fossil Fuels Are Ancient Reservoirs of Solar Power

As the name suggests, fossil fuels are the remains of ancient organisms. These remains primarily consist of organic matter (carbon-rich matter) that has been altered by extremes of heat and pressure following burial in oxygen-poor conditions. Carbon in the form of organics is relatively rare on Earth (actually carbon itself is pretty rare – see chemical composition of the Earth). Mostly carbon is in the form of carbon dioxide – and most of that is locked up in oceanic and continental rocks.

Organic matter, as the utility of fossil fuels illustrates, contains a lot of available energy. Energy is liberated when a catalyst is used to break molecular bonds. New bonds are formed, producing different molecules (with a lower energy state). Forming these new bonds produces energy. An illustration of this is the combustion reaction that powers most automobiles, where gasoline is combined with atmospheric oxygen to produce water, carbon dioxide, and heat. The heat causes gas to expand and moves a piston, which produces useful work and drives the engine. A similar reaction is aerobic respiration, where your body combines organic compounds from your food with oxygen to produce water, CO2, and energy (which is used to generated ATP). Respiration is, in fact, a combustion reaction.

What does this have to do with solar power? Well, something had to create those organic compounds in the first place. Energy-rich matter doesn’t just fall from the sky (well it does, but not at a high rate!).  That thing is photosynthesis.

Photosynthesis is the process of generating organic matter using carbon dioxide, solar energy (consisting of photons), and a source of electrons. Almost all photosynthesis on the modern Earth proceeds with water as the electron source (or “reductant”). This is known as oxygenic photosynthesis oxygen is a waste product of the reaction.

Photosynthesis allows an organism to achieve a chemical reaction that would not be spontaneous in the absence of biological mediation. The Sun provides a source of “free energy” that allows this reaction to proceed. Organisms can then use this material to build their bodies or recombine the organic material with oxygen to yield energy.

Most of the dead organisms that, after millions of years of geological and geochemical alteration, became fossil fuels were photosynthesizers. Even if they weren’t photosynthesizers, they ultimately got their organic fuel from photosynthesizers. So fossil fuels are really an enormous time-integrated reservoir of biologically produced solar energy.

(There is an obvious tie in here with the release of carbon dioxide from fossil fuels and the anthropogenic climate change we are now experiencing. The carbon that constitutes the fossil fuels we burn ultimately came from the atmosphere, but was sequestered into the ground over the course of hundreds of millions of years. We are releasing substantial fractions of that global reservoir in timespans measured in decades – hundreds of thousands of times faster.)

What about wind, hydro, geothermal, etc.?

Wind power refers to the collection of energy from turbines that convert the mechanical energy from the movement of the air into electric energy with the use of an electric motor. But where does the mechanical energy of air come from? Wind is a consequence of differences in atmospheric pressure between two places. Air will move from areas of high pressure to areas of low pressure in order to reach equilibrium. The pressure differences themselves arise primarily from differences in solar insolation (air expands when heated thus causing higher pressure). On a global scale, the difference in insolation between the poles and the equator is the major factor driving large-scale winds. Therefore the Sun is the source of energy input to winds. This is true on both a global and local scale.

Hydroelectric power is obtained from moving water in much the same way that wind power is extracted from moving air. Water moving down an elevation gradient (from a reservoir to an outflow) has gravitational potential energy that is converted to electricity by moving through a turbine. It’s obvious that the renewable nature of hydroelectric power is predicated on the replenishment of the reservoir with more water and that is achieved ultimately by rainfall. Rainfall is part of the hydrological cycle, which depends on the Sun for evaporation. The Sun provides the energy for evaporation into the atmosphere, allowing rain to fall on high elevation areas, which then drains into hydroelectric reservoirs.

Geothermal power is a bit harder to tie to the Sun. The major contributors to the internal energy of the Earth are the decay of radioactive isotopes and the initial heat of formation. It turns out that all radioactive isotopes such as thorium, uranium, and potassium-40 were forged in the crucible of massive dying stars, the type II supernovae. These isotopes can only be formed with massive fluxes of neutrons only achievable by a supernova explosion. Thus, nuclear decay and fission power is really the release of small portions of energy temporarily stored in unstable atomic nuclei by billions-year-old supernova explosions (like little atomic batteries). Clearly this is stellar power if not Solar. The energy of formation is accounted for by the gravitational potential energy that was converted into kinetic energy (heat) billions of years ago as smaller bodies were drawn to our nascent world’s gravitational pull.  Of course, the formation of the Earth and the other planets in the Solar System cannot be separated from the same process that formed our Sun. Both are the results of the collapse of a massive molecular cloud (perhaps spurred by a local supernova), but since the Sun contains 99.99% of the mass of the Solar System, the planets can really be thought of as associated byproducts of the Sun’s formation.  Perhaps geothermal power is better describes as “stellar-associated” power.

I heard there’s life not dependent on the Sun. Is that true?

Kind of, but this has been very exaggerated. Life that uses chemical redox gradients for energy (a very small part of the biosphere, but interesting for many reasons) is often heralded as a type of life that is independent of the Sun. A redox gradient is an area where chemicals with different oxidation states meet and can release energy. We have to be very careful to exclude redox gradients that are indirect result of the Sun, however, such as chemical gradients that result from photolysis, weathering, or the hydrological cycle. Also, any organism that uses oxygen is dependent on the Sun, as all free oxygen results from oxygenic photosynthesis. The claim that the entire ecosystems surrounding deep-sea vents are independent of the Sun is demonstrably incorrect, as the animals there require oxygen for respiration. (Let’s also ignore that these ocean depths would freeze if not for the heat from the Sun). There are microorganisms at the Lost City hydrothermal vents that get their energy from serpentinisation reactions that could occur in the subsurface of extraterrestrial locales such as Mars. The chemical energy that isn’t directly or indirectly created by the Sun was ultimately created by the nucleosynthesis of evolved stars, so you really can’t escape the dependence on stellar processes.

That was certainly a lot of information. I hope I’ve done a good job tying the role of the Sun and stars in general into many disparate processes that aren’t normally associated with them. The Universe is actually a vastly interconnected web of physics and chemistry, so nothing really exists in isolation.

*The biggest exception to the “everything is solar powered” thesis is tidal power. Only about 1/3 of the tidal forces the Earth experiences are due to the Sun. The rest are a result of our closest neighbor, the Moon. (Side note: many folks assume the Moon is the only source of tides. In reality we would still have tides even if there was no Moon, but they would be weaker and less variable).

Friday, April 26, 2013

No Green Stars Part II: Effects of Color Contrast, the "Greenest" Blackbody, and Why There are No Violet Stars!

In my first post, I described why there are no green stars in the night sky. I'm assuming you've read that post before this one, so please do if you haven't yet. As a reminder, the main conclusion was "there are no green stars because the blackbody function is very broad, and the cone cell responsible for sensing green overlaps substantially with the other two cones cells." There's just no temperature a blackbody can have that produces a substantial amount of light in the green portion of the spectrum, but not in the other parts of the visual spectrum. It's not that strongly peaked.

However, there are some people who claim to see some green stars in the sky. A couple examples are Almach and Antares B. While these observers claim to see these stars as green, all photographs reveal them as white or blue. What's going on? The likely explanation for these two is that while they are truly blue-white, they have orange or red companions and can appear green due to the color contrast effect. A particularly compelling illustration was provided by French chemist Michel Chevreul, who did pioneering work on color contrasts:

Color plates with complementary colors surrounding
While the motivation for Chevreul's work came from his directorship of Gobelins Manufactory and focus on tapestry dyes, the same principle applies to simultaneous viewing of stars of different spectral types. Look at the bottom right color plate in the above illustration and imagine a relatively smaller white-blue main sequence star against the ruddy brilliance of an evolved red supergiant. It isn't surprising the smaller white star would look green! 

There is one example of a single star that some have claimed to look green, but has no orange/red companion, and that is Beta Librae (as noted by Phil Plait). Beta Librae, also known as Zubeneschamali, is a B8 (hot!) main sequence star located in the constellation Libra.

Before I looked up the exact temperature of the star, I had a thought. For a minute, let's take the claim that Beta Librae has a green tinge seriously and entertain the possibility that perhaps there is some narrow temperature range where a star may appear green. What is the greenest possible blackbody temperature?  This isn't simply a problem of determining at what wavelength the energy flux of a blackbody peaks.

As I stressed in my last post, you must consider: 1) the visual wavelength sensitivity of each color-sensing cone and 2) the fact that your eyes (and astronomical instruments for that matter) are sensitive to  photons rather than to energy. The peak of a blackbody in energy flux is different from the peak in photon flux. In the figure below I've plotted several blackbodies in terms of relative energy brightness (solid lines) and photon brightness (dashed lines). To orient you, our Sun has an effective blackbody temperature of about 5800 K.

Plot of blackbody function in terms of normalized brightness in energy and in photons
The way I tackled this problem was to generate several hundred different blackbody functions (in terms of photon brightness) from 100K to 40,000K (main-sequence stars are roughly 3,000+ K). I then convolved (combined) the results from these with the wavelength sensitivity of human cone cells. As a reminder, our eyes contain three sets of cone cells: S, M, and L, sensitive to blue, green, and red light, respectively.

Wavelength-dependent sensitivity of cone cells
The highlighted region is where the green cone is the most sensitive.

I formulated a custom measure I call the "greendex", which is simply the ratio of the number of photons  in the visual range where the green cone is the most sensitive to the number of photons in the rest of the visual range. I weighted according to wavelength-dependent cone sensitivity and normalized to unity. This is a bit more advanced than simply finding a peak in the energy or photon distribution. Here are the results, showing the "greendex" as a function of blackbody temperature:

The "greendex" plot shows why there are no green - or violet - stars.
Note that the colors I have overlaid on the plot are merely estimates for what color the blackbodies at the relevant temperature would appear to our eyes (informed by the color temperature page on Wikipedia). I have to admit I was a bit surprised when I plotted this baby up. It's true that I did expect the "peak" to be fairly flat - what I didn't expect was the plot to be flat throughout wavelength space after ~5000 K. The graph behavior continues all the way through 40,000 K (not shown), which is basically the upper limit for main sequence photospheric temperatures. This plot shows quite clearly why we don't see any green or purple stars in the night sky. Let me explain.

At the lowest temperatures, the peak of the blackbody is in the non visual infrared range, but as we get above about 1,000 K, even thought the majority of the photons are in the infrared, we start to get visually perceptible red photons from the  short-wavelength "tail" of the distribution.  We move more and more of the photons into the visual range as we increase the temperature. The actual point at which the "greendex" "peaks" is 8600 K, though this is not a very strong peak. Not coincidentally, the temperature at which the greatest number of green photons are produced is also the temperature at which roughly equal numbers of red and blue photons are also produced - creating a white star rather than a green one. 

Now, as we get hotter the blackbody peak shifts into the invisible UV range, but we still have a white-blue star. This is because the slope of the long-wavelength tail of the blackbody, (called the Rayleigh-Jeans tail) is very shallow. It's even more shallow in terms of photons than in terms of energy. What this means is that a blackbody only weakly becomes bluer the hotter it gets because it continues to produce copious amounts of green, yellow, orange, and red photons, which register in your green and red cones. In reality, I expect you'd have to have a blackbody much hotter than the hottest star to make it look violet to your eyes.

Okay, but what about our old friend Beta Librae? I looked up it's temperature and it's about 12,700 K - pretty far off from my peak of 8600 K. So, honestly, I have no idea why it looks green to some people. But remember this, stars aren't actually perfect blackbodies. Atomic absorption (and molecular absorption at lower temperatures) takes a bit out of certain parts of the stellar spectrum, though this effect is muted for high temperature stars. There's also limb darkening, and the effect of stellar rotation. Rapidly rotating stars are hotter at the poles and cooler at the equator due to centrifugal forces. Actually, Beta Librae is a pretty rapid rotator, spinning over 100 times more rapidly than the Sun. There's also the possibility that the apparent greenish tinge some observers see in Beta Librae has nothing to do with the intrinsic properties of the star. If anyone has any more information or insight into this problem I'd be happy to hear it. 

*In case anyone is curious, I also have versions of the "greendex" plot that show the measure in terms of energy, in addition to photons:

In this case, the peak is shifted to 6600 K rather than 8600 K, and the greendex "tail" is a bit less flat in terms of energy. However, I maintain that the photon measure is more relevant to this problem. 

Sunday, April 14, 2013

Fish Love Chasing Lasers

If you know me, you also know I am a huge aquarium hobbyist. I have several fresh water tanks at home (to the slight irritation of my girlfriend) and often spend several minutes now and then just staring in at the majesty of these artificial underwater worlds. I was absent-mindedly playing with my green laser pointer one day, and noticed that my fish (mostly danios and guppies) were quite interested in it! This stands in stark contrast to their normal impassivity. I was captivated by their response, and took a short video before I left Seattle for Edinburgh (where I am now - more on that later!). Anyway - enjoy my freshwater fish chasing a laser!

Saturday, March 9, 2013

How Cool: Bacteria That Respire Uranium and Other Radionuclides

Note: "How Cool" is a feature where I quickly describe some interesting topic relevant to astrobiology or astronomy, as opposed to more in depth articles.

I'm enrolled this quarter is a fascinating geomicrobiology course taught by the eminent Roger Buick at the University of Washington. As we're winding down the quarter, we've begun to discuss some interesting side topics that are relevant to astrobiology, including unusual metabolisms employed by microbes. ('Metabolism' is the process by which organisms obtain energy and/or synthesize their organic material). One that struck me as particularly remarkable was the ability of some bacteria to respire radionuclides like uranium and plutonium in order to obtain energy. One of them is this little dude, Desulfovibrio desulfuricans:

Credit: Electron Microscopy Core of the University of Missouri-Columbia
These organisms can be found at locations with nuclear contamination, such as the Hanford Site on the Columbia River here in Washington state.

Respiration is the process of combining an oxidant (for us humans, other eukaryotes, and some bacteria this is oxygen, O2) with organic matter (say, sugar) in order to obtain energy. Basically, an electron is transfered from the organic material (the reductant) to the oxidant. Schematically the reaction looks like this for oxygen respiration:

C6H12O6(s) + 6O2(g) → 6CO2(g) + 6H2O(l) + Energy (as ATP) 

Translating into words:

Glucose (sugar) + Oxygen → Carbon dioxide + Water + Energy (as ATP)

(We often think of getting our 'energy' from eating food, but it is really the combination of oxygen with the food we eat that is our primary avenue to obtaining energy. This is why we must breath to live!).

Respiration can also be accomplished with oxidants other than oxygen, such as oxidized iron or sulfur species. These types of reactions yield much less energy than oxygen respiration, but are useful to organisms who live in environment without oxygen, such as deep under ground. Environments with no oxygen are called 'anoxic'. (The entire Earth was anoxic for a large part of its early history, so these metabolisms were much more important for life at those times). Some of the organisms that primarily reduce sulfur or iron for energy can also do the same for soluble radionuclides like uranium and plutonium (in the forms of UO22+ and Pu(IV,V,VI)), combining them with organic matter to produce energy. (They are not in anyway using the energy released from radioactive decay!). 

Because the reduction of these radionuclide species makes them less soluble in water, and thus a less dangerous environmental toxin, bacteria that can engage in this metabolism have been of much interest to those who work on bioremediation efforts at contaminated sites. Bioremediation is the very cool process of using biology to remove pollutants and ameliorate the environmental damage caused by harmful chemical spills or leakage. Here is a peer-reviewed journal article that reviews bioremediation of radioactive waste (warning: somewhat dense). 

What does this have to do with astrobiology? We know that radioactive elements decay with time. The Earth has a certain inventory of radioactive elements, some with half lives measured in billions of years. In the past, Earth had a lot more of these elements (because there was less time to decay). So in the past, the radionuclides these organisms can use to generate energy were much more abundant and these metabolisms would have been much more important. In fact, a few scientists think that natural plutonium reactors are a plausible site for the origin of life.  This is by no means a popular view, but it is intriguing nonetheless. (Natural fission reactors are cool in their own right, and while we haven't found any fossilized Pu reactors, we have found Uranium ones). How cool!

Wednesday, March 6, 2013

Why Are There No Green Stars?

It’s a clear dark and Moonless night. You look skyward and see a cornucopia of twinkling lights – stars, some much brighter than the others, some faint enough to almost be invisible. Most of the stars appear white to your eye, but of the brighter ones a few have an obvious colored tint – perhaps a light blue or ruddy orange. If you were to pick up a pair of binoculars or a small telescope and scan the heavens you may fill in the spectrum a bit more, maybe some deeper reds, yellows, and more blues. But no greens*.

Why are there no green stars?  This is actually a common question and one that others have provided answers to elsewhere. (One of my favorite astronomy bloggers, Phil Plait aka the “Bad Astronomer” explains here. Also, I really enjoy this piece from the Jet Propulsion Laboratory's “Ask an Astronomer” series).  But I feel like most of the explanations that I have found lack a key piece of information, as I will explain below. The answer to this question has as much to do with human vision as it does astrophysics!

Relative brightness vs. wavelength

First, the basics. Hot objects emit light. Actually, "objects" of any temperature emit light in a very particular way that depends on their temperature. An idealization we use in physics is called the "blackbody", which basically is just an ideal object that absorbs all light/radiation that is incident upon it. The spectrum of light emitted by a blackbody is characterized by an equation called the Planck function. Using the Planck function you can find out how much light energy is emitted at every wavelength. The plot above shows Planck functions for three different temperatures: 4500 K, 5800 K, and 7500 K. I've also shown the region of the visual EM spectrum. Radiation that is shortward of about 390 nm is ultraviolet light (more violet than violet) and radiation that is longward of about 750 nm is infrared (redder than red). Human eyes are only sensitive to radiation in the colored portion of the plot.  

 Stars are basically really hot dense balls of mostly ionized hydrogen and helium gas. Blackbodies approximate the spectra of hot stars (and the hotter the star is the better a job the blackbody does, this is due to the relative absence of atomic and molecular absorption). This mean we can assign an "effective temperature" to a star based on its spectrum. For our Sun this temperature is about 5800 K. You can see that the Sun's blackbody spectrum peaks in the green part of the spectrum (more on this later)! So what's going on?

Well, consider what other objects act like blackbodies. Imagine a piece of iron a blacksmith heats to successively higher temperature. At first the metal glows a dull red, then perhaps an orange, then a yellow, then white, and finally blue. No green! That metal transitions through all the temperatures in the figure above, the blackbody peaks at all the visual wavelengths. However, if we look at the blackbody function, when it peaks in the green it's also emitting radiation at all the other wavelengths as well - the combination appears to our eyes as white.

We can see why (beyond just waving our hands and saying "combining the colors in this ratio makes white") if we consider how humans perceive color. Our eyes contain specialized photoreceptor cells called cones that allow us to distinguish between different wavelength of light. There are three types of cones, labeled S, M, and L. They are sensitive to blue, green, and red light respectively. Our eye perceives colors other than blue, green, and red by interpolating between the input from these cone cells, in other words, taking into account the ratios of light detected by each one (e.g., orange is lots of red and a little green). Below is a plot of the relative sensitivity each cone cell has as a function of wavelength (data found here).

Plot of cone sensitivity vs. wavelength

Notice that the green cone, M, overlaps substantially with the red cone, L, and somewhat with the blue one, S. In fact, it overlaps so substantially, and the blackbody function is so broad, that when a blackbody peaks in the middle of the visual spectrum, the combination appears white to our eyes. In truth, there is no temperature where there is substantial radiation in the green part of the spectrum and much less in the other parts.

So are we done now? Well, not quite. Remember that key piece of information I mentioned earlier that other authors hadn't considered? Here it is. Our eyes are not sensitive to the energy output of an object. In fact, neither are our telescopes or scientific instruments. What they are sensitive to, however, is photons. Photons are just little packets of light, and photons are what interact with the proteins in your eyes that register a visual signal. What's key to remember is that the amount of energy each photon carries is inversely proportional to its wavelength (and directly proportional to its frequency). 

There is a very important implication here. Since a photon with a longer wavelength carries less energy, at any given energy there are more photons at longer wavelengths. You can use this information to adjust the Planck function to give us a spectrum in terms of photon radiance rather than in terms of energy radiance. If you do this, the blackbody curve noticeable shifts and peaks in a different place. Below is another plot, of a 5800 K blackbody (e.g., representing the Sun). The solid line is in terms of energy and the dashed is in terms of photons.

Comparing blackbody in energy brightness and photon brightness

Now instead of peaking in the green, the Sun peaks in the orange/red.  Of course, we are ignoring the wavelength sensitivity of the human eye here. If we convolved (combined) that sensitivity with the blackbody, we'd probably shift the peak back to shorter wavelengths a bit, but not nearly to green.  Notice also that the shape of the blackbody is flatter near the peak in terms of photons, making it less strongly peaked and easier to explain the "whiteness" of stars like the Sun. 

So, some people like to say the Sun is green in many respects, but this isn't really true. It's only true in terms of energy emitted at a given wavelength, which eyes and instruments don't measure. We only get the energy radiance by measuring photons and converting to energy by knowing how much energy each photon carries.

In summary, there are no green stars because the blackbody function is very broad, and the cone cell responsible for sensing green overlaps substantially with the other two cones cells. The Sun's blackbody function peaks in the green, but only in terms of energy, not photons, which are what our eyes actually detect.

In a second, follow up, post I will try to determine the "greenest" actual blackbody temperature, in terms of photon brightness, using the sensitivity function of the cone cells. Stay tuned!

Technical notes: You can determine the exact wavelength where a blackbody peaks by using an equation called Wien's Displacement Law, which is derived from the Planck function. There is a different Displacement Law for the peak (energy) radiation in terms of wavelength and frequency. Interestingly, the Sun's blackbody peak is even further into the red when using the frequency version of Wien's Law than in terms of photon flux. Actually, the photon peak is the 'compromise' value between the wavelength and frequency versions of Wien's Law.

*Some people claim that they do see a green star or two in the sky. More on that in a second post!