Wednesday, October 2, 2013

Discussion Questions: 9/17

Round two of Suvrath's discussion questions. This time, I didn't even try to answer some of the questions because they involved discussions of ethics that I am definitely not qualified to do. I will stick to the scientific questions that I can actually answer without projecting my opinion into the answer (too much).

Why is an incandescent bulb a good example of a blackbody where a fluorescent light bulb is not?
This all comes down to how the two different bulbs work.

An incandescent bulb works by running a current (moving electrons) through a filament that acts as a resistor. A resistor is just any material that doesn't allow charges to move through it quite so easily. Electrons moving through a resistor will lose energy as they go. This energy heats up the resistor, which will eventually get hot enough to glow. Because the filament is a hot, dense object, it will emit like a blackbody, which means it emits light all across the entire visible spectrum. Of course, this also means it is emitting light at non-visible wavelengths also, which is a huge part of why they are so inefficient.

Fluorescent bulbs work by running a current through a diffuse (generally) mercury gas. And, as you know by now, a hot, diffuse gas gives off an emission spectrum. Why do we use mercury though? (Hint, it's not because someone wants to poison you, though it's a good reason not to inhale too deeply right after you break a fluorescent bulb.) Here's an emission spectrum of mercury.
Mercury is a good choice because it emits light at colors that span the whole visible spectrum. Unfortunately, it also emits an awful lot of UV light as well. But we can fix this! We have the technology The coating on a flourescent bulb (this coating seems to be what causes them to appear that milky whitish color) specifically absorbs UV photons and spits the energy back out as visible light, covering even more of the visible spectrum. So you can get all of your basic colors looking like they're supposed to and get the same amount of light far more efficiently than incandescent bulbs. Sounds good to me.

This is not to say that fluorescent bulbs produce no waste heat. They just produce less of it than equivalent (visual) brightness incandescent bulbs.

Are there any stars whose peak emission is not invisible light. If so, would they still be capable of supporting life?
Absolutely! In fact, we can calculate exactly when the surface temperature of a star makes the peak wavelength of its spectrum no longer corresponding to visible light using Wein's law!
Where T is the surface temperature of the star and λ is the wavelength (color) at which the star emits the most light. The violet edge of the visible spectrum occurs at about 400 nanometers, or 0.4 microns (in the units given above) while the red edge occurs at about 700 nm (0.7 microns). Wein's law tells us that stars with temperatures higher than 7250 K and lower than 4100 K will have peak colors outside of the visible spectrum.

Can these stars have habitable zones? Absolutely! Whether or not a star has a habitable zone doesn't depend on its peak color, but on its total energy output. For main sequence stars, a star's temperature, mass, luminosity, and size are all correlated to one another, so bigger stars tend to be hotter and more luminous. The only difference will be that the cooler stars will have smaller habitable zones that are closer in to the star, while hotter stars have larger habitable zones that are farther away. For more than you probably ever wanted to know on habitable zones, check out my previous post specifically on the topic of habitable zones.

There is one critical difference between hotter and cooler stars that would affect the potential for life to develop. Hotter stars live shorter lives. Why does this matter? Life as we know it on Earth took 4.6 billion years from the formation of the solar system to develop. Could intelligent life develop faster? Possibly, but it may also take longer than it did for us. With a sample size of 1, there's no way to tell. But it's probably a safe bet that life needs a decent amount of time to come into existence in the first place, thereby favoring smaller, cooler stars.

What do the spectra of non-blackbody radiators look like?
Conveniently, I was able to cover some of these in class when I subbed for Suvrath. Of course, I only really covered the basics that we know of from (you guessed it) Kirchoff's Laws of Spectroscopy. There is another type of spectrum that isn't covered in typical undergrad astronomy: the power law. A "power law" spectrum is a spectrum whose shape is given by the mathematical relationship
The symbol Iν stands for the specific intensity, or the amount of light emitted at a given frequency, while the symbol ν is generally used to represent frequency, for some reason. α here is just used as a stand-in for some positive number Ultimately, a power-law spectrum will look like Figure (number this appropriately).
General shape of a power law shown on a linear plot. Image courtesy Wikipedia.
Now, the math-savvy readers may note that the equation above should asymptote (approach infinity) as ν approaches zero. This is generally fixed by limiting the range of the power law at low values of whatever variable you're considering. In typical jargon, this is to say that the power law "turns over". Power laws occur an awful lot in nature, but that's a subject for another time.

So what kind of weird objects produce a continuous spectrum that isn't a blackbody? Anything with jets. A "jet", in astronomical terms, is a beam of radiation and energetic particles travelling in the same direction. Generally, objects that emit jets are emitting two jets in opposite directions and are actively accreting matter from a disk. The most interesting of these are black holes. A stellar-mass black hole that is stealing matter from a nearby star with which it shares an orbit (low-mass x-ray binary) or a supermassive black hole that is eating anything unfortunate enough to come too close will have a disk of rather hot material orbiting it. As shown in the artist's depiction below, the two jets will be emitted perpendicular to the hot accretion disk.

While the precise origin of jets is still a bit uncertain, there is reason to believe that they, to some degree, are related to the magnetic fields created from the rotating disk of material around the black hole. The evidence for this is in the spectrum of the radiation. Synchotron radiation is emitted from charged particles rotating in a magnetic field. We expect that particles in the jet will, themselves, have a power-law distribution of energies, which gives the emitted radiation a power-law spectrum as well, where the emitted power (energy emitted every second) at a given frequency goes as
P just stands for the emitted power and p is a variable whose value depends exactly on the source of the synchotron radiation. In general, synchotron emission comes out at radio wavelengths.

Edit: We also get power law spectra from what is known as inverse Compton scattering. In inverse Compton scattering, the hot accretion disk emits photons thermally that bump into very energetic electrons that are flying around in the accretion disk's corona. The corona in this case is just the region above and below the accretion disk which contains very high energy particles flying around. The photons will crash into a relativistic electron and actually gain energy from the collision, which makes them into x-ray photons. However, this has nothing to do with the jets. It's just another source of continuous power-law emission.

Man, I had to dig up my 502 notes for that question. If any of my friends see fit to correct me on what I've said about jets, I'll post updates.

What is it about "green" stars that causes them to appear white to the human eye? Also, why aren't there purple stars?
A star whose peak color (see Wein's Law above) occurs at green wavelengths (~550 nanometers) isn't just emitting green light. In fact, it isn't even emitting mostly green light. It just happens to emit more green light than it does light at any other individual color, but not by much. To illustrate this, I've created a little plot in Excel that shows the blackbody spectrum of an object whose emission peaks at 550 nm (about 5270 K) that spans the whole visible spectrum of light.
That's not a huge difference. While there is definitely a maximum at 550 nm, emission at other colors isn't too far behind.

Now we get into how the human eye works a bit. We have two different types of receptors: rods and cones. Your rods just detect light while your cones are responsible for detecting color. The cones in human eyes, in particular, detect light at red, green, and blue wavelengths, and blend the combination of these three into any color we can perceive. This is why old cathode tube TVs and computer monitors have pixels comprised of red, green, and blue bars, or why Photoshop or MS Paint create colors as a mixture of red, green, and blue. If you have roughly equal amounts of red, green, and blue, the object will look white. This is what happens for "green" stars.

This is also why we can't see purple stars. A given star's spectrum could very well peak at purple wavelengths, but the detectors in our eyes will only see them as blue.

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