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The Warmth of Starlight

That would make a great title for one of those creepy-looking self-published Amazon romance novels that has a picture of two werewolves having sex on the cover. Not that I know anything about that, of course.

Anyway… This post is just to tide all three of my dear readers over until I can make the time to write a proper full-length one.

One of the really cool things about the laws of physics is that they seem to apply everywhere, or at the very least everywhere in our neighborhood. That means that you can compute how far a one-inch cube of cheddar cheese traveling at half the speed of light would penetrate into the crust of a neutron star. The answer, according to Newton’s impact depth approximation is 12.54 nanometers, which is about the width of a protein. (I got some help from Wolfram Alpha and the USDA’s handy nutrient list for foods (because, to my own surprise, I haven’t memorized the density of cheddar)).

But you can calculate other things, too. Things that are somehow both stranger and somehow more relevant than cheese dropping onto a hyperdense star-corpse.

One of the really cool things about physics is that they take pretty messy stuff like stars and gas clouds and gravity (and poo, if you land in the wrong branch of biology) and turn them into equations that are good approximations. And the cool thing about equations is that you can take the output from one and put it into the input of another, and have the result actually mean something.

And that’s the point I’ve been drunkenly weaving my way towards this whole time. With nothing more than a table of known numbers and a few relatively simple equations, you can figure out how much starlight warms the Earth.

The nearest star (that we know of) is Proxima Centauri. But Proxima Centauri’s a weakling. Poor little red dwarf. Can’t even photoionize vanadium oxide, which is apparently important if you’re a star. It’s so faint, in fact, that it doesn’t even have a cool proper Chinese/Arabic/Greek name, since it took the development of the telescope to make it visible. It’s totally lame. (Sorry. My ’90s is sticking out again.)

But Proxima Centauri has a pair of traveling companions: Alpha Centauri and Beta Centauri (this is starting to sound like a weird version of the sex-talk parents give their children…). We’ll lump them together as one star, because we’re lazy. (Don’t pretend you’re not part of this.) Divide that luminosity by the surface area of a sphere whose radius is the distance to the Alpha Centauri twins, and you’ll get an answer in watts per square meter, also known as irradiance. When it comes to the study of how light travels and is measured, there’s a terrifying profusion of different units. Lux. Candela. Lumen. Go hunting, and you’ll be knee-deep in steradians and watts and Angstroms before you know it. But I like irradiance. Irradiance is simple: a certain amount of power falls on a certain area. Just simple enough for my Swiss-cheese brain to handle. Here on Earth, the sun bathes us in about 1300 watts per square meter.

But the distance to the Centauri Twins (who’ll be appearing in a David Lynch movie soon, I’m sure) is measured in light-years, and light-years, as Douglas Adams put it, are so unfathomably huge that it’s just about pointless to try and wrap your feeble human meat-computer around them

. So, although we’re talking about the light from two stars here, it’s going to be spread over an enormous area. The cross-sectional area of the Earth compared to the surface area of that gigantic 4.2-light-year-radius sphere is about one part in 170 million trillion. That’s about the same proportion as one grain of sand compared to the number of grains of sand on Earth.

Unsurprisingly, the result has nano in it. Proxima Centauri A and B together irradiate Earth with about 25.6 nanowatts per square meter. I think the phrase “weaker than a mosquito fart” is appropriate. Maybe that’s why they don’t let me in nice restaurants. But, as small as 25.6 nanowatts is, it’s not zero. From the Stefan-Boltzmann black-body law, we can say that, if Earth’s only source of light were the Centauris, Earth would freeze solid, but wouldn’t drop below 0.8 Kelvin.

But Alpha Centauri A and B are ordinary sunlike stars. The next nearby star (excluding the red dwarfs, because frankly, there are a lot of stars and I don’t want to be here for the next trillion years) is Sirius. If you live in the Northern Hemisphere, it’s the brightest star in the sky. It’s also a pretty big, energetic bugger, twice as massive as our Sun and twenty-five times as luminous. (Sirius is actually a binary star, but Sirius B is a white dwarf, and so small that its light makes a mosquito fart look like an atom bomb. Weirdly, though, our telescopes can still see it. Science rules.) Sirius bathes Earth in a whole 165 nanowatts. If it was just Sirius and Alpha Centauri shining on us, Earth would never cool to below 1.4 Kelvin.

But a star’s closeness isn’t everything. If two stars are equally luminous, but one is twice as close, that one will irradiate us four times as much. But the thing about stars is that some of them get really bright. Insanely bright. Vaporize-you-before-you-can-feel-the-pain-let-alone-wonder-why-you’re-suddenly-hovering-over-a-star-bright. That’s bright.

Take, for example, Betelgeuse, the red star on the shoulder of Orion (up there with all those burning attack ships, no doubt). Betelgeuse is a red giant. A senile star. And like many humans, when stars get old, they get cranky. As they frantically burn through their nuclear fuel, all that energy inflates them like balloons. Their surfaces get cooler, which means they don’t radiate as strongly, but their surfaces get so much bigger that their brightness boggles the mind. Betelgeuse is a diffuse, lumpy star that’s constantly wobbling and boiling like a drop of water in a hot skillet, but if you placed it where the Sun is (I don’t recommend it), its envelope would extend at least beyond the orbit of Mars. Therefore, even though its surface is only as hot as an acetylene torch (which might as well be ice, as far as cosmic temperatures go), it shines as bright as 300,000 suns. This means that, even though it’s something like 600 light-years away, it irradiates Earth with almost twice the power of Sirius: 271 nanowatts per square meter. That’s enough, all by itself, to raise Earth’s temperature to 1.5 Kelvin.

So, while we’re not exactly going to be going skinny-dipping if the Sun vanishes, the Earth won’t drop to absolute zero. And actually, it turns out that the sheer number of stars, and the insane brightness of the really bright ones, is enough to almost double the contribution from mighty Betelgeuse. On a moonless night with no other light sources, starlight bathes Earth in about 3 microwatts per square meter, which is enough to raise the surface temperature to 2.7 Kelvin.

To be fair, though, 2.7 Kelvin is cold. It’s not even warm enough to melt nitrogen. Heck, it’s not even warm enough to melt hydrogen, and hydrogen loves melting, little molecular lightweight that it is. But at the same time, 2.7 kelvin isn’t nothing. Far from it. Starlight, after all, is powerful enough to reach us over trillions and trillions and trillions of miles or kilometers or any other ordinary distance unit. It’s bright enough to see the world by, if you’ve got good vision. And although it makes no real difference to Earth’s energy budget, there’s something comforting about the fact that even here, on a tiny sphere of rock a trillion miles from anywhere, we’re never quite alone. Right now, above the clouds outside my window, light spewed from Sirius, when I was a one-year-old toddling around in diapers and trying to stick keys in lightsockets, is making a tiny dent in the darkness.

Holy crap… I got all sentimental there at the end. I think I need to go get my blood chemistry checked. And, for the record, for about the last half-hour, Muse’s Starlight has been playing on an endless loop in my head. If it doesn’t stop, I think I’m gonna need a ball-peen hammer.

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5 thoughts on “The Warmth of Starlight”

1. peoplethings says:

Awesome blog! I am thinking of pursuing similar themes in my blog.

2. Am an amateur writer…I wanted to know what according to you would be an exceptional article ? If at all you were to read one…what would you focus on..? what attracts you towards that article such that you would come again to read them..???

• I’m not exactly a great literary thinker, so I don’t know how well I can answer your question, but I’d say the most important thing that attracts me to an article is if it talks about something or makes me think about something new, something I’d never thought of before. It helps if the prose itself is pleasant to read, too.

3. cpgubbio17 says:

Awesome post!

4. PhysicsStudent says:

Hi, thanks for the great post. I’m wondering if you could provide a source for the flux of starlight on earth (3 microwatts per square meter). I’ve been searching all over for an experiment that measured this with no luck. Thanks!

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