Nuggets of Wisdom: Explained (Part 1)
Hi folks!
It's been a while! I've been busy, and during my procrastination I was busy putting together an April Fool's Day paper called Nuggets of Wisdom: Determining an Upper Limit on the Number Density of Chickens in the Universe. My collaborator, Dr. Zachary Claytor, and I applied various complex astrophysical regimes to answer the question
How many chickens could there be in space before we notice them?
In this series of posts, I want to break down and explain the science and math that went into the sections of this paper for a general audience. I'm really proud of this work, not just as an astronomer but as a budding science communicator. While the average Joe can appreciate the puns and jokes throughout the paper, I want to take some time to explain everything in between.
What is a density function?
A density function is a term astronomers (and probably other scientists) use to describe how many things or how much stuff there is based on some other metric. In this paper, we're talking about how many chickens there could be based on a given volume. A common density function we use in astronomy is a probability density function, which describes the likelihood of a certain result, given some uncertainties. There are also distribution functions, which is another phrase we probably could have used in this paper; a distribution function describes how spread out something is over an area or volume (e.g. the distribution of stars in a galaxy's disk).
We are calculating the upper limit of this "chicken density function" (a term we made up for this paper) because this would be the most chickens there could be before we notice them in space. The lower limit, then, is how many chickens we know are available - those on Earth. There are about 26 billion chickens on Earth; if we say this is all the chickens in the Universe, then the chicken density function is 26 billion chickens divided by the volume of the observable Universe (I'll make another post about this later). The volume of the universe is something like 10^23 cubic lightyears; if all of Earth's chickens were evenly distributed throughout this volume, there would be about 6*10^-23 chickens per cubic lightyear, which is really really sparse.
Solar System Chickens
Moving on to Section 2.1, we discuss what would happen if chickens were asteroid-like objects in the Asteroid Belt, between Mars and Jupiter. Actual asteroids here experience something called "solar radiation pressure" as well as "the Yarkovsky effect." Here's how we described it:
Solar radiation pressure slowly perturbs asteroid orbits outward... Rotating asteroids absorb some sunlight on the sunward side. As they rotate, they re-radiate in a different direction, which transfers some momentum from the asteroid. If the asteroid re-radiates in the direction of motion, it slows the object, perturbing its orbit outward. The combined effects from radiation pressure and Yarkovsky could perturb asteroids into a region which is in resonance with Jupiter, disrupting their orbits dramatically and ultimately dislodging them from the asteroid belt altogether. These asteroids can then become meteors, colliding with other objects in the Solar System such as the Moon and Earth.
The key thing here is understanding that photons - individual packets of light - have momentum, or energy in the form of motion. Solar radiation pressure describes photons hitting a surface and being absorbed into that surface, transfering the momentum to the object. It's super duper tiny from each photon, which is why we don't feel any pressure when we go sunbathing. But an asteroid is constantly in the sunlight, and over a long period of time can absorb many, many photons along with their momentum to feel a bit of a push outwards away from the Sun.
In a similar vein, the Yarkovsky effect takes into account if an asteroid is rotating. The sunny side absorbs photons and radiation pressure, but then rotates to the dark side of the asteroid. Now this section has a chance to radiate out some photons (probably in the form of heat). Giving off photons has the opposite effect as absorbing photons when it comes to momentum: the asteroid is losing energy and momentum on the side that radiates photons outward. This occurs on the "dusk" side of the asteroid, and propels the asteroid a bit. On the "dawn" side of the asteroid, photons are just beginning to be absorbed, and the solar radiation pressure pushes it outward. Both of these photon interactions - absorbing and emitting - effect the energy of the asteroid's orbit, either slowing it down or speeding it up, pushing it farther from the Sun or pulling it closer. This gets us to the final part:
Orbital resonance
Orbital resonance is when two (or more) celestial bodies orbiting a common center complete a certain number of full orbits together. For example, the inner three moons of Jupiter - Io, Europa, and Ganymede - are in orbital resonance. Every time Ganymede completes 1 orbit, Europa has completed 2 orbits, and Io has completed 4 orbits. Their orbital resonance, then, is 4:2:1 as they orbit the common center which is Jupiter. Because they meet up very regularly, they pull and tug on each other via gravity, and actually help keep each other locked into that resonance.
Similarly, there are certain sections of the Asteroid Belt which can be in orbital resonance with the most massive, most gravitationally influential planet, Jupiter. Where this occurs, there are large gaps in the asteroid belt, because Jupiter has essentually flung them out. These are called the Kirkwood gaps:
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| Kirkwood gaps, where Jupiter flings out asteroids that are in orbital resonance. |
In the above figure, distance from the Sun is on the horizontal axis, and the number of asteroids (a distribution, if you will) are on the vertical axis. Four major gaps are highlighted, with the orbital resonance of the asteroid-to-Jupiter ratio indicated (in the same notation I used for Jupiter's moons).
Putting it all together
So. Asteroids in the Asteroid Belt can change their position and orbit within the Belt due to solar radiation pressure and the Yarkovsky effect. If they end up shifting into orbital resonance with Jupiter, they'll quickly be flung out of the Belt altogether due to Jupiter's graviational influence. With an orbit gone wild, we can start to call it a meteor, as it's likely to go crazy and crash into something (hopefully not us).
Back to chickens
What does this have to do with chickens? Well, if chickens were in the Asteroid Belt, they would be subject to the same phenomena as these asteroids: solar radiation pressure and the Yarkovsky effect. One last variable I've yet to mention is how effectively asteroids/chickens can absorb and emit, or simply reflect, photons. Very bright, white chickens would be heavily influenced by these photon interactions, and if they were in the Asteroid Belt, would often be pushed into a Kirkwood gap, then flung out of the Belt and maybe impact the Moon or Earth. We haven't seen this (yet) so there probably aren't many white chickens in the Asteroid Belt.
Darker, black chickens, however, might be able to hide out in the Asteroid Belt longer, because they wouldn't have the same reaction to these photon effects. Their orbits would be more stable, and would not be pushed into the Kirkwood gaps.
This is science, folks. We take systems, understand how they work, develop models and predictions on what should occur, and see if those match the results. If (white) chickens are in the Asteroid Belt, they should show up as meteors often; because we haven't seen any chicken meteors, there probably aren't many or any white chickens in the Asteroid Belt. But this doesn't necessarily mean there are no black chickens out there.
In the next post, I'll go through some of the other science we consider in this paper. Hopefully it doesn't ruffle too many feathers ;)
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