Sunday, January 22, 2012

Science Sunday: The Stars - Part I: Introduction to Shiny Things

I've thought a lot about this, and I've decided—really for my own benefit—that I should spend some time once per week thinking and writing about a science topic that interests me.  I figured that it'd be good to just choose something and go somewhat in-depth about it.  In the future, should I continue, I won't always choose something astronomical, though anything outside of what I've been fortunate enough to learn will take extensive use of Wikipedia (and maybe even *gasp* a book!).  However, to start, I think that I should talk about something(s) that has interested me since the first time that I actually cared about astronomy: Stars.

The Sun—our closest star
There is so very much to say about stars that it's really difficult to know quite where to start, and my level of exposure to them it's also quite difficult to know how to proceed without getting too technical.  Let's start with this: stars are the massive balls of gas in the Universe that shine brightly and live dynamically by way of a constant balance against the inward force of gravity with the outward force of radiative pressure from nuclear fusion.  Wow, that is definitely a packed sentence.  Let's take it back to basics and build up some understanding so that we can come back and actually appreciate what all of that meant.

Nevermind all the lines, the apple is falling
 on this dude's head due to gravity!
Gravity, as we all know so very well, is responsible for making things on the Earth that go up come back down.  It's also what keeps us tethered to the Earth's surface, what keeps the Moon orbiting the Earth, and what keeps the Earth orbiting the Sun.  The law of gravity, in essence, states that any two physically-existing objects with some mass (call them M1 and M2) that are separated in space by some distance, d, will experience a force that will always act to pull them toward one another.  This force—this affinity for action—will weaken fairly quickly as the distance grows between these two objects (if the distance doubles, the force between the two objects will reduce to 1/4th of its former strength). However, no matter how far apart they may be, the force will always be there.

Gravity always acts radially.  So, if you have a box full of particles that experience no other force aside from gravity, they will eventually collapse into a sphere (or sphere-like object, depending on what that initial distribution is).  Gravity doesn't make boxes or pyramids, nor does it build buildings or cars.  It just pulls things 1 and 2 together.  Gravity is love!  I digress...

The gas that makes up the physical objects that we know of as stars acts much like that hypothetical box of particles that I mentioned before.  However, where one might imagine that box of particles with the length of a side comparable to our own size, stars themselves (like our own Sun) are balls of gas that span sizes that are almost beyond our comprehension!  And this is AFTER the gas has already collapsed from a far-larger reservoir, called a Giant Molecular Cloud (which I may get to in the future).  Though this may prove to not actually help very much for visualizing this scale, for a sense of scale regarding the size of the Sun (our nearest star), the United States is roughly 2,500 miles wide from east to west.  According to Google Maps, driving from Sacramento, CA to Washington, D.C. covers 2,731 miles and would take...1.83 days?!  An average speed of ~62 mph?  That seems...a little ambitious...I'm digressing again.  Anyway, in contrast, the average diameter of the Sun is *very roughly* 865,000 (really ~864,950) miles! That amounts to 346 cross-country road trips (or close to 2 years of constant driving) in order to travel from one end of the Sun to the other, going through the center.  Its circumference on the other hand is *again very roughly* 2.7 million miles.  It's crazy huge.

A very artistic and barely-accurate
rendering of a hydrogen atom
Packed within this gargantuan volume is enough gas to equate to ~333,000 Earth masses.  The stuff that comprises this gas isn't what we usually think of when we think of gas (certainly not what's in your car).  It is almost entirely a gas of hydrogen atoms (~75% hydrogen and ~25% helium by mass, but they exist in an almost 12:1 ratio by number in our own Sun; the ratio may be even higher when you account for the mass fraction of heavier elements), which themselves are extreeeeemely tiny (using the Bohr radius of the hydrogen atom, you can fit ~700,000 hydrogen atoms along the width of a single hair), and are extreeeeemely light (I could give a sense-of-scale factoid here, but I don't feel like it).  Hydrogen is honestly worthy of its own article, but that's for another time.  What I will say about basic hydrogen (there are isotopes, as well as ionization states), that hasn't already been said within parentheses, is that it is the most basic atom in existence, with each atom being composed of a single proton orbited by a single electron (though the force that keeps the electron tethered is not gravity!).  This will become useful later.

So, what do we have so far?  Star's are physically large, physically massive, and are made of gas that is gravitationally bound to itself.  Awesome, we have progress.  However, out of these facts come an interesting question: with all of this mass experiencing all of this gravitational force pulling everything inward, how is it that all of this material doesn't just collapse indefinitely until it becomes just an extremely massive point in space?  An initial guess might be that the atoms that comprise this gas act like solid billiard balls, where the gas ensemble will compact down in volume until each atomic "sphere" is physically touching the next one.  Let's do a quick and dirty calculation of what that might be like (Christ, there will be so many approximations....).

Let's first approximate the Sun as a hypothetical star being entirely comprised of hydrogen atoms.  This comes out to roughly ~10^57 atoms (this symbol "^" means "the numbers following this are the exponent of the preceding number") if you divide the mass of the Sun by the mass of an individual hydrogen atom.  Each of these atoms has a radius of roughly 5.3 x 10^(-11) meters, resulting in a volume for every atom of ~6.2 x 10^(-31) cubic meters.  I'm going to do something really stupid and highly incorrect and invert this, giving a number density (# of atoms per unit volume) of one atom per 6.2x10^(-31) cubic meters, or 1.6 x 10^30 atoms per cubic meter of space.  Given that we have ~10^57 atoms in this hypothetical pure hydrogen star, we divide the total number of atoms by the number density of atoms, giving ~6 x 10^26 cubic meters for the volume of our pure-hydrogen star.  Now, if you look up the radius of the Sun and do the volume calculation, you get something like 1.4 x 10^27 cubic meters for the Sun's volume.  Then, you can look at the two numbers side by side and say, considering all the approximations we made along the way, that this could possibly work.

HOWEVER, remember that the Sun is not purely hydrogen, and instead has roughly 1 helium atom per 12 hydrogen atoms, with the size of an individual helium atom being roughly 60% of a hydrogen atom.  Thus if we were to make our hypothetical star a little more realistic and include helium, as well as some of the heavier elements present in the Sun like oxygen, nitrogen, carbon, neon, and even iron, our hypothetical star with atoms bumping up against one another like billiard balls begins to shrink drastically in size, and the volume may decrease by an order of magnitude (meaning a factor of 10, and no I do not have a calculation for that.).  But, the Sun is puffed up to a much greater volume than that.  On top of that, the Sun also shines, which an inert ball of hydrogen billiard balls cannot do.  What gives?  What is it that's holding the Sun up against that ever-present collapse of gravity?  The answer: radiative pressure.

Radiative pressure is a fancy way of saying the force produced on a surface by light, that same phenomenon that makes it so that we can see the world around us.  You might be thinking to yourself, aside from my argument above being...fairly weak, "self, what the hell is he talking about?  You need something that has the ability to PUSH in order to hold against gravity!  Light doesn't push anything, it just shines!"  Well, mon frère, that is where you're wrong.  Light (another topic to discuss at great and painful length! Woo!) is energy, and has the ability to imbue particles with motion when it interacts with matter (in many different ways that will be detailed later).  This motion can then translate into a pressure, as these newly-energized particles smack up against other particles and physically push them outward.  But how, pray tell, does this light get produced?  What is the source at the center of it all?

The proton-proton chain of
nuclear fusion
FUUUUUUUUUSION!!!  Hydrogen in the core of the Sun is packed together really tightly, and is fairly heavily ionized, meaning that the central proton has been stripped of its electron companion.  It's also really hot (~27 million degrees Fahrenheit, vs ~10,300° F on the Sun's surface, and ~1,800° F for magma on Earth), and heat makes things want to move, so these free protons in high densities jet around really really quickly.  Now, for visualization, try to imagine yourself in any given mall on Black Friday.  It's extremely crowded, and everyone within the mall is trying to move as quickly as they can in order to get to a sale.  Inevitably these people will collide, sometimes even with you.  Let's take this analogy back to the Sun, where we instead have protons colliding at very high energies.  When people in the mall collide when they're under high pressure, in high density, and are really hot, they tend to explode into a fight.  When protons collide under these conditions, they fuse into a single nucleus of one proton and one neutron called deuterium, which one can think of as heavy hydrogen.  The reaction also produces a positron (the antimatter form of an electron), a neutrino (a mysterious little particle that seems to only interact with matter when it feels like it), and a little energy that is given off in the form of light.  The positron eventually goes on to meet up with a free electron, annihilate, and produce some energy.  The next leg of fusion, the major energy-releasing part, occurs when another free proton smacks into the deuterium atom, creating helium-3 (called as such because there's 3 particles comprising it's nucleus: 2 protons and 1 neutron), and releasing energy in the form of light.  This is all amazing and whatnot, but it is important to note that the time scale for a single proton-proton fusion interaction is on the order of one billion years per reaction.  This would be an incredibly long wait if not for the fact that there are far more than billions of protons in the Sun's core.  The sheer vastness in the number of protons in this region means that even though the time scale is so long, every second there are roughly 3.6 x 10^38 protons going through the reaction and being converted into helium nuclei.  This, according to Wikipedia, releases energy at a rate of ~9.1 x 10^10 megatons of TNT per second!  PER SECOND!  That's about the power in 9 billion nuclear bombs of the highest yield, PER SECOND.  Crazy.  Stars are objects that are at constant nuclear war, with themselves, in order to stay alive.  That's some serious personal issues.

So now what do we have?  We've discussed that stars are giant balls of gas.  We've covered that these giant balls of gas are bound together by gravity, but are held up against collapse by radiative pressure.  We've also covered that this radiative pressure is due to nuclear fusion occurring in their cores.  And so, stars live dynamically, balancing radiative pressure against gravity!  It's dynamic because there's constant action in this stand-off.  If the radiative pressure relents just a bit, gravity acts right away to contract the star.  If gravity contracts the star just a bit, the core will heat up from this contraction, and the radiative output will increase, puffing the star back up.  Now that I've gotten through all that, where do we go from here?  There's just so much to cover.  I think that next time, I'll start talking about all of the different types of stars and their physical and observational properties, moving up through their evolution, and going over how different stars die.  I'd like to go into detail about every stellar population, just so that we (read: I) have a good idea of what makes each population special.  I'd then like to go into how they're distributed throughout the galaxy, whether they're in clusters or are cruising along in the galactic field, and how their locations and compositions tell us more about the galaxy that we live in.  After that, I think it might be a good time to cut the star stuff, because there's so much more of the natural world to explore, and I'm interested to see what I can dig up.

Até então!




*Physical quantities like the mass of hydrogen and diameter of the Sun were obtained from the textbook that I used to TA for Astronomy 101 last quarter, whatever that is.  I don't feel like looking for it.  It's got stars on the front.  Unit conversions from km to miles, as well as all calculations were done by me using anything from IDL to my Macbook's Spotlight calculator to my iPhone, and may be a little (or a lot) off due to rounding errors and general laziness.  This is certainly not an ultimately-reliable source for facts and figures, just an astronomer rambling about stuff that gets him excited.  Enjoy for your own pleasure, but cite at your own peril!

6 comments:

  1. I think I will bookmark this page and use it when I am TA in a few years.

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  2. This seems like a good method of qual studying actually. Write up a couple page post on each subject =)

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    1. It'd be great if I had the time, but this post actually took me a few hours to write (since I wanted to get it right). I'm definitely getting back to at least Science Sundays after the qual. It was a good idea and will be a good idea to continue.

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