Wednesday, September 11, 2013

Discussion Questions: 9/5

As part of doing the stuff that pays my tuition for this semester, I am TAing for Suvrath Mahadevan's AST-140: Life in the Universe class. Suvrath takes attendance on a semi-random basis by having his students submit "discussion questions" relating to the material covered in class that day. My job is to grade the question based on how insightful it is, and how relevant it is to the material covered that day. After the test round of questions, I decided that some of them were so interesting that they deserved answers, so I scribbled answers on the papers. Some questions deserved much longer answers, so I thought to make answering such questions part of my blog. All questions will be anonymous, and the students may opt out simply by indicating as such when submitting the question. I may answer some questions in combination with other questions when convenient. Without further ado, I present the first round of questions.

Why is it that elements such as hydrogen, helium, carbon, and oxygen are common within the universe when elements like lithium and beryllium are not?
I actually got this question from a few different students, and it's a good one. The three elements that occur between helium and carbon on the periodic table, lithium, beryllium, and boron, exist in noticeably smaller quantities throughout the universe than the elements surrounding them (as you can see in Figure 1 below). The answer to this question is based on how these elements are created.
Figure 1: The full solar abundance pattern of naturally-occurring elements.
As I have mentioned briefly in my previous post on cosmology, a number of elements were created in the Big Bang. The most common element in the universe, hydrogen, was solely created in the Big Bang; it has only been destroyed in stellar fusion since then. Helium was also created in fairly large amounts; 1 helium nucleus was created for every 12 hydrogen nuclei in the early universe. Very small amounts of lithium, beryllium, and boron also came out of the Big Bang, but far less of them than hydrogen or helium. Helium's abundance has increased a bit for the same reason that hydrogen has decreased, but the changes are mostly negligible (1 to 2 percent). Today, Li, Be, and B are actually created when high-energy cosmic rays slam into other atoms (like carbon) and actually knock protons out of the nucleus which turns it into boron. This process has the kind of awesome name of "cosmic ray spallation".

The reason carbon, nitrogen, and oxygen are so abundant relative to the previous three elements is because they are all created in stars. I'll discuss the major processes for this a bit later on, because they're relevant to another question, but these elements are created in the cores of stars that have evolved off the main sequence. This process occurs in every star as it grows old and dies. We expect that, over the lifetime of the universe, enough stars have gone through their life cycles that the universe has been able to accumulate a relatively large amount of these common, relatively easy to make, elements.

Ultimately, the processes that create carbon, nitrogen, and oxygen are far more common in the universe than those that can create lithium, beryllium, and boron, so we get more C, N, and O in the universe.

How rare is lithium compared to gold or silver? It seems that using it for batteries is wasteful if there isn't that much of it.
We can actually answer this by looking back at Figure 1. Lithium (Li) and gold (Au) are both marked on the figure I grabbed off the Internet, while silver (Ag) occurs at atomic number 47 (on the x-axis). You should be able to tell fairly quickly that lithium is actually more abundant than both gold and silver. Of course, that's just elements in the universe as a whole. If we look at the amount of each Earth's crust, you'll see that... there's still more lithium than gold or silver. I was actually interested to learn that even uranium is more abundant in Earth's crust than either gold or silver.

Also, if we weren't using lithium for batteries and such, what would it used be for? OK, maybe there would be a market for shiny rock-looking things that can float in oil (it can float in water, but it also tends to chemically react with water). The value of an elements isn't just based on how rare it is, but also how useful it happens to be. So if it was useless, who cares that it's rare?

Can massive stars fuse helium into other elements like they can fuse hydrogen into helium?
Is there a limit on how many elements can form in a star? If so, how are the other elements formed?
These two questions are just literally begging to be answered together. Before I dive into this question head-on, I should clarity that it doesn't take a massive star to fuse helium into heavier elements. Our own sun will eventually get to a point where it can fuse helium into carbon, but that won't happen for another 5 billion years or so.

As main sequence stars age, they slowly "burn" (when I say "burn" with respect to stars, I mean nuclear fusion, not chemical burning) through all of the hydrogen in their cores. Now, keep in mind that stars are stable bodies because the energy released from nuclear fusion works to balance out the gravitational force that would otherwise cause the star to collapse on itself. When you run out of hydrogen fuel for fusion, things become unstable, and the core shrinks rapidly. Squeezing the now mostly helium core causes its internal temperatures and pressures to increase. Under these conditions, you can squeeze three helium nuclei together to create carbon.

I need to pause my narrative here to explain a few things. Helium fusion can only occur under such extreme temperatures because helium has a more positively charged nucleus than hydrogen does (two protons rather than one). This means that squeezing two helium nuclei together takes a lot more energy because the repulsive force is much stronger. Helium fusion is also discouraged because the nucleus that would be formed from two helium nuclei coming together (beryllium-8) is hilariously unstable. A beryllium-8 nucleus will break apart into two helium nuclei within about billionth of a billionth of a second. Therefore, you need to actually bring three helium nuclei together within a very, very short period of time to get a stable nucleus out (carbon).

So post-main sequence stars can stay stable by "burning" helium into carbon. Now we get carbon building up in the star's core (with some carbon combining with helium to create oxygen). At this point, we get two very different paths in stellar evolution. To make a long story short, stars with masses similar to that of the Sun will stop here, become unstable, and blow off their outer layers forming a planetary nebula with the former core of the star eventually becoming a white dwarf.

Even more massive stars can reach higher still temperatures and pressures, which allows them to fuse even heavier elements. Stars with masses higher than about 8 times the mass of the Sun can fuse elements up to iron in their cores, with shells of previously fused elements surrounding the core like the layers of an onion (ogres are like onions and post-main sequence stellar cores). An illustration of this (with the core shown dramatically expanded with respect to the remainder of the star) is shown in Figure 2.
Figure 2: Illustration of the layers that form around the core of an evolved high-mass star. Not to scale at all.
There is actually a limit on what elements can be created in stars. Stellar fusion can only create elements as heavy as iron. Why iron? Iron happens to be the most stable nucleus in the universe. It takes more energy to stick anything to an iron nucleus than you would get out of the resulting fusion reaction. Therefore, high-mass stars build up an iron core and basically stop there. How the other elements are formed will be discussed in the next questions.

If a star is constantly contracting, then when does it expand before it goes supernova?
How is uranium formed?
I am so happy that someone asked these questions, in part because they make an excellent follow-up to the previous two questions, in part because I f***ing love supernovae.

To start, stars are not constantly contracting. As I described above, once stars begin fusing hydrogen into helium, they are actually very stable until the stars start fusing much heavier elements. But once enough iron builds up in the center of a star, you have a problem. Because you can't fuse iron to make heavier elements, you lose the star's main source of energy. NOW the star's core begins to collapse because the star's gravity finally wins. The core is too massive to be supported by normal gas pressure, and everything gets squeezed so close together that the free electrons flying around are forced to combine with protons, yielding neutrons. The core of this massive star will eventually become a neutron star (or, under the right circumstances, a black hole).

Once the core has collapsed, there's literally nothing holding up the rest of the star. The inner layers collapse first, because they're the first parts of the star to realize that something has gone horribly wrong. The inner layers fall onto the proto-neutron star (PNS). However, the proto-neutron star is as dense as physically possible without becoming a black hole (this takes much more mass than a typical proto-neutron star has). The material that collapses onto the PNS will essentially bounce back outwards away from the core. This all happens very fast, and the rebounding material will quickly run into other layers that are still falling towards the PNS. This collision will create an outward-moving shockwave that ultimately shoves out the remaining layers of the star in what we call a supernova explosion.

At some point during this process (exactly when is still a matter of much study and debate), conditions are just right for the r-process to occur. The r-process, or rapid neutron capture process, occurs when nuclei are literally bombarded with free neutrons. The nuclei will capture these neutrons and become very unstable. Instead of just breaking apart though, the captured neutrons will change into protons and thus change the nucleus into a heavier element. This process works to create elements as heavy as uranium. Creating elements beyond this point doesn't work because the nuclei will break apart under neutron bombardment. And this is how pretty much all elements heavier than iron are formed, uranium included!

How long will it take before the Sun grows so large that Earth will no longer be habitable? Please explain.
A little less than 1 billion years.

As the Sun ages, it is actually getting steadily brighter. Over time, as the Sun fuses its core hydrogen into helium, the helium steadily builds up in the core. Because each single helium nucleus takes the place of what were once four separate particles, this decreases the gas pressure in the core very slightly. To adjust for this, the core contracts, heats up, and increases its fusion rate. Increasing the fusion rate also increases the energy output of the Sun. The predicted increase in brightness is shown graphically in Figure 3. Under the current circumstances, in a little less than 1 billion years, the inner edge of the Sun's habitable zone will have moved out beyond Earth's orbit, so Earth would become too hot for liquid water to exist on its surface.
Figure 3: The solid black line shows how the Sun's energy output has changed over time as a fraction of its current brightness. The shaded gray region shows the temperature range of the Earth if Earth's atmosphere remained unchanged. Figure is adapted from Kasting & Catling 2003.
Long story short, we've got a billion-year timer to get off this rock.

Why do the eccentricities of planets vary so greatly?
Planets' orbits are eccentric because planets don't form or exist in isolation. Planets don't just feel the gravitational pull of the stars they orbit; they're also getting tugged every which way by the other objects in their planetary systems. In many cases, planets appear to have migrated since their formation. This means pretty much what you think it would; planets may not necessarily have formed where we find them today. The different types of migrations, classified by what type of interaction causes them can be found here. When planets move into different orbits, the eccentricity of the orbit will almost certainly change as well. Interactions with other objects can both increase and decrease a planet's eccentricity. It just depends on the specific interaction that takes place.

To finally answer your question, the reason that all of the planets in our solar system have different eccentricities is because each planet experiences different sets of interactions that every other planet.

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