How Could the Sun Be Destroyed?

It recently came up in conversation about how (hypothetically) one might be able to destroy the sun. The ideas included...


1. Stop fusion

If we were somehow able to make the sun inert (i.e. stop fusion), then it would seem to have no way to replenish the energy radiated away. Thus, it would cool, the pressure would fall, and the sun would begin to contract. However, this contraction is itself a source of energy -- in fact, they used to think that this was what powered the sun. This means that the sun will live for a while even after burning ceases...about 10 million years.

2. Disrupt it with a black hole

A very low mass black hole would have no noticeable effect on the sun, while a very large one (of order the sun's mass) would gravitationally disrupt it -- but we couldn't create such a beast artificially. In the intermediate range, a black hole at the center of the sun might even make it live longer. The reason for this is that the lifetime of the sun depends on the efficiency of its energy source; that is, the more effectively it can turn matter into energy, the longer it can keep itself up from the pull of gravity. Other than matter-antimatter annihilation, accretion onto a black hole is the most efficient source of energy that we know of, converting of order 10% of the rest mass of its fuel into energy. If the star reached a stable equilibrium with the black hole at its center, then slow accretion onto the black hole could maintain the star for a very long time.

There a lot of "ifs" in this one, however. It's not clear what kind of equilibrium (if any) the star would reach with a sizable black hole at its center. The efficiency of an accreting black hole is also extremely uncertain. Finally, depending on the initial mass of the black hole, it may be a problem even getting it to the center without seriously disturbing the star's structure.

3. Shoot it with a laser beam

Shooting it with a laser beam wouldn't put a hole in it, but it would heat it up. Unfortunately (or fortunately), to have a noticable impact, you'd need an extremely powerful laser beam, powerful enough to provide an energy comparable to the gravitational binding energy I quoted above.

4. Add Mass

If you add enough of anything to the sun, you can shorten its lifespan. However, to shorten the lifespan to anything less than a million years, you would have to add on the order of 100 times the sun's current mass.

5. Change its chemical makeup

For example, one person suggested that you could accelerate the nuclear reactions by introducing vast quantities of some mediator isotope, but that wouldn't destroy the sun, it would just cause it to expand and reach a new equilibrium. If the reactions increased the energy production very quickly, one might be able to blow the sun apart before it could equilibrate, but I'm pretty sure there aren't any known isotopes that could do this.

Decreasing the hydrogen content is another option, but since the sun is made mostly of hydrogen, this would be practically equivalent to pulling it apart, piece by piece. The gravitational binding energy of the sun is

$E \sim \frac{GM^2}{R} \sim 10^{48}~ergs$

so we won't be fulfilling these energy requirements anytime soon.

6. Other

There are a variety of timescales on which changes in the sun can take place. Some of the most important ones are:

Nuclear timescale - The approximate time it takes for the sun to burn the available nuclear fuel. This timescale is obviously relevant for the evolution of the sun, since this is the sun's energy source. In general, you'll see major changes in its position on the Hertzsprung-Russel diagram on the nuclear timescale. For hydrogen burning in the sun, it comes out to about 10 billion years.

Kelvin-Helmholtz timescale - The time it takes for the sun to radiate away its gravitational binding energy. If nuclear burning were to stop or become insufficient for compensating the energy losses, this would be the approximate lifetime of the sun. It comes out to around 10 million years.

Thermal timescale - This is the time on which the temperature profile of the sun changes. The virial theorem makes it so that the gravitational and thermal energies of the sun are about the same, so this timescale turns out to be approximately equivalent to the Kelvin-Helmholtz timescale.

Diffusion timescale - The average time it takes for a photon to undergo a random walk from the core to the surface. I'm guessing this is the one you were referring to. I've seen estimates that range from 50,000 to 10 million years, but to my knowledge, this timescale doesn't play a big role in calculating changes in the sun, so the precise time isn't very important.

Dynamical timescale - The time on which gravitational perturbations are communicated across the sun. It turns out to be comparable to the sound-crossing time, the free-fall time, and the hydrostatic time. For the sun, all of these come out to about 30 minutes.

If we wanted the sun to be "destroyed" on any timescale that was relevant for a science fiction novel, for example, the process would pretty much have to be occurring on the dynamical timescale. One of the most promising scenarios would involve a collision with another object. When the sun and the object collided, the sun would be disrupted on the dynamical timescale.

Another process that's known to occur on the dynamical timescale is stellar pulsation. When a star is unstable to hydrostatic perturbations, it can pulsate. If the amplitude of these pulsations were large enough, presumably the star could be blown apart. Perhaps if there was some contraption that created gravitational perturbations at one of the sun's resonant frequencies, a futuristic society could succeed in causing the sun to pulsate itself to pieces. It's a bit far-fetched, but then science fiction usually is...

What is the Cosmic Microwave Background? I: Primordial Blackbody

Let's start with the big picture and ask the simple question, "What is the cosmic microwave background (CMB)?". Let's imagine we have a radio/microwave telescope that operates at frequencies near 100 GHz and allows us to tune to a range of frequencies. How do we observe the CMB? Simple, point to any location on the sky! Unless you happen to be looking in the galactic plane or at a synchrotron source, then the majority of light hitting your telescope will be coming from the CMB. Once we've found the CMB, let's try changing our observed frequency a bit. If we compare the strength of the light in the range from, say, 50 to 500 GHz, we'll find that its intensity follows:

$I(\nu)=\frac{2h}{c^2}\frac{\nu^3}{e^{\frac{h\nu}{k T}}-1}$

This is a blackbody curve. We can find the temperature that the blackbody curve represents by simply measuring the location of the peak of the spectrum:

$T\sim 2\frac{\nu_p}{c}~K$

Measuring the peak, you ought to find that the temperature is around ~2.7 K. Alright, so that's the radiation field that we see, but what of it? Where did it come from? Well, we know that light is redshifted as the universe expands, following the basic law:

$\nu=\nu_0(1+z)$

where $\nu_0$ is the frequency we measure now and $\nu$ is the frequency of the same light at the time corresponding to redshift z. Thus, the light we see today would have redshifted by the above amount. Wouldn't this redshifting distort the spectrum so that it wasn't a blackbody anymore? No, it turns out if you redshift all of the light in blackbody radiation, you just get another blackbody with a lower temperature:

$T=T_0(1+z)$

This means that the effective temperature of the cosmic microwave background radiation decreases with time (or increases with redshift).

So, we now have the following two facts:

1) In all directions, we see a blackbody spectrum of temperature 2.7 K.
2) At earlier times, this radiation would have followed a blackbody spectrum represented by a higher temperature.

This implies something rather striking, that the universe itself was once a blackbody emitter! If you believe the Big Bang theory, then this was indeed the case. In fact, current theories suggest that the radiation "decoupled" at z ~ 1100. What does that mean? Well, at some point, the matter in the universe was so dense that light would not be able to travel very far without being absorbed by an atom or electron. "Decoupling" is basically the era in cosmic time in which this is no longer true.

It's not immediately obvious that such an era would be well-defined (that is, it could take a while for the photons to decouple), but it turns out that the transition is very sharp. This allows us to define what's commonly referred to as a "surface of last scattering". Don't be confused by the terminology -- the transition does not occur at a surface in space, but rather a surface in spacetime. In other words, the entire spatial volume of the universe was decoupling in a thin slice of time.

Although the term "decoupling" is common, you'll also frequently hear people talking about "recombination". Turns out this is referring to the same era in cosmic time and if you can understand the reason that the two terms refer to the same thing, you can go a long way to understanding where the CMB came from.

What is the Cosmic Microwave Background? II: Recombination

So, I mentioned in the previous post that the CMB was "decoupled" from matter at z~1100 and that this era is also referred to as "recombination". I'll explain why that is in this post.

First, what does "recombination" mean? In general, it's a term used to describe a process in which a free electron "recombines" with an ion to form either an atom or another ion of different charge. In a hot gas in local thermodynamic equilibrium, there will be a balance between a process that removes electrons from their host atoms or ions (ionization) and the process that puts them back (recombination). If the gas is really hot, then most of the electrons will be free. Why? It's mainly because a faster-moving electron is less likely to be captured by an ion and recombine.

We said before that the universe was getting colder with time, so if we assume that the universe was once really hot, then there must have been a time in which nearly all of the electrons were free. This was basically the case prior to z~1100. As the universe expanded and cooled, however, it eventually reached a point at which a given ion would recombine with an electron much more quickly than it would be ionized. It is at this time that "recombination" occurred and the universe switched from a plasma with mainly free electrons and protons to a gas composed mainly of neutral atoms.

Let's get to the main issue at hand; that is, why recombination implies a decoupling of photons from the gas. The answer to this question can be understood classically by looking at the natural frequency of an atom. Since the universe is 90% hydrogen, we can get a rough idea of what's going on just by looking at this simple atom. We know that it has many resonant frequencies, ranging from the UV (the Lyman series) to the optical (the Balmer series) and even on into the infrared (the Paschen series). Thus, one might expect that any frequency of radiation has a decent chance of being absorbed by neutral hydrogen. However, a given atom will only absorb in a specific series and the series in which it absorbs will depend on its energy state. It turns out that most hydrogen atoms in space are in their ground state (n=1), meaning that it will have resonant frequencies in the UV (Lyman series). This will apply to the newly-recombined atoms at z~1100 as well.

Now, let's look at the frequency of the CMB light and determine whether or not we expect it to be absorbed. If we plug z=1100 into the temperature equation I gave in my previous post, we find that the CMB was at ~3000 K at decoupling. From the Wein displacement law that followed, we can determine the peak frequency at this temperature and we find that it lies in the infrared range. There we have it! Since hydrogen in its ground state absorbs mainly in the UV, we won't expect the CMB photons to interact with it very much. Prior to recombination, the electrons were free and could resonate at any frequency they desired, so light was much more readily absorbed. Afterwards, resonances were restricted mainly to the UV and CMB light could readily pass through the see of neutral atoms.

Thus, the light we see in the CMBR today is a very sensitive probe of the distribution of matter at the time of decoupling. This, it turns out, is why the CMB is such a good cosmological probe.

What is the Cosmic Microwave Background? III: The Power Spectrum

Normally, when we're describing objects, we describe them as some set of three-dimensional spatial coordinates. For example, if I wanted to describe a ball, I would specify the position of its center in space and then say that it constituted the sum of all points (or "delta functions") within a radius "R" of the center. Since the ball is really simply described in this coordinate system, it turns out this is a nice way of representing it. What about something else; say, a sound wave? Would I want to represent that as a sum of points? Probably not. Instead, we would usually think of it as a sum of sine waves, each with different phase and amplitude. Obviously, it's much simpler to say that a sound is composed of, for example, a combination of 400 Hz and 200 Hz sine waves than it is to describe the position of all of the particles in the wave as a function of time.

So what about the ball? Can I also represent this as a set of sine waves? Yes, it turns out that, as a consequence of Fourier's theorem, I can describe any function as a combination of sines and cosines. The theorem is generally applied to things that vary as a function of time (like sound waves), but it works just as well on things that only "wave" in space. This is not a good description of the ball, however (try thinking about how you might combine sines and cosines to describe it's shape -- it's not simple), so we were better off with the set of points.

But what if we were to make small modification to the ball that would make it more realistic. That is, let's say that the ball does not have a smooth surface, but is instead "rough", either by the intrinsic structure of the solid or by wearing with use. Many of these imperfections are very small and there are quite a large number of them, so it would take a lot of points to describe them well. What about our combination of sine waves? Can that do any better? Since the imperfections are not evenly periodic (there's clearly a lot of randomness involved), it's not obvious that this description would be any simpler. However, fourier space provides us with a nice function, known as the power spectrum, that describes how prominent the imperfections are on a given scale.

To make this more concrete, let's try to see if we can reason out where we might find "peaks" in the power spectrum of, say, a beach. For simplicity, let's only stick with variations that we can see. What's the smallest variation? That's likely to be about the size of a grain of sand. Thus, we expect a peak in the power spectrum at around a millimeter. On what other scales is the beach "wavey"? Well, there will likely be pebbles and rocks interspersed with the sand (washed up by the waves), so we might also expect the power spectrum to rise on ~10 cm scales. There's a lot less fluctuation on this scale, however, so we wouldn't expect it to rise as much as on sand grain scales. Finally, what about on scales comparable to the size of the beach itself? In my experience, one will often find that the sand is somewhat wavey on these scales, implying that some mechanism is adding extra power at the longest wavelengths. I don't know exactly what it is, but it may have something to do with the wavelengths in the water hitting the beach or the collective weight of beach goers.

Hopefully you get the basic idea. The reason I'm talking about all this is that it's very common in cosmology to talk about the universe in terms of its power spectrum. We want to know how it fluctuates on a given scale and why. You can calculate power spectra for galaxy distributions, gas distributions, and even the CMB. The CMB is a bit different, however, because it's only a power spectrum in two dimensions (angular position) and on a spherical surface (the entire sky). Thus, rather than talking about wavelengths or wave vectors, we represent the power spectrum in terms of spherical harmonics (low l -> long wavelength, high l -> short wavelength). Here's a sample of recent data on the CMB power spectrum:

http://kicp.uchicago.edu/~davemilr/ISW/wmap_p_spec.JPG

Review of Mainstream Cosmology, Part I: Expansion and the Big Bang

With all the crazy ideas that get thrown around the internet these days, I thought it would be good to step back and review the mainstream view on cosmology in 2009. The field is advancing very rapidly, so it's possible that even the most reliable websites will be woefully out of date, both in terms of results and the evidence for them. Let's review, starting from the most secure and ending with the most puzzling/dubious aspects of the standard theories.

1) Expansion

The universe is, without a doubt, expanding. The most striking evidence for this is the fact that nearly every object in the sky exhibits a redshift in the spectrum of light that is emitted from it. Furthermore, more distant objects are observed to have larger redshifts, exactly what you would expect for expansion. Alternative theories (such as Zwicky's "tired light hypothesis") were put forth and seriously considered in the first half of the 20th century, but have had limited predictive power and are not consistent with any known physics. They have not been seriously considered by the mainstream for quite some time.

It should be noted that redshift is not the only reason we think the universe is expanding, but it was certainly the first evidence. Since the discovery of Hubble's Law in 1929, a great deal has been deduced under the assumption of expansion (most notably, the Big Bang Theory) that also produces testable predictions. The success of theories about large-scale structure, the cosmic microwave background, nucleosynthesis, etc., can be viewed retroactively as evidence for the expanding universe.


2) The Big Bang Theory

There is a lot of confusion amongst the general public about what the Big Bang Theory is really saying and which aspects of it are taken as gospel truth by the scientific community. In its simplest form, you can think of the argument as follows:

"If space is expanding, then the contents of our observable universe must have been much more condensed in the past".

How condensed? Well, the standard assumption is that the universe had a creation event and expanded from a singularity to its present size. Such a distant extrapolation can't possibly be verified by the current observations, but we can safely say that the universe expanded from a much more condensed state than its current one. There is good observational evidence for an epoch of nucleosynthesis (the creation of the elements) approximately one minute after the creation event (z ~ 10⁸). Physical models of the conditions in this early phase of the universe were able to predict the relative abundances of the light isotopes (including hydrogen, helium, and deuterium) to a very high degree of accuracy.

There is even stronger evidence for recombination, an event that occurred when the scales in the universe were ~1000 times smaller than today (~400,000 years after the big bang). Recombination is what gives rise to the cosmic microwave background (CMB) radiation, a nearly blackbody spectrum that can also be modeled very accurately. The models are so accurate, in fact, that they have also allowed us to precisely measure some of the parameters of our universe. More on this later.

In addition, there is increasing evidence for an epoch of inflation, thought to occur 10^-35 seconds after the creation event, during which the universe may have expanded by as much as a factor of 10⁵⁰! If we could observationally confirm such a hypothesis, it would be an overwhelming success for both the Big Bang Theory and the scientific method itself. I'll also discuss the evidence for this in more detail later. There are a lot of nice websites on the Big Bang Theory (see here, for example), so web surf if you want to know more.

Review of Mainstream Cosmology, Part II: Homogeneity and Isotropy

Most models of the universe assume that it is uniform to translations in space (homogeneous) and uniform in all directions (isotropic). This does not mean that every point in space is the same on all scales (it obviously isn't), but rather that the universe is smooth on the largest scales. By analogy, the surface of a spherical balloon is homogeneous and isotropic, despite having small bumps and wiggles if you look at it closely enough. Although this point is not controversial (even believers in steady-state cosmology like homogeneity and isotropy), it is actually more difficult to prove than, for example, expansion.

The first and most convincing line of evidence is the cosmic microwave background radiation. If it really is a fingerprint of the early universe, then its extreme uniformity implies homogeneity to one part in 10⁴. There are some indications of a possible asymmetry in the recent WMAP measurements of the CMB, but it is very small and seems to line up with the ecliptic, indicating that it may be due to contamination from the solar system.

There are many other things that we can observe to test homogeneity and isotropy, including galaxies, radio sources, the x-ray background, and Lyman-alpha absorption clouds. A nice (though outdated) review can be found here:

http://arxiv.org/PS_cache/astro-ph/pdf/0001/0001061.pdf

Review of Mainstream Cosmology, Part III: Age of the Universe

One of the obvious implications of the Big Bang Theory is that the universe has a finite age. A precise determination of the age of the universe will come out of the cosmological model, including all of the parameters, but we can make several independent estimates from other arguments.

First, there are globular clusters. From what we know about stellar evolution, we can model populations of stars and, under the assumption that they were all born at the same time, determine their age. When we do this with Milky Way globular clusters, we get an age of around 12 +- 3 billion years. Not technically a determination of the universe's age, but certainly a lower limit.

What about radioactive elements? Can we somehow use them to infer the age of the universe? It turns out that we can. Recent detections of Uranium-238 and Thorium-232 in stars have allowed us to use the traditional radioactive dating method to obtain an age of 12.5 +- 3 billion years. Again, a lower limit, but completely independent from and consistent with that from stars.

Finally, there are the measured cosmological parameters. When brought together and analyzed carefully, we can very tightly constrain the age of the universe to be 13.7 +- 0.2 billion years. It is very reassuring that this is consistent with both of the above ages. In fact, the standard model predicts that the Milky Way should have formed very early in the life of the universe, so the fact that the other two ages are of the same order (and not much less) is also consistent. One way to falsify the standard model would be to find something that is significantly older than 13.7 billion years. For a while, the globular cluster measurements were thought to represent such a falsification, but with the improvement of both our globular cluster measurements and our cosmological measurements, we are now finding nice agreement.

Note that there are many other ways of estimating the age of the universe, but the above are the most accurate and precise. I got the numbers from this nice review paper:

http://lanl.arxiv.org/find/astro-ph/.../0/1/0/all/0/1