Neutrino Astrophysics: PeV-energy neutrinos!

Well, I thought I was done with neutrino astrophysics yesterday, but then I read about the recent discovery of two extremely high-energy neutrinos by the IceCube collaboration. As I've mentioned before, IceCube is a Cerenkov detector. Its 'detector' consists of about a cubic kilometer of ice in the Antarctic, and it has 86 strings of detectors suspended in the ice. They typically detect solar and atmospheric neutrinos, but in an article submitted to Phys. Rev. Letters last month, they report the detection of two peta-electron volt neutrinos. That's $10^{15}$ electron volts! These high-energy events are very unlikely to have resulted from cosmic ray interactions with the atmosphere (though the collaboration is investigating the possibility that they resulted from the decay of charmed particles produced by high-energy cosmics), and the collaboration is fairly sure that they're actually a product of some extremely high-energy astrophysical events. In the paper, they suggest gamma ray bursts or active galactic nuclei as potential sources, and they're hopeful that further analysis will reveal more similarly energetic neutrinos or give clues to their origin.

Oh, and just as proof that physicists have a sense of humor, the detected neutrinos have been named Bert and Ernie. It's even in the graphics for the paper!

From First observation of PeV-energy neutrinos with IceCube,
IceCube collaboration, 2013

The above graphic (taken from the paper) provides a visualization of the events in question. Each sphere shows the data from one photomultiplier tube embedded in the ice. The size of the sphere shows how many photoelectrons were detected, and the color shows the time at which the detection occurred, from red for the first detections to blue for the last. The energy of the event can be determined from the total number of photoelectrons detected, and the collaboration calculated energies of 1.04 and 1.14 PeV for Bert and Ernie, respectively.

For those interested, the paper in question can be found here.

Other neutrino-related posts can be found here.

Neutrino Astrophysics: Outstanding mysteries

As you've probably guessed by now, there's a lot we don't know about neutrinos and how they function in astrophysics. They have a lot of mysteries in store for us. Here are a few:

• Value of $\theta_{13}$ and the neutrino mass hierarchy. Remember the mixing angles from the discussion of neutrino oscillations? Well, we know two of them fairly well, including their signs, but we have very little information on $\theta_{13}$. This is particularly interesting because the sign of that particular mixing angle will tell us how the masses of the mass eigenstates are related. There are two possibilities: the natural mass hierarchy, in which $m_{\nu_1}<m_{\nu_2}<m_{\nu_3}$ (shown at left below), and the inverted mass hierarchy, in which $m_{\nu_3}<m_{\nu_1}<m_{\nu_2}$ (shown at right below).

  

  From Nishikawa, K. 2010
  Recent Status of Accelerator Neutrino Experiments

• Dirac/Majorana neutrinos. There is a bit of an outstanding question on whether the neutrino has a distinct antiparticle (Dirac neutrino) or is its own antiparticle (Majorana neutrino). If it is a Majorana particle, then processes such as neutrinoless double-beta decay could occur, in which two neutrinos annihilate in joint beta decay of two neutrons. This is a highly sought-after reaction, and there are legions of physicists working to find or rule out such a reaction.

  

  From wikipedia.org.

• Other neutrino sources. We've spotted neutrinos from a supernova before, but we should also be able to detect some from other astrophysical sources, like active galactic nuclei (really bright spots caused by accretion around a supermassive black hole) and gamma ray bursts (possibly bright bursts from rapidly rotating supernovae - is physics awesome, or what?). Detecting neutrinos from such events may help us understand what's going on in high-energy events.

In summary, neutrinos are pretty awesome little particles. They can be useful in understanding phenomena that light can't easily bring us information about, and they have a lot of mysteries left for us to sort out.

This is the seventh and final post in a series on neutrino astrophysics. Other neutrino-related posts can be found here.

Neutrino Astrophysics: Cosmic neutrino background

Once upon a time, almost 14 billion years ago, there was a Big Bang. In the milliseconds afterwards, everything in the Universe (mostly electrons, positrons, photons, and neutrinos) was in thermal equilibrium. What that means is that the reaction
\[
\nu+\overline{\nu}\leftrightarrow e^+ + e^-
\]
could occur in both directions. That means the energy of the neutrinos has to be high enough to produce two more massive particles, and the cross section for the interaction has to do with the temperature of the Universe. At a temperature of around $10^{10}$ K, the temperature of the Universe dropped below the critical temperature for the reaction shown above to proceed in both directions, so neutrinos could fly free through the Universe without having to worry about interacting with much else.
These neutrinos play a role in things like the ratio of protons to neutrons and the frequency components of the cosmic microwave background, and we believe that they are still around to this day. They're called the cosmic neutrino background. While general relativity is needed to understand the time evolution of the neutrino background, essentially what happens is that the neutrinos cool as the Universe expands. Theorists predict the current energy of the neutrinos in this background to be around $10^{-4}$ eV. To fully appreciate how cold these guys are, let's take another look at our favorite neutrino-related graph, the one showing flux vs. energy of neutrinos produced in hydrogen fusion.

Image from Bahcall, Solar Neutrinos.
http://www.sns.ias.edu/~jnb/Papers/Popular/Wiley/paper.pdf 

Note that the neutrinos we were so excited to detect with gallium detectors have energies around 0.3 mega electron volts. So the detection of the cosmic neutrino background is, for the time being, an insurmountable experimental challenge.

Even though we can't directly see the neutrino background, we have some good reasons to believe that it exists. For one thing, the presence of neutrinos affects the ratio of protons to neutrons, based on reactions like the following:
\[
n\leftrightarrow p+e^-+\overline\nu_e\\
p+e^-\leftrightarrow n + \nu_e
\]
As such, the presence of neutrinos throughout the Universe has dramatic effects on nucleosynthesis, the process by which nucleons combine into larger nuclei, and the current abundances give indirect evidence for the cosmic neutrino background.
For another thing, apparently the angular frequency components of the cosmic microwave background's temperature fluctuations are "damped" relative to predictions in the absence of the neutrino background. I believe that has to do with the way in which vibrations propagate through the very early Universe. Neutrinos provided a certain amount of diffusion, which served to make the Universe more isotropic than it would have been in their absence.

Why do we care about this? We know very little about the early stages of the Universe's evolution. Some of our most useful information comes from observations of the cosmic microwave background, which decoupled from the rest of matter when the Universe was around 300 years old. The neutrino background, if detected, can tell us quite a bit about the intervening time period, which gets us that much closer to understanding the highest-energy event in the history of the Universe.

This is the sixth post in a series on neutrino astrophysics. Other neutrino-related posts can be found here.

Neutrino Astrophysics: Supernova 1987A

Apart from the neutrinos from the Sun, we can also observe neutrinos from high-energy cosmic events. The best example of this is supernova 1987A, a stellar explosion in the Large Magellanic Cloud, a nearby galaxy, whose light reached us in February of 1987.
As we've seen, in the early stages of a supernova, the iron core's electron degeneracy pressure isn't enough to oppose gravitational collapse, and electron capture ensues, in which the reaction $p+e^-\rightarrow n+ \nu_e$ turns the core into an enormous atomic nucleus called a neutron star. This produces a huge flux of neutrinos. And to make matters even more interesting, as these neutrinos propagate through the incredibly dense core, they lose energy, much of which is released in the form of neutrino-antineutrino pairs. (At least, that's what I get from reading bits and pieces of the literature on the subject.) The net result is an immense flux of neutrinos heading away from the collapsing star. Outside the extremely dense core, the neutrinos can happily propagate through just about everything, whereas light from the ensuing explosion has to bounce around for quite a while before escaping. As a result, the neutrinos leave the immediate vicinity of the star long before the actual light, and carry well over 95% of the collapse's total energy.

Luckily for astrophysicists, there were several neutrino detectors in operation on February 23, 1987. These detected an enormous flux of neutrinos for a short period of time. In fact, Kamiokande-II saw such high detection rates that they were able to use more of their detector than usual for detection, because the background was such a low fraction of events compared to normal.* Just because I found this figure, I'm going to inflict it on you as well. It's the original data from Kamiokande-II showing the huge number of events. They detected 11 events in a matter of minutes, as compared with just a couple each day under normal circumstances. Another neutrino detector, IMB, near Lake Erie, detected 8 neutrinos at the same time.

Kamiokande-II spots supernova 1987A. Nhit is the number
of photomultipliers that recorded an event; any more than 20
is considered a neutrino detection.
M. Koshiba et al., 1988

Furthermore, these neutrinos were detected around three hours before the light from the explosion reached Earth, which confirms once again how awesome neutrinos are as astrophysical tools. It also allowed physicists to place upper limits on the mass of the neutrino, since more massive particles would have had to travel much slower than light, and would likely have been overtaken by the explosion's light on the way to Earth.

* The way that Kamiokande operates, as far as I can tell, is that it only uses the central portion of the water chamber. The outer layers are simply there to filter out background, like cosmic rays and radiation from detectors or other nearby objects. Only a small portion can be used for the real detection of neutrinos because of the incredibly low interaction rates. Any false positives would have a major impact on the resulting data.

This is the fifth post in a series on neutrino astrophysics. Other neutrino-related posts can be found here.

Neutrino Astrophysics: Neutrino oscillations

When last we left our heroes, the Sudbury Solar Neutrino Observatory (SNO) had concluded that while predictions for the total flux of neutrinos at the Earth were accurate, only about a third of those that reach us are electron neutrinos. This naturally begs the question: what are the rest of them? Subsequent experiments, using both astrophysical and accelerator neutrinos, concluded that they oscillated into muon- and tau-flavored neutrinos. This process is highly analogous to strangeness oscillations in the neutral kaons I've written so much about. In essence, neutrinos are produced and interact in flavor eigenstates, as the electron neutrino $\nu_e$, the muon neutrino $\nu_\mu$, and the tau neutrino $\nu_\tau$, but propagate through space in mass eigenstates creatively named $\nu_1$, $\nu_2$, and $\nu_3$. Since these particles have distinct masses, they also have distinct time evolution, and based on oscillation frequencies, we can determine the mass differences between various eigenstates.
Unlike in the kaon system, however, in which the $K^0$ had an equal probability of being a $K_1$ compared to a $K_2$, it turns out the $\nu_e$ is much more likely to be a $\nu_1$ than any other mass eigenstate, so in order to describe the probabilities associated with converting between the two bases, we have to introduce the concept of mixing angles. For simplicity, let's just look at two of the three neutrino types in both bases: $\nu_e$ and $\nu_\mu$ for the flavor eigenstates and $\nu_1$ and $\nu_2$ for the mass eigenstates. We could choose two constants to represent the components of $\nu_e$ in the two mass eigenstates, but in order to ensure normalization, we instead use the sine and cosine of an angle, $\theta_{12}$, and end up with
\begin{align}
\nu_e &= \cos(\theta_{12})\nu_1 + \sin(\theta_{12})\nu_2\\
\nu_\mu &= -\sin(\theta_{12})\nu_1 + \cos(\theta_{12})\nu_2
\end{align}
We can similarly convert from the mass eigenstates to the flavor eigenstates. Throwing in a third state complicates matters somewhat: we have to add two new mixing angles in order to describe the pairwise relationship between the states, and also have to add what's called a CP violating phase $\delta$. Overall, the relationship is a little messy:
\[

\left(\begin{array}{c}\nu_e\\ \nu_\mu\\ \nu_\tau \end{array}\right)= \left(\begin{array}{ccc}
c_{12}c_{13} & s_{12}c_{13} & s_{13}e^{-i\delta}\\
-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\delta} &
c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\delta} & s_{23}c_{13}\\
s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\delta} &
-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\delta} & c_{23}c_{13}
\end{array}\right)\left(\begin{array}{c}\nu_1\\ \nu_2\\ \nu_3 \end{array}\right)

\]
And if that weren't crazy enough, the matrix above uses shorthand: $c_{ij}=\cos(\theta_{ij})$ and $s_{ij}=\sin(\theta_{ij})$. If you set these equations in motion and let time run for a bit, you find that an initial electron neutrino, like one produced in the sun, propagates like this:

Mathematica source code from en.wikipedia.org

There are periods of time during which it is far more likely to detect this neutrino as a muon or tau neutrino than as an electron-flavored one! This explains the deficit of electron neutrinos observed from the sun, and relieved (astro)physicists of much distress.

This is the fourth post in a series on neutrino astrophysics. Other neutrino-related posts can be found here.

Neutrino Astrophysics: Solar neutrino problem

The neutrino detectors discussed in the last post are all well and good, but there's a bit of a problem. It's substantial enough to have earned itself a catchy name: the solar neutrino problem. See, the theory of electroweak interactions and astrophysical models of the Sun makes fairly precise predictions about the fluxes of neutrinos that should be measured by these various detectors. But when the detectors go and look for these neutrinos, they find substantially fewer - around a third to a half as many as theorists predicted. This is true all across the board, from the chemical to the Cerenkov detectors, and caused physicists quite the headache.

From Bahcall, Solar Neutrinos.

Initially, it seemed like this was bad news for us. Neutrinos come to us straight from the center of the sun, as opposed to photons, which take thousands to tens of thousands of years to bounce their way out of the center, so it seemed possible that the lack of neutrinos meant that against all odds, the sun's fusion was dying!

Luckily, SNO came to the rescue. As you can see at the right of the image above, the electron-neutrino reaction monitored by SNO, like all the other detectors, finds less than 30% as many neutrinos as expected. But, when we look at the other reaction, the one insensitive to neutrino flavor, we find around 90% of the expected flux, within uncertainties. So it seems that somehow the neutrinos produced in the center of the Sun, which are all electron neutrinos, somehow morph into other types as they travel to us. This phenomenon is called neutrino oscillations, and will be discussed briefly in the near future.

This is the third post in a series on neutrino astrophysics. Other neutrino-related posts can be found here.

Neutrino Astrophysics: Detectors

Neutrino detection is a tricky enterprise in the best of cases. Since neutrinos interact only via the weak interaction, their interactions have fantastically low cross-sections, which means that detectors end up seeing only a couple of neutrinos per day in some of the better cases.

The very first neutrino detector is typically called the Homestake or Davis experiment, and involved ${}^{37}$Cl in the form of perchloroethylene, a common cleaning chemical. The interaction monitored by the experiment was $\nu_e+{}^{37}\text{Cl}\rightarrow e^- + {}^{37}\text{Ar}$. For those of you without a periodic table handy, this is just the conversion of a neutron in chlorine to a proton in argon. The lowest-energy neutrinos that could participate in this reaction had energies of around 0.8 MeV. Luckily for science, the results of the experiment were interesting enough to warrant a new generation of detectors, based on gallium-71.

Gallium detectors monitor the reaction $\nu_e+{}^{71}\text{Ga}\rightarrow e^- + {}^{71}\text{Ge}$, but have a much lower threshold energy: just 0.2 MeV, which is low enough to detect pp chain neutrinos. Oh, and another fun fact: one of the gallium neutrino detectors contained 60 tons of gallium, at a time when the world production of gallium was just 10 tons per year! The threshold energies for these detector types are shown in the figure below. Both of these experiment types are chemically based: physicists set up the detectors, leave them alone for a couple of months, then chemically separate out the desired atoms, and somehow count them one by one. While these can detect solar neutrinos, this experimental model has some drawbacks: it can't tell you exactly when an interaction occurred, and it gives little to no information about the direction or energy of the incoming neutrino. These drawbacks led to the next generation of neutrino detection: Cerenkov detectors.

The first Cerenkov detectors looked for elastic scattering between neutrinos and electrons. In such a process, the electron may be accelerated to faster than the speed of light in the detector medium (water or ice). When this occurs, Cerenkov radiation is emitted as the electron decelerates. This is the source of that beautifully toxic blue you see around nuclear waste in underwater facilities. The basic structure for a Cerenkov detector is a huge tank of water (or a cubic kilometer of Antarctic ice, in the case of Ice Cube) for neutrinos to interact with, surrounded by hundreds or thousands of photomultiplier tubes to detect the Cerenkov radiation. Elastic scattering of neutrinos and electrons requires fairly high-energy neutrinos (around 7 MeV), so it can't detect the pp chain neutrinos that gallium detectors can, but it has the advantages of time resolution and directional resolution, since Cerenkov radiation is produced in a cone around the accelerated electron. Note that the neutrinos that scatter with electrons are primarily electron neutrinos, though small fractions of the interactions can involve the other flavors.

Based on this idea is a fourth detector, the Sudbury Solar Neutrino Observatory (SNO). It is a Cerenkov detector with heavy water, which contains a lot of deuterium, instead of the normal old hydrogen. The beauty of this detector is that it's sensitive to two reactions: $\nu_e+D\rightarrow e^-+p+p$, which only detects electron neutrinos, and $\nu+D\rightarrow \nu'+n+p$, which can detect all three flavors of electrons. This ability will turn out to be very beneficial in the resolution of the solar neutrino problem.

Modified image from Bahcall, Solar Neutrinos.
http://www.sns.ias.edu/~jnb/Papers/Popular/Wiley/paper.pdf 

This is the second post in a series on neutrino astrophysics. 

Other neutrino-related posts can be found here.

Neutrino Astrophysics: Rationale and production

This is the first in a series of posts about neutrinos and astrophysics.
Other neutrino-related posts can be found here.

At first, neutrinos seem like puzzling particles; they interact only by the weak force, carry almost no mass, and seem insignificant to the grand scheme of things. On the contrary, they've played a fundamental role in the evolution of the Universe, and are a uniquely powerful tool in our understanding of certain astrophysical phenomena. This is precisely because of their low interaction rates; they can propagate effortlessly through optically thick material and bring us information that light cannot.

As you may know, there are three types of neutrinos, the electron, muon, and tau flavors, which correspond to specific leptons. There are a variety of neutrino sources. The nearest and most accessible is the Sun, which sends neutrinos to us at a rate of around a billion per square centimeter per second. Then there are energetic events like supernovae and gamma ray bursts, which provide short-lived fluxes of neutrinos. There's also this thing called the cosmic neutrino background, which is analogous to the cosmic microwave background. Finally, there are atmospheric neutrinos, which are produced by cosmic ray interactions with the atmosphere.

In order to discuss neutrino detection, it is beneficial to examine the largest source of neutrinos in our neighborhood: fusion in the center of the Sun (discussed in much greater depth in the post here). The plot below shows the neutrino flux as a function of its energy as a result of various steps in hydrogen fusion.

Image from Bahcall, Solar Neutrinos.
http://www.sns.ias.edu/~jnb/Papers/Popular/Wiley/paper.pdf 

The solid lines show neutrino fluxes versus the energy of the produced neutrinos for various steps in the proton proton chain. In particular, the lowest-energy neutrinos shown (the spike on the left) are produced in the first step of the pp chain, while the other reactions, like boron-8 and He-p fusion, occur in only a small fraction of solar fusion reactions. The dashed lines show predicted neutrino fluxes from the CNO cycle, which isn't terribly relevant to the Sun, since its core is too cool for the CNO cycle to function.