Cosmic Static: The Stochastic Gravitational Wave Background

What would you hear if you could listen back to the very moment the universe burst into existence? Using the Cosmic Microwave Background (explained in Beatrice’s blog post), we have a picture of what the Universe looked like at ~380,000 years old, but we can’t use light to look any farther back in time because before the moment captured by the CMB, the universe consisted of an opaque plasma. Instead of using light, however, we can use gravity to probe our Universe’s earliest days. As explained in Sydney’s blog post, violent acceleration of extremely massive objects emits gravitational waves, and turbulent early universe processes like inflation (see Anne-Sylvie’s post) created the perfect environment for gravitational waves. The stochastic gravitational wave background is analogous to the CMB; it comes from the superposition of many gravitational wave signals that are individually indistinguishable, so it appears as a persistent background signal. The stochastic background can be dominated by cosmological sources like inflation, phase transitions, and cosmic strings, in which case it would provide a soundbite of the early days of our cosmic history. It can also be dominated by astrophysical sources- many overlapping individual signals coming from compact objects like black holes and neutron stars smashing into each other that are too weak or too distant to be detected individually- in which case it would provide a soundbite of our present astrophysical environment.


Why do we see the CMB but listen to gravitational waves? As a gravitational wave passes over Earth, it stretches space in one direction and contracts it in the perpendicular direction, so using extremely sensitive detectors, we can measure the frequency of these expansions and contractions, or measure their pitch. In order to explain some of the properties of the stochastic background, we will use the analogy of a crowded rock concert. Before the show, all the spectators are packed into the venue, each having a separate conversation. You can’t hear individual conversations, but you can hear the buzz of chatter. Each conversation represents an individual gravitational wave signal, too weak to be detected on its own, but combined with all the other conversations which are conducted at around the same volume, the room is filled with background noise. This background noise is the stochastic gravitational wave background.


If the concert is sold out, there is an equal conversation density in all directions. No matter which way you turn to listen, the background sounds the same in all directions, which means it’s “isotropic” in physics lingo. Cosmological backgrounds, a relic of an earlier time in the universe when matter was distributed nearly evenly across space, are expected to be isotropic. Now imagine several really loud groups of people come and sit down a few rows in front of you. You still can’t really hear their individual conversations, but you can definitely tell that the background is louder in their direction. If there was a dense population of coalescing stars or black holes in one specific region of the universe, the stochastic background would be louder in that direction, so it would be “anisotropic”.

If you’ve been waiting for the concert to start for a while already, the background chatter sounds the same now as it did 5, 10, or 15 minutes ago; it’s a stationary background that doesn’t depend on the time when you started listening. Similarly, if the background consists of independent conversations that last longer than the time between them, it is called a Gaussian background due to the Central Limit Theorem. However, if you’re one of the first people to arrive, you may be able to pick out bits and pieces of individual conversations starting up around you. The time between conversations is longer than the conversations themselves; this is a popcorn background. The same would be said of a stochastic background caused by overlapping gravitational wave signals whose duration is shorter than the period of time between individual events. This results in a background that sounds like popcorn in a microwave.


When Einstein predicted the existence of gravitational waves 100 years ago, his Theory of General Relativity (GR) predicted that gravitational waves could only move or stretch space in two ways, the plus and the cross tensor polarizations modes. Since we are interested in using gravitational waves to test GR, we can compare the polarization of the stochastic background predicted by GR to that predicted by alternative gravity theories, which allow gravitational waves to move in up to six directions, adding two vector and two scalar polarization modes to the two tensor modes already predicted by GR. The image below shows how a gravitational wave of each polarization would stretch and squeeze a test mass ring. Just like the ring responds differently to each polarization, so does the gravitational wave detector, so we can measure the polarization content of the stochastic background by analyzing the detector’s response and allowing for the possibility of all six modes. If we were to detect any polarization mode besides the two tensor modes predicted by GR, this would prove that GR is incorrect and force us to reconsider everything we thought we knew about gravity. For this reason, the stochastic background is a powerful tool not only for learning about our cosmic history and our astrophysical environment, it can also be used to learn about gravity itself.


For more information about stochastic backgrounds and testing general relativity, check out this arXiv preprint!

Whispers in the cosmos: gravitational waves

Chances are good that you’ve thought about the concept of gravity once or twice. If you’ve ever taken a high school physics class, you might have heard that gravity is an invisible force that is responsible for keeping you planted on the earth. At the beginning of the 20th century, the young Albert Einstein was also interested in gravity. The accepted theory of gravity at that time had first been put forth by Isaac Newton in the 17th century, and it had seen great success in physics for centuries.

But Einstein was bothered by one of the key foundations of Newton’s gravity: that space and time are both independent, absolute entities. In his Principia Mathematica, Newton stated that

“Absolute, true, and mathematical time, of it self and from its own nature, flows equably without relation to anything external… absolute space, in its own nature, without relation to anything external, remains always similar and immovable”.

In the early 20th century, physicists were just beginning to understand electricity and magnetism, and while carefully scrutinizing these developments Einstein came up with a new idea: that space and time are not distinct, absolute quantities as Newton said, but rather that they are intertwined in a very special way.

Putting the dimensions of space and time together, into what we now call spacetime, turned out to be necessary to avoid paradoxical outcomes in electricity and magnetism. But the concept of spacetime also leads to some very strange outcomes. A new theory of gravity, called General Relativity, is one of these outcomes.

In General Relativity — Einstein’s theory of gravity — gravity is the curvature of spacetime itself. Physicists often say that spacetime is the “fabric of the cosmos”, but it’s not exactly made up of “stuff”, so how can it be curved?

This is difficult to conceptualize, but one can use an analogy to understand a little better. If you were to place a baseball on a spandex sheet of fabric, the ball would distort the sheet by bending it. A bowling ball would also bend the sheet, even more than the baseball. If you took a marble and added it to the sheet, the marble would follow the spandex surface, curving around the bowling ball (an orbit).

In this image, two masses both bend spacetime. [You can ignore the yellow lines, which are part of a bigger image not included.] This is the essence of Einstein’s gravity: massive objects bend spacetime, and in turn, spacetime tells matter how to move. Now we’re ready to talk about gravitational waves.
In this image, objects with different mass bend spacetime. The heaviest object, in yellow, bends spacetime more than the other two. Image credit: ESA – C. Carreau
This is the essence of Einstein’s gravity: massive objects bend spacetime, and in turn, spacetime tells matter how to move. Now we’re ready to talk about gravitational waves.

Imagine for a moment that you rotate the bowling ball about its vertical axis on the spandex sheet. The bowling ball has a smooth surface and is round, so there isn’t any effect on the sheet. However, if we took a pair of bowling balls and rotated them around each other, ripples would begin to spread outward on our spandex sheet. Similarly, if we took a bowling ball that wasn’t quite round (maybe with a lump of cement stuck to a side) and tried to rotate the ball, the lump would “catch” on the spandex and create ripples.

These ripples, produced either by two objects orbiting each other (we call this a binary system), or a lumpy object rotating about its axis, are gravitational waves. They propagate radially outward from the objects that produce them and travel at the speed of light. As you can imagine, this means that gravitational waves are being produced all the time, all over the universe, from all kinds of systems: the moon and Earth in their orbit; a pair of ice-skaters spinning while holding hands; a football wobbling from a poor throw; a distant rotating planet with mountains.

When the gravitational waves produced by any of these examples hit matter like you and I, the effect they have is to stretch and squeeze it. All the stretching and squeezing happens in the direction that’s perpendicular to the gravitational wave’s travel path (using more technical physics lingo, we would say that gravitational waves are transverse).

The amount of stretching and squeezing is extraordinarily small because gravity is actually fairly weak [just think: you can defy the entire gravitational pull of the earth just by jumping or using a refrigerator magnet to pick up a paper clip!]. To produce “big” gravitational
waves, we have to look for waves that are produced by something called compact objects. To explain what a compact object is, imagine that you have a large round bread roll. The roll is made up of ordinary atoms and has mass; we could weigh it on a kitchen scale, and measure its diameter. Now imagine squashing the roll with your hands until it forms a dense lump of bread. If we place the squashed bread roll on our scale, it would have the same weight as it did before. It contains the same number and type of atoms it had before we squashed it. But now, the roll occupies a much smaller region of space, and the bread is more dense than it was before. It is now a compact object.

This figure shows how spacetime is curved for objects with the same mass, but increasing compactness from left to right. You can see that the most compact object, on the far right, distorts spacetime in a much more violent way than the others. Image credit: National Geographic

Compact objects bend spacetime in a much more extreme way than other objects, and as a result, the gravitational waves they produce stretch and squeeze matter enough that we can actually detect it. Don’t get too excited about the amount of stretching, though. The most compact astrophysical objects in the universe (that we know of) are black holes and neutron stars, which are dead remnants of very massive stars. If a “big” gravitational wave produced by a pair of orbiting black holes or neutron stars were to hit you head-on, your height would only change by one thousandth the diameter of a proton!

Detecting gravitational waves is thus a very tricky business; the detectors we use must be capable of measuring changes in length that are smaller than the atoms the detectors are made of! We will discuss the methods that we use to construct such detectors and conduct searches for gravitational waves in a future blog post.

But before you go, it’s important to understand why any of this matters. One reason we’re interested in detecting gravitational waves is to test Einstein’s gravity. Although we have significant experimental evidence that supports General Relativity, there are feasible contending theories that are similar and vary only from Einstein’s in the way that gravitational waves behave. So far, our detections of gravitational waves have continued to support Einstein’s theory, but it is important to continue to test this.

The second reason to search for gravitational waves is to learn from them. Every telescope ever built has relied on light of some form (x-ray, gamma ray, infrared, visible, radio, etc.) to observe the universe. Gravitational wave detectors are completely different; they use gravity instead of light to observe the universe. This allows us to study systems, such as black hole binaries, that can’t be directly studied using light. We now have the potential to unlock mysteries about black holes, neutron stars, stellar evolution, the Big Bang and much more.

And that’s not all. Any time our species has found a new way to observe the universe around us, we find unexpected things, things we didn’t even know that we didn’t know. There is no reason to suspect that this will be any different. We’re standing on the cutting edge of a new observational experience for mankind, and there are all kinds of beautiful, bizarre and unexpected things to be discovered!

Stay tuned to hear more about gravitational waves from the IGC. In the meantime, if you’ve got questions, I love to talk science! Feel free to email me.

The Origin of the most energetic particles in the Universe

Cosmic-rays, that is, the high energy subatomic particles, which constantly bombard the Earth’s atmosphere, were discovered by Victor Hess in 1912 in a series of very daring, high altitude balloon flights. With the measurements they made, Hess and his team showed that the ionization level of air in the atmosphere increases with altitude, a confirmation that extra-terrestrial high-energy particles, were constantly impacting atmospheric molecules.

Fifty years later, in the Volcano Ranch experiment, led by John Linsley, the first ultra-high energy cosmic ray (UHECR) with energy exceeding 1020 eV, roughly 1 billion times higher than the energy of protons accelerated at the Large Hadron Collider, was discovered. This discovery led to the development of the scientific field dedicated to the search for the origin of UHECRs, the most energetic particles ever produced after the Big Bang.

Extensive Air Showers

When a 1020 eV particle collides with an air molecule in the upper atmosphere, a shower of lower energy particles develops in the atmosphere. By the time the shower reaches ground level, millions of these lower energy, secondary particles have been produced, and the footprint of the shower can extend more than 3 km2 across, that is, roughly 1/3rd of the surface area of State College, PA. By studying the air showers, scientists can measure the properties of the original cosmic ray particles.

Illustration of extensive air-showers induced by UHECRs. Image credit:
Illustration of extensive air-showers induced by UHECRs. Image credit:

The Pierre Auger Observatory

The world’s largest UHECR detector, the Pierre Auger Observatory (hereafter Auger), is located in the Pampa Amarilla, in the Mendoza region of Argentina. The experiment covers an area of 3000 km2, that is, more than 30 times the surface area of Paris. Auger consists primarily of two types of extensive air-shower detectors. Water Cherenkov surface stations, and Fluorescence telescopes. The water Cherenkov stations are large plastic tanks, each containing 10 tonnes of purified water that register the blueish Cherenkov light which gets produced when particles travelling at the speed of light collide with the water molecules inside the tank. There are 1660 such stations, spaced 1.5 km apart, forming the Auger surface array. They have 100% duty cycle. At the four edges of the array, surrounding the surface detectors are 27 fluorescence telescopes. These operate only on dark moonless nights, detecting the fluorescence light produced by the de-excitation of nitrogen molecules as the shower propagates in the atmosphere. The power produced by a single UHECR shower is roughly that produced by a single 60 watt light bulb travelling at the speed of light, so this is a challenging measurement. The combination of the fluorescence technique and surface detectors allows us to see UHECR showers in “hybrid” mode, providing the most accurate measurement of the properties of the air shower.

Two Auger Collaborators posing with "Alaide", one of the 1660 surface stations of the Pierre Auger Observatory
Two Auger Collaborators posing with “Alaide”, one of the 1660 surface stations of the Pierre Auger Observatory

Where do UHECRs come from?

The origin of UHECRs is a mystery. In what kinds of sources do particles get accelerated to 5×1019 eV? It is this question that scientists working in Auger have been addressing. Although we don’t yet have a definitive answer, there are certain minimal requirements that an astrophysical source must satisfy in order to be a plausible UHECR accelerator. A simple requirement can be stated as follows: the Larmor radius of the particle in the magnetic field of the source, must be larger than the radius of the acceleration site, in order for the particle to be effectively confined in the source. This requirement is what limits the energy to which protons can be accelerated in the Large Hadron Collider; the strength of the magnets, and the radius of the tunnel. This simple argument, known as the Hillas criterion, rules out many known classes of powerful astrophysical sources as possible UHECR acceleration sites: supernova explosions, regular galaxies, including our own Milky Way, white dwarf stars, etc.; the list is long. It only leaves a few known source classes as possible UHECR accelerators, all of which are extragalactic: gamma-ray bursts, active galactic nuclei, neutron starts, and rare, powerful shocks in the intergalactic medium.

Arrival Directions

Two features of the intergalactic propagation of UHECRs make us hopeful that we can discover the origin of UHECRs, by finding associations between known powerful astrophysical accelerators and UHECR arrival directions. Firstly, cosmic rays with energy exceeding 5×1019 eV have a short propagation horizon. They are so energetic that when they collide with a photon from the Cosmic Microwave Background, the cosmic photons that are left over from the Big Bang, they produce a Pi meson (or pion). This is an interaction that results in significant energy loss (generally between 14-50%) for the cosmic ray. The average distance that a 6×10^19 eV a stripped Hydrogen nucleus (i.e. a proton) can travel, while retaining 0.23 of it’s energy is 100 megaparsecs (Mpc): a small distance in extragalactic terms. An analogous (and often smaller) horizon exists for heavier elements such as Helium, Carbon, Oxygen, Iron, Silicon: other frequently observed cosmic ray species. In summary, independent of the chemical composition, the sources of UHECRs must be powerful astrophysical accelerators within ~100 Mpc.

Secondly UHECRs are expected to experience small deflections, after they escape their sources, in the weak magnetic fields that permeate the intergalactic medium. A 5×1019 eV proton is expected to experience a deflection, θ, of 3 degrees or less, over 100 Mpc of propagation. Therefore, the arrival direction of protons are expected to exhibit a correlation with the positions of their sources, within a few degrees. Deflections scale linearly with charge Z, as θZ(E) = Z x θproton(E), hence heavier nuclei are expected to have more significantly deviated arrival directions.


The arrival directions of UHECRs observed in Auger with energy exceeding 5x1019 eV (grey circles), and the predicted UHECR arrival distribution in a model in which known extragalactic sources within ~100 magaparsecs are the sources of UHECRs observed with Auger, reproduced from Oikonomou et al. 2013. A statistical analysis as in Oikonomou et al. 2013 is required to determine the degree of correlation of the data with the model in question.
The arrival directions of UHECRs observed in Auger with energy exceeding 5×1019 eV (grey circles), and the predicted UHECR arrival distribution in a model in which known extragalactic sources within ~100 magaparsecs are the sources of UHECRs observed with Auger, reproduced from Oikonomou et al. 2013. A statistical analysis as in Oikonomou et al. 2013 is required to determine the degree of correlation of the data with the model in question.

Searches for associations so far, have not resulted in statistically significant correlations between known extragalactic sources, and observed UHECR arrival directions (see e.g. Oikonomou et al. 13, Oikonomou et al. 15, Abreu et al. 14). The absence of a clear correlation is slightly disappointing, as well as puzzling: we still haven’t solved this mystery! This absence of associations could mean that UHECRs are heavy nuclei (e.g. Carbon nuclei), thus suffering large deflections, and not pointing back to their sources, or that magnetic fields in the direction of (at least some of) the sources of UHECRs are stronger than we previously inferred from independent astrophysical measurements. Other possibilities include an origin of UHECRs in some unknown population of astrophysical sources, or something more exotic, like the decay of supermassive primordial particles left over from the Big Bang. Despite the lack of a clear answer so far, the origin of UHECRs remains a very active research topic within the Auger Collaboration, and beyond. As more data get collected with existing, and future experiments, we will get closer to the answer to this mystery.

The HAWC Observatory and multi messenger astrophysics

Panorama of the HAWC site, with Sierra Negra visible in the background.
Panorama of the HAWC site, with Sierra Negra visible in the background.

Two of the major questions in the field of high-energy astrophysics are how and where cosmic rays are accelerated.  However, tracing cosmic rays back to their origins is a bit tricky: since they are charged particles, they bend in the Galactic magnetic fields on their way to Earth.  Luckily, there are also gamma rays associated with these cosmic ray acceleration processes.  Gamma rays are neutral, so they point back to their sources, and are therefore excellent candidates to learn more about cosmic ray processes.  These sources include supernova explosions, gamma-ray bursts, and active galactic nuclei and are some of the most intense, highest-energy events known in the Universe.  The High Altitude Water Cherenkov (HAWC) Observatory is a fairly new experiment dedicated to studying these gamma rays.  This observatory looks very different from the astronomical observatories you may be familiar with: it consists solely of giant (~5 meter tall) tanks of water which detect gamma rays using a unique method known as the Water Cherenkov technique.

The beginning of an electromagnetic shower, showing the creation of gamma rays, electrons, and positrons.
The beginning of an electromagnetic shower, showing the creation of gamma rays, electrons, and positrons. (Source, shared under a Creative Commons License)

When a cosmic ray or gamma ray hits the Earth’s atmosphere, it interacts with the air molecules and starts a cascade of electromagnetic particles via the processes of Bremsstrahlung emission (resulting in the emission of photon) and pair creation (an electron and a positron are created). Each successive step of the chain reaction has exponentially more particles, with each individual particle having less energy than those in the previous step, until the energy of the individual particles hits some critical energy and the shower begins to die out.

One of HAWC's 300 tanks, with the author standing in front of it for scale.
One of HAWC’s 300 tanks, with the author standing in front of it for scale.

HAWC is built at an altitude of 4100m on the saddle point between Pico de Orizaba and Sierra Negra in Mexico, where the number of air shower particles is much greater than at sea level.  It consists of an array of 300 tanks of water, each of which is 7.3 meters in diameter, 5 meters high, and has four photomultiplier tubes at the bottom.  When the charged particles from the air shower reach the array, they are traveling faster than the phase velocity of light in water.  This leads to an emission of a faint blue light known as Cherenkov radiation, which is amplified by the photomultiplier tubes.  By looking at the pattern of hits in all the tanks during an event, we can determine where in the sky the event came from as well as its approximate energy.  For example, an event with an energy of >10 TeV is expected to hit every tank in the array, while a smaller event would only hit a fraction of the tanks.  Gamma/hadron separation techniques are employed to separate the gamma rays from the extremely large background of cosmic rays (Here is a fun game to see if you can distinguish gamma rays from cosmic rays by eye!).

Illustration showing the placement of the PMTs inside each tank, as well as the Cherenkov light (Credit: HAWC Collaboration)
Illustration showing the placement of the PMTs inside each tank, as well as the Cherenkov light (Credit: HAWC Collaboration)

HAWC officially finished construction and was inaugurated last spring, but opportunistic data taking with the partially completed array was taken during the construction phase.  A few papers with early results have already been published, with many more to come.  HAWC operates 24 hours a day, making it a perfect experiment to survey the entire overhead sky in gamma rays.  In addition to searching for new TeV gamma-ray sources, it is capable of monitoring existing sources for flares to get a sense of the time variability of these possible cosmic ray accelerators as well as searching for transients such as gamma-ray bursts.

There are also exciting implications for multi-messenger astrophysics.  In addition to notifying other observatories of flaring sources as mentioned above, it can also extend the spectra of sources to higher energies than satellite experiments are capable of.  This is especially interesting because the energy range that HAWC operates in is where we expect to see differences in the spectra of gamma rays originating from electron accelerations vs. those originating from hadronic accelerators.  HAWC also shares information with non-gamma-ray experiments.  An example of this would be the IceCube Neutrino Observatory: both experiments study similar energies and can see the same part of the sky.  Both neutrinos and gamma rays are expected in hadronic cascades.

An image of a few of the water Cherenkov tanks
An image of a few of the water Cherenkov tanks

The future is bright for HAWC.  Even though the experiment is still in its infancy and the ~100 collaboration members are still busy sifting through early data, an upgrade consisting of a sparse array of smaller “outrigger” tanks was recently funded and will begin construction soon.  This will increase the effective area of the detector and in turn, its sensitivity to the higher energy (>10 TeV) air showers.