What are cosmic ray particles that exceed theoretical limits?

Ultra-high-energy cosmic rays are extremely high-energy cosmic rays, with energies far exceeding any particle beams that humans can currently produce. Recently, astronomers have confirmed an ultra-high-energy cosmic ray particle, the Amaterasu particle, but we do not know its origin.

Written by | Xia Chen

On May 27, 2021, the US Telescope Array (TA) experiment detected an ultra-high energy cosmic ray particle. This discovery was published in the journal Science two years later in November 2023 [1]. A Japanese researcher in the TA collaboration group also named it Amaterasu, which means "Amaterasu", referring to the Amaterasu, the sun goddess in Japanese mythology. (Friends who have watched the anime "Naruto" should be familiar with this term. When the Uchiha brothers activated the Sharingan Amaterasu skill, they shouted "Amaterasu!")

What is so magical about this particle? Its energy is very high, reaching 244EeV (1EeV=10^18eV)! This energy is 300 million times higher than the energy that can be produced by the most powerful particle accelerator currently available to humans. Although the name of the Amaterasu particle is borrowed from the sun, it has nothing to do with the sun. It is a trillion times more energetic than solar cosmic rays. The Amaterasu particle ranks second in the energy ranking of cosmic ray particles detected by humans. The first place is the Oh-My-God (OMG) particle note 1 , which was detected in 1991 by the HiRes (High Resolution Fly's Eye) experiment, the predecessor of the TA experiment, with an energy of about 310EeV.

The energy ranking is obviously not the only reason for being on the cover of Science. What is really interesting is that the particle energy of this event exceeds 100EeV, which is impossible according to existing theories and astronomical observations.

Introduction to cosmic rays

Let's first learn about cosmic rays. In 1912, Austrian-American physicist Victor Hess took a hot air balloon to an altitude of 5 kilometers in order to study the cause of air ionization. He found that the air ionization rate decreased with increasing altitude, which was consistent with the traditional speculation that radioactivity came from the surface; but at about 700 meters, the ionization rate began to increase, and finally exceeded the surface ionization rate by several times. He proposed that there was highly penetrating radiation outside the atmosphere that ionized the air. Robert Millikan believed that the radiation speculated by Hess was gamma rays (i.e. high-energy photons), and introduced the name cosmic rays, which is usually abbreviated as cosmic rays in Chinese.

Subsequent studies confirmed that cosmic rays do exist, and Hess won the 1936 Nobel Prize in Physics for discovering cosmic rays. However, its main component is not photons, but high-energy charged particles, 90% of which are protons, and the rest are ionized nuclei, electrons, positrons, and antiprotons. The types of elements in cosmic rays are very rich, and the relative abundance of most elements is close to that of the elements in the solar system, which shows that our solar system is not special in the universe. According to existing theories, most of the elements heavier than protons and helium, such as carbon, oxygen, and calcium that make up life, are generated by nuclear fusion inside stars. When a massive star evolves to the end, a supernova explosion occurs. This process not only synthesizes heavier rare elements, but also ejects a large amount of matter into space. Some matter continues to be accelerated into cosmic rays in the shock wave of the supernova remnant, some cool down to form planets, and may also synthesize some organic matter and become the seeds of the birth of life. It can be said that cosmic rays are stardust, and we are all stardust.

Cosmic rays are closely related to the development of particle physics in history. Before the invention of large particle accelerators, cosmic rays were almost the only source of high-energy particles. In 1932, Carl Anderson, an American physicist and a student of Millikan, discovered positrons in cosmic rays, which was the first time that humans saw antimatter. Anderson and Hess won the Nobel Prize in Physics in the same year. In the late 1940s, people discovered muons, mesons and exotic particles through cosmic rays, which were all milestone discoveries. Today, the capabilities of particle accelerators are close to the limits of what humans can build. In order to find new physics, people once again turn their attention to high-energy astrophysical objects such as cosmic rays. For example, looking for signals of dark matter particles through antimatter in cosmic rays, looking for the violation of Lorentz symmetry in ultra-high-energy cosmic rays, etc.

Since interstellar space is full of irregular magnetic fields and cosmic rays are charged, they will keep turning during propagation. From the perspective of galaxies, the movement of cosmic rays is similar to the random walk of Brownian motion. Therefore, cosmic rays are not straight lines, but more like a cloud of fog that covers the entire galaxy. This is the difficulty in studying cosmic rays. The cosmic rays we detect are almost isotropic, and it is difficult to speculate where they come from.

In addition to charged cosmic rays, the atmosphere also receives electrically neutral high-energy gamma photons and neutrinos. These neutral particles do propagate in straight lines and can be traced back to high-energy celestial activity sources, which helps to understand the origin and propagation process of cosmic rays. The High Altitude Cosmic Ray Observatory (LHASSO, Lasso) in Daocheng, Sichuan, discovered a giant bubble-like structure in the star-forming region of Cygnus through gamma-ray observations, and for the first time in history, found the origin of 10PeV (1016eV) energy cosmic rays. (See: "Lasso discovered a giant ultra-high-energy gamma-ray bubble and certified the first super cosmic ray acceleration source") This celestial body is located in the Milky Way and is called a super cosmic ray source, but its energy is still 10,000 times lower than that of the Amaterasu particles. Therefore, the Amaterasu particles are more likely to be produced in more violent celestial activities outside the Milky Way.

For the first time in history, Chinese researchers have discovered the origin of cosmic rays with energies higher than 10PeV. The results were published in Science Bulletin. Image source: sciengine.com

Energy spectrum and detection of cosmic rays

The energy span of cosmic rays is very large, from 1MeV (106eV) to 300EeV (3×10^20eV) at the OMG particle level. The figure below shows the cosmic ray flux, or energy spectrum (the number of particles passing through a unit area per unit time, unit energy, and unit solid angle):

Energy spectrum of cosmic rays. Image credit: Particle Data Group (PDG).

The total energy spectrum of cosmic rays represented by the black dots in the figure approximately satisfies the power-law spectrum, that is, it is a straight line on the double logarithmic coordinate graph. The main structure based on the power-law spectrum is several small inflections in the high-energy region. Astrophysicists figuratively compare the energy spectrum of cosmic rays to a human leg, with the inflection on the left being the "knee" and the inflection on the right being the "ankle". After the data is enriched, a small inflection can appear between the knee and the ankle, which is called the "second knee". These inflections may suggest different origin mechanisms of cosmic rays. The place where the energy spectrum on the right ends is the location of the Amaterasu particle and the OMG particle, sometimes also called the "toe".

In general, the flux of cosmic rays is mainly concentrated near a few GeV, and decreases rapidly with increasing energy. Ten thousand cosmic rays with an energy of 1GeV can be collected per square meter per second, and the probability of detecting cosmic ray particles with energy higher than 10EeV is once in a century even in an area of ​​1 square kilometer.

Different energy bands require different detection methods. The lower energy part can be detected directly, while the higher energy part can only be detected indirectly. Direct detection of cosmic rays is to use a particle detector to directly receive cosmic ray particles. Because of the existence of the atmosphere, the cosmic rays received on the ground are actually secondary cosmic rays produced after the collision of primary cosmic rays with the atmosphere. To directly detect primary cosmic rays, you can only go outside the atmosphere. You can use a hot air balloon to send the detector to high altitudes where the air is thin, or launch a satellite into outer space. For example, my country's Wukong Dark Matter Exploration Satellite (DAMPE) is essentially a cosmic ray detector. The detector type used by Wukong is a calorimeter, which distinguishes the type and energy of particles by measuring the energy deposition of incident particles in the calorimeter. It indirectly searches for dark matter through observed anomalies in the cosmic ray energy spectrum.

The Alpha Magnetic Spectrometer (AMS-02) experiment, led by 1976 Nobel Prize winner in Physics Samuel Ting, is another famous direct cosmic ray detection experiment. AMS-02 was launched in 2011 and installed on the International Space Station. The magnetic spectrometer has a magnet and uses the different deflection angles of particles with different charges in the magnetic field to distinguish particle types more strongly than the calorimeter. However, due to the limitation of the magnetic field strength of the magnet, the upper limit of the energy detected is usually lower than that of the calorimeter.

There are many other cosmic ray detectors launched by humans, such as the famous Voyager 1 and 2. Although their main observation targets are Jupiter and Saturn, they are equipped with cosmic ray systems. Currently, they are the only pair of detectors that directly detect cosmic rays outside the solar system. (Editor's note: See "This photo she took made humans rethink the universe and themselves")

However, the cosmic ray detectors on satellites are only 1 square meter in size. Not to mention that the upper limit of the energy they can measure is not high enough, even if they can measure the energy of Amaterasu particles, the chance of encountering it is only one in a billion. There are so few high-energy cosmic rays that direct detection is obviously unrealistic. Fortunately, although the atmosphere interferes with direct detection, it is also equivalent to a huge calorimeter, and we can infer the properties of the original cosmic rays.

After a single high-energy cosmic ray particle collides with matter in the atmosphere, it may produce secondary particles such as muons, neutrinos, positrons and anti-electrons, and high-energy gamma photons. These secondary particles still have high energy and continue to produce new particles while moving in the atmosphere. New particles regenerate new particles. This process is called a cascade reaction. The number of secondary particles that finally reach the ground can reach millions. The cascade reaction of cosmic rays in the atmosphere is also called an extended air shower, or simply an air shower. In fact, the calorimeter used for direct detection of cosmic rays uses a similar cascade reaction principle, but it is a smaller version of what occurs in artificial detectors.

Schematic diagram of an extended air shower. Image source: sott.net.

Indirect detection of cosmic rays is to use atmospheric showers to lay out detection arrays on the ground (such as the LHASSO mentioned above), detect secondary particles to infer the energy deposition in the atmosphere, and then infer the energy and direction of the original cosmic rays, and even distinguish its particle type. Detectors on the ground can be placed every few kilometers, spreading out into a detection network of thousands of square kilometers. Such a large area can capture ultra-high energy cosmic rays in a limited time.

TA experiment

The TA experiment that saw the Amaterasu particles this time is a ground-based indirect detection experiment. It is located in the western desert of Utah, USA, at an altitude of 1,400 meters. There are 507 3-square-meter plastic scintillator detectors arranged at intervals of 1.2 kilometers to form a ground detection array with a detection area of ​​700 square kilometers.

Schematic diagram of TA experiment. Image source: telescopearray.org

In the case of the Amaterasu particle event, astronomers detected a large number of muons, from which they inferred that the Amaterasu particles should be atomic nuclei rather than high-energy photons, and used their energy information to reconstruct the energy of the original cosmic rays. The time sequence of each detector's response can be used to infer the direction of movement of the original cosmic rays.

The TA experiment is also equipped with a fluorescence telescope to measure the fluorescence emitted by nitrogen molecules in the atmosphere after being excited (the principle is similar to the fluorescent lamps used in daily life). In other words, we can know what elements the cosmic ray particles are composed of through the fluorescence telescope. The atmospheric shower is centered on the incident cosmic ray and expands forward in a cone shape, reaching its maximum at a certain depth, which is usually recorded as Xmax. 78% of the air is nitrogen. Nitrogen molecules emit low-energy fluorescence after being excited by high-energy photons in the atmospheric shower. By observing the range of fluorescence through a fluorescence telescope, the degree of atmospheric shower development can be obtained and Xmax can be measured. If cosmic rays are atomic nuclei, generally speaking, the heavier the nuclide, the smaller the Xmax corresponding to the nuclide. Through simple linear fitting or complex machine learning methods, the nuclide of cosmic rays can be inferred from Xmax. However, compared with the artificially designed calorimeters in the direct detection of cosmic rays, there is a large uncertainty in the calculation of atmospheric showers, so the indirect detection of cosmic rays is not very accurate in distinguishing nuclides.

Particles beyond the limit

Why is it said that Amaterasu particles and OMG particles with energies exceeding 100EeV should not appear? This has to start with the Big Bang.

In 1965, American radio astronomers Arno Penzias and Robert Wilson discovered that when debugging an antenna for satellite communications, they would always detect microwave noise with a wavelength of about 7.35 cm, regardless of the direction the antenna was pointing, whether it was day or night. The noise they discovered was actually the cosmic microwave background radiation (CMB) predicted by American physicists George Gamow, Ralph Alpher and Robert Herman in 1948. CMB is the key evidence supporting the Big Bang theory, and modern cosmology is based on the Big Bang theory.

Temperature map of the cosmic microwave background (CMB), measured by the Planck satellite; small anisotropies in temperature reflect the uneven distribution of matter in the early universe, which tells us that 80% of the matter in the current universe is unknown. Image source: sci.esa.int.

Modern cosmology believes that the universe originated from a big bang at a point. At the beginning of its birth, the temperature of the universe was very high, and the elementary particles could easily break free from each other's constraints. Particles and antiparticles were constantly produced and annihilated, and the entire universe was in a chaotic state of thermal equilibrium. Then the universe continued to expand and cool. In the process of lowering the temperature, the elementary particles began to break away from thermal equilibrium and combined with each other to form various substances. About 380,000 years after the Big Bang, the temperature dropped to 3000K, and electrons and protons combined to form neutral hydrogen atoms. Photons in the universe were no longer bounced back and forth by electrons and protons, and began to propagate freely in a straight line. From then on, the universe became transparent. These free photons are evenly distributed throughout the universe, and they are still propagating freely today, 13.7 billion years later, but the temperature has dropped to 2.7K, becoming the CMB we observe. The energy distribution of these photons meets the blackbody radiation spectrum, which is a strong proof that the universe was in thermal equilibrium at the beginning.

In 1966, just one year after the discovery of the cosmic microwave background radiation, American astronomer Kenneth Greisen, Soviet astronomer Georgiy Zatsepin and Vadim Kuzmin published a paper in April and August of the same year, respectively, pointing out that ultra-high-energy cosmic rays will collide with photons in the ubiquitous CMB during their flight, thereby losing energy. They predicted that above a certain energy, the cosmic ray energy spectrum will be truncated, which is the famous GZK truncation, named after the first letters of their surnames.

If ultra-high-energy cosmic rays are protons, the collision between protons and photons may cause an inverse Compton scattering process, producing positive and negative electron pairs, and may also produce pions. These processes will cause protons to lose some energy. The first two processes are dominated by electromagnetic interactions, while the production of pions comes from strong interactions. The energy loss is much greater than the previous two, but the energy threshold that protons need to reach is higher. Through the blackbody radiation spectrum, the average energy and average number density of photons can be calculated given the temperature. Grayson used the average energy of the current universe CMB photons, 7×10^(-4)eV (the measured value of the CMB temperature at that time was 3K), and estimated that the energy threshold for the production of pions is about 10^20eV, which is 100EeV. There are about 550 photons per cubic centimeter, and it can be calculated that the average free path of cosmic ray protons is about 1.3Mpc (Mpc is the astronomical unit of one million parsecs, which is about 3 million light years). In other words, a proton will collide with a photon once it flies about 1.3Mpc to produce a pion. About 20% of the energy is lost with each collision, until the energy drops below 100 EeV, at which point pion production can no longer occur.

If the ultra-high-energy cosmic rays are heavier atomic nuclei, they will also collide with CMB photons and undergo photodisintegration, that is, heavy nuclei will break into light nuclei. The energy threshold of this process is about 5×10^18eV per nucleon (protons and neutrons are collectively called nucleons). Therefore, no matter what nuclide the ultra-high-energy cosmic rays are, the GZK cutoff exists.

Therefore, it is unlikely to detect ultra-high energy cosmic rays with energies higher than 100EeV on Earth, unless they originate from a place relatively close to the Earth, such as the Andromeda Galaxy next door (about 2.54 million light-years). Although this is an astronomical figure, don't think it is too far away. If the Amaterasu particle with an energy of 244EeV is a proton, its speed is only 1/10^23 (1/100 billionth) slower than the speed of light. Due to the length contraction effect of special relativity, the 2.54 million light-years we see is only 100 million kilometers from the perspective of the Amaterasu particle, which is 100 times closer than Voyager 1 Note 2 ! For the Amaterasu particle, it is only a 5-minute journey. Even if the Amaterasu particle is a neutron with an average lifespan of only 15 minutes, it can still run from Andromeda to the Earth. For observers on Earth, 2.54 million light-years does take 2.54 million years, which does not contradict the 5 minutes felt by the Amaterasu particle itself, because the time dilation effect complements the length contraction effect, and observers on Earth will find that the time of the Amaterasu particle passes very slowly.

The mystery of Amaterasu particles

The energy of the Amaterasu particle of 240EeV obviously exceeds the GZK cutoff of 100EeV. With such high energy, the deflection in the interstellar magnetic field will not be too significant. By modeling the magnetic field, researchers can calculate the trajectory of the particle and infer its direction of origin. Unfortunately, when the Amaterasu particle arrived, the moonlight was very bright and the TA's fluorescence detector was not turned on, so it was impossible to distinguish which nuclide it was. The researchers could only make assumptions first and then analyze. It was found that no matter whether it was assumed to be a proton, carbon, silicon or iron nucleus, and the model of the intergalactic magnetic field was adjusted, the result was that the source of the Amaterasu particle pointed to a void with no active galaxies. In this void there is a distant galaxy that may produce ultra-high-energy cosmic rays, but it is 600Mpc away, and it is basically impossible for the energy to exceed the GZK cutoff after propagating such a long distance.

The TA collaboration's paper calculations show that if the Amaterasu particle is a proton and the initial energy is 1000EeV, it can only be produced within a distance of 27Mpc. If the initial energy is increased by 10 times, it also needs to be produced within a distance of 61.9Mpc. Switching to heavier iron nuclei, the calculation results are closer, 10.3Mpc and 13.1Mpc respectively. There is no suitable cosmic ray source within these distances.

At the end of the paper, it was also reported that the TA experiment detected a total of 28 cosmic ray events with energies greater than 100EeV between May 2008 and November 2021, and their directional distribution was isotropic. Interestingly, there is indeed a GZK cutoff in the energy spectrum of ultra-high-energy cosmic rays, which was first confirmed by HiRes, the predecessor of the TA experiment, in 2010. For the super-GZK region, more events are needed to count a smooth energy spectrum. The GRAND (Giant Radio Array for Neutrino Detection) project proposed in 2019 plans to build 20 10,000-square-kilometer radio antenna arrays around the world by 2030, with a total of 200,000 antennas covering an area of ​​200,000 square kilometers. The goal is to explore the mystery of the origin of ultra-high-energy cosmic rays.

Conclusion

The TA experimental group did what they could to analyze, but in the end they still couldn’t figure out the origin of the Amaterasu particles. They wrote at the end of the paper:

"The absence of nearby sources of cosmic rays producing energies of 244 EeV could be due to larger deflections of particles than predicted, caused by heavier primaries or stronger magnetic fields than the models used. Apart from this, the presence of ultra-high-energy cosmic rays beyond GZK could also indicate that our understanding of particle physics is incomplete. If there are unknown types of particles that do not interact with the CMB, they could perhaps be transmitted to Earth from more distant active galaxies and retain their energy. We cannot distinguish between these possibilities with the events we observe."

This is how scientific research works. Faced with unsolved mysteries, researchers rack their brains and come up with a bunch of wrong theories. After new experimental data is obtained, they are eliminated one by one. In the end, the theories of a few lucky ones stand the test, and the rest become cannon fodder, but everyone's efforts are worth it. Note 3 .

Cosmic rays have been discovered for more than a hundred years, and we have made remarkable achievements - we have measured the full energy spectrum of cosmic rays across 10 orders of magnitude, know the composition of cosmic rays, developed theories to calculate their interactions, and even sent probes to the edge of the solar system and maintained contact. Despite this, we still know very little about their origin and propagation. Humans, confined to the tiny blue planet, try every possible means to explore more mysteries of the universe.

Notes

1. OMG particle: can be translated as Wardtian particle.

2. Forgive me for deliberately confusing the concepts. 100 million kilometers is in the Amaterasu particle rest reference frame, and Voyager 1 is about 24 billion kilometers away from the earth in the geostationary reference frame.

3. To borrow a line from the movie “Love Myth”: There is no such thing as worthwhile or unworthwhile in this world, only happy or unhappy.

References

[1] RU Abbasi, MG Allen, R. Arimura, and others, An Extremely Energetic Cosmic Ray Observed by a Surface Detector Array, Science 382, ​​903 (2023).

This article is supported by the Science Popularization China Starry Sky Project

Produced by: China Association for Science and Technology Department of Science Popularization

Producer: China Science and Technology Press Co., Ltd., Beijing Zhongke Xinghe Culture Media Co., Ltd.

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