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New simulations refine axion mass, focussing the quest for dark matter


Axions are the most favored candidate for dark matter today, and several experiments are being conducted to find them in microwave cavities, where the axion should seldom transition into an electromagnetic wave. A recent simulation of the formation of axions in the early universe, however, gives a more precise mass estimate as well as a higher frequency for the EM wave, which is outside the scope of our tests. Adaptive mesh refinement in supercomputer simulations generates the new mass.

According to a recent supercomputer simulation of how axions were formed just after the Big Bang 13.6 billion years ago, physicists seeking for today’s most popular candidate for dark matter, the axion, have been looking in the wrong location.

Benjamin Safdi, assistant professor of physics at the University of California, Berkeley; Malte Buschmann, a postdoctoral research associate at Princeton University; and colleagues at MIT and Lawrence Berkeley National Laboratory simulated the era when axions would have been produced, approximately a billionth of a billionth of a billionth of a billionth of a billionth of a billionth of a billionth of a billionth of a billionth of a billionth

The simulation at Berkeley Lab’s National Research Scientific Computing Center (NERSC) discovered that the axion’s mass is more than twice as large as theorists and experiments had predicted: between 40 and 180 microelectron volts (micro-eV, or?eV), or roughly one-tenth the mass of the electron. According to Safdi, there are evidence that the mass is close to 65 eV. Since scientists started seeking for the axion 40 years ago, estimates of its mass have fluctuated from a few eV to 500 eV.

“We give over a thousandfold increase in the dynamic range of our axion simulations compared to previous work and answer a 40-year-old puzzle about axion mass and axion cosmology,” Safdi added.

The increased mass means that the most common type of experiment for detecting these elusive particles – a microwave resonance chamber with a strong magnetic field, in which scientists hope to capture the conversion of an axion into a faint electromagnetic wave – will be unable to detect them, no matter how much the experiment is tweaked. To detect the higher-frequency wave from a higher-mass axion, the chamber would have to be smaller than a few millimeters on a side, according to Safdi, and that volume would be insufficient to collect enough axions for the signal to rise above the noise.

“Our study gives the most exact estimate of the axion mass to date and points to a particular range of masses that is not presently being investigated in the laboratory,” he said. “I truly believe it makes sense to concentrate experimental efforts on axion masses ranging from 40 to 180 eV, but there’s a lot of work being done to prepare for that mass range.”

A plasma haloscope, which searches for axion excitations in a metamaterial — a solid-state plasma — could be sensitive to and possibly identify an axion particle of this mass.

“The basic studies of these three-dimensional arrays of fine wires have worked out amazingly well, much better than we ever expected,” said Karl van Bibber, a UC Berkeley nuclear engineering professor who is building a prototype of the plasma haloscope while also participating in the HAYSTAC experiment, which searches for microwave cavity axion. “Ben’s most recent achievement is incredibly exciting. If the post-inflation scenario is correct, the finding of the axion might be considerably hastened after four decades.”

If axions exist at all

The findings will be published in the journal Nature Communications on February 25.

Axion is the leading candidate for dark matter

Dark matter is a mystery element that scientists know exists because it influences the motions of every star and galaxy, yet it interacts with the stuff of stars and galaxies so weakly that it has escaped discovery. That is not to say that dark matter cannot be researched or even weighed. Astronomers know exactly how much dark matter exists in the Milky Way Galaxy, and even in the whole universe: it accounts for 85 percent of all matter in the universe.

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To present, dark matter searches have concentrated on massive compact objects in our galaxy’s halo (referred to as MACHOs), weakly interacting massive particles (WIMPs), and even hidden black holes. None of them seemed to be a plausible possibility.

“The majority of stuff in the cosmos is dark matter, and we have no clue what it is. ‘What is dark matter?’ is one of science’s most intriguing puzzles.” Safdi said. “We believe it is a new particle that we are unaware of, and the axion might be that particle. It might have been generated in abundance during the Big Bang and is floating about explaining astrophysical data.”

Though not precisely a WIMP, the axion interacts with conventional matter in a weak way. It readily goes through the ground without causing any interruption. In 1978, it was postulated as a new fundamental particle that may explain why the spin of a neutron does not precess or wobble in an electric field. According to theory, the axion inhibits neutron precession.

“To this day, the axion is the best concept we have for explaining these strange neutron data,” Safdi added.

The axion became popular as a candidate for dark matter in the 1980s, and the first efforts to detect axions were made. It is possible to calculate the axion’s precise mass using the equations of the well-vetted theory of fundamental particle interactions, the so-called Standard Model, in addition to the theory of the Big Bang, the Standard Cosmological Model, but the equations are so difficult that we have only estimates, which have varied enormously. Because the mass is so imprecisely known, searches using microwave cavities (basically complex radio receivers) must tune through millions of frequency channels in order to discover the one matching to the axion mass.

“With these axion studies, they don’t know what station they’re meant to be listening to, so they have to scan through a lot of options,” Safdi said.

Safdi and his colleagues established the most recent, if inaccurate, axion mass estimate that experimentalists are now aiming for. However, as they worked on better simulations, they contacted a Berkeley Lab team that had created a specialized code for a superior simulation method known as adaptive mesh refinement. During simulations, a tiny portion of the expanding cosmos is represented by a three-dimensional grid on which equations are solved. The grid is made more detailed around regions of interest and less detailed in parts of space where nothing much occurs in adaptive mesh refinement. This focuses computational resources on the simulation’s most relevant sections.

The approach enabled Safdi’s simulation to observe thousands of times more information surrounding the locations where axions are formed, allowing for a more exact calculation of the total number of axions produced and, given the entire quantity of dark matter in the universe, the axion mass. The simulation used 69,632 actual computer processing unit (CPU) cores of the Cori supercomputer and approximately 100 terabytes of random access memory (RAM), making it one of the biggest dark matter simulations ever performed.

The simulation revealed that following the inflationary era, little tornadoes, or vortices, develop in the early cosmos like ropey threads and toss off axions like riders bucked from a bronco.

“You can think of these strings as being made up of axions hugging vortices while these strings whip around forming loops, connecting, and undergoing a lot of violent dynamical processes during the expansion of our universe, and the axions hugging the sides of these strings are trying to hang on for the ride,” Safdi explained. “However, if anything too forceful occurs, they are flung off and whip away from these cords. And the axions that are flung off the threads become dark matter much later on.”

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Researchers can forecast the quantity of dark matter formed by keeping track of the axions that are whipped off.

Adaptive mesh refinement enabled the researchers to model the cosmos for considerably longer and across a far larger region of the universe than earlier simulations.

“We solve for the axion mass in a more creative approach, as well as by using all of the computational power we could possibly locate to this issue,” Safdi said. “We’d never be able to model our whole world because it’s too large. However, we do not need to arouse the whole cosmos. We just need to replicate a large enough patch of the cosmos for a long enough length of time to capture all of the dynamics we know are present inside that box.”

The team is collaborating with a new supercomputing cluster that is now being created at Berkeley Lab to allow simulations that will offer an even more exact mass. The next-generation supercomputer, named Perlmutter after Saul Perlmutter, a UC Berkeley and Berkeley Lab physicist who earned the Nobel Prize in Physics in 2011 for finding the rapid expansion of the cosmos caused by so-called dark energy, would double the processing capability of NERSC.

“We intend to run even larger simulations at better resolution, which will enable us to reduce these error bars to 10% or less, allowing us to give you a very accurate value, such as 65 plus or minus 2 micro-eV. That fundamentally alters the game experimentally, since it becomes easy to validate or eliminate the axion in such a small mass range “Safdi said.

The new mass estimate, according to van Bibber, who was not a part of Safdi’s modeling team, challenges the limitations of microwave cavities, which perform less effectively at high frequencies. So, even if the bottom limit of the mass range is still detectable by the HAYSTAC experiment, he is excited about the plasma haloscope.

“New theoretical knowledge has relaxed the restrictions on the axion mass over the years; it may be anywhere within 15 orders of magnitude if axions generated before inflation. It’s become a maddening challenge for experimenters “Van Bibber is the Shankar Sastry Chair of Leadership and Innovation at UC Berkeley. “However, a recent work by Frank Wilczek’s Stockholm theory group may have addressed the problem by developing a resonator that can be both extremely vast in volume and very high in frequency. An actual resonator for a genuine experiment is still a ways off, but this might be the path to Safdi’s anticipated mass.”

Once simulations provide a more exact mass, the axion may be straightforward to locate.

“It was critical that we collaborated with this computer science team at Berkeley Lab,” Safdi added. “We truly went beyond the physics sector and turned this into a computer science challenge.”

Malte Buschmann of Princeton, MIT postdoctoral researcher Joshua Foster, Anson Hook of the University of Maryland, and Adam Peterson, Don Willcox, and Weiqun Zhang of Berkeley Lab’s Center for Computational Sciences and Engineering are among Safdi’s collaborators. The Exascale Computing Project (17-SC-20-SC) and the Early Career program of the US Department of Energy sponsored the majority of the research (DESC0019225).


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