An artist’s impression of the surface of Jupiter’s icy moon Europa. Image credit: NASA / JPL-Caltech / SwRI.

Advertisement

“Six different models have been published in an attempt to explain the radar signatures of the icy moons that orbit Jupiter and Saturn,” said Southwest Research Institute senior research scientist Dr. Jason Hofgartner.

“The way these objects scatter radar is drastically different than that of the rocky worlds, such as Mars and Earth, as well as smaller bodies such as asteroids and comets.”

The Jovian and Saturnian moons are also extremely bright, even in areas where they should be darker.

“When we look up at Earth’s moon it looks like a circular disk, even though we know it’s a sphere,” Dr. Hofgartner said.

“Planets and other moons similarly look like disks through telescopes.”

“While making radar observations, the center of the disk is very bright and the edges much darker.”

“The change from center to edge is very different for these icy satellites than for rocky worlds.”

Dr. Hofgartner and his colleague, Dr. Kevin Hand from NASA’s Jet Propulsion Laboratory, argue that the extraordinary radar properties of these satellites, such as their reflectiveness and polarization (the orientation of light waves as they propagate through space) is very likely to be explained by the coherent backscatter opposition effect (CBOE).

“When you’re at opposition, the Sun is positioned directly behind you on the line between you and an object, the surface appears much brighter than it would otherwise,” Dr. Hofgartner said.

“This is known as the opposition effect. In the case of radar, a transmitter stands in for the Sun and a receiver for your eyes.”

“An icy surface has an even stronger opposition effect than normal.”

“For every scattering path of light bouncing through the ice, at opposition there is a path in the exact opposite direction.”

“Because the two paths have precisely the same length, they combine coherently, resulting in further brightening.”

In the 1990s, studies were published stating that the CBOE was one explanation for the anomalous radar signatures of icy satellites, but other explanations could explain the data equally well.

Dr. Hofgartner and Dr. Hand improved the polarization description of the CBOE model and also showed that their modified CBOE model is the only published model that can explain all of the icy satellite radar properties.

“I think that tells us that the surfaces of these objects and their subsurfaces down to many meters are very tortured,” Dr. Hofgartner said.

“They’re not very uniform. Icy rocks dominate the landscape, perhaps looking somewhat like the chaotic mess after a landslide.”

“That would explain why the light is bouncing in so many different directions, giving us these unusual polarization signatures.”

A paper describing the findings was published in the journal Nature Astronomy.

_____

J.D. Hofgartner & K.P. Hand. A continuum of icy satellites’ radar properties explained by the coherent backscatter effect. Nat Astron, published online March 23, 2023; doi: 10.1038/s41550-023-01920-2

Black holes exist in our universe. That’s widely accepted today. Physicists have detected the X-rays emitted when black holes feed, analyzed the gravitational waves from black hole collisions and even imaged two of these behemoths.

But mathematician Elena Giorgi of Columbia University studies black holes in a different way. “Black holes are mathematical solutions to the Einstein equation,” Giorgi says — the “master equation” that is the basis of the general theory of relativity.

She and other mathematicians seek to prove theorems about these solutions and otherwise probe the math of general relativity. Their goal: unlock unsuspected truths about black holes or verify existing suspicions.

Within general relativity, “one can understand clean mathematical statements and study those statements, and they can give an unambiguous answer within that theory,” says Christoph Kehle, a mathematician at ETH Zurich’s Institute for Theoretical Studies. Mathematicians can solve equations that have bearing on questions about the nature of black holes’ formation, evolution and stability.

Last year, in a paper posted online at arXiv.org, Giorgi and colleagues settled a long-standing mathematical question about black hole stability. A stable black hole, mathematically speaking, is one that if poked, nudged or otherwise disturbed will eventually settle back into being a black hole. Like a rubber band that has been stretched and then released, the black hole doesn’t rip apart, explode or cease to exist, but returns to something like its former self.

Black holes seem to be physically stable — otherwise they couldn’t endure in the universe — but proving it mathematically is a different beast.

And a necessary feat, Giorgi says. If black holes are stable, as researchers presume, then the math describing them had better reflect that stability. If not, something is wrong with the underlying theory.

“Most of my work,” Giorgi says, “is about proving things that we already expected to be true.”

Mathematics has a history of big contributions in the realm of black holes. In 1916, Karl Schwarzschild published a solution to Einstein’s equations for general relativity near a single spherical mass. The math showed a limit to how small a mass could be squeezed, an early sign of black holes. More recently, British mathematician Roger Penrose won the 2020 Nobel Prize in physics for his calculations showing that black holes were real-world predictions of general relativity. In a landmark paper published in 1965, Penrose described how matter could collapse to form a black hole with a singularity at its center.

Just a couple of years earlier, in 1963, New Zealand mathematician Roy Kerr found a solution to Einstein’s equation for a rotating black hole. This was a “game changer for black holes,” Giorgi noted in a public lecture given at the virtual 2022 International Congress of Mathematicians. Rotating black holes were much more realistic astrophysical objects than the non-spinning black holes that Karl Schwarzschild had solved the equations for.

“Physicists really had believed for decades that the black hole region was an artifact of symmetry that was appearing in the mathematical construction of this object but not in the real world,” Giorgi said in the talk. Kerr’s solution helped establish the existence of black holes.

In a nearly 1,000-page paper, Giorgi and colleagues used a type of “proof by contradiction” to show that Kerr black holes that rotate slowly (meaning they have a small angular momentum relative to their mass) are mathematically stable. The technique entails assuming the opposite of the statement to be proved, then discovering an inconsistency. That shows that the assumption is false. The work is currently undergoing peer review. “It’s a long paper, so it’s going to take some time,” Giorgi says.

The result doesn’t yet extend to Kerr black holes that rotate quickly with respect to their mass, which are also known to exist in the universe.

Though the result isn’t likely to upend our view of black holes, these kinds of mathematical journeys can yield new insights.

That’s been true in Giorgi’s study of black holes with an electric charge, which are also solutions to Einstein’s equations. She’s been exploring what happens to those black holes in the face of disturbances that feature both electromagnetic radiation and gravitational waves. These waves may surround black holes, fall inside them or interact with them at a distance, she says. Through that work, she reached a new mathematical definition of electromagnetic radiation that could be used in additional research on charged black holes.

Giorgi has straddled the fields of physics and math since high school, when she realized that “if I know math, I can also do physics.” Her enduring interest in physics and attraction to differential geometry, which deals with geometry of smooth spaces, made general relativity a natural fit. But her straddling has led some colleagues to misunderstand her work.

Some physicists think black hole mathematicians are proving things “more rigorously that they have already sort of proven, that they’re convinced of,” Giorgi says. Meanwhile, some mathematicians consider her work “more physics than math” — that is until they see the length of her full mathematical proofs.

Giorgi likes the freedom she has found in research. “You can choose to work on whatever you want,” she says. “You have to find your own problems.”

Oba et al. report the detection of uracil, one of the four nucleobases in ribonucleic acid, in aqueous extracts from Ryugu samples. Image credit: NASA’s Goddard Space Flight Center / JAXA / Dan Gallagher.

Advertisement

Ryugu was discovered in May 1999 by astronomers with the Lincoln Near-Earth Asteroid Research.

Also known as 1999 JU3, this asteroid measures approximately 900 m (0.56 miles) in diameter and orbits the Sun at a distance of 0.96-1.41 astronomical units once every 474 days.

JAXA’s Hayabusa-2, a sample-return mission to Ryugu, was launched on December 3, 2014 and arrived at the asteroid on June 27, 2018.

There, the spacecraft deployed rovers and landers onto Ryugu’s surface, and collected samples from near the surface.

On December 6, 2020, a total of 5.4 grams of pristine samples was returned to Earth in a hermetically sealed sample container within the re-entry capsule.

“Scientists have previously found nucleobases and vitamins in certain carbon-rich meteorites, but there was always the question of contamination by exposure to the Earth’s environment,” said Hokkaido University’s Dr. Yasuhiro Oba.

“Since Hayabusa-2 collected two samples directly from asteroid Ryugu and delivered them to Earth in sealed capsules, contamination can be ruled out.”

In the new research, Dr. Oba and colleagues searched for nucleobases and other classes of nitrogen molecules in the Ryugu samples.

They extracted these molecules by soaking the asteroid particles in hot water, followed by analyses using liquid chromatography coupled with high-resolution mass spectrometry.

The analysis revealed the presence of uracil and nicotinic acid, as well as other nitrogen-containing organic compounds.

“We found uracil in the samples in small amounts, in the range of 6-32 parts per billion (ppb), while vitamin B₃ was more abundant, in the range of 49-99 ppb,” Dr. Oba said.

“Other biological molecules were found in the sample as well, including a selection of amino acids, amines and carboxylic acids, which are found in proteins and metabolism, respectively.”

The newly-detected compounds are similar but not identical to those previously discovered in carbon-rich meteorites.

“The difference in concentrations in the two samples, collected from different locations on Ryugu, is likely due to the exposure to the extreme environments of space,” the scientists said.

“The nitrogen-containing compounds were, at least in part, formed from the simpler molecules such as ammonia, formaldehyde and hydrogen cyanide.”

While these were not detected in the Ryugu samples, they are known to be present in cometary ice — and Ryugu could have originated as a comet or another parent body which had been present in low temperature environments.

“The discovery of uracil in the samples from Ryugu lends strength to current theories regarding the source of nucleobases in the early Earth,” Dr. Oba said.

“NASA’s OSIRIS-REx mission will return samples from asteroid Bennu this year, and a comparative study of the composition of these asteroids will provide further data to build on these theories.”

The results were published this week in the journal Nature Communications.

_____

Y. Oba et al. 2023. Uracil in the carbonaceous asteroid (162173) Ryugu. Nat Commun 14, 1292; doi: 10.1038/s41467-023-36904-3