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Statistics of the Invisible

In order to obtain information about dark matter and dark energy from the huge amounts of data to be generated by the new ESA probe Euclid, astrophysicist Laila Linke and her team in Innsbruck are using novel statistical methods. As soon as Euclid sends its first data to Earth, the researchers intend to have a tool ready to gain new information on the most important questions concerning the invisible side of the cosmos.

The Euclid space telescope is creating the largest and most accurate 3D map of the universe to date, observing galaxies out to 10 billion light-years. The ESA mission will explore important questions about the role of gravity and the nature of the dark universe. Image Credit: ESA/ATG, CC BY-SA 3.0 IGO

Floating gas nebulae, scintillating clusters of stars and majestic galaxies – this is how our universe looks through the lenses of modern space telescopes like Hubble and Webb. A luminous structure seems to crisscross our universe. But the elements that really shape our cosmos remain invisible in these images.

Astronomical measurements revealed that an unknown world lies hidden among all the pretty stars, nebulae and galaxies. Known as the “dark universe”, this part of the cosmos consists of two components: dark matter and dark energy. It takes these two forces in combination with conventional matter to produce the standard model of cosmology.

“This model describes the universe really well, because it can explain observations on a wide variety of size and time scales,” says astrophysicist Laila Linke of the University of Innsbruck. “While we know that this model must include dark matter and dark energy, we don’t know what they are.”

Dark Enigmas

Dark matter provides the additional gravity necessary to hold together galaxies and clusters of galaxies that could not exist without this mysterious substance. Dark energy, on the other hand, causes the accelerated expansion of the universe, as shown by measurements of distant galaxies. But what these two forces really are remains completely unresolved. Experts have proposed numerous theories on dark matter, their ideas ranging from unknown, massive particles that hardly interact with matter to a population of different black holes that emerged shortly after the Big Bang.

Dark energy makes the cosmos rise like a cake. So far, however, attempts to explain this hyper-pressure with Einstein’s “cosmological constant” lack conviction: the values for dark energy predicted by these attempts miss the mark by many orders of magnitude. Scientists around the world are striving to find answers to the enigmas of the dark universe – a vastly important task, since calculations show that conventional matter accounts for only five percent of all the mass contained in the cosmos. Hence, the lion’s share of the universe is dark.

Distorted Galaxies

It is the declared goal of the Euclid mission of the European Space Agency ESA to shed light on the dark universe. But how will the Euclid probe that was launched on July 1 this year get closer to its invisible observation targets? As Linke explains, “Euclid will specifically survey galaxies, covering about a third of the sky.” Euclid is scheduled to measure the shape of a staggering one and a half billion galaxies, some of which are very far away. Due to the finite speed of light, great distances in space are equivalent to looking back in time. Thus, Euclid’s data also contains information about the evolution of the universe over time.

In order to solve the mysteries of the cosmological standard model, experts mainly concentrate on the shapes of galaxies: as impressively shown by Hubble images, no two galaxies are alike. Nevertheless, it is possible to categorize these star islands by how far they deviate from the shape of a circle. “The technical term we use is ellipticity,” Linke explains.

While this means that every galaxy is more or less egg-shaped, there is a hitch: from Earth, their true shape cannot be perceived, not even with the help of space telescopes, because of the gravitational lensing effect: when light on its way to us passes through a cluster of matter it is deflected from its path, because such a mass bends space and forces the light rays onto new paths. This process has spectacular consequences: galaxies that lie behind massive galaxy clusters show up on crazy arcs or are even depicted multiple times. Since almost every line of sight between extragalactic objects and Earth passes by mass clusters, virtually every image is distorted – even if only slightly in some cases.

Cosmology of the Many

The distortion of a galaxy does not in itself teach us anything about the dark universe: “Galaxies can be intrinsically elliptical, which means we cannot glean from individual specimens how much of their ellipticity is due to gravitational lensing,” Linke explains. For this reason, Linke and her team evaluate several stellar islands simultaneously. “We measure the ellipticity of a great number of neighboring galaxies. If they were all randomly oriented, averaging over a great number would lead to their intrinsic ellipticity cancelling out,” Linke says. “So what remains is only the portion that is due to gravitational lensing.” Hence; if the group of galaxies is skewed in a common direction – experts refer to this as shear – this method will make it stand out.

This allows the researchers to learn something about the distribution of mass in the cosmos – valuable information, as Linke confirms: “This enables us to understand two things: first, how structures have emerged in the universe. And second, changes in the distribution of mass over time tells us something about the expansion history of the universe, which is governed by dark energy.”

Mass distribution constitutes a relevant statistical quantity for cosmology. If it is known for each distance, we know how matter has conglomerated or drifted apart in the past. But to obtain the parameters of the distribution, such as variance, the experts have to dig through the vast amount of data from probes like Euclid.

This is how Linke describes the method used so far: “Starting with one galaxy, we compare the ellipticity of many pairs of galaxies at the same distance. This way, if there is some distortion at one point, we know how large the shear is at another location. This information correlates with the variance of the mass distribution.”

New Method

Given that cosmic mass distribution is not Gaussian in shape but looks more complicated, variance in itself is not enough to characterize it. More information is needed. Instead of forming pairs of galaxies, Linke groups them into triads. “This gives us a higher moment of distribution that depends on the parameters of the distribution in a different way,” Linke says. “Together with the measurements on the pairs, we learn more about the mass distribution from the groups of three.”

Although this statistical method provides deep insights into the cosmos, it has hardly been used so far, because the humongous data involved in comparing three galaxies with each other requires massive computing power – which was not available until recently. Linke was able to show, however, that graphics cards can overcome this problem.

Another additional problem was the lack of practical algorithms. Linke’s ESPRIT project, which receives funding from the FWF, is set to change that. “The models of third-order shear statistics are more complicated. They include systematic effects that have not been taken into account so far. That is something we simply have to do now,” Linke adds.

At present, Linke and her team are still fine-tuning their methods. But as soon as Euclid sends the first data to Earth, we will have a new tool to coax information about the invisible side of the cosmos from the vast amounts of data. No matter how fascinating individual objects may be, one thing has become clear: statistics hold the key to the dark universe.


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