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Combination of Instruments Enables Reconstruction of Solar X-ray Sources in Three Dimensions

By Jillian Kunze

“We live in a universe of three perceivable spatial dimensions, yet so much of the science that we do—certainly in astronomy—relies on measurements in two of those dimensions,” Daniel Ryan of the University of Applied Science Northwest Switzerland (FHNW) said. “That’s not because two is better than three, but simply because of the limitations of our technology.” However, new capabilities in astronomical imaging have made the possibility of three-dimensional (3D) measurements a reality. During a minisymposium presentation at the 2022 SIAM Conference on Imaging Science last week, Ryan explained how combining observations from the Spectrometer/Telescope for Imaging X-rays (STIX) instrument on the Solar Orbiter satellite and the X-Ray Telescope (XRT) on the Hinode satellite enables 3D X-ray measurements of solar flares.

Figure 1. A medium-sized solar flare that occurred on July 14, 2017. Figure courtesy of NASA/GSFC/Solar Dynamics Observatory and the AIA, EVE, and HMI science teams.
A solar flare occurs when magnetic fields in the Sun’s corona become very stressed and twisted, eventually undergoing magnetic reconnection and releasing a huge amount of energy within a small area. Charged particles accelerate along the magnetic field lines and slam into the denser lower atmosphere, leading to high-intensity emissions and rapid heating. Gas then expands rapidly back into the atmosphere along the magnetic field lines, creating post-flare loops (see Figure 1). Ryan focused on two sources of X-rays that can occur in solar flares: at the footpoints where the loop meets the Sun’s chromosphere, and at the top of the loop where the hottest plasma coalesces.

Until recently, researchers have been unable to determine the exact location of X-ray sources within the 3D magnetic field structure. Open questions also remain surrounding the amount of thermal energy in a flare (which depends on the flare volume) and the amount of energy that is transferred via different mechanisms like conduction and radiation (which depends on the density). Addressing these questions requires 3D X-ray images of solar flares to measure the position and volume of X-ray sources. 

Figure 2 illustrates the process of creating 3D images from satellite observations. Two instruments at two different points of view observe an X-ray source; neither knows exactly where the source is, because they each only have a two-dimensional (2D) image. One can then define a 2D epipolar plane that crosses through both the source and the observers, and project this plane onto the images as a line. By determining where the plane crosses the boundary of the object on each observer’s image, one finds four spatial lines that define a quadrilateral wherein the source must lie. By repeating this process for multiple stacked epipolar planes, researchers can build up a 3D image and learn about the source object’s location.

Figure 2. Diagram demonstrating how observations from two different satellites are combined to create a three-dimensional image. Figure courtesy of Daniel Ryan.

Utilizing this technique to reconstruct sources of X-ray emission requires two X-ray telescopes with substantially different viewing angles that observe similar intervals of X-ray energy. This was made possible in 2020 when the Solar Orbiter launched with STIX onboard; since this satellite orbits the Sun and the Hinode satellite orbits the Earth, their viewing angles can be significantly different. STIX can detect plasmas at temperatures greater than eight million degrees Kelvin, while XRT is sensitive to temperatures greater than five million degrees Kelvin. Both of these instruments are therefore capable of seeing the hot emission in solar flare loops.

Ryan presented a case study of a medium-sized flare that occurred on May 7, 2021. Figure 3a depicts where the satellites were located when the flare occurred; the Solar Orbiter was separated from Hinode by just over 90 degrees. Figures 3b and 3c show the flare as observed by STIX and XRT, respectively. The red contours in the images represent the lower energy thermal emission that both instruments were able to observe. Since there were observations from different angles, the researchers were able to use JHelioviewer—a free software that visualizes solar imaging observations from many different instruments—to reconstruct this data in 3D (see Figure 4). “This is an exciting new capability in the area of X-ray solar physics, because we can now get an idea of the 3D position and 3D volume of these sources,” Ryan said.

There are of course some challenges and complications to this reconstruction technique. Given the different designs of STIX and XRT, one might ask whether the instruments actually observe the same flare volume. XRT is more sensitive at lower temperatures; if a flare involved a large amount of plasma at lower temperatures with a different spatial distribution than the plasma at higher temperatures, then STIX and XRT would observe differently-sized areas of plasma. This could lead researchers to derive the wrong flare volume.

Figure 3. A case study of a solar flare that occurred on May 7, 2021. 3a. A schematic of observation positions when the flare occurred. STIX was at the location marked by SOLO SC, while XRT was around Earth. 3b. The flare as seen by STIX. The black points in the background are the footpoints that were detected in ultraviolet by an instrument on Hinode, and are appropriately adjusted for how they would have appeared at STIX’s viewing angle. The blue contours are high-energy non-thermal emission that STIX detected from X-rays plummeting back into the atmosphere. The red contours show the lower-energy thermal emission seen by STIX. 3c. The flare as seen by XRT. The red contours show the lower-energy thermal emission that XRT observed. Figure courtesy of Daniel Ryan.

Ryan investigated this potential problem by checking whether STIX and XRT detected the same flare area when they observed a flare from similar viewing angles on November 1, 2021. The size scales of the observations were indeed similar, which indicated that the two instruments see the same volume in at least some cases. More work remains to be done to see how common that scenario is.

A related way to test the commonality between the two instruments is to calculate the intensity of the flare based off the temperature and amount of emitting material as derived by STIX, and see if that is consistent with the XRT-observed intensity. If they were not consistent, that would indicate that different temperatures dominate the images from the different telescopes. However, the agreement was within about 20 percent. “Given the uncertainties that we sometimes have with these response functions, this is not too far away from agreement,” Ryan said. “At least at this stage, this suggests to me that the plasma seen by STIX is consistent with what we see with XRT.”

Figure 4. A 3D reconstruction of the solar flare seen by STIX and XRT on May 7, 2021 created in JHelioviewer. The blob in the upper middle of the image is the X-ray-emitting area of plasma that was visualized in 3D. Figure courtesy of Daniel Ryan.
Another challenge lies in determining the shape of the X-ray source, as the only definitive information is that the source must lie within and touch all the sides of a certain area. Following Occam’s razor, one can assume that the geometry is the simplest shape that is consistent with the data—which would be an ellipse—and create a unique solution by assuming that the ellipse occupies the maximum area. It is then essential to keep in mind that the derived geometry is an approximation and the derived volume is an upper limit when doing further calculations and drawing scientific conclusions.

Though the design differences between STIX and XRT impose challenges, those can be mitigated; however, one must address the additional uncertainties in the derived 3D volumes and positions that doing so creates. “Can we perform 3D X-ray measurements of solar flares with currently available instruments?” Ryan asked. “I think the answer is yes: we can combine STIX and XRT to enable 3D reconstruction of thermal X-ray sources in solar flares. This is a brand-new capability in X-ray solar physics, and these types of measurements can help us make advances on open science questions regarding the flare geometry, energy transport, and energetics.” 

Acknowledgements: Contributors to the research described in Daniel Ryan’s minisymposium presentation include Silvan Laube (FHNW), Andrea Battaglia (FHNW and ETH Zürich), Säm Krucker (FHNW and University of California, Berkeley), André Csillaghy (FHNW), Alexander Warmuth (Leibniz Institute for Astrophysics Potsdam), Bogdan Nicula (Royal Observatory of Belgium), and Daniel Müller (ESA-ESTEC).

  Jillian Kunze is the associate editor of SIAM News