Astrophysics and Astronomy Commons^™

Investigation Of Biofilm Formation And Osmotic Stress Tolerance Of Nonmotile E. Coli Mg1655 In Simulated Microgravity, Tyler Jenkins

Student Research Symposium (SRS)

Simulated microgravity presents multiple physiological stressors for astronauts, including bone demineralization, muscle loss, and weakening of the immune system (Chavez et al., 2024). Bacteria serve as viable model organisms to study physiological changes because of their abundance in the human digestive system and skin. Motility in bacteria plays a significant role in cell survival, but few studies have been conducted on microgravity’s effect on motility phenotypes. While motile strains like K12 have been studied extensively under microgravity conditions (Topolski et al., 2022; Chavez et al., 2024), the effects of simulated microgravity on non-motile strains are largely unknown. To better understand …

Characterizing The Solar Sources Of Periodic Mesoscale Solar Wind Structures Responsible For Radiation Belt Particle Loss: Results And Implications For Space Weather Forecasting, Grace Gratton

Student Research Symposium (SRS)

It is now well-established that the ambient solar wind is dynamic and highly structured at mesoscales – scales larger than kinetic, but smaller than CMEs/SIRs. These structures are often created at the Sun and survive to 1 AU, where they form the ground-state of space weather as they continually buffet Earth's magnetosphere, the moon, and Mars. Two primary ways that mesoscale structures pose significant risks to spacecraft and astronauts are through driving radiation belt depletion, and amplifying the hazards of CMEs and SIRs through upstream solar wind preconditioning. Characterizing the solar origins and solar wind properties of geoeffective mesoscale structures …

X-Ray Microcalorimeter Observations Of High-Mass X-Ray Binaries With The Resolve Instrument Onboard Xrism, Pragati Pradhan, Masahiro Tsujimoto

Publications

The X-ray Imaging and Spectrometer Mission (XRISM) was put into orbit successfully in September 2023. Resolve, one of the scientific instruments onboard XRISM, hosts an X-ray spectrometer based on X-ray microcalorimetery technology. It excels in high spectral resolution, a large throughput, a large bandpass, low background, and good timing accuracy. These properties are suited to bring new insights especially in high-mass X-ray binaries (HMXB). We describe these unique features of Resolve and present initial highlights of two HMXB sources.

The Giant Outburst Of Exo 2030+375, P. Thalhammer, R. Ballhausen, E. Sokolova-Lapa, J. Stierhof, A. Zainab, R. Staubert, K. Pottschmidt, J.B. Coley, R.E. Rothschild, G.K. Jaisawal, B. West, P.A. Becker, Pragati Pradhan, P. Kretschmar, J. Wilms

Publications

The Be X-ray binary EXO 2030+375 went through its third recorded giant outburst from June 2021 to early 2022. We present the results of both spectral and timing analysis based on NICER monitoring, covering the 2−10 keV flux range from 20 to 310 mCrab. Dense monitoring with observations carried out about every second day and a total exposure time of ∼160 ks allowed us to closely track the source evolution over the outburst. Changes in the spectral shape and pulse profiles showed a stable luminosity dependence during the rise and decline. The same type of dependence has been seen in …

The Unaltered Pulsar: Gro J1750-27, A Supercritical X-Ray Neutron Star That Does Not Blink An Eye, C. M. Malacaria, L. Moritz Ducci, M. Falanga, D. A. Altamirano, E. Bozzo, S. J. Guillot, G.K. Jaisawal, P. Kretschmar, M. Ng, Pragati Pradhan, R. Rothschild, A. Sanna, P. Thalhammer, J. Wilms

Publications

When accreting X-ray pulsars (XRPs) undergo bright X-ray outbursts, their luminosity-dependent spectral and timing features can be analyzed in detail. The XRP GRO J1750-27 recently underwent one such episode, during which it was observed with NuSTAR and monitored with NICER. Such a data set is rarely available, as it samples the outburst over more than 1 month at a luminosity that is always exceeding ∼5 × 1037 erg s−1 . This value is larger than the typical critical luminosity value, where a radiative shock is formed above the surface of the neutron star. Our data analysis of the joint spectra …

Determining The Light Curve And 3d Shape Of Asteroid Eunomia And Egeria Using Relative Photometry, Skylar G. Butler, Jackson Ladd Sackrider

Discovery Day - Daytona Beach

Asteroids are relics of our solar system’s early formation, preserving valuable information about planetary evolution. Understanding their rotational properties and surface features provides deeper insights into the dynamical and thermophysical processes that shape their evolution. This study aims to conduct photometric observations of two main-belt asteroids, Egeria and Eunomia, using the Embry-Riddle Aeronautical University 1-meter telescope. Observations will be conducted in the red band on February 28 and March 14, 2025, over five-hour sessions, capturing full rotational light curves for each asteroid. These data will be analyzed using MPO Canopus to generate 3D surface models through photometric inversion techniques. The …

Multi-Wavelength Study Of 1erass J085039.9−421151 With Erosita, Nustar, And X-Shooter, A. Zainab, A. Avakyan, V. Doroshenko, P. Thalhammer, E. Sokolova-Lapa, R. Ballhausen, N. Zalot, J. Stierhof, S. Hämmerich, C. M. Diez, P. Weber, T. Dauser, K. Berger, P. Kretschmar, K. Pottschmidt, Pragati Pradhan, N. Islam, C. Maitra, J.B. Coley, P. Blay, R.H.D. Corbet, R.E. Rothschild, K. Wood, A. Santangelo, U. Heber, J. Wilms

Publications

The eROSITA instrument on board Spectrum-Roentgen-Gamma (SRG) has completed four scans of the X-ray sky, leading to the detection of almost one million X-ray sources in eRASS1 alone, including multiple new X-ray binary candidates. We report on analysis of the X-ray binary 1eRASS J085039.9−421151, using a ∼55 ks long NuSTAR observation, following its detection in each eROSITA scan. An analysis of the eROSITA and NuSTAR X-ray spectra in combination with X-shooter data of the optical counterpart provide evidence of an X-ray binary with a red supergiant (RSG) companion, confirming previous results. However, we did determine a cooler spectral type for …

Stable Coronal X-Ray Emission Over 20 Yr Of Xz Tau, Steven M. Silverberg, Hans Moritz Günther, Pragati Pradhan, David A. Principe, P.C. Schneider, Scott J. Wolk

Publications

XZ Tau AB is a frequently observed binary young stellar object in the Taurus Molecular Cloud; XZ Tau B has been classified as an EXOr object. We present new Chandra/HETG-ACIS-S observations of XZ Tau AB, complemented with variability monitoring of the system with XMM-Newton, to constrain the variability of this system and identify high-resolution line diagnostics to better understand the underlying mechanisms that produce the X-rays. We observe two flares with XMM-Newton but find that outside of these flares the coronal X-ray spectrum of XZ Tau AB is consistent over 20 yr of observations. We compare the ensemble of XZ …

A Search For Subdwarf B Binaries Using Pulsation Timing From Tess, Tomomi Otani, Andrzej S. Baran, Lindsay C. Spence, Ted A. Von Hippel, Ellesse A. Lynum-Lozano, Julia M. Clark

Publications

Hot subdwarf B (sdB) stars are post-main-sequence stars of high temperature and gravity. Approximately 30% of sdBs exhibit stable pressure and/or gravity-mode pulsations, which can be used via the timing method to test for companion stars and determine their orbital solutions. We used short cadence data from the Transiting Exoplanet Survey Satellite (TESS) to search for previously undiscovered companions to sdBs. In this paper, we focus on searching for companions with orbital periods shorter than 13.5 days which are detectable within one sector of TESS data (about 27 days). The timing method requires that we derive pulsation frequencies in subsets …

The Core-Collapse Supernovae Particle Physics Interactions, Skylar G. Butler

Beyond: Undergraduate Research Journal

This study investigates the role of specific particle physics interactions in simulations of core collapse supernovae, with a focus on understanding how varying levels of inclusion impact the accuracy of gravitational wave predictions and results of simulations. Different research groups often approach these simulations with varying degrees of complexity, cutting corners by omitting certain reactions or simplifying others. This project systematically evaluates the implications of these choices, comparing the particle physics interactions included, the dimensionality of the simulations, and the governing equations used. Our goal is to identify how these factors influence the precision of numerical simulations. By providing a …

Orbital Evolution Of The Datura Asteroid Family, Skylar G. Butler

Beyond: Undergraduate Research Journal

To research the Datura Family of asteroids, we used an orbital evolution code to track the orbital decay of asteroid fragments released in an asteroid disruption. Different particle sizes of 10, 100, 500, 750, and 100 micrometers were tracked including the semi-major axis, eccentricity, and inclination in order to observe how certain particle sizes’ orbital elements evolve. Using a young asteroid family like the Datura family gives more insight into the parent asteroid structure and formation because the time is closer to before the asteroid’s breakup. We use these models to constrain the parameters of the dust by comparing the …

Statistical Study Of Solar Wind Conditions Prior To Substorm Onsets, Luke H. Francis

Doctoral Dissertations and Master's Theses

Due to complex, multi-region, coupled plasma systems, auroral substorm onsets have been historically difficult to predict. The northward turning of the interplanetary magnetic field was considered the primary candidate as an external triggering mechanism for substorm onsets. However, that was later shown to be coincidental in nature. This study is motivated by recent multi-spacecraft observations that show how several magnetosheath jets at the bow shock were heavily correlated to substorm onsets, indicated by a strongly radial IMF interval. In the past, studies have looked at small samples of substorms in order to make large-scale predictions. However in this study, a …

Dual Quaternions For Gravity Recovery Missions, Ryan Kinzie

Doctoral Dissertations and Master's Theses

A dual quaternion-based modeling, state estimation and control approach is introduced as a better alternative to the traditional methods which are currently utilized for gravity recovery missions. The proposed modeling and control approach was verified against and compared to the tangent bundle to Special Euclidean Group 3 through MATLAB simulations. The dual quaternion-based approach shows superior performance over traditional linearized and uncoupled methodologies, in both modeling accuracy of spacecraft translational position, and the ability to control the pose of a test mass relative to its host spacecraft. Utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a …

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

Rapid Mid-Infrared Spectral Timing With Jwst: Grs 1915+105 During An Mir-Bright And X-Ray-Obscured State, P. Gandhi, E.S. Borowski, J. Byrom, R.I. Hynes, T.J. Maccarone, A.W. Shaw, O.K. Adegoke, D. Altamirano, M.C. Baglio, Y. Bhargava, C.T. Britt, D.A.H. Buckley, D.J.K. Buisson, P. Casella, N. Castro Segura, P.A. Charles, J.M. Corral-Santana, V.S. Dhillon, R. Fender, A. Gurpide, C.O. Heinke, A.B. Igl, C. Knigge, S. Markoff, G. Mastroserio, M.L. Mccollough, M. Middleton, J.M. Miller, J.C.A. Miller-Jones, S.E. Motta, J.A. Paice, D.D. Pawar, R.M. Plotkin, P. Pradhan, M.E. Ressler, D.M. Russell, T.D. Russell, P. Santos-Sanz, T. Shahbaz, T. Shahbaz, G.R. Sivakoff, D. Steeghs, A.J. Tetarenko, J.A. Tomsick, F.M. Vincentelli, M. George, M. Gurwell, R. Rao

Publications

No abstract provided.

From Poetry To Policy: How H-Stem Has Guided My Research Path, Kayla D. Taylor

Student Works

Embry-Riddle PhD student Kayla Taylor was invited to share how Humanistic STEM has shaped her educational journey at the third annual Humanistic STEM symposium.

Pulse-Profile Modeling And Spin–Orbit Alignment In A Suzaku Sample Of Accreting X-Ray Binary Pulsars, Silas G.T. Laycock, Rigel C. Cappallo, Pragati Pradhan, Dimitris M. Christodoulou, Biswajit Paul

Publications

We report pulse-profile modeling of a sample of 23 X-ray binary pulsars observed with the Suzaku X-ray satellite. These pulsars have spin periods ranging from 0.7 to 9400 s, and their X-ray emission is powered by the accretion from their stellar companions. We fitted each individual pulse profile with the Polestar geometric model, which accounts for X-ray emission from two hot spots modeled as a simple combination of fan+pencil beam components, including an approximation for gravitational light bending. In 14 of 21 cases, our measurements of the inclinations of the pulsar spin axes broadly agree with the corresponding inclinations of …

A Time-Dependent Spectral Analysis Of Γ Cassiopeiae, Sean J. Gunderson, David P. Huenemoerder, José M. Torrejón, Dustin K. Swarm, Joy S. Nichols, Pragati Pradhan, Richard Ignace, Hans Moritz Guenther, A.M.T. Pollock, Norbert S. Schulz

Publications

We investigated the temporal and spectral features of γ Cassiopeiae’s X-ray emission within the context of the white dwarf (WD) accretion hypothesis. We find that the variabilities present in the X-ray data show two different signals, one primarily due to absorption and the other due to flickering like in nonmagnetic cataclysmic variables. We then use this two-component insight to investigate previously unreported simultaneous XMM and NuSTAR data. The results of model fitting find WD properties consistent with optical studies alongside a significant secondary, thermal source. We propose a secondary shock between the Be decretion disk and WD accretion disk as …

Detection Of The Orbital Modulation Of Fe Kα Fluorescence Emission In Centaurus X-3 Using The High-Resolution Spectrometer Resolve On Board Xrism, Yuto Mochizuki, Masahiro Tsujimoto, Richard L. Kelley, Bert Vander Meulen, Teruaki Enoto, Yutaro Nagai, Chris Done, Pragati Pradhan, Natalie Hell, Katja Pottschmidt, Ken Ebisawa, Ehud Behar

Publications

The Fe Kα fluorescence line emission in X-ray spectra is a powerful diagnostic tool for various astrophysical objects to reveal the distribution of cold matter around photoionizing sources. The advent of the X-ray microcalorimeter on board the XRISM satellite will bring new constraints on the emission line. We present one of the first such results for the high-mass X-ray binary Centaurus X-3, which is composed of an O-type star and a neutron star (NS). We conducted a 155 ks observation covering an entire binary orbit. A weak Fe Kα line was detected in all orbital phases at an equivalent width …

Legal And Ethical Considerations For Balancing Space Innovation And Dark Sky Preservation, Sara M. Langston, Kayla D. Taylor

Publications

The proliferation of satellites in Earth’s orbit has significantly enhanced capabilities in communication, Earth observation, and scientific research. However, this rapid expansion presents considerable legal and ethical challenges, particularly regarding the preservation of dark and quiet skies. As low Earth orbit becomes increasingly congested, the implications for astronomical observation, environmental integrity, and cultural heritage require critical examination.

This presentation provides an interdisciplinary perspective on the legal, practical and ethical considerations essential for preserving dark and quiet skies. It begins by exploring the legal frameworks governing the use of space, highlighting relevant international treaties, national responsibilities, and emerging issues aimed at …

Sharp Periodic Flares And Long-Term Variability In The High-Mass X-Ray Binary Xte J1829−098 From Rxte Pca, Swift Bat, And Maxi Observations, Robin H.D. Corbet, Ralf Ballhausen, Peter A. Becker, Joel B. Coley, Felix Fuerst, Keith C. Gendreau, Sebastien Guillot, Nazma Islam, Gaurava Kumar Jaisawal, Peter Jenke, Peter Kretschmar, Alexander Lange, Christian Malacaria, Mason Ng, Katja Pottschmidt, Pragati Pradhan, Paul S. Ray, Richard E. Rothschild, Philipp Thalhammer, Lee J. Townsend, Joern Wilms, Colleen A. Wilson-Hodge, Michael T. Wolff

Publications

XTE J1829−098 is a transient X-ray pulsar with a period of ∼7.8 s. It is a candidate Be star system, although the evidence for this is not yet definitive. We investigated the twenty-year-long X-ray light curve using the Rossi X-ray Timing Explorer Proportional Counter Array (PCA), Neil Gehrels Swift Observatory Burst Alert Telescope, and the Monitor of All-sky X-ray Image. We find that all three light curves are clearly modulated on the ∼244 days orbital period previously reported from PCA monitoring observations, with outbursts confined to a narrow phase range. The light curves also show that XTE J1829−098 was in …

Exploring Machine Learning, Feature Engineering, And Explainability To Constrain Spica’S Apsidal Constant Through Mesa Simulations, Hannah C. Woodruff

Doctoral Dissertations and Master's Theses

Spica (α-Virginis) is a notable binary star system located in the constellation of Virgo and offers valuable insights into stellar interiors and dynamics. Within binary systems, gravitational forces between the two stars cause minor distortions that alter their orbital motion. The steady rate of this alteration is known as the apsidal constant, which provides key information about a star’s internal structure and its evolutionary state. Traditionally, stellar environments like Spica are studied using simulations, such as MESA (Modules for Experiments in Stellar Astrophysics). These simulations allow researchers to explore various aspects of stellar behavior through the entire evolution of the …

Prospects For Time-Domain And Multi-Messenger Science With Axis, Riccardo Arcodia, Franz E. Bauer, S. Bradley Cenko, Kristen C. Dage, Daryl Haggard, Wynn C.G. Ho, Erin Kara, Michael Koss, Tingting Liu, Labani Mallick, Michela Negro, Pragati Pradhan, J. Quirola-Vásquez, Mark T. Reynolds, Claudio Ricci, Richard E. Rothschild, Navin Sridhar, Eleonora Troja, Yuhan Yao

Publications

The Advanced X-ray Imaging Satellite (AXIS) promises revolutionary science in the X-ray and multi-messenger time domain. AXIS will leverage excellent spatial resolution (< 1.5 arcsec), sensitivity (80× that of Swift), and a large collecting area (5–10× that of Chandra) across a 24-arcmin diameter field of view at soft X-ray energies (0.3–10.0 keV) to discover and characterize a wide range of X-ray transients from supernova-shock breakouts to tidal disruption events to highly variable supermassive black holes. The observatory’s ability to localize and monitor faint X-ray sources opens up new opportunities to hunt for counterparts to distant binary neutron star mergers, fast radio bursts, and exotic phenomena like fast X-ray transients. AXIS will offer a response time of < 2 h to community alerts, enabling studies of gravitational wave sources, high-energy neutrino emitters, X-ray binaries, magnetars, and other targets of opportunity. This white paper highlights some of the discovery science that will be driven by AXIS in this burgeoning field of time domain and multi-messenger astrophysics. This White Paper is part of a series commissioned for the AXIS Probe Concept Mission; additional AXIS White Papers can be found at the AXIS website.

Role Of Planetary Wave-Tide-Gravity Wave Interactions In Whole Atmosphere Coupling, Zishun Qiao

Doctoral Dissertations and Master's Theses

This dissertation investigates the mechanism by which the Earth's whole atmosphere couples from the bottom to the top, pole to pole. The work in this dissertation utilizes observational data and numerical simulations, with a particular emphasis on sudden stratospheric warming (SSW) events. The development of a new multi-static meteor radar at 30ºS, named Chilean Observation Network De MeteOr Radars (CONDOR), provides a key dataset for the present studies. Wind validation of this new radar system is performed across different sites and compared to a co-located sodium lidar. Wave-wave interactions in the mesosphere and lower thermosphere (MLT) that may be responsible …

Space Radiation Assessment And Mitigation: Meeting The Growing Demand For Shielding Solutions By Enhancing Models And Exploring Novel Shielding Opportunities, M. Laura Sorgi Johann

Doctoral Dissertations and Master's Theses

The rapid growth of satellite technology and the increasing presence of vulnerable technology and human life in space have highlighted the need for improved shielding materials. Industry standard protocols for shielding are being pushed to their limits as we gain a deeper understanding of the harsh space environment and as chip sizes approach the scale of radiation wavelengths. Furthermore, the commercialization of space is attracting interest from industries such as pharmaceuticals and semiconductor crystal growing, as they explore the potential benefits of zero-gravity production environments. However, the eagerness to develop lighter shielding and the lack of consideration for existing tools …

An In-Depth Analysis Of The Variable Cyclotron Lines In Gx 301−2, Nicolas Zalot, Ekaterina Sokolova-Lapa, Jakob Stierhof, Ralf Ballhausen, Aafia Zainab, Katja Pottschmidt, Felix Fürst, Philipp Thalhammer, Nazma Islam, Camille M. Diez, Peter Kretschmar, Katrin Berger, Richard Rothschild, Christian Malacaria, Pragati Pradhan, Jörn Wilms

Publications

Context. The high-mass X-ray binary system GX 301−2 is a persistent source with a well-known variable cyclotron line centered at 35 keV. Recently, a second cyclotron line at 50 keV has been reported with a presumably different behavior than the 35 keV line. Aims. We investigate the presence of the newly discovered cyclotron line in the phase-averaged and phase-resolved spectra at higher luminosities than before. We further aim to determine the pulse-phase variability of both lines.

Methods. We analyze a NuSTAR observation of GX 301−2 covering the pre-periastron flare, where the source luminosity reached its peak of ∼4×1037 …

Chandra Hetg X-Ray Spectra And Variability Of Π Aqr, A Γ Cas-Type Be Star, David P. Huenemoerder, Pragati Pradhan, Claude R. Canizares, Sean Gunderson, Richard Ignace, Joy S. Nichols, A.M.T. Pollock, Norbert S. Schulz, Dustin K. Swarm, José M. Torrejón

Publications

High-resolution X-ray spectra of π Aqr, a γ Cas-type star, obtained with the Chandra/HETG spectrometer, revealed emission lines of H-like ions of Mg, Si, S, and Fe; a strong, hard continuum; and a lack of He-like ions, indicating the presence of very hot thermal plasma. The X-ray light curve showed significant fluctuations, with coherent variability at a period of about 3400 s in one observation. The hardness ratio was relatively constant except for one observation in which the spectrum was much harder and more absorbed. We interpret the X-ray emission as arising from accretion onto the secondary, which is likely …

Energy Dependence Of Quasi-Periodic Oscillations In Accreting X-Ray Pulsars, Hemanth Manikantan, Biswajit Paul, Rahul Sharma, Pragati Pradhan, Vikram Rana

Publications

We present the results from an investigation of the energy dependence of quasi-periodic oscillations (QPOs) exhibited by accreting X-ray pulsars using data from archival XMM-Newton, NuSTAR, RXTE, and NICER observations. In a search for the presence of QPOs in 99 XMM-Newton and NuSTAR observations, we detected QPOs in eleven observations of five sources, viz., 4U 1626–67 (48 mHz), IGR J19294+1816 (30 mHz), V 0332+53 (2, 18, and 40 mHz), Cen X–3 (30 mHz), and XTE J1858+034 (180 mHz). A positive correlation of the QPO rms amplitude with energy is exhibited by 4U 1626–67, IGR J19294+1816, Cen X–3 and XTE J1858+034, …

Factors Predicting Public’S Willingness To Support National Aeronautics And Space Administration’S Artemis Mission, Sean Crouse

Doctoral Dissertations and Master's Theses

NASA's Artemis program aspires to return astronauts to the moon and aims to land the first woman and person of color on the lunar surface. The endeavor symbolizes the next evolution in space exploration and serves as a testament to the human spirit of discovery. In the face of this significant undertaking, gauging public sentiment and understanding the factors driving public support becomes necessary. The current study aimed to address a critical gap in the literature by examining public support for NASA’s Artemis mission, which is essential for sustaining the program’s momentum and cultivating a culture of innovation and exploration. …

Density And Magnetic Field Asymmetric Kelvin‐Helmholtz Instability, Xuanye Ma, Peter Delamere, Katariina Nykyri, Antonius Otto, Stefan Eriksson, Lihui Chai, Brandon Burkholder, Andrew Dimmock, Yu-Lun Liou, Shiva Kavosi

Publications

The Kelvin‐Helmholtz (KH) instability can transport mass, momentum, magnetic flux, and energy between the magnetosheath and magnetosphere, which plays an important role in the solar‐wind‐ magnetosphere coupling process for different planets. Meanwhile, strong density and magnetic field asymmetry are often present between the magnetosheath (MSH) and magnetosphere (MSP), which could affect the transport processes driven by the KH instability. Our magnetohydrodynamics simulation shows that the KH growth rate is insensitive to the density ratio between the MSP and the MSH in the compressible regime, which is different than the prediction from linear incompressible theory. When the interplanetary magnetic field (IMF) …