How do foreshock waves propagate through Earth's bow shock?

Plasma waves forming in the turbulent foreshock upstream of Earth’s bow shock have long been known to transmit into Earth’s magnetosphere. Yet the exact mechanism allowing their propagation through the shock remained unknown. In this work, we propose a new scenario to explain the wave transmission.
How do foreshock waves propagate through Earth's bow shock?

The interaction of the solar wind plasma emitted by the Sun with Earth’s magnetic field gives rise to a profusion of interesting plasma phenomena in the space surrounding our planet. Near-Earth space forms a relatively easily accessible natural laboratory to study universal plasma processes such as magnetic reconnection, particle acceleration and plasma instabilities, which are known to occur in distant astrophysical environments and also play an important role in fusion and laboratory plasmas.

Of these complex plasma phenomena, I find the dynamics of Earth’s bow shock and its associated foreshock particularly fascinating. As it approaches our planet, the supersonic solar wind is slowed down and deflected by a collisionless shock wave arched ahead of the protective bubble formed by Earth’s magnetic field, the magnetosphere. As part of the energy dissipation process at the shock, a fraction of the solar wind particles are reflected back towards the Sun, and trigger plasma instabilities and waves in a region of space called the foreshock. What makes these waves particularly intriguing is that while the foreshock extends well outside of the outer boundary of Earth’s magnetosphere, spacecraft and ground-based observations show that foreshock waves can penetrate Earth’s magnetic shield and excite resonances on the terrestrial magnetic field lines. How this transmission occurs is however unclear, because a major obstacle lie in their way: Earth’s bow shock.

Foreshock waves forming ahead of the Earth's bow shock, from the Vlasiator numerical simulation.
(Image credit: L. Turc/Vlasiator team)

Early theoretical works have predicted that the waves could simply cross the shock without changes to their properties, but no evidence of those waves had ever been found on the other side of the shock despite extensive surveys using spacecraft measurements. Other scenarios have been proposed, but they cannot explain satisfactorily the wave propagation towards the magnetosphere.

To solve this long-standing open question, I gathered a group of experts of plasma waves, specialising in the different regions of near-Earth space, through the International Teams program of the International Space Science Institute (ISSI) in Bern, Switzerland. Our ISSI team met for the first time in Bern in May 2019, where we worked together for a week on the transmission of foreshock waves. Part of our group investigated their propagation into the magnetosphere during unusual solar wind conditions - resulting in a publication led by K. Takahashi -, while others focused on their transmission through the shock.

The conditions felt ideal to revisit this science question, as we could rely on recent developments in the field in terms of numerical simulations and spacecraft observations to shed new light on this old issue. In preparation for the meeting, the Vlasiator team at the University of Helsinki had performed global numerical simulations with the Vlasiator model, which describes foreshock waves in their global context, and their analysis would allow us to track the waves as they propagate earthwards. Complementing this numerical approach, we also had access to the extensive database of satellite measurements in the foreshock and downstream of the shock, collected by the Cluster, THEMIS and MMS missions in the past two decades. This first week of work at ISSI certainly made it clear that we were facing a complex issue even in the idealised framework of our global simulations, and that further in-depth investigation was required to unravel the processes at play.

Members of the ISSI team 448 during our meeting in Bern in 2019
Top row, from left to right: Primoz Kajdic, Kazue Takahashi, Andrew Dimmock, Emilia Kilpua and Minna Palmroth
Bottom row, left to right: Jan Soucek, Naoko Takahashi, Lucile Turc and Yann Pfau-Kempf

Our second team meeting was scheduled in mid-March 2020, and as it turned out, it was one of the first meetings to be cancelled by ISSI due to the COVID-19 pandemic. We instead continued our collaboration online, through regular videoconferences. We first directed our efforts at understanding the wave transmission in the global simulations, as we could follow the waves through all the steps of their earthward journey. We then used those findings to guide our search for relevant events in the spacecraft data, in order to test our hypotheses against actual satellite measurements in near-Earth space.

As the study progressed, new collaborators joined us on this journey, in particular Owen W. Roberts from the Space Research Institute in Austria, with whom I had worked before on foreshock waves, who contributed his expertise in wave analysis using multi-spacecraft data, and Daniel Verscharen from the Mullard Space Science Laboratory in the UK, who helped us with the comparison with theoretical wave dispersion relations. This collaborative work, within our ISSI team and beyond, was key to achieving this comprehensive investigation, combining numerical simulations, spacecraft observations and theory, which is now published in Nature Physics.

Our findings show that the transmitted foreshock waves retain similar properties downstream of the shock as in the foreshock, and in particular their fast-magnetosonic nature – fast-magnetosonic waves are a class of plasma waves with correlated variations in plasma density and magnetic field strength. At first, we thought that the waves traversed the shock unchanged, as predicted in early works. However, this direct transmission was incompatible with the change in the orientation of the wavevectors that we found in our simulations.

To understand the wave transmission, one needs to take a closer look at the processes happening when foreshock waves impinge on the shock. We noticed that the waves modulate the plasma properties just upstream of the shock, and in particular the Mach number, which controls the shock strength. This results in a periodic variation of the compression of the plasma as it crosses the shock, which in turn creates regions of enhanced and decreased pressure in the downstream. This pressure imbalance launches a succession of compression and rarefaction waves, at the same period as the foreshock waves, which traverse the magnetosheath and impact the magnetosphere.

Artist view of the MMS spacecraft (Image credit: NASA)

The Vlasiator simulations also brought us new insight into why transmitted foreshock waves had remained elusive so far: while these waves are relatively easily detected with the global view provided by the model, they are generally masked by other wave modes in the turbulent region downstream of the shock, except near the Sun-Earth line. That is likely why these waves were missed in previous surveys carried out with the Cluster spacecraft, which rarely cross this region. The MMS satellites, on the other hand, can regularly be found at appropriate locations, and their data revealed waves at the same period as in the foreshock, with properties consistent with those obtained from our simulations, confirming our numerical results.

These findings are important as they advance our understanding of the interaction of the solar wind with near-Earth space, in providing the missing link in the propagation of foreshock waves from the foreshock into the magnetosphere. While these waves originating in the foreshock play only a limited role in space weather at Earth, they are of great importance to understand the fundamental physics of our universe. Shocks, such as the bow shock forming ahead of Earth’s magnetosphere, are found everywhere in space, near other planets, supernovae remnants or active galactic nuclei, and are one of the main sources of high energy particles in our universe. Understanding how foreshock waves interact with Earth’s bow shock, how they modify it and how they are transmitted to the other side of the shock brings us crucial new insight into collisionless shock waves in general.

An example of an astrophysical shock: The Pencil Nebula Supernova Shock Wave
(Image Credit & Copyright: Greg Turgeon & Utkarsh Mishra - Astronomy Picture of the Day on 14 April 2021)

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