Simulations of proton-driven instabilities in the solar wind

2023-2024
The solar wind is the continuous stream of electrons and ions outflowing from the Sun and filling the interplanetary space. Recent observations from NASA’s spacecraft Parker Solar Probe (PSP) now identified a new population of protons traveling at very high speeds in comparison to the “quiet” solar wind.

This population is significantly hotter in the direction perpendicular to the magnetic field that stretches out from the Sun and permeates the heliosphere. This feature drives instabilities which we study with numerical simulations.

Newly found proton populations in the interplanetary space

Proton populations in the solar wind are usually found either in a quiet and randomly moving state (which we call “core”) or as fast-moving, focused “beams” of particles along a specific direction. 

The newly discovered population instead exists in a sort of in-between state, called “hammerhead” after the peculiar shape it assumes in observed data (Fig. 2). This population exhibits temperature anisotropy, meaning that the local temperature is higher when measured in the direction perpendicular to the local magnetic field. 

Understanding the mechanisms responsible for generating hammerheads is crucial for unraveling the processes governing heating and acceleration in the solar wind.

Investigating the solar wind with numerical simulations

To study hammerhead formation, we simulated protons from initial conditions as observed in the inner heliosphere, with a core and a beam structure (but without hammerhead) and including temperature anisotropy. 

Our calculations showed that a hammerhead population naturally arises from the initial state via basic plasma instabilities driven by the anisotropy. The drifting proton beam undergoes relaxation: it excites magnetosonic and whistler waves (Fig. 3), which resonate with the beam protons and scatter them to higher energies.

This process creates a denser region in velocity space reminiscent of the observed hammerhead (Fig. 4).

Our simulations also indicate that the hammerhead only partially develops via this process. Additional free energy may be required to sustain the full development of the hammerhead structure. This energy could potentially originate from external sources, such as small-scale waves generated by the decay of larger waves, or from expansion and turbulent interactions in the solar wind.

References

  • Pezzini L., Zhukov A.N., Bacchini F., Arrò G., López R.A., Micera A., Innocenti M.E., Lapenta G. (2024), Fully Kinetic Simulations of Proton-beam-driven Instabilities from Parker Solar Probe Observations, The Astrophysical Journal 975, 37
     
  • Pierrard V., Péters de Bonhome M., Halekas J., Audoor C., Whittlesey P. and Livi R. (2023), Exospheric Solar Wind Model Based on Regularized Kappa Distributions for the Electrons Constrained by Parker Solar Probe Observations, Plasma, 6, 518
     
  • Verniero J.L., Chandran B.D.G., Larson, D.E., Paulson K., Alterman B.L., Badman S., Bale S.D., Bonnell J.W., Bowen T.A., Dudok de Wit T., Kasper J.C., Klein K.G., Lichko E., Livi R., McManus M.D., Rahmati A., Verscharen D., Walters J., Whittlesey P.L. (2022), Strong Perpendicular Velocity-space Diffusion in Proton Beams Observed by Parker Solar Probe, The Astrophysical Journal 924, 2
Continuous stream of electrons and ions outflowing from the Sun
The solar wind is the continuous stream of electrons and ions outflowing from the Sun and filling the interplanetary space.
Observation of proton velocity distribution from PSP
Figure 2. Observation of proton velocity distribution from PSP, displaying a core, beam, and hammerhead population.
Basic plasma instabilities in our simulations
Figure 3. Basic plasma instabilities in our simulations excite waves that interact with core and beam protons.
Proton velocity distribution in our simulation
Figure 4. Proton velocity distribution in our simulation, after the wave-proton interaction has occurred. This interaction creates mildly elongated structures reminiscent of the hammerhead.