Acceleration in Exoplanet Magnetospheres

Abstract

We briefly review the various acceleration mechanisms working in exoplanetary magnetospheres. The proposed scenarios are based on the investigation of planetary magnetospheres of the Solar System. Primary attention is paid to Earth and Jupiter, as the most characteristic examples of the various types of magnetospheric features determining different acceleration processes.

1. Introduction

At present, various types of particle accelerations in space are known. One of the most effective mechanisms is acceleration at shock waves. Acceleration on shock waves around supernovae and novae allows to obtain very high energies of gamma (γ) and cosmic rays. An example of a nova is a white dwarf gathering hydrogen from a companion star and forming a shock wave after a thermonuclear explosion. During this process, the dwarf is not destroyed.

A supernova arises when a massive star, at the end of its life, ejects its envelope during an explosion, becoming a compact object. Around it, a shock wave develops. The matter and energy ejected by a supernova during an explosion is much greater than that of a nova, and the acceleration on the shock wave is more intensive. On a time scale of weeks to years, a nova may periodically become brighter and then return to its original brightness level. A supernova becomes much brighter during its single explosion. This is a very rare phenomenon. The shock waves around novae and supernovae are very important for particle acceleration in the cosmos.

It is widely believed that the shock waves arising after supernovae explosions accelerate galactic cosmic rays. It is considered that during a supernova explosion approximately 10% of the released energy goes to the acceleration of cosmic rays. On the base of the Earth’s direct observations, which confirm the diffusive shock acceleration mechanism at the bow shock, it is assumed that this mechanism also acts at supernovae shocks. The synchrotron emission of radio and X-rays from the massive star remnants shows that the particle acceleration at the supernova shocks is in the energy region from the Gev to Tev, while the γ ray observations show nuclei acceleration up to TeV [1].

During thermonuclear explosions of novae, ejected material hits the stellar wind of a white dwarf’s companion in a binary system. This leads to the acceleration of particles to energies ≥100 GeV. In the dense stellar wind of the companion star, the effective gamma rays are accelerated by the outer propagating shocks. A hadronic emission scenario is preferable to a leptonic one. The hadronic scenario means that γ rays are generated by accelerated protons impacting the dense matter, while the leptonic scenario implies that γ rays are created by high-energy electrons scattering photons with low energy from an active white dwarf.

The acceleration of charged particles exists at shocks in the heliosphere and in interplanetary space (e.g., [2]). The authors, based on Ulysses measurements, suggested that in field turbulence the diffusion of ions plays a significant role in the acceleration at shocks. The theory of diffusive shock acceleration is described in detail by Giacalone [3], who emphasizes the significant role of the magnetic field (its value and direction) in the particle acceleration process. In particular, it was noted that the rate of acceleration inversely depends on the coefficient of diffusion, which is smaller across the magnetic field than along it. For this reason, shocks moving perpendicular to the magnetic field accelerate more efficiently.

Puzzoni et al. [4] studied reconnection as a mechanism for particle acceleration in an astrophysical medium. The authors showed that a resistive electric field accelerates charged particles during their crossing of the neutral X-point of the magnetic field. Only due to this initial acceleration a high energy can be obtained.

Heating and acceleration of the solar and stellar winds are due to the fact of small-scale reconnections acting at neutral points where oppositely directed magnetic fields merge. As a result of these processes, hot plasma jets and Alfven waves flow out from the stellar/solar corona, forming stellar/solar winds.

In this paper, we are interested in acceleration processes operating in the exoplanet magnetospheres. The study of the Solar System’s planets has shown that the reconnection process plays a cardinal role in their magnetospheres and in particle acceleration. Here, we briefly discuss the main mechanisms of acceleration operating in Earth’s and Jupiter’s magnetospheres, which allows us to draw some conclusions regarding acceleration in the exoplanet magnetospheres.

2. Acceleration in Earth’s Magnetosphere

Paschmann et al. [5] emphasized that magnetic reconnection leads to particles acceleration in the terrestrial magnetosphere. During reconnection, magnetic energy is converted into kinetic and heat. High-energy jets flow out from the diffusion region, where reconnection takes place, over long distances. Many spacecraft have observed reconnection at Earth’s magnetopause and in the magnetotail for the southward interplanetary magnetic field (IMF) or in cusp regions for the northward IMF. This is because when the magnetic field of the solar wind is parallel to the planetary magnetic dipole axis (oriented southward for Earth), a two-dimensional reconnection occurs at a quasi-neutral line going from the subsolar magnetopause to the tail; however, if the IMF is antiparallel to the dipole axis, then two neutral points arise in the cusp regions, where three-dimensional reconnection occurs.

Fu et al. [6] stated that high-energy electrons are generated by reconnection in the Earth’s magnetosphere, which is confirmed by numerous observations, in particular, by the MMS (Magnetospheric Multiscale) mission. The authors concluded that the whistler waves were generated at the neutral point, where reconnection occurred, which leads to the wave–particle interaction. Via this process, electrons are accelerated to very high energies.

Reconnection takes place at two points. At the first one, open field lines (with one end at the planet and the other in interplanetary space) appear, and in the second they disappear. Acceleration occurs in each of these reconnection places in series. After the second reconnection, the accelerated charged particles flow to the planet, where the magnetic field enhances, accumulating energy due to the energy of the solar wind, the work of which generates convection towards the planet in the low-latitude magnetosphere. As a result, the plasma receives a very high energy and replenishes the radiation belts due to magnetic drift (gradient and curvature). This is the adiabatic heating and acceleration during inward plasma motion.

Milan and Baker [7] stated that there are multi-MeV electrons and protons in the radiation belts of Earth. Some of them originated on the Sun or Jupiter, others were accelerated in the terrestrial magnetosphere.

3. Acceleration in the Jovian Magnetosphere

Similar acceleration processes (due to the fact of reconnection and plasma inward drifts) also act in the Jovian magnetosphere. However, Jupiter’s magnetosphere has its own unique features, which distinguish it and determine special acceleration processes. Salveter et al. [8] listed the main factors of Jupiter’s magnetosphere determining its dynamics and structure: the rapid rotation of the planet, its strong magnetic field, and the source of additional plasma—the volcanic moon Io. Due to these factors, Jupiter’s magnetosphere is cardinally different from the terrestrial one. While the Earth’s magnetosphere is mainly controlled by the interaction with the solar wind, Jupiter’s is energetically dependent on the planetary rotation. Io supplies many neutrals, which, after ionization, provide ~1 ton/s (or even more [9]) of sulfur and oxygen ions.

Under the action of the centrifugal force, these ions, together with the rest of the near equatorial magnetospheric plasma, radially outflow beyond the Alfvenic radius. The Alfvenic radius is the distance from the center of Jupiter, where the Alfven Mach number is equal to 1. Closer to the planet from it, the density of the magnetic energy exceeds the density of kinetic energy; beyond it, the reverse situation occurs, and, therefore, the radial outflow of plasma controls the magnetic field, creating a magnetodisk, which is the main element of the Jovian magnetosphere. It enlarges the magnetic field and the size of the magnetosphere by approximately two times.

Due to the conservation of angular momentum, an increase in the radial velocity leads to a decrease in the azimuthal velocity, which is equivalent to a differential rotation starting from the Alfvenic radius. Consequently, a unipolar inductor works at the Alfvenic radius in the equatorial plane. It generates strong field-aligned currents outflowing from the ionosphere, associated with the main auroral ovals. Energetic magnetospheric electrons, precipitating into the ionosphere in these currents and causing emission in the main ovals, can be accelerated due to the fact of unipolar induction.

In the equatorial magnetodisk, these currents create outflowing radial currents, which are connected with the downward into the ionosphere field-aligned currents coming from the distant magnetodisk and closing by the Pedersen ionospheric currents, with the upward field-aligned currents going to the Alfvenic radius in the equatorial plane (see, for example, Figure 1 in [9]). In the equatorial plane, the Alfvenic radius is placed approximately at 18–20 R_J, where R_J is Jupiter’s radius (R_J = 7.14 × 10⁷ m). The potential drop at the ionospheric level, U_r, is given by the expression:

U_r = B_0J Ω_J (R_J³/r) sin²θ

(1)

where Ω_J = 1.76 × 10⁻⁴ s⁻¹ is the Jovian angular velocity; r is the distance from the planetary center; θ is the colatitude; and B_0J is the magnetic field at Jupiter’s equator (B_0J = 4.2 G). Consequently, B_0J Ω_J R_J² = 377 × 10⁶ V [10]. This potential drop, in principle, can accelerate charged particles in the region associated with the main auroral ovals.

After receiving the first data from the Juno spacecraft, which has been operating as a Jupiter orbiter since 2011, a new vision of acceleration processes in the Jovian magnetosphere has emerged. This is because Juno is the first satellite, working over the polar regions, very close to the planet. Recently, many papers have been devoted to the discussion of the observational data of Juno, which leads to the development of theories concerning the mechanisms of acceleration in Jupiter’s magnetosphere.

The examination of Juno’s data for the first 20 orbits [8] showed that in the region connected with the main ovals (magnetic latitudes >76° but less than 82°), the field-aligned accelerated electrons were recorded in 87.65% of all cases. Salveter et al. [8]. stated that among these field-aligned distributions, during ~93% of the time they were broadband, and only for ~7% of the time monoenergetic flows were observed. The input of the pancake distribution was only 13.8% (see Table 1 in [8]).

The connection between the magnetosphere and ionosphere by magnetic field lines leads to stochastic acceleration by the wave–particle interaction [11]. Whistler and Alfven waves are very important for this process. The electromagnetic energy of the waves is transferred to the acceleration of electrons, generating a diffuse aurora. Salveter et al. [8] found that below magnetic latitude 76°, diffusion auroral emission was observed with a pancake pitch-angle distribution in 86.2% of all cases, and only 12.4% was field-aligned. The authors concluded that stochastic acceleration in Jupiter’s magnetosphere is predominant.

In the spectra of particles’ energy, obtained by Juno, inverted V structures were observed. This means that an acceleration occurs in these regions. In Earth’s magnetosphere, an inverted V arises when the applied voltage drop is large, but the number of current carriers is not enough. In Jupiter’s magnetosphere, inverted V (electrostatic potentials from hundreds of keV to MeV) were measured close to the planet. Thus, in the Jovian magnetosphere, there are field-aligned quasi-static regions of acceleration. Mauk et al. [12] noted that field-aligned electron beams can be symmetric (bidirectional) or asymmetric. Thus, contrary to Earth, where monoenergetic electrons contribute the largest input to the main auroral emission, a stochastic acceleration process operates in the Jovian magnetosphere, leading to intense diffusion emissions.

Thereby, in the Jovian magnetosphere, there are the following acceleration mechanisms: unipolar induction; reconnection; a betatron speeding up during the inward convection in the equatorial magnetosphere to the increased magnetic field; wave–particle interaction.

Protons are accelerated in the Jovian magnetosphere from <1 keV to energies of a dozen MeV, according to Juno measurements [13]. Based on Galileo data, Kollmann et al. [14] found that electrons are accelerated up to tens of MeV in the radiation belts and in Jupiter’s magnetosphere. The authors concluded that the main acceleration is due to the fact of adiabatic motion. The mechanisms mentioned above may be relevant for the exoplanetary magnetospheres of the Earth and Jovian types.

4. Acceleration in the Exoplanet Magnetospheres

By analogy with the Earth, many researchers investigate terrestrial-type exoplanets. For example, Sciola et al. [15] studied the radio emission from the auroral zone of terrestrial exoplanets. They considered that this emission is created by field-aligned currents. In the terrestrial-type exoplanets, magnetic drift and convection determine the plasma motion and, consequently, the acceleration, as well as for Earth.

Accelerated charged particles in the auroral zone generate radio emission at the electron gyro frequency. As usual, the radiometric Bode law (RBL), previously derived for the magnetic planets of the Solar System and Jupiter’s Galilean satellites, was extrapolated to exoplanets [16]. This law describes the connection of the emitted power with the power of the interaction of an outer flow with an obstacle (planet, exoplanet, or moon). It was shown in [16] that the radio emission power (P_radio) is proportional to the incident power of the outer flow (P_d) regardless of whether the last one is kinetic or magnetic:

P_radio ~η P_d

(2)

where η is the coefficient of proportionality. Equation (2) is an empirical generalized RBL. Zarka [16] noted that for the Solar System, η is of the order of 10⁻⁵ for the kinetic outer flow and η ~2·10⁻³ for the magnetic flow. Thus, Zarka [16] concluded that the interplanetary magnetic field plays a major role relative to the kinetic energy in the conversion of the incident power into the acceleration of electrons. Louis et al. [17], considering the magnetospheres of magnetized exoplanets, described how accelerated electrons, gyrating along magnetic field lines, resonate with a wave with elliptical polarization. As a result, a cyclotron maser instability (CMI) arises associated with auroral emission. Under a positive gradient of the perpendicular electrons’ velocity, the CMI can amplify an extraordinary wave mode that propagates as a radio wave. The CMI characterizes the acceleration process. Its frequency is close to the electron gyro frequency, which is proportional to the magnetic field in the source of radio waves. Thus, the radio emission is associated with the acceleration region above the aurora. The CMI radio emission in the form of a cone is symmetric around the magnetic field direction. Louis et al. [17] noted that the same acceleration mechanisms, which we listed above in the present paper for the magnetospheres of Earth and Jupiter, also operate in the magnetic environments of exoplanets.

Varela et al. [18] noted that, as in the planetary magnetospheres of the Solar System, the acceleration of electrons to an energy of several keV occurs due to the reconnection process, and the same mechanism is expected to be relevant for extrasolar planets. By analogy, the authors considered that another acceleration mechanism, working in Jupiter’s magnetosphere, unipolar induction, can operate under the appropriate conditions in the magnetospheres of rapidly rotating magnetic exoplanets. A possible source of additional magnetospheric plasma was also mentioned. Varela et al. [18] provided calculations for typical stellar winds from the Sun-type stars, interacting with exoplanets around them near the habitable zone.

The interaction of the sub-Alfvenic stellar wind with exoplanets has no analogues in the Solar System, since all planets are located in the super-Alfvenic solar wind. Nevertheless, we can use our knowledge of the interaction of the Galilean moons with the sub-Alfvenic plasma of Jupiter’s magnetosphere to understand what will happen. Instead of a comet-like magnetosphere, the Alfven wings arise around the exoplanets in sub-Alfvenic stellar wind. These structures slow down the stellar wind plasma flow, creating a unipolar inductor, the potential drop of which can be a source of an increase in the charged particles’ energy. For magnetic exoplanets, the reconnection of their intrinsic magnetic field with the magnetic field of the stellar wind increases acceleration. This situation is also relevant for the interaction of exoplanets with their moons located in the sub-Alfvenic flow of magnetospheric plasma.

5. Future Directions

As mentioned above, accelerated particles generate radio emission above planetary auroral zones. As this emission has a frequency of the order of the electron cyclotron frequency, which is proportional to the magnetic field, the magnitude of the magnetic field can be determined. Zarka [19] noted that the radio telescope FAST (Five-hundred-meter Aperture Spherical Radio Telescope), with the ability to determine polarization, can measure radio emission with a frequency ≥70 MHz. The authors stated that this frequency corresponds to a magnetic field value >25 G and that such emission may be associated with the star–planet interaction.

In [19], the sources of particle acceleration up to keV energies are listed. These energies are characteristics of the magnetized planets in the Solar System. The authors describe how to detect a source of radiation within a star–planet system based on its polarization and periodicity. The expected measurements could improve our understanding of the accelerated processes in planetary magnetospheres producing these emissions.

Zarka et al. [19] paid primary attention to the FAST telescope, because the others, such as LOFAR (Low-Frequency Array) or NenuFAR at the Nançay Observatory near Orleans (which will extend the existing LOFAR telescope), will work later, while FAST operates now. Thus, there are perspectives to observe radio emission from the exoplanet magnetospheres in the future by giant radio telescopes of the present and next generation (LOFAR, GMRT (Giant Metrewave Radio Telescope), NenuFAR, SKA (Square Kilometre Array), etc.), which could expand our understanding of acceleration processes [17].

In the coming years, understanding the acceleration processes in exoplanetary magnetospheres will be crucial for studying the habitability of extrasolar planets. The search for life on exoplanets is a modern problem in magnetospheric science, astrobiology, and astrophysics [20]. The authors note that now is a transition period from the era of exoplanetary discoveries to the investigation of conditions in exoplanetary environments suitable for life. Strong beams of accelerated particles will be dangerous for life if the planet’s magnetic field and sufficiently dense atmosphere protected their impact.

6. Conclusions

Our review shows that the following acceleration mechanisms can be expected in exoplanets’ magnetospheres.

The interaction of a super-Alfvenic and super-sonic stellar wind, possessing a magnetic field, with a magnetic exoplanet leads to reconnection, which can be an energy driver for the acceleration of electrons to keV energies. In this case, the betatron speeding up during the inward convection in the equatorial magnetosphere to the increased planetary magnetic field is also significant.

In magnetospheres with a strong magnetic field and rapid rotation, a unipolar inductor operates in magnetosphere–ionosphere coupling, increasing the electron energy to a higher level. This process becomes more efficient in the presence of an additional source of plasma (for example, volcanic moons). The wave–particle interaction can also be effective for increasing the charged particle energy at the expense of wave energy.

The interaction of the sub-Alfvenic stellar wind with an exoplanet leads to the formation of Alfven wings. This situation has no analogy with the Solar System’s planets but is realized in Jupiter’s magnetosphere associated with its Galilean satellites (Io, Europa, and Ganymede). In this case, during a star–planet interaction, in the Alfven wings around the exoplanet, the plasma is breaking down, and a unipolar inductor is formed, which can accelerate charged particles. If an exoplanet in a sub-Alfvenic stellar wind flux has its own magnetic field, then reconnection contributes to the acceleration process. This situation is relevant for the interaction of exoplanets with their moons located in the sub-Alfvenic flow of magnetospheric plasma.