Elsevier

Planetary and Space Science

Volume 88, November 2013, Pages 76-85
Planetary and Space Science

Evolution of the Io footprint brightness II: Modeling

https://doi.org/10.1016/j.pss.2013.08.005Get rights and content

Highlights

  • Io footprint brightness varies with longitudes.

  • The general trend of the brightness variation is well-modeled.

  • The relative brightness of the spots in a footprint is explained.

  • Main modulations factors: local interaction, acceleration efficiency and transmission through the torus.

Abstract

The interaction of Io with the Jovian magnetosphere creates the best known and brightest satellite-controlled aurorae in our solar system. These aurorae are generated by the precipitation of electrons, which are accelerated by the Alfvén waves carrying the current between the satellite and the planet. A recent study computed the energy deposited on top of Jupiter's ionosphere due to the electron precipitation and retrieved the correct mean brightness of Io-related aurorae. The model developed in this study takes into account the acceleration mechanism and the Alfvén wave propagation effects. We use the same method to investigate the brightness variation of the different components of the Io footprint as a function of longitude. These observations are discussed in a companion paper. We identify several effects that act together to modulate the footprint brightness such as Alfvén wave reflections, magnetic mirroring of the electrons, the local interaction at Io and kinetic effects close to Jupiter. We identify the effects contributing the most to the modulation of the brightnesses of the three brightest components of the Io footprints: the main and reflected Alfvén wing spots and the transhemispheric electron spot. We show in particular that the modulation of the efficiency of the electron acceleration can be of greater importance than the modulation of the power generated at Io. We reproduce the average modulation of the spot brightnesses and present an extensive discussion of possible explanations for the observed features not reproduced by our model.

Introduction

Io is the innermost Galilean satellite of Jupiter. Its interaction with the Jovian magnetosphere generates intense aurorae in the Jovian ionosphere. These emissions are observed from the Infrared (Connerney et al., 1993) to the X-rays (Branduardi-Raymont et al., 2008), but are most studied in the UV domain (Prangé et al., 1996, Clarke et al., 1996), which gives the best spatial and temporal resolutions (Gérard et al., 2006, Bonfond et al., 2009). Because of the non-axisymmetric nature of the magnetic field of Jupiter, this interaction is expected to be modulated by the System III longitude of Io. Such a modulation has indeed been observationally confirmed (Serio and Clarke, 2008, Wannawichian et al., 2010, Bonfond et al., in this issue). The purpose of the present paper is to theoretically investigate this modulation, and to compare our results with the observations discussed in a companion paper (Bonfond et al., in this issue; hereafter Paper I). We first present a short introduction of Io's vicinity and its electromagnetic interaction with Jupiter.

Io is the most active volcanic body of our solar system, releasing about 1 ton/s of neutral matter in the Jovian magnetosphere. Roughly half of this matter is ionized and remains frozen in the Jovian magnetic field (Bagenal, 1997, Saur et al., 2003, Thomas et al., 2004, and references therein) forming a dense and cold plasma torus concentrated along the centrifugal equator and corotating with Jupiter in 9 h 55 min. Io orbits with a Keplerian period of 42.5 h in the jovigraphic equator. The centrifugal equator is inclined by ~7° from Io's orbital plane, intersecting it at the ~22° and ~202° System III longitudes (Schneider and Trauger, 1995).

The motion of Io relative to the Jovian magnetic field – with a velocity of VIo=57km/s – and the perturbation of the plasma flow around Io generate an electric field (EIo=VIo×B), which in turn induces a current (J) (Goldreich and Lynden-Bell, 1969). Due to the short (<1minute) duration of the satellite–magnetosphere interactions, the current is not in steady-state but mostly transient (Neubauer, 1980, Goertz, 1983, Hess et al., 2011c). In this case, the current is essentially carried by an Alfvén wave packet propagating at the Alfvén velocity (Va) toward Jupiter's ionosphere, where the current system finally closes. However, Alfvén waves are partially reflected on the torus borders (Gurnett and Goertz, 1981) due to strong gradients of the plasma density affecting the Alfvén velocity (Va):Va=B2μ0ρ,where B is the magnetic field strength, rho the plasma density and μ0 the vacuum permittivity. Upon reflection, a fraction of the wave and thus a part of the current are reflected back in the torus. Hence, the current directly reaching Jupiter is smaller than the one generated at Io. The Alfvén travel time from Io to Jupiter is longer than the time it takes for a magnetic field line to pass Io. As a consequence, remote conductances – e.g. the Jovian ionosphere conductance – do not impact the current generated at Io, and the current can be deduced from the electric field across Io and the height-integrated Alfvén conductance (ΣA) (Neubauer, 1980, Goertz, 1983):J=4EIoRIoΣA4VIoRIoρμ0perhemisphere.Note that the current expression depends only on local values, indicated by the Io subscript. Every term in the current formula remains constant, except for the plasma density. Since Io's orbit does not lie in the plasma torus plane, the value of the density at Io varies with Io's longitude (λIo), reaching a maximum where the Io orbit and plasma torus planes intersect (i.e. at λIo110° and 290° according to Schneider and Trauger, 1995).

Close to Jupiter, the convergence of the magnetic field lines forces the Alfvén perpendicular wavelengths toward small values, close to that of the electron inertial length. In this case, a parallel electric field appears due to kinetic effects and accelerates electrons (Lysak and Song, 2003, Swift, 2007, Hess et al., 2010a). Part of these electrons precipitate in the Jovian atmosphere and generate aurorae by collision with thermospheric neutrals. The interaction of Io with the Jovian magnetosphere generates the brightest satellite-related auroral emissions of the solar system, fed by the large amount of power radiated by Io:Pw=2EIoRIoJ8VIo2RIo2BIoρμ0perhemisphere.

Io auroral footprints have a complex substructure. They are composed of a Main Alfvén Wing (MAW) spot located where the Alfvén wing reaches the Jovian ionosphere and of a Transhemispheric Electron Beam (TEB) spot (Bonfond et al., 2008), both of which are traces of the electron acceleration by Alfvén waves (Swift, 2007, Hess et al., 2010a) that accelerate electrons in the planetward and anti-planetward directions. The planetward electrons precipitate on the MAW spot, whereas the anti-planetward electrons precipitate in the opposite hemisphere, powering the TEB spot. Finally, dimmer Reflected Alfvén Wing (RAW) spots and an extended (up to several tens of degrees) tail (Clarke et al., 2002, Gérard et al., 2006, Bonfond et al., 2009) are mostly due to the multiple reflections of the Alfvén waves carrying the current (Gurnett and Goertz, 1981, Goertz, 1983). The relative positions of these spots vary with Io's longitude (Gérard et al., 2006, Bonfond et al., 2009) in accordance with the geometry of the interaction. Depending on the Io position relative to the plasma torus center, an asymmetry appears between the northern and southern Alfvén wings and their respective footprints, affecting the positions of the auroral spots.

The brightness of these spots is also modulated with the longitude of Io (Serio and Clarke, 2008, Wannawichian et al., 2010). The latest and most precise study of the modulation of the Io footprints with the longitude is published in Paper I. In this study, the authors carefully separated the brightness of each spot comprising the Io footprints, and obtained brightness profiles as a function of the longitude of Io. The main results of Paper I are

  • (1)

    the determination of the relative brightnesses of the spots;

  • (2)

    the brightness of the spots presents a quasi-sinusoidal modulation with an amplitude of about ± 30% of the average, whose phase is determined by the position of Io relative to the torus center;

  • (3)

    all observed spots present a large peak of brightness in a narrow range of longitudes around 110° of Io's longitude; and

  • (4)

    the emissions in the southern hemisphere are on average twice as bright as those in the north.

These results are summarized in Fig. 1, Fig. 2 of the present paper, in which crosses represent the energy flux precipitated over each of the observed auroral spots. These fluxes have been computed from the brightness values measured in Paper I. The measured brightnesses have been converted in precipitating energy fluxes using the conversion formula determined by Gérard et al. (2006). More details on these results are presented in Paper I.

The purpose of the present paper is to investigate theoretically the brightness modulation of the main Io spots as a function of the longitude of Io and to compare it with the observations of Paper I. According to the current observational and theoretical understanding of Io's interaction with the Jovian magnetosphere described above, we propose four possible origins for the observed variations in auroral footprint brightness:

  • (1)

    The modulation of the power radiated at Io, which depends only on the magnetic field and plasma density at Io (Eq. (3)).

  • (2)

    The reflection of the Alfvén waves on the torus border, which varies as the position of Io in the torus varies with longitude.

  • (3)

    The modulation of the efficiency of the electron acceleration, which depends on the magnetic field topology and varies with longitude (Hess et al., 2011b).

  • (4)

    The modulation of the magnetic mirroring of the accelerated electrons between the acceleration region and the surface.

These phenomena are carefully discussed in 2 Modulation of the power generated at Io, 3 Power transmission along the magnetic field lines, 4 Power transfer to the electrons, 5 Modulation of the precipited power, respectively. We show that all of them contribute to the modulation of the Io footprint brightness with different relative contributions. We determine that the dominant ones are the modulation of the power radiated at Io and the modulation of the efficiency of the electron acceleration. This permits us to explain two out of the four results of Paper I (±30% amplitude variation, and relative brightness of the spots within each hemisphere). We are not able to present an explanation for results 3 and 4 of Paper I, since none of the aforementioned phenomena presents the required signature. However, based on the comparison of the longitudinal profiles of all spots, we discuss some possible origins.

Section snippets

Modulation of the power generated at Io

The power generated at Io by the satellite interaction with the Jovian magnetosphere is given by Eq. (3). The variables in this equation are only the magnetic field strength and the plasma density at Io.

The magnetic field model most commonly used for the study of the Io–Jupiter interaction is the VIP4 internal magnetic field model (Connerney et al., 1998). It is obtained from the inversion of the magnetic field measurements performed by the Pioneer and Voyager spacecraft and the fit of the Io

Model of the Alfvén wave packet

The power transmission along the Io flux tube depends strongly on the Alfvén wavelengths (Hess et al., 2010a). The interaction of Io with the magnetosphere involves Alfvén waves with a characteristic perpendicular wavelength of the order of the satellite diameter, and a parallel wavelength of the order of the Alfvén wave speed close to Io multiplied by the duration of the interaction (i.e. a few Io diameters). While simple Gaussian distributions would be expected to describe well the Alfvén

Power transfer to the electrons

The parallel electric field generated by an inertial Alfvén wave can be approximated by Lysak and Song (2003):δEωakλe2δBwhere ωa is the Alfvén frequency, λe is the electron inertial length, k the Alfvén perpendicular wavevector and δB the magnetic field perturbation associated with the wave. The amplitude profile of the parallel electric field along the magnetic field lines associated with the Alfvén waves has a narrow peak just above the Jovian ionosphere (i.e. at an altitude of ~0.5RJ),

Main Alfvén wing spot

The power carried by the electrons accelerated toward Jupiter may be obtained using Eq. (9). Still, between the acceleration region and the aurorae location, the magnetic field dramatically increases. This results in the magnetic mirroring of the accelerated electrons, which varies with longitude. Magnetic mirroring reflects electrons if their velocity is such that V/V>B/Bsurface. The power lost by magnetic mirroring depends on the electron velocity distribution.

Alfvén waves accelerate

Mean values and slow modulation

Both observations and modeling are summarized in Fig. 1, Fig. 2 which show the energy fluxes precipitating above the Io spots, in the northern and southern hemispheres respectively. On these figures, blue, green and red colors stand for the MAW, RAW and TEB spots, respectively. Crosses stand for energy fluxes deduced from the observed brightnesses, whereas lines stand for the modeled energy fluxes.

All four models of Fig. 2 (standing for the southern hemisphere) are similar, even if the

Conclusion

In the present study, we modeled the power transfer between the local magnetosphere interaction at Io and the UV emissions, based on our current knowledge of the interaction (Hess et al., 2010a). This modeling was performed for different longitudes of Io in order to investigate the modulation of the brightnesses of the Io spots. We succeeded in explaining the average brightness of the spots, even though we could not match exactly the brightness of the northern spots which are about half as

Acknowledgments

The authors thank the reviewers for their careful and valuable reviews.

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    Formerly at: Institut für Geophysik und Meteorologie, Universität zu Köln, Germany.

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