Plasma wave observations on Voyager, Ulysses, and Galileo have shown that whistler-mode hiss at frequencies below one kHz is continuously present in the extended Io torus of Jupiter. Cyclotron resonant energies at frequencies below 1 kHz are extremely high (typically > MeV), and the Jovian resonant electron flux is too low to cause significant local wave amplification. We consequently explore the possibility that Jovian hiss could be generated elsewhere, and then propagate into the torus to form the observed hiss band. Based on previous studies of the properties and excitation region of Jovian chorus emissions, we demonstrate that whistler-mode waves originating as discrete chorus emissions in the tenuous region from 10 to 15 RJ can refract and propagate inwards into the dense Io torus and there merge into a band of low-frequency hiss. This proposed mechanism for the origin of Jovian hiss is analogous to the formation of plasmaspheric hiss at Earth.
 Plasma wave observations on the Voyager spacecraft first identified the presence of whistler-mode hiss in the extended Io plasma torus region over the radial range between 5.5–12 RJ [Scarf et al., 1979]. Subsequent analysis showed that the low-frequency band of hiss (below one kHz) was often observed together with discrete chorus emissions [Coroniti et al., 1980] as shown in Figure 1. Later, the Ulysses spacecraft detected similar hiss emissions while it passed through just above the torus and peak intensities at the hundreds of Hertz regime were observed [Farrell et al., 1993]. The Galileo spacecraft also observed essentially continuous hiss emission below 1 kHz throughout the Io torus [Gurnett et al., 1996]. These waves can result in scattering loss of high-energy electrons [Thorne and Tsurutani, 1979] and may possibly be the cause of the pronounced drop in electron phase space density between the orbits of Europa (L∼10) and Io [Ye and Armstrong, 1993]. Here we explore the origin of this important hiss emission.
 The frequency of Jovian hiss is typically well below 0.05 fce (when normalized to the electron gyro-frequency). The emission cannot be generated locally because the cyclotron resonant energies are very high (typically > MeV) and the resonant fluxes of electrons are too low to cause significant local wave growth. But intense chorus emissions are excited both in the middle magnetosphere (6–16 RJ) of Jupiter [e.g., Horne et al., 2008] and in the Earth's outer radiation belts [Meredith et al., 2003] at frequencies between 0.05–0.6 fce. At each planet the free energy for chorus excitation is provided by the injection of anisotropic electrons with energy comparable to a few to a few 10's of keV [Xiao et al., 2003; Li et al., 2008]. The absence of a viable source of energy for the local excitation of whistler-mode hiss at either Earth or Jupiter, has lead us to consider alternate mechanisms for the wave origin. Recently, the origin of plasmaspheric hiss at Earth has been explained in terms of excitation as discrete whistler-mode chorus emissions in the outer radiation belt (L > 6) and subsequent inward propagation into the dense plasmasphere where the waves merge into a continuum with the observed characteristics of low frequency plasmaspheric hiss [Bortnik et al., 2008]. Here we explore the possibility that Jovian hiss might originate by a similar process. The ray paths of whistler-mode emissions, generated in the middle magnetosphere of Jupiter, are traced from the observed chorus source location in a heterogeneous medium, modeled with realistic gradients in density and magnetic field, to assess the access of waves of different frequency to the Io torus region.
 A plasma environment model is built for Jupiter covering the radial range below 15 RJ to allow us to follow the propagation paths of whistler-mode waves. Waves are traced using the HOTRAY code [Horne, 1988, 1989] and where we use the cold raytracing option. This code uses a dipole field model by default. Nevertheless, at the larger radial distances, Jovian plasma sheet effects need to be taken into account. Therefore, 80 nT in z-component is uniformly subtracted from the dipole field to simulate the sheet-like field in this region. The Io torus and plasma sheet plasma density models are modeled based on Voyager and Galileo observations [Thomas et al., 2004]. Two components of ion species are included to incorporate the important effect of the lower hybrid frequency (flhr) on the whistler-mode propagation paths. O+ ions are dominant and tend to be strongly confined near the magnetic equator, while H+ is a minor ion near the equator, but tends to become dominant at high latitudes. Contours of model electron density and cyclotron frequency are shown in Figure 2. All the magnetic field and density profiles have been analytically formulated so the gradients are continuous, as required for raytracing.
 Rays with frequencies at an interval of 50 Hz within the anticipated chorus emission range (0.05 fce to 0.5 fce) are launched at the equator from RJ = 10, 11, 12, 13, 14, and 15. This corresponds to lower wave frequencies at larger radial distance. For example, at R = 15, the local fce is 1.15 kHz so we select the frequency range of waves from f = 50 Hz to 600 Hz as our launching wave frequencies. Based on this criterion, the selected frequency ranges in our ray tracing are 100 Hz to 1 kHz at R = 14; 150 Hz to 1.5 kHz at R = 13; 200 Hz to 2.2 kHz at R = 12; 300 Hz to 3.1 kHz at R = 11; and 450 Hz to 4.5 kHz at R = 10. Note that the 300 Hz waves, which correspond to the peak spectral intensity of hiss (Figure 1), can originate from a broad range of radial distance from R = 11 to R = 15.
 The initial wave normal ψ0, i.e., the angle between the k vector of the wave and the magnetic field direction, at each source location are also selected from a broad range to explore the effects of different ψ0. The group time is run for 300 seconds to explore wave propagation paths and subsequent equatorial radial crossing distances. In the depicted results ψ0 > 0° denotes wave vectors k pointing toward the planet; ψ0 < 0° denotes wave vectors k pointing away from the planet. Since chorus waves with larger ∣ψ0∣ may be subject to strong Landau damping [e.g., Bortnik et al., 2007] our ray tracing results for ∣ψ0∣ < 40° are the primary results used in this study.
Figure 3 shows the ray paths (solid) of 300 Hz waves launched with ψ0 = 30° from various equatorial locations corresponding to different values of f/fce from 0.07 to 0.26, which are characteristics of lower frequency chorus emissions observed by the Galileo wave detector [e.g., Horne et al., 2008]. Also plotted are contours of lower hybrid frequencies (dotted lines) and a shading area for the Io torus region. These waves all migrate inwards into the high density Io torus, experience a magnetospheric reflection near the lower hybrid frequency [Thorne and Kennel, 1967], and propagate across the equator many times in the extended torus region. Similar ray trajectories (but with different subsequent equatorial crossing distances) are obtained for other choices of initial frequency and wave normal angle ∣ψ0∣ < 40°, which characterize the expected angular distribution of chorus emissions [e.g., Li et al., 2008]. Consequently, we anticipate that the lower frequency components of discrete chorus emissions, which are excited in the middle Jovian magnetosphere, should be refracted and migrate into the Io torus and there merge together form an incoherent band of hiss. However, the ability of waves to access the torus will depend on the initial frequency and on the Landau damping experienced along the ray paths.
 When the wave frequency is increased to 1000 Hz, the wave normal angle tends to stay closer to 90° along the ray path than the 300 Hz ray which will lead to differences in the rate of electron Landau damping. To illustrate this difference, Figure 4 shows ray tracing results for both 300 Hz-waves (left plots) and 1000 Hz-waves (right plots) with ψ0 = 20°. Both of these waves migrate inward and exhibit multiple crossing of the equator. The variations of L-shell and wave normal angle ψ along the ray paths are shown in the middle plots. Landau resonance energies along the ray path, EL = 1/2 me c2/(n2cos2ψ), where me is the electron mass, and n is the wave refractive index, are shown in the bottom plots. The Landau resonance energies are lowest near the equator and become extremely high near the high latitude magnetospheric reflection point. Although a complete evaluation of the rate of Landau damping is beyond the scope of this letter, some assessment of the relative damping at different frequencies can be made with information on the flux of Landau resonant electrons, and the wave normal angle [e.g., Bortnik et al., 2007]. Strongest damping should occur when the Landau resonant energies become small as the electron flux is generally higher at lower energies. For the waves under investigation, this occurs near the equator, but only for highly oblique waves. For the wave at 1000 Hz, the wave normal angle near the equator exceeds 70 degrees after the fifth equatorial crossing and the Landau resonant energy is comparable to a few keV for most of the remaining path. The wave should therefore be subject to strong Landau damping. In contrast, for the 300 Hz ray shown in Figure 4, wave normal angles near the equator always remain below 65 degrees (and are generally much smaller), which suggests that Landau damping should cause relatively weaker wave attenuation. This conclusion is consistent with Landau damping of chorus in the Earth's magnetosphere, which becomes more effective at higher frequencies [Bortnik et al., 2007].
 An overall assessment of the access of chorus emissions into the Io torus is illustrated in Figure 5, which shows the number (color coded) of equatorial crossing (in bins of 0.5 RJ) of all waves with frequency between 0.05 fce and 0.5 fce in the chorus source region (from RJ = 10 to 15) launched with ψ0 less than 40° pointing toward the planet. Lower-frequency waves (<700 Hz) are far more effective at accessing the torus between 6 and 10 RJ, consistent with the observed characteristics of Jovian hiss (Figure 1). A few high-frequency waves are also able to propagate into the torus, but such waves are probably subject to more severe Landau damping and are consequently expected to be observed much less often. Although some waves launched from the chorus source region with wave vectors pointed away from the planet can also ultimately gain access the torus, the inward migration of such waves tends to be slower, and we consequently expect their Landau damping to be more severe and such waves have consequently not been included in Figure 5.
4. Discussion and Conclusion
 Detailed ray tracing in a model Jovian environment has been performed to demonstrate that whistler-mode waves originating as chorus emission from a source region in the middle magnetosphere (10–15 RJ) can refract and propagate inwards into the extended Io torus. The waves cross the equator many times, and should eventually merge into a structure-less band of hiss at frequencies below 1 kHz, consistent with the observed properties of Jovian hiss. The weaker intensity of hiss at high frequency is related to both the sporadic propagation into the torus, and the enhanced Landau damping of these waves, but detailed path integrated damping calculations will be needed to quantify the latter.
 The authors wish to thank F. Bagenal for valuable discussion on the Io torus density model, J. Bortnik for valuable comments, and student assistants T. Y. Lin, P. F. Wu, W. C. Cho, and H. H. Lin for assistance with the modeling. This research was performed under the facilities of PSSC/NCKU, MUST, NCHC and supported by grant NSC 95-2111-M006-003 and by NASA grant NNX07AL27G.