Juno spacecraft gravity measurements provide evidence for normal modes of Jupiter

Understanding Jupiter's interior structure is crucial to deciphering its origin and evolution. Previous missions have provided insights, but unanswered questions remain about the planet's deep interior. The Juno mission, with its highly eccentric orbit, offers unprecedented opportunities for probing Jupiter's gravitational field. The Juno spacecraft's onboard gravity science experiment, utilizing X-band and Ka-band dual-frequency Doppler tracking, allows for precise measurements of Jupiter's gravity field with high temporal resolution. This high precision allows for the detection of subtle variations in the gravitational field that were previously undetectable, offering a new window into the planet's internal dynamics. This paper focuses on analyzing these high-precision data to investigate previously unexplained accelerations observed in the spacecraft's trajectory, hypothesizing that these could be caused by internal oscillations, or normal modes, within Jupiter. The detection and characterization of these modes would provide invaluable information about Jupiter's internal structure, composition, and dynamics, significantly advancing our understanding of giant planet formation and evolution. This study aims to determine if the observed unexplained accelerations are consistent with the presence of internal oscillations, paving the way for a new era of planetary seismology for gas giants.

Prior analysis of Juno's gravity data, assuming a zonal gravity field (no longitudinal dependence), inferred the possible existence of a dilute core. Studies also determined the north-south asymmetric part of Jupiter's gravity field, revealing that zonal winds extend to several thousand kilometers depth. However, unexplained accelerations at levels of 2–5 × 10⁻⁸ m/s² remained unaccounted for when using a model limited to zonal harmonics. Similar unexplained accelerations, although with larger amplitudes, have been observed in Cassini data during its Grand Final orbits around Saturn. Several hypotheses have been proposed to explain these discrepancies, including localized density anomalies (e.g., the Great Red Spot), non-zonal density anomalies, or internal oscillations (normal modes). Ground-based observations had previously hinted at the existence of Jupiter's p-modes (pressure-driven oscillations) within a specific frequency range. At Saturn, ring observations provided insights into its oscillation spectrum, with ring seismology successfully constraining its interior structure by detecting f-modes (fundamental modes). Cassini gravity data also suggested the presence of p-modes in Saturn's oscillation spectrum. These previous studies provided the motivation for a similar search within Juno's more precise data, especially given numerical simulations predicting the observability of Jupiter's normal modes in the Juno Doppler data.

The study analyzed Juno's gravity-dedicated passes up to PJ33, encompassing 22 passes and 12,299 Doppler points (60s integration time). The data included Doppler information from both the pericenter pass and the outbound pass, until the orbit trim maneuver. X-band and Ka-band data were combined to reduce noise from charged particles. The data were calibrated for wet tropospheric noise using the Advanced Water Vapor Radiometer (AWVR) whenever available. Juno's orbit, with its high eccentricity, concentrates observations around perijove, limiting the observability of time-varying phenomena. The analysis focused on identifying spectral amplitudes compatible with observed signatures using a multi-arc least square estimation filter. The Juno's Doppler data were fitted using this filter, solving for local parameters (initial position, velocity, normal mode amplitudes) for each observation arc and global parameters (common to all arcs) including Jupiter's gravitational parameter, zonal and non-zonal harmonic coefficients, tidal Love numbers, Jupiter's spin axis position, polar moment of inertia, and GRS mass. Normal modes were incorporated into the model, with amplitudes and phases estimated as local parameters for each arc. The model included zonal coefficients (m=0) up to degree 8 and periods larger than 10 minutes (radial order up to 7). A Gaussian profile was used to model the amplitude of each mode based on frequency, with parameters determined using the Akaike information criterion (AIC). The AIC was used to assess the compatibility of different models with the observations, selecting the model that best fits the data while minimizing the number of parameters.

The analysis shows that the unexplained accelerations observed in Juno's data are best explained by the presence of Jupiter's normal modes. The best-fit model indicates a peak radial velocity of 10–50 cm/s for p-modes in the 900–1200 μHz frequency range. The amplitude of f-modes are constrained to be less than 1 cm/s. This is consistent with previous ground-based observations. Alternative explanations, such as static tesseral fields or localized density anomalies, were ruled out due to a significantly poorer fit to the data. The analysis also tested the hypothesis of energy equipartition (a flat velocity profile as a function of frequency), finding that it does not adequately fit the data. Models with dominant f-modes significantly underperform in comparison to the p-mode dominant model, further supporting the findings. The ratio of p-mode to f-mode amplitudes (in terms of radial velocity) is approximately 30-100, similar to that observed in the Sun. The Full Width at Half Maximum (FWHM) of the detected modes is found to be approximately 1/6-1/8 of the peak frequency, similar to observations on the Sun, though the significance of this is unclear.

The findings strongly support the existence of large-amplitude p-modes and small-amplitude f-modes within Jupiter. The detected p-mode amplitudes are compatible with previous ground-based observations, while the small f-mode amplitudes suggest they are significantly weaker. The similar ratio of p-mode to f-mode amplitudes between Jupiter and the Sun may hint at common excitation mechanisms, although the vastly different luminosities and convective processes make a direct analogy challenging. The excitation and dissipation of modes in giant planets remain poorly understood, requiring further research into potential energy sources such as moist convection and turbulent viscosity. The detection of normal modes in Jupiter, similar to Saturn, represents a significant step forward in planetary seismology. Future missions can leverage precise frequency measurements to gain deeper insights into planetary interiors, overcoming many of the ambiguities inherent in gravity observations. Detailed information on core structure and regions of static stability can be determined more effectively through seismological approaches.

This study provides compelling evidence for the existence of normal modes within Jupiter, using highly precise gravity data from the Juno spacecraft. The detected p-modes are consistent with previous ground-based observations, while f-modes are constrained to be significantly weaker. Alternative explanations for the observed accelerations are shown to be less likely. The findings open exciting possibilities for future planetary seismology investigations, suggesting the development of specialized onboard instrumentation for more accurate normal mode detection and characterization, which could lead to transformative improvements in our understanding of gas giant interiors. Future studies should focus on exploring the energy sources that drive these modes and investigating the implications of the observed mode characteristics for Jupiter's interior structure and evolution.

The high eccentricity of Juno's orbit limits the observation window for time-varying phenomena, making the identification of individual normal modes challenging. The analysis relies on modeling assumptions, such as the choice of a Gaussian profile for the mode amplitudes and the simplified polytropic model of Jupiter's interior. Although efforts were made to account for various factors influencing the Doppler measurements, uncertainties might still exist.