Re-Analysis of the 1976 Mars Occultation of Epsilon Geminorum: Detection of Gravity (Buoyancy) Waves

Introduction: Stellar occultations have been used for decades to measure properties of neutral atmospheres of terrestrial planets, giant planets, icy bodies, and minor planets. Stellar occultations utilize the line-of-sight alignment of a star with a solar system body, which means targets can be predicted but not selected. The occultation of Epsilon Geminorum by Mars on April 8, 1976 remains the brightest stellar occultation by Mars to date.

This occultation was observed in three channels by the 91 cm telescope aboard the Kuiper Airborne Observatory, and published in 1977 just after the arrival of Viking 1 at Mars [1]. Here we present results of a re-analysis effort of the Epsilon Geminorum occultation, employing modern computational techniques and interpreting results in the context of recent discoveries about the Martian atmosphere.

Motivation and Aims: The original analysis made a number of assumptions and limitations that are no longer required today.  These include favoring analytical expressions over exact solutions, omitting error propagation, and binning the original 4 ms time resolution to 0.1 s [1, 2].  Relaxing the latter is a fundamental tenant of this work—we believe this high-resolution observation contains detailed structure on the Martian atmosphere not identified in the original work.

Furthermore, we interpret our results in the context of the many orbital remote sensing and in situ measurements of Mars that have occurred in the decades since this observation [e.g., 3, 4, 5, 6]. Developments in modeling such as the Mars Climate Database [7] provide additional sources of comparison.

Methods: We use an improved computational procedure closely following the steps of the original work [8]. Data is first normalized such that flux varies from 1.0 at pre-occultation baseline to 0.0 during occultation.

Inversion begins at 0.9 flux level using boundary conditions from an isothermal model fit to the entire occultation profile [3]. We integrate time resolution into altitude resolution of occultation ray penetration depth and into differential refraction, which is then inverted following the procedure of [8] to determine neutral number density, temperature and pressure as a function of altitude. These result products are compared to the original work [1]. Error is carefully propagated by taking partial derivatives at each integration step [8].

Further investigation is performed into the small-scale wave structures present in the atmospheric profiles of temperature versus pressure. We use a Lomb-Scargle periodogram (a fast Fourier transform for unevenly sampled data) on the density perturbations to identify consistent wave structures. Wave amplitude is compared to a basic model of gravity wave propagation and to atmospheric static stability.

Results and Conclusions: Figure 1 shows the temperature versus pressure result of the immersion (ingress) portion of the light curve for channels 2 and 3 of the observations, compared to the original results and to the Mars Climate Database. Present in the profile is small-scale perturbations we sought to isolate and identify. We use a density excursion—the deviation of the density profile from an exponential model atmosphere (assuming hydrostatic equilibrium)—and further removed large-scale variations with a moving average.

The result is the red curve shown in Figure 2, showing a consistent wave growing in amplitude with altitude. The black curve in Figure 2 (left) is a simple model of internal gravity wave (buoyancy wave) propagation in a stratified atmosphere, including amplitude growth following [9]. The vertical wavelength of the wave was determined to be 5-6 km from periodogram results, with confidence between the 2σ and 3σ level.

These findings indicate that the small-scale waves detected in this dataset are likely internal gravity waves. A host of evidence from in situ and remote observations of the Martian atmosphere indicates the atmosphere is stable enough to support and does contain gravity waves at many altitudes. This re-analysis effort has indicated that old stellar occultation data taken with high cadence has the potential for further discovery. Additionally, the model fitting, inversion, and wave analysis techniques developed in this effort for Mars will be applied to new and old occultations by the Ice Giants, where lack of comparison data makes it the only reliable way of measuring the vertical structure of those planets. We encourage those with access to archival datasets to consider performing re-analysis.

Figure 1. Temperature-pressure plot of the Martian atmosphere from the immersion (ingress) light curve. Re-analysis results in full resolution are compared to original profiles as well as the Mars Climate Database. The shaded regions represent uncertainty in temperature shifts of the entire profile because adjacent inversion results are highly correlated. Small-scale perturbations superimposed on the primary temperature inversion motivated detailed wave analysis. The pressure scale is exact for all comparison data but the altitude scale is approximate to within 15 km accuracy.

Figure 2. Extracted wave (red) overlaid with gravity wave model (black) and residual (right). The gravity wave model incorporates the peak wavelength of 5-6 km from the periodogram results and approximate fits of additional parameters, such as the amplitude growth following [9]. The fit is by eye and for illustrative purposes only. Residuals are given as data minus model, in percent.

 

References:

[1] J. L. Elliot et al. (1977) The Astrophysical Journal, 217, 661-679.

[2] R. G. French, J. L. Elliot, and P. J. Gierasch (1978) Icarus, 33, 186-202.

[3] A. G. Siddle, I. C. F. Mueller-Wodarg, S. W. Stone, & R. V. Yelle (2019) Icarus, 333, 12.

[4] A. Spiga, F. Gonzalez-Galindo, et al. (2012) Geophysical Research Letters, 39, L02201.

[5] S. Tellmann, M. Patzold, et al. (2013) Journal of Geophysical Research (Planets), 118, 306.

[6] J. E. Creasy, J. M. Forbes, & D. P. Hinson (2006)., Geophysical Research Letters, 33, L01803.

[7] E. Millour, F. Forget, A. Spiga, et al. (2019) Geophysical Research Abstracts, Vol. 21.

[8] J. L. Elliot, M. J. Person, & S. Qu (2003) The Astronomical Journal, 126, 1041.

[9] I. C. F. Mueller-Wodarg, D. F. Strobel, & J. I. Moses. (2008) Space Science Reviews, 139, 191.