Stellar Occultation Light Curves Research Articles

The Upper Atmosphere of Uranus from Stellar Occultations. I. Methods and Validation

Measurements made by the Voyager 2 spacecraft during its flybys of Uranus in 1986 found warm stratospheric and hot thermospheric temperatures that cannot be explained by solar energy alone. It contributes to what has become known as the “giant planet energy crisis”; there is a fundamental lack of understanding of the energy balance of giant planets in the solar system. Uranus, in particular, has both the hottest thermospheric temperatures and the weakest internal heat flux of all four giant planets. Moreover, the Voyager 2 UV temperature measurements are at odds with the many contemporaneous Earth-based stellar occultation observations. In this work, we examine the 1977 Uranus stellar occultation (U0) and compare the observed light curve to reported Voyager 2 temperature profiles by simulating the latter into stellar occultation light curves. In this investigation, we find that the observed light curves are in tension with the simulated light curves to a high degree of statistical confidence. Next, we reprocess the U0 light curves using a modern approach, with some significant adjustments described herein, and report updated profiles. We find that the lower thermosphere of Uranus is much cooler than the Voyager 2 profiles suggest but slightly warmer than those originally published from the U0 occultation. In Paper II, we will present the results of applying these methods to many of the dozens of archival Uranus stellar occultations.

Study of Pluto’s atmosphere based on 2020 stellar occultation light curve results

On 6 June 2020, Pluto’s stellar occultation was successfully observed at a ground-based observatory in Iran, and Pluto’s atmospheric parameters were investigated. We used an atmospheric model of Pluto, assuming a spherical and transparent pure N2 atmosphere. Using ray-tracing code, the stellar occultation light curve was satisfactorily fit to this model. We found that Pluto’s atmospheric pressure at the reference radius of 1215 km was 6.72 ± 0.48 μbar in June 2020. Our estimated pressure shows a continuation of the pressure increase trend observed since 1988 and does not confirm the rapid pressure decrease tentatively reported in 2019. The pressure evolution is consistent with a seasonal transport model. We conclude that the N2 sublimation process from Sputnik Planitia is continuing. This study’s result is shown on the diagram of the annual evolution of atmospheric pressure.

Global climate model occultation lightcurves tested by August 2018 ground-based stellar occultation

Pluto's atmospheric profiles (temperature and pressure) have been studied for decades from stellar occultation lightcurves. In this paper, we look at recent Pluto Global Climate Model (GCM) results (3D temperature, pressure, and density fields) from Bertrand et al. (2020) and use the results to generate model observer's plane intensity fields (OPIF) and lightcurves by using a Fourier optics scheme to model light passing through Pluto's atmosphere (Young, 2012). This approach can accommodate arbitrary atmospheric structures and 3D distributions of haze. We compared the GCM model lightcurves with the lightcurves observed during the 15-AUG-2018 Pluto stellar occultation. We find that the climate scenario which best reproduces the observed data includes a N2 ice mid latitude band in the southern hemisphere. We have also studied different haze and P/T ratio profiles: the haze effectively reduces the central flash strength, and a lower P/T ratio both reduces the central flash strength and incurs anomalies in the shoulders of the central flash.

Composition of Titan's upper atmosphere from Cassini UVIS EUV stellar occultations

Identifying seasonal and spatial variability in Titan's atmospheric structure is a key factor in improving theoretical models of atmospheric loss and understanding the physical processes that control the loss rate. In this work, the extreme ultraviolet (EUV) stellar occultation lightcurves from the Cassini Ultraviolet Imaging Spectrograph (UVIS) experiment are analyzed. N2 and CH4 atmospheric profiles between 1000 and 1400km are determined by using an optimized grid search retrieval method to provide a complete χ2 surface for the two species abundance parameters at each level in the atmosphere. Kinetic temperature is extracted from hydrostatic analysis of the N2 profiles, and indicates a high level of variability related to energy deposition in the upper atmosphere. These results are compared to in situ measurements by the Ion Neutral Mass Spectrometer (INMS), which also probes this region of Titan's atmosphere.

A 3D general circulation model for Pluto and Triton with fixed volatile abundance and simplified surface forcing

We present a 3D general circulation model of Pluto and Triton’s atmospheres, which uses radiative–conductive–convective forcing. In both the Pluto and Triton models, an easterly (prograde) jet is present at the equator with a maximum magnitude of 10–12ms−1 and 4ms−1, respectively. Neither atmosphere shows any significant overturning circulation in the meridional and vertical directions. Rather, it is horizontal motions (mean circulation and transient waves) that transport heat meridionally at a magnitude of 1 and 3×107W at Pluto’s autumn equinox and winter solstice, respectively (seasons referenced to the Northern Hemisphere). The meridional and dayside–nightside temperature contrast is small (⩽5K). We find that the lack of vertical motion can be explained on Pluto by the strong temperature inversion in the lower atmosphere. The height of the Voyager 2 plumes on Triton can be explained by the dynamical properties of the lower atmosphere alone (i.e., strong wind shear) and does not require a thermally defined troposphere (i.e., temperature decreasing with height at the surface underlying a region of temperature increasing with height). The model results are compared with Pluto stellar occultation light curve data from 1988, 2002, 2006, and 2007 and Triton light curve data from 1997.

Comparison of a simple 2‐D Pluto general circulation model with stellar occultation light curves and implications for atmospheric circulation

We use a simple Pluto general circulation model (sPGCM) to predict for the first time the wind on Pluto and its global, large‐scale structure, as well as the temperature and surface pressure. Wind is a fundamental atmospheric variable that has previously been neither measured nor explicitly modeled on Pluto. We ran the sPGCM in 2‐D mode (latitude, height, and time varying) using the Massachusetts Institute of Technology general circulation model dynamical core, a simple radiative‐convective scheme, and no frost cycle. We found that Pluto's atmosphere is dynamically active in the zonal direction with high‐speed, high‐latitude jets that encircle the poles in gradient wind balance and prograde with Pluto's rotation. The meridional and vertical winds do not show evidence for a Hadley cell (or other large‐scale structure) due to the low‐altitude temperature inversion. The horizontal variation in surface pressure is a small fraction of the previously derived interannual variation in surface pressure. The simple general circulation model output was validated with stellar occultation light curve data from the years 1988, 2002, 2006, and 2007. For 2006 and 2007, the best fit global mean surface pressure was 24 microbar, in 2002 it was 22 microbar, and in 1988 it was 12 microbar (1 microbar error bars). For all years the methane mixing ratio was 1% (0.2% error bars). This work is a first step for future Pluto, Triton, and Kuiper Belt object atmosphere general circulation models that will also include longitudinal variations and a volatile cycle.

Morphology and variability of the Titan ringlet and Huygens ringlet edges

We present a forward modeling approach for determining, in part, the ring particle spatial distribution in the vicinity of sharp ring or ringlet edges. Synthetic edge occultation profiles are computed based on a two-parameter particle spatial distribution model. One parameter, h, characterizes the vertical extent of the ring and the other, δ, characterizes the radial scale over which the ring optical depth transitions from the background ring value to zero. We compare our synthetic occultation profiles to high resolution stellar occultation light curves observed by the Cassini Ultraviolet Imaging Spectrograph (UVIS) High Speed Photometer (HSP) for occultations by the Titan ringlet and Huygens ringlet edges. More than 100 stellar occultations of the Huygens ringlet and Titan ringlet edges were studied, comprising 343 independent occultation cuts of the edges of these two ringlets. In 237 of these profiles the measured light-curve was fit well with our two-parameter edge model. Of the remaining edge occultations, 69 contained structure that could only be fit with extremely large values of the ring-plane vertical thickness ( h > 1 km) or by adopting a different model for the radial profile of the ring optical depth. An additional 37 could not be fit by our two-parameter model. Certain occultations at low ring-plane incidence angles as well as occultations nearly tangent to the ring edge allow the direct measurement of the radial scale over which the particle packing varies at the edge of the ringlet. In 24 occultations with these particular viewing geometries, we find a wide variation in the radial scale of the edge. We are able to constrain the vertical extent of the rings at the edge to less than ∼300 m in the 70% of the occultations with appropriate viewing geometry, however tighter constraints could not be placed on h due to the weaker sensitivity of the occultation profile to vertical thickness compared to its sensitivity to δ. Many occultations of a single edge could not be fit to a single value of δ, indicating large temporal or azimuthal variability, although the azimuthal variation in δ with respect to the longitudes of various moons in the system did not show any discernible pattern.

An investigation of Pluto’s troposphere using stellar occultation light curves and an atmospheric radiative–conductive–convective model

We use a radiative–conductive–convective model to assess the height of Pluto’s troposphere, as well as surface pressure and surface radius, from stellar occultation data from the years 1988, 2002, and 2006. The height of the troposphere, if it exists, is less than 1 km for all years analyzed. Pluto has at most a planetary boundary layer and not a troposphere. As in previous analyses of Pluto occultation light curves, we find that the surface pressure is increasing with time, assuming that latitude and longitude variations in Pluto’s atmosphere are negligible. The surface pressure is found to be slightly higher ( 12.5 - 2.4 + 1.9 μbar in 1988, 18.0 - 1.7 + 11 μbar in 2002, and 18.5 ± 4.7 μbar in 2006) than in our previous analyses with the troposphere excluded. The surface radius is determined to be 1173 - 10 + 20 km . Comparison of the minimum reduced chi-squared values between the best-fit radiative–conductive–convective (i.e., troposphere-included) model and best-fit radiative–conductive (i.e., troposphere-excluded) shows that the troposphere-included model is only a slightly better fit to the data for all 3 years. Uncertainties in the small-scale physical processes of Pluto’s lower atmosphere and consequently the functional form of the model troposphere lend more confidence to the troposphere-excluded results.

An analysis of Pluto occultation light curves using an atmospheric radiative–conductive model

We use a radiative–conductive model to least-squares fit Pluto stellar occultation light curve data. This model predicts atmospheric temperature based on surface temperature, surface pressure, surface radius, and CH 4 and CO mixing ratios, from which model light curves are to be calculated. The model improves upon previous techniques for deriving Pluto’s atmospheric thermal structure from stellar occultation light curves by calculating temperature (as a function of height) caused by heating and cooling by species in Pluto’s atmosphere, instead of a general assumption that temperature follows a power law with height or some other idealized function. We are able to fit for model surface radius, surface pressure, and CH 4 mixing ratio with one of the 2006 datasets and for surface pressure and CH 4 mixing ratio for other datasets from the years 1988, 2002, 2006, and 2008. It was not possible to fit for CO mixing ratio and surface temperature because the light curves are not sensitive to these parameters. We determine that the model surface radius, under the assumption of a stratosphere only (i.e. no troposphere) model in radiative–conductive balance, is 1180 - 10 + 20 km . The CH 4 mixing ratio results are more scattered with time and are in the range of 1.8–9.4 × 10 −3. The surface pressure results show an increasing trend from 1988 to 2002, although it is not as dramatic as the factor of 2 from previous studies.

RAPID COMPUTATION OF OCCULTATION LIGHTCURVES USING FOURIER DECOMPOSITION

Calculation of a stellar occultation lightcurve from an assumed refractivity profile involves the integral of the refractivity or its derivatives along the line of sight through an atmosphere. For the general case, normal numerical integration can be time consuming for least-squares fitting with a modest number of free parameters, or for calculation at a fine grid for comparison with local refocusing (spikes) in a lightcurve. A new method, based on the Fourier decomposition of the refractivity profile, can rapidly calculate the line-of-sight integrals needed for occultations. The method is formulated for small planets, to be applicable to Pluto and Triton. The Fourier decomposition method may have applicability to a wider range of atmospheric studies.

Changes in Pluto's Atmosphere: 1988-2006

The 2006 June 12 occultation of the star P384.2 (2UCAC 26039859) by Pluto was observed from five sites in southeastern Australia with high-speed imaging photometers that produced time-series CCD images. Light curves were constructed from the image time series and fit by least-squares methods with model light curves. A new modeling procedure is presented that allows a simultaneous fit of the atmospheric parameters for Pluto and the astrometric parameters for the occultation to all of the light curves. Under the assumption of a clear atmosphere and using this modeling procedure to establish the upper atmosphere boundary condition, immersion and emersion temperature profiles were derived by inversion of the Siding Spring light curve, which had our best signal-to-noise ratio. Above ~1230 km radius, atmospheric temperatures are ~100 K and decrease slightly with altitude—the same as observed in 1988 and 2002. Below 1210 km, the temperature abruptly decreases with altitude (gradients ~2.2 K km-1), which would reach the expected N2 surface-ice temperature of ~40 K in the 1158-1184 km radius range. This structure is similar to that observed in 2002, but a much stronger thermal gradient (or stronger extinction) is implied by the 1988 light curve (which shows a kink or knee at 1210 km). The temperature profiles derived from inversion of the present data show good agreement with a physical model for Pluto's atmosphere selected from those presented by Strobel et al. (1996). Constraints derived from the temperature profiles (and considering the possibility of a deep troposphere) yield a value of 1152 ± 32 km for Pluto's surface radius. This value is compared with surface-radius values derived from the series of mutual occultations and eclipses that occurred in 1985-1989, and the limitations of both types of measurements for determining Pluto's surface radius are discussed. The radius of Pluto's atmospheric shadow at the half-intensity point is 1207.9 ± 8.5 km, the same as obtained in 2002 within measurement error. Values of the shadow radius cast by Pluto's atmosphere in 1988, 2002, and 2006 favor frost migration models in which Pluto's surface has low thermal inertia. Those models imply a substantial atmosphere when New Horizons flies by Pluto in 2015. Comparison of the shape of the stellar occultation light curves in 1988, 2002, and 2006 suggests that atmospheric extinction, which was strong in 1988 (15 months before perihelion), has been dissipating.

Analysis of Stellar Occultation Data. II. Inversion, with Application to Pluto and Triton

We present a method for obtaining atmospheric temperature, pressure, and number density profiles for small bodies through inversion of light curves recorded during stellar occultations. This method avoids the assumption that the atmospheric scale height is small compared with the radius of the body, and it includes the variation of gravitational acceleration with radius. First we derive the integral equations for temperature, scale height, pressure, number density, refractivity, and radius in terms of the light-curve flux. These are then cast into summation form suitable for numerical evaluation. Equations for the errors in these quantities caused by Gaussian noise in the occultation light curve are also derived. The method allows for an arbitrary atmospheric boundary condition above the inversion region, and one particular boundary condition is implemented through least-squares fitting. When the inversion equations are applied to noiseless test data for a simulated isothermal atmosphere, numerical errors in the calculated temperature profile are less than 5 parts in 104. Nonisothermal test cases are also presented. We explore the effects of (1) the boundary condition, (2) data averaging (in the time, observer-plane, and body-plane domains), (3) systematic errors in the zero stellar flux level, and (4) light-curve noise on the accuracy of the inversion results. A criterion is presented for deciding whether inversion would be an appropriate analysis for a given stellar occultation light curve, and limitations to the radial resolution of the inversion results are discussed. The inversion method is then employed on the light curves for the 1988 June 9 occultation by Pluto observed with the Kuiper Airborne Observatory and the 1997 November 4 occultation by Triton observed with the Hubble Space Telescope. Under the (possibly incorrect) assumption that no extinction effects are present in the occultation light curve, the Pluto inversion yields a 110 K isothermal profile down to approximately 1215 km radius, at which point a strong thermal gradient, 3.9 ± 0.6 K km-1, abruptly appears, reaching 93 K at the end of the inversion. The Triton inversion yields a differently shaped profile, which has an upper level thermal gradient, ~0.4 K km-1, followed by a ~51 K isothermal profile at lower altitudes. The Triton inversion shows wavelike temperature variations in the lower atmosphere, with amplitudes of ~1 K and wavelengths of ~20 km, that could be caused by horizontal or vertical atmospheric waves.

Triton's distorted atmosphere.

A stellar-occultation light curve for Triton shows asymmetry that can be understood if Triton's middle atmosphere is distorted from spherical symmetry. Although a globally oblate model can explain the data, the inferred atmospheric flattening is so large that it could be caused only by an unrealistic internal mass distribution or highly supersonic zonal winds. Cyclostrophic winds confined to a jet near Triton's northern or southern limbs (or both) could also be responsible for the details of the light curve, but such winds are required to be slightly supersonic. Hazes and clouds in the atmosphere are unlikely to have caused the asymmetry in the light curve.

A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

ABSTRACT We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmospheric model that has spherical symmetry. This improved speed makes least squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10-4 of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a 1/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal mode. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for best accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

On the Vertical Thermal Structure of Pluto's Atmosphere

A radiative–conductive model for the vertical thermal structure of Pluto's atmosphere is developed with a non-LTE treatment of solar heating in the CH43.3 μm and 2.3 μm bands, non-LTE radiative exchange and cooling in the CH47.6 μm band, and LTE cooling by CO rotational line emission. The model includes the effects of opacity and vibrational energy transfer in the CH4molecule. Partial thermalization of absorbed solar radiation in the CH43.3 and 2.3 μm bands by rapid vibrational energy transfer from the stretch modes to the bending modes generates high altitude heating at sub-microbar pressures. Heating in the 2.3 μm bands exceeds heating in 3.3 μm bands by approximately a factor of 6 and occurs predominantly at microbar pressures to generate steep temperature gradients ∼10–20 K km−1forp> 2 μbar when the surface or tropopause pressure is ∼3 μbar and the CH4mixing ratio is a constant 3%. This calculated structure may account for the “knee” in the stellar occultation lightcurve. The vertical temperature structure in the first 100 km above the surface is similar for atmospheres with Ar, CO, and N2individually as the major constituent. If a steep temperature gradient ∼20 K km−1is required near the surface or above the tropopause, then the preferred major constituent is Ar with 3% CH4mixing ratio to attain a calculated ratio ofT/M(= 3.5 K amu−1) in agreement with inferred values from stellar occultation data. However, pure Ar and N2ices at the same temperature yield an Ar vapor pressure of only ∼0.04 times the N2vapor pressure. Alternative scenarios are discussed that may yield acceptable fits with N2as the dominant constituent. One possibility is a 3 μbar N2atmosphere with 0.3% CH4that has 106 K isothermal region (T/M= 3.8 K amu−1) and ∼8 K km−1surface/tropopause temperature gradient. Another possibility would be a higher surface pressure ∼10 μbar with a scattering haze forp> 2 μbar. Our model with appropriate adjustments in the CH4density profile to Triton's inferred profile yields a temperature profile consistent with the UVS solar occultation data (Krasnopolsky, V. A., B. R. Sandel, and F. Herbert 1992.J. Geophys. Res.98, 3065–3078.) and ground-based stellar occultation data (Elliot, J. L., E. W. Dunham, and C. B. Olkin 1993.Bull. Am. Astron. Soc.25, 1106.).

Analysis of stellar occultation data for planetary atmospheres. I - Model fitting, with application to Pluto

Consideration is given to an analytic model for a stellar-occultation light curve developed for a small, spherically symmetric planetary atmosphere that includes thermal and molecular weight gradients in a region that overlies an extinction layer. The model incorporates two equivalent sets of parameters. One set specifies the occultation light curve in terms of signal levels, times, and time intervals. The other set specifies physical parameters of the planetary atmosphere. Equations are given for the transforming between the sets of parameters, including their errors and correlation coefficients. Detailed numerical calculations are presented for a benchmark case. The results obtained are consistent with the isothermal prediction of the 'methane-thermostat' model of Pluto's atmosphere.

Nonisothermal Pluto atmosphere models

We calculate the thermal profile of a model Pluto atmosphere containing a substantial number fraction of methane molecules, taking into account the heating of the atmosphere by absorption of solar infrared flux and the cooling by conductive transport to the planet's surface. We assume an equilibrium temperature of the high atmosphere equal to 106°K and an atmospheric composition with an appreciable fraction of molecules heavier than methane (such as, perhaps, CO or N 2). For surface pressures of a few microbars, we find that an appreciable temperature gradient must exist close to the surface. The predicted stellar occultation lightcurve for such a Pluto atmosphere agrees with observations, suggesting that an inferred Pluto haze layer may not exist. Instead, similar effects on the lightcurve could be produced by the strong temperature gradient near the surface. Our alternative model implies that Pluto's solid surface probably lies in the vicinity of 1180 km from the planet's center and that the normal and tangential optical depth of the atmosphere is quite negligible. We calculate an upper limit to the escape rate for the model atmosphere deduced here and find that the minimum time for depletion of the atmospheric methane inventory is about 30 Earth years.