LONG-WAVELENGTH DENSITY FLUCTUATIONS RESOLVED IN PLUTO'S HIGH ATMOSPHERE

Figure 1 shows the 1.6 μm light curve compared with a reference theoretical light curve for a simple pure-nitrogen atmosphere at constant temperature and pressure (T = 100 K, P = 30 μbar at 1150 km radius). This model atmosphere provides a smooth reference for analyzing the numerous fluctuations recorded throughout the occultation event. Since these fluctuations were not detected in a reference star recorded simultaneously in the same field of view at a separation of ∼6 arcsec, they are clearly associated with Pluto. The isothermal model does not constrain the true surface pressure because these data give no information about atmospheric radii less than about 1348 km.

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Based on a study of additional observations of this occultation (Person et al. 2008), we use values for the Mt. Hopkins impact parameter to the shadow center (1319 ± 4 km) and shadow-plane speed (6.77 km s⁻¹) and take the time of closest approach to be 10:30:00 UTC + 1428.26 ± 0.25 s. The isothermal model has a minimum relative stellar flux at midoccultation equal to 0.69. The corresponding minimum closest approach distance for the primary ray is 1348 km from Pluto's center.

The unusually slow shadow speed for this event, together with unprecedented S/N at 1.6 μm and the grazing geometry for the occultation, permits us to perform a detailed investigation of the prominent, well-sampled fluctuations visible in the data. These fluctuations span a pressure range of ∼0.1–0.7 μbar (0.01 to 0.07 Pa) corresponding to an altitude range of 1500–1350 km, respectively.

The bottom portion of Figure 1 shows that the residuals between the H-band and somewhat noisier V-band (Person et al. 2008) data are indistinguishable from the small predicted color difference due to dispersion in Pluto's nitrogen atmosphere. Therefore, there are no detectable chromatic effects in the two-wavelength data set, and no haze layers were detected over this altitude range. The refractivity of nitrogen gas increases by 0.8% from the H-band to the visible band (Bennett 1934), implying a maximum occultation depth difference due to differential refraction of 0.18% for this event.

The absence of chromatic effects is consistent with the spatial width of the fluctuations in the data, which is always in excess of 5 km along the occultation chord. The Fresnel scale for this occultation was 1.8 km at 0.75 μm and 3.2 km at 1.6 μm, significantly greater than the projected diameter (∼0.7 km) of an MIII-type star implied by infrared photometry (Skrutskie et al. 2006). Therefore, the fluctuations are not the diffractive scintillations ("spikes") frequently observed in planetary occultations or the twinkling of stars in the Earth's atmosphere (Hubbard et al. 1988). Because of the unusual grazing geometry of the present event, the fluctuations are amenable to interpretation using weak-scintillation theory (Hubbard et al. 1978). This theory is applied to our data in W. B. Hubbard et al. (2008, in preparation). Here we emphasize a robust, essentially theory-independent result from our initial data analysis: the long wavelength nature of the density fluctuations suggests that a physical mechanism filters out shorter wavelength fluctuations with increasing altitude in Pluto's atmosphere.

The fluctuations show some degree of symmetry about mid-occultation, but the symmetry is not perfect. Figure 2 shows the H-band light curve fluctuations plotted as a function of the closest-approach distance of the ray from the center of Pluto, assuming the geometric parameters of the isothermal model. The fluctuations in the immersion and emersion segments of the light curve show some symmetry about the closest-approach point but are typically misaligned by ∼1–5 km. This result implies that atmospheric density fluctuations giving rise to the light curve fluctuations are not strictly a function of radius but are inclined to the limb by angles ∼10⁻² radians.

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The theory that we apply (W. B. Hubbard et al. 2008, in preparation) makes the following approximations: we neglect any background winds, assume that the unperturbed atmosphere has a constant scale height H ∼ 60 km (corresponding to an average temperature $\bar T$ = 100 K), and assume a plane-parallel atmosphere (i.e., we ignore sphericity). We focus on inertia-gravity waves, although Rossby waves, as suggested by Person et al. (2008), may also be present in the data. Following Fritts (1984), we consider a wave in two dimensions, varying in x (parallel to the limb) and z (perpendicular to the limb). The corresponding spatial wavenumbers are k in the x-direction and m in the z-direction. For gravity waves, wavenumbers and frequency ω are related by the dispersion relation (French & Gierasch 1974)

$$\begin{equation} \omega ^2 = \frac{{\omega _B^2 {\kern 1pt} k^2 + f^2 m^2 }}{{k^2 + m^2 }}, \end{equation} \tag{ 1 }$$

wheref is the Coriolis frequency and ω_B is the Brunt–Väisälä frequency for an isothermal atmosphere at temperature $\bar T$, given by

$$\begin{equation} \omega _B^2 = \frac{{\gamma - 1}}{\gamma }\frac{g}{H} = \frac{{g^2 }}{{C_P \bar T}}, \end{equation} \tag{ 2 }$$

where g = 45 cm s⁻² is Pluto's average gravity in the range considered here, C_p is the heat capacity at constant pressure, and for N₂ gas γ = 1.4.

In the case of the present observation, we observe waves with k² ≪ m², because the occultation geometry averages out atmospheric disturbances over an effective path length $\ell \approx 2\sqrt {2rH} \approx$ 1000 km, where r ∼ 1400 km. We adopt k ∼ 2π/1000 km⁻¹, whereas m ∼ 2π/10 km⁻¹. We adopt ω_B = 1.44 × 10⁻³ s⁻¹ and f ∼ 2 × 10⁻⁵ s⁻¹. Sincef/ω_B ∼ 0.01, dispersion relation (1) reduces to

$$\begin{equation} m^2 \approx \frac{{k^2 \omega _B^2 }}{{\omega ^2 - f^2 }}. \end{equation} \tag{ 3 }$$

Define

$$\begin{equation} \nabla = \frac{{d\ln T}}{{d\ln P}}. \end{equation} \tag{ 4 }$$

Using Houghton's (1977) Equations (8.16)–(8.19), one can show that

$$\begin{equation} \frac{{(P^\prime\!{/}\!\bar P)}}{{(\rho ^\prime\!{/}\!\bar \rho)}} = - \frac{1}{{Hm}}, \end{equation} \tag{ 5 }$$

where P' is the gravity wave's pressure perturbation to the local pressure $\bar P$ of the background isothermal atmosphere, and ρ' is the mass density perturbation to the background density $\bar \rho$. For an ideal gas, we have

$$\begin{equation} \frac{{T^\prime }}{{\bar T}} = \frac{{P^\prime }}{{\bar P}} - \frac{{\rho ^\prime }}{{\bar \rho }} = \frac{{P^\prime }}{{\bar P}}(1 + Hm), \end{equation} \tag{ 6 }$$

so

$$\begin{equation} \nabla = H^2 m^2 \frac{{P^\prime }}{{\bar P}} = - Hm\frac{{\rho ^\prime }}{{\bar \rho }}. \end{equation} \tag{ 7 }$$

A gravity wave with vertical wavenumber m breaks when |∇|>(γ − 1)/γ, or when

$$\begin{equation} (\rho ^\prime /\bar \rho) \approx \frac{{\gamma - 1}}{\gamma }\frac{1}{{Hm}}. \end{equation} \tag{ 8 }$$

Equation (8) predicts a density amplitude (relative to the reference density profile) equal to 0.006 for λ_z = 8 km and 0.015 for λ_z = 20 km. The relative density fluctuations inferred from our data and the visual-band data (Person et al. 2008) are suggestively close to these values, which may support the hypothesis that the observed fluctuations are produced by nearly-breaking gravity waves high in Pluto's atmosphere. If the long-wavelength fluctuations that we observe are indeed gravity waves, Equation (3) implies that their frequencies are close tof, which will provide a further constraint on the gravity-wave interpretation (W. B. Hubbard et al. 2008, in preparation).

Liller & Whipple's (1954; pp. 112–130) observations of meteor trails were among the first detections of breaking gravity waves in the Earth's atmosphere at heights of ∼80 km to ∼115 km (pressures similar to those investigated here). Over a few hours, the meteor trails became distorted by mainly horizontal winds, over vertical scales ∼5–15 km. The wind velocities and vertical distortion scales were observed to increase with height. The density fluctuations that we have observed in Pluto's atmosphere resemble this phenomenon.

The results reported here demonstrate the effectiveness of high S/N occultation measurements made possible with a large aperture telescope and a sensitive camera. The density fluctuations which we have detected correspond to bending angles of ∼5 × 10⁻¹¹ radians in the refraction of starlight. Stellar occultation is the only technique capable of reaching such precision. In contrast, the radio-occultation experiment on New Horizons can detect refractive bending angles of ∼10⁻⁸ radians (Tyler et al. 2008). As Pluto's location heads into the galactic plane, new stellar-occultation opportunities are expected to arise (McDonald & Elliot 2000) and should be explored to further characterize and monitor the dynamics of Pluto's atmosphere before New Horizons arrives in the year 2015.