Radiative Transfer Modeling of Uranus’ Atmospheric Structure at Equinox

1. Jim Norwood and Nancy Chanover New Mexico State University RESULTS Shown below in black are portions of four sample spectra, extracted from locations shown in Fig. 3. All spectra were obtained on 10 Sep 2006, when Uranus’ sub-observer latitude was 5.3° S. The red lines in each plot show the calculated spectra for the atmospheric model shown in Fig. 4, at the four different planetary locations. While this model overall matches the mid-latitude spectra and the low-latitude limb spectrum fairly well, it is a poor match for the spectrum from the center of the disk. The blue line shows an attempt to lessen the brightness ratio between the methane window and the absorption region by increasing the haze optical depth by a factor of 10. This hazier atmosphere better matches the disk-center spectrum, but it provides a much poorer match for the limb spectrum from a similar latitude. MOTIVATION The transition through equinox in December 2007 has been a time of great change in Uranus’ atmosphere. Observers have witnessed brightness changes and the advent of bright cloud features as Uranus’ northern hemisphere has become more exposed to sunlight. Changes have been observed over time spans as short as 12 months (Norwood and Chanover 2009), much smaller than Uranus’ full 84-year orbital period. We have begun applying radiative transfer models in comparisons with near-infrared spectra of Uranus near equinox to better quantify the atmospheric changes undergone at this seasonal extreme. • MODELING • We investigate Uranus’ atmospheric structure with the help of a radiative transfer code. This code accepts as input a model atmosphere with specified parameters, then produces a synthetic spectrum of the planet’s expected brightness at any location. The output spectra from this program are then compared to the observational data to assess how closely the model atmosphere resembles the actual Uranian atmosphere. The parameters are varied to determine which atmospheric structures best reproduce observations. • Model atmospheres tested in this manner are constructed of alternating aerosol and non-aerosol layers, as shown in Fig. 4. Each cloud or haze layer is characterized by the pressure levels defining the layer’s boundaries, an optical depth, and a single-scattering albedo. The overall atmosphere also has parameters describing the single-scattering albedo for Rayleigh gas particles, and the abundance of methane. • Methane absorption is calculated using the band-model coefficients of Irwin et al. (2006), and collision-induced absorption due to H2-H2 and H2-He interactions are calculated after Borysow et al. (1985, 1988). Because a thick atmospheric layer may experience significant differences in absorption levels between top and bottom, each layer is divided into 20 sublayers to calculate the optical depths due to methane absorption and collision-induced absorption. • Due to Uranus’ small angular size (3.7’’ in diameter at opposition), each aperture contains a variety of different observing angles. This program accounts for this, and sums the effects from numerous specified locations in the construction of each spectrum. Furthermore, seeing causes nearby locations just outside of the aperture to influence the resultant spectrum. These locations are accounted for as well, with relative weights calculated using a PSF extracted from Uranian satellites visible in the guide images. This ability to account for viewing angle allows production of spectra from any location on the planet, from the center of the disk out to the limb. • Anticipated improvements to the modeling program include the following: • The treatment of the atmospheric methane content will be adjusted so at high altitudes, the concentration of methane relative to other constituents decreases. • The methane absorption coefficients of Karkoschka and Tomasko (in press) will be used as well, to see what advantages they offer over those of Irwin et al. Radiative Transfer Modeling of Uranus’Atmospheric Structure at Equinox Haze: 0.02-0.04 bar, τ = 0.0011 Figure 1: IRTF. OBSERVATIONS We obtained near-infrared spectra of Uranus at NASA’s Infrared Telescope Facility (Fig. 1) near two recent Uranian oppositions, on September 9-11, 2006; and September 9-10 and 30, 2007. We used the near-infrared spectrograph SpeX in short-wavelength cross-dispersed mode to acquire medium-resolution (R = 1200) spectra of Uranus from 0.8 to 2.4 μm, using a 0.5´´ × 15´´ slit. Taking advantage of the unique viewing geometry presented at Uranian equinox, we chose to orient the slit perpendicular to Uranus’ central meridian (Fig. 2), thus minimizing the range of latitudes observed in each individual spectrum. With this orientation, we stepped the slit across the Uranian disk to obtain spectra from all visible regions of the planet. Each spectrum was preceded by a guide-camera image to better ascertain the slit location relative to the Uranian disk. Example (annotated) guide images are shown in Fig. 3. Upper cloud: 1.5-1.7 bar, τ = 0.13 Figure 3: Guide images associated with the mid- and low-latitude spectra. Apertures for the central-meridian and limb spectra are indicated. In both cases, Uranian south is to the right. The satellites shown (Titania and Oberon) indicate the level of seeing in the spectra. However, the satellite Ariel (outside of the cropped images) was used for PSF determination, as it was more isolated. Lower cloud: 5.0-6.0 bar, τ = 0.1 Figure 4: The atmospheric model used in the above synthetic spectra denoted by the red line. This model atmosphere is 1.3% methane; the rest is a 85%-15% H2-He mix. The model producing the blue line is identical to the above, except the haze optical depth has been increased to 0.01. Analysis is ongoing. Future work includes perfection of the models’ ability to reproduce the observed spectra, with use of a fitting routine. Spectra from all six nights of observation will be investigated in this manner, ultimately describing the structure of Uranus’ atmosphere and how it varies with location, over 1-day timescales, and over the 12-month equinoctial period in which it was observed. REFERENCES Borysow, J., Frommhold, L., Birnbaum, G., 1988. Collision-induced rototranslational absorption of H2-He pairs at temperatures from 40 to 3000 K. ApJ 326, 509-515. Borysow, J., Trafton, L., Frommhold, L., Birnbaum, G., 1985. Modeling of pressure-induced far-infrared absorption spectra: Molecular hydrogen pairs. ApJ 296, 644-654. Irwin, P.G.J., Sromovsky, L.A., Strong, E.J., Sihra, K., Bowles, N., Calcutt, S.B., Remedios, J.J., 2006. Improved near-infrared methand band models and k-distribution parameters from 2000 to 9500 cm-1 and implications for interpretation of outer planet spectra. Icarus 181, 309-319. Karkoschka, E. and Tomasko, M. G. 2009. Methane absorption coefficients for the Jovian Planets from Laboratory, Huygens, and HST Data. Icarus, in press. Norwood, J. and Chanover, N. 2009. Spatial and short-term temporal variations in Uranus’ near-infrared spectrum. Icarus 203, 331-335. Figure 2: Slit orientation with respect to Uranus. The sizes are to scale, with the slit 0.5’’ wide compared to Uranus’ 3.7’’ diameter. The grid is shown for the September 2006 observations, when the sub-observer latitude was 5.3° S. This project is funded by a NASA Earth and Space Science Fellowship.