Modeling H2 Fluorescence in Planetary Atmospheres with Partial Frequency Redistribution
aa r X i v : . [ a s t r o - ph ] D ec Modeling H Fluorescence in PlanetaryAtmospheres with Partial FrequencyRedistribution
R. E. Lupu ∗ , P. D. Feldman ∗ , S. R. McCandliss ∗ and K. France † ∗ Dept. of Physics and Astronomy, Johns Hopkins University, Baltiomre, MD 21218 † Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309
Abstract.
We present the modeling of partial frequency redistribution (PRD) effects for the fluo-rescent emission lines of molecular hydrogen, the general computational approximations, and theapplications to planetary atmospheres, as well as interstellar medium. Our model is applied to
FUSE observations of Jupiter, Saturn, and reflection nebulae, allowing an independent confirmation of theH abundance and the structure of planetary atmospheres. Keywords: radiative transfer, spectroscopy, far-UV, planetary atmospheres, reflection nebulae
PACS:
PRD FLUORESCENCE MODEL
Frequency Redistribution. FU SE observations of planetary atmospheres and re-flection nebulae have revealed the need to include PRD in H fluorescence radiativetransfer models. The angle-averaged laboratory frame redistribution function describesthe conditional probability that a photon absorbed at x i Doppler widths from the centerof line i , is emitted at x f Doppler widths from the center of line f [1]. Completeredistribution (CRD) refers to the photons being re-emitted in the line core accordingto the Voigt profile, while PRD takes into account the changes in the line profile due tocoherent scattering in the line wings. PRD becomes important for fast transitions andintegrated optical depths larger than 10 . Observable effects include shifts in the peakwavelength in emission due to variations of the exciting spectrum over the absorbingline profile, a decrease in the line-to-continuum contrast, and a decrease in the numberof photons scattered in subordinate lines (cross redistribution, XRD). Radiative Transfer.
The PRD radiative transfer problem is more complex than theCRD case, due to the heavy couplings in frequency in addition to spatial correlationsand detailed balance [2, 3]. Even restricting the geometry to the plane-parallel case, andassuming fixed level populations, the problem remains computationally expensive dueto intrinsically large optical depths and fine frequency grids. We investigated a set ofnumerical methods (see Table 1) that would allow the full treatment of the H molecule(10 transitions) to become feasible. We find that the multilayer approximation is the bestapproach, with a computing time independent of optical depth, and no matrix inversionsrequired. This method is a layer-by-layer extension of the optically thin single layersolution of Liu and Dalgarno [4]. The results are consistently within 10% of the Feautrierlambda iteration [1] for grids of at least 10 points per dex in optical depth. ABLE 1.
Characteristics of the radiateve transfer methods used.
Lambda Iteration(Feautrier solution) Multilayer Singlelayer
Resources High Moderate LowConsistency Can be unstable Constrained ConstrainedConvergence Scales with optical depth 2-pass layer-by-layer Single stepSpatial variations Yes Yes No
RESULTS
Planetary Atmospheres.
The PRD effects on resonance lines and overlapping transi-tions in planetary atmospheres have been discussed previously [5, 6]. The current
FU SE observations represent the first account of PRD effects in subordinate molecular fluores-cent lines. The lines in the Lyman (6 − v") progression of molecular hydrogen pumpedby the solar Ly b show a broad asymmetric profile, consistent with the shape of the over-lap between the (6 −
0) P(1) line and Ly b , and emphasize the importance of coherentscattering in the line wings. The FU SE spectra of the Jupiter limb and Saturn disk shownin Figure 1 and Figure 2, respectively, are well-fitted by the XRD model (red). For com-parison, the CRD model is also shown in blue. The synthetic spectra have been obtainedby integrating the full atmospheric models, and using the multilayer approximation.
Lyman (6−1) P(1) B r i gh t ne ss ( R Å − ) Lyman (6−2) P(1) B r i gh t ne ss ( R Å − ) Lyman (6−3) P(1) B r i gh t ne ss ( R Å − ) FIGURE 1.
FUSE
MDRS Jupiter data, FWHM 0.08 Å (black), PRD (red), and CRD (blue) models.
Lyman (6−1) P(1) B r i gh t ne ss ( R Å − ) Lyman (6−2) P(1) B r i gh t ne ss ( R Å − ) Lyman (6−3) P(1) B r i gh t ne ss ( R Å − ) FIGURE 2.
FUSE
LWRS Saturn data, FWHM 0.12 Å (black), PRD (red), and CRD (blue) models.
GC 2023.
In spite of predictions based on the infrared H observations [7], highexcitation non-thermal H absorption detected in the UV [8], and UV H emission at1575 − FU SE bandpass donot match the CRD model predictions. Here we test the assumption that this discrepancyis due to the effects of PRD and XRD. We employ a toy model, with an incident 22,000 Kblackbody spectrum normalized to 5000 times Harbig galactic mean [8], illuminatinga uniform H cloud with rotational temperature of 1500 K, Doppler b parameter of1.8 km s − , and an integrated column of 5 × cm − . The radiative transfer wasperformed in a single layer approximation, to minimize computational resources. Theresults shown in Figure 3 represent the first XRD calculation of a fluorescent molecularspectrum. This exercise shows that the PRD effects will decrease the line contrast,making the H features less prominent at high spectral resolution. In future work, weexpect stronger peak suppression in a multilayer treatment due to the effects of multiplescattering. − e r g s s − c m − s r − Å − FIGURE 3.
Comparison between the H spectrum predicted by the CRD (black) and PRD (red) models. ACKNOWLEDGMENTS
We thank Prof. D. Strobel for providing the atmospheric models of Jupiter and Saturn,and the FUSE ground system personnel for planning and executing the observations.The data was obtained for the Guaranteed Time Team by the NASA-CNES-CSA
FU SE mission operated by the Johns Hopkins University. Financial support was provided byNASA contract NAS5-32985, and NASA grants NAS5-13085 and NAG5-13719.
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