Evidence for condensed-phase methane enhancement over Xanadu on Titan
EEvidence for condensed-phase methane enhancement over Xanaduon Titan
M. ´Ad´amkovics and I. de PaterAstronomy Department, University of California, Berkeley, CA 94720M. HartungGemini Observatory, La Serena, ChileJ. W. BarnesDepartment of Physics, University of Idaho, Moscow, ID 83844Received ; accepted a r X i v : . [ a s t r o - ph . E P ] J u l
1. Introduction
A methane-based meteorological cycle involving clouds and rain has been suspectedto occur on Titan since the time of Voyager, when methane was measured by IRIS (Hanelet al. 1981). Pioneering radiative transfer models of the atmosphere (Toon et al. 1989;McKay et al. 1989) were used to interpret these spectra, predicting rain and patchy cloudsfrom 10 – 30 km (Toon et al. 1988). Ground-based measurements at shorter wavelengthssupported the presence of clouds and discovered their daily variation (Griffith et al. 1998,2000). Advances in imaging technologies lead to spatially-resolved observations of cloudsnear the south pole (Brown et al. 2002; Roe et al. 2002), as well as a region of cloudsconfined to southern mid-latitudes (Roe et al. 2005a). Since the arrival of Cassini it hasbeen possible to resolve complex cloud structures (Porco et al. 2005), measure updraftvelocities (Griffith et al. 2005), and identify polar clouds that may be composed of ethane(Griffith et al. 2006).Global scale precipitation has been suggested using the methane relative humidityprofile measured by Huygens (Tokano et al. 2006). While it was first predicted that dropletswould evaporate before reaching the surface (Lorenz 1993), recent models suggest raincan fall to the ground (Graves et al. 2008). Fluvial channels indicate that a liquid was incontact with the surface at some time (Tomasko et al. 2005).Near-IR observations in two methane transmission windows (1.6 and 2.0 µ m) have beenused with radiative transfer models to measure the column of condensed-phase methane onTitan ( ´Ad´amkovics et al. 2007). These data revealed a global cloud of solid methane in the25 - 35 km altitude range, with an enhancement of opacity on the morning hemisphere thatis consistent with methane drizzle. Recently, these results have been called into questionusing observations made at the Gemini-North telescope with the NIFS spectrometer (Kimet al. 2008). 3 –Here we present measurements over consecutive nights, together with radiative transfermodeling, to show that the signature of increased condensed-phase methane cannot bedue to surface reflectivity artifacts as suggested by Kim et al. (2008), and use high(Sun-target-observer) phase angle measurements to rule out phase angle artifacts. Weaccount for the conclusions and analysis of Kim et al. (2008) by quantifying the errorsthat can arise in the surface subtraction due to noise and bias. Our observations indicatethat while precipitation occurs predominantly near Xanadu, it is not solely a morningphenomenon as suggested earlier ( ´Ad´amkovics et al. 2007).
2. Observations
Ground-based observations were performed between 2006 Dec 28 and 2007 Mar 11UT with the adaptive-optics aided integral-field spectrometer, SINFONI (Eisenhauer et al.2003), at the Very Large Telescope (VLT). The spectrometer uses two sets of 32 stackedmirrors to divide the field of view (FOV) into 32 ‘slitlets’, which are then optically arrangedinto a single synthetic long slit that is dispersed onto a cryogenically-cooled 2K × × . (cid:48)(cid:48) × . (cid:48)(cid:48) FOV, corresponding to a pixel scale of 0 . (cid:48)(cid:48) × . µ m at a resolving power, R = λ/ ∆ λ , of 2000 to 3400.Data-reduction follows the SINFONI pipeline (Modigliani et al. 2007). The pipelineincludes a reference bad-pixel map, a check for pixels approaching a non-linear detectorresponse, dark current correction, and flat fielding. All of the spectra are distortion(curvature) corrected using standard flats and arc lamps frames, along with wavelengthcalibration from a reference arc line table. Spectra are interpolated onto a commonwavelength grid before reconstruction of the datacube using the slitlet position and slitletedge tables. 4 –Mosaicking is performed using AO pointing keywords to overlap images to the nearestpixel and then taking the median value for overlapping pixels. Telluric correction isperformed with the extracted spectra of standard stars. Flux calibration is performed bynormalization to the disk-integrated stratospheric flux from Keck/OSIRIS observations( ´Ad´amkovics et al. 2007), and are reported in units of albedo, I/F . The observation datesand viewing geometries are given in Table 1.The Visual and Infrared Mapping Spectrometer (VIMS) on the Cassini spacecraft usesa spectral mapping technique (Brown et al. 2004) to assemble images at 352 wavelengths,covering 0.3 to 5.1 µ m. Channels near 1.6 and 2.0 µ m can be used for direct comparisonwith ground-based observations, and provide the opportunity for high phase angle viewinggeometries that are not obtainable from Earth. We use VIMS data that are publiclyavailable from the T10 flyby on 2006 January 15 UT. The data are reduced from observeddata numbers to units of albedo, I/F , according to Barnes et al. (2007).
3. Radiative Transfer Model
In order to interpret the observed spectral datacubes, we create a forward modelto simulate the flux that is reflected from Titan’s atmosphere and surface. Our modelincorporates well-established numerical solutions to the radiative transfer (RT) equation(Griffith et al. 1991; Brown et al. 2002; ´Ad´amkovics et al. 2004, 2007) that reproducenear-IR observations exceptionally well. Updates to the model presented in ´Ad´amkovicset al. (2007) include the treatment of the surface reflectivity; including the specification of aunique surface spectrum for Xanadu, averaging the surface albedo map over the footprint ofa pixel in the model, and an explicit fit for converting the observed surface albedo map to asurface reflectivity map that is input to the model (described in Section 3.3). Limitationsin current analyses are due to input parameters (e.g., CH opacities, surface albedo spectra, 5 –and aerosol scattering) and not the numerical methodology or assumed geometry. A2-stream approximation (at small phase angles) or discrete ordinates method (at highphase angles) is used to solve the radiative transfer equation for 16 pseudo-plane-parallellayers from 0 – 200 km altitude (Toon et al. 1989; McKay et al. 1989; Stamnes et al.1988). We correct for the curvature of the atmosphere with an established geometricalcorrection (Tran and Rannou 2004). We use the atmospheric temperature and pressureprofiles measured in situ by Huygens/HASI (Fulchignoni et al. 2005), which are in excellentagreement (below 200 km) with the Voyager profiles (Lellouch et al. 1989). Starting withthe in situ measurements of aerosol extinctions made by Hugyens/DISR (Tomasko et al.2005), we vary the extinction at other locations on Titan to reproduce our observations ofthe global distributions of haze. The uncertainty of the CH opacity, which is greatest forweak transitions, translates into an uncertainty in both the retrieved surface albedo and toa lesser extent the tropospheric aerosol extinction that is constrained at other wavelengths. The vertical profile of CH mixing ratio measured by Huygens/GCMS (Niemannet al. 2005) is applied globally and the absorption coefficients for CH presented by Irwinet al. (2005) are used to calculate CH opacities. Corrections to these coefficients havebeen published using the measurements made by Huygens/DISR (Tomasko et al. 2008c),however the corrections do not extend to 2 µ m and are not applied here. An alternativedetermination of the CH opacity may be performed with line-by-line calculations that usethe very high resolution, high sensitivity, CH spectra of Brown (Brown 2005). These dataare currently available in the HITRAN database. However, the line strengths for thesetransitions are only applicable at room temperature, and quantum mechanical assignmentsof individual CH lines are required before opacities can be calculated at the temperatures 6 –applicable to Titan. As described by Brown (2005), assigning these transitions requiresconsiderable laboratory and computational effort.Other sources of gas-phase opacity in the 2.0 µ m band include low temperaturecollision-induced absorption by N and H (McKellar 1989). The H -N collision complexis a significant source of opacity near 2.1 µ m, which decreases the observed slope of Titan’sspectrum in the 2.0 µ m band relative to the 1.5 µ m band. Since the magnitude of theobserved flux can be roughly mapped onto the altitude where most of the scattered photonsoriginate — that is, regions of weak atmospheric absorption are bright and probe thesurface, whereas regions of high gas opacity are dim and probe the upper atmosphere — thegradual variation in the 2.0 µ m band extinction facilitates altitude discrimination relativeto the 1.5 µ m band. This collision-induced opacity is critically dependent on the mixingratio of molecular hydrogen, which we take to be well mixed throughout the atmosphere atlevels of ∼ Observations at IR wavelengths can be represented by models with an approximatedscattering phase function (e.g., a one-term Henyey-Greenstein). When calculating the IRflux reflected from Titan at low phase angles there is, in general, a degeneracy between theaerosol scattering phase function and the extinction. For example, an increase in albedocan result either from a greater aerosol density or aerosols that are more backscattering.The DISR instrument on Huygens was used to measure the haze extinction profilefrom 0.5 – 1.5 µ m (Tomasko et al. 2005), and our ground-based observations made duringprobe entry (at 1.5 µ m) use these measurements as a benchmark for the extinction near thelatitude of the Huygens landing site, 10 ◦ S. The cumulative DISR extinction is extrapolated 7 –to observations at 2 µ m ( ´Ad´amkovics et al. 2007). Recently, a parameterization of aerosolscattering in three altitude regimes on Titan has been fit to the DISR data (Tomaskoet al. 2008a). The authors propose a model of the wavelength dependence of the scatteringphase function that is derived using the DISR data and scattering that is treated with theT-matrix method (Mishchenko et al. 1996). The net solar flux both in Titan’s atmosphereand at the surface, calculated using the detailed optical properties and distribution ofparticles, is in good agreement with the values calculated by McKay et al. (1989) (Tomaskoet al. 2008b).We use a simplified parameterization of the phase function, following McKay et al.(1989). The two-stream methodology we use incorporates the total flux that is scatteredin the forward and backward directions. This method is not sensitive to further subtletiesin the scattering phase function. For the 1.5 and 2.0 µ m windows, a one-parameterHenyey-Greenstein phase function has been adequate for interpreting the observations andhas accurately predicted the heat balance in the atmosphere (Tomasko et al. 2008b).The spatial variation in aerosol density is modeled using the method presented in´Ad´amkovics et al. (2006). The stratospheric aerosol extinction increases northward at arate of 0.55% per degree latitude from 45 ◦ S up to ∼ ◦ N, the highest latitudes observedhere. The tropospheric aerosol extinction is uniform below 40 km altitude.
The surface reflectivity is modeled with the simplest representation that can reproduceboth spatial and spectral variations in the observations. We start with a high-resolutioncylindrically-projected map of the 2.018 µ m albedo (Barnes et al. 2007) and re-project itonto a sphere viewed on the plane of the sky, at the instrument plate scale, using the 8 –JPL HORIZONS ephemerides. For each detector pixel the albedo map is integrated overthe spatial region that corresponds to the polygon enclosed by the corners of that pixel,creating an albedo array, α x,y . If the corner of a pixel is located off the edge of the diskthen the region of the albedo map that is enclosed by the remaining three corners is used.Since the observed 2.018 µ m albedo has a contribution from atmospheric scattering, itwould be a mistake to use α x,y as the input for the surface reflectivity, R x,y , in the model.This would result in an overestimate of the flux at surface-probing wavelengths. We use alinear scaling and offset of the entire map to convert from albedo to reflectivity, R x,y = α x,y p + p (1)where the parameters are determined by fitting the output model spectrum to theobservations. A series of models are calculated over a range of input values for p and p .In each case the mean squared residual between the model and observations is calculatedover the entire datacube, and the parameter combination corresponding to the model withthe smallest residual is selected as the best fit, p =0.83 and p =0.02In the radiative transfer calculation we assume isotropic scattering at the surface. Asdescribed in Toon et al. (1989), the total upward flux from the surface is the sum of thereflected downward diffuse flux and flux from any other sources, S sfc . At 2 µ m, the otherrelevant source of flux is the reflection of the incident sunlight that reaches the surface,given by S sfc = R x,y µ exp ( − τ /µ ) πF s (2)where µ is the cosine of the solar incidence angle, τ is the optical depth of the atmosphere,and πF s is the incident solar flux.The Huygens probe measured the surface reflectivity spectrum in situ from the 9 –visible up to 1.5 µ m (Tomasko et al. 2005). At longer wavelengths, remote observationsthrough narrow regions of low methane opacity are only sensitive to portions of the surfacereflectivity spectrum. Since a flat spectrum does not reproduce the observations, i.e. thesurface reflectivity in the 1.6 µ m window is systematically larger than in the 2.0 µ m windowand the contrast between bright and dark regions is different (Coustenis et al. 2005; dePater et al. 2006), we incorporate a surface reflectivity spectrum in our model.We use a set of Gaussian features in the surface spectrum to resolve discrepanciesbetween the calculated albedo and the observations. The surface reflectivity for the modeldatacube is given by R ( x, y, λ ) = R x,y n (cid:89) i =0 (cid:0) − A i exp( − ( λ c,i − λ ) /δλ i ) (cid:1) (3)where we call the product term the surface reflectivity scale factor. Each spectral feature, i , is defined by a central wavelength, λ c,i , line width, δλ i , and amplitude, A i , for n features.Values for the Gaussian features are given in Table 2. Three narrow absorptions are usedin the base model and (since R x,y is determined at 2 µ m) another Gaussian feature is usedto represent the increase in reflectivity toward 1.6 µ m. It is unclear if these transitions canbe uniquely related to the surface composition. The surface reflectivity scale factor is fitglobally and individual spectra in the observed datacubes are integrated over vast regionscovering more than 10 km .The surface reflectivity scale factor is plotted in Figure 1 with an example comparisonof the model output and observations. By considering the surface reflectivity a freeparameter, it is possible to mask uncertainties in atmospheric opacity and fit the spectraarbitrarily well at wavelengths that sense the surface. The relative contribution of surfaceflux depends on wavelength, surface reflectivity, and viewing geometry. To approximatethe fraction of flux arising from the surface in the 2 µ m window, we compare a spectrum 10 –calculated with the base model to a model spectrum with the surface reflectivity, R x,y ,set to zero; the two spectra are plotted in Figure 2. The minimum contribution of theatmospheric flux is 17% of the total , at 2.04 µ m for a surface reflectivity of 0.12, and willbe larger for lower reflectivity surfaces, and locations near the edge of the disk where thesurface is limb-darkened while the atmosphere limb brightens. After Voyager it was suggested that methane is saturated in some regions of Titan’satmosphere (Flasar et al. 1981; Toon et al. 1988). The methane relative humidity profilemeasured by Huygens (Fulchignoni et al. 2005) and the presence of clouds both conclusivelyindicated that methane exists in solid and liquid form in Titan’s atmosphere. Despite thisevidence, RT models used for direct comparison to near-IR observations have only recentlyincluded a rudimentary treatment of condensed-phase methane opacity ( ´Ad´amkovics et al.2007). The morphology of condensed-phase methane (e.g., particles, droplets, or grains) isunconstrained by these models. A solid cloud of methane (Tokano et al. 2006; ´Ad´amkovicset al. 2007) is included in the 25-35 km altitude layer of the model with a methane columnvolume of 1.5 cm cm − . The column volume is equivalent to a uniform layer of condensedmethane with a thickness, (cid:96) =1.5 cm. The optical depth of condensed-phase methane isgiven by τ c ( λ ) = (cid:96)α ( λ ) (4)where the absorption coefficient spectrum, α ( λ ), is from laboratory measurements (Grundyet al. 2002). The base model has no additional methane precipitation. This basic treatmentof the condensed phase opacity assumes only absorption and negligible scattering — i.e, thescattering at these altitudes is dominated by aerosol haze. 11 – The surface reflectivity (from the VIMS albedo map) and the stratospheric aerosolgradient (a free parameter) are the two spatially-varying inputs in the model. After theseinputs have been determined, the RT calculation of a spectrum is performed for each ofthe approximately 4000 spatial locations, building a model datacube at the plate scaleof the observations. The last step is to convolve the model with a point spread function(PSF). We use the telluric calibration star datacube, collapsed in wavelength across H- andK-bands separately, as the reference images for the PSF. A 2d Gaussian is fit to the PSFsand used as the convolution kernel for each band. Fitting the PSF and then using centeredconvolution kernel avoids the addition of noise into the model.
4. Surface Subtraction
Atmospheric scattering at 2 µ m accounts for at least ∼
17% of the total observed flux,the rest is from the surface. Changes in surface reflectivity at different locations on Titangenerally swamp the signal from spatial variations in atmospheric scattering.Images probing the lower atmosphere are also sensitive to the surface. The latter canbe subtracted as described below, to discern atmospheric phenomena ( ´Ad´amkovics et al.2007). We calculate surface subtracted, ∆
I/F , images using the method of ´Ad´amkovicset al. (2007) for all of the observations and corresponding models. Each pixel in thesubtracted images is defined according to∆
I/F = (
I/F ) λ − f × ( I/F ) λ , (5)where the bandpasses for ( I/F ) λ and ( I/F ) λ are given in Table 3. The bandpass for( I/F ) λ is selected to cover the wavelength region that probes the surface with the least 12 –atmospheric contribution, while ( I/F ) λ is integrated over a bandpass with increasedmethane absorption and therefore contains a larger contribution from the atmosphere.The linear Pearson correlation coefficient, r , between the ∆ I/F image and the (
I/F ) λ is determined for a range of f . Surface subtracted images using a range of values for f demonstrate that small values ( f < .
57) yield images correlated with surface probingimages, while large values ( f > .
74) are anti-correlated with the surface image — that is,they yield and inverted image of the surface albedo pattern and large negative r (Figure 3).Intermediate values minimize the absolute value of the correlation coefficient. Althoughthe contribution of flux from the surface depends on a reflectivity, the value of f thatcorresponds to minimum | r | is the optimal value used in this simplistic image subtraction.A single f may be used in a model-independent, approximate method for removing surfacealbedo variation from images.Since the background noise in regions of the image with sky can affect the statisticalanalysis, we performed the calculation of f for each night using only the pixels on the diskof Titan, yielding ¯ f =0.67, with a mean absolute deviation σ =0.011. The scale factorsfor each night are presented in Table 4 for the 1.5 µ m and 2 µ m bands. These values aresignificantly lower than when the analysis is performed on the entire image, which includesnoise from the sky; in that case ¯ f = 0.76 and σ =0.013. The values of f calculated whileincluding regions of the sky are consistent with the smallest value calculated by Kim et al.(2008) and larger than f =0.72 used in ´Ad´amkovics et al. (2007). The ∆ I/F images for theobservations and all models — each calculated with ¯ f =0.67 — are presented in the bottomfour rows of Figure 4.Comparison of the observations and the models, in both wavelength regions ( λ and λ )demonstrates that where the surface albedo is well mapped by Cassini/VIMS, the modelsreproduce the observations well. Additionally, changes due to additional condensed-phase 13 –methane opacity do not produce significant changes to the images in the λ bandpass.The small variations in the flux from subtle changes in opacity and reflectivity are moreclearly observed after subtraction of the surface albedo variation. The 1 σ pixel-to-pixelnoise is between 0.0012 and 0.0016 for all of the observed ∆ I/F images. These values arecalculated two ways: first, a conservative estimate is made by calculating the mean of theabsolute value of the residuals between the base model and the observations, and secondlyby calculating the FWHM of the histogram of the ∆
I/F values at the center of the disk ineach image. In the following discussion, we investigate the suggestion of Kim et al. (2008)that bright regions of the surface cause artifacts in the difference images.
5. Discussion
The ground-based observations and RT models are presented in Figure 4. Although theentire observed datacube is calculated (covering 1.45 – 2.45 µ m) we focus here on imagesfrom the wavelength windows that are used to identify condensed phase methane opacity.Kim et al. (2008) argue that anti-correlations are created in ∆ I/F images due toregions of high surface albedo having different f values than dark regions. The argumentpredicts that bright regions will, in general, be anti-correlated with dark regions in ∆ I/F images. Observations in Figure 4 demonstrate that a gross anti-correlation does not occur.The brightest regions in the top row of images does not correspond with the dark regionsin the subtracted images. Due to limb darkening, regions of the surface with the brightest(
I/F ) λ always occur at the center of the disk, whereas dark regions in the ∆ I/F (if presentat all) occur near the limb. There is no gross anti-correlation between (
I/F ) λ and ∆ I/F images.Perhaps the argument of Kim et al. (2008) applies only to the region of highest surface 14 –reflectivity, Xanadu, or as they suggest, the spectrum of the surface needs to be taken intoconsideration. The four consecutive nights of observations from 2007-01-28UT through2007-01-31UT are used to test this hypothesis. On 2007-01-28UT the eastern tip of Xanaduis visible on the limb of Titan, and by 2007-01-31UT this location is observed at the centerof the disk. In the ∆
I/F images from these dates, there is a darker region over the tip ofXanadu on 2007-01-28UT, however, the same location is no longer dark on 2007-01-31UT.This sequence of observations suggest that artifacts related to static properties of thesurface — which are expected to track with rotation — do not account for the dark regionsof the surface. To further test this hypothesis, we employed a systematic change in thesurface reflectivity spectrum, but only near Xanadu.The Xanadu region is outlined (somewhat arbitrarily) using a high resolution ISSmap (Porco et al. 2005). A test case is modeled where the spatial locations in theobserved datacubes that are bounded by Xanadu (plotted in the top row of Figure 4)have two additional surface absorption features, listed in Table 2, and shown graphicallyin Figure 1. The features are centered on the wavelength regions that are used to probethe atmosphere, above the surface in both H- and K-bands, and are narrow enough to fitwithin the λ bandpass used for the images. The effect of this mildly contrived changeon the surface-subtracted images is demonstrated in the bottom row of Figure 4. Notunexpectedly, the region of Xanadu is darker in the difference images. Altering the surfacespectrum in such a way could be modified slightly to fit an individual observation verywell. However, the series of observations from 2007-01-28 through 2007-01-31 illustratethat a systematic change to the surface reflectivity over Xanadu cannot reproduce all theobservations. For these dates, the mean of the absolute value of residuals between thecondensed-phase model and the observations is smaller than the residuals of the model withthe artificial surface spectrum. On 2007-02-23, 2007-03-10, and 2007-03-11, the modelswith either additional methane opacity or the surface spectrum change both have larger 15 –residuals than the base model.The observed ∆ I/F image on 2007-01-29 has a darker region near the limb than inthe model with a unique Xanadu surface spectrum. This suggests that the absorptionspectrum of the Eastern tip of Xanadu is underestimated in the model. However, on2007-01-31 this same region of Xanadu is near the center of the disk and the absorptionspectrum is overestimated in the model. A change to the surface reflectivity spectrumcannot simultaneously match both observations. A similar effect was noted qualitatively in´Ad´amkovics et al. (2007), and is also illustrated in Figure 5 with the observations from Kimet al. (2008). Whereas the two regions of Eastern and Western Xanadu are both labelled ‘A’in Figures 1 and 3 by Kim et al. (2008), here we label the East and West regions separatelyas ‘A’ and ‘A1’, respectively. This clarification shows that while ‘A1’ is a bright albedoregion that shows up as a dark feature in the Keck/OSIRIS difference images from 2006Apr 17, this same bright feature — near the center of disk — is no longer a dark region inthe difference image viewed with VLT/SINFONI.We test for surface scattering phase artifacts by performing our analysis onCassini/VIMS data from the T10 flyby. Since the dark regions in the ∆
I/F images occurnear the limb, it is possible that some property of the surface scattering is the cause ofan artifact that causes Xanadu to always be dark in the ∆
I/F images near the limb.However, the images in Figure 6 demonstrate that Xanadu is not an inherently dark regionin ∆
I/F images. Intensity variation in the VIMS ∆
I/F image does indicate that a singlevalue of f will not remove all the spatial variation in the subtracted image, however, thegross over-correction for bright regions is avoided for a minimum value of the correlationcoefficient, | r | . Our RT models also reproduce the high phase angle observations withLambertian surface scattering and a surface reflectivity scale factor spectrum that does notvary across the disk. 16 –The observations and models presented here can be reconciled with the measurementsof Kim et al. (2008) by quantitatively evaluating factors that can affect the determinationof f . We calculate f for a subset of pixels in a circle centered on Titan and plot theresultant f as a function of Titan radius, R T , in Figure 7). Near the center of the disk( R T < .
7) , f is roughly constant. There is a decrease in f when limb-darkened regions —where contributions from the surface are small — are included in the correlation analysis.Including regions of the sky adds noise and increases the calculated value of f . We furtherinvestigate this effect by systematically adding noise to the images and reproducing ouranalysis. We generate images with Gaussian noise (of a given FWHM in I/F ), add theimage of noise to our observations, and then recalculate f (lower scale bar in Figure 7).Additional noise leads to a systematically higher determination of f (dotted line Figure 7)such that 1% of additional noise can lead to a increase in f by ∼ I/F ) λ image (dashed line in Figure 7). This is anapproximation of uncertainties due to flat-fielding, bias-correction, or telluric correction.Both positive or negative deviations in f can occur due to biased images. Data from2007-01-28UT are used above for illustration, however the results generalize to each nightof our observations. These tests demonstrate that using the entire image in the analysis,an offset during data reduction, or a noisier dataset can all lead to larger values of f , andthus an ‘over-subtraction’ of the surface. Overestimating f will lead to anti-correlatedartifacts from regions of bright surface reflectivity, as detailed in ´Ad´amkovics et al. (2007),and evidenced in Kim et al. (2008). Figure 5 demonstrates that the Gemini/NIFS datapresented by Kim et al. (2008) are noisier than either the VLT/SINFONI or Keck/OSIRISimages presented in ´Ad´amkovics et al. (2007). 17 –
6. Conclusions
Atmospheric phenomena are most likely responsible for the observed dark regions inthe ∆
I/F images and have been quantitatively reproduced in models using additionalcondensed-phase methane (as in ´Ad´amkovics et al. (2007)) and tested here againstsurface scattering artifacts. Since the extinction properties of haze are not stronglywavelength-dependent in the 2 µ m region, spatial variations in haze are removed during theimage subtraction and cannot reproduce the dark regions in ∆ I/F images. Altering thehaze properties enough to create the dark ∆
I/F regions results in discrepancies that fail toreproduce the observed albedo in tropospheric or stratospheric images ( ´Ad´amkovics et al.2007). Localized meteorology has already been observed (Roe et al. 2005b), so perhapsprecipitation is also geographically linked. On 2007-03-09 we observe condensed-phasemethane over Xanadu on the evening limb, Figure 4, indicating that precipitation can occureither in the morning or in the afternoon.Further modeling of scattering by strongly absorbing droplets or ices is needed todetermine if the rain can reach the ground and if there is a predicted signature of rain atlonger wavelengths (e.g, 5 µ m). There is also a possibility that the condensed methanecoexists as a surface coating on aerosols. Alternatively, the optical properties of haze maybe such that they mimic methane transmission spectrum, which is unexpected but cannotbe ruled out. Currently, enhancement in condensed-phase methane over Xanadu remainsthe least speculative and the only modeled description of dark regions in ∆ I/F images.
Acknowledgments
This work was supported by NSF and the Technology Center for Adaptive Optics,managed by the University of California at Santa Cruz under cooperative agreement 18 –AST-9876783, NASA grant NNG05GH63G, and by the Center for Integrative PlanetaryScience at the University of California, Berkeley. Observations were performed at the VLToperated by the European Southern Observatory. 19 –
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Notes du Pre dePlanetologie de l’Institut Pierre Simon Laplace 2, 18–38.This manuscript was prepared with the AAS L A TEX macros v5.2. 26 –Table 1: Observation dates and viewing geometry.
Obs. Date Airmass Diameter Sub-observer Point Sub-solar Point Phase Angle(UT) (arcsec) ◦ W Long. Lat. ◦ W Long. Lat. (degrees)2006 Dec 28 1.31 0.835 22.5 -12.3 26.8 -14.1 4.6 ∗ ∗ ∗ ∗ ∗ ∗ Sub-solar longitude is greater than sub-observer longitude. For these observations, thesub-solar point is to the left of the center of the disk in the images in Figure 4.
Table 2: Surface reflectivity spectrum features
Line center, Line width, Amplitude, Notes λ c,i δλ i A i ∗ base model1.505 0.052 0.95 base model1.563 0.012 0.55 base model1.982 0.035 0.80 base model1.605 0.002 0.07 only near Xanadu2.065 0.010 0.07 only near Xanadu ∗ Since R x,y in Equation 3 corresponds to observations at 2 µ m,a negative amplitude is used to represent the increase in reflectivitytoward 1.6 µ m (Figure 1).
27 –Table 3: Bandpasses ( µ m) used for ∆ I/F images
VLT/SINFONI Cassini/VIMS a µ m band 2.0 µ m band 2.0 µ m bandSurface 1.593 – 1.596 2.027 – 2.037 2.026 – 2.042Surf & Trop 1.603 – 1.606 2.060 – 2.070 2.059 – 2.076 a Approximated bandpass for individual VIMS channels centered at2.034, 2.068, 2.117, and 2.150 µ m. Table 4: Surface subtraction parameters.Obs. Date (UT) 1.5 µ m band 2.0 µ m band f best | r | min f best | r | min f best * * Fig. 1.— Surface reflectivity spectrum used in RT models is a combination of the surfacealbedo measured by Cassini/VIMS at 2.018 µ m and a wavelength-dependent scale factor(dotted line, left axis). The surface reflectivity spectrum is used to calculate the I/F spec-trum (thick line, right axis) and compare to observations (thin line, right axis). The basemodel surface reflectivity scale factor (dotted line, left axis) fits both the dark and brightregions, and a contrived spectrum with two additional absorptions (indicated near ‘*’) isused only for the region of Xanadu to test the differential imaging analysis. 29 – μ m]0.000.020.040.060.080.100.12 I/ F surfacecontrib.atmosphere contrib. Model (base)Model (
Rx,y =0)
Fig. 2.— The contribution of flux from the surface in the 2 µ m window was calculated bycomparing a spectrum of a bright region near the center of the disk in the base model (solidline) with a model that has the surface reflectivity, R x,y , set to zero (dotted line). In thecase that R x,y =0, all of the flux is from scattering in the atmosphere. The atmosphericscattering is assumed to be the same in the base model, which also includes the light thatis reflected from the surface. The maximum surface contribution occurs at 2.04 µ m, wherethe flux from the atmosphere is 17% of the total flux. Integrating the surface contributionover the entire 2 µ m window gives a minimum atmospheric contribution of 32% of the totalobserved albedo. 30 – µ mSurface2.060 - 2.070 µ mLower Troposphere f = r = f = r = f = r = f = r = f = r = f = r = -0.297 f = r = -0.531 f = r = -0.685 f C o rr e l a t i on c oe ff i c i en t, | r | f best = 0.670| r | min = 0.0039 Fig. 3.— The scaling factor for the image of the surface flux is determined by an empiricaltest of the correlation between the surface probing image and the subtracted image. I/ F ObservationsModel (base)Model with increased condensed-CH4 opacity I/ F λ : 2.027-2.037 μ m λ : 2.060-2.070 μ m λ - 0.67* λ ObservationsModel (base)Model with increased condensed-CH4 opacityModel with unique Xanadu surface spectrum Δ I/ F Fig. 4.— K-band (2 µ m) VLT/SINFONI observations and radiative transfer models bothwith and without an increase in condensed phase methane near Xanadu. The increase ismodeled to occur from 30 ◦ S to 20 ◦ N, and from the limb to within 35 ◦ of the sub-observerlongitude for all observations. A prominent southern mid-latitude cloud (identified at longerwavelengths) contaminates the ∆ I/F image on 2007-01-30 UT, appearing as a bright featurebetween 30 – 45 ◦ S. An incorrectly high value for f affects areas with the same surface albedouniformly and would result in all of Titan’s bright regions showing small ∆ I/F values. Thisis not the case here. While Xanadu corresponds to low ∆
I/F , other high-albedo surfaceterrains such as Dilmun (10 ◦ N 175 ◦ W), Tsegihi (40 ◦ S, 35 ◦ W), and Adiri (10 ◦ S 210 ◦ W) donot show similar negative excursions — however, this is not the case for Figure 3b in Kimet al. (2008). 32 –
I/F
I/F I/ F I/ F A1A1A1 A1A11
Lower Troposphere [2.060 - 2.070µm]Surface subtracted images
AABB
Surface [2.027 - 2.037µm]VLT/SINFONI Keck/OSIRIS Gemini/NIFS
Fig. 5.— Comparison of field-integral spectrometer images from three instruments:VLT/SINFONI, Keck/OSIRIS, and Gemini/NIFS. The VLT and Keck data are from´Ad´amkovics et al. (2007), while with lower S/N and lower resolution Gemini data are com-bined from Figures 1 and 3 in Kim et al. (2008). For clarity, the two regions labeled in ‘A’by Kim et al. (2008) are separated here as ‘A1’ and ‘A’. The ‘A1’ regions are dark in thedifference image from Keck while appearing bright in the VLT observations. 33 – I/ F Δ I/ F CassiniModel
Surface, λ Surf & Trop, λ Δ I/F
Fig. 6.— Cassini/VIMS observations and surface subtracted images at high phase angle(top), with radiative transfer models of the same observing geometry (bottom). The outlineindicates Xanadu. Limb brightening in the ∆
I/F images due aerosol scattering is reproducedin the models. Bright scattering at the poles is due to optically thin clouds. 34 –Fig. 7.— The optimal surface-subtraction scale factor f depends on the region of interest inthe image (solid line, lower axis), bias between the ( I/F ) λ and ( I/F ) λ image (dashed line,top axis), and the noise in the analyzed images (dotted line, lowest axis). Calculations forbias and noise were made using R T < ..