CHAPTER 2

THE NATURE OF THE IRIS DATA SET

As most of this dissertation is concerned with the Voyager IRIS thermal infrared spectra of the Galilean satellites, I first give an overview of the IRIS instrument and the satellite observations that it carried out at Jupiter.

The IRIS Instrument

The two Voyager spacecraft carried on their scan platforms almost identical versions of an Infrared Interferometer Spectrometer and Radiometer, known by the acronym IRIS. A description of the instrument is given in Hanel et al (1980a), and a post-encounter description of the technical aspects of the Jupiter data set can be found in Hanel et al (1980b).
The instrument is a Michelson interferometer, which obtains a complete spectrum over the duration of a single Voyager FDS count. An FDS (Flight Data Subsystem) count is one count of the spacecraft reference clock, which increments every 48 seconds. Images and IRIS spectra may be taken at a maximum rate of once every FDS count, and the FDS count at the time of an observation is the usual method of referring to a particular image or spectrum. The circular field of view has a diameter of 0.25o , compared to the 0.42o square field of view of the narrow-angle camera. Because the device is an interferometer, information of varying spectral resolution is obtained at varying times during the integration. All the low-resolution information, the total integrated flux and general slope of the spectrum, is gathered during a brief period (the interferogram peak) almost precisely midway between the times of shuttering of the Voyager cameras. An unfortunate consequence of this lack of synchroneity, discussed in the next chapter, is that the locations of Voyager images do not coincide with the precise locations of IRIS spectra.
\figinsert \vfill Fig. 1. Two Representative IRIS Spectra of Callisto. Voyager 1 spectra, plotted both in `raw' form using radiance ($\mu$W/cm2/sr/cm-1), and converted to brightness temperature, TB. On the TB plot, plotting is continued to large wavenumbers until the first occurence of a negative radiance. This figure demonstrates the larger useful wavenumber range of warmer spectra. The warm spectrum is 16421.59 and the cooler one is 16425.22
Calibration and Fourier transformation of the raw interferogram results in a spectrum, linear in wavenumber, with a high spectral resolution of 4.3 cm-1 (though point spacing is 1.4 cm-1 ) and a wavelength range of 180--2500 cm-1 (4--55 microns). (Since the data comes with constant wavenumber increment, spectra shown in this dissertation are presented on a linear wavenumber scale, although wavelengths are more familiar to most people, including me). In practice the useful wavelength range is smaller, as the signal to noise ratio (S/N hereafter) becomes very small at short wavelengths. Because of the extreme temperature and wavelength dependence of blackbody flux at wavelengths short of the blackbody peak, the minimum useful wavelength depends strongly on the temperature of the particular spectrum, as illustrated in Figure 1. For Voyager 1, S/N exceeds unity only longward of 7.4 microns for a temperature of 150o K, and 16.5 microns for a 80o K spectrum. The Voyager 2 spectra are noticeably noisier due to a slight misalignment in the instrument, as seen in Fig. 5. Averaging, curve-fitting, or smoothing techniques actually allow the extraction of information even from spectral regions where the S/N is less than one.
The main method of calibration of the instrument involved taking periodic interferograms of deep space. Instrument temperature was maintained very precisely at 200.0o K, and in the deep space observations the interferometer effectively observed itself at this temperature, providing a reference response. The success of the calibration can be judged from the very subtle but systematic differences in the spectra of warm regions of Ganymede and Callisto, discussed in Chapter 4, which are consistently observed by the instruments on both spacecraft.
Though calibration appears to be excellent when the instrument's field of view is filled, there are problems calibrating the spectra of objects that do not fill the field (J.C. Pearl, pers. comm.). The instrument sensitivity appears to vary across the field of view in a manner that is poorly known. This means, unfortunately, that the many disk-integrated spectra of the satellites taken at far encounter, which would be useful for comparison with ground-based disk-integrated observations, are of limited use. Neither total radiated flux nor spectrum shape can be reliably determined for them.
The IRIS instrument also includes a visible and near-infrared radiometer, which measures the total reflected sunlight from the target between 0.33 and 2.0 microns. Measurements are made at 8 equally-spaced times (every 6 seconds) during each thermal spectrum, with the same field of view as the interferometer. The main purpose of the radiometer is to assist in heat­ balance calculations by measuring the radiation not absorbed by the target body, but, by providing a time history of the brightness of the field of view during the interferometer integration, it also provides useful information about instrument pointing.
 

Table II. Voyager IRIS coverage of the Galilean Satellites 

Dimensions are in kilometers. `Range of Longitudes' refers to low latitudes and includes dark-side coverage 
Closest Approach
 Range of
Longitudes		 No. Spectra with Range
<300,000
Satellite Spacecraft Range Latitude Local Time Diam. IRIS field
Io V.1 21,000 -90 noon 90 250-30 250
Europa V.2 210,000 -25 7pm 920 70-190 100
Ganymede V.1 115,000 +23 7pm 500 210-30 300
Ganymede V.2 62,000 -46 7pm 270 20-220 300
Callisto V.1 126,000 +80 6pm 550 150-60 350
Callisto V.2 215,000 +17 6am 940 180-340 250

The Nature of the Observations

The geometries of the Voyager encounters with Jupiter and the Galilean satellites are described in Stone et al (1979a, 1979b). Each spacecraft made quite close approaches to both Ganymede and Callisto, Voyager 1 made a very close approach to Io, and Voyager2 encountered Europa at moderate distance. Some relevant parameters for the various satellite encounters are listed in TableII. An IRIS spectrum was obtained during every FDS count while imaging sequences of the satellite were being obtained, so that infrared mosaics were produced simultaneously with imaging mosaics. There were also some IRIS-only sequences, mostly of the night hemispheres where imaging would be pointless. An example of an IRIS mosaic, covering the daytime hemisphere of Ganymede, is shown in Figure2. Figs. 13 and 14 in Chapter 5 show the extent of global coverage from the two spacecraft for each icy satellite, as well as global temperature distributions. Appendix F gives the viewing geometry and other pertinent information for all spectra.
IRIS reduced data records, consisting of calibrated spectra and header information for each, in binary format, have been produced by the IRIS science team at the Goddard Space Flight Center, and are generally available. The Galilean satellite data used in this study were kindly provided to me on magnetic tape by John Pearl, and I transferred them to an IBM PC for analysis.
Anyone requiring the IRIS Galilean satellite data in a convenient form can obtain it from me in IEEE format, MS-FORTRAN readable DOS files on standard IBM 5 1/4" diskettes. The icy satellite near-encounter data totals almost 30 megabytes, with 11076 bytes of data and 500 bytes of header information per spectrum. However I have produced condensed files containing only the header information, the terrain type (for Ganymede) and information on the effective temperature and spectrum shape, determined as described in Chapter 4, for each spectrum. In this form there are only 550 bytes per spectrum and all the Voyager 1 Callisto spectra, for instance, occupy only 300 kilobytes total.

CHAPTER 3

POINTING ACCURACY AND TERRAIN CLASSIFICATION

The Voyager IRIS Reduced Data Records contain pointing information for each spectrum, in the form of the latitude and longitude of the point in the center of the IRIS field of view at a time close to the interferogram peak. Unfortunately, this information is subject to significant error. The nominal 3 sigma pointing uncertainty is 0.15o , compared to the 0.25o IRIS field of view, (Hanel et al, 1980b) but systematic errors sometimes occur that are larger than this. The pointing errors cause uncertainties in the terrain type, time of day, amount of dark-sky contamination, etc., for each spectrum and thus make analysis less accurate.

Pointing Corrections

Pointing can be corrected by reference to the adjacent images (unfortunately not simultaneous, but taken 24 seconds before or after the peak of the IRIS spectra). These show, by reference to published maps, the actual pointing of the scan platform, which can be compared to the predicted image pointing to give a correction that can be applied to the predicted IRIS pointing information.
I attempted to use this method to refine the pointing of the Voyager 2 Ganymede spectra, but encountered numerous problems which probably resulted in `corrected' spectra being little more accurately located than the uncorrected ones. I will therefore not describe the procedure in detail.
Problems included differences in the the longitude systems used in the published USGS 1:5 million scale maps of Ganymede and in the IRIS pointing information, and suspected systematic errors in the maps, which are based on an outdated control network (M.E. Davis, pers. comm.). There was also a lack of consistency in calculated pointing corrections between adjacent images, which rendered suspect any interpolation to get corrections for intervening IRIS spectra. For instance, there were systematic differences in the pointing corrections calculated from narrow- and wide-angle images.
A successful pointing correction effort is probably possible, but would be best done using latitude/longitude grids, based on spacecraft navigation data, as overlays on the images to get accurate locations, rather than relying on the published maps. Despite the problems, I have applied pointing corrections to the Voyager 2 Ganymede data (only) that is presented in this dissertation. The presence of pointing errors sometimes amounting to a sizeable fraction of the IRIS field of view, possibly even in the Voyager 2 Ganymede data, should be kept in mind in subsequent discussions.

Identification of Terrains in Ganymede Spectra

Ganymede displays a variety of well-defined terrain types which differ in both albedo and morphology. Most notable is the dichotomy between the old, dark `cratered terrain' and the younger, brighter, `grooved terrain'. There are also conspicuous bright rayed craters. The spatial resolution of the Ganymede IRIS data is such that individual fields of view can be entirely occupied by either grooved or cratered terrain, or occasionally by bright crater ejecta blankets (Fig. 2), so that there is an opportunity to look for differences in the thermal emission from the three terrain types. I have therefore recorded, for all on-planet Ganymede spectra, the relative proportions of the field of view occupied by cratered and grooved terrain, and bright crater materials. I accomplished this by constructing a series of overlays for particular wide-angle Ganymede images, very much like Fig. 2, showing the location of each spectrum field of view on the surface of Ganymede, and also the locations of several control points, from Davis and Katayama (1981). I superimposed the overlay on an enlargement of the relevant image, using the control points and the satellite limb for alignment.
I then estimated by eye the fraction of cratered terrain and bright crater materials filling each field of view. A more precise measurement technique would have been extremely time-consuming and would not have been justified, given the abovementioned pointing uncertainties. Also, the definition of `bright crater materials' is subjective, and dependent on illumination conditions and image enhancement, but should still be useful. By using far-encounter narrow angle images (which give low-resolution coverage of areas that were in darkness at close approach) as additional bases for overlays I was able to estimate the terrain content of all nightside spectra too. The terrain classifications of the Ganymede spectra are shown in the data tabulation of Appendix F.

CHAPTER 4

THE SHAPE OF THE IRIS SPECTRA

Figure3 shows several typical Voyager IRIS spectra of the Galilean satellites. The Io spectrum, shown for completeness, is very distinctive, though typical of non-`hot spot' Io spectra, but is outside the scope of this study. The three icy satellite spectra are notable mostly for their smoothness and for the steady increase in brightness temperature (TB hereafter) with wavelength.
In this chapter I systematically measure the spectrum shapes and describe differences in the shapes between satellites and across the surfaces of each. First, however, I look for possible discrete spectral features.

Search for Spectral Features

IRIS Spectrum Averaging and Results

The IRIS spectra of Io show distinctive emission minima at several wavelengths, thought to be due to various sulfur compounds (Pearl, 1984). These features are best seen after averaging many spectra to increase the S/N, though some are visible in Fig.3. The Earth's moon also shows features in its emission spectrum, due to silicates (Murcray et al, 1970).
To check whether similar subtle features might be visible in the spectra of the icy satellites, I averaged many spectra of each of them, with the results shown in Fig. 4. The averages have been smoothed with a 10-point (14cm-1 ) wide boxcar filter to further improve the S/N at the expense of some spectral resolution. Experimentation showed that the best S/N resulted when cold spectra were excluded from the average: they added more noise than signal. The overall slope of these averaged spectra is an artifact of the averaging process and the nonlinearity of the Planck curve.
Fig. 4 shows averages of all Ganymede and Callisto spectra with 22-$\mu$m TB above 130o K, with Voyager 1 and 2 done separately. The greater noise of the Voyager 2 spectra is obvious, as is the correlation of the `noise' between the Ganymede and Callisto observations. Out to 1600cm-1 (6.25 microns) there are no spectral features visible above the noise even in the Voyager 1 spectra for either satellite.
The Europa spectra are much colder than the Ganymede and Callisto spectra (the warmest one has a 22-micron brightness temperature of only 115o K). Also, only Voyager2 spectra, which are noisier, are available. The average shown in Fig.4, including all spectra warmer than 90o K, shows no features in the low-noise region below 800 cm-1 . An apparent feature around 830 cm-1 is seen also in cold Voyager 2 Callisto spectra (but not in warm ones) and is probably noise (but see the discussion of the spectral properties of water ice below).

Thermal Emission Spectroscopy

Particulate silicate surfaces in the laboratory generally show features in their emission spectra (e.g. Conel, 1969), as does the Moon (Murcray et al, 1970). The physics of thermal emission from a rough or particulate surface is extremely complex, as photons emitted from one level can be re-absorbed or scattered at other levels, possibly at different temperatures, before emerging from the surface. The resulting spectrum depends not only on composition but also critically on compaction, grain size, temperature, and surface temperature gradient as determined by solar heating and radiative cooling (Logan et al, 1975).
To first order, the surface emissivity $\epsilon(\lambda)$ is equal to $1-A(\lambda)$ at each wavelength $\lambda$, where $A(\lambda)$ is the albedo. If $\epsilon(\lambda)$ has structure, spectral features will be seen in the emission spectrum. Particulate ices and silicates are highly absorbing in the thermal infrared, so $\epsilon(\lambda)$ is close to unity. Where the absorption coefficient k is especially high there is an increase in surface reflectivity (the {\it restralen} effect), and an emission minimum occurs, especially for large grain sizes. The surface is very dark in wavelength regions where the refractive index n is close to unity, (usually on the short wavelength side of peaks in k), because of reduced scattering, and an emission peak is likely. Decreasing particle size reduces spectral contrast but does not remove it entirely. Large near-surface thermal gradients, more likely on an atmosphereless planetary surface radiating to space than in most laboratory measurements, greatly increase spectral contrast, but isothermal surfaces can also show spectral features.
Hansen (1972, Appendix C) calculated $\epsilon(\lambda)$ between 8 and 30 microns for an isothermal water ice surface composed of spherical particles with varying grain size, using the theory of Conel (1969) and water ice optical properties from Irvine and Pollack (1968). He showed significant spectral structure in the 8--14 microns (1250--700 cm-1) region, for grain sizes 1 microns or larger, but none for 0.3 microns grains.
Figure 5 shows the optical properties of water ice (n and k) from the more recent compilation of Warren (1984), through the entire wavelength range of the IRIS data. There is an maximum in k at 820 cm-1 (12.2 microns), tending to give an emission trough with a corresponding minimum in n at 920 cm-1 (10.9 microns), tending to give an emission peak. This is an intriguing co-incidence with the possible Europa feature mentioned above, and these wavelengths are indicated next to the Europa spectrum in Fig.4. Nothing is seen here, however, in the low-noise Voyager1 Ganymede and Callisto spectra in the 820--920 cm-1 wavelength region.
The other k maximum in Fig.5 is at 214 cm-1 (46.7 microns), with the corresponding n minimum at 262 cm-1. The original data used by Warren in this spectral region (reproduced in Warren's Figs.5 and 9) was taken at temperatures as low as 100o K, and transformed to 264o K in Warren's tabulation. The 100o K data shows that this k peak is more prominent at lower temperatures, and occurs at the higher wavenumber of 230 cm-1 (43.5 microns) at 100o K. However, there is no sign of a feature in this wavelength range in any of the averaged IRIS spectra.
The lack of features in the icy Galilean satellite emission spectra (assuming the Europa features around 830 cm-1 are noise) makes an interesting contrast to the Moon, Io, and laboratory silicate spectra. The flat Ganymede and Callisto spectra in this region may be an indication of ice grain sizes smaller than 1 microns, if the emission from a real planetary surface is similar to that calculated using the idealized assumptions of Hansen (1972), and if most of the thermal radiation is from water ice surfaces.
If the surfaces of Ganymede and Callisto are segregated into bright icy and dark non-ice regions as suggested in Chapter 8, it is possible that the emission from these two bodies is dominated by radiation from the darker, warmer non-ice material. Reflection spectra, in contrast, would be dominated by the light from the bright icy regions. In this case, the lack of emission features might constrain the nature of the dark non-icy material. Europa might be the only one of the three objects whose thermal emission comes mostly from water ice.

Fitting the Spectrum Shapes

As mentioned above, the steady increase in brightness temperature with wavenumber is a characteristic of every icy Galilean satellite IRIS spectrum. A positive slope of this sort is a natural consequence of the presence of unresolved local temperature contrasts, due to a variety of possible sources, within each IRIS field of view. Because of the nonlinearities of the Planck curve, warm surface regions always contribute proportionally more of the radiation as wavenumber increases, resulting in higher brightness temperatures. However, the slopes might also be due to non-unit, perhaps wavenumber dependent, emissivity, or a combination of factors.
One of the major goals of this dissertation was to try and explain the spectrum slopes, and to see how they might be used to understand the nature of the satellite surfaces. I also needed to check the possibility that the slopes might be a result of calibration errors in the IRIS instrument. To reach these goals I needed a method of characterizing each IRIS spectrum, composed of several thousand data points, with a few numbers that could be compared between spectra or modelled theoretically. The chosen technique is now described.

Choice of Fitting Technique

Because the spectra plot almost as straight lines on a brightness temperature vs. wavenumber plot, the first approach I considered was to fit each spectrum with a straight line, or a low-order polynomial, in these coordinates. I rejected this approach for the following reasons:
 1) The spectra, especially the colder ones, are quite noisy at higher wavenumbers. In brightness temperature coordinates the noise becomes very `asymmetrical' as the S/N decreases towards unity. A doubling of the true spectrum radiance due to noise at high wavenumbers may only increase the brightness temperature by 20%, but a reduction of the radiance to zero due to the same amount of noise subtracted from the true radiance will reduce the brightness temperature by 100%. Negative radiances, which are common in low S/N portions of the spectrum, result in undefined brightness temperatures. A fit to brightness temperature can thus only be done where S/N is much larger than 1, and the wavelength range where this is true varies depending on the spectrum temperature and the spacecraft.
2) A brightness temperature / wavenumber gradient is not itself very physically meaningful. The way the gradient varies with spectrum temperature, for instance, does not indicate in an obvious way how local temperature contrasts vary with `average' temperature.
 I thus used a second fitting approach, a direct least-squares fit of the spectrum radiances (rather than brightness temperatures) to combinations of blackbody curves at different temperatures. Radiances can be fit even in low S/N regions of the spectrum, and the parameters of the fit have a direct physical meaning. This technique has already been applied to Voyager IRIS spectra, to obtain the temperatures of the Io hot spots (Pearl and Sinton, 1982). The fitting algorithm I used was the Marquandt chi2 minimization routine from Bevington (1969), designed to fit arbitrary differentiable functions to noisy data.

Choice of Fit Parameters

When fitting the IRIS spectra with combinations of blackbodies, the possible variables are the number of surface components, the temperature of each, and the fractional surface coverage of each. The total fractional surface coverage of all components can also be allowed to vary from unity, which is equivalent to allowing a non-unit, wavelength-independent, emissivity. If there are insufficient free parameters a good fit will not be possible, and if there are too many the fit will not be unique and thus not very useful.
Blackbody combinations with a total fractional areal coverage of all components (equivalent to the overall surface emissivity) equal to 1.0 always give spectra that are concave upwards at small wavenumbers on a TB  wavenumber plot, whereas all the IRIS spectra plot as straight lines or are slightly concave downwards. Experimentation showed that the small wavenumber shape of the spectra could be accurately matched by allowing the total fractional areal coverage to be less than1. I thus selected emissivity as a free parameter.
There is no a priori reason to expect a wavelength-independant non-unit emissivity over the large wavelength range considered here. What I call emissivity is an empirical parameter used to fit the spectra and only coincides with a `real' emissivity (which could be used in calculations of actual surface temperature, for instance) if the assumption of wavelength-independence is valid. Even then, the emissivity is an average value for the various assumed surface components and the individual emissivities of each cannot be determined.
I could fit all spectra well with just two components. Addition of more components did not reduce chi2 but prevented a unique fit. However, even with 2 components there was no unique solution if I allowed their relative fractional coverage to vary. Fixing the 2 components to have equal surface coverage gave poor fits to many spectra, but all spectra were fitted well if I fixed the fractional areal coverage of the warmer of the two components at 30%, and the cooler component at 70% (both these percentages being multiplied by the emissivity so that the total fractional coverage equalled the emissivity). This resulted in 3 free parameters; the temperatures of the 2 components and the total (wavelength independant) emissivity. I have not investigated the possible significance of the 30/70 surface coverage ratio: it probably does not imply that all the surfaces observed actually have a discrete warm component occupying 30% of the surface. For my purposes this is simply an empirical number useful in characterizing the spectrum shapes.
The synthetic radiance spectrum $R(\lambda)$ fitted to each IRIS spectrum was thus given by:

with emissivity \ep\ and warm and cold component temperatures T1 and T2as the free parameters. $B(\lambda,T)$ is the Planck blackbody curve for temperature T.
Another variable to be chosen was the wavenumber interval over which to fit the spectra. I chose a range of 218--1400 cm-1 in order to fit the warmest spectra over the full range of useful data (S/N is unity for a 160o K Voyager 1 spectrum at 1400 cm-1 ). I used the same fitting interval for all spectra regardless of spacecraft or temperature to avoid biasing the fits, though this meant that for the colder spectra there was essentially no signal over a large fraction of the fitted interval. The Marquandt search algorithm weights different portions of the fitted interval by the local S/N so this lack of signal at high wavenumbers in cold spectra does not cause a problem for the fit. I provided the algorithm with noise level as a function of wavenumber for typical spectra for each spacecraft, and these noise levels were used in calculating the chi2 for each fit.
Fig.4 shows the presence of systematic errors in the Voyager 2 spectra that become serious beyond about 900 cm-1 , which might be expected to cause errors in the fits to these spectra. I tested this by fitting several hundred Voyager 1 and 2 spectra over the shorter interval of 218--800 cm-1 and comparing these to the `standard' fits. The differences in the fits are very minor, and no greater for the Voyager 2 spectra than for the Voyager 1 ones. The S/N in the `badly behaved' region of the Voyager 2 spectra is apparently low enough that this region doesn't affect the fits very much.
With these parameters and reasonable first guesses for their values, the Marquandt algorithm generally converged on unique fits in 3 or 4 iterations. Values of chi2 for the fits were generally in the range 1--2 (chi2= 1 indicates a `perfect' fit if the noise has been properly accounted for).  Figure 6 shows an example of the fit to two typical Callisto spectra. Almost all fits are as close as these: larger values of chi2 generally indicate an unusually noisy spectrum rather than a poor fit.
 

Results of the Spectrum Fitting

In this section I will describe the patterns of variation in spectrum shape between and on each satellite. Interpretation will be generally avoided, and saved for Chapters 6 and 7.
The three fit parameters are the temperatures of the two components and the overall emissivity. However it is more useful to look at the results in terms of the emissivity \ep , the effective temperature, TE, defined by

which is the temperature of a blackbody emitting the same total flux over all wavelengths, and the temperature contrast, \dt , given simply by

TE is an accurate measure of the total radiant energy at all wavelengths (including the contribution from the extrapolated portion of the spectrum longward of 50 microns, beyond the IRIS spectral range). \dt\ and \ep\ measure the spectrum slope. Crudely, \dt\ controls the overall, linear, slope, and \ep\ controls the downward curving of the spectrum at small wavenumbers. Because neither \dt\ or \ep\ alone uniquely determines the slope in any wavenumber interval, it is also also useful to look at the spectrum slope directly. In subsequent discussions and figures I will sometimes use the difference in TB between 500 and 250 cm-1 (20 and 40 microns) as a standard measure of the spectrum slope. I determine the slope from the synthetic spectrum fit to each IRIS spectrum, not the IRIS spectrum itself, in order to avoid noise in the raw data. Appendix F tabulates these fit parameters for every fitted IRIS spectrum.
Spectra whose field of view is not filled by the target, and includes dark sky, have unreliable temperatures and shapes (they are always steeper than comparable on-planet spectra), and I have excluded them from plots such as Figs.7--9. For every spectrum I calculated the minimum separation of the edge of the field of view from the target's limb, and, unless otherwise stated, did not plot spectra for which this distance is less than 0.10o (compared to the 0.25o IRIS field of view diameter), to allow for pointing uncertainties. For Europa, where there are few spectra this far from the limb, I used the more generous limit of 0.05o. The `limb separation' is tabulated in Appendix F along with the other spectrum parameters.
In warm spectra, \ep\ is remarkably constant at close to 0.94 except for Voyager 2 Callisto spectra which have a significantly lower value closer to 0.92. See Figure 7 which plots all on-planet spectra. At lower temperatures there is increased scatter in \ep , including values as low as 0.5 and as high as 1.15. The scatter in the Ganymede data is fairly symmetrical about the high-temperature value of 0.94, but on Callisto this value appears to be an upper limit to \ep\ except in the coldest spectra. Much of the scatter is noise: at low temperatures the wavenumber interval with good S/N is too short to uniquely determine both \ep\ and \dt , and only an average slope can be derived from the data. As a result the Marquandt algorithm settles on a \ep, \dt\ combination that gives the correct slope, but the value of \ep\ (or \dt ) alone is not usefully constrained. The shape of cold spectra is best characterized by the standardized spectrum slope.
After noting the approximately constant value of the fitted emissivity, I tried fitting the IRIS spectra holding \ep\ constant at 0.94, and having T1 and T2 as the only free parameters. While this generally gave acceptable fits, many spectra with low `free' values of \ep\ were matched less well with \ep\ fixed at 0.94 (as checked by comparing chi2 and also by direct plotting of spectrum and fit). Much of the \ep\ variation in Fig.7 is therefore real.
Figures 8 and 9 plot TE against \dt\ and spectrum slope for all on-planet spectra of the three icy satellites. These figures reveal one of the most striking results of this IRIS analysis. There are well-defined correlations between spectrum shape and TE, which are dramatically different for each satellite. Also worth noting are the large values of \dt : if the spectrum slopes are due to thermal contrasts then substantial fractions of each field of view must be occupied by areas with temperatures differing by up to 50o K.
The different trends must reflect a fundamental difference between the surfaces of Ganymede and Callisto, and probably Europa also. There are many sampling biases resulting from the geometry of each Voyager flyby, which might produce distinctive correlations between spectrum parameters that would disappear if we had spectra at all possible viewing geometries and positions on the surface. However, the very distinctive \dt\ / TE trend on Callisto in Figs.8 and 9, for instance, is equally apparent, and only slightly different, in the spectra from both Voyager flybys, and the two flyby geometries have virtually nothing in common (TableII). The same is true for Ganymede. The differences between the two pairs of data sets must therefore be intrinsic differences between the surfaces of Ganymede and Callisto, and not a result of different viewing geometries at each object. For Europa there is only one flyby and a limited range of sampling of the surface, but the Europa spectra are a different (less steep) shape than Ganymede spectra with similar geometries, and again almost certainly reflect an intrinsic difference in surface properties.
I now discuss separately the shapes of the thermal spectra from the three satellites.

Ganymede

\dt\ decreases steadily with decreasing TE,  from a value near 40o K for the warmest, subsolar, spectra to a mean value around 20o K for the cold nighttime spectra. Spectrum slope, in contrast, is remarkably constant with temperature, though Fig.11, with an expanded x-axis scale, shows some dependence of slope on temperature.
Figure 10 shows the distribution of spectrum slope with latitude and local time on Ganymede, for both spacecraft observations. Note that all the steep cold spectra seen in Fig.9 are from the south polar region, but that otherwise only small regional variations are visible. Southern hemisphere nighttime spectra appear steeper than those in the northern hemisphere, but as the northern spectra are from Voyager 1 and the southern from Voyager 2, and they refer to different longitudes, this may be a calibration difference or a variation with longitude rather than latitude.
Figure 11 shows variations in spectrum slope with terrain type (subject to the provisos about pointing accuracy mentioned in Chapter 3). Fig. 11a shows that bright crater materials have noticeably less steep spectra than other areas of Ganymede with similar temperatures. All these bright-crater spectra are of the ejecta blanket of Osiris, the very fresh large ray crater at 38o S, 165o W seen in Fig. 2, and another bright crater south of it.
There is less of an obvious difference in the shapes of the spectra of dark (cratered) and light (grooved) terrain. Fig. 11b suggests that among Voyager 2 spectra colder than around 125o K, dark terrain has steeper slopes than light terrain, with an opposite trend prevailing at temperatures between 135 and 140o K. However, the correlation is too subtle to be entirely convincing, and there are many possible biases in the data set. Voyager might, for example, have simply happened to be observing dark terrain during a period when something else about the viewing geometry, such as phase angle, was tending to give steeper spectrum slopes. There is too little data to be able to separate out the effects of all the possible variables. There is no clearly visible correlation of slope with light/dark terrain fraction in the Voyager1 data, not shown in Fig. 11b. The Voyager 2 correlation may be real but the data is insufficient to demonstrate its reality.

Callisto

Callisto shows the most dramatic variations in spectrum slope. Except for the coldest spectra, both \dt\ and slope increase steadily as TE decreases, in a well-defined trend opposite to the Ganymede \dt\ trend. This can be seen in the raw spectra, in Figs.1 and 6. The warmest spectra are considerably shallower than the warmest Ganymede spectra. Again, Fig.10 shows the global distribution of spectrum slopes. The steepest slopes are generally on the daytime hemisphere near the terminator, which may be an important clue as to their origin (see Chapter 6). The steepest slopes of all (apart from one anomalously-steep post-sunset spectrum), occur in the morning at high latitudes, which, intriguingly, is also the location of the steepest Ganymede spectra. Most of the nightside spectra are steeper than those on Ganymede.
Unlike Ganymede, there is a difference in trend between the Voyager1 and 2 data sets visible on Figs.8 and 9. The warm Voyager 2 spectra are distinctly steeper than those from Voyager 1. The difference is less apparent in the \dt\ plot, because some of the slope difference is interpreted by the least-squares fitting as a difference not in \dt\ but in \ep , as already noted above and on Fig.7. The Voyager 2 warm (near-subsolar) spectra have both lower \ep\ and higher \dt\ values than Voyager1, both of which contribute to an increased slope.
As both spacecraft saw essentially the same shape for the warm Ganymede spectra, it is unlikely that the slope difference is due to a calibration difference between the two Voyager IRIS instruments. The difference might be a diurnal effect: the warm Voyager 1 spectra are of the afternoon regions of Callisto, while Voyager 2 saw only the morning regions. However Fig.10 shows no gradation in slope with local time across the noon meridian: there is a sharp jump in slope between the steep late-morning Voyager 2 spectra and the shallower early-afternoon Voyager 1 spectra (see also Fig. 29, Chapter 7). Alternatively, the slope difference might be a reflection of the global asymmetries in Callisto's surface properties seen in groundbased visible-wavelength photometry and polarimetry. The warm (TE > 140o K) Voyager 1 spectra cover longitudes 0o--60o , (leading hemisphere) while Voyager 2 warm spectra are of the longitude 180o--240o region (trailing hemisphere). As discussed in Chapter1, the trailing hemisphere of Callisto is the more Ganymede-like in its ground-based photometric and polarimetric properties. It is therefore very interesting that the same may be true of the spectrum slopes: the trailing (Voyager 2) hemisphere has warm spectrum slopes that are intermediate between the shallow slopes of the leading (Voyager 1) hemisphere and the steeper slopes seen in warm Ganymede spectra.

Europa

There are only about 20 Europa spectra, also shown on Figs. 8 and 9, that are probably not contaminated by dark sky in the field of view, and thus have reliable shapes. All are from low latitudes near the evening terminator or in the early part of the night. Despite this poor sampling the spectra appear distinctive from either of the Ganymede or Callisto trends. \dt\ and spectrum slope are very small, indicating spectra closer to simple blackbodies than for the other two objects. There appears to be a trend of increasing spectrum slope with increasing temperature.
Note that several Europa spectra were fitted with \dt\ = 0. This appears to be an eccentricity of the Marquandt algorithm: in these cases it chose to fit the spectrum slope using non-unit emissivity alone. This only happens with cold spectra where, as mentioned previously, S/N is low enough that \ep\ and \dt\ cannot be determined independently. The fitted slope for the \dt\ =0 spectra should still be reliable.

Possible Explanations of Spectrum Slopes

This section will give a brief description of the possible causes of the observed spectrum slopes, to set the stage for the quantitative modelling of later chapters.

Calibration Errors

The consistent detection of the different slope/temperature trends on Europa, Ganymede and Callisto by the two Voyager IRIS instruments is a good check on the instrument calibration. The spectrum slopes seen by both instruments must be real, not artifacts due to calibration errors, or no consistent Ganymede/Callisto difference would be seen. It is also comforting that despite the calibration problems with the Voyager 2 instrument mentioned in Chapter 2, when looking at a given temperature region on a given object it detects very similar spectrum slopes to the Voyager1 instrument (with the exception of the warm Callisto spectra already discussed, where there is probably a real shape difference between the two encounters).

Constant, Non-Unit Emissivity

Wavenumber-independent emissivity is included as a fit parameter in the least-squares fitting procedure, and does appear to contribute to the observed slopes. However a good fit also requires sometimes large temperature contrasts: non-unit emissivity cannot explain the observed spectrum shapes alone.

Wavenumber-Dependent Emissivity

As shown above (Fig. 9) the spectra of Ganymede have a slope that hardly varies at all with spectrum temperature. At first sight this suggests the possibility of an emissivity that varies steadily with wavenumber, but does not depend much on temperature, as an explanation for the slope. We can check this possibility as follows:
Suppose a spectrum $R(\lambda)$ is emitted by an isothermal surface at temperature T0 that has wavelength-dependent emissivity $\epsilon'(\lambda)$. Then

If $R(\lambda)$ can also be fit using the standard least-squares procedure, with fit parameters T1, T2, and ep , then from Equation 1

and

so $\epsilon'(\lambda)$ can be determined as a function of T1, T2, and \ep . A typical warm Ganymede spectrum can be fit with \ep\ = 0.94 and \dt\ = 40o K. If T1 and T2 are 170o K and 130o K respectively, TE = 143.5o K (Equation 2). Figure12a shows $\epsilon'(\lambda)$ as derived from Equation 6 with these values, and the assumption of T0 = 155o K. In order to produce an almost constant slope in the \tb\ spectrum from an isothermal surface, $\epsilon'$ must vary drastically and non-uniformly with wavenumber. Though little is known about the emissivity of cold, rough, icy surfaces (see the `Thermal Emission Spectroscopy' section of this chapter), such behavior does not seem very physical. The Galilean satellite thermal spectrum slopes are thus probably not due to wavelength-dependent emissivity.
In addition, if the emissivity is constant with temperature, Fig.12b shows that such an $\epsilon'(\lambda)$ will give a TB spectrum slope which decreases with decreasing surface temperature, at variance with the data. So the constant spectrum slopes on Ganymede certainly do not reflect a temperature-independent, wavenumber-dependent emissivity.

Global Temperature Gradients

Every IRIS field of view covers a range of latitudes and times of day, and thus includes temperature gradients related to the global temperature distribution (Chapter 5). It is not possible to calculate the spectrum slopes produced by these gradients because the variations in instrument sensitivity across the field of view are not well known. However, I was able to constrain the contribution of the global temperature gradients to the spectrum slopes by comparing spectra with differing temperature gradients across their fields of view.
By drawing isotherms on plots similar to Fig .2 it is a simple matter to determine the approximate variation in effective temperature across the diameter of an IRIS field of view. For a typical near-terminator low-latitude Voyager 2 Europa spectrum there is a variation of about 12o K across the field. For Voyager1 and 2 Ganymede the equivalent values are 10oK and 7oK respectively, and for Voyager 1 and 2 Callisto spectra typical variations are 18o K and 35o K. So for Callisto, the temperature gradient across Voyager 2 spectra is typically twice that across Voyager1 spectra, yet the near-terminator spectrum slopes (Fig. 18) are much the same for each spacecraft. Similarly, there is a larger gradient across the Europa fields of view than the Ganymede ones, but the Ganymede spectra are steeper. Therefore the temperature variation across the field of view is a small contribution to the total observed spectrum slope for most IRIS spectra.

Local Temperature Contrasts

Local temperature contrasts are left as the most likely major cause of the observed spectrum slopes. They can be produced by a variety of mechanisms, and the likely ones are now listed:
1) Topography. A rough surface (on whatever scale) will give local variations in illumination conditions, and thus varying temperatures also. Shadowed regions will be cooler than those tilted towards the sun. Less obviously, under a high sun, depressions will be warmer than elevations because a depressed point receives thermal radiation from other points in the same depression. Elevations, in contrast, receive little radiation from their surroundings.
 2) Albedo variations. Other things (such as thermal inertia) being equal, high-albedo regions will be colder than dark regions at all times of day. A `checkerboard' surface of bright and dark regions mixed on a scale smaller than the IRIS field of view will result in a sloped IRIS spectrum.
3) Thermal inertia variations. Low thermal inertia materials show large diurnal changes in surface temperature, high thermal inertia gives small diurnal changes. This means that high thermal inertia materials (e.g. rocks) will tend to be colder during the day than low thermal inertia materials (e.g. dust), with the reverse being true at night. So a mixed rock/dust surface, for instance, will also show temperature contrasts.
 Each of these mechanisms would be expected to produce different patterns of variation of spectrum slope with sun angle, time of day, etc., and each is amenable to theoretical modelling (to varying degrees), in order to determine these patterns. I will describe the modelling in Chapters 6 and 7.