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Hubble Space Telescope
WFPC2 Photometry for the Solar System - 1995

-Erich Karkoschka, Lunar and Planetary Lab, November 1995

For more information, send E-mail to: erich@pirl.lpl.arizona.edu.

For each WFPC2 filter, calibration constants for the albedo of Solar System objects are given. The transmission properties of filter FQCH4N-D, the filter most often used by Solar System observers, is analyzed.

Calibration Constants:

Solar System observers constitute a small minority among the users of the WFPC2. It is not surprising that the WFPC2 Handbook (Version 3.0, June 1995) does not have the planetary observer in mind. For example, the estimation of exposure times is given in detail for galaxies with known brightness in magnitude/arc-second2, but Solar-system objects are not mentioned.

Photometric calibration of a WFPC2 exposure yields the average flux of the object over a certain wavelength range. This wavelength range is given by the mean wavelength and filter width listed in Table 6.2 of the WFPC2 Handbook, or more accurately by the filter+system response curves shown in section 8.2. For Solar System objects, most published spectra are calibrated in terms of albedos or I/F, not in flux. The wavelength range of the albedo spectrum probed by each filter is not the same as for the flux spectrum unless the Solar flux can be considered constant with wavelength. For many filters in the visible and near infrared, this may not be a bad approximation. However, at ultraviolet wavelengths, the filter+system response has to be multiplied by the Solar flux spectrum first before a useful interpretation of a calibrated albedo is possible. In Fig. 1, the product of filter+system response and Solar flux is displayed for six ultraviolet filters. It is evident that these curves are significantly different and shifted towards longer wavelengths compared to the filter+system response curves shown in the WFPC2 Handbook.

The ordinate in Fig. 1 has been converted from Solar flux to count rates per unit wavelength for a large object of I/F=1 at 1 AU from the Sun, imaged in PC1 with gain=14. Areas below the curves correspond to count rates. Note that the horizontal and vertical scales change at wavelength 500 nm by a factor of five in the opposite way so that equal areas remain the same. Considering the inverse square law, these count rates can be easily adapted to objects at different distances from the Sun. Exposures with gain=7 give twice as many counts, exposures in Wide Field Cameras give 4.8 times as many counts as with PC1. If the object is smaller than the extent of the point spread function, the count rate in the center of the object is smaller according to the enclosed energy given in Fig. 5.2 of the WFPC2 Handbook. The throughput varies also with time since the last decontamination. Its spectral dependence was estimated on the basis of data in Whitmore (1995). The Figure assumes an average date, 15 days after decontamination. Table I gives a summary of the count rates for all filters, also for 15 days after decontamination. Where the decontamination cycle is important, data is given for 0 and 30 days after decontamination. Since the throughput of Wide Field Cameras decreases faster than that of the Planetary Camera, the factor of 4.8 in count rate between both cameras decreases somewhat after decontamination.

Three special wavelengths are marked in Fig. 1 by vertical dashed lines for each filter. The central one is the average wavelength of all deteceted photons. The left one is the average wavelength of the 50% of photons of shorter wavelength, and the right one is the average wavelength of the 50% of photons of longer wavelength. The dotted rectangle shown is the one rectangle with the same three averages and the same area (= count rate) as the filter. Average wavelengths and width of these fitted rectangles are listed in Table I.

Filters F300W and F336W have red leaks of 1.3 and 1.8 percent for an object of constant albedo. These leaks can be quite important for objects bright in the red but dark in the ultraviolet.

Methane Absorption:

The last column of Table I lists the mean methane absorption coefficient for each filter. Data was taken from Karkoschka (1994) below 1000 nm wavelength and from Fink et al. (1977) above 1000 nm. For narrow filters, this is the effective methane absorption coefficient. If the albedo of the object varies significantly inside the width of the filter, the listed number is an upper limit of the effective methane absorption coefficient since the albedo as a function of absorption coefficient is not linear, it has positive curvature. The effective methane absorption coefficient is the coefficient yielding the observed average I/F over the filter bandpass.

Three of the four methane filters and many other narrow filters are narrow enough, so that mean and effective coefficients are essentially the same. However, one methane filter, FQCH4N-D, probes wavelengths from deep methane absorptions to continuum wavelengths which has to be considered when interpreting images taken with this filter. The long wings of the filter transmission curve are not shown nor mentioned in the WFPC2 Handbook. Fig. 2 displays the distribution of detected photons with this filter for several objects. At 885 and 900 nm, the horizontal and vertical scales change by a factor of five, so that areas (=count rates) are preserved. The contribution from the wings is very dependent on the position on a planetary disk. For the three positions on Saturn's disk shown in Fig. 2, the contribution from the wings varies between 42% and 160% of the contribution from the main band. This causes an error of up to 160% in the measured I/F if the contribution from the wings is neglected. The relative contribution from the wings is 72% for Saturn and 21% for Titan (not shown).

The contribution of the wings can be subtracted if another image probing the region near the methane band is available. Filters F850LP and F953N are best suited. This requires the accurate knowledge of the filter transmission in the wings. This may not be possible currently as discussed in the next section.

The importance of the wings of the other three methane filters has not been studied, though they seem to be less important than the wing of FQCH4N-D.

Photometric Accuracy:

The accuracy of the listed count rates depend on the accuracy of both, the filter+system response functions and the Solar flux spectrum. The filter+system response function were taken from files at STScI dated 21 August 1995. Above 330 nm wavelength, the Solar flux was taken from Neckel and Labs (1983). It is better known (1%) than the filter+system response (estimated at 3%). At shorter wavelengths, the accuracy of the filter+system response may be similar to that of the Solar flux (6%) taken from Mount and Rottman (1982).

Count rates for filters used in the July/August 1994 imaging sequence of Jupiter were independently calculated using Jupiter's albedo derived from ground-based spectrophotometry by Karkoschka (1994) of 4% accuracy. With an estimated accuracy of 3% of the filter+system response, both calibrations should agree to about 5%. The differences are: F336W: +2%, F410M: +2%, F547W: -1%, F555W: -1%, F953N: +7%, FQCH4N-D: -36% (positive numbers mean that Jupiter's observations favor a higher count rate than that in the table). The ultraviolet and visible filters agree all within 2%, much better than expected. The value for filter F547W was derived by averaging many exposures, while total counts between exposures varied by 6% due to shutter timing of the short, 0.1s exposures. Calibration numbers for filter F953N changed a lot from 1994 to 1995. Last year, the discrepancy was +26%, this year only +7%, showing the progress in calibration.

The methane filter with a discrepancy of -36% clearly needs some more consideration. It is definitely the filter most often used by Solar System observers. Nevertheless, Whitmore (1995) includes calibration data for almost all WFPC2 filters, but he does not mention the methane filters. The analysis of the Jupiter data yielded the following. There seems to be a spatial variation in the sensitivity of about 30%. However, this is only seen for Jupiter while Galilean satellites yieled more consistent counts across the field. One explanation for this discrepancy is, that the transmission of the wings of the filter is spatially variable. Also, counts on Galilean satellites showed a much smaller than 36% discrepancy in absolute calibration. This may be due that most of the error in the filter+system transmission is in the wings of the filter. The observations indicate that across the location where Jupiter's disk was placed, the wings are shallower than current data files suggest. Further analysis is required before filter FQCH4N-D can be used photometrically.

Below 300 nm wavelength, the same technique (using Jupiter images) was applied to albedos of Jupiter by Wallace et al. (1972) of 10% accuracy, adjusted to the Solar flux by Mount and Rottman (1983). With the uncertainty in the solar flux and in the filter+system response, one would expect agreement to about 13%. The observed differences are: F218W: +15%, F255W: -5%. While it is hard to prove anything with statistics of two data points, it is clear that an improvement of the calibation below 300 nm wavelength is desireable. The listed calibration requires a jump of almost 30% in Jupiter's albedo near 255 nm wavelength which is not reasonable. The jump needs to be stronger than the 20% relative discrepancy because both filters significantly overlap. Spectra of Jupiter do not display a discontinuity at that wavelength. The listed count rate for the F218W filter is almost certainly too low. This discrepancy may be solved by WFPC2 observations of a solar analog star such as 16 Cyg B, or of Uranus or Neptune. Both planets are known to have albedo variations of not more than a few percent in the 200-350 nm wavelength range (Wagener et al. 1986). Such calibration exposures could be done within one orbit and would improve the interpretation of more than 30 orbits of existing images.

Appendix: Definitions of Average Wavelength and Width:

In section 8.1 and 8.2 of the WFPC2 Handbook, filter transmission curves are approximated by rectangular functions. This is done in a slightly inconsistent way. Since the mean wavelength is calculated via logarithms of wavelength, the calculation of the left and right edge of the approximated rectangular function should be done also via logarithms. Otherwise, the approximation of symmetric functions is always shifted towards shorter wavelengths. For example, the F702W transmission curve (section 8.1.6) is close to symmetric, but the approximated rectangle is apparently slightly shifted to the left. If the average wavelength is used (as it is done in this text) instead of the unconventional definition for the mean wavelength, this bias disappears.

The definition of the width in the WFPC2 Handbook yields only 82% of the width of a rectangular function. The values listed in the Table 6.2 and used in the filter transmission curves is only 83% of that value (probably a misprint in the definition of width). The result is that many filters with close to rectangular curves get approximated by rectangles seemingly too narrow. The definition of filter width used here yields the correct width for a rectangular curve.

Average Wavelength = Integral{Q(l)T(l)F(l) l dl} / Integral{Q(l)T(l)F(l) dl}

 Width = 4 (Average Deviation)

       = 4 Integral{Q(l)T(l)F(l) |l-m| dl} / Ingetral{Q(l)T(l)F(l) dl}

(m=median, F(l)=solar photon flux, l=wavelength).

References:

Fink, U., D.C. Benner, and K.A. Dick  1977. Band model analysis of 
laboratory mathane absorption spectra from 4500 to 10500 A. J. Quant. 
Spectrosc. Radiat. Transfer 18, 447-457.

Karkoschka, E. 1994. Spectrophotometry of the Jovian planets and Titan at 
300- to 1000-nm wavelength: The methane spectrum. Icarus 111, 174-192.

Mount, G.H. and G.J. Rottman 1983. The solar absolute spectral irradiance 
1150-3173 A:  May 17, 1982. J. Geophys. Res. 88, 5403-5410.

Neckel, H. and D. Labs  1983. The solar radiation between 3300 and 12500 A.
Solar Phys. 90, 205-258.

Wagener, R., J. Caldwell, and K.-H. Fricke 1986. The geometric albedos of 
Uranus and Neptune between 2100 and 3350 A. Icarus 67, 281-288.

Wallace, L., J.J. Caldwell, and B.D. Savage 1972. Ultraviolet photometry 
from the Orbiting Astronomical Observatory. III. Observations of Venus, 
Mars, Jupiter, and Saturn longward of 2000 A. Astrophys. J. 172, 755-769.

Whitmore, B. 1995. Photometry with the WFPC2. Space Telescope 
Science Institute.

Table I:

WFPC2-Filter Data for Solar-System Objects (August 1995)
--------------------------------------------------------

Filter        Mean   Fitted    Count Rate   Mean Methane   Comment
Name          Air-   Rectang.  I/F=1  1AU   Absorption
          Wavelength  Width    PC1 Gain14   Coefficient
              (nm)     (nm)      (DN/s)     (1/km-am)

F122M         657      614           46.5   1.1                     
F130LP        641      429      1200000      .61                    
F160BW   d0   186       57            0.15   .000    decontamination
F160BW   d1   189       48            0.11   .000    decon + 1 month
F165LP        641      428      1210000      .60                    
F170W         573      715           49.3    .80                    
F185W    d0   423      754           10.9    .48     decontamination
F185W    d1   436      772           10.3    .51     decon + 1 month
F218W    d0   241       85           33.0    .000    decontamination
F218W    d1   243       88           29.6    .000    decon + 1 month
F255W    d0   275       61          236      .000    decontamination
F255W    d1   276       62          224      .000    decon + 1 month
F300W         329      120         7160      .015                   
F300W    uv   323       99         7070      .000    UV part only   
F300W    rl   764      211           90     1.2      red leak only  
F336W         344       76        11900      .015                   
F336W    uv   338       51        11700      .000    UV part only   
F336W    rl   720       55          200      .89     red leak only  
F343N         342.7      3.2        183      .000                   
F375N         373.2      3.5        241      .000                   
F380W         407       88        43600      .000                   
F390N         389.0      6.5       1320      .000                   
F410M         409.1     20.3      12600      .000                   
F437N         436.9      3.5       1880      .001                   
F439W         434       69        46400      .000                   
F450W         465      120       159000      .003                   
F467M         467.1     23.8      27200      .001                   
F469N         469.4      3.6       2870      .000                   
F487N         486.5      3.8       3520      .022                   
F502N         501.2      3.9       4850      .002                   
F547M         549       69       188000      .021                   
F555W         549      172       412000      .034                   
F569W         567      137       339000      .042                   
F588N         589.3      7.1      22500      .004                   
F606W         604      209       703000      .074                   
F622W         620      132       468000      .070                   
F631N         630.6      4.5      14100      .007                   
F656N         656.4      3.2       7490      .077                   
F658N         659.1      4.1      11500      .089                   
F673N         673.2      6.8      19600      .047                   
F675W         672      125       405000      .33                    
F702W         691      200       599000      .32                    
F785LP        865      190       158000     3.4                     
F791W         785      175       309000     1.6                     
F814W         796      215       351000     1.7                     
F850LP        910      139        81500     6                       
F953N         954.5      7.6       2420      .32                    
F1042M       1022       56         2840     6                       
FQUVN-A       376.6     10.3       1200      .000                   
FQUVN-B       382.8      8.8       1100      .000                   
FQUVN-C       391.2      8.2       1670      .000                   
FQUVN-D       399.7      8.6       2840      .000                   
FQCH4N-A      543.6      4.9      11400      .11                    
FQCH4N-B      619.9      4.9      14600      .59                    
FQCH4N-C      727.9      5.7      11900     3.5                     
FQCH4N-D      889.4     23.0       5410    23                       
FQCH4N-D bw   848       91          464     2.8      blue wing only 
FQCH4N-D mb   893.1      7.4       4920    25        methane band only
FQCH4N-D rw   935      106           27.0   3.5      red wing only  
POLQ_par      650      434       866000      .68                    
POLQ_per      786      361       225000     2.0