-Erich Karkoschka, Lunar and Planetary Lab, February 1998
For more information, send E-mail to: erich@pirl.lpl.arizona.edu.
An older version of this memo from November, 1995 is also available.
NOTE: This document was submitted by a WFPC2 user, and not the WFPC2 Group at STScI. Please send comments/corections to the author.
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. Most publications on WFPC2 photometry have the stellar astronomer in mind and require extra work when applied to Solar System objects. Here, filter constants are given to simplify the calibration of exposures of Solar System objects in albedo.
Photometric calibration of a WFPC2 exposure yields the average flux of the object over a certain wavelength range. For Solar System objects, most published spectra are calibrated in terms of albedo 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. Especially at ultraviolet wavelengths, this would be a bad assumption.
Table I lists mean wavelengths and filter widths after the filter+system response has been multiplied by the Solar flux spectrum. The solar flux was taken from Woods, et al. (1996) for the ultraviolet and from Labs and Neckel (1970) and Neckel and Labs (1984) for the visible and near-infrared. It becomes evident that the "ultraviolet" filters F122M, F170W, and F185W effectively probe the visible albedo and not the ultraviolet albedo due to their extended wings and due to the large increase of Solar flux from the ultraviolet to the visible. The other ultraviolet filters probe the albedo at significantly longer wavelengths than suggested by their names.
The next columns of Table I give the count rates for a large object of unity albedo at 1 AU heliocentric distance. The given values apply for a gain of 14. They are twice as high for a gain of 7. The accurate gain ratios are given in the WFPC2 Handbook (Biretta, et al. 1996) as 1.987 for PC1, 2.003 for WF2, 2.006 for WF3, and 1.955 for WF4. 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.
Count rates are proportional to the albedo and inverse proportional to the square of the heliocentric distance. They vary with time since the last decontamination as described in the WFPC2 Handbook. For several filters, data in Table I is given for 0 and 30 days after decontamination, indicated as "d0" and "d1". For the other filters, an average date of 15 days after decontamination is assumed.
Filters F300W and F336W have red leaks of 1.3 and 1.8 percent for an object of constant albedo. Table I lists their ultraviolet transmission section ("uv") separately from their red leak ("rl"). These leaks can be quite significant for objects bright in the red but dark in the ultraviolet. For example, for Titan, the red leak accounts for 5-6 percent of the detected photons.
Methane Absorption:
For objects with smooth albedo spectra, the count rates listed in Table I are sufficient to predict count rates based on known albedos or to calibrate an exposure in albedo. The filters can be assumed to probe the average albedo over the listed width of the filter. However, the spectra of the Jovian planets and Titan display methane absorptions that vary strongly on scales smaller than the width of many filters. In this case, the effective albedo probed by a filter is not accurately determined by the average albedo over the width of the filter, but requires convolution of the spectrum with the filter response curve.
The resulting count rates are listed in Table I for the Jovian planets and Titan. They are based on the spectra by Karkoschka (1998) longward of 300 nm wavelength and Wallace et al. (1972) and Wagener et al. (1986) shortward of 300 nm. In order to give count rates for zero phase angle, albedos of Jupiter, Saturn, and Titan were multiplied by an estimated factor of 1.05. Heliocentric distances were assumed to be 5, 10, 20, and 30 AU for the four Jovian planets. All listed planetary count rates are disk averages and apply for the PC1 camera whenever a filter can be selected with PC1.
Finally, the last column of Table I lists the mean methane absorption coefficient for each filter, also taken from Karkoschka (1998). For narrow filters, this is the effective methane absorption coefficient. For wide filters, it is an upper limit to the effective methane absorption coefficient. The effective methane absorption coefficient is the coefficient yielding the observed average I/F over the filter bandpass.
Photometric Accuracy:
The accuracy of the listed count rates depends on the accuracy of both, the filter+system response functions and the solar flux spectrum. The filter+system response functions were taken from files at STScI dated 2 June 1997, estimated to be good to about 3 percent. The Solar flux is accurate to 1 percent.
Observed count rates for Jupiter, Saturn, Titan, and Uranus in 1994-1997 in several filters were compared with data listed in Table I, taking into account the actual heliocentric distance and phase angle. For all but two filters, the agreement is very satisfactory with differences of a few percent at most. Observed and predicted counts for filters F218W and FQCH4N-D do not agree.
Problems with Filters F218W and FQCH4N-D:
Filter F218W gives observed count rates consistently 15 percent larger than expected. For Uranus, the nominal throughput of filter F218W would require an albedo that is almost physically impossible. Therefore, it is likely that the throughput data is in error and that the count rates of filter F218W in Table I need to be increased by as much as 15 percent.
Filter FQCH4N-D is the filter most often used by Solar System observers. It seems to display a spatial variation in the sensitivity of about 30% over a 40 arc-second distance across Jupiter's disk. Objects with a flat albedo spectrum do not show this variation. This can be explained by a spatially varying filter transmission. A flat spectrum is similar to the flatfields' spectrum. Thus, the flatfielding takes care of any spatial variations. This does not apply for planets with strong methane absorptions. If the filter transmission varies in the wings probing methane continuum, it hardly gives a noticable variation of detected photons for objects with flat spectra or for flatfields. However, the variation is large for Jovian planets since their aledo is so much larger in the continuum than in the deep methane band. Note that for Jupiter and Saturn, almost half of the detected photons come from continuum regions far away from the methane band.
Table I lists the methane band section ("m") and the wings ("w") for this filter separately. Observations suggest that near the aperture center for the PC1, the wings are shallower than according to current filter throughput files. Thus, the count rates for Jovian planets at that location are about 20 percent smaller than listed in Table I. Further analysis is required before filter FQCH4N-D can be used photometrically.
The wings of the other three FQCH4N methane filters are much shallower and cause photometric errors in the order of 1 percent only, which is negligible for most purposes.
Appendix: Definitions of Average Wavelength and Width:
Most of the WFPC2 filters have an almost rectangular response function. The definitions for average wavelength and width used here return the central wavelength and the width for a rectangular function. This is not the case for other definitions of average wavelength and width. For example, the definitions used in the WFPC2 Handbook (chapter 6.1, Table 6.1) yield a smaller value for the mean wavelength and only 68 percent of its width. The definitions used here are:
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} / Integral{Q(l)T(l)F(l) dl}
(m=median, F(l)=solar photon flux, l=wavelength).
References:
Biretta, J.A. et al. 1996. WFPC2 Instrument Handbook, Version 4.0. Baltimore, STScI. Karkoschka, E. 1998. Methane, ammonia, and temperature measurements of the jovian planets and Titan from CCD-spectrophotometry. Submitted to Icarus. Similar publication: Karkoschka, E. 1994. Spectrophotometry of the jovian planets and Titan at 300- to 1000-nm wavelength: The methane spectrum. Icarus 111, 174-192. Labs, D. and H. Neckel 1970. Transformation of the absolute solar radiation data into the "International practical temperature scale of 1968". Solar Phys. 15, 79-87. 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. Woods, T.N., D.K. Prinz, G.J. Rottman, J. London, P.C. Crane, R.P. Cebula, E. Hilsenrath, G.E. Brueckner, M.D. Andrews, O.R. White, M.E. VanHoosier, L.E. Floyd, L.C. Herring, B.G. Knapp, C.K. Pankratz, and P.A. Reiser 1996. Validation of the UARS solar ultraviolet irradiances: Comparison with the ATLAS 1 and 2 measurements. J. Geophys. Res. 101, 9541-9569.
TABLE I:
WFPC2-Filter Data for Solar-System Objects (June 1997)
------------------------------------------------------
Filter Mean Width Count Rate at I/F=1 r=1AU Gain=14 Count Rate at Gain=14 for PC1 (WF) Mean Methane
Name Air-Wave- = 4 x --------------------------------- ---------------------------------- Absorption
length Av.Dev. PC1 WF2 WF3 WF4 Jupiter Saturn Titan Uranus Neptune Coefficient
(nm) (nm) (DN/s) (DN/s) (DN/s) (DN/s) (DN/s) (DN/s) (DN/s) (DN/s) (DN/s) (1/km-am)
F122M 664 615 51.6 249 250 250 .93 .23 .10 .04 .02 1.3
F160BW 189 47 0.1 1 1 1 .00 .00 .00 .00 .00 .000
F170W 585 731 53.2 257 253 256 .93 .22 .09 .05 .02 .95
F185W 346 502 9.2 44 42 44 .14 .03 .01 .01 .01 .12
F218W d0 240 83 32.8 167 157 162 .50 .10 .02 .04 .02 .000
F218W d1 242 87 28.2 125 117 128 .43 .08 .01 .04 .02 .000
F255W d0 275 62 222 1109 1073 1088 2.82 .61 .11 .29 .13 .000
F255W d1 276 62 207 951 918 952 2.62 .57 .11 .27 .12 .000
F300W d0 329 119 7180 35300 35000 35100 87.6 17.1 4.45 9.66 4.45 .017
F300W d1 329 119 6970 32700 32400 32700 85.1 16.6 4.34 9.38 4.32 .017
F300W d0uv 323 98 7090 34900 34600 34700 86.0 16.7 4.24 9.63 4.44 .000
F300W d1uv 324 97 6880 32300 32000 32300 83.4 16.1 4.12 9.34 4.30 .000
F300W rl 764 210 90 400 400 400 1.62 .46 .22 .04 .01 1.3
F336W d0 344 76 12570 61500 61300 61300 156 28.4 8.27 17.0 7.87 .015
F336W d1 344 77 12320 58200 57900 58100 153 27.8 8.12 16.7 7.71 .015
F336W d0uv 338 51 12350 60400 60300 60300 152 27.3 7.75 16.9 7.84 .000
F336W d1uv 338 51 12100 57100 56900 57100 149 26.7 7.60 16.6 7.68 .000
F336W rl 721 53 220 1100 1000 1000 3.91 1.06 .52 .09 .03 .87
F343N d0 342.7 3.3 91.4 447 446 446 1.14 .20 .06 .12 .06 .000
F343N d1 342.7 3.3 89.8 425 424 425 1.12 .19 .06 .12 .06 .000
F375N d0 375.2 11.6 282 1368 1377 1372 4.00 .59 .22 .40 .18 .010
F375N d1 375.2 11.7 279 1325 1334 1329 3.97 .59 .21 .39 .18 .010
F380W d0 407 88 43700 212000 214000 213000 715 117 41.7 63.7 28.3 .000
F380W d1 407 88 43500 207000 209000 208000 711 117 41.5 63.3 28.2 .000
F390N d0 389.0 6.4 1319 6390 6450 6420 19.8 2.91 1.10 1.88 .86 .000
F390N d1 389.0 6.4 1309 6230 6290 6250 19.7 2.89 1.10 1.86 .85 .000
F410M d0 410.0 23.6 12850 62100 62800 62400 211 33.3 12.3 18.5 8.26 .000
F410M d1 410.0 23.6 12780 60900 61600 61200 210 33.1 12.2 18.4 8.22 .000
F437N d0 436.9 3.5 1886 9110 9200 9150 34.5 6.23 2.13 2.83 1.21 .001
F437N d1 436.9 3.5 1881 9000 9090 9030 34.4 6.22 2.12 2.82 1.21 .001
F439W d0 434 69 47400 229000 231000 230000 855 153 53.2 71.3 30.7 .000
F439W d1 434 69 47200 226000 228000 226000 852 152 53.0 71.1 30.6 .000
F450W 465 121 157900 761000 764000 762000 3080 603 217 241 98.9 .003
F467M 467.1 24.0 27300 131400 132000 131600 542 108 37.3 42.9 17.6 .001
F469N 469.4 3.6 2870 13820 13880 13840 57.4 11.5 3.97 4.62 1.90 .000
F487N 486.5 3.8 3530 17040 17060 17030 72.5 15.0 5.40 4.65 1.78 .021
F502N 501.3 4.0 4880 23600 23600 23600 104 22.0 8.20 7.91 3.11 .002
F547M 549 69 188500 916000 903000 908000 4210 961 403 260 95.5 .021
F555W 549 173 412000 2000000 1976000 1988000 9010 2060 861 552 205 .035
F569W 567 137 340000 1657000 1627000 1640000 7570 1776 764 438 158 .043
F588N 589.4 7.1 22600 110500 107800 109000 519 127 56.9 32.9 11.8 .004
F606W 604 210 696000 3400000 3310000 3350000 15350 3790 1688 762 265 .074
F622W 620 132 470000 2300000 2240000 2270000 10530 2660 1218 491 166 .070
F631N 630.6 4.5 14170 69500 67200 68300 325 84.5 39.6 17.6 6.09 .006
F656N 656.4 3.2 7600 37300 36000 36600 169 44.8 20.9 5.87 1.75 .076
F658N 659.1 4.1 11630 57200 55100 56100 259 68.2 31.6 8.30 2.44 .090
F673N 673.2 6.8 19750 97200 93400 95200 448 120 56.2 16.6 5.05 .048
F675W 672 125 406000 1995000 1922000 1958000 8510 2260 1072 295 93.4 .32
F702W 691 201 597000 2930000 2840000 2890000 12290 3310 1554 401 127 .31
F785LP 867 192 159300 757000 790000 783000 2280 671 309 32.1 10.4 3.5
F791W 786 176 305000 1490000 1466000 1485000 5190 1479 701 99.7 31.1 1.7
F814W 798 218 350000 1698000 1689000 1704000 5870 1678 789 111 34.4 1.8
F850LP 911 141 81900 382000 416000 406000 921 278 130 11.5 3.80 6
F953N 954.5 7.5 2700 12190 14130 13480 48.9 13.9 5.20 .51 .14 .37
F1042M 1022 58 2740 11590 15280 13920 18.6 7.26 3.15 .17 .07 6
FQUVN-A 376.6 10.3 1314 6310 - - 18.8 2.76 1.02 1.84 .85 .000
FQUVN-B 382.8 8.8 - - - 5230 76.8 11.2 4.20 7.55 3.48 .000
FQUVN-C 391.3 8.2 - - 7490 - 114 16.8 6.36 10.8 4.92 .000
FQUVN-D 399.7 8.6 - 13110 - - 206 31.1 11.7 18.5 8.38 .000
FQCH4N-A 544.6 9.1 - 51000 - - 1096 247 103 44.3 15.2 .12
FQCH4N-B 621.4 10.9 14700 72000 - - 284 69.1 33.2 5.39 1.93 .62
FQCH4N-C 728.8 10.0 - - - 59900 612 155 105 7.40 3.14 3.5
FQCH4N-D 889.5 22.8 4090 - 20400 - 12.4 3.94 3.97 .23 .09 23
FQCH4N-D m 893.1 7.3 3730 - 18600 - 7.24 2.43 3.27 .15 .07 25
FQCH4N-D w 853 105 360 - 1800 - 5.21 1.51 .70 .07 .02 2.9
d0: first day after decontamination
d1: 30 days after decontamination
uv: ultraviolet part only
rl: red leak only
m: main band only (885-900 nm)
w: wings only (<885 nm, >900 nm)