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Hubble Space Telescope
WFPC2 Photometry for the Solar System

-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)