On-orbit Calibration of ACS CTE Corrections for Photometry

Transcription

1 On-orbit Calibration of ACS CTE Corrections for Photometry Adam Riess August 15, 2003 ABSTRACT We present the first on-orbit calibration of the photometric losses due to imperfect CTE on ACS HRC and WFC. We utilized images of 47 Tuc from a CTE calibration program (GO 9648; PI Riess) to measure the dependence of stellar photometry on the number of parallel and serial transfers. For WFC, photometric losses are apparent for stars undergoing numerous parallel transfers (y-direction) and are ~1-2% for typical observing parameters rising to ~10% in worst cases (faint stars, low background). The size of the photometric loss appears to have a strong power-law dependence on the stellar flux, as seen for other CCD s flown on HST. However, the dependence on background is surprisingly weak implying that post-flashing may have little advantage to mitigate CTE. No losses are apparent for WFC due to serial transfer (x-direction). Also for HRC, photometric losses arise from parallel transfer (~1% for typical observations, ~5% for worst case) but are not seen for serial transfer. Correction formulae are presented to correct photometric losses as a function of a source s position, flux, background, time, and aperture size. The time dependence term will be better constrained from future data but is currently found to be approximately linear from measurements of charge deferred tails in dark frames. Copyright 1999 The Association of Universities for Research in Astronomy, Inc. All Rights Reserved.

2 1. Introduction To date, all CCD s flown in the harsh radiation environment of HST suffer degradation of their charge transfer efficiency (CTE). The effect of CTE degradation is to reduce the apparent brightness of sources, requiring the application of photometric corrections to restore measured integrated counts to their true value. The principle of correcting for CTE losses to achieve unbiased measurements is straightforward, but in practice it can be quite difficult to utilize. The charge loss due to imperfect CTE depends on combinations of scene characteristics such as the total counts and the physical extent of a source on the detector, its background (global and local), the number of parallel and serial transfers, and elapsed time in the life of the detector. It is difficult to quantify and calibrate the degree to which each of these factors affects the measurements of a source over time. The general solution has been to use repeated observations of cluster fields to quantify the impact of CTE on point sources, to use internal measures of CTE degradation to track the changes between costly, external calibrations, and to do additional studies of the impact to more complicated sources (e.g., extended sources) when the CTE losses become large. ACS has two CCD s which clock charge, WFC and HRC, and therefore are subject to CTE losses. In this report we describe the first external calibration of their photometric losses due to imperfect CTE. The order of this report is to first describe the dataset used to measure CTE, its reduction, how it was photometered, the measurement of CTE trends, and the derivation and constraining of a CTE correction formula. The measurement and application of CTE corrections requires the careful utilization of statistics from large numbers of stars, which individually give a very weak and poor constraint on CTE. The inference of CTE corrections is further challenged by the wideassortment of photometry practices (and pitfalls) as well as the continual degradation of CTE (i.e., the calibration is not static, it is always changing). We have been careful to describe our choices and procedures here to allow others to match them (or at least compare them) to the photometry methods they use before accepting and applying our CTE corrections. Experience from WFPC2 suggests that differences in photometry methods may somewhat alter the overall size of CTE corrections, but by significantly less than ~25% of the size of the correction (B. Whitmore, private communication). An equally viable though far more time consuming approach for those ACS users who demand the very highest photometry precision is to retrieve the CTE calibration data from the archive and apply their own photometry methods in identical fashion as to their own data. 2

3 2. CTE Calibration from 47Tuc From Jan-March, 2003, we initiated a calibration program, GO 9648 (P.I. Riess) to obtain a sequence of observations of the off-core field (6 West) of the rich cluster 47 Tuc (00h 22m 37.2s +/- 1", -72d 4 14" +/- 1 ). For each camera, our goal was to compare the relative photometry of individual stars as a function of the number of pixel transfers during read-out. Because the read-out architecture of the WFC and HRC are dissimilar, a different observing strategy was designed for each camera. WFC For WFC, pixels are clocked away from the center and towards the corners to be read out by 1 of 4 corner amplifiers as shown in Figure 1. Each pixel requires from 1 to 2048 transfers in the parallel and serial directions. 2 Dither Positions used for Parallel CTE calibration Figure 1: Schematic showing the location of the read-out amplifiers and the WFC direction of read-out. The right panel illustrates the two FOVs used to vary the number of parallel transfers for individual stars. To vary the relative positions and hence the number of pixel transfers of individual stars we utilized 2 large scale dithers of ~1/2 the size of the WFC (102 ) along each axis to reposition stars relative to the fixed framework of corner amplifiers. For the large-scale dither in the parallel (y coordinate) direction, this shift resulted in the displacement of the 3

4 entire field-of-view of chip 1 onto chip 2 as shown in the right panel of Figure 1. Because of the corner placement of the amplifiers, individual stars which undergo n parallel pixel transfers when imaged on chip 1 (where 1 < n < 2048), will undergo ~(2048-n ) transfers when imaged on chip 2. In this case the differential number of transfers is (2048-2n ). This technique of reimaging the field of view with mirror symmetry with respect to the read-out direction using two different chips is similar to the strategy employed by Whitmore, Heyer, and Casertano (1999) to measure the degradation of CTE on WFPC2. Small differences in the zeropoints of the two chips are removed in the analysis by measuring the change in flux (here and elsewhere flux refers to total counts, not counts per unit time) with pixel transfer for the two chips (i.e., the slope of the relation), ignoring any offset at n =1024 (where the differential transfer would be zero). To measure the affect of differential transfers in the serial direction, we reimaged the field with a large scale dither (102 ) in the x-direction. To assess the impact of background on CTE losses, we varied the background of the image pairs by utilizing different exposure times and different filters. Specifically we used F606W for 30 sec, 400 sec, and 1100 sec, F775W for 30sec and 400 sec, and F502N for 30 sec and 400 sec. The resulting sky backgrounds varied from <1 e to 120 e per pixel. B Figure 2: Schematic showing the location of the read-out amplifiers and the HRC direction of read-out. The right panel illustrates two independent amplifiers used to vary the number of parallel transfers for individual stars. D 4

5 HRC Like WFC, HRC pixels can be clocked away from the center towards read-out amplifiers in the chip corners as shown in Figure 2. An important difference is that the field of view is not unavoidably divided into 4 quadrants (via the physical and electronic bifurcations of WFC) allowing the field of view to be read-out entirely by any individual corner amplifier (routine science data is readout through the C Amp). As a result, we can obtain pairs of images on the HRC with a different number of pixel transfers for individual stars by using a sequence of different corner read-out amplifiers as shown in Figure 2. This technique of reimaging the field of view with mirror symmetry with respect to read-out direction using different amplifiers is the same as that employed by Goudfrooij et al for the STIS CCD. To fill the orbits, we were able to obtain an exposure for each unique corner amplifier with every combination of filter and exposure time. As for WFC, the impact of background was assessed by using combinations of filters and exposure times; F606W, F775W, and F502N each for 30sec and 360sec. 3. Analysis Each aforementioned combination of FOV position, amplifier read-out, filter, and exposure time was obtained and processed through the standard OPUS pipeline (overscan and bias correction, dark frame subtraction, flat correction, and drizzled using the geometric distortion table.) Cosmic ray splits were not utilized but cosmic rays are accounted for in the analysis by using robust analytic tools. For both WFC and HRC, a deep, clean master image was made by combining the long exposure F606W images (3600 sec for WFC, 2400 sec for HRC) with min-max rejection. From these a master star list was generated with DAOfind run in IDL (find.pro). The list of sources was visually inspected to verify its purity. For WFC the final star list contained ~19,800 stars, half of which were present in any pair of large scale dithers. For HRC, the master star list contained ~250 stars. WFC For WFC images, the master star list was used to provide an initial guess for the stellar positions in the shifted 400-sec F606W images. A more precise coordinate list in the shifted (and unshifted) frames was then derived using individual centroids with a box width of 1.3*FWHM (~5) pixels. For every WFC image, these deep, centroided master star lists were used as an initial guess to derive coordinate lists by (re)centroiding on the stars. These two lists (master and individual) were then differenced and a median of the 5

6 differences was used to determine the size of any global shift between the 400 sec F606W images and other images obtained at the same commanded position. The final coordinate list utilized for the photometry of individual frames was the list of stellar centroids in the matching 400 sec F606W with the addition of the individual, global shifts. The intent of this procedure was to derive star lists which are globally precise but do not overfit to the noise of individual, faint stars. Photometry of all stars in the starlists was measured using the aperture photometry package in IDL (aper.pro). The sky background was determined from a global median of matching portions of the FOV (see Figure 1). A comparison of regional median sky values shows agreement to better than 0.1% indicating no significant gradient in the sky across the field and attests to the suitability of a single sky value. Individual sky annuli can avoid the problems of sky gradients but can be biased high by inclusion of flux from faint cluster members. More importantly, any systematic sky errors for individual stars due to sky gradients effectively cancel out in the process of calculating the magnitude differences of individual stars at different large dither positions as seen in Figure 1 (assuming the origin of any sky gradients were from the cluster and not from errors in flat fielding). To evaluate the dependence of CTE loss on stellar flux, background and aperture size, the relative photometry of individual stars for each filter and exposure time combination was compared in 2 mag wide flux bins. The specific procedure was to measure a linear relationship between relative photometry and relative pixel transfer for all filter, exposure time, flux bin, and aperture size combinations. Because CR splits were not implemented (to save orbits), star pairs whose relative photometry differed by more than 0.5 mag were rejected. To further mitigate against CR contamination, the linear relationships were determined using the least-absolute-deviation method (LAD; a more robust, less tail weighted statistic) and cross-checked with a 4 sigma-clipped least-squares fit. The y- intercept of the fits were not constrained to provide a net photometric loss of magnitudes at 0 relative transfers to allow for possible zeropoint differences between the two chips (though any seen were quite small). Figure 3 shows a single example of the linear relationship determined for one filter and exposure time (F606W for 30 sec providing a sky background of 3.6 electrons) at one fitted brightness range (stars with an average of ~400 electrons and a full range of +/-1 mag) contained within a r=3 pixel aperture. For the example shown, the stars would have an average magnitude of F606W=23.3 mag and have a signal-to-noise ratio of ~10 in the aperture in the 30 sec exposure. The upper panel shows the parallel CTE quantification. For individual stars, their difference in parallel read-out transfers in shown versus their magnitude differences for the paired observations illustrated in Figure 1. The dashed line 6

7 shows the results of the LAD fit and the dotted line shows the results from the sigma clipped least squares fit. Fit errors were determined from the least squares fit. For the example shown, a 4% +/- % photometric loss was measured after 2048 transfers (the maximum possible transfers), a 7 σ detection of imperfect CTE. The lower panel of Figure 3 shows a similar example relationship for serial transfer CTE. In contrast, the photometric loss due to 2048 serial transfers was 0.3% +/- %, a result consistent with no loss due to imperfect CTE. In the Appendix we show all the linear relationships (i.e., as in Figure 3) for all combinations of filter and exposure time and stellar flux bins used to derive our constraints on CTE. Figure 3 and the ~50 fits in the Appendix give a clear and consistent snapshot of the impact of imperfect CTE on photometry in early The statistics are sufficient to detect non-trivial CTE losses from individual bins (~a few hundred stars) at the ~5-10 sigma confidence level for faint stars. All photometric losses are given in units of the amount expected for 2048 reads, the maximum possible of parallel transfers. Observed values range from % +/- % for bright stars (with ~10^5 electrons) and significant backgrounds (sky ~ ten s of electrons) to as much as 7%-10% for faint stars (with a few hundred electrons) and faint backgrounds (e.g., < 5 electrons). For each fit, the resultant loss per 2048 reads and its uncertainty were tabulated along with the sky level, median stellar flux inside the aperture. (The sky level includes the contribution from dark current, calculated as the exposure time times the mean dark rate.) The tabulated values were then used to fit for the CTE loss as a function of the sky and stellar flux using a fitting formula. Parallel CTE for WFC As seen in Figure 4 the parallel WFC CTE loss appears to be a strong function of the stellar flux. This is not surprising given similar experience with WFPC2 and STIS. Charge traps may be present at varying depths of the silicon substrate of WFC. Larger charge packets (from brighter stars) may be subject to greater absolute flux losses by accessing deeper traps, but smaller charge packets (from fainter stars) appear to lose a larger fraction of their flux. As seen in Figure 4, the data suggests a power-law relationship between CTE loss and stellar flux which we have utilized in the following correction formulae. 7

8 WFC Parallel CTE F606W,30s, <f>= (e), <s>=3.5602(e), ap=3 % loss=4.076 % error=0.578 F606W,30s, <f>= (e), <s>=3.7983(e), ap=3 Serial CTE % loss=0.328 % error=0.590 Figure 3: An example of the linear relationship determined for WFC for one filter and exposure time (F606W for 30sec providing a sky level of <s>=3.6 electrons) at one brightness range (stars with an average of <f>~400 electrons and a full range of +/-1 mag) contained within a r=3 pixel aperture. The upper panel shows a parallel transfer relation, the lower panel illustrates the serial transfer dependence. In Figure 5 we show the relationship between CTE loss and background. Increased background can mitigate the CTE losses (presumably by filling traps in advance of the arrival of the stellar charge packet during read-out) and this phenomenon has been seen for WFPC2 and STIS. For WFC, the dependence of CTE loss on background appears significantly weaker than on stellar flux (in the sense of a geometric progression) and is even insignificant for larger aperture sizes. Nevertheless, we used a power-law fitting function for both parameters to keep them on the same footing. 8

9 Low Background (2-4 e) Parallel CTE mag log(mag 2048 parallel trans) stellar flux (electrons, r=3 pix) log(stellar flux) (electrons, r=3 pix) Figure 4: The dependence of parallel transfer CTE loss versus stellar flux contained within an r=3 pixel aperture (all images at low sky level). As shown the relation is strong and suggests a power-law relation which was utilized in the correction formulae. The panel on the right shows the same in log-log space. 9

10 8 Parallel CTE Stellar Flux ~1000 e, r=3 6 mag sky (electrons) Figure 5: The relationship between parallel transfer CTE loss and sky background for WFC. As seen, the correlation is weak (and is insignificant for apertures of r=5 and 7) and in the sense of reduced loss with higher background. The measurement was made for stars with a flux ~1000 electrons to remove the dependence on stellar flux. Our resulting parallel CTE parameterization was: YCTE 10 A SKY B FLUX C Y ( MJD 52333) = Y total ( ) The term, Y/Y total reflects the linear relationship of the CTE loss with pixel transfer as seen in Figure 3 and the Appendix analogues. The maximum number of y-transfers, Y total is 2048 pixels for the WFC and 1024 pixels for the HRC. The last term involving the modified Julian date (MJD) characterizes the time evolution of the degradation of CTE away from the calibration date (MJD=52714) and will be justified in the next section 1. The full range of sky values sampled extends from ~0.1 e (F502N for 30 sec) 1. Another viable time-dependence matching equation 1 at the current time is a power-law of the form: YCTE = 1 1 A SKY B FLUX C Y, where N is the number of years past launch N 10

11 to 125 e (F606W for 1100 sec). The full range of aperture flux values sampled ranged from ~100 e to 300,000 e. However, due to the limited depth of the master star image, the faintest count levels are only sampled from short exposures (and hence low background). In the future we plan to add sampling of low flux levels with large backgrounds by utilizing the postflash/pre-readout capability of ACS. This future CTE+postflash calibration may also provide calibration of CTE losses for large backgrounds encountered in scenes with high apparent surface brightness (e.g., nearby galaxies). However, the fitting formula appears to be appropriate over the large dynamic range currently studied and should even be suitable as an estimate (or guide) for modest extrapolations. Table 1 contains the best fit values of the parameters A,B, and C and their uncertainties for equation 1 for 3 different aperture sizes. Observers should select the appropriate aperture size, measure the flux in the aperture and the sky value (if working with drizzled data in electrons/sec one must multiply by the exposure time), the number of parallel transfers, Y (Y=y coordinate for 1<y<2048, Y=4096-y for y>2048), and the MJD, and evaluate the correction. The correction must be derived for the actual exposures, not for a stack. Figure 6 shows the corrections derived from the formula for different observing parameters. Table 1: CTE Correction Coefficients for WFC Parallel Transfer A( σ ) B( σ ) C( σ ) ap 5(0.10) -0.11(3) -5(4) (0) 1(5) -0.77(7) (0.32) 0.14(9) -0.79(0.11) 7 In principle, first fitting the CTE trends in bins of stellar flux (and individual sky levels) followed by the step of constraining the multi-parameter fitting formula could result in information loss. However, the combination of contaminants (CR s) and the large range of photon statistics (requiring different sigmas for sigma-clipping) dicatated the adopted approach. 11

12 Predicted Photometric Losses for WFC from Parallel CTE* 5 extrapolation predicted mag loss at y= M31 Faint-end CMD SN Ia at peak, z~1.8 PSF flux=zeropoint 1/2 orbit integration flux in r=3 (e) Figure 6: The predicted photometric losses for WFC due to imperfect parallel CTE. The three functions are derived from the correction formula, equation 1, and the coefficients from Table 1 for r=3 pixels. The upper, middle, and lower lines are for 3 different background levels, 3 e, 30 e, and 100 e. The corrections are calculated for a typical source position, i.e., y=1024. Three specific science applications are shown as examples: the measurement of the faint end of M31 s CMD (GO 9453), the measurement of high-redshift supernovae (GO 9528), and the measurement of any PSF whose brightness is the zeropoint (i.e., 1 e/sec), for a half-orbit integration. Serial CTE for WFC Using the same methodology described above for parallel CTE, we measured the impact of imperfect serial CTE on the relative photometry of stars in 47Tuc. An example is show in Figure 3. Our conclusion is that we see no evidence of photometric losses due to imperfect serial CTE on the WFC. Figure 7 shows the mag loss per 2048 pixel transfers in the x-direction versus stellar flux for a narrow range of sky (2-4 e), and versus sky for a narrow range of stellar flux ( e). With low sky and low stellar flux, the parameter ranges where we would expect the largest impact of imperfect CTE, our measurements are consistent with 0 mag loss with a dispersion of ~1 mag. There is also no evidence of a loss trend with decreasing stellar flux as seen for parallel CTE. Utilizing a simple fitting formula for photometric loss versus stellar flux and sky yields correlation coefficients which are negligible (i.e., predicting losses of less than 1 mag 12

13 for the explored range of stellar fluxes and sky values) and are also consistent with zero. As a result, we believe there are no photometric corrections for photometric losses due to imperfect serial CTE on WFC required at this time. Figure 7: The dependence of photometric losses due to imperfect serial CTE on WFC on stellar flux and sky background. As seen, the losses and dependencies are negligible. HRC The same procedure described above for WFC was utilized to analyze the HRC data and to quantify the photometric losses due to imperfect CTE. By utilizing all 4 read-out amplifiers, we obtained 2 independent measures of the CTE loss trend for all combinations of filter and exposure time and stellar flux. The parallel transfer losses are measured by differencing stellar magnitudes in exposure pairs from amplifiers A and C and from B and D. The serial transfer losses were measured with the A and B pairing and the C and D pairing. An example of a photometric loss trend as a function of parallel and serial transfers is shown in Figure 8. In this example, (F606W for 30 sec yielding a sky of 0.75 e, stellar flux ~3300 e, i.e., a 22.0 mag star), a significant parallel transfer loss is detected for individual frames. The A-C and B-D amplifier read-outs yield 5%+/-1% losses after 1024 transfers (the maximum possible), a ~5 σ detection of imperfect parallel CTE. The A-B and C-D pairings show negligible loss (~% +/- 1.3%). 13

14 HRC Tuc_F606W_30s r=5 <f>=3355, s= % loss=5.509 % error= % loss=5.075 % error= % loss=54 % error= % loss=-0.11 % error=1.483 Figure 8: An example of the linear relationship determined for HRC for one filter and exposure time (F606W for 30 sec providing a sky background of 0.75 electrons) at one brightness range (stars with an average of ~3000 electrons and a full range of +/-1 mag). The upper panels show the relation for parallel transfer, the bottom for serial transfer. Parallel and Serial CTE for HRC Overall, the quantification of photometric losses due to imperfect CTE on HRC is of much lower accuracy than for WFC due to the small field of view of HRC (45 times less area) and the resulting paucity of stars. Only ~250 stars were culled from the HRC master images and many of these are undetected in the frames with shorter exposure times of 30 sec as well as in the F502N images. In future iterations of this calibration program we intend to move the HRC field a few arcminutes closer to the core of 47 Tuc to increase the number of stars in the field (though not too close in order to avoid crowding ). Despite the rather limited statistics, small but significant photometric losses are detected arising from parallel transfers. As shown in Figure 8, the size of the losses depends on stellar flux and the sky level in the same sense as for WFC (as well as WFPC2 and STIS). For typical observing parameters (well-detected stars of a few 1000 e, moderate sky values of ~5 electrons, and sources in the middle of the detector) the losses are ~1%, but rise to ~5-6% for the worst case: sky~1 electron, stars with ~100 electrons which are located far from the amplifier. One interesting difference suggested by the data is that the dependence of loss 14

15 on the background is greater for HRC than for WFC (where the background dependence is slight). Conversely, the dependence of loss on stellar flux is somewhat weaker for HRC than for WFC. Table 2: CTE Correction Coefficients for HRC Parallel Transfer A( σ ) B( σ ) C( σ ) ap -0.89(6) 4(0.13) 1(7) (0.36) 7(0.17) 1(9) (1.10) -0.58(6) 0.12(8) 7 The origin of these differences may come from the differences in the pixel size and sampling of the two detectors. We tentatively suggest that the greater sampling of HRC results in more self-background trap-filling for stars. That is, the leading edge of the charge packet likely fills the traps in advance of the trailing edge. In the limit of extreme sampling, the situation would mimic what is seen for extended sources for WFPC2 (Riess 2000) and hence the specific stellar flux is less indicative of the quantity of charge trapping. Background counts generally fill the shallower traps (which reemit charge on shorter time scales) and its impact would be counter to the self-background scenario. We utilized the same fitting formula as for WFC, equation 1, to derive a correction for the photometric loss due to parallel transfers for HRC. The method to correct HRC data is the same as for WFC. Observers should select the appropriate aperture size, measure the flux in the aperture and the sky value (if working with drizzled data in electrons/sec one must multiply by the exposure time), the number of parallel transfers, Y (Y=y coordinate for read-outs with amps C or D, Y=1024-y for readouts with amps A or B), and the MJD, and solve for the correction. For most observations the default amplifier, C, is used but users can determine which amplifier was used by consulting the header keyword CCDAMP. 15

16 Low Background ( e) Low Flux ( e) mag mag stellar flux (electrons, r=4 pix) sky (electrons) Figure 9: The dependence of parallel transfer CTE loss versus stellar flux (left panel) at low background and on background (right panel) for low flux. As shown, both dependencies and associated losses are of significance. Derived correction formulae and a range of uncertainty are shown. Similar to WFC, we see no significant photometric loss in HRC due to serial transfers. Figure 10 shows the serial transfer loss at low background and low flux, parameters where the CTE loss should be maximized. Instead, we find measurements consistent with 0% loss with a dispersion of 1-2%. At this time we suggest no corrections be applied to images for serial transfer loss on HRC. 16

17 Low Background ( e) Low Flux ( e) mag mag stellar flux (electrons, r=4 pix) sky (electrons) Figure 10: The dependence of photometric losses due to imperfect serial CTE on HRC on sky background and stellar flux. As seen, the losses and dependencies are negligible. 4. CTE Trending and Evolution The observations of 47 Tuc obtained in the first half of 2003 provide the first calibration of the photometric losses due to imperfect CTE using external, on-orbit data. Experience with all CCD s flown on HST as well as radiation testing of ACS flight spares indicates that on-going radiation damage will cause continuous growth of the charge trap population and the photometric losses will evolve (grow) with time. As a result, we intend to bi-annually recalibrate the photometric losses in order to derive time-dependent CTE correction formulae which are applicable to users at any time. Because this process has only just begun, it is too early to be able to derive the time-dependence of the correction formulae from the external data. Nevertheless we included a linear time-dependence term which is bounded by the condition that the photometric losses due to imperfect CTE were zero at launch (MJD=52333) and as measured at the approximate time of the first calibration (MJD=52714), one year 17

18 after launch. While future data will help refine the time-dependence, we believe the linear time-dependence is well motivated by other, on-orbit data. Still, other time dependencies such as a power-law of the form included as a footnote to equation 1 may be possible. Such an evolution would provide similar results at the current epoch but may diverge somewhat in the future. Figure 11: The time-dependence of a CTE metric: the charge deferred tails of cosmic rays and hot pixels due to short time-scale trapping and releasing of charge. Strong tails are seen for WFC for parallel transfers and weak tails for HRC parallel transfers, in good accord with the photometric results presented here. The approximately linear trends allow us to provide a preliminary time-evolution term in the photometric correction formulae. 18

19 We utilized a tracer of CTE degradation, the flux contained in the charge deferred tails (CDTs) of cosmic rays and hot pixels from dark frames (Riess, Biretta, and Casertano 1999) to track the evolution of CTE since launch. This is the same technique successfully employed for WFPC2 and STIS to track changes in CTE and has been shown to correlate with photometric loss measurements for WFPC2. The upper panel of Figure 11 (Riess 2002) shows the development of the CDTs for WFC. As seen, the CDTs were negligible at launch and grew linearly (to the precision of the data) and are now well-detected in a single dark frame. In contrast, the serial transfer tails have remained negligibly small and show little evidence of any growth. The same summary applies to the CDTs for HRC as seen in the bottom panel of Figure 11. This internal data from dark frames matches what is seen from the external data (imperfect CTE is significant for HRC and WFC for parallel transfers and negligible for serial transfers) and additionally motivates the two aspects of the time-dependence of equation (1), i.e., at launch it was nearly perfect and has been degrading linearly with time since then. 5. The Relationship between field-dependent Charge Diffusion and CTE The CCDs in HRC and WFC are both thinned and the thinning process inevitably results in large-scale variations in the CCD thickness. Because the charge diffusion of the CCD depends on thickness (thicker regions suffer greater diffusion), the breadth of the PSF and aperture corrections can also exhibit a field-dependence. Krist 2003 has characterized the spatial variation of charge diffusion as well as its impact on fixed-aperture photometry. For intermediate and large apertures (r> 4 pixels), the spatial variation of photometry is very small (less than 1%), but becomes significant for small apertures (r<3 pixels). It may be of interest to decouple the impact of imperfect CTE and charge diffusion on the field dependence of photometry. In principle, it is not necessary for observers to consider these two effects separately. The correction formulae given in this report include both effects and hence corrects photometry for both effects (as long as the user seeks to correct photometry to a perfect CTE and fiducial PSF width standard). However, it is possible that the impact of charge diffusion is at least as large as imperfect CTE and that the validity of the fitting formula used here could be invalid in form if charge diffusion produces a different signature (i.e., invalidating a linear characterization of charge loss with transfers or an extrapolation of the time dependence back to ~zero at launch). 19

20 pixel aperture % loss= pixel aperture % loss= Figure 12: The difference magnitude of the maps of encircled energy (whose spatial variation is induced by charge diffusion; see Krist 2003), WFC1-WFC2 versus parallel read-out position. This plot shows the small contribution to the imperfect CTE signature, e.g., Figure 3, and acts as a net CTE gain. Both effects are included in the correction formulae in this report. The solid line shows the bin median and the dashed shows the LAD fit. To investigate the impact of charge diffusion on our analysis of WFC we used the results of Krist 2003 (see their Figure 16) and divided the encircled energy maps for WFC1 by the maps for WFC2 for r=3 pixels and r=5 pixels. We then examined the magnitude of these ratios as a function of parallel read-out position. The result, plotted in bins of 128 by 128 pixels is shown in Figure 12 and is directly analogous to the CTE trend plots shown throughout this report (e.g., Figure 3 and the Appendix). As seen, the effect of charge diffusion is to act as a net linear CTE-like gain in our analysis though very small in size (a 0.82% gain for r=3 pixel aperture, a 2% gain for r=5 pixel aperture). An importance difference is that this effect is independent of the brightness of the star, time 20

21 since launch, or background level. Indeed some evidence of this may appear in our analysis as the four bins in our analysis with the brightest stars and largest backgrounds have modestly negative CTE measurements. For the vast majority of users it is not necessary to decouple the effects of charge diffusion and imperfect CTE, but special or unusual applications may require such a consideration. 6. Implications Based on even the preliminary CTE calibration provided here, a few interesting inferences can be drawn. 1) For WFC, post-flashing may be ineffective at mitigating CTE This statement is a direct implication of the weak dependence of photometric loss on sky background. However, it is too soon to know for sure if this holds at sky levels much higher than those studied here but are readily achieved by post-flashing. Perhaps sky levels of a few hundred electrons will mitigate CTE (though such behavior would appear to conflict with the extrapolation of the WFC correction formula), but if the sky levels required are too high, the added shot noise may make such post-flashing undesirable. An additional curiosity would be why post-flashing would appear more effective in ground-testing than on orbit. The source of such a difference may be the difference in the spectrum of damaging radiation and the trap species formed in the detector. 2) The future photometric losses for WFC can now be predicted and are expected to grow faster than for WFPC2 Assuming the linear time-dependence justified by the internal data is correct, predictions can be made. In N years, the typical/worst case losses will be N*(2%/10%). By the end of life for HST (2010), 8 years after launch, we can anticipate typical case losses of 16% and worst case losses of 50%-80% (here the range of predictions reflects the difference given by linear and power-law time dependence). For comparison WFPC2 had typical/worst case losses of 6%/40% 7 years after launch (Whitmore et al 2000). Such a faster rate of degradation for WFC is expected from the greater number of transfers edgeto-amplifier (2048 for WFC versus 800 for WFPC2). (Indeed, ACS WFC may even have lower CTE per pixel than WFPC2. An even comparison at y=800 would yield a lower expected net loss for ACS WFC than WFPC2.) 21

22 Acknowledgements We wish to thank Max Mutchler who provided an important spot-check of the HRC analysis, Stefano Casertano, Brad Whitmore, John Krist, Ron Gilliland, and Roeland van der Marel for helpful consultations, and the ACS phot-cal group for commenting on earlier versions of these results. References Riess, Biretta, and Casertano 1999, ISR WFPC Whitmore, Heyer, and Casertano, 1999, PASP, 111, 1559 Goudfrooij, P. and Kimble, R. A., 2002, HST Calibration Workshop, page 105 Krist, J., 2003, ACS ISR, Appendix Here we show a large subset of the range of CTE linear relationships for WFC and HRC used to derive the correction formulae. These are provided to give a better sense of the impact of CTE. We also provide a table of the individual linear relations for WFC in the parallel direction. The contents of each plot and table entry are labeled (albeit with very small print) for r=3 pixels. 22

23 Linear CTE Relationships for WFC F502N,30s, <f>= (e), s=437(e), ap=3 F502N,30s, <f>= (e), s=437(e), ap=3 F502N,30s, <f>= (e), s=437(e), ap=3 % loss=2.202 % error=1.105 % loss=5.123 % error=0.758 % loss=7.731 % error=1.037 F502N,30s, <f>= (e), s=437(e), ap=3 F502N,30s, <f>= (e), s=437(e), ap=3 F775W,30s, <f>= (e), s=2.4550(e), ap=3 % loss=8.245 % error=1.585 % loss=3.037 % error=2.055 % loss=0.360 % error=12 F775W,30s, <f>= (e), s=2.4550(e), ap=3 F775W,30s, <f>= (e), s=2.4550(e), ap=3 F775W,30s, <f>= (e), s=2.4550(e), ap=3 % loss=0.789 % error=48 % loss=1.639 % error=65 % loss=3.137 % error=0.372 F775W,30s, <f>= (e), s=2.4550(e), ap=3 F775W,30s, <f>= (e), s=2.4550(e), ap=3 F775W,30s, <f>= (e), s=2.4550(e), ap=3 % loss=5.625 % error=0.531 % loss=7.078 % error=0.775 % loss=6.881 % error=1.491 F606W,30s, <f>= (e), s=3.5602(e), ap=3 F606W,30s, <f>= (e), s=3.5602(e), ap=3 F606W,30s, <f>= (e), s=3.5602(e), ap=3 % loss=70 % error=0.195 % loss=1.091 % error=54 % loss=1.284 % error=

24 F606W,30s, <f>= (e), s=3.5602(e), ap=3 F606W,30s, <f>= (e), s=3.5602(e), ap=3 F606W,30s, <f>= (e), s=3.5602(e), ap=3 % loss=2.390 % error=05 % loss=4.234 % error=0.588 % loss=5.573 % error=0.831 F606W,30s, <f>= (e), s=3.5602(e), ap=3 F502N,40s, <f>= (e), s=1.3348(e), ap=3 F502N,40s, <f>= (e), s=1.3348(e), ap=3 % loss=3.553 % error=1.473 % loss=1.418 % error=26 % loss=2.419 % error=25 F502N,40s, <f>= (e), s=1.3348(e), ap=3 F502N,40s, <f>= (e), s=1.3348(e), ap=3 F502N,40s, <f>= (e), s=1.3348(e), ap=3 % loss=2.712 % error=07 % loss=3.451 % error=20 % loss=5.341 % error=0.890 F502N,40s, <f>= (e), s=1.3348(e), ap=3 F502N,40s, <f>= (e), s=1.3348(e), ap=3 F775W,40s, <f>= (e), s=24.644(e), ap=3 % loss=5.378 % error=1.195 % loss=3.177 % error=1.381 % loss=-0.16 % error=0.178 F775W,40s, <f>= (e), s=24.644(e), ap=3 F775W,40s, <f>= (e), s=24.644(e), ap=3 F775W,40s, <f>= (e), s=24.644(e), ap=3 % loss=4 % error=0.152 % loss=-7 % error=0.179 % loss=0.123 % error=22 24

25 F775W,40s, <f>= (e), s=24.644(e), ap=3 F775W,40s, <f>= (e), s=24.644(e), ap=3 F775W,40s, <f>= (e), s=24.644(e), ap=3 % loss=83 % error=75 % loss=1.005 % error=0.326 % loss=2.639 % error=0.564 F775W,40s, <f>= (e), s=24.644(e), ap=3 F775W,40s, <f>= (e), s=24.644(e), ap=3 F606W,40s, <f>= (e), s=38.415(e), ap=3 % loss=4.178 % error=1.328 % loss=1.898 % error=3.407 % loss=-0.17 % error=0.182 F606W,40s, <f>= (e), s=38.415(e), ap=3 F606W,40s, <f>= (e), s=38.415(e), ap=3 F606W,40s, <f>= (e), s=38.415(e), ap=3 % loss=4 % error=0.167 % loss=34 % error=25 % loss=77 % error=92 F606W,40s, <f>= (e), s=38.415(e), ap=3 F606W,40s, <f>= (e), s=38.415(e), ap=3 F606W,40s, <f>= (e), s=38.415(e), ap=3 % loss=79 % error=0.384 % loss=1.367 % error=49 % loss=1.950 % error=60 F606W,40s, <f>= (e), s=38.415(e), ap=3 F606W,40s, <f>= (e), s=38.415(e), ap=3 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 % loss=4.291 % error=1.299 % loss=9.643 % error=5.197 % loss=-0 % error=

26 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 % loss=88 % error=0.157 % loss=79 % error=04 % loss=0.772 % error=0.367 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 % loss=0.785 % error=18 % loss=1.006 % error=0.522 % loss=0.751 % error=0.845 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 F606W,1100.s, <f>= (e), s=125.66(e), ap=3 % loss=-0.71 % error=1.503 % loss=1.430 % error=

27 Linear CTE Relationships for HRC HRC Tuc_F606W_30s r=5 <f>=18060, s=0.75 HRC Tuc_F606W_30s r=5 <f>=497, s= % loss=1.645 % error= % loss=1.461 % error= % loss=0.955 % error= % loss=1.008 % error= % loss=0.908 % error= % loss=04 % error= % loss=-4.83 % error= % loss=-1.62 % error=3.040 HRC Tuc_F606W_30s r=5 <f>=6501, s=0.75 HRC Tuc_F775W_30s r=5 <f>=17341, s= % loss=2.252 % error= % loss=2.217 % error=43 - % loss=7 % error= % loss=-8 % error= % loss=1.670 % error=90 - % loss=1.963 % error= % loss=0.834 % error= % loss=2.262 % error=3.227 HRC Tuc_F606W_30s r=5 <f>=3355, s=0.75 HRC Tuc_F775W_30s r=5 <f>=5625, s= % loss=5.509 % error= % loss=5.075 % error= % loss=54 % error= % loss=-0.11 % error= % loss=4.152 % error= % loss=1.514 % error= % loss=1.265 % error= % loss=-1.80 % error=0.802 HRC Tuc_F606W_30s r=5 <f>=911, s=0.75 HRC Tuc_F775W_30s r=5 <f>=2473, s= % loss=5.208 % error= % loss=2.036 % error= % loss=-4.26 % error= % loss=-2.26 % error= % loss=3.976 % error= % loss=5.014 % error= % loss=2.727 % error= % loss=-3.61 % error=2.337 HRC Tuc_F775W_30s r=5 <f>=988, s=0.51 HRC Tuc_F606W_36s r=5 <f>=-31868, s= % loss=4.737 % error= % loss=2.242 % error= % loss=-6.76 % error= % loss=41 % error= % loss=0.827 % error= % loss=1.272 % error= % loss=-0.14 % error= % loss=2 % error=3.521 HRC Tuc_F775W_30s r=5 <f>=403, s=0.51 HRC Tuc_F606W_36s r=5 <f>=11132, s= % loss=4.768 % error= % loss=1.806 % error= % loss=-7.52 % error= % loss=-8.36 % error= % loss=-1.52 % error= % loss=1.453 % error= % loss=0.521 % error= % loss=-0.12 % error=3.354 HRC Tuc_F606W_36s r=5 <f>=18489, s=6.23 HRC Tuc_F606W_36s r=5 <f>=5138, s= % loss=96 % error= % loss=0.597 % error= % loss=0.147 % error=93 - % loss=-0.16 % error=67 - % loss=0.304 % error= % loss=2.039 % error= % loss=-1.16 % error= % loss=-2.37 % error=2.249 HRC Tuc_F606W_36s r=5 <f>=13548, s=6.23 HRC Tuc_F775W_36s r=5 <f>=11881, s= % loss=0.133 % error=89 - % loss=0.769 % error= % loss=31 % error= % loss=-7 % error= % loss=54 % error= % loss=1.187 % error=88 - % loss=0.381 % error= % loss=0.788 % error=

28 HRC Tuc_F775W_36s r=5 <f>=879, s= % loss=0.574 % error=33 - % loss=1.030 % error= % loss=0.390 % error= % loss=0.342 % error=0.882 HRC Tuc_F775W_36s r=5 <f>=32327, s= % loss=0.784 % error= % loss=0.173 % error= % loss=66 % error=51 - % loss=77 % error=1.683 HRC Tuc_F775W_36s r=5 <f>=12102, s= % loss=1.053 % error= % loss=0.954 % error= % loss=-0.85 % error= % loss=-0.12 % error=2.739 HRC Tuc_F775W_36s r=5 <f>=5274, s= % loss=1.429 % error= % loss=70 % error= % loss=-2.51 % error= % loss=-0 % error=3.075 HRC Tuc_F502N_36s r=5 <f>=7886, s=5 - % loss=3.965 % error= % loss=1.697 % error= % loss=0.977 % error= % loss=00 % error=7.212 Tabulated Linear CTE Relationships for WFC sky (e) <flux> (e) loss/2048 pix (mag) error ap # stars data set Tuc_F502N_ Tuc_F502N_ Tuc_F502N_ Tuc_F502N_ Tuc_F502N_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F606W_30 28

29 sky (e) <flux> (e) loss/2048 pix (mag) error ap # stars data set Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F502N_ Tuc_F502N_ Tuc_F502N_ Tuc_F502N_ Tuc_F502N_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F775W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_ Tuc_F606W_