PERFECTING THE PHOTOMETRIC CALIBRATION OF THE ACS CCD CAMERAS

Photometric calibration uncertainties are the dominant source of error in current SN Ia dark energy studies and other cosmology efforts; the precision of the constraints on the constants in the Einstein equations of general relativity are directly related to the precision of absolute flux calibrations (Scolnic et al. 2014).

The Advanced Camera for Survey (ACS) charge-coupled device (CCD) flux calibration was updated fairly recently in a series of four Instrument Science Reports² that covered the philosophy and techniques, including charge transfer efficiency (CTE) corrections, encircled energy (EE) corrections, changes in sensitivity with time, and the absolute flux calibration itself (Bohlin 2011, 2012; Bohlin & Anderson 2011; Bohlin et al. 2011). However, additional data, updates to the processing, and revised fluxes for the primary standard stars, which change by up to ∼1% (Bohlin & Proffitt 2015), mandate a fresh analysis of the complete body of calibration observations. ACS has two CCD channels and a Solar Blind Channel (SBC). The CCD channels are a Wide Field Channel (WFC) and a High Resolution Channel (HRC), both of which ceased functioning in 2007. However, the WFC was revived during Servicing Mission four (SM4) in 2009.

Changes to the data reduction with generally subpercent effects include updated bias reference files, a better removal of the weak striping in data obtained with the new electronics installed during SM4, a refined correction for the sensitivity degradation with time, and a fix of a minor flaw in the calculation of the sky background in the IDL ${apphot}.{pro}$ routine used to extract the photometry of the standard stars from the _crj.fits files. The low-level striping in the post-SM4 WFC data is removed using the median for each row, which works nicely for the sparse standard star fields in the 1024 × 1024 subarrays after masking a 5.5 × 55 box centered on the star. The Space Telescope Science Institute (STScI) pipeline data processing begins with the _raw.fits data files, and then applies the flat field correction along with other corrections associated with CCDs to make _flt.fits files. If multiple exposures at the same pointing are taken to permit the rejection of cosmic-ray hits, then the _crj.fits files are also produced from the _flt.fits files. If multiple exposures are taken of the same target but with small dithered pointing offsets, then the _flt.fits data are combined with the drizzle software task to make _drz.fits files that have both hot pixels and cosmic-ray rejection. The flat fields are designed to produce the same response in each pixel when observing a perfectly uniform diffuse source. However, optical distortions cause variations in the size of the pixels in arcsec on the sky; thus a multiplication by a pixel-area map (PAM) file is required for the _flt.fits and _crj.fits files to correct for the pixel size variation and make a uniform response anywhere in the field for the same stellar point source. The PAM correction is built into the drizzle software; no PAM correction is needed for the _drz.fits files.

The logical flow of the derivation of the ACS flux calibration starts with extracting the latest version of the standard pipeline data products from the Mikulski Archive for Space Telescopes (MAST).³ Then, the aperture photometry is extracted from the _crj.fits files for various aperture radii. These photometry data files form the basis for subsequent analyses, including the derivation of the fractional encircled energy (EE) as a function of radius, of the change in sensitivity as a function of time on orbit, and of the absolute flux calibration. The main goal of this work is to establish this flux calibration with a better than 1% precision at the WFC1-1K reference point for the heavily used broadband filters. The Hubble Space Telescope (HST) method of parameterizing the instrumental calibration of flux sensitivities relies on pre-launch estimates for the fractional throughput or quantum efficiency (QE) of each element in the optical path from the primary mirror through to the detector that registers the photon events. Instrumental sensitivities depend directly on the product of all these component efficiencies and the collecting area of the 2.4 m primary mirror. In-flight updates to the pre-launch estimates are derived from observations of standard stars with known flux distributions and are implemented via changes to the detector QE as a smooth function of wavelength or by scaler correction factors to the filter throughput functions. In this work, wavelength dependent corrections for two filter bandpass functions are also derived. Because no new updates to the QE versus wavelength are needed, the calibration reference files that must be delivered for the pipeline data reduction include only files to define the changing sensitivity versus time, and files that update the filter throughputs.

Section 2 reviews the observational data and its pipeline reduction, while Section 3 covers the details of the bias subtraction. Section 4 augments the EE fractions, which now include apertures of radii from 005–2'' (i.e., 1–40 WFC pixels). Section 5 reviews the sensitivity change with time, Section 6 justifies a change in the F814W bandpass throughput function, and Section 7 covers the absolute flux calibration for photometry. An analysis of the problematic _drz.fits files appears in the appendix and shows that more than a quarter of the 334 _drz images of standard stars are erroneous.

The original comprehensive ACS calibration paper (Sirianni et al. 2005) also covered these topics, except for changes in sensitivity with time and wavelength dependent bandpass adjustments. While the Sirianni et al. (2005) EE results are for the center of the 1024 × 1024 pixel HRC channel, those WFC EE values are averages of data at the centers of the ACS CCD 1 and CCD 2, which are butted to make the 4096 × 4096 pixel WFC detector. Any location can be used for the absolute flux calibration, as long as the flat field is perfect in making all locations equivalent. For efficient use of the ACS calibration time, the center of the WFC1-1K subarray is the chosen flux calibration reference point for the WFC. The flat fields are derived from dithered observations of 47 Tuc (Mack et al. 2002), and the pioneering pilot check of these flats with dithered observations of bright standard stars with a wide range of stellar color temperature is Bohlin & Grogin (2015) for F814W and F435W. With the bandpass adjustment of Section 6, F814W is now uniform to 1% for stars of type K and hotter. For F435W, further analysis of these new flat field checks will be forthcoming.

Table 1 lists the HST standard stars used for the flux calibration; the three primary hot WD stars—G191B2B, GD153, and GD71—define the ACS flux calibration and its change over time. Multiple observations of these stars have a subpercent repeatability and provide a robust measure of the cross-calibration between the Space Telescope Imaging Spectrograph (STIS) and the ACS average response in each filter. For the secondary standards, three separate ACS visits and three STIS measures of their spectral energy distributions (SEDs) are required for each star to provide minimal confirmation of repeatability and $\ll 1 \%$ statistical significance. Results based on stars with fewer observations are less reliable. The measured STIS SEDs are from CALSPEC (Bohlin 2014), while ACS data obtained after 2011 July are not previously analyzed. The standards are observed at the center of the ACS WFC1-1K subarray to provide a standard reference point and anchor for the flat field calibrations.

Since the previous analysis by Bohlin (2012), the USEAFTER dates for some superbias reference files were adjusted to be earlier. CCD detectors are operated with a positive electronic bias level, so noise or drifts in the analog circuitry before digitization does not drive the measured charge to negative levels. The pattern in the bias frames taken with zero exposure time changes slowly and must be monitored as a function of time. The USEAFTER date is the time when a reference file first becomes relevant. For example, the bias observations that occurred four days AFTER the G191B2B observation on 2011 November 10 has a USEAFTER of 2011 October 27, so the bias correction is closer in time than the previously used reference file with a USEAFTER of 2011 August 25. While the change in the 1'' photometry is negligible (<0.02%), the bias is important for the infinite (55) aperture, which changes by up to 0.6%. The EE in the infinite aperture defines the diffuse source calibration, but the point-source flux calibration in the smaller apertures is unaffected, as long as the same EE factor for conversion from the smaller standard radius to infinite is used to convert back to the smaller radius. Perhaps the absolute calibration PHOTFLAM header keyword for infinite aperture should be augmented to include the small aperture EE keyword values for convenience and to avoid erroroneous usage of obsolete EE values.

Standard practice for ACS pipeline data processing is to obtain and subtract a CCD bias image, which consists of data obtained within the same CCD anneal cycle (currently every four weeks). Data fetched from the MAST shortly after a program execution should always be re-extracted from the archive after the final bias and dark reference files are delivered with their usual 1–2 month delay. Before the ACS electronics repair in 2009 April on SM4 that included an Application-Specific Integrated Circuit (ASIC) to read the CCD data, the subarray bias could be extracted from the full-frame biases; but different clocking speeds in the ASIC for subarrays now mandates separate subarray bias observations. Full-frame WFC bias reference files have a regular two-week cadence, but the post-SM4 subarray bias observations occur only as needed in association with the science observations. Originally, a regular cadence of post-SM4 WFC1-1K subarray bias observations executed through 2012 October, but calibration programs must schedule any required bias frames along with the external observation. There are no WFC1-1K bias observations with USEAFTER dates between 2012 October 14 and 2014 September 3. Of the cooler stars used in this work, the only observations that lie in this WFC1-1K bias desert are for BD+17°4708 on 2013 September 4 and VB8 on 2013 March 11.

Before the proper associated bias data were reduced to reference files, some of the WFC1-1K subarray observations were processed with a bias reference file that was obtained up to 666 days earlier. An aperture photometry of 1'' and smaller is the same to 0.1% for current and out-of-date bias reference files. Even though individual measures with the 55 radius have errors of up to 1%, the effect on the average EE tabulated in the Appendix is less than 0.2% for any filter.

For the flat field mapping program 13602 (Bohlin & Grogin 2015), the 400 × 400 subarrays have associated bias observations without overscan columns. Unfortunately, the pipeline data processing requires bias observations with overscan, and the archival 13,602 data are processed with the bias data extracted from a full-frame bias image. The errors in the 20-pixel radius photometry for the archival MAST versions range up to 1.7% in comparison to the custom reduction of Bohlin & Grogin (2015).

To verify consistency with the various community photometry packages, Table 2 includes the extracted $\mathrm{electrons}\,{{\rm{s}}}^{-1}$ used in the current flux calibration for aperture radii of 3, 5, 10, 20, and 110 pixels for the WFC1-1K subarray observations of GD71 obtained at 2003.84 on 2003 November 3. The images are j8v602*_crj.fits files, as processed by the CALACS pipeline on 2015 November 17 and then corrected by the pixel-area map (PAM). Changes from the same 20-pixel 1'' photometry shown in Table 3 of Bohlin (2012) are $\lt 0.06 \%$. Changes in the sky background are similarly negligible but do become more consistent with a range of −0.024 to 0.094 versus the previous −0.011 to 0.221 $\mathrm{electrons}\,{{\rm{s}}}^{-1}$.

4.1. Equations

Following the methodology of Bohlin (2012) but with the improved notation of Bohlin et al. (2014), the photon weighted mean flux over the bandpass in wavelength (λ) units is

$$\begin{eqnarray}&&\langle F\rangle =\displaystyle \frac{\int {F}_{\lambda }\,\lambda \,R\,d\lambda }{\int \lambda \,R\,d\lambda }=S\,{N}_{e},\end{eqnarray} \tag{ 1 }$$

where our flux F is $\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}\,{\mathring{\rm A} }^{-1},{\rm{R}}$ is the system fractional throughput (i.e., the total system QE as a function of wavelength), S is the instrumental calibration constant photflam that appears in the ACS data headers, N_e is the measured instrumental count rate in photoelectrons ${{\rm{s}}}^{-1}$ in the ACS "infinite" 55 radius aperture, and the integral is over the bandpass range of the filter. Equation (1) includes all the photons from starlight incident on the primary, regardless of where the light hits the detector, so that N_e implicitly includes all the detected photons in an infinite radius aperture. An actual infinite radius is not feasible, and 55 is about as large an aperture as is practical. In principle models of the instrumental point-spread function (PSF) could help define the encircled energy for an infinite aperture. In the case of HST, considerable effort has been expended on the Tiny Tim PSF modeling software. However, the Tiny Tim user manual states: "Generally, the models are not very good past a radius of ∼2'', due to the effects of scatter and high-frequency aberrations" (Krist & Hook 2004). Because of the small gains in the enclosed signal as the aperture size increases toward 55, the error in the infinite aperture estimate should be <1%; this uncertainty applies only to the diffuse source calibration. The precision of the point-source flux calibration is not affected by errors in the adopted infinite aperture EE estimate. The sky background annuli are 6''–8'' for WFC and 56–65 for HRC. The count rate N_e can also be predicted from the known instrumental throughput parameters and the known CALSPEC flux F_λ for each standard star

$$\begin{eqnarray}&&{N}_{e}=\displaystyle \frac{A}{{hc}}\int {F}_{\lambda }\,\lambda \,R\,d\lambda ,\end{eqnarray} \tag{ 2 }$$

so that

$$\begin{eqnarray}&&S=\displaystyle \frac{{hc}}{A\int \lambda \,R\,d\lambda },\end{eqnarray} \tag{ 3 }$$

where h is Planck's constant, c is the speed of light, and A is the collecting area of the primary mirror, taken to be 45,239 cm². The traditional method of flux calibration for HST that is followed in this paper involves adjusting R in Equation (2), so the computed N_e equals the measured count rate. Systematic deviations between the computed and measured N_e for all the filters are accounted for by smooth adjustments of the detector QE versus wavelength, while residuals for each filter are corrected by adjusting the filter throughput. The point-source calibration S for the infinite aperture is required for computing the diffuse source surface brightness calibration (Bohlin et al. 2014).

For aperture photometry with a radius of i, the EE fractions E_i are the average of the measured ${E}_{i}={N}_{i}/{N}_{e}$ for each filter (i.e., the sum of the counts ${{\rm{s}}}^{-1}$ N_i within a radius i divided by N_e). Once the average E_i are established, the infinite aperture N_e can be computed from any small aperture photometry by dividing by the encircled energy fractions E_i, which are the aperture corrections used to correct small radius aperture photometry to a larger reference aperture (i.e., the infinite aperture for ACS).

For example, the commonly used 3, 5, 10, and 20 pixel radii for WFC (double for HRC) are approximately 0.15, 0.25, 0.5, and 1 arcsec, where

$$\begin{eqnarray}&&{N}_{e}={N}_{3}/{E}_{3}={N}_{5}/{E}_{5}={N}_{10}/{E}_{10}={N}_{20}/{E}_{20}.\end{eqnarray} \tag{ 4 }$$

Thus, the mean flux $\langle F\rangle$ is S ${{\rm{N}}}_{i}/{E}_{i}$, where the most appropriate radius subscript can be chosen.

For many science images, the use of the proper sky annulus at 6–8'' is not appropriate, and a correction is required to the photometric calibrations presented here, which are all based on that fixed sky annulus. Ignoring these corrections for an inner sky radius of only a few pixels causes photometric errors of a few percent. Because of gradients in the sky background in many science images from the star to the WFC standard sky annulus at 6–'', smaller sky annuli are often required. For example, three-pixel WFC photometry N3 with an inner sky radius of four pixels and an outer sky radius of six pixels requires a correction of 0.976 for F850LP.

4.2. EE Changes Over Time

Plots of the aperture photometry versus time illustrate the reproducibility and determine the best aperture for the absolute flux calibration. For example, Figure 1 compares the measured WFC F606W count rate N_i to the predicted N_e for an infinite aperture for five of the most relevant photometry apertures from 3 to 110 pixels. The measured photometry for each star is divided by the predicted value to preserve the intrinsic rms scatter of the data and avoid large fluctuations that would be caused by dividing by the measured infinite aperture values. The rms scatter is tabulated for all eight of the WFC broadband filters in Table 3. There are no obvious trends with time or with stellar color in Figure 1.

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Table 3.  Photometric rms Scatter for Various Radii at the WFC1-1K Reference Point

Filter	${\sigma }_{3}$(%)	${\sigma }_{5}$(%)	${\sigma }_{10}$(%)	${\sigma }_{20}$(%)	${\sigma }_{110}$(%)
F435W	1.00	0.43	0.37	0.35	1.08
F475W	1.76	0.39	0.31	0.30	0.51
F555W	1.26	0.41	0.41	0.41	0.69
F606W	1.65	0.46	0.38	0.37	0.58
F625W	2.00	0.43	0.30	0.30	0.77
F775W	2.23	0.60	0.50	0.51	0.76
F814W	1.40	0.39	0.33	0.31	0.64
F850LP	1.94	0.87	0.58	0.44	0.81

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For the bright, isolated standard stars, the 20-pixel (∼1'') aperture generally has the best repeatability at 0.30%–0.51% for ${\sigma }_{20}$ and, therefore, defines the best photometry for each observation; although there is little loss in precision with an aperture as small as five pixels, where $0.39\lt {\sigma }_{5}\lt 0.87$. While the infinite 55 radius aperture contains all the signal by definition, there is more scatter because of the excess sky noise in such a huge aperture. The three-pixel radius aperture has up to seven times the uncertainty of a 1'' aperture; if possible, the use of E₃ to calibrate science data should be avoided because of exact centering uncertainties and focus variations that could be systematic over an entire image.

Figure 2 is similar to Figure 1, except for the addition of the problematic M star VB8. The infinite (110 pixel) radius values for all four VB8 observations are high by 0.5%–1% with respect to the hotter star average. This offset could be caused by a low value of the predicted N_e from the STIS SED. In the region of the F814W sensitivity, the VB8 flux is on the short wavelength, rapidly declining side of the SED, where stellar variability is common. In addition, a large contribution to the VB8 predicted count rate is from 9000–9600 Å where STIS has a low sensitivity and worse rms repeatability. In Figure 2, the 20-pixel radius VB8 points are also high, but not as high as the 110 pixel values, which accounts for the slightly low F814W, VB8 average for the WFC in Figure 3. At the three-pixel radius in Figure 2, VB8 is significantly low, indicating that there must be some extra loss into the red halo of Section 4.4 for such a small aperture.

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4.3. Hot, Early Type Stars

EE values are the measured N_i divided by the noisy measured N₁₁₀ values; fitting techniques are required to lower the uncertainties. While the large 110-pixel infinite aperture should recapture all the trapped and re-emitted charge, the smaller aperture data require a CTE correction. The pipeline processing now supplies the Anderson & Bedin (2010) CTE corrected full frame 4096 × 4096 pixel images, but CTE corrected subarrays are not provided, so the WFC1-1K subarrays used here must be corrected for CTE losses in the post-pipeline processing by the method of Bohlin & Anderson (2011). A fit as a function of wavelength for the broad filters of Table 3 reduces the uncertainty, while at the same time providing fitted values for the problematic narrow filters (Bohlin 2012). Figures 3 and 4 are examples of polynomial fits to the average EE as a function of the pivot wavelength for the 1'' aperture from the hot stars to the K1.5III KF06T2. The plotted symbols are the averages for each star, but the fit is to the global averages of all of the individual observations for each broadband filter. The final results of similar fitting for 12 aperture sizes appear in Tables 8 and 9 in the appendix, where typical uncertainties in the EE fits for WFC and the 015, 025, 05, and 1'' radii are 0.4, 0.2, 0.4, and 0.1%, respectively. Correspondingly for HRC, the respective uncertainties are 0.4, 0.3, 0.4, and 0.3%. The _flt.fits files must be used for the sometimes saturated WFC data for the bright BD+17°4708 because saturated pixels cannot be combined with the cosmic-ray rejection algorithm used to produce the _crj.fits files. These final EE values are fits to the measured ratios of the small to infinite aperture count rates, where a few of the later single exposure _flt.fits BD+17°4708 observations in the big 55 aperture deviate from the mean by $\gt 3\sigma$ and are omitted. The ACS CCDs are linear through saturation, as long as the entire saturated signal is included in the aperture (Gilliland 2004), which means that some of the smaller aperture measures of BD+17°4708 must also be omitted. The maximum deviation from Sirianni et al. (2005) for the broadband WFC filters is for the three-pixel F435W EE value of 0.792, whereas Sirianni et al. (2005) has 0.775.

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4.4. Cooler, Late Type Stars

4.5. EE Variations Around the Field of View

To specify a flux calibration for the ACS CCD imaging data, the photometry must be corrected for gradual losses in the instrumental throughput since the installation of ACS into HST on 2002 March 7 (2002.16). The side-1 electronics failure occurred on 2006 January 27 (Bohlin et al. 2011), and the activation of the side-2 electronics with the reduction of the set-point temperature from −77C to −81C for the WFC CCD on 2006 July 6 (2006.50) introduced a discontinuity in sensitivity (Mack et al. 2007). In addition, the lowering of the set point to −81C caused minor flat field changes of up to 0.6%, which are automatically included in the STScI ACS pipeline data products (Gilliland et al. 2006). A second discontinuity in sensitivity is due to the CCD Electronics Box Replacement (CEB-R) with its ASIC sidecar circuit board during the HST Servicing Mission SM4 in 2009 May at 2009.4 (Grogin et al. 2010).

This work updates the results of Bohlin et al. (2011), which provides more details about the analysis. The reference positions for the flux calibration are at the center of the HRC CCD and at the center of the standard WFC1-1K subarray at pixel (3583,1535) on chip-1; the change in sensitivity is determined by the photometry with the best repeatability (i.e., the 1'' N₂₀ photometry of the three HST primary WD standard stars G191B2B, GD153, and GD71). The subpercent CTE corrections of Bohlin & Anderson (2011) are applied for WFC and should be negligible for the early HRC data, which is heavily exposed. The three stars are on a common scale defined by their observed infinite aperture count rate C = ${N}_{20}/{E}_{20}$ divided by the predicted total count rate $P={N}_{e}$ from the synthetic photometry of Equation (2). The P values depend only on the stellar flux and the system throughput for the filter and are corrected only for the discontinuity due to the change in the WFC temperature from −77C to −81C. The stellar SEDs for these three fundamental HST standards are the measured STIS fluxes on the HST scale (Bohlin 2014) from the HST CALSPEC database.⁴

For the first years of ACS operations, the change in response that is measured by C/P for each filter is fit with a straight line. Then, to reduce measurement noise and enforce the prior of the expected smooth change with wavelength, these line slopes are fit with a polynomial as a function of the filter pivot wavelengths, as shown in Figure 5 for the broadband filters available to both WFC and HRC. The HRC and WFC photometry are in red and black, respectively, along with their separate linear fits. The P values for WFC are corrected for the first sensitivity discontinuity for the switch of the set-point temperature from −77C to −81C at 2006.5 (Mack et al. 2007) but are NOT adjusted for the second discontinuity at 2009.4 for the SM4 repair. While the HRC red solid lines are the actual linear least-square fits to the data, the WFC pre-SM4 fits are for the constant term only and adopt the final fitted slopes from Figure 6 to get the best estimate of the post-SM4 normalization level. The WFC fits generally appear to agree with the data within the rms noise. However, for F850LP the positive slope of 0.06% yr⁻¹ from Figure 6 and Table 5 is clearly a better fit to the minimal WFC data.

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The data are rather sparse for the pre-SM4 ACS epoch because the policy of monitoring of the sensitivity changes at the WFC1-1K reference point with the three primary standard stars once per year had not yet been established. The filter F814W is typical of the better data sets with seven WFC data points that agree well with the seven HRC observations, as shown in Figure 5. F475W is a worst case, where there are only four WFC data points, and the main constraint on the rate of sensitivity loss is the lone GD153 point at 2007.0 from program 11054. The planned observations of G191B2B in cycle 15 were not executed because of the ACS failure at 2007.1. Given the scatter in the data, the WFC loss rate is uncertain but would coincide with the slope from the fitted results if the lone 2007.0 point that has all the leverage on the fit were ∼1σ lower. Furthermore, the lone HRC point at 2006.9 for GD71 is probably a low statistical outlier. Statistically, the best result is from accepting both the WFC and HRC measures and adopting the fitted mean for F475W.

Bohlin et al. (2011) present a Figure 1 for F555W that is similar to F555W in Figure 5, but where the results for GD153 are systematically low by a fraction of a percent. In particular, the GD153 observation at 2009.6 was below the fit by 0.7%, while the revised results for F555W have the same data point with the typical scatter of only 0.4% low. The primary reason for this improvement is that the new CALSPEC fluxes for GD153 in the 5500 Å region are ∼0.4% lower with respect to the other two primary standards, which makes the denominator smaller and raises that point to only ∼1σ below the fit. Now, the F555W scatter is typical of the other filters and the Bohlin et al. (2011) anomaly is remedied.

For the later years of ACS after SM4 at 2009.4, the eight WFC broadband filters are well monitored with ∼18 visits; all show a consistent sensitivity loss with a statistical significance ranging from 0.9 to 2.4σ. This average post-SM4 loss rate is 0.00061 per year (i.e., 0.061% yr⁻¹ with an error-in-the-mean of 0.007% yr⁻¹, which differs at most by $\lt 1\sigma$ from the measured rate of 0.035 ± 0.037% yr⁻¹ for F850LP). The average loss rate of 0.061% yr⁻¹ is adopted for all WFC data after 2009.4. The general trends of reduced loss rates with time and increased loss rates toward UV wavelengths are the expected behavior for a gradually slowing outgassing of hydrocarbons and their polymerization on the optical surfaces. The observed trends in STIS follow this model.

Following Bohlin et al. (2011), Figure 6 shows the slope of the rates of sensitivity loss (${\rm{\Delta }}S$) for each filter and a fourth-order polynomial fit to the pre-SM4 data for both cameras as a function of the pivot wavelength (λ).

$$\begin{eqnarray}&&{\rm{\Delta }}S=a+b\lambda +c{\lambda }^{2}+d{\lambda }^{3}+e{\lambda }^{4}.\end{eqnarray} \tag{ 5 }$$

The medium and narrow-band data are shown but are omitted in the fitting procedure because of the minimal ACS observation sets and also because of the finite STIS resolution that affects the predicted count rate P. The F850LP WFC and HRC 1σ error bars nearly touch, and the other seven broadband pairs of 1σ error bars all overlap. There are no systematic differences between the two cameras, so the HRC and WFC slopes are fit together. Among the 16 data points for the eight pairs of WFC and HRC broadbands, only the WFC F850LP lies more than 1σ from the fourth-order fit; the 1σ uncertainty of 0.08% yr⁻¹ in the fit encompasses most of the pre-SM4 measurements. The coefficients of the fourth-order polynomial, pre-SM4 fit in Figure 6 are a = −0.044561, b = 3.0376e–05, c = −7.7328e–09, d = 8.3760e–13, and e = −3.2569e–17, while the loss rates evaluated at the average pivot wavelengths appear in Table 5 along with the measured values. The fitted loss rates also appear in mag yr⁻¹ for comparison with the pre-SM4 47 Tuc results of Ubeda & Anderson (2013) for the WFC. The two different methods agree with a maximum difference in slope of 0.017–0.0018 mag yr⁻¹ for F475W, F658n, and F660N, where Ubeda & Anderson (2013) have the largest uncertainties of 0.0015–0.018 mag yr⁻¹. The main difference between the two methods is that Ubeda & Anderson (2013) did not enforce the prior of a smooth variation of the loss rates versus wavelength. The STIS loss rates appear as dashed lines in Figure 6 and suggest that the ACS sensitivity losses should also be a smooth function of wavelength. The overall level and not the slopes of the STIS loci should be compared to ACS because the STIS slope is affected by the grating blaze shifts due to sublimation of the epoxy that bonds the replica gratings to the substrate.

The sensitivities for each WFC filter after SM4 are based on the fits to ∼18 available WD observations for each of the eight broadband filters, as illustrated by the solid lines in Figure 5. The typical 1σ rms scatter of 0.003 about the fits establishes the uncertainty of an individual C/P value. These fits evaluated at 2009.4 appear in Figure 7, where each value represents the sensitivity at 2009.4 relative to the initial sensitivity at 2002.16. However, the QE curve for the −81C set-point temperature is used for the post-SM4 calibration, which means the Figure 7 corrections must be applied to the post-2006.5-81C QE because this QE is used to calculate the post-2009.4 sensitivities. Since −81C QE is designed to match the photometry to the −77C 2002.16 QE calibration, this approach also matches the post-2009.4 fluxes to the 2002.16 flux scale. The cubic fit in Figure 7 has coefficients as in Equation (5) of a = 1.1536, b = −7.2839e–05, c = 1.0806e–08, d = −5.0274e–13, and e = 0 as a function of wavelength in Angstroms, while the final column of Table 5 has the evaluations of this cubic at the pivot wavelengths.

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Originally, the post-SM4 calibration was set by adjusting the post-SM4 gain to match the 2002.4 epoch photometry of 47 Tuc for F606W (Bohlin et al. 2011). Figure 7 and Table 5 show that an additional small shift in sensitivity by 0.997 improves the match at F606W, while the adjustments range from 0.996–1.007 for the other filters at 2009.4. The post-SM4 corrections at 2009.4 in Table 5, along with the average loss rate of 0.061% yr⁻¹, determine the post-SM4 photflam flux calibration for the time of the observation as detailed in Section 7.

After fully correcting the photometry for the three primary WD standards, their average C in relation to the synthetic predictions P (i.e., $\langle {\rm{C}}/{\rm{P}}\rangle$), is unity after making the calibration updates in the following section. Any systematic offset in the C/P for a cooler star is suggestive of errors in the bandpass response function. For example, Bohlin (2012) found that the bandpass function for F435W required a shift of the long wavelength cutoff of +18 Å at the WFC1-1K reference point, and there are lab measures for all the broad filters that show bandpass variations of this order. Figure 8 illustrates the SEDs of the stars used for bandpass adjustments along with the system throughput of the WFC broadband filters. Shifting the effective wavelength of a filter changes the relative response of hot to cool stars. For example, moving F435W (shortest wavelength black line in the lower panel) to longer effective wavelengths decreases the response to hot WDs (black line SED), while increasing the signal for the K star (purple line SED).

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For both F435W and F814W, there are now at least 14 measurements of C/P spaced over the WFC FOV for the K1.5III star KF06T2 with respect to the WD GD153 (Bohlin & Grogin 2015). Both stars are observed and differences are computed at each of the field positions, so the hot–cool star offsets are unaffected by any flat fielding errors. The F814W C/P fractional offset of the K star from the WD ranges up to ∼−1.5%, while the K star is offset by −0.005 (−0.5%) in C/P at the WFC1-1K reference point based primarily on three observations of KF06T2. Figure 9 illustrates the −16 Å bulk shift of the entire F814W bandpass transmission function, which corrects this offset of −0.005 at WFC1-1K. While the −16 Å correction is precise for KF06T2, the C/P value for the G star agrees within its $3\sigma$ error bar, the variable F star BD+17°4708 (Bohlin & Landolt 2015) is slightly low, and the less reliable M star VB8 moves from 1% low to ∼0.5% high. Over the full FOV, the maximum residual offset for KF06T2 with the new −16 Å shift becomes −0.01 (i.e., a $1\pm 0.4 \%$ error), which is now within our 1% precision goal for the ACS flux calibration for the first time. With a C/P based primarily on only three F814W observations of the K star at WFC1-1K and without the confirming observations spaced over the full FOV, an adjustment for a subpercent bandpass discrepancy is not justified. A bulk shift for F814W is better than shifting the usually suspect long wave cutoff because the photometry is relatively insensitive to the cutoff wavelength; an unreasonably large shift of ∼5 times the bulk shift of −16 Å is required to make the same adjustment of the K star photometry with respect to the WDs. The new bandpass reference files for F435W and F814W are in the ACS calibration database.

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The new observations and newly reprocessed data for F435W leave a small residual in hot versus cool star C/P values at the WFC1-1K reference point; a minor adjustment is required from the +18 Å long wavelength cutoff shift of Bohlin (2012) to +21 Å, as illustrated in Figure 10. Even though the maximum error is reduced, the F435W C/P offset between KF06T2 and GD153 still has a 5% range from −0.02 to +0.03 for 30 positions that are spaced around the FOV. This means that a bandpass for F435W that varies over the FOV is required to achieve a 1% photometric precision for stars of different color temperature. For HRC, the lack of robust data sets limit the validity of any bandpass adjustments.

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6.1. Alternatives to Bandpass Shifts

To explain the discrepant comparison of ACS photometry to STIS fluxes for cooler stars, Bohlin (2007) considered and dismissed alternatives to bandpass adjustments. In particular, out-of-band transmission errors are one alternative; Figure 11 shows the contribution to the observed ACS photometric signal as a function of wavelength for F435W in 20 equal wavelength bins across the full measured range of the filter transmission. The fractional contributions are computed from the CALSPEC SEDs for a hot WD G191B2B, a K star KF06T2, and the M star VB8 using the ACS system throughput R. The central three bins contain >99% of the F435W signals for all three stars, while the bin on the short wavelength shoulder of the response contains most of the remaining contribution. As expected, the out-of-band red leak is more than an order of magnitude higher for the K star than for the WD in the 12 points longward of ∼5900 Å, while VB8 is another two orders of magnitude larger. However, these 12 bins for KF06T2 are ∼10⁻⁶ on average for a total red leak fraction of ∼10⁻⁵, which is a factor of 300 below the 0.3% tweak achieved by updating the F435W filter edge shift from +18 to +21 Å. The ACS filter transmissions were all carefully measured in the lab before launch and have excellent out-of-band rejections. Bohlin (2007) showed a similar figure for F625W; the results for all eight broadband filters are similar, with total red+blue leaks of $\lt {10}^{-4}$ (i.e., $\lt 0.01 \%$ for K and hotter stars). The transmission of F850LP was not measured longward of the CCD QE cutoff of 11000 Å.

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7.1. Adjustments for Individual Filters

Following any correction for filter bandpass shifts, the average residual deviation of C/P from unity is corrected by multiplying each filter transmission by the average residual to correct the P values that are computed from the total system QE (i.e., R, which is the product of the throughput of all the HST+ACS mirrors, the filter transmission, and the detector QE). The C values are for the 1'' (20 pixel) photometry from the *_crj.fits files, as corrected for the pixel-area maps (PAMs), the CTE losses, and the EE. Table 6 contains these average C/P residuals; Figure 12 shows the final WFC average values (squares) for the three primary WDs at unity with the cooler stars, which are shown as colored symbols. There is no consistent significant trend for the corrections with wavelength that would mandate an update of the detector QE functions. The new filter throughputs include the correction for these residuals, which are then propagated to the final photflam values according to Equation (3).

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Table 6.  Filter Transmission Updates

	Residuals
Filter	WFC	3σa	HRC	3σa
F220W	...	...	0.988	0.005
F250W	...	...	0.990	0.005
F330W	...	...	0.991	0.003
F344N	...	...	0.992	0.005
F435W	1.001	0.002	0.992	0.003
F475W	1.003	0.002	0.996	0.004
F502N	1.001	0.003	0.997	0.007
F555W	1.004	0.002	0.998	0.001
F550M	1.000	0.002	0.995	0.005
F606W	1.006	0.002	1.000	0.002
F625W	1.006	0.002	0.999	0.004
F658N	1.007	0.003	1.003	0.009
F660N	1.018	0.007	1.010	0.008
F775W	1.008	0.002	1.001	0.001
F814W	0.994	0.002	1.000	0.003
F892N	1.006	0.004	1.015	0.009
F850LP	1.008	0.002	1.007	0.005

Note.

^aThe  3σ uncertainties of the residuals are errors-in-the-mean.

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The fully corrected photometry for the F, G, and K stars in the eight broadbands in Figure 12 is within the goal of 1% agreement, except for one measure of the variable star BD+17°4708, which is consistently low in all eight broadbands. The variable BD+17°4708 (Bohlin & Landolt 2015) is observed at different epochs for the ACS numerator values and the STIS denominator. The subpercent internal consistency shown in Figure 12 is achieved for the first time and is indicative of the consistency of the revised ACS flux calibration relative to STIS (B14).

7.2. Uncertainty in the Flux Calibration

7.3. QE Reference Files

7.4. Implications of Updated Calibration

For stellar types of K and hotter, Figure 12 demonstrates the achievement of the goal of 1% precision of the ACS/WFC flux calibration relative to the STIS standard stars for the eight well-observed broadband filters. Small adjustments of the filter transmission functions for F555W, F775W, and F850LP, similar to those for F435W and F814W, would bring the agreement for all eight filters to within 0.5% at the WFC1-1K reference point. However, before making those three new transmission corrections, confirming observations should be obtained like those mapping the FOV for F435W and F814W.

If precision photometry of the coolest stars of type M and later is important, then the WFC calibration for these types could be improved by more observations both with ACS/WFC and STIS. Action to augment the header keywords, solve the drizzle problem, and derive color dependent F435W flat fields is not yet scheduled. However, the new photflam flux calibration should be implemented by the time this article is published. The photflam data header keyword for the infinite aperture includes the changes with time of Section 5, which are encapsulated in the reference files acs_hrc_ccd_mjd_016_syn.fits and acs_wfc_ccd*_mjd_022_syn.fits, where the asterisk can be either of the identical 1 or 2 files. The revised filter throughput curves are named by filter and detector, and are also available as reference files, while EE values must be read from Tables 8 and 9 herein.

Thanks to J Mack for re-drizzling the jcr601081_drz.fits image and for suggesting that the WHT drizzle extent can be used to distinguish between good and bad drz photometry. Wayne Landsman provided the IDL photometry routine apphot.pro. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.

In principle, extracting photometry from the geometrically corrected drizzled *_drz.fits files is more straightforward than using the *_crj.fits files. There is no need to apply PAMs and the plate scale is constant at exactly 005 per pixel for WFC (0025 for HRC). However, the *_drz.fits files are problematic when combining pairs of images, and use of the default pipeline products requires extreme caution. The second extension of the drz product is the weight (WHT) image, which offers clues to the drizzle validity. If the pair of *_flt.fits images that are combined into the drz have slightly different or misaligned PSFs or even mis-matched backgrounds (Avila et al. 2015), a reduced WHT coincident with the core of the star usually indicates improper cosmic-ray (CR) flagging. A data quality (DQ) parameter can be defined as the percent drop from maximum to minimum WHT weight in the 3 × 3 set of pixels centered on the star. Setting a DQ = 13.1% limit provides a fairly good dividing line between good and bad drz photometry for pairs of images, and most of the errors are flagged without flagging many of the valid drz results. The crj photometry is validated by the small ${\sigma }_{20}\,\lt$0.5% in Table 3 for the baseline 20-pixel photometry.

Figure 13 compares the WFC drz with the baseline crj 1'' photometry of the standard stars as a function of the response in the peak pixel of each observation. There are 239 unflagged comparisons shown as the filled circles that are all within 1% of perfect agreement. However, the 95 flagged ratios are 28% of the total, are usually in error by more than 1%, and occasionally are in error by more than a factor of two. The crj pipeline product from the MAST data archives is not always perfect, even for the short standard star exposures where hot pixels are not a problem. Of the 334 exposures in Figure 13, one (jcga02081_crj.fits) requires special reprocessing with relaxed CR rejection parameters because the CR-split pair is slightly misaligned.

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One case of combining the jcr601lhq and jcr601liq flt files to make the jcr601081 crj and drz files is investigated in detail. The pipeline drz/crj photometry ratio is 0.91, while the peak is 79,000 (open red circle in Figure 13). Reprocessing this observation with relaxed drizzle constraints for cosmic-ray rejection of driz_cr_scale = (1.5, 1.2), rather than the pipeline default (1.2, 0.7) values (Gonzaga et al. 2012), produces a revised ratio of unity (filled red circle in Figure 13). The ACS drizzle product could be much more useful to the science community by a relaxation of the pipeline parameters that would bring drz photometry into agreement with the robust crj results.

The ACS/CCD flux calibrations at the WFC1-1K reference point for the good, unflagged WFC drz photometry are equivalent to the crj calibrations, except for the small, three-pixel radius where the drz photometry and EE are systematically ∼0.5% smaller. The average 1''  (20 pixel) drz photometry for the three WDs is the same as the crj results within 0.1%, and the drz flux calibration is the same as the crj calibration in Table 6 to 0.1%. Except for the 0.5% difference for the three-pixel radius, any systematic difference between drz and crj WFC photometry at the WFC1-1K reference point is less than the uncertainty, and the crj calibration is accurate for drz results. At other locations in the FOV, the sparse data set combined with the problematic drz results prohibit reliable measures of any differences between drz and crj EE.

Tables 8 and 9 include EE values for 12 aperture radii as computed according to the quartic fitting procedure of Section 4.3.