Photometric CTE Corrections

Updated coefficients and accuracy

• Calibration Data and Derived Coefficients

  The target of the calibration program is a field ~7’ West off the core of the globular cluster 47 Tucanae. Images are taken using two different filters (F502N and F606W) and with a range of exposure times (between 30s and 400s), in order to sample at least five different background levels. For a more extensive description of both the characteristics of the datasets and the method for the data analysis we refer the user to ACS ISR 2012-05. In the following we summarize the main steps and the latest results.

  Point source photometric CTE losses are described by the following model:

  \(Dmag2000 (MJD, F, SKY) = a_1 Log(SKY) * MJD * 1/Log F + a_2 MJD * 1/(Log F)^2 \\ + a_3 1/(Log F) + a_4Log(SKY) * 1/(Log F)^2 + a_5 Log(SKY) * Log F + a_6 1/(Log F)^2 \\ + a_7 Log F + a_8Log(SKY) + a_9 \)

  The model is normalized at Y=2000 pixel transfers; therefore, the value of Dmagy can be obtained using DmagY = Dmag2000 * (Y/2000). Y is the distance (in pixels) of the center of the measured point source to the amplifiers, MJD is the modified julian date, SKY is the local background level, and F is the star brightness in e- within a 3 or 5 pixel radius aperture. For a star located on the WFC2 chip, Y is simply the y coordinate of the point source in the FLT frame. For WFC1, Y = (2049-y), where y is the y-coordinate.

  The values of the coefficients for a 3 pixel aperture radius derived using data from Cycle 17 through Cycle 32 are reported below:

  Estimate	Std. Error	Coefficient
  \(-1.593782e^{+00}\)	\(6.947025e^{-02} \)	\(a_9\)
  \(1.368024e^{+00}\)	\(5.680310e^{-02}\)	\(a_8 \)
  \(1.021886e^{-01}\)	\(8.415726e^{-03}\)	\(a_7\)
  \(-5.147439e^{+01}\)	\(5.262972e^{-00}\)	\(a_6\)
  \(-1.067867e^{-01}\)	\(6.515256e^{-03}\)	\(a_5\)
  \( 3.793302e^{+00}\)	\(1.055782e^{-01}\)	\(a_4\)
  \( 6.349856e^{+00}\)	\(1.720214e^{-01}\)	\(a_3 \)
  \( 8.412415e^{-04}\)	\(8.570207e^{-06}\)	\(a_2 \)
  \(-8.623534e^{-05}\)	\(2.587255e^{-06}\)	\(a_1\)

   

  The values of the coefficients for a 5 pixel aperture radius derived using data from Cycle 17 through Cycle 32 are reported below:

  Estimate	Std. Error	Coefficient
  \(-2.751016e^{+00}\)	\(1.037224e^{-01} \)	\(a_9\)
  \(1.729924e^{+00}\)	\(7.716899e^{-02}\)	\(a_8 \)
  \(2.168872e^{-01}\)	\(1.147010e^{-02}\)	\(a_7\)
  \(-6.192969e^{+01}\)	\(8.125789e^{-01}\)	\(a_6\)
  \(-1.505302e^{-01}\)	\(8.165219e^{-03}\)	\(a_5\)
  \(4.030754e^{+00}\)	\(1.771554e^{-01}\)	\(a_4\)
  \(9.993043e^{+00}\)	\(2.847983e^{-01}\)	\(a_3 \)
  \(9.527729e^{-04}\)	\(1.254937e^{-05}\)	\(a_2 \)
  \(-9.926297e^{-05}\)	\(3.801887e^{-06}\)	\(a_1\)

   

  For a CTE correction cookbook, please refer to Chiaberge, M. ACS ISR 2012-05.

• Expected Accuracy

  The updated formula was tested for different levels of background and stellar flux. Stars in the field range from ~100 to ~100,000e^- (measured within 3 pixel aperture radius on drizzled images), depending on the exposure time. The global accuracy is better than 3% for all background levels. Note that the global accuracy is measured averaging out all stars in the calibration field. 

  In these figures, we show magnitude loss referenced to Y ≈ 2000 (i.e., at the far edge from the amplifiers; “worst case”) as a function of stellar brightness, for 3‑ and 5‑pixel aperture photometry (as labeled) and for two background levels (6 and 45 e⁻ pix⁻¹). Red points are the measured CTE losses from uncorrected photometry; because loss scales approximately linearly with Y, the loss at the chip center (Y ≈ 1024) is about half the plotted value. Green and purple points are the residuals after applying the pixel‑based and the photometric model corrections, respectively (positive = under‑correction, negative = over‑correction). These comparisons illustrate the accuracy of the model correction across brightness and background, relative to the measured losses and the pixel‑based approach. The photometric model has a residual standard error of 0.04 mag for both 3- and 5-pixel apertures. The resulting correction is accurate to better than 3% across most of the explored sky-background and brightness range at all post-SM4 epochs.