A Position-Dependent Error Correction

Determining the level of broadening in the CMD requires accurate photometry, so it is important to account for any position-dependent instrumental effects that might lead to errors in the measured colours. These might be caused by differential reddening, inadequacies in the PSFs, telescope breathing, or inadequacies in the charge-transfer efficiency correction built into the HST pipeline andDOLPHOT.

Charge transfer efficiency (CTE) is a measure of how well the CCD is able to move charge from one pixel to the next during the chip readout phase. A perfect device would transfer all of the charge and would have CTE of 100%. In reality, defects in the silicon cause charge to be trapped momentarily in certain pixels and released some time (microseconds to seconds) later. Some defects may be intro-duced during the manufacturing of the device, but more develop over time as a result of radiation damage. HST CCDs are particularly susceptible to CTE degrada-tion, because HST’s low-Earth orbit frequently crosses through parts of the Earth’s Van Allen radiation belt. Moreover, the CTE degradation in HST’s newest instru-ment, WFC3, is considerably worse than anticipated. This may be as a result of the last few years’ increase in solar activity, resulting in an increase in solar wind strength and more charged particles in the magnetosphere.

CTE problems manifest themselves in two ways. Firstly, they cause a loss in source flux, so sources falling on affected pixels appear fainter. Secondly, the de-layed release of charge gives erroneously high flux readings for pixels further from the CCD chip amplifiers, making sources appear to have tails. Figure 6.1 shows an example of the visual effect of CTE problems.

The amount of source flux lost due to CTE inefficiencies depends on three major factors: pixels further from the amplifiers are more prone to problems than those near to the amplifiers, because the charge must transfer via more pixels, so is more likely to encounter a trap; fainter sources are affected more than bright sources, because they lose proportionally more of their flux; images with lower background flux suffer more than those with high background, because a higher background flux is more likely to fill some of the charge traps, reducing the loss of source flux during readout.

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Figure 6.1: The effect of CTE inefficiencies. This is part of a 30 s, HST/ACS/WFC exposure of the GC 47 Tuc (image ja9bw2ykq flt.fits). The trails extending upward from the stars are due to imperfect CTE (Anderson & Bedin, 2010).

In this investigation, CTE problems are far more obvious in the NUV and U-band images than in the V- and I-band ones. Moreover, the V- and I-band images are taken with the ACS, for which the level of CTE is well understood and well-established corrections are available.² Furthermore, the V- and I-band images were taken at almost the same alignment, so sources positioned farthest from the amplifier (which are, therefore, most prone to flux loss) in V-band images are also farthest from the amplifier in the I-band images³. The NUV and U-band images, on the other hand, were taken with the WFC3, for which CTE problems are less well understood and are poorly accounted for by current correction algorithms. The images taken with the U-band filter are aligned almost perpendicular to the NUV images. This means that, unlike in the V- and I-band case, sources are affected differently in the two data sets.

2Note that a new version of the CTE correction for the ACS/WFC has been released since this investigation was completed. The new version is based on work by Anderson & Bedin (2010) and Ubeda & Anderson (2012), and includes a correction algorithm which takes into account pixel-based CTE, and time and temperature dependent CTE losses.

3I note that there is no reason to assume that the flux loss in the two filters is the same; merely that there is likely to be a spatial trend in the proportion of flux lost in two filters at the same alignment.

164 Chapter 6. NGC 6752: The Search for Broadening in the Main-Sequence

1000 2000 3000 4000 (a)

1000 2000 3000 4000

1000 2000 3000 4000 (c)

X [pixels]

1000 2000 3000 4000 (b)

1000 2000 3000 4000 1000

2000 3000 4000 (d)

X [pixels]

Figure 6.2: Before and after the catalogues are corrected for position-dependent instrumental colour effects. Panel (a) shows the X, Y positions of MS sources from the NUV - U CMD, before the correction algorithm is applied. Sources are coloured red and blue depending on their CMD positions relative to an MSRL.

The red and blue sources are not distributed isotropically; areas of almost entirely red or blue can be seen. Panel (b) shows the same thing, for the V- and I-band MS sources. Panels (c) and (d) show the positions of the red/blue NUV and U-band, and V- and I-band sources, respectively, after the colour correction algorithm has been applied. The red and blue sources are much more evenly distributed.

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Consider, for example, a source positioned far from the amplifier in the NUV images. This source will appear fainter than it should in the NUV measurements. It is not necessarily among the most affected sources in the U-band images, however, so may lose less flux in U-band, and appear red in the CMD. Sources most prone to flux loss in the U-band images, on the other hand, appear fainter in the U-band, but not necessarily in the NUV, so appear blue. Furthermore, the NUV exposures are fairly short (120 s each; see Table 6.1), so there is a low background (. 10 counts), and the MS sources considered in this investigation are relatively faint (.

700 counts), making these images susceptible to CTE effects. The U-band images are longer (348 s each), with higher background and source flux (8 − 30 and 5000 − 60000 counts, respectively), so CTE problems have less impact than in the NUV case, but the effect is still not negligible.

In the top panels of Figure 6.2, sources are coloured red or blue depending on their position relative to a main-sequence ridge-line, to demonstrate the different ways that CTE and other position-dependent problems manifest in the two CMDs.

In the NUV and U-band case (panel (a)), there is an excess of red sources along the near-horizontal axis (the gap along this axis is the chip gap in the NUV images), and a large population of blue coloured sources along the near-vertical, U-band chip gap. In the V- and I-band case (panel (b)), the pattern is not so obvious, but it is still clear that something is affecting the colours and creating excessively red and blue areas.

Regardless of the reason for the position-dependent colour variations shown in Figure 6.2, an empirical, star-by-star correction can be applied to improve the mea-sured colours. The procedure, which follows Milone et al. (2010), is as follows.

The steps are illustrated in Figure 6.3.

1. Refer to panel (a) of Figure 6.3.

Use the overall V - I CMD to plot a main-sequence ridge-line (MSRL) by finding the median colour in successive, narrow magnitude bins. Refine the result using sigma-clipping, performed using the perpendicular distance from the ridge-line to each source. This ensures that the whole MSRL is treated equally, regardless of the direction of the MSRL at a given magnitude, to give as precise a ridge-line as possible.

2. Refer to panel (b) of Figure 6.3.

Select a ‘target’ source to be corrected. Calculate the distance (defined as difference in colour, rather than perpendicular distance) from this source in the (overall) CMD to this ridge-line.

166 Chapter 6. NGC 6752: The Search for Broadening in the Main-Sequence

3. Refer to panel (c) and (d) of Figure 6.3.

From the ‘target’ source, find the nearest 50 − 100 MS stars (on the image) that are

• ‘well-behaved’ (i.e. the DOLPHOT output shows a high signal to noise, very small photometric error, and good values for the χ, sharpness, crowding and roundness parameters),

• within ± 2 I-band magnitudes of the ‘target’ source,

• within 250 pixels (10^′′) of the target source. This leads to some ‘target’

sources having< 100 ‘calibration’ sources (but all ‘target’ sources have at least 50 ‘calibration’ sources).

4. Refer to panel (d) and (e) of Figure 6.3.

Find the mean distance in colour from these sources to the MSRL.

5. Refer to panel (f) of Figure 6.3.

Correct the ‘target’ source’s colour by this amount.

6. Choose the next source to be used as a ‘target’ source and repeat steps 2 − 5.

A similar process is carried out for sources in the NUV - U CMD, with two changes:

• Due to the more exaggerated change in the width of the MS spread with mag-nitude (see Figures 4.1 and 6.4), I limit the sources to those within ± 0.7 U-band magnitudes of the chosen source.

• The lower stellar density in the NUV and U-band mean that I use the nearest 10 − 50 MS stars to calculate the correction factor in these wavebands.

Experiments with different, reasonable, magnitude limits gave consistent results, as did using the median distance for the colour correction instead of the mean.

As the groups of images are taken at almost identical pointings, creating separate MSRLs for the Group 1 and Group 2 images, and running the correction algorithm on each group independently of the overall image, made little difference.

The lower panels of Figure 6.2 show the position of red and blue sources after the colour correction algorithm has been applied. The distributions of red and blue coloured sources are much more even in these panels, indicating that the position-dependent colour gradients have been reduced.

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6.4 The Search for MS Broadening in the NUV - U