ULTRACAM Pipeline processing

Calibration frames

The first stage in the analysis of the WASP-33 data was to calibrate the science data and then perform aperture photometry on the resulting frames to obtain the

required flux measurements from the target and the comparison stars.

The first step in the calibration involved creating master bias frames. Bias frames are 0 s exposures taken to measure the offset signal applied during the readout of the CCDs. Due to the fact that the science data was taken in a windowed mode, whilst the flat field frames were not, separate bias frame sets were taken for these two cases (since the bias signal is expected to be different for these different modes). In both cases, separate bias frame sets were taken for each of the ULTRACAM channels, resulting in 6 separate bias frame sets, each containing 101 individual frames. Master bias frames were created for each set by averaging the individual frames using a 4σ clipped mean. This process reduces the effects of read out noise on the master bias. The master biases were then subtracted from individual flat field and science data frames to correct for the bias offset.

Master flat field frames were then created, again one for each channel of the instrument. Flat fields are frames that have been exposed to an illumination that is constant across the field-of-view. Variations in the pixel signals in these frame are then interpreted as variations in the pixel response (e.g. due to varying quantum efficiencies between pixels). Thus, by dividing the science frames by a flat field one can remove the pixel response variations from the science data. The flat fields in this study were measured by taking multiple images of the sky near the zenith around the time of sunset, which provides a suitably evenly illuminated field. Flats were also taken at sunrise, but they were affected by clouds and were not used here.

Master flats were created for each channel in the following way: first, the relevant bias frame was removed from each of the images. Then frames with a mean count level above or below specified limits were removed. The upper limits were set so that non-linear detector effects were avoided, while the lower limits were set to avoid needlessly low counts and significant stellar contamination. These flats were then split into groups of 11 frames with similar mean levels. Within each group the individual frames were normalised to their mean levels and a ‘group master’ was created using median pixel values. Since the field-of-view was continually being rotated with respect to the sky during the flat exposures, this process should have removed any stars present in the flats as they would illuminate different pixels in each frame. The various ‘group master’ frames were then scaled to the mean level of their input groups and added together. The resulting frame was then normalised to its mean level to create the master flat. The final steps here assign a higher weighting to the brighter flats (which have smaller fractional noise) than the fainter flats, giving a better quality master flat.

Setting up apertures

With the calibration frames made, the apertures used for aperture photometry on the science frames were then set up. Stacked images, using 100 individual frames, were created for each channel and apertures were specified on these images for the three stars in the field of view: WASP-33 (V = 8.1), a bright comparison star (V = 9.4, referred to here as ‘comparison 1’) and a fainter comparison (V = 11.3, ‘comparison 2’). Moffat profile fitting was carried out on each of these stars (see Section 2.3.1), in each channel, to provide an initial centroid position in each case.

At this stage I decided on the sizes of the sky annulus radii, which were the same for each object and each channel. The inner sky radius was chosen to be at 35 pixels, such that the sky estimate was not affected by the wings of the defocussed stellar PSFs. This was assessed using visual inspection of the frames and the PSFs from Moffat fitting. The outer sky radius was set such that the uncertainty in the sky estimate did not give a significant contribution to the overall photometric error. However, the outer radius could not be too large otherwise large scale variations in the sky across the CCD could have biased the sky estimate. A value of 50 pixels was chosen to provide a good balance between these two considerations.

Aperture photometry

With the initial aperture positions specified, I ran thereduceprogram (see Section 2.3.1) to extract time-series information from the science data frames, most notably flux measurements of the three stars in each of the three ULTRACAM channels. Moffat fitting was carried out here to determine the centroid positions of each star, as described in Section 2.3.1 (and equation 2.6). A number of user specified parameters could be chosen to customise the running of this program. Some of the key parameter values used here were:

rinner = 35 pix Inner sky radius

router= 50 pix Outer sky radius

profile fit fwhm = 14 pix Initial FWHM used in Moffat profile fitting

profile fit beta = 18 pix Initial beta parameter used in Moffat profile fitting profile fit hwidth = 25 pix Half-width of box used for Moffat profile fitting Customisation of the last 3 parameters here was important as their values were chosen to reflect the highly defocussed nature of the PSFs (which is not typical for ULTRACAM observations).

0 50 100 150 200 250 300 350 S NR ( re d cha nne l) 0 50 100 150 200 250 S NR ( gre en cha nne l) 15 20 25 30 35 40 r_source [pixels] 0 50 100 150 200 SNR (b lue cha nne l)

Figure 5.3: Signal-to-noise ratios for a typical image from the red (top panel), green (middle) and blue (bottom) ULTRACAM channels. The signal-to-noise is maximised in these channels atrsource= 20, 18 and 18 pixels, respectively. The source aperture

size I used for the aperture photometry wasrsource= 25 pixels (marked by the ver-

tical dotted lines), which was chosen to avoid potential systematic effects associated with using a smaller source aperture.

A key choice in the aperture photometry reduction was the size of the source aperture radius,rsource. I used fixed apertures throughout, with a size chosen such it

contained most of the stellar flux, without the background significantly contributing to the photometric error budget. Figure 5.3 shows the signal-to-noise ratios for a typical image in each of the three ULTRACAM channels, as a function of source aperture radius. Maxima in the signal-to-noise ratios occur atrsource= 18–20 pixels.

However, after visual inspection of the images and WASP-33’s radial flux profile, I decided to use a slightly larger source aperture, withrsource= 25 pixels (marked in

Figure 5.3 with the vertical dotted lines). This was done to ensure that systematic effects (e.g. flux spilling out of the aperture due to variable seeing) were minimised, whilst still maintaining a decent signal-to-noise level. This source aperture size was used for each of the three stars in each of the three ULTRACAM channels.

Using this set up, the times, centroid positions, fluxes, flux errors and sky background estimates were extracted for each star in each channel, as described in Section 2.3.1. Before the science frames were evaluated, the calibration frames, described in earlier in this section, were applied to the science data by subtracting the master bias and then dividing by the master flat.