Three methods of creating light curves from CCD data

An explanation follows of three methods used to extract specific stellar magnitude infor- mation from CCD data. All of these methods only are used after the corrections of the bias frames and flat frames. Aperture photometry is conceptually an easy way to measure the brightness of each star by summing all the light within a circle of pixels. Point Spread Function (PSF) fitting is a method to attempt to model each occurrence of a star as a PSF. Differential Image Analysis (DIA) is the method used in this thesis, and consists of measuring the differences between two images to precisely determine the light from a star.

Aperture photometry

Aperture photometry essentially defines a circular aperture around the star and cumula- tively adds all the light from within those boundaries to determine the total light from a star. This relatively simple concept can have more complicated details, such as the use of feathering or anti-aliasing at the edge in order to only take some brightness information from distant pixels. One of the drawbacks of the aperture photometry method is that some crowded fields might have many stars within the desired aperture size; that is, the light measured might be from two nearly indiscernible stars instead of one.

Point spread function fitting

PSF fitting is another way to measure the light of the stars in a systematic way, in order to produce light curves. In PSF fitting, a preliminary identification of stars is made by setting a high threshold and recording all those points that are sufficiently higher than the sky background. Then a function is fit to each of those stars which attempts to describe the way the light is blurred around the central point of maximum light. The function is assumed to remain the same shape on all the stars on a given frame, though the scaled size of the function might change with a variability of starlight. Thus, changes in a star’s

brightness can be quantified.

A benefit of PSF fitting is that the function fitted to each star can be used to subtract the stars from the science frame if the function accurately fits the data. Then, more stars can be identified with a lower threshold for brightness, which can provide more data points and make the function a better approximation of the actual star blurring. PSF fitting is more complicated, but gives better results than simple aperture photometry.

Difference image analysis

A final way the images can be reduced to light curves is through difference imaging analysis (DIA), which is in some ways an extension of PSF fitting. DIA specifically targets the changes in magnitude of the observed stars as the most important measurable quantity. The absolute magnitude is helpful, but not as helpful for finding variables and eclipsing systems as an accurate determination of the difference over time of the stars’ brightness (Alard & Lupton 1998).

The process begins with a reference image which is built by averaging several aligned science frames. This reference image has a better signal-to-noise ratio than any individual frame. This reference frame is then subtracted from each of the individual science frames in order to produce residual images of the differences between the frames. A constant star will have the same brightness at all times, so the image subtraction should leave only noise at its position. However, a variable star will grow dimmer or brighter and the residual image will either have a bright bump or a dark dimple depending on the brightness of the star in the reference images.

This residual image is then used with the PSF fitting method to determine how much each star has changed since the reference image (where aperture photometry determines the magnitudes of each star). The benefit of DIA is that it more fully subtracts the blended stars which are often found in a crowded field. Whereas PSF fitting alone will only be able to correct for blending perfectly if the function is a perfect description of the light blurring, image subtraction relies much more on simply using the data to find the changes in brightness. The difficult part of DIA is creating a convolution kernel to blur the science

frames so the reference frame will have the same quality of observation as each science frame. This allows the images to be subtracted successfully (Alard & Lupton 1998).

A drawback of the DIA method is that it must be possible to align the images for subtraction. On a small field this is usually not difficult, but large fields present some problems, largely due to atmospheric refraction. Large fields of view can have significantly different air masses in different locations on the chip, due to the differing amounts of atmo- sphere the light must travel to the telescope. This can shift the positions of stars noticeably depending on the colour of the stars. These and other problems will not necessarily negate DIA as a method of reducing large field images, but will increase the complexity of using it.