Photometry

Photometry is the measurement of light – the brightness of stars.  Very high precision is needed because the transit of a planet across the face of its star will dim the light by only a tiny amount – usually 2% or less.  Of the PEST co-discoveries so far, half have transit depths of less than 1% (or 0.01 mag = 10 mmag).

We do photometry on a star to obtain a light curve.  This charts the brightness of the star with time.  An exoplanet transit has a characteristic shape – a flat-bottomed dip (‘ingress’) and rise (‘egress’), as the planet starts to block a bit of its star’s light, travels across the face of the star, then exits.

Transit of KELT-1b, and light curve, below. Image credit: Jason Eastman, KELT.

PEST photometry follows the following steps:

  1. Images are acquired through the telescope and saved to the processing computer.
  2. These images are reduced.  Reduction is the process of calibrating images to correct for;
    • noise – the grainy spots you get when you take a long exposure with a digital camera.
    • uneven illumination – the corners of an image are darker than the centre, or there may be some dust on the sensor.
    • uneven pixel response – each pixel in a CCD outputs a number corresponding to the amount of light it receives.  But CCDs are not perfect and there will be some variation even with completely even illumination.
  3. The brightness of every star on every image is measured.  There may be a thousand stars in each PEST image, and hundreds of images per observing run.  That’s a lot of data.
  4. The target star’s brightness is calculated relative to a set of reference stars (the ‘ensemble’) and its light curve plotted.  This corrects for variations in brightness that are not due to the star itself.  For example as a star rises we see it through less air and it will appear brighter (this is why the sun is hottest at mid-day).

Typical PEST image with the star hosting HATS-17b circled. Image Credit: TG Tan.

 

The PEST light curve contributing to the discovery of HATS-17b. The dimming was just 0.5%. Image Credit: TG Tan

Technical details

Reduction and photometry are done using the software package C-Munipack ver. 2.1.7 running on linux (ver. 1.1.27 running on Windows prior to March 2015).

Raw flat frame images are bias subtracted then median combined to obtain a master flat frame.  Sky flats from the dusk preceding, or dawn succeeding the observations are used where possible, otherwise the latest available master flat is used.  The number of raw flat frames combined into master is usually about 100.

I maintain a library of master dark frames for different exposure times.  Master dark frames are renewed about every month.  Each master dark is an average of 40 raw dark frames.

The science frames are dark subtracted, then flat field corrected.  C-Munipack then performs aperture photometry on each detected star in the field.  3 radii are specified – for object, inner sky and outer sky apertures.  The object aperture (usually between 5 and 8 pixels) is selected based on FWHM of the image, but is kept constant for a particular target over multiple observations sessions.  The inner and outer sky radii are kept constant at 30 and 60 pixels.

C-Munipack then registers each image to a selected (good quality) reference image.  On this reference image, several high SNR stars have been selected (‘reference stars’), and instrumental magnitudes and errors for these stars are written to a text file, together with observation date.  The date may be in JD, or HJD.

This output text file is then post-processed by a Python script called Magpy, which I wrote, to produce differential magnitudes and errors for all reference stars.  Magnitudes are calculated with respect to a set of ensemble stars selected from amongst these stars.  Each star’s contribution to the ensemble is weighted inversely to the variance of its measured instrumental magnitudes – i.e. the larger the scatter of a star’s measured magnitude, the less its weight in the ensemble.  The resultant error of the ensemble is also calculated at this stage.  Magpy is able to auto optimise the selection of ensemble stars.  Light curves are produced for the target star as well as all reference stars so that ensemble stars can be checked for variability/ high noise.  No de-trending is done.  Magpy is based on the Everett & Howell paper referenced below.

Reported magnitudes are shifted onto a magnitude scale relative to a nominated COMP star.  If the magnitude of COMP in the passband of the observation is known, this results in the magnitudes reported being on that standard magnitude scale (albeit un-transformed).  However in most cases we are more interested in changes in magnitude, rather than accuracy with respect to a standard scale, so I usually use Vmag for COMP, whereas the passband of the observations might be different, e.g. Rc.

Errors are calculated as being the addition in quadrature of the errors for the target and the ensemble, with a term added for atmospheric scintillation that is a function of exposure time and telescope aperture.  I use the formula for scintillation by Radu Corlan – see the section “Bright Star Photometry” here.  The scintillation term is very small for exposure times longer than about 60s.