Photometric Simulation of Transiting Extrasolar Planets

1
Photometric Simulation of Transiting Extrasolar
Planets
Introduction
Results

Observations for the EXPLORE Project, a deep
search for transiting extrasolar planets, are
well underway, with preliminary results from the
first data run released. Continuing analysis of
the data will include completeness corrections
for planet detections, or limits on types of
planetary systems that are not detected. One
requirement for this statistical analysis is
knowledge of the experimental detection limits.
To probe these bounds, we attempt to create
photometric simulations of transits which mimic
the noise characteristics of the actual data,
including the effect on the photometry of image
jitter and variations in image PSF, by crafting
our simulations at the image level. We present
here results of preliminary simulations. We
create our simulations by modifying actual frames
from the EXPLORE II data, a 14 night observing
run using the wide field CFH12K camera at CFHT.
The simulated images are then reduced to light
curves using the same photometry pipeline
utilized for the actual data. We then carry out
blind tests of our ability to retrieve evidence
of simulated transits.
Three members of the EXPLORE collaboration
(those who scanned the actual data) scanned the
simulated light curves, then submitted their
guesses for which light curves contained
transits. The guesses were scored, and the
results (correct guesses and missed transits)
binned as a function of the light curves rms and
the transits depths. From their results, the
EXPLORE collaborators were seen to be roughly
equally conservative in their guesses, making
almost no incorrect guesses. Because they were
similar, and because all three scanned the actual
data, detection statistics were derived based on
the average detectability of simulated transits.
The results form a two-dimensional surface (at
right), which gives the fraction of times that an
average EXPLORE collaborator will discover a
transit, as a function of signal and noise. In
this set of simulations, the signal strength was
varied by changing the transit depth, and the
noise was simply the rms (magnitudes) of the
photometry. As expected, the probability of
transit detection increases with greater signal
and decreases with greater noise.
By B. L. Lee (U. Toronto) H. K. C. Yee (U.
Toronto) G. Mallén-Ornelas (Princeton) S.
Seager (IAS/DTM-CIW)

• Method

• Pick a set of well-characterized template stars
  which appear on a series of actual EXPLORE data
  frames.
• Copy each star to a number of new locations in
  sky coordinates (using a sinc-shift algorithm to
  resample to the pixel grid), preserving the noise
  and image shape characteristics appropriate to
  each new location.
• Multiply each simulated star thus created by the
  appropriate value on a light curve, to simulate
  variability.

Left Transit detectability as a function of
signal and noise. Above Two slices through the
surface at constant rms. Below left Two slices
through the surface at constant
detectability. Below Example of photometric
quality of the EXPLORE survey.
Preservation of photometric noise characteristics
Original data
The two images at left demonstrate the
consistency of the sky background before (top)
and after addition of a simulated star. Below,
observe that the light curve of a simulated star
as produced by EXPLOREs photometry pipeline is
not easily distinguished from the light curves of
four real stars of similar brightness.
Data copied star
x light curve
Data scaled star
For the actual EXPLORE data, the light curves
for a single star, spanning multiple nights, are
placed on a single page and scanned for transits
by eye. To minimize possible human biases, we
must emulate this tabular format in our
single-night preliminary simulations, using
stacks of single-night light curves from several
different simulated stars (see example at right)
to mimic the appearance of true multi-night
single star data.
For sure detection of simulated transits of 1
depth, very high quality light curves with
0.0025 mag rms were required (above left).
These high quality light curves exist (above
right), so our preliminary simulations show we
can achieve 100 completeness, for our best light
curves, in detecting transit depths as small as
1. Our preliminary results have shown that by
using our copy-and-paste image-based transit
simulation, we can derive the selection function
for EXPLOREs transit surveys. Future
simulations will come even closer to reproducing
all the conditions that influence transit
identification in the real data. In particular,
the introduction of multi-night light curves and
more sources of non-transit variability should
improve the validity of our derived detection
limits.