Detection of period variations in extrasolar transiting planet
OGLE-TR-111b.
1
Rodrigo F. D´ıaz
1
, Patricio Rojo
2
, Mario Melita
1
, Sergio Hoyer
2
, Dante Minniti
3,4
,
Pablo J.D. Mauas
1
,Mar
´
ia Teresa Ru
´
iz
2
ABSTRACT
Two consecutive transits of planetary companion OGLE-TR-111b were ob-
served in the I band. Combining these observations with data from the literature,
we find that the timing of the transits cannot be explained by a constant peri-
od, and that the observed variations cannot be originated by the presence of a
satellite. However, a perturbing planet with the mass of the Earth in an exterior
orbit could explain the observations if the orbit of OGLE-TR-111b is eccentric.
We also show that the eccentricity needed to explain the observations is not ruled
out by the radial velocity data found in the literature.
Subject headings: planetary systems — stars: individual (OGLE-TR-111)
1. INTRODUCTION
The observations of transiting extrasolar planets have produced some of the most in-
teresting results in the study of other planetary systems. Their orbital configuration have
permitted the first direct measurements of radius, temperature, and composition (Swain
et al. 2008; Harrington et al. 2007, and references therein). All of these parameters are
critical to constraining the theoretical models which are necessary to understand the physics
of the exoplanetary interiors and their evolution (e.g. Fortney 2008).
1
Instituto de Astronom´ıa y F´ısica del Espacio (CONICET- UBA) Buenos Aires, Argentina; rodri-
go@iafe.uba.ar.
2
Department of Astronomy, Universidad de Chile, Santiago, Chile.
3
Department of Astronomy, Pontificia Universidad Cat´olica, Casilla 306, Santiago 22, Chile.
4
Specola Vaticana, V-00120 Citta del Vaticano, Italy.
1
Based on observations collected with the Very Large Telescope a t Paranal Observatory (ESO Programme
278.C-5022).
–2–
It has been further realized that the presence of variations in the timing of transits can be
attributed to otherwise undetectable planets in the system (see, for example, Miralda-Escud´e
2002; Holman & Murray 2005; Agol et al. 2005; Heyl & Gladman 2007; Ford & Holman 2007;
Simon et al. 2007). Deeg et al. (2008) and Ribas et al. (2008) reported indirect detections of
unseen companions by monitoring eclipse timing of the binary stellar system CM Draconis
(1.5 M
J
to 0.1 M
candidate) and variations in the orbital parameters of the planetary system
around GJ 436 (5 M
⊕
companion), respectively. However, this last case has been recently
argued against by Alonso et al. (2008). Besides, recently-discovered transiting planets (Pont
et al. 2007; Udalski et al. 2008) exhibiting shifts in their radial velocities are promising new
candidates to search for variations in the timing of their transits. On the other hand, Steffen
& Agol (2005) found no evidence of variations in the timing of transits of the TrES-1 system,
after analysing data for 12 transits. Also, after monitoring 15 transits of the star HD 209458,
Miller-Ricci et al. (2008) were able to set tight limits to a second planet in the system.
Here we report a significant detection of variability in the timing of the transits of
extrasolar planet OGLE-TR-111b (Pont et al. 2004) and discuss its possible causes, including
a second unseen planet OGLE-TR-111c.
In a previous work (Minniti et al. 2007), we reported a single transit observed in the V
band which occurred around 5 minutes before the expected time obtained using the ephemeris
of Winn et al. (2007, hereafter W07) , but the result was inconclusive since it only had a
2.6-σ significance. In the present work we analyse data of two consecutive follow-up transits
of the same planet.
Section 2 presents the new data and the reduction procedures, in Section 3 we describe
the technique used to measure the central times of the transits. Finally, in Section 4 we
present our results and discuss their implications.
2. OBSERVATIONS AND DATA REDUCTION
We observed two consecutive transits of planetary companion OGLE-TR-111b in the I
band with the FORS1 instrument at the European Southern Observatory (ESO) Very Large
Telescope (VLT). The observations were acquired during a Director’s Discretionary Time
run on service mode during the nights of December 19 and December 23, 2006. Since the
orbital period of OGLE-TR-111b (P =4.01444 days) is almost an exact multiple of Earth’s
rotational period, those were the last events visible from the ESO facilities in Chile until
May 2008.
FORS1 is a visual focal-reducer imager who had a 2048x2048 Tektronik CCD detector
–3–
and a pixel scale of 0.2 arcsec/pix. For the observations, a nearby bright star was moved out-
side the field of view, leaving OGLE-TR-111 near the center of the north-eastern quadrant.
The chosen integration time of 6 seconds was the maximum possible to avoid saturation of
the star in case of excellent seeing. A total of over 9 hours of observations were obtained
during the second half of both nights. During the first night the seeing remained stable below
0.6”, but it oscillated between 0.6” and 1.4” during the second night. Observations finished
near local sunrise producing a non-centered bracketing of the events and an additional source
of scatter as the sky background increased near sunrise.
We used the ISIS package (Alard & Lupton 1998; Alard 2000) to compute precise d-
ifferential photometry with respect to a reference image in a 400×400 pix sub-frame. The
reference image was obtained combining the 10 images with best seeing, which produced
an image with FWHM ≈ 0.46 arcsec. The resulting subtracted images were checked for
abnormally large deviations or means significantly different from zero; an image from the
first night and three images from the end of the second night were discarded in this way,
leaving a total of 488 images.
Aperture photometry was performed on the difference images using IRAF DAOPHOT
package (Stetson 1987), which was found to give better results than the ISIS photometry
routine phot.csh (for a detailed description of the ISIS routines see Hartman et al. 2004). In
agreement with Gillon et al. (2007), we found that the scatter increased rapidly with aperture
size, although in our case the transit amplitude remained constant (within a 0.1% level). We
therefore choose a 5-pixels aperture since our goal is to obtain precise measurements of the
central times of transits, and therefore the relevance of obtaining the correct amplitude is
diminished.
The uncertainty in the difference flux was estimated from the magnitude error obtained
from DAOPHOT/APPHOT, which uses Poisson statistics, and considers the deviation in the
sky background. The flux in the reference image was measured using PSF-fitting photome-
try with DAOPHOT/ALLSTARS. The systematic error introduced by this measurement is
studied further in Sect. 3.
To remove possible systematics effects from the light curves we employed the Trend
Filtering Algorithm (TFA; Kov´acs et al. 2005), which assumes that the time-series is domi-
nated by systematics. In the present case, however, what we want to do is to recover a signal
whose basic characteristics are already known to us. In the same paper Kov´acs et al. (2005)
present an iterative method to reconstruct signals affected by systematics effects, based on
the TFA method. We refer readers to this paper for a detailed description of the method
as well as for an illuminating discussion of the possible causes of systematics effects. We
obtained photometry of 19 stars distributed as uniformly as possible around OGLE-TR-111
–4–
to use as template light curves for the TFA. The obtained curves were checked for obvious
variability or uncommonly large scatter. The signal-reconstruction algorithm was iterated
until the relative difference in the curves obtained in two successive steps was less than 10
−5
.
The resulting science light curves for both nights are shown in Fig. 1. The standard
deviation before the transit of the second night is 2.65 mmag, almost reaching the photon
noise limit of 2.55 mmag.
3. MEASUREMENTS
Planetary and orbital parameters, including the central times of transits, were fitted to
the OGLE-TR-111 light curve. The model used consisted on a perfectly opaque spherical
planet of radius R
p
and mass M
p
, orbiting a limb-darkened star of radius R
s
and mass M
s
(Mandel & Agol 2002) in a circular orbit of period P and inclination i.Weconsidereda
quadratic model for the limb-darkening, with coefficients taken from Claret (2000) for a star
with T
eff
= 5000 K, log g =4.5cms
−2
and [Fe/H]=0.2 and microturbulent velocity ξ =2
km/s. The mass of the planet and the star were fixed to the values reported by Santos et al.
(2006), M
s
=0.81 M
and M
p
=0.52 M
Jup
. The remaining five parameters for the model:
R
p
, R
s
, i and the central time of each transit (T
c1
and T
c2
) were adjusted using the 488 data
points of the light curve.
The parameters were obtained by minimizing the χ
2
statistic using the downhill simplex
algorithm (Nelder & Mead 1965) implemented in the Scipy library
2
. The parameters found
in this manner are presented in Table 1, and the best-fit model and the residuals in Fig. 1.
Note that, except for the planetary radius and the time between first and last contact, the
parameters reported in Table 1 are in agreement with previously published values (see Sect.
4).
The uncertainties in the parameters were estimated using the Markov Chain Monte
Carlo method, which is described in detail by Tegmark et al. (2004), Ford (2005) and Holman
et al. (2006). We constructed chains with 500.000 points each, and discarded the first 100.000
to guarantee convergence. The jump function employed was the addition of a Gaussian
random number to each parameter, and a global scaling of the sigma of the random Gaussian
perturbations was adjusted after convergence was reached so that between 20% and 30% of
the jumps were executed.
In this manner, we built five independent chains and found that the mean values and
2
http://www.scipy.org
–5–
the confidence intervals of the parameters (computed as described below) are in excellent
agreement for all chains, a sign of good convergence. Besides, the correlation length, defined
as the number of steps over which the correlation function (see Tegmark et al. 2004, Appendix
A) drops to 0.5 was about 80 for the central times of the transits, and around 800 for the
highly covariant parameters R
p
, R
s
and i, in agreement with W07. This produces an effective
length of about 5000 for T
c1
and T
c2
, a sign of good mixing.
For each chain we took a random subset of 5000 values (the effective length) of the
central times and test the hypothesis that the sets were drawn from identical populations
using the Wilcoxon’s rank sum test (see Frodesen et al. 1979, §14.6.9). For all cases the test
statistic (which is approximately Gaussian) falls within 2.5-sigma of the expected value, and
therefore the hypothesis cannot be discarded for significance levels below ≈ 1.2%.
Fig. 2 shows two representative probability density distributions corresponding to the
two central transit times and Table 1 reports the median and the upper and lower 68%
confidence limits, defined in such a way that the cumulative probability below (above) the
lower (upper) confidence limit is 16%. As a solid curve we plot the Gaussian probability
density having the same mean and standard deviation as the data.
To test the robustness of our results, the fit was repeated fixing the values of R
p
, R
s
and
i to those reported by W07 (R
p
=1.067R
Jup
, R
s
=0.831R
, i =88.1 degrees) and including
the out-of-transit flux as an adjustable parameter. The obtained times for the center of the
transits are in agreement with those reported above. The same results are obtained if only
R
s
is fixed to the value of W07.
Additionally, to check that the systematics-removal procedure (TFA) does not modify
the shape of the light curves, we also measured the central times in the original curves
obtained with aperture photometry. Again, the obtained values are in excelent agreement
with the ones presented above, and the errors computed with MCMC are larger by a factor
between 1.04 and 1.99, depending on the parameter, as expected.
Possible systematic errors may be introduced by the choice of the stellar mass, the
orbital period — which affects the determination of the orbital radius—, the model for the
limb darkening, and the flux in the reference image. To study these effectes we obtained
new fits to the data varying the fixed parameters and the function for the limb darkening.
The stellar mass was varied by ±10%, the photometry in the reference image was varied by
±0.1 mag and the orbital period by ±10 σ (see Eq. 3). The coefficients for the quadratic
limb-darkenning model were adjusted from the data instead of fixed to the values of Claret
(2000) and, additionally, a linear limb darkenning model was considered, both fixing the
linear coefficient to the value computed by Claret (2000) and adjusting it as part of the fit.