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.