Five new transit epochs of the exoplanet OGLE-TR-111b111Based on observations made with ESO Telescopes at the Paranal Observatories under programme ID 278.C-5022
We report five new transit epochs of the extrasolar planet (catalog OGLE-TR-111b), observed in the v-HIGH and Bessell I bands with the FORS1 and FORS2 at the ESO Very Large Telescope, between April and May 2008. The new transits have been combined with all previously published transit data for this planet to provide a new Transit Timing Variations (TTVs) analysis of its orbit. We find no TTVs with amplitudes larger than minutes over a 4-year observation time baseline, in agreement with the recent result by Adams et al. (2010a). Dynamical simulations fully exclude the presence of additional planets in the system with masses greater than 1.3, 0.4 and 0.5 at the 3:2, 1:2, 2:1 resonances, respectively. We also place an upper limit of about 30 on the mass of potential second planets in the region between the 3:2 and 1:2 mean-motion resonances.
The method of Transit Timing Variations (TTVs) has been proposed by several recent theoretical works as of great potential to detect additional exoplanets in transiting exoplanetary systems (Miralda-Escudé et al., 2002; Agol et al., 2005; Holman et al., 2005), and even exomoons (Sartoretti & Schneider, 1999; Kipping et al., 2009a,b). In a system with additional planets, the predicted central time of a transit can change periodically by a significant amount of time if a second planet, the perturber, is in mean motion resonance with the transiting one. In the case of exomoons, TTVs of up to few minutes can be produced by moons larger than 1 depending on the physical parameters of the orbital system. Variations of other transit parameters, such as the depth or duration of the transits, have been predicted to also indicate the presence of additional planets in those systems (Miralda-Escudé et al., 2002). Another application of the TTV technique is the detection of long-term orbital period secular variations produced by tidal interactions between the star and the planet, star oblateness and general relativity. Those effects are predicted to introduce changes in the orbital periods of the transiting planets with amplitudes of the order of 0.3-10 ms/yr (Miralda-Escudé et al., 2002; Heyl & Gladman, 2007; Jordán & Bakos al., 2008) and would be detectable in 10-20 years timescales given the precision of the current techniques.
These theoretical predictions have prompted the work of several observational groups, who in the past few years have started to monitor various transiting exoplanets from the ground. More recently, dedicated transit search space missions like CoRoT (Barge et al., 2008) and Kepler (Borucki et al., 2010) have also started to collect high duty cycle and long-term monitoring data which allow TTV studies of the new transiting planets they find (e.g. Bean, 2009). Most of the findings from observational efforts are still preliminary, but include the potential detection of TTVs with amplitudes of up to 3 min for the hot Jupiter WASP-3b, which could be explained by the presence of a 15 planet near the outer 2:1 mean motion resonance with WASP-3b (Maciejewski et al., 2010), and the also preliminary detection of a ms/yr orbital period decay of the hot Jupiter OGLE-TR-113b by Adams et al. (2010b). Other preliminary results include the hints of transit duration and orbital inclination variations in the hot Neptune (catalog Gliese 436b) system reported by Coughlin et al. (2008) and the shift of about 3 seconds in the orbital period of XO-2b reported by Fernández et al. (2009). Several other system have been monitored without showing any clear evidence of TTVs, e.g. Steffen & Agol (2005) found no evidence of a second planet using timing data of eleven transits of (catalog TrES-1b), and Agol & Steffen (2007) ruled out Earth-mass planets in low order resonances in (catalog HD 209458b) system. In a later work, Miller-Ricci et al., 2008a, b found no TTVs with amplitudes larger than 45 seconds on the transits of (catalog HD 209458b) and (catalog HD 189733b) based on MOST data, and Winn et al. (2009) found no variations from a constant orbital period for (catalog WASP-4b), after combining two precise mid-transit timing measurements with another five measurements for this planet reported by Gillon et al. (2009). Recently, Holman et al. (2010) announced the first unquestionable evidence of TTVs in the double transiting planetary system (catalog Kepler-9).
OGLE-TR-111b was the first hot Jupiter for which tentatively significant TTVs were reported by Minniti et al. (2007), hereafter M07. The first two precision transit timing data points for this planet were published by Winn et al. (2007), W07. Shortly after, M07 published a third data point which deviated by about 5 minutes from the predicted W07 transit ephemerides. In a subsequent paper, Díaz et al. (2008) (D08) reported two new consecutive transits and combined their new data with the other three epochs to find TTVs with amplitudes of up to 2.5 minutes, which the authors suggested could be explained by the presence of a 1.0 perturbing planet in an outer eccentric orbit to OGLE-TR-111b. The most recent TTVs analysis publication on this planet (Adams et al., 2010a, A10) reports six new transit observations and no TTVs for this planet with amplitudes larger than seconds.
In this new work we present five additional transits of OGLE-TR-111b observed between April and May 2008, and we perform a new homogeneous timing analysis of all available 16 epochs to further study the presence or absence of additional planets in this system. In section 2 we present the new observations and the data reduction. Section 3 describes the modeling of the light curves. In sections 4 and 5 we describe the timing and possible parameters evolution. In 6 we discuss the mass limits for a unseen perturber and finally in section 7 we present our conclusions.
2 Observations and data reduction
Between April and May 2008, we observed five transits of the exoplanet (catalog OGLE-TR-111b) with FORS1 and FORS2 (Appenzeller et al., 1998) at the ESO Very Large Telescope. The first four transits were fully covered in phase. The fifth transit was only partially covered because the target reached the telescope’s airmass limit, and is only complete between phases 0.97 and 1.01, which includes the out-of transit baseline before the transit, the ingress and most of the bottom of the transit. The UT date of the mid-time of the transit, instrument, filter band, exposure time, airmass range and number of frames of each observation are summarized in Table 1. FORS1 and FORS2 are visual focal-reducer imagers composed of two E2V/MIT CCD detectors mosaics with a pixel scale of 0.126 arcsec pixel each (high resolution mode). The field of view (FoV) of each camera is therefore arcminutes, large enough to include OGLE-TR-111 and several comparison stars. FORS1 and FORS2 have the same wavelength coverage (3000-11000 Å) but FORS1 is optimized for blue wavelengths ( Å) while FORS2 is for the red ( Å). Our first transit was observed with FORS1 using a v-HIGH filter ( nm) while the rest of the transits were observed with FORS2 using a Bessell I filter ( nm). A very close star appears partially blended with the target given the resolution of the instrument and the typical seeing conditions during the observations (Figure 1). The center of the field was selected so that (catalog OGLE-TR-111) and several good comparisons stars would fall on a single detector, while also locating a bright nearby star out of the field. However, diffraction spikes from that bright star moved across the field of view, occasionally reaching the location of the target, as illustrated in Figure 1. Our subsequent analysis revealed additional background noise in some of the images due to this effect. This problem was most evident in the 2008-05-03 light curve (Figure 2) where pronounced bumps were visible in the bottom of the light curve of this night. Along the images obtained during this night, the diffraction spikes rotated trough the FoV reaching the comparison stars at different phases of the transit. The bumps also appeared in the light curves of these comparison stars. We use the peak of the larger bump in the light curve of the target to match in phase the bumps of all the other light curves (see Figure 2). We average the light curves of the comparison stars in a small region where the bumps were more evident (between the horizontal lines in Figure 2) and finally in order to remove the bumps, we substracted this average to the light curve of the transit. In the other nights it was not possible to identify clearly the bumps produced by the diffraction spikes, and therefore we could not reproduce the process mentioned before but we attributed some of the noise in the lights curve to this effect.
We worked with the processed data provided by the VLT pipeline which performs the bias and flatfield corrections. The times at the start of the exposure are recorded in the images headers, in particular we used the value of the Modified Julian Day keyword of each image and transformed it to Barycentric Julian Day (see section 4 for details).
Our photometric analysis was done with the Difference Image Analysis Package (DIAPL) written by Woźniak (2000) and recently modified by W. Pych222The package is available at http://users.camk.edu.pl/pych/DIAPL/index.html. The package is an implementation of the method developed by Alard & Lupton (1998), and it is optimized to work with very crowded fields and/or blended stars, as is the case of (catalog OGLE-TR-111) (Figure 1). DIAPL models PSF variations along the X-Y coordinates, scales and subtracts the flux of the stars of a template image for each frame, among other calculations. One of the disadvantages of this code is the time required to complete the process, specially since it is not possible to verify the suitability of the input parameters and the quality of the products until the last steps (subtraction and/or photometry). In our case, due the large size of the frames and the large number of stars in the FoV, one iteration required up to 20 minutes. To eliminate a few nearby saturated stars in the field that hindered the photometry and to reduce considerably the processing time we worked on pixel subframes. Working with these subframes, DIAPL estimations of the PSF, background and flux levels are more representative of the vicinity of our target in each frame and in the reference image; noise as well as obvious systematics in the final photometry are considerably reduced. Reference frames for each night were constructed by combining the 20-27 best images (in terms of seeing and signal-to-noise) depending on the night’s conditions. We used aperture radii between 4 to 10 pixels (in DIAPL’s task phot.bash) to perform the relative photometry of the target and comparison stars (8 to 15 stars) on each subtracted frame.
To obtain an absolute normalization, we performed aperture photometry (DAOPHOT / ALLSTARS, Stetson (1987)) in the reference frame of each night using a curve of growth analysis to select the ideal aperture radii.
The resultant light curve contains some remaining systematic variations, which we have modeled using linear regression fits of the out-of-transit data points against the airmass, average FWHM of the point spread function and/or background level around our target of each frame. Doing this we were able to achieve an RMS precision of in the light curves (almost reaching the Poisson noise level in the best nights or doubling it in the worst).
3 Modeling Light Curves
We fitted our five new light curves together with all the light curves previously published by W07, D08 and A10, using JKTEBOP333http://www.astro.keele.ac.uk/ jkt/codes/jktebop.html (Southworth et al., 2004). The fit also includes the light curve by Pietrukowicz et al. (2010, P10 hereafter), obtained from the reanalysis of the VIMOS data published by M07. P10 found a problem with the times reported by M07, which results in a mid-transit epoch time difference of 5 minutes. We only consider the P10 analysis of this transit from this point onwards.
Among the parameters fitted by JKTEBOP for each light curve are: the planet to star radii ratio (), the inclination () and eccentricity () of the orbit, the out-of-transit baseline flux (), the mid-time of transit (), the quadratic limb darkening coefficients ( and ), and the sum of the fractional radii, . The terms and are defined as and , where and are the absolute stellar and planetary radii, and is the orbital semi-major axis. In the case of the limb darkening coefficients, we fixed to the values given by Claret (2000) and Claret (2004) for each observation’s filter (for the v-HIGH filter we use the coefficient) and only left as free parameter during the fitting process described below, where denotes the filter band. We performed the same fitting method using a linear limb-darkening law obtaining basically the same final for each transit, which reveals that the photometric precision of the light curves is not sufficient to distinguish between limb darkening laws. Also, to minimize potential degeneracies between parameters, we fixed the eccentricity and the longitude of the periastron of the orbit to zero, and the planet to star mass ratio to , adopting the mass values derived by Santos et al. (2006).
JKTEBOP also allows for an statistical determination of the error of each parameter, as well as an analysis of the impact of systematics in the light curves, via Monte Carlo simulations. We ran Monte Carlo simulations adding random simulated gaussian noise to the input parameters to estimate the uncertainty of each parameter while also testing for potential correlations. When all the parameters described above are left free, there are clear correlations between , , and , and also between and , as illustrated in Figure 3. No significant correlation was observed between any of the other parameters.
These correlations can be minimized by fitting the parameters in three steps, also running Monte Carlo simulations on each step. First, we fixed the inclination of the orbit to the value obtained by A10, together with the corresponding value of from the Claret tables and fitted and for each light curve. Next, we fixed and to the weighted average of the individual fits obtained in step I, and left and as a free parameters. Finally, we adopted the weighted average of the resulting inclinations and the corresponding for each filter (because we have only one transit observed with v-HIGH and one with V we adopted directly the results of JKTEBOP for its ), and fitted only for . In Table 2 we summarized each step of the fitting process. An example of the histograms of the distribution of values for each parameter for the night 2008-05-12 are represented in Figure 4. The adopted values of each parameter for the individual light curves are summarize in Table 3. The average values for the system based on all light curves are summarized in Table 4. To test the consistency of the Monte Carlo error estimates, we compared it to the results of the prayer-bead method (Bouchy et al., 2005). While the Monte Carlo method gives an idea of the white noise in the data, any level of red noise (time correlated noise, ) is best characterized by the prayer-bead method. The errors obtained by the prayer-bead method were, in general, larger than the Monte Carlo errors, showing that red noise is the dominant factor in the light curves. In Table 3 we show the ratio of the errors estimated by the Prayed-Bead and the Monte Carlo method. We adopted as 1 errors of the parameters reported in Table 3, the larger values between these two error estimations.
The Levenberg-Marquardt Monte Carlo (LMMC) fitting method implemented by JKTEBOP, can present some disadvantages with respect to the Markov Chain Monte Carlo (MCMC), method used by several other recent TTVs studies. For example, LMMC can be trapped in a local mimima or/and can underestimate the errors of the fitted parameters (e.g. Fisher et al., 2009; Driscoll, 2006). Despite this, our results in Table 3 for the analysis of previously published light curves are fully consistent with the parameter fit values reported in Table 5 of A10 using MCMC. LMMC and MCMC are expected to yield similar results in well-behaved parameter space, i.e. with no multiple minima, as seem to be the case of our dataset. Even though, it is possible that the errors of LMMC best-fit parameters (provided by the parameter distribution of the Monte Carlo iterations) can be under estimated, but our adopted parameter errors are dominated/scaled by the red noise contribution (see the values in Table 3 ), indeed our errors are very conservative in comparison with A10 estimations.
4 Timing Analysis
The mid-time for each transit derived in the previous section and listed in Table 2 was converted to Barycentric Julian Days, expressed in terrestrial time, i.e. BJD(TT), following the standard timing reference system recommendations by Eastman et al. (2010). Since our analysis includes data from different instruments/telescopes, spanning over four years, and reduced by different groups we checke carefully for any possible systematics. As example, A10 has already pointed out how previously published results on (catalog OGLE-TR-111b) had not corrected the reported times for leap seconds (UTC to TAI) nor for the 31.184 second conversion between TAI and TT, where TAI is defined as the . We have applied the same corrections to all the literature light curves used in our analysis.
As an additional check to our reduction, light curve fitting and timing correction procedure, we compared our final BJD(TT) times to those published by A10. Particularly valuable for this test is the 2008-05-12 transit epoch, which was independently observed by us and A10. As illustrated in Figure 6, in spite of adopting completely different approaches to fit the light curves, all our derived transit mid-times agree well with the values obtained by A10. When comparing the of our 2008-05-12 transit with A10’s, both times agree within the error of our observation, although our mid-transit time occurs 124 seconds earlier. Four of the five transits we measure also produce mid-transit times on average 100 seconds earlier than the ephemerides predict (see Figure 6), although the differences are not statistically very significant. However, we have decided to further investigate the potential source of this discrepancy. First, we confirmed with the VLT staff that the times recorded in the image headers are the UTC times at the beginning of each exposure of our data (including all leap seconds). We further tested for any potential systematics between datasets by binning our data to 60 seconds, and removing the last 50 points in our light curve to make it match the light curve sampling and phase coverage of A10. The result was only a 10 second time shift in the resulting compared with the previous fit value. The two transits were observed in different filters, but we find no correlations between the limb darkening coefficients and (see Figure 3) that could account for this mid-time discrepancy. We attributed this difference to the red noise in the FORS light curve, possibly due to weather (the value of of this transit in Table 3 is almost twice the value of A10 light curve).
Figure 7a shows the updated (O-C) diagram with all the final BJD(TT) mid-time values calculated from the literature light curves and our five new transits. The data show a linear trend which can be attributed to the accumulation of timing uncertainties with respect to the adopted transit ephemerides (D08). After removing that linear trend (Figure 7b), the data are consistent with a constant period ephemeris equation of the form:
where is the central time of a transit in epochs since the reference time . This fit has a reduced of 1.8, so the errors in have been rescaled by a factor of to make them consistent with (see errorbars in Figure 7b), The new period is fully consistent with the one obtained by A10.
5 Analysis of additional parameters of the light curves
We tested for possible variations of the physical parameters of the (catalog OGLE-TR-111) system using the values of the transit duration, , the inclination, the planet to star radius ratio, and the sum of the fractional radii derived for each transit with JKTEBOP. The value of each of those parameters over time is represented in Figure 8.
There is no evidence of trends for any of the inspected parameters. However, it is noticeable that the results from the light curves observed by different groups appear clustered around the same values. We attribute that clustering to systematics introduced by the way the photometry is performed (i.e. aperture or PSF photometry, differential image analysis, and so on), and probably also by the way the light curve systematics are treated by the different groups. For example, D08 already pointed out that the depths of their transits were smaller than the average and that this was due to a reduction artifact of the differential image subtraction techniques previously noticed by Gillon et al. (2007). Although we used DIAPL instead of aperture photometry, our results are consistent with those of A10. Notice, however, that systematics in the transit depths have no effect in the determination of the transit midtimes.
6 Limits to additional planets
Based on the timing constrain of our diagram, i.e. no TTV variations with amplitudes larger that minutes over a three year period, we run dynamical simulations to place limits on the mass and the semi-major axis of a possible orbital companion of the transiting planet using the mercury code (Chambers, 1999). The first step was to explore stable orbital regions by assuming a massless point particle over a range of initial semi-major axes, and fixing all the other input variables to the known physical parameters of the system. The orbital evolution of the massless particle was integrated over . This test yields a strip of unstable orbits between , where encounters between the test particle and (catalog OGLE-TR-111b) would occur. For all the other orbits we calculate TTVs of the transiting body with the hypothetical coplanar perturber using a wide range of masses (), variable density (from Earth to Jupiter density depending on the mass) and semi-major axes ( in steps of ) with simulations over 7 years. All the initial relative angles were fixed to zero. Near resonances, the steps in the variables were reduced to increase precision. Only the last 5 years were used for the timing analysis, since that is about the same time span covered by the observations, and also to minimize any effects introduced by the choice of initial parameters. Then we calculated the central time of each transit during all the simulations. Similarly to what was done in section 4, we did a linear fit of these central times and we defined the TTV of each simulation as the standard deviation of the central times with respect to this linear fit. We checked that the final period of the transiting planet did not change by more than 3 from its initial value due the gravitational interaction. With this method we were able to make a vs diagram (Figure 9-A) where the solid line represents TTVs of 1.5 minutes. For comparison we also plot the mass limits of TTVs of 0.5 and 5 minutes (dotted and dash-point lines). The dashed line corresponds to the detectability limit placed by radial velocity observations (Santos et al., 2006). Our mass constrains are upper limits since for perturbers with an orbital eccentricity different from zero, the mass necessary to produce TTVs of the same amplitude will be lower. We confirm this by performing a set of simulations with and using as input parameters the values (, ) which produced TTVs in the case (see Figure 9-B). With this configuration the unstable region becomes wider due to encounters between the orbital bodies and the TTVs produced for a given mass were larger than in the case of . Same results were obtained setting the initial values of the longitude of the periastron different from zero (, and ) and . Combining TTV RMS and radial velocities we can rule out the presence of a perturber body with mass greater than 1.3, 0.4 and 0.5 at the 3:2, 1:2, 2:1 resonances with OGLE-TR-111b and lower the upper limit in the region exterior to the planet until AU to companions of less than .
We present 5 new transit light curves of (catalog OGLE-TR-111b). We homogeneously model all available light curves in the literature and search for any variation in the timing of the transits. With our updated ephemeris equation we find no TTVs with amplitudes larger than 1.5 minutes and therefore we rule out the presence of a companion in the 2:1, 3:2 and 1:3 orbital resonances. If the system has an additional orbiting body, its mass has to be lower than 30 if is located between 3:2 and 1:2 resonances. The mass limits we place with our dynamical simulations based in the TTV data are lower than the limits obtained with radial velocities alone. We search for any trend in the duration, depth of the transit and inclination of the orbit but we do not see any clear evidence of variation with statistical significance. We point out that systematics of no evident source in the observations, reduction and/or analisys processes can induce differences in the values of the parameters obtained from the light curves and therefore a monitoring of transiting exoplanets carry out by the same group can contribute to reduce these differences.
S.H. and P.R. acknowledgements support from Basal PFB06, Fondap #15010003, and Fondecyt #11080271. Additionally, S.H, recieved support from GEMINI-CONICYT FUND #32070020, ALMA-CONICYT FUND #31090030. M.L.M. acknowledgements support from NASA through Hubble Fellowship grant HF-01210.01-A/HF-51233.01 awarded by the STScI, which is operated by the AURA, Inc. for NASA, under contract NAS5-26555. We thanks to P. Pietrukowicz for the help in the use of DIAPL and to E. Adams for helpful discussions about her OGLE-TR-111b TTVs analysis.
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|Transit Date||Instrument||Filter||Integration Time [s]||airmass range||# imagesccThe number of images descarted in the analisys is shown in parenthesis.|
|2008-04-26||FORS1||v-HIGH||30||1.25 - 1.43||323|
|2008-04-30||FORS2||Bessell I||12||1.25 - 1.59||488|
|2008-05-04||FORS2||Bessell I||12||1.25 - 1.75||522(2)|
|2008-05-12aaThis transit was also observed by Adams et al. (2010a).||FORS2||Bessell I||4||1.25 - 2.18||601(94)|
|2008-05-20bbThis transit has a incomplete phase coverage.||FORS2||Bessell I||8||1.29 - 2.07||373|
|Step||Free||Fixed||ReferenceaaThis column shows the origin of the adopted value of the fixed parameter.|
|II||, ,||,||Step I|
|Transit dateaaThe Epoch number is shown in parenthesis.||bb: Prayer-Bead and Monte Carlo errors ratio. See text for details.||(BJD)|
Note. – The values shown in parenthesis correspond to the errors in the last digits.