SIX HIGH-PRECISION TRANSITS OF OGLE-TR-113b^*

In the decade since detecting the first transiting exoplanet (Charbonneau et al. 2000; Henry et al. 2000), over 90 transiting systems have been identified. As instrumentation, observations, and analysis techniques have improved, so has the precision with which parameters of transiting systems can be measured, prompting theoretical work to extract more information from each light curve. One focus is on how light curves are modified by gravitational interactions with other planets or tidal interactions with the star. For example, variations in the inclination or duration of successive transits would indicate a precessing planetary orbit, potentially from a second planet (Miralda-Escudé 2002). Periodic midtime variations could indicate additional planets or moons (Holman & Murray 2005; Agol et al. 2005; Heyl & Gladman 2007; Ford & Holman 2007; Simon et al. 2007; Kipping 2009; Kipping et al. 2009). A long-term decrease in the orbital period of the transiting planet could indicate orbital decay, a consequence of tidal dissipation (Sasselov 2003; Pätzold et al. 2004; Carone & Pätzold 2007; Levrard et al. 2009).

In this work we present six new transit light curves of the hot Jupiter OGLE-TR-113b, with a focus on the timing effects. In Section 2 we describe the observations, data analysis, and light curve fitting. Section 3 describes our timing analysis and the physical implications of our findings. We discuss our results in Section 4.

OGLE-TR-113b was reported by Udalski et al. (2002) as a planet candidate transiting a K dwarf (I = 14.4; R.A.(J2000) = 10:52:24.40, decl.(J2000) = −61:26:48.5). Its planetary nature was confirmed by Bouchy et al. (2004) and Konacki et al. (2004). OGLE-TR-113 is an excellent target for differential photometry, since it is located in a dense region of the sky toward the Galactic plane and has numerous nearby, bright comparison stars. We observed six transits of OGLE-TR-113b as part of a larger campaign to detect transit timing variations of OGLE planets (Adams 2010). All transits were observed in the Sloan i' band with the dual-CCD instrument MagIC on the Magellan Telescopes, located at Las Campanas Observatory in Chile.

Both MagIC CCDs have low readout noise (about 6 e⁻ pixel⁻¹), small fields of view, and high-resolution pixels (SITe: 142'' × 142'', or 0069 pixel⁻¹; e2v: 38'' × 38'', or 0037 pixel⁻¹), which both minimizes blends and produces stellar images that are spread over many pixels (typical FWHM = 10–20 pixels depending on seeing and binning). This last feature reduces differential pixel response effects and increases the total number of photons that can be collected per frame, without requiring defocusing. The SITe gain was 2.0 e⁻/ADU, while the e2v gain was 2.4 e⁻/ADU in 2008 and 0.5 e⁻/ADU in 2009 (due to engineering changes). The main advantage of the e2v is its frame-transfer capability: the readout time per frame is only 5 s in standard readout mode and 0.003 s in frame-transfer mode, surpassing the 23 s readout time of the SITe chip and other conventional CCDs.

We used MagIC-SITe for two transits in 2007 January and 2008 February, henceforth denoted by their UT dates as 20070130 and 20080225. MagIC-e2v was used for four additional transits between 2008 April and 2009 May (20080424, 20080514, 20090315, and 20090510). The nightly sky conditions ranged from photometric to partly cloudy. Therefore, exposure times were adjusted from 10–120 s to maintain at least 10⁶ photons per frame for both the target and one or more comparison stars. All transits were observed at air mass <1.7 to minimize differential color effects. The positions of the stars remained within 5–10 pixels each night, while seeing values oscillated from 04 to 07. All transits were observed with 1 × 1 binning, except for 20090510, which was binned 2 × 2. Observations lasted from 3.5 to 5 hr to include the full transit and out-of-transit baseline. Observations were cut short for 20070130 due to clouds. We also truncated the 20080424 light curve due to a strong systematic slope, which we were unable to remove (see Section 2.1).

Given the utmost importance of accurate timing, we took special care to correctly record the time in the image headers. The MagIC-SITe and 2008 MagIC-e2v times came from the network server, which we verified to be synchronized with the observatory's GPS clocks at the beginning of each night. The 2009 MagIC-e2v times came from an embedded PC104 computer, which receives unlabeled GPS pulses every second, and is synchronized to the observatory's GPS every night. The intrinsic error for all header times is thus much less than a second.

2.1. Photometry

All data were overscan-corrected and flatfielded using standard IRAF routines.⁶ Simple aperture photometry, using the IRAF apphot package, provided optimal results, since the target and comparison stars appear well isolated on all frames. We ran a wide grid of apertures and sky annuli to locate the optimal values, which minimized the out-of-transit photometric dispersion of the differential light curves. The comparison stars were iteratively selected to be similar in brightness to the target, photometrically stable and un-blended. We examined 10–20 stars for each transit, using 1, 3, or 10 in the final light curves, depending on the night. The best aperture radii were 4–24 pixels, while the sky annuli had inner radii of 30–120 pixels and 10 pixel widths. A few images were discarded because of low counts or saturation. For 20080424, a 4 pixel aperture (significantly smaller than the 15 pixel FWHM radius) was adopted to eliminate a slope in the light curve before and during transit but failed to correct the slope after transit.

We examined the out-of-transit baseline of each light curve for systematic trends with respect to air mass, seeing, telescope azimuth, (x, y) pixel location, and time (for more details, see Adams et al. 2010). No trends were found in three light curves (20080225, 20080514, and 20090510), and a fourth (20080424) was not detrended, but rather truncated after transit since the slope could not be modeled against any variable. We removed a slope in telescope azimuth (0.022% deg⁻¹) from the 20070130 light curve; the transit midtime was unchanged but the photometric scatter improved and the depth now agrees with the other light curves. We also removed a slope in seeing from the 20090315 light curve (−0.16% pixel⁻¹), observed with variable sky transparency conditions.

The photometric data for each new transit are excerpted in Table 1. All light curves are illustrated in Figure 1, binned to 2 minutes for visual comparison, though the full data were used in all fits.

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Table 1. Transit Flux Values

Mid-exposure (UTC)	Mid-exposure (BJDTDB)	Flux	Error
2454130.599893	2454130.601328	0.9989367	0.001434
2454130.60128	2454130.602715	1.002827	0.001434
2454130.602397	2454130.603832	1.003337	0.001434
2454130.603408	2454130.604843	1.000978	0.001434
2454130.604375	2454130.60581	0.998505	0.001434
⋅⋅⋅

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Our analysis also includes four literature light curves: 20050404 and 20050414 in R band (Gillon et al. 2006), 20050411 in V band (Pietrukowicz et al. 2010; Díaz et al. 2007), and 20060318 in K band (Snellen & Covino 2007). The first three light curves were kindly provided by the lead author of each paper. The original K-band data were lost to a hard-drive crash (I. A. G. Snellen 2010, private communication), so we reconstructed the unbinned light curve from Figure 3 of their paper. We were able to extract the points within a few seconds and reconverted the phased data to UTC times with zero phase at 2006 March 18 04:56:00 UTC (transit epoch 1038 from the quoted ephemeris). Finally, we did not re-fit the OGLE survey photometry but instead used the transit epoch from Konacki et al. (2004) in our timing analysis (see Section 3).

2.2. Light Curve Fitting

2.3. Systematic Errors

To ensure uniform timing analysis, all times in Table 2 are reported in Barycentric Julian Days, using the UTC-TT and TT-TDB conversions (BJD_TDB) after Eastman et al. (2010).⁸ The Gillon et al. (2006) light curves were supplied with UTC times, which we converted to BJD_TDB along with our transits. We similarly converted the reconstructed UTC times from the Snellen & Covino (2007) light curve. We added 64.184 s to the data from Pietrukowicz et al. (2010) and Konacki et al. (2004), after confirming that the UTC-TT conversion had not been applied.

Four attempts to fit a transit midtime ephemeris are illustrated in Figure 2. Panel (A) shows the Gillon et al. (2006) ephemeris, derived using three epochs: 20020220 (OGLE survey), 20050404, and 20050414 (Gillon et al. 2006). After accounting for the 64.184 s UTC-TT conversion, the ephemeris is

$$\begin{equation} T_{C}(N)=2453464.61740(10) [\mbox{BJD}_{\rm TDB}]+1.43247570(130)N, \end{equation} \tag{ 1 }$$

where T_C is the predicted transit midtime in BJD_TDB, the first term is the reference midtime, T₀, and the second term is orbital period, P, times N, the number of elapsed transits since T₀. Although the original data are well fit, this ephemeris cannot account for the full data set, giving a reduced χ² = 26.

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Panel (B) shows a new ephemeris fit to all eleven epochs:

$$\begin{equation} T_{C}(N)=2453464.61762(27) [\mbox{BJD}_{\rm TDB}]+1.43247425(34)N, \end{equation} \tag{ 2 }$$

with a reduced χ² = 1.6. (The errors in Equation (2) have been re-scaled by $\sqrt{1.6}=1.3$ to account for the deviation of the fit from χ² = 1.) Although this equation produces a fair fit to the data, it fails to reproduce some of the most accurate transit midtimes, e.g., the 20090510 transit, which deviates by more than 2σ from the fit.

Panel (C) shows a third ephemeris fit to only the 2007–2009 epochs:

$$\begin{equation} T_{C}(N)=2453464.61857(15) [\mbox{BJD}_{\rm TDB}]+1.43247315(13)N. \end{equation} \tag{ 3 }$$

This fit has a reduced χ² = 0.3 and low errors but cannot account for the 2002–2006 epochs.

The orbital period in Equation (3) differs by −0.22 ± 0.11s from the period in Equation (1), with most of the error associated with the sparser, lower-precision 2002–2005 data. Possible explanations for this period discrepancy are: (1) the timing errors of the new transits have been underestimated—however, the very low reduced χ² of Equation (3) suggests the opposite; (2) the literature midtimes contain yet-unaccounted-for systematic errors, a possibility which should be investigated, since timing errors of hundreds of seconds have been reported before (Adams et al. 2010; Johnson et al. 2010); or (3) the observed orbital period of OGLE-TR-113b has decreased with time. The third explanation, which must be tested with additional data, could be due to a yet-undetected binary star companion (Montalto 2010) with modulation period longer than the eight years of observations, or to a real, linear decrease in the period due to orbital decay of the planet.

If the change in period is real, it is also rapid. Assuming for simplicity a linear rate of change, all 11 transit epochs are well fit if the orbital period decreases by $\dot{P}= -60\pm 15$ ms yr⁻¹, with

$$\begin{eqnarray} T_{C}(N)&=& 2453464.61873(8) [\mbox{BJD}_{\rm TDB}]\nonumber\\ &&+1.43247426(11)N+\delta P*N(N-1)/2, \end{eqnarray} \tag{ 4 }$$

where δP = −(2.74 ± 0.66) × 10⁻⁹ days is the amount by which the orbital period changes per orbit, assuming P(N) = P₀ + δP × N; note $\dot{P}=\delta P\times 365.25/ P_0$. The reduced χ² = 0.6 indicates that this is a better fit to all epochs by a factor of 2.7 than the constant-period fit in Equation (2). Only the 20050411 epoch deviates by more than 1σ (1.7), with residuals of −80 ± 47 s.

As another check on the robustness of this detection, we also fit for the average number of periods between each pair of midtimes. We find a similar rate, $\dot{P}=-76\pm 11$ ms yr⁻¹, with reduced χ² = 0.7; the fit assuming a constant average period has reduced χ² = 2.

3.1. Theoretical Orbital Decay

3.2. Mass Limits on Short-period Perturbers

To place upper mass limits on additional objects near OGLE-TR-113b, we numerically integrated objects with periods from 0.3 to 6.3 days, using the approach of Steffen & Agol (2005) as described in Adams et al. (2010). We restricted the analysis to the six new transits, which can acceptably be fit with a constant period, an underlying assumption of the method. In Figure 3, we show results for perturbers on both initially circular (e = 0) and slightly eccentric (e = 0.05) orbits, with similar constraints. The strongest constraints are placed near the 1:2 and 2:1 mean-motion resonances, where objects as small as 1–2 M_⊕ would have been detectable. Several additional resonances, including the 5:2 and 3:1, also exclude objects larger than 2–20 M_⊕. We therefore find no evidence for timing variations caused by close companion planets.

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We have measured six new transits of OGLE-TR-113b, which provide the highest-quality data for this planet to date. The new transits have timing precisions from 9 to 28 s and photometric precisions as good as 0.6–0.7 mmag in 2 minutes (20080514 and 20090510). The error on the refined planetary radius, R_p = 1.084 ± 0.029R_J, is dominated by stellar radius uncertainties.

Observations of OGLE-TR-113b span eight years of data (2002–2009) after including five previously published epochs. We find no evidence of short-period timing variations, and therefore no sign of other planets in close proximity to OGLE-TR-113b. However, there are hints that the orbital period calculated from the 2007–2009 epochs does not agree with orbital period calculated from earlier epochs. One explanation for this discrepancy is that the period is decreasing by $\dot{P}=-60\pm 15$ ms yr⁻¹.

Given the small number of data points, this detection is still quite tentative, and systematic effects must be carefully considered before any claim is secure. However, the fact that the transit parameters are all self-consistent, as noted in Section 2.2, suggests that systematics do not play a large role. In particular, we find no variation greater than 1σ for any of the non-timing parameters when each light curve is independently fit. In addition, the fits in Equations (2) and (4) have reduced χ² values significantly smaller than 1.0, indicating that we may be overestimating, not underestimating, the timing errors in Table 2.

If the detection is real, one possibility is a wide-period, possibly stellar-mass companion producing the perturbations over decades-long timescales, as recently noted by Montalto (2010). Another possibility is that the orbital period of the planet is decaying. Assuming a linear decay rate, the observed rate of period change agrees with the theoretical estimates of planetary lifetime of Levrard et al. (2009) if the host star has a tidal energy dissipation factor Q_* = 16000⁺⁵⁰⁰⁰₋₃₀₀₀.

This preliminary hint of orbital period decay needs to be verified with observations of the OGLE-TR-113 system, which next becomes observable in 2011 January. If confirmed, this system has the potential of becoming a key laboratory to improve current dynamical and tidal stability models of close-in planetary systems, and to provide observational constraints on Q_*.

E.R.A. received support from NASA Origins grant NNX07AN63G. M.L.M. acknowledges 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 thank Adam Burgasser, Josh Carter, Dave Charbonneau, Dan Fabrycky, Jenny Meyer, Paul Schechter, Brian Taylor, Josh Winn, and the Magellan staff for contributions to the observations and analysis; Michael Gillon, Pawel Pietrukowicz, Ignas Snellen, and Andrzej Udalski for helpful communications regarding their data; and an anonymous referee for improving this manuscript.