Twenty-One New Light Curves of OGLE-TR-56b: New System Parameters and Limits on Timing Variations
E. R. Adams, M. Lopez-Morales, J. L. Elliot, S. Seager, D. J. Osip, M. J. Holman, J. N. Winn, S. Hoyer, P. Rojo
DDraft version October 26, 2018
Preprint typeset using L A TEX style emulateapj v. 12/01/06
TWENTY-ONE NEW LIGHT CURVES OF OGLE-TR-56B: NEW SYSTEM PARAMETERS AND LIMITS ONTIMING VARIATIONS E. R. Adams , M. L´opez-Morales , J. L. Elliot , S. Seager , D. J. Osip , M. J. Holman , J. N. Winn , S.Hoyer , P. Rojo Draft version October 26, 2018
ABSTRACTAlthough OGLE-TR-56b was the second transiting exoplanet discovered, only one light curve,observed in 2006, has been published besides the discovery data. We present twenty-one light curvesof nineteen different transits observed between July 2003 and July 2009 with the Magellan Telescopesand Gemini South. The combined analysis of the new light curves confirms a slightly inflated planetaryradius relative to model predictions, with R p = 1 . ± . R J . However, the values found for thetransit duration, semimajor axis, and inclination values differ significantly from the previous result,likely due to systematic errors. The new semimajor axis and inclination, a = 0 . ± . i = 73 . ± . ◦ , are smaller than previously reported, while the total duration, T = 7931 ± Q ∗ = 10 , with a three-sigma lower limit of 10 . . Subject headings: stars: planetary systems – OGLE-TR-56 INTRODUCTION
OGLE-TR-56b was the second transiting exoplanetdiscovered, after HD209458b (Charbonneau et al. 2000;Henry et al. 2000), and the first found by a photometricwide-field survey (Udalski et al. 2002). The planetarynature of this object was confirmed by Konacki et al.(2003), who derived a mass of 1 . M J from radial veloc-ity measurements of the host star. An initial flurry offollow-up observations included radial velocity measure-ments by Torres et al. (2004) and Bouchy et al. (2005);the determination of the host star’s fundamental param-eters and chemical composition by Santos et al. (2006);and more recently the detection of OGLE-TR-56b’s at-mosphere by Sing and L´opez-Morales (2009). However,due to the faintness of the target ( V = 16 . I = 15 . I (Udalski et al. 2002), and a This paper includes data gathered with the 6.5 meter MagellanTelescopes located at Las Campanas Observatory, Chile. Harvard-Smithsonian Center for Astrophysics, 60 Garden St.,Cambridge, MA, 02138 Department of Earth, Atmospheric, and Planetary Sciences,Massachusetts Institute of Technology, 77 Massachusetts Ave.,Cambridge, MA, 02139 Institut de Ci`encies de l’Espai (CSIC-IEEC), Campus UAB,Facultat de Ci`encies, Torre C5, parell, 2a pl, E-08193 Bellaterra,Barcelona, Spain Visiting Investigator; Carnegie Institution of Washington, De-partment of Terrestrial Magnetism, 5241 Broad Branch Road NW,Washington, DC 20015-1305 Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Ave., Cambridge, MA, 02139 Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff, AZ86001 Las Campanas Observatory, Carnegie Observatories, Casilla601, La Serena, Chile Astronomy Department, Universidad de Chile, Casilla 36-D,Santiago de Chile, Chile single light curve in 2006 observed alternately in Bessel R and V filters (Pont et al. 2007). The precision of theplanetary parameters for this system has thus far beenlimited by the photometric quality of the available tran-sit light curves (Southworth 2008) and not by the preci-sion of the stellar parameters, as is currently the case formany other planets.OGLE-TR-56b was selected in 2006 as part of our cam-paign of high-quality photometric observations to searchfor transit timing variations (see Adams 2010; Adamset al. 2010a,b, 2011). Its short orbital period allows formany observational opportunities, and it remains one ofthe better candidates to search for changes in the orbitalperiod due to orbital decay. Predictions vary widely onthe time scale over which orbital decay would be ob-servable (Sasselov 2003; P¨atzold et al. 2004; Carone andP¨atzold 2007; Levrard et al. 2009), with estimates of theremaining lifetime of this system ranging from a few bil-lion years (Sasselov 2003) to a much shorter 7 Myr (as-suming Q ∗ = 10 Levrard et al. 2009) using very differentassumptions about tidal equilibrium modes. Therefore,the estimates for the decrease in the orbital period dueto orbital decay range from 0.1 to 10 ms yr − . This valueis only a few times smaller than the current error on theorbital period (86 ms from Pont et al. 2007).Here we present twenty-one new light curves of nine-teen transits of OGLE-TR-56b, observed from 2003 to2009, which we use to improve the planetary system pa-rameters and also to search for potential timing anoma-lies in this system, including transit timing variations(TTVs) caused by interactions other bodies in the sys-tem, and transit duration variations (TDVs) caused byorbital precession, among other effects. In § § § § a r X i v : . [ a s t r o - ph . E P ] A ug OBSERVATIONS AND DATA ANALYSIS
Nineteen transits were observed between 2003 July and2009 July, all but one with the Magellan telescopes. Alltransits are referred to by the UTC date of observations;when multiple light curves exist for a given UTC date,e.g. the two light curves on 2005 April 19 UT in theJohnson B and I band, they are denoted respectively as20050419B and 20050419I. Seven full or partial transitswere observed by the Transit Light Curve (TLC) collabo-ration (e.g., Holman et al. 2006) during 2003-2006, usingMagIC-SITe. Thirteen transits were observed between2006-2009 on Magellan using three instruments: POETS(3 transits), IMACS (1 transit), and MagIC-e2v (9 tran-sits). One additional transit was observed in 2009 usingGMOS on Gemini South. Details on instrument setupand observational conditions are summarized in Table 1.The Magellan instruments all had relatively smallfields-of-view with high spatial sampling. The earliesttransits used the Magellan Instant Camera (MagIC) withthe original SITe CCD on the Clay telescope. MagIC-SiTe had a field of view of 140 (cid:48)(cid:48) × (cid:48)(cid:48) and a plate scaleof 0.069 (cid:48)(cid:48) per pixel; the CCD gain was about 2 e-/ADUand the read noise 6 e-. Four filters were used: Harris B , Mould I , and Sloan r (cid:48) and z (cid:48) (the filter transmissioncurves are shown in the legend of Figure 1). In June andJuly 2006, POETS (Portable Occultation, Eclipse, andTransit System) was installed as a visiting PI instrumenton the Clay telescope. POETS has a field of view of 23 (cid:48)(cid:48) × (cid:48)(cid:48) and a plate scale of 0. (cid:48)(cid:48)
046 per pixel. The camerais a frame-transfer CCD which can be GPS triggered andis described in Souza et al. (2006). POETS was operatedfull-frame (no binning) in conventional mode with a gainof 3.4 e-/ADU and read noise of 6 e-. For the first twotransits observed, a Schuler Astrodon Johnson-Cousins Is filter was used. For the third transit, observed on20 July 2006, coincidentally the same night as the tran-sit by Pont et al. (2007), no filter was used as a test toachieve greater throughput; the POETS CCD is sensitiveto wavelengths between 400-900 nm (Gulbis et al. 2008).We refer to this as 20060720N to distinguish it from thePont et al. (2007) observations.One transit was observed in 2007 with the InamoriMagellan Areal Camera and Spectrograph (IMACS) onthe Magellan Baade telescope (Dressler et al. 2006). Weused the f /4 imaging mode with a subraster on one of theeight instrument CCDs (chip 2), reading out 1200x1200pixels centered around x=1080 and y=3015, in orderto decrease the readout time to roughly 35 seconds perframe in FAST mode. The area imaged was thus 133 (cid:48)(cid:48) × (cid:48)(cid:48) , with a plate scale of 0.11 (cid:48)(cid:48) per pixel. This chiphas a gain of 0.9 e-/ADU and read noise of 4.6 e-. Awideband filter, WB6300-9500, was used.Between January 2008 and December 2009, the Magel-lan Instant Camera (MagIC) was mounted on the Magel-lan Baade telescope with the addition of a new e2v CCD.The MagIC-e2v detector, which shares a dewar with theolder SITe CCD, is identical to the red CCD on HIPO(one of the first generation instruments to be flown onSOFIA), a fast read-out direct imaging camera that usesthe LOIS control software (Dunham et al. 2004; Tayloret al. 2004; Osip et al. 2008). All of the MagIC-e2v tran-sits were observed in the Sloan i (cid:48) filter. The MagIC-e2vcamera has a field of view of 38 (cid:48)(cid:48) × (cid:48)(cid:48) and a plate scale of 0. (cid:48)(cid:48)
037 per pixel unbinned. The camera can be oper-ated in two different modes: single exposure mode, witha readout time of about 5 seconds per exposure, whichwas used for the first three transits in 2008; and frametransfer mode, with a readout time of only 3 millisec-onds between frames in an image cube, which was usedfor the following six transits. The gain and read noise ofthe transits observed in 2008 were 2.4 e-/ADU and 5.5e- per pixel, respectively, and two amplifiers were usedduring readout; after July 2008, the CCD was reconfig-ured to have a gain of 0.54 e-/ADU and 5 e- read noiseper pixel and a single readout amplifier.The transits observed with the frame transfer cameraPOETS were observed at a very rapid cadence (2-6 s perexposure), in order to get good time sampling duringtransit ingress and egress. However, the noise per framewas such that we chose to bin every 10 frames (20 s) for20060622, 8 frames (32 s) for 20060714, and 10 frames (60s) for 20060720N. In subsequent transits, the exposuretimes were adjusted to maintain roughly 10 integratedphotons for both the target and multiple nearby com-parison stars. Exposure times for unbinned (1 ×
1) dataranged from 17-60 sec, and for binned data from 10-60sec. Details of the observing settings are noted in Ta-ble 1. Gaps in the data for transits 20060622, 20060714,and 20080727 were caused by separate instrument com-puter glitches, while the gap in transit 20090510 was dueto observing a gamma ray burst for another project whileOGLE-TR-56b passed through zenith.The observation strategy for the transits observed bythe Transit Light Curve collaboration between 2003-2006is similar to that of OGLE-TR-111b. Details are pro-vided in Winn et al. (2007).The transit on 20090428 was observed using GMOS(Gemini Multi-Object Spectrograph) at Gemini SouthTelescope. The observations were done in service modeusing a Sloan i filter ( i GO327 ), 2 × (cid:48)(cid:48)
146 per pixel. The chip hasa gain of 5 e-/ADU and read noise of 7.8 e-.Accurate timing is of the utmost importance for thisproject, so special care was taken to ensure that thecorrect times were recorded in the image headers. Forthe transits observed with POETS in 2006, each imageframe was triggered by a GPS, so the UTC start timesare accurate to the microsecond level. For the transitsobserved with GMOS, MagIC-SITe, IMACS and MagIC-e2v (in 2008), the UTC start times for each image wererecorded from network time servers, which in most caseswere verified by eye to be synchronized with the observa-tory’s GPS clocks at the beginning of each night. For theMagIC-e2v observations in 2009, the times came from asmall embedded control computer (a PC104), which re-ceived unlabeled GPS pulses every second. As with thenetwork time servers, the PC104 was synchronized withthe observatory’s GPS before each transit observation.In all cases the UTC time signals written to the imageheaders agree within one second with the GPS time, asverified by examining the system control logs.
Data analysis
All data were calibrated using IRAF . The zero levelfor POETS and IMACS data frames were calculated frombias frames taken before or after the transits, while theMagIC data frames were corrected using overscan regionson each image. The images were flat-fielded using eitherdome or twilight flats in the appropriate filter, as avail-able. The GMOS data were reduced using the Geminipipeline.Although OGLE-TR-56 is in a very crowded field (Fig-ure 2), the generally excellent seeing and good spatialresolution of the detectors allowed for high-quality lightcurves using aperture photometry. Most of the photom-etry was done using the IRAF routine phot , part of the apphot package. A wide range of apertures and differ-ent comparison stars were examined, depending on thenightly conditions (e.g., seeing) and specific field of view,in the same way as described for other planets we haveanalyzed (Adams et al. 2010a,b, 2011).For a few transits, an alternative aperture photometrymethod was used to achieve greater precision. In thismethod, boxes were drawn around the target and com-parison stars, and the sky was determined using a single30-pixel box drawn around an empty region of sky (noteasy to find for targets in crowded fields, such as OGLE-TR-56b). This method, as implemented in Mathematica ,is both slower and not as robust as IRAF’s phot , partic-ularly for data sets in which the stars shifted by morethan a few pixels; but for two transits (20060622 and20080514) it produced lower out-of-target scatter andcleaner light curves. The sky region for 20060622 wascentered 2.1 (cid:48)(cid:48) west and 0.1 (cid:48)(cid:48) south of the transiting planethost star; for 20080514 the region was located 2.0 (cid:48)(cid:48) eastand 0.3 (cid:48)(cid:48) south.We additionally explored using image subtraction(Alard and Lupton 1998; Alard 2000) to create the lightcurve for one transit, 20090504. This test produced alight curve with slightly better scatter compared to theaperture light curve (1.0 vs 1.1 mmag in 2 min), butthe depth of the image-subtracted light curve is muchshallower ( k = 0 . ± . k = 0 . ± . k = 0 . ± . x, y ) pixel location, and time since beginning oftransit. These parameters were chosen because they areeither directly correlated with photometric trends (e.g.seeing, airmass), or are proxies for other effects that maybe harder to measure (e.g. the telescope azimuth, whichis a major component in the de-rotator rates, which were IRAF is distributed by the National Optical Astronomy Ob-servatories, which are operated by the Association of Universitiesfor Research in Astronomy, Inc., under cooperative agreement withthe National Science Foundation. not recorded in the headers of all transit files). Thedata presented no significant systematics, except in threetransits, for which we fit and remove linear trends forslight slopes in the flux over time (transits 20070830 and20090504), and a slope with seeing (transit 20080727).Since these slopes were removed before the light curveparameter fitting step (see § Literature light curves
The only published high-quality light curve for OGLE-TR-56b was observed on 2006 July 20 UT with the VLTin both R and V , with alternating sequences in each filterof 7-8 exposures of 15-40 s each (Pont et al. 2007). Uponrefitting that light curve (provided by F. Pont 2007, per-sonal communication), we found that the shape of thetransit does not agree well with the one obtained fromthe new light curves, most notably in an 18-minute dis-crepancy in the transit duration (see § R -band and1.2 mmag in V -band, compared to 0.7 mmag for the orig-inal combined V/R curve. However, the aperture lightcurves are consistent in transit depth and duration withthe 19 other light curves presented in this paper. Therevised curves, referred to as 20060720R and 20060720Vhenceforth, are used in all subsequent analyses, exceptas noted for comparison with the original photometry,which we call 20060720P. We also note that the timesused in the Pont et al. (2007) light curve appear to bethe start time, rather than the mid-exposure time of eachframe, and thus are earlier than the corresponding pointsin our analysis by 8-20 s; however, this slight time offsetis less than the midtime error on the transit, and cannotaccount for the duration difference.We did not refit the OGLE survey light curve, whichis a composite of 13 full and partial transits spanningseveral hundred nights (Udalski et al. 2002). However,we do use the most up-to-date published midtime of thatcomposite light curve (Torres et al. 2004) in our timinganalysis, after adding 66.184 s to correct for the UTC-TToffset ( § TRANSIT FITTING RESULTS
Model
Our transit model fits use the algorithm of Mandel andAgol (2002) as implemented by Carter and Winn (2009),assuming white noise. We assumed that OGLE-TR-56bhas zero obliquity, oblateness and orbital eccentricity.The stellar mass and radius values used to convert themodel output into physical parameters were taken fromTorres et al. (2008) and are listed in Table 4. We alsofixed the orbital period to P = 1 . a/R ∗ into an orbital speed, and therefore has no major effectin the other model parameters. To model the stellarlimb darkening, we assumed a quadratic law with initialvalues for the u and u parameters set to the ATLASvalues for the appropriate filter (Claret 2000, 2004) Inall transits we found it necessary to fix the quadraticterm u . In addition, we only fit for the linear term u in the transits observed in the i (cid:48) and I -band filters, whileleaving it fixed for the transits observed in the B , r (cid:48) , z (cid:48) , W B -bands and with no filter because the precision ofthese light curves is insufficient to constrain the valueof u . The values for u and u are calculated usingthe jktld program by Southworth (2008) , assuming thestellar parameter values T = 6119 K , log g = 4 . ,[ M/H ] = 0, and V micro = 2 km/s. We fixed the coeffi-cients for the wideband transit 20070830 to be the sameas the Sloan i (cid:48) filter, since the actual filter used, WB6300-9500, is centered at the same wavelength, though abouttwice as wide. The limb darkening parameters for thetransit with no filter were derived by setting all otherparameters fixed to a joint-fit value excluding this lightcurve, then fitting for u ,none and u ,none alone. Light curve fits
Each light curve was fit both independently and jointlywith all other light curves using a Markov chain Monte Initial values: u ,none = 0 . u ,none = 0 . u ,B = 0 . u ,B = 0 . u ,r (cid:48) = 0 . u ,r (cid:48) = 0 . u ,z (cid:48) = 0 . u ,z (cid:48) = 0 . u ,I = 0 . u ,I = 0 . u ,i (cid:48) = u ,WB =0 . u ,i (cid:48) = u ,WB = 0 . u ,V + R = 0 . u ,V + R =0 . Carlo (MCMC) method, using Gibbs sampling andMetropolis-Hastings stepping (Tegmark et al. 2004; Hol-man et al. 2006). This method is described in greaterdetail in e.g. Carter et al. (2011). Three independentchains of a million links each were combined, discardingthe first 50,000 links of each chain, to avoid any potentialsolution biases due to the initial values of the input pa-rameters. For each fitted parameter – the radius ratio, k ,inclination, i , semimajor axis ratio, a/R ∗ (global param-eters for all transits), limb darkening coefficients u and u (global for each filter), and out-of-transit flux, F OOT and transit midtime, T C (specific to each transit) – wefind the posterior distribution, all of which are roughlyGaussian. The median value and 68.3% confidence in-tervals of each parameter distribution are reported inTable 4.To account for excess correlated noise in the lightcurves, we calculated the time-averaged residuals. Thisis done by binning the residuals for each light curve intobins from 10 to 30 minutes, the typical time scales ofcorrelated noise (Pont et al. 2006), and then calculatinghow much greater the actual noise is compared to theideal noise assuming photon statistics. The excess noisevaried from 1-2.8 times the predicted noise level, and hasbeen included in the error bars on all transit midtime andindividual parameters.As a check that there were no additional slopes in thedata that could affect the photometry, we ran a testMCMC fit to 12 light curves that included a slope withrespect to airmass as an additional free parameter. Noneof the 12 full light curves fit in this way had a significantshift in transit parameters, so we did not included air-mass slopes in the rest of our analysis.Table 4 summarizes the joint model fit values for theplanet-star radius ratio, k , inclination, i , semimajor axisratio, a/R ∗ , total transit duration, T , full transit dura-tion, T , and ingress/egress duration, T = T . (Thetotal transit duration is the time from first to last con-tact, while the full transit duration is the time when thedisk of the planet is entirely overlapping the disc of thestar. The ingress and egress duration are the times ittakes for the transition, and are equal if the orbit is cir-cular. See Winn (2010) for a mathematical descriptionof the transit nomenclature.)We also fit each light curve independently. Table 5reports each individual parameter and error, along withthe time-averaged residual factors by which those errorshave been increased. To explore variations with time, thevalues are plotted in Figure 3, with the joint-model fitshown as a horizontal line with 1- σ errors. A few partialor noisy light curves (20050419B, 20050419I, 20060714)have been omitted from the individual results; similarly,the radius ratio for 20030730z was fixed to the joint-fitvalue. In general, the independent fit resultss are con-sistent with the joint fit, with the notable exception ofthe original photometry for 20060720P, shown as a redtriangle. No significant variations are seen in any of thestudied parameters over the 6-year time span of the ob-servations. Comparison to previous system parameters
With twenty-one new light curves, the combined fitprovides a more precise determination of the system pa-rameters, as summarized in Table 4. The errors derivedfrom the photometry for the radius ratio, inclination,and semi-major axis are now significantly smaller thanthe error in the measured stellar radius; the componentof the error in the planetary radius ratio due to stellarnoise is fifteen times greater than the contribution fromthe photometry. Any improvement in the stellar param-eters will significantly improve the precision with whichthe radius of OGLE-TR-56b is now known.The radius ratio remains consistent with the value re-ported by Pont et al. (2007), based on a single high-precision light curve. Moreover, of the nineteen lightcurves with independently fit radius ratio values in Ta-ble 5, none lies more than 1.3 σ from the joint-fit value.Most of the new light curves have radius ratio precisionsranging from 1-4%. The lack of change in the transitdepth over time indicates that either the star is less ac-tive than the few percent level, or that the pattern ofstar spots changes very slowly. No evidence was seen ofstar spot crossings.Although our radius ratio agrees with Pont et al.(2007), the transit duration, T is significantly longer,by 18 minutes, with corresponding differences also seenin the highly-correlated inclination and semi-major axis.The duration difference can be seen by eye, as is illus-trated in Figure 4 with three light curves of the sametransit on 2006 July 20. The top curve in Figure 4 cor-responds to the original photometry reported in Pontet al. (2007) for the observations with the VLT. The sec-ond curve shows the same Pont et al. (2007) data frames,but with new aperture photometry in the same manneras the other transits reported in this paper. The thirdcurve shows the same transit epoch observed indepen-dently on Magellan. The solid (black) and dashed (gray)lines in each panel show, respectively, the best fit to allnew light curves, and the best fit to the Pont et al. (2007)light curve alone. A fourth curve for a different transit(20080514) is shown to illustrate the good agreement be-tween the aperture photometry light curves and the restof the data, though not the photometry of Pont et al.(2007).The duration of all transits, except for 20060720P, arebest fit by the longer-lasting transit model (black solidline). We thus conclude that the photometry from Pontet al. (2007) most likely suffers from some unidentifiednoise source that shortens the apparent duration of thetransit; this problem was likely exacerbated by the lackof data immediately before transit. This finding shouldbe taken as a caution against using single-transit lightcurves to argue for transit duration variations due, forexample, to planetary orbital precession.The new value obtained for the semi-major axis ratioof the system, a/R ∗ = 3 . ± .
022 versus the value of3 . ± .
15 derived by Pont et al. (2007), means that theplanet is somewhat closer to the star than previously es-timated. The implications for the planetary temperatureare discussed in § i = 73 . ± .
18, also means that the planet is closer to agrazing orbit than previously thought ( b = 0 . ± . −
100 m s − (Torreset al. 2004; Bouchy et al. 2005). Therefore the am- plitude of the radial velocity signal, and subsequentlythe mass of the star, are not well constrained. Torreset al. (2008) derived a value of M ∗ = 1 . ± . M (cid:12) ,based on the stellar density derived from the photom-etry of Pont et al. (2007). Combined with the or-bital period, P = 1 . . +0 . − . , inconsistent with our new result( a/R ∗ = 3 . ± . − σ in mass and +3 σ in stellar radius needed to achieve con-sistent values for a/R ∗ . A re-analysis of the the radialvelocity data, perhaps including new measurements, arerecommended to accurately determine the stellar param-eters. Implications for the observed planetary occultation
Sing and L´opez-Morales (2009) obtained a z (cid:48) -band oc-cultation depth for OGLE-TR-56b of 0 . ± . T z (cid:48) = 2718 +127 − K, us-ing the values of the system parameters derived by Tor-res et al. (2008) and an effective temperature for thestar of 6119 ± § a/R ∗ , the planet-to-star ra-dius ratio, and the orbital inclination by the new valuesin Table 4. The new fit gives an occultation depth of0 . φ = 0 . ± . . T z (cid:48) = 2708 +102 − K, also consistent with thevalue derived before. Therefore, the atmospheric prop-erties of the planet derived in Sing and L´opez-Morales(2009) remain valid, unless significantly different valuesfor the stellar radius and temperature are found. TIMING
With twenty different transit epochs of OGLE-TR-56bmeasured over eight years, the timing of the system canbe quite well constrained. In Table 6, we present allavailable transit midtimes, including the OGLE surveytime from Torres et al. (2004) as well as the new transitspresented in this work and the re-analyzed data fromPont et al. (2007).We calculate a new transit ephemeris using the tran-sit times derived from the joint fit and also includingthe OGLE survey time (transit 20010615). Two tran-sits observed in alternating filters (20030730 in r (cid:48) and z (cid:48) and 20060720 in R and V ) had divergent transit mid-times when split by filter, so we fit a single combinedlight curve for each transit individually (see also the com-bined fit parameter results in Table 5). In both cases, themidtime from the combined light curve lies between thetimes derived from individual filter curves and is closerto the expected time of transit; this indicates the poten-tial for timing errors if only a partial or poorly-sampledlight curve is fit. (The individual filter curves for a thirdtransit, 20050419, observed in two filters, B and I , wasleft alone, because both filters cover only half a transitand yield large overlapping errors; although included inthe weighted fit, this transit has minimal impact on theresulting ephemeris.)We find the new transit ephemeris to be: T C = 2453936 . BJD ] + 1 . N. (1)where T C is the predicted central time of a transit (notethat this is the same epoch as Pont et al. 2007), N isthe number of periods since the reference midtime, andthe values in parentheses are errors on the last digits.The residuals from this ephemeris are shown in Figure 5,with the lower panel zoomed in on the crowded regionaround the zero epoch. We note that the transit mid-time is robustly measured for the zero epoch, with consis-tent timing results whether we use the original photom-etry (20060720P), the new photometry (20060720V+R)for the VLT light curve, or the independent time fromMagellan (20060720N). The best linear fit has a reduced χ = 2 .
6, so we have scaled the errors on the parame-ters in Equation 1 by √ . .
6. The relatively poorreduced χ suggests that the errors on some transits arestill underestimated; removing the most discrepant 3-4transits from the fit results in a reduced χ of just over1. If these errors really are correct, then it is possiblethat the assumption of a constant ephemeris is incor-rect. The most deviant points are 20060720N at transitnumber 0 ( − . σ ), and 20090612 at transit number 873( − . σ ), but there is no reason to conclude at this timethat intrinsic timing variations are responsible. Limits placed on timing variations
The error on the revised period estimate is 56 ms, withno evidence of decrease seen over the eight year time spanfrom 2001-2009. If we fit for a linear decrease in the or-bital period over time, the rate in change of the periodis ˙ P = − . ±
17 ms yr − , consistent with a constantperiod. Based on this result, we can derive a conserva-tive lower limit estimate for the value of the stellar tidaldecay factor, Q ∗ . Assuming a three-sigma upper limiton the period change (5.4 ms yr − ) and Equation 5 fromLevrard et al. (2009), we find that the tidal decay factorfor OGLE-TR-56 is no less than Q ∗ = 10 . . Further-more, the nominal value obtained for the period changeimplies a Q ∗ = 10 .No evidence is seen of transit duration variations. Thebest fit to the individual transit durations listed in Ta-ble 5, using the combined light curves 20030730r+z and20060720R+V in place of the curves separated by fil-ter, and omitting the much-shorter duration light curve20060720P, finds that the total transit duration haschanged by ˙ T = − . ±
32 s yr − , consistent with nochange. Since the planet has a large impact parameterand nearly-grazing transits, it is possible that in the fu-ture orbital precession might lead to observable changesin the planetary duration. However, no such changeshave been seen to date.We performed numerical integrations to place limitson the perturber mass for a subset of the data, usingthe same method for other planets described in Adamset al. (2010a,b, 2011). Using 11 transits from 2006-2009,companion mass limits were placed down to 12 M J in theexterior 2:1 mean motion resonance. However, we wereunable to successfully run the analysis on the full set oftransit times, most likely owing either to intrinsic insta- bility in the system (meaning very few potential compan-ions would be stable) or an error in our assumptions (thatthe timing residuals are intrinsically flat). Given the highreduced χ value of the constant-period fit in Equation 1,it is most likely that either a few transit errors remainunderestimated, or that there are timing variations thatwill require more data to conclusively identify and char-acterize. CONCLUSIONS
In this work we have presented 21 new light curvesof 19 transits of OGLE-TR-56b, vastly increasing thesupply of high quality data on the planet. Our fittedradius value of 1 . ± . R J is almost identical to thepreviously published value, and we note that the error isalmost entirely supplied by error on the stellar radius; thecomponent of uncertainty from the photometry alone isfifteen times smaller.The values presented for the transit duration, inclina-tion, and semi-major axis in this work are significantlydifferent from those reported earlier, the most likely ex-planation being an error in the previous photometry. Thenew value for a/R ∗ = 3 . ± .
022 places the planetslightly closer to its star than previously thought, whilethe inclination, i = 73 . ± .
18 degrees, means thatplanet is closer to a grazing orbit ( b = 0 . ± . P = 1 . ± . T = − . ±
32 s yr − . The orbital period has likewisebeen constant, with ˙ P = − . ±
17 ms yr − , consistentwith no change. Taking the three-sigma upper limit onthe period change (5.4 ms yr − ) means we can place alower limit on the stellar tidal decay factor of Q ∗ = 10 . ;the nominal value implies Q ∗ = 10 .E.R.A. received support from NASA Origins grantNNX07AN63G. M.L.M. acknowledges support for partsof this work from NASA through Hubble Fellow-ship grant HF-01210.01-A/HF-51233.01 awarded by theSTScI, which is operated by the AURA, Inc. for NASA,under contract NAS5-26555. This paper makes use ofobservations made with the European Southern Obser-vatory telescopes and obtained from the ESO/ST-ECFScience Archive Facility.We thank Paul Schechter for ob-serving a transit of OGLE-TR-56b as part of MIT’s Mag-ellan queue; Brian Taylor and Paul Schechter for theirtireless instrument support; and Georgi Mandushev for assistance with image subtraction. REFERENCESAdams, E. R.: 2010,
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Transit Instrument Frames a Exposure Filter Binning Read Airmass Time observed Atm. Seeing(UT) (sec) (sec) (before ingress) stability (arcsec)20030730r MagIC-SITe 47 (0) – r (cid:48) z (cid:48) −
54 min) – –20050419I MagIC-SITe 59 (0 – I 1x1 23 1.0–1.6 3.3 hrs ( −
53 min) – –20050730 MagIC-SITe 140 (0) – I 1x1 23 1.0–1.4 3.2 hrs (+10 min) – –20050731 MagIC-SITe 113 (0) – I 1x1 23 1.1–1.9 3.0 hrs (+37 min) – –20060622 POETS 6642 (121) b c d c e c f
15, 30 WB g i (cid:48) h
17, 20 i (cid:48) i i (cid:48) i (cid:48) i
23, 25 i (cid:48) c f
20, 30 i (cid:48) c i (cid:48) c f
17, 20 i (cid:48) c i (cid:48) c f i (cid:48) c a Number of frames used (additional frames that were discarded). b Discarded during meridian crossing (images elongated). c Readout is a few miliseconds in frame transfer mode. d Discarded baseline after transit at a different pointing, which did not return to the same ratio level as before. e Discarded 31 frames during meridian crossing, 1347 frames at airmass > f Discarded a few anomalous frames, e.g. due to a seeing spike on one or more frames g WB6300-9500, a wide band filter from 630-950 nm. h Discarded initial frames with low counts on target (50 points) and a minor seeing spike (14 points). i Discarded frames with large target diameters (poor seeing): > > TABLE 2Aperture photometry parameters for each transit
Transit Comp. Aperture a Sky radius, width Slope removed Scatter b (UT) Stars (pixels) (pixels) (mmag)20060622 5 10 c – – 1.020060714 2 8.2 30, 10 – 1.720060720R 6 6.0 50, 5 – 1.020060720V 5 7.0 40, 5 – 1.220060720N 2 14 70, 5 − . − . d − . e c – – 0.620080612 5 12.2 50, 10 – 0.920080727 3 9.0 25, 30 +0 . f . e a Except as noted, the aperture is a circular radius around the star. b Scatter on out-of-transit flux, binned to 2 minutes. c Box half-width for alternate photometry method described in § d Trend removed for each star, individually, against airmass, in units of Z day − . e Trend removed against time, in units of flux day − . f Trend removed against seeing in pixels, in units of flux pixels − . TABLE 3Flux values for new transits of OGLE-TR-56b a Mid-exposure ( JD UTC ) Mid-exposure (
BJD
TDB ) Flux Error2453908.670845 2453908.677416 1.002203 0.0016412453908.670868 2453908.677439 1.007551 0.0016412453908.670891 2453908.677462 0.9947374 0.0016412453908.670914 2453908.677485 1.003771 0.0016412453908.670937 2453908.677508 0.9926688 0.001641 · · · a Full table available online.
TABLE 4New system parameters for OGLE-TR-56
Parameter Value a Radius ratio, k . ± . a/R ∗ . ± . i (deg) 73 . ± . e u ,i (cid:48) . ± . u ,I . ± . b . ± . T (sec) 7931 ± T (sec) 2896 +106 − Ingress/egress duration, T = T (sec) 2518 +59 − Orbital period, P (days) 1 . ± . T (BJD TDB ) 2453936 . ± . a (AU) 0 . ± . b Planetary radius, R p ( R J ) 1 . ± . b Planetary mass, M p ( M J ) 1 . ± . b Stellar radius, R ∗ ( R (cid:12) ) 1 . ± . b Stellar mass, M ∗ ( M (cid:12) ) 1 . ± . ba Median value of parameter distribution from joint fit to 23 light curves,with errors reported from the 68 .
3% credible interval. b Stellar mass and radius values from Torres et al. (2008).
TABLE 5Parameters for independent fits to each transit of OGLE-TR-56b
Transit TAR a k i (deg) a/R ∗ T T T = T . ± . . ± . . ± .
32 8688 . ± . . ± . . ± . . ± . . ± .
17 7707 . ± . . ± . . ± . b . ± .
004 74 . ± . . ± .
28 7500 . ± . . ± . . ± . . ± . . ± . . ± .
21 7728 . ± . . ± . . ± . . ± . . ± . . ± .
14 8143 . ± . . ± . . ± . . ± . . ± . . ± .
54 7938 . ± . . ± . . ± . c . ± . . ± . . ± .
15 6817 . ± . . ± . . ± . . ± . . ± . . ± .
24 7764 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . d . ± . . ± .
14 7822 . ± . . ± . . ± . . ± . . ± . . ± .
15 7858 . ± . . ± . . ± . . ± . . ± . . ± .
11 8025 . ± . . ± . . ± . . ± . . ± . . ± .
07 7817 . ± . . ± . . ± . . ± . . ± . . ± .
18 7924 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
17 7829 . ± . . ± . . ± . . ± . . ± . . ± .
33 7817 . ± . . ± . . ± . . ± . . ± . . ± .
19 8182 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
15 8039 . ± . . ± . . ± . . ± . . ± . . ± .
32 7801 . ± . . ± . . ± . . ± . . ± . . ± .
33 7524 . ± . . ± . . ± . a Multiplicative factor indicating excess noise, as derived from the time-averaged residual method. b Combined r (cid:48) and z (cid:48) photometry. c New fit to original photometry of Pont et al. (2007) d Combined V and R photometry. TABLE 6OGLE-TR-56b Transit Midtimes and Residuals
Transit Number Midtime (
BJD
TDB ) O-C (s) σ Source20010615 a -1536 2452075 . ± . − ±
147 -0.1 Torres et al. (2004)20030730r -896 2452850 . ± . ±
80 2.9 this work20030730z -896 2452850 . ± . − ±
72 -1.4 this work20030730r+z b -896 2452850 . ± . ±
39 1.4 this work20050419B -377 2453479 . ± . ±
466 0.1 this work20050419I -377 2453479 . ± . − ±
246 -0.6 this work20050730 -293 2453581 . ± . − ±
83 -0.0 this work20050731 -292 2453582 . ± . ±
63 0.8 this work20060622 -23 2453908 . ± . − ±
51 -1.2 this work20060626 -19 2453913 . ± . − ±
114 -2.0 this work20060714 -5 2453930 . ± . ±
148 0.8 this work20060720P c . ± . − ±
86 -1.9 Pont et al. (2007)20060720V 0 2453936 . ± . − ±
69 -4.2 this work20060720R 0 2453936 . ± . ±
62 2.2 this work20060720V+R d . ± . − ±
79 -1.1 this work20060720N 0 2453936 . ± . − ±
39 -3.6 this work20070830 335 2454342 . ± . ±
40 2.0 this work20080514 548 2454600 . ± . ±
27 1.9 this work20080612 572 2454629 . ± . ±
71 1.3 this work20080727 609 2454674 . ± . − ±
73 -0.1 this work20090428 836 2454949 . ± . − ±
56 -0.4 this work20090504 841 2454955 . ± . − ±
92 -0.7 this work20090510 846 2454961 . ± . ±
60 0.6 this work20090521 855 2454972 . ± . ±
38 2.2 this work20090612 873 2454994 . ± . − ±
52 -3.4 this work20090613 874 2454995 . ± . − ±
68 -1.6 this work20090728 911 2455040 . ± . − ±
80 -0.0 this work a Time has been adjusted from the published times into the
BJD TT time system by adding UTC-TTconversion of 64.184 sec. b Midtime value when the r (cid:48) and z (cid:48) light curves are combined and fit independently. c Light curve from Pont et al. (2007); the midtime reported is from our independent fit of the originalphotometry. d Midtime value when the R and V light curves are combined and fit independently.
400 600 800nm noneB V r R WBi M i G Is I z Filtercolorkey0.9800.9850.9900.9951.0001.005 20030730r 20030730z 20050419B 20050419I0.9800.9850.9900.9951.0001.005 20050730 20050731 20060622 200606260.9800.9850.9900.9951.0001.005 20060714 20060720N 20060720R 20060720V0.9800.9850.9900.9951.0001.005 20070830 20080514 20080612 200807270.9800.9850.9900.9951.0001.005 20090428 20090504 20090510 200905210.05 0.00 0.050.9800.9850.9900.9951.0001.005 20090612 0.05 0.00 0.0520090613 0.05 0.00 0.0520090728
Time since midtime (days) N o r m a li z e d F l u x Fig. 1.—
Twenty-three light curves observed over nineteen different transit epochs of OGLE-TR-56b. All data are binned to 2 minutesto aid comparison. The solid lines show the best model for all curves, color-coded by the instrument and filter used: SITe/ B = black,FORS1/ V =purple, SITe/ r (cid:48) = dark blue, FORS1/ R =light blue, IMACS/WB6500-9300 = cyan, e2v/ i (cid:48) = green, GMOS/ i (cid:48) = dark green,POETS/ Is = yellow, SITe/ I = orange, SITe/ z (cid:48) = red, and POETS/no filter = gray. The residuals from the model are plotted below eachcurve. Fig. 2.—
The field of view for OGLE-TR-56, as observed on 2008 May 14 with MagIC-e2v on the 6.5 m Baade telescope. Field of viewis 38 (cid:48)(cid:48) x 38 (cid:48)(cid:48) , with north up and east to the left. k d e g i a/R ∗ h r s T h r s T h r s T = T Transit Number
Fig. 3.—
Parameter variation of individual transits of OGLE-TR-56b. Data from the individual MCMC fits (Table 5) is shownfor the inclination ( i ), semimajor axis ( a/R ∗ ), planet-star radius ratio ( k ), total transit duration ( T ), full transit duration ( T ), andingress/egress duration, assuming a circular orbit ( T = T ). Note that all errors have been scaled upward based on the factor calculatedfrom residual permutation. For comparison, the value derived from the joint MCMC fit is plotted as a solid blue lines with dashed ± σ errors. We highlight our independent fit to the light curve published by Pont et al. (2007) in red to illustrate that it is markedly discrepantfor all parameters except the radius ratio. (cid:43) RVLTthis work20060720NMagellanthis work20080514Magellanthis work (cid:45) (cid:72)
BJD (cid:76) N o r m a li z ed F l u x Fig. 4.—
Three light curves of the transit on 2006 July 20, observed independently by two instruments, with a fourth curve on a differentnight for comparison. Data has not been binned. Top curve: original image-subtraction photometry for transit 20060720P observed withFORS1 on the VLT by Pont et al. (2007), with R -band data in red and V -band data in black. Second curve: the same VLT transit, redonewith aperture photometry for this work. Third curve: independent observation of the same transit with no filter, 20060720N, using POETSon Magellan (discussed in § O - C ( s e c ) (cid:242)(cid:242) (cid:243)(cid:243)(cid:230)(cid:230) (cid:230)(cid:230) (cid:230)(cid:230)(cid:230)(cid:230) (cid:230) (cid:230)(cid:230)(cid:230) (cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:231)(cid:231) (cid:231)(cid:231)(cid:224) (cid:224) (cid:45) (cid:45) (cid:45)
500 0 500 (cid:45) (cid:45) (cid:45) (cid:243)(cid:243)(cid:230) (cid:230) (cid:230) (cid:230)(cid:231)(cid:231)(cid:224) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) Orbital Periods
Fig. 5.—
Observed minus calculated midtimes for OGLE-TR-56b. Timing residuals using the new ephemeris (Equation 1). Solid symbolsmark transits that were used to calculate the ephemeris. The solid red triangle at − § σ and 3 σ errors on the calculated orbital period, indicating the slopes that result for a mis-determinedperiod. Notice that the 1 σ and 3 σσ