System parameters, transit times and secondary eclipse constraints of the exoplanet systems HAT-P-4, TrES-2, TrES-3 and WASP-3 from the NASA EPOXI Mission of Opportunity
Jessie L. Christiansen, Sarah Ballard, David Charbonneau, Drake Deming, Matthew J. Holman, Nikku Madhusudhan, Sara Seager, Dennis D. Wellnitz, Richard K. Barry, Timothy A. Livengood, Tilak Hewagama, Don L. Hampton, Carey M. Lisse, Michael F. A'Hearn
aa r X i v : . [ a s t r o - ph . E P ] N ov System parameters, transit times and secondary eclipse constraints of theexoplanet systems HAT-P-4, TrES-2, TrES-3 and WASP-3 from the NASA
EPOXI
Mission of Opportunity.
Jessie L. Christiansen , Sarah Ballard , David Charbonneau , Drake Deming ,Matthew J. Holman , Nikku Madhusudhan , Sara Seager , Dennis D. Wellnitz ,Richard K. Barry , Timothy A. Livengood , Tilak Hewagama , , Don L. Hampton ,Carey M. Lisse , and Michael F. A’Hearn ABSTRACT
As part of the NASA
EPOXI
Mission of Opportunity, we observed seven knowntransiting extrasolar planet systems in order to construct time series photometry ofextremely high phase coverage and precision. Here we present the results for four “hot-Jupiter systems” with near-solar stars—HAT-P-4, TrES-3, TrES-2 and WASP-3. Weobserve ten transits of HAT-P-4, estimating the planet radius R p = 1 . ± . R Jup ,the stellar radius R ⋆ = 1 . ± . R ⊙ , the inclination i = 89 . ± .
30 degrees andthe transit duration from first to fourth contact τ = 255 . ± . R p = 1 . ± . R Jup , R ⋆ = 0 . ± . R ⊙ , i = 81 . ± .
30 degrees and τ = 81 . ± . R p = 1 . ± . R Jup , R ⋆ = 0 . ± . R ⊙ , i = 84 . ± . τ = 107 . ± . R p = 1 . ± . R Jup , R ⋆ = 1 . ± . R ⊙ , i = 84 . ± .
81 degrees and τ = 167 . ± . Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA;[email protected] Goddard Space Flight Center, Greenbelt, MD 20771, USA Massachusetts Institute of Technology, Cambridge, MA 02159, USA University of Maryland, College Park, MD 20742, USA University of Alaska Fairbanks, Fairbanks AK 99775, USA Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
Subject headings: planetary systems — eclipses — stars: individual (HAT-P-4, WASP-3, TrES-2, TrES-3)
1. Introduction
The EPOXI Mission of Opportunity is a re-purposing of the Deep Impact flyby spacecraft, andcomprises the Extrasolar Planet Observation and Characterization (EPOCh) investigation and theDeep Impact eXtended Investigation (DIXI). The primary goal of EPOCh was to scrutinize asmall set of known transiting extrasolar planets. From 2008 January to 2008 August, we used thehigh resolution imaging (HRI) instrument (Hampton et al. 2005) and a broadband visible filterto construct high precision, high phase coverage and high cadence light curves for seven targets.We observed each target nearly continuously for several weeks at a time. The main science goalsof EPOCh were to refine the system parameters of the known planets, to search for additionalplanets both directly (via transits of the additional body) and indirectly (via induced changes inthe transits of the known planet), and to constrain the reflected light from the known planet atsecondary eclipse. It is also useful to provide updated periods and times of epoch for these systemsin order to reduce uncertainties on predicted transit and eclipse times, and therefore maximizethe return of follow-up observations. In previous EPOCh papers we have presented the search foradditional planets in the GJ 436 system (Ballard et al. 2010) and the secondary eclipse constraintsfor HAT-P-7 (Christiansen et al. 2010). In this paper we present the updated system parameters,including constraints on the transit timing and changes in the transit parameters, and secondaryeclipse constraints for a further four targets: HAT-P-4, TrES-3, TrES-2 and WASP-3, introducedbelow. The search for additional planets in these systems will be presented in a separate paper(Ballard et al. in prep).The exoplanet HAT-P-4b (Kovacs et al. 2007), orbits a slightly evolved metal-rich late F star.With a mass of 0.68 M Jup and a radius of 1.27 R Jup , it joined the ranks of inflated planets thathave continued to challenge models of the physical structure of hot Jupiters.TrES-3 (O’Donovan et al. 2007) is notable for its very short orbital period of 1.30619 days.This proximity to the star makes TrES-3 a promising target for observations of reflected light atvisible wavelengths; the planet-to-star flux ratio as measured in reflected light during the secondaryeclipse is given by A g ( R p /a ) , where A g is the geometric albedo, R p is the planetary radius and a is the semi-major axis of the planetary orbit. Winn et al. (2008), de Mooij & Snellen (2009)and Fressin et al. (2010) have observed secondary eclipses of TrES-3 at visible and near-infraredwavelengths, and the emerging picture of the planetary atmosphere is one with efficient day-nightre-circularization and no temperature inversion in the upper atmosphere. This is in contrast topredictions of a temperature inversion based on the high level of irradiation (Fortney et al. 2008).Sozzetti et al. (2009) studied the transit timing variations of TrES-3 and noted significant outliers 3 –from a constant period. Gibson et al. (2009) monitored further transit times of TrES-3 and ruledout sub-Earth mass planets in the exterior and interior 2:1 resonances for circular orbits.TrES-2 (O’Donovan et al. 2006) was the first transiting planet found in the field of view ofthe NASA Kepler mission (Borucki et al. 2009). Holman et al. (2007) noted that the high impactparameter ( b ≈ .
85) of TrES-2 made transit parameters such as inclination and duration sensitiveto changes due to orbital precession. Mislis & Schmitt (2009) and Mislis et al. (2010) claimed asignificantly shorter duration for TrES-2 transits two years after the measurements of Holman et al.(2007). They proposed that this was caused by a change in orbit inclination due to precession, andthat the duration would continue to decrease. However, Scuderi et al. (2009) measured a durationconsistent with O’Donovan et al. (2006) and Holman et al. (2007) and did not see the predictedtrend of decreasing transit duration. Secondary eclipses of TrES-2 have been observed in the near-infrared (O’Donovan et al. 2010), and the results favor a thermal inversion in the upper atmosphere,supporting the hypothesis that highly irradiated planetary atmospheres have inversions. The transittiming variations of TrES-2 have been studied by Raetz et al. (2009) and Rabus et al. (2009), whofind no statistically significant variations.WASP-3b (Pollacco et al. 2008), with a short period (1.84634 days) and a hot host star (F7-F8V, T eff = 6400K), is one of the hottest transiting planets known, and another very good targetfor observing reflected light at secondary eclipse.The paper is organized as follows. The observations and generation of the light curves aredescribed in Section 2, the transit analysis is presented in Section 3, the secondary eclipse analysisis presented in Section 4 and the results are discussed in Section 5.
2. Observations and analysis
The EPOCh observations were made using the high resolution imager (HRI), which has a 30-cmaperture and a 1024 × ×
128 pixel sub-array of the full CCD, to ensure full phase coverage between data downlinksfrom the spacecraft. The CCD comprises four quadrants that are read out independently, and thesub-array is centered on the CCD where the four quadrants meet. The pixel scale is 0.4 arcsecpixel − , resulting in a sub-array field of view of 0.72 square arcminutes. The images are significantdefocused, resulting in a stellar point-spread function (PSF) with a full-width half maximum of 4arcseconds. Typically this meant that the target star was the only star in the field of view, andwe were unable to employ relative photometry techniques for removing correlated noise in the lightcurves.Table 1 summarizes the observing schedules for each of the four targets. HAT-P-4 and TrES-3, 4 –along with GJ436 and XO-2, were observed during the initial observing block from 2008 Januaryto 2008 May. The project was awarded an additional contingent observing block from 2008 Juneto 2008 August, during which time HAT-P-4 was re-observed, and TrES-2 and WASP-3 were alsoobserved. During the contingent observations we began observing in a larger 256 ×
256 pixel sub-array mode, to reduce losses from pointing drifts that occasionally resulted in the target star lyingoutside of the 128 ×
128 pixel sub-array field of view. The number of images that could be obtainedwith the larger sub-array mode between data downlinks from the spacecraft was constrained bythe data storage capacity on board the spacecraft. Therefore, in order to maximize the phasecoverage we chose to restrict observations in the 256 ×
256 pixel sub-array mode to the times ofparticular interest—during the transits and secondary eclipses. One event per data downlink couldbe observed in the larger sub-array mode without reducing the temporal coverage. Table 1 showsthe total number of transits and eclipses observed for each target, with the number observed in the256 ×
256 pixel sub-array mode given in parentheses. As discussed in Section 1, TrES-2 was claimedto show changes in the transit inclination with time. Therefore, we used the larger sub-array modeto observe the transits of TrES-2 where possible. WASP-3 was a promising target for secondaryeclipse observations, and therefore we observed the secondary eclipses of WASP-3 in the largermode where possible. For HAT-P-4 we observed two of the three transits and two of the threeeclipses obtained in the contingent observations in the 256 ×
256 pixel sub-array mode. TrES-3 wasobserved in the initial observing block and no observations were obtained in the larger mode.
We receive calibrated FITS images from the extant Deep Impact data reduction pipeline(Klaasen et al. 2005). These data have been bias- and dark-subtracted and flat-fielded, usingcalibration images obtained on the ground before launch. Due to the very high precision requiredin the light curves, we perform several additional calibration steps to account for changes in theCCD since launch. The spacecraft pointing drifts considerably with time, resulting in significantcoverage of the CCD by the stellar PSF and placing paramount importance on the flat-fielding.The procedure is described in Ballard et al. (2010) and summarized here.Table 1. EPOCh observations
Target V Mag UT Dates observed (2008) No. of Transits a No. of Eclipses a HAT-P-4 11.22 01/22–02/12, 06/29–07/07 10 (2) 9 (2)TrES-3 11.18 03/06–03/18 7 (0) 6 (0)TrES-2 11.41 06/27–06/28, 07/19–07/29 9 (7) 8 (2)WASP-3 10.64 07/17–07/18, 07/30–08/07, 08/10–08/15 8 (0) 9 (8) a Including partial events. The number in brackets is the subset of events observed in 256 ×
256 pixelsub-array mode. σ outliers from the PSF fit, assumingthe stellar PSF to be contaminated by an energetic particle hit. We subtract a time-dependent biascalculated for each quadrant from the corresponding overscan region. We reduce the pixels in thecentral columns and rows of the CCD (forming the internal boundaries between the quadrants) byroughly 15% and 1% respectively, to correct an artifact produced by the CCD readout electronics.For data obtained in the 256 ×
256 pixel mode, we scale the images by a constant (typically differingfrom unity by one part in a thousand) to correct an observed flux offset between the two sub-arraymodes.In order to track time-dependent changes in the flat-field since launch, there is a small greenLED stimulation lamp that can be switched on to illuminate the CCD. We obtained blocks of 200calibration frames using this lamp, which were taken every few days throughout the observations,alternating between blocks in the smaller and larger sub-array modes in the contingent observations.We correct each science frame by the flat-field generated from lamp images taken in the same sub-array mode. We assume any remaining flat-field errors to be color-dependent and therefore unableto be addressed by the monochromatic lamp.We perform aperture photometry, using a circular aperture of radius 10 pixels. The resultinglight curves exhibit significant correlated noise on the order of 1%, which is associated with thedrift in the spacecraft pointing. In order to correct for this, we use the data itself to generate asensitivity map of the CCD. We assume the out-of-transit and out-of-eclipse data to be of uniformbrightness, with two caveats. First, the star may have intrinsic variations in stellar brightness dueto spots. Only one of the four targets displayed long-period variability (Figure 3), and this wasremoved by fitting and removing a polynomial in time before producing the CCD sensitivity map.Second, transits of additional planets may be present, which will be suppressed with this treatment(Ballard et al. 2010). We randomly draw several thousand of the out-of-transit and out-of-eclipsepoints and find a robust average flux of the 30 spatially nearest neighbors. We use this set ofaverages to generate a two-dimensional surface spline to the flux distribution across the CCD. Eachpoint in the light curve is then corrected by interpolating onto this surface. The entire procedureis iterated several times to converge on the positions and scaling factors that result in the lowestscatter in the out-of-transit and out-of-eclipse data in the final light curve.The robustness of the surface spline for each target depends on the coverage of the CCD bythat target. If the coverage is small and the corresponding density of photometry apertures high,then there is a high probability that the same pixel will be returned to multiple times over theobservations. Having flux measurements separated in time reduces the influence of stellar activityon our calibration of the sensitivity of each pixel. Figure 1 shows the complete CCD coverage fortwo targets. TrES-2 is well confined on the CCD and the density of photometry apertures leadsto a more robust surface spline. The TrES-2 light curve prior to and post the application of thesurface spline is shown in Figure 4. On the other hand, the photometry apertures for WASP-3sample a much larger area of the CCD, and in addition many of the observations obtained in the 6 –256 ×
256 pixel sub-array mode do not overlay the central 128 ×
128 pixel sub-array. The resultingsurface spline is therefore more sensitive to noise introduced by stellar activity or systematics thatare not an artifact of the pointing jitter. The WASP-3 light curve prior to and post the applicationof the surface spline is shown in Figure 5. The lower panel of Figure 5 shows how the noise in thefinal calibrated WASP-3 light curve bins down compared with the expectation for Gaussian noise,and the poor quality of the data is due to the low density of the CCD coverage for WASP-3.Fig. 1.— The CCD positions of the photometry apertures for two targets.
Left : TrES-2 is confinedto the center of the CCD and therefore the same pixels are sampled well for creating a robust surfacespline.
Right : WASP-3 is spread over a much larger fraction of the CCD, including large excursionsout of the central 128 ×
128 pixel sub-array when observations were obtained in the 256 ×
256 pixelsub-array. This reduces the quality of the surface spline and results in a larger component ofcorrelated noise in the WASP-3 light curve.
The final HAT-P-4 light curve is shown in Figure 2. HAT-P-4 was the first EPOCh targetobserved, initially for 22 days from 2008 January 22 to 2008 February 12, during the originalEPOCh target schedule, and again for 8 days from 2008 June 29 to 2008 July 7 during the contingentobservations. Of the 45,320 images obtained of HAT-P-4, 5434 were discarded due to the star beingeither out of the field of view or too close to the edge of the CCD to measure accurate photometry,1305 were discarded due to energetic particle hits, and 76 were discarded due to readout smear,for a final total of 38,505 acceptable images. All of the data obtained in the initial run are in the128 ×
128 pixel sub-array mode. Of the contingent data, two of the three transits and two of the 7 –three eclipses are in the larger 256 ×
256 pixel sub-array mode, and the remaining data are in thesmaller mode. The bottom panel of Figure 2 shows how the scatter in the final light curve scalesdown with increasing bin size—for Gaussian noise the expectation is the scatter will decrease as1 / √ N , where N is the number of points in the bin.Fig. 2.— Upper panel : The full HAT-P-4 EPOXI light curve. The left panel shows the originalrun of seven consecutive transits. The right panel shows the three transits observed five monthslater during the EPOCh contingent observations. In each panel the lower curve is before the firstapplication of the surface spline and the upper curve is the final calibrated light curve. The reddata points were obtained in the larger 256 ×
256 pixel sub-array mode.
Lower panel : The scatterin the out-of-transit data with increasing bin size (diamonds) and comparing to the expectationfor Gaussian noise (1 / √ N , where N is the number of points in the bin, shown as the solid linenormalized to the unbinned value of the scatter). The points do not follow the line, indicatingresidual correlated noise in the light curve.The final TrES-3 light curve is shown in Figure 3. TrES-3 was the second EPOCh targetobserved, for 12 days from 2008 March 6 to 2008 March 18. The gap in the light curve from 2–5days is due to a ‘pre-look’ for the subsequent EPOCh target, XO-2, which was performed in orderto refine the pointing for that target. We obtained a total of 14,195 images of TrES-3, of whichwe discarded 1165 due to the star being out of or too close to the edge of the field of view, 1632 8 –due to energetic particle hits and 127 due to readout smear, leaving 11,271 images. We obtainedall of the TrES-3 data in the 128 ×
128 pixel sub-array mode. After the initial application of thetwo-dimensional surface spline a long timescale, low amplitude variability was evident in the lightcurve. This can be seen in the lower light curve in Figure 3. In order to remove this variability webin the out-of-transit data by two hours and fit with a time-dependent fifth-order polynomial forthe data occurring later than 4.0 days. We divide out this feature before iterating over the previoussteps to produce the final light curve. The polynomial is plotted on the lower light curve, and thefinal light curve is shown as the upper curve in Figure 3. As with HAT-P-4, the bottom panel ofFigure 3 shows the noise properties of the data.Fig. 3.—
Upper panel : The TrES-3 EPOXI light curve. The gap from 2.5–5 days is during thepre-look for a subsequent target. Seven transits of TrES-3 were observed in total. The lowestlight curve is prior to the first application of the surface spline, the middle light curve is after theapplication of the spline but prior to the removal of the time-dependent polynomial, and the upperlight curve is the final calibrated data set.
Lower panel : See Figure 2 for explanation. In the caseof TrES-3, where all data were obtained in the smaller sub-array mode and the total time span isrelatively short, the scatter bins down close to the expectation for Gaussian noise.The final TrES-2 light curve is shown in Figure 4. We observed TrES-2 during the contingentEPOCh observations, from 2008 July 7 to 2008 July 30, in addition to a pre-look for pointing on 9 –2008 June 28 and 29. In total, we obtained 31,210 images of TrES-2, with 1979 discarded due tothe star lying out of or too close to the edge of the field of view, 1427 discarded due to energeticparticle hits and 80 discarded due to readout smear, for a total of 27,724 acceptable images. Weobserved nine transits in total, including seven in the 256 ×
256 pixel sub-array mode. The lowerpanel of Figure 4 shows that correlated noise remains in the final light curve.Fig. 4.—
Upper panel : The TrES-2 EPOXI light curve. The data obtained from days 1–3 are thepre-look, for refinement of the spacecraft pointing. From days 3–11 the spacecraft was observing adifferent target before returning to TrES-2 with updated pointing parameters. The gap from days21–23 spans the pre-look for the subsequent target. Nine transits of TrES-2 were observed in total.The lower curve is prior to the first application of the surface spline and the upper curve is the finalcalibrated light curve. The red data points were obtained in the larger 256 ×
256 pixel sub-arraymode.
Lower panel : See Figure 2 for explanation.The final EPOCh light curve for WASP-3 is shown in Figure 5. We observed WASP-3 duringthe contingent observations, from 2008 July 29 to 2008 August 16, with a pre-look from 2008 July17 to 2008 July 19. We obtained 24,015 images of WASP-3, of which we discarded 4,182 due tothe star being out of or too close to the edge of the field of view, 403 due to energetic particlehits, and 808 due to readout smear, leaving 18,622 acceptable images. For WASP-3, none of theeight transits were observed in 256 ×
256 pixel sub-array mode, however eight of the nine secondary 10 –eclipses were observed in this mode. The two-dimensional surface spline relies on multiple visits tothe same part of the CCD to characterize robustly the interpixel variations. This is particularlytrue for the data that occur during the transits and eclipses, since they cannot be assumed to beof uniform flux and are therefore excluded from the creation of the surface. In order to effectivelyflat-field the data that are taken during transit and eclipse, the observations taken during thesetimes must be gathered at the same spatial positions as data obtained at other times. In the case ofWASP-3, four of the eight secondary eclipses occurred at locations that were poorly sampled. Noout-of-transit or out-of-eclipse observations fell on these pixels, and therefore we cannot estimatethe true sensitivity of these pixels in order to produce an effective flat-field. These eclipses occurat 1.0, 17.6, 19.3 and 26.6 days, and can be seen in the light curve as increases in flux. Thesefour eclipses are discarded for the final analysis. Besides these events, a significant fraction of theWASP-3 data are distributed in poorly-sampled areas of the CCD, degrading the robustness of thetwo-dimensional surface spline. The bottom panel of Figure 5 demonstrates the adverse effect thishas on the noise properties of the final light curve, as the data do not bin down as expected forGaussian noise.
3. Transit analysis
For the transit analysis, we make several additional calibration steps. The two-dimensionalsurface spline uses only a fraction of the data to generate the surface, in order to preserve as muchof the information in the light curve as possible, and to minimize the suppression of transits ofputative additional planets. However for the transit analysis, we use all of the available data tocalibrate each event. For each transit, we define a window approximately three times the durationof the transit, centered on the predicted transit time. We take each point in this window and dividethe flux by a robust average of the 30 spatially nearest points that do not fall in any of the transitwindows. This is essentially a point-by-point application of the full two-dimensional surface spline.We then fit a slope, linear with time, to the out-of-transit data across each transit and divide itout, to remove any residual long timescale trends.For TrES-3, TrES-2 and WASP-3, we generate non-linear limb-darkening coefficients of theform given by Claret (2000), I µ /I = 1 − P n =1 c n (1 − µ n/ ), where I is the specific intensity atthe center of the disk and µ = cos ( γ ), with γ the angle between the emergent intensity and the lineof sight. We use photon-weighted stellar atmosphere models of Kurucz (1994, 2005) that bracketthe published values of stellar T eff and log g , and convolve these with the total EPOXI responsefunction, including filter, optics and CCD response. We fit for the four coefficients of the non-linearform of the limb-darkening using 17 positions across the stellar limb, at 2 nm intervals along the350–1000 nm bandpass. We calculate the final set of coefficients as the weighted average whenintegrated over the bandpass, and bi-linearly interpolate across T eff and log g for each target. Thefinal set of coefficient for each targets is given in Table 3 for TrES-3, Table 4 for TrES-2 and Table5 for WASP-3. 11 –Fig. 5.— Upper panel : The WASP-3 EPOXI light curve. The first two days of data are the pre-lookto refine the pointing. The gap between 22 and 24 days is due to the pre-look for the subsequenttarget. The significant positive deviations seen at 1.0, 17.6, 19.3 and 26.6 days are instrumental innature; see the text for details. The lower curve is prior to the first application of the spatial splineand the upper curve is the final calibrated light curve. The red data points were obtained in thelarger 256 ×
256 pixel sub-array mode.
Lower panel : See Figure 2 for explanation.The quality of the EPOCh light curves is nearly sufficient to fit for the limb-darkening coeffi-cients rather than assuming theoretical values. Ultimately, the degeneracies between the geometricparameters of the transiting system and the limb-darkening coefficients prevent us from placingmeaningful constraints on the coefficients. In the case of HAT-P-4 however, the system is very closeto edge-on ( i = 89 . +0 . − . degrees), which reduces the parameter space considerably. Therefore, forHAT-P-4 we instead use a quadratic equation for the limb-darkening, I µ /I = 1 − a (1 − µ ) − b (1 − µ ) ,and allow two linear combinations of the coefficients, c = 2 a + b and c = a − b to be free param-eters in the transit analysis, which produced a better fit to the data as defined below.When fitting the transits, we use the analytic equations of Mandel & Agol (2002) to generatea model transit, and use χ as a goodness-of-fit estimator. We use the Levenberg-Marquardtalgorithm to fit three dimensionless geometric parameters of the system: R p /R ⋆ , R ⋆ /a and cos i ,where R p is the planetary radius, R ⋆ is the stellar radius, a is the semi-major axis of the planetary 12 –orbit and i is the inclination of the orbit. We fix the period to the published value, but allow the timeof center of transit to vary independently for each of the transits. We then use the published massvalues for each of the systems to convert the transit parameters to physical properties, drawingvalues from Kovacs et al. (2007) for HAT-P-4, Sozzetti et al. (2009) for TrES-3, Sozzetti et al.(2007) for TrES-2 and Pollacco et al. (2008) for WASP-3. The final results of these fits are givenin Table 2 for HAT-P-4, Table 3 for TrES-3, Table 4 for TrES-2 and Table 5 for WASP-3. Wealso give the transit duration from first to fourth contact for each best-fit model. For WASP-3, wediscard the final transit (which was significantly offset in flux due to correlated noise), and also apartial transit (which included only the ingress), for a total of six transits. The phase-folded andbinned transits for each target are shown in Figure 6 for HAT-P-4, Figure 7 for TrES-3, Figure 8for TrES-2 and Figure 9 for WASP-3.The errors on the parameters are calculated using the residual permutation “rosary bead”method (Winn et al. 2008). For each target, we find the residuals to the best-fit model. We shiftthese residuals forward collectively to the next time stamp and add the best fit models back to thenew residuals, generating a new realization of the light curve which retains the correlated noisesignals in the original light curve. We repeat this process 8000 times (covering approximately sixdays) and each time we fit for and record the geometric parameters, times of center of transit, andlimb-darkening coefficients where appropriate. For each parameter we construct a histogram of the8000 measurements, to which we fit a Gaussian. We then define the error on that parameter bythe half-width half-maximum value of the best fit Gaussian. We find that increasing the numberof iterations beyond 4000 does not significantly change the calculated errors.To find the errors in the transit times, we perform a second rosary bead analysis, holdingthe geometric and limb-darkening values fixed and allowing only the times of center of transit tovary. We find that 4000 iterations are sufficient to sample the range of correlated noise signals, andcalculate the errors in the same fashion as the geometric parameters. For each target we calculatea new orbital period and epoch by performing a weighted linear fit to the EPOCh transit timesand any published transit times.
4. Secondary eclipse constraints
Our constraints of the secondary eclipse depths are limited by the correlated noise in the
EPOXI data. Ideally, for each target we would combine our multiple observations of the secondaryeclipses to increase the signal to noise. However, the fluctuations due to the correlated noisepreclude this. For example, Figure 11 shows six of the TrES-3 secondary eclipses, where in somecases correlated noise results in an increase in flux at the time of secondary eclipse, instead ofthe expected decrement. If we assume that the secondary eclipse in the EPOCh bandpass, with acentral wavelength of 650 nm, is due exclusively to the reflected light of the planet, then the eclipsedepths we would anticipate, for a geometric albedo of 1, would range from 0.02% for HAT-P-4 to 13 –Table 2. HAT-P-4 system parameters
Parameter ValueAdopted values a M ⋆ ( M ⊙ ) 1 . ± . M p ( M Jup ) 0 . ± . R p /R ⋆ . ± . a/R ⋆ . ± . i (deg) 89 . ± . P (days) 3 . ± . T c (BJD) 2 , , . ± . R ⋆ ( R ⊙ ) 1 . ± . R p ( R Jup ) 1 . ± . τ (mins) 255 . ± . a b , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . a Masses are from Kovacs et al. (2007).
14 –Table 3. TrES-3 system parameters
Parameter ValueAdopted values a M ⋆ ( M ⊙ ) 0 . +0 . − . M p ( M Jup ) 1 . +0 . − . Transit fit values R p /R ⋆ . ± . a/R ⋆ . ± . i (deg) 81 . ± . P (days) 1 . ± . T c (BJD) 2 , , . ± . R ⋆ ( R ⊙ ) 0 . ± . R p ( R Jup ) 1 . ± . i (deg) 81 . ± . τ (mins) 81 . ± . c c -0.6008 c c -0.5743Transit times (BJD) 2 , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . a Masses are from Sozzetti et al. (2009).
15 –Table 4. TrES-2 system parameters
Parameter ValueAdopted values a M ⋆ ( M ⊙ ) 0 . ± . M p ( M Jup ) 1 . ± . R p /R ⋆ . ± . a/R ⋆ . ± . i (deg) 84 . ± . P (days) 2 . ± . T c (BJD) 2 , , . ± . R ⋆ ( R ⊙ ) 0 . ± . R p ( R Jup ) 1 . ± . τ (mins) 107 . ± . c c -0.1391 c c -0.0329Transit times (BJD) 2 , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . a Masses are from Sozzetti et al. (2007).
16 –Table 5. WASP-3 system parameters
Parameter ValueAdopted values a M ⋆ ( M ⊙ ) 1 . +0 . − . M p ( M Jup ) 1 . +0 . − . Transit fit values R p /R ⋆ . ± . a/R ⋆ . ± . i (deg) 84 . ± . P (days) 1 . ± . T c (BJD) 2 , , . ± . R ⋆ ( R ⊙ ) 1 . ± . R p ( R Jup ) 1 . ± . i (deg) 84 . ± . τ (mins) 167 . ± . c c c -0.1040 c -0.0426Transit times (BJD) 2 , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . a Masses are from Pollacco et al. (2008).
17 –Fig. 6.— The seven HAT-P-4 transits from the original observing schedule, phase-folded and binnedin five minute intervals. light curve. The solid line is the best fit transit model.
Lower panel : Theresiduals when the best-fit model is subtracted from the data.0.08% for TrES-3. Since the fluctuations from correlated noise in the measured eclipse depths are sometimeslarger than the signal we expect to measure, we choose not to combine the multiple observationsand instead analyze each eclipse independently. Our intent is to use the scatter of individual eclipsemeasurements to constrain the amplitude of the correlated noise. As for the transits, for each eclipsein the data we apply a point-by-point correction to the data in and adjacent to the eclipse. For thetargets presented here we assume that e = 0 and therefore that the secondary eclipse occurs at aphase of 0.5. For TrES-3 and TrES-2 this assumption is strongly supported by previous secondaryeclipse measurements with the Spitzer
IRAC instrument which demonstrated no evidence of non-zero eccentricity (Fressin et al. 2010 and O’Donovan et al. 2010 respectively). For HAT-P-4 andWASP-3, the extant radial velocity data are consistent with circular orbits (Kovacs et al. 2007 In fact, the CCD is found to be quite efficient at the redder wavelengths, and it is therefore feasible that for thehottest planets there may be a contribution from the thermal emission of the planet, resulting in deeper secondaryeclipses.
18 –Fig. 7.—
Upper panel : The seven TrES-3 transits, phase-folded and binned in two minute intervals.The solid line is the best-fit transit model.
Lower panel : The residuals when the best-fit model issubtracted from the data.and Pollacco et al. 2008 respectively). In addition to the point-by-point correction, we fit a lineartime-dependent slope to the adjacent out-of-eclipse data to remove any remaining long timescaletrends. Finally, we separate the data into 10 minute bins and remove 3 σ flux outliers from eachbin. For TrES-2, we discard the first observed eclipse, which was obtained during the pre-look forthis target, since the pre-look data are not well calibrated by the surface spline generated for theremaining data. We assume this is due to changes in the CCD in the time that occurred betweenthe pre-look and the full set of observations. We also discard eclipses where less than half the eventis observed, one for TrES-2, one for WASP-3 and one for HAT-P-4. As discussed in Section 2.2,we finally discard four of the nine WASP-3 secondary eclipses that fall on regions of the CCD wecannot calibrate.We fit the eclipses using a transit model with the best-fit parameters from the transit analysisand no limb-darkening. We then scale the depth of this model to fit the data, finding the depththat minimizes the χ value. For each target we then find the mean (¯ x ) and standard deviation( σ x ) of the individual best-fit depths, and define the 95% confidence upper limit on the eclipsedepth as ¯ x + 2 σ x . The secondary eclipses of HAT-P-4, TrES-3, TrES-2 and WASP-3 are shown in 19 –Fig. 8.— Upper panel : The nine TrES-2 transits, phase-folded and binned in two minute intervals.The solid line is the best-fit transit model.
Lower panel : The residuals when the best-fit model issubtracted from the data.Figures 9–12. The upper limits are given in Table 6. We note that we achieve a useful constraintonly in the case of TrES-3.
5. Discussion5.1. HAT-P-4
For HAT-P-4, our estimates of the system parameters are consistent with (and in the case ofinclination, more precise than) those published by Kovacs et al. (2007) and Torres et al. (2008).We calculate R p = 1 . ± . R Jup , R ⋆ = 1 . ± . R ⊙ , i = 89 . ± .
30 degrees and τ = 255 . ± . τ is the transit duration from first to fourth contact. We use thediscovery epoch and the ten EPOCh transit times presented in this paper to produce a new refinedephemeris of T c (BJD) = 2454245 . ± . . ± . E . Figure 14 shows theresiduals to the new ephemeris. We see no evidence for transit timing variations in the residualswhich have a scatter of roughly 2 minutes. 20 –Fig. 9.— Upper panel : The eight WASP-3 transits, phase-folded and binned in two minute intervals.The solid line is the best-fit transit model.
Lower panel : The residuals when the best-fit modelis subtracted from the data. The significant in-transit deviation from the model is discussed inSection 5.We use eight of the nine observed secondary eclipses to constrain the depth of the eclipse inthe EPOCh bandpass, discarding the ninth due to poor coverage of the event. The eclipses areshown in Figure 10. We set a 95% confidence upper limit on the eclipse depth of 0.073%, which, ifit were produced entirely by reflected light, would correspond to a planetary geometric albedo of A g = 3 .
5, a physically impossible value. In the future, full phase curves of HAT-P-4 are scheduledto be observed in the near-infrared 3.6 and 4.5 micron IRAC bands, as part of the Warm
Spitzer census of exoplanet atmospheres, at which point we may begin to study the atmosphere in moredetail.
For TrES-3, we find system parameters consistent with those published by O’Donovan et al.(2007), Sozzetti et al. (2009) and Gibson et al. (2009), with R p = 1 . ± . R Jup , R ⋆ = 0 . ±
21 –Fig. 10.— Eight EPOCh secondary eclipse observations of HAT-P-4, offset in relative flux forclarity and binned in five minute intervals. The error on each point is σ/ √ N , where σ is the scatterin the bin and N the number of points. The solid lines are the best fit eclipse model in each case.The bottom three eclipses were obtained in the contingent block of observations.0 . R ⊙ , i = 81 . ± .
30 degrees and τ = 81 . ± . σ level, and hence not significant (and largelydependent on the most recent value from Sozzetti et al. 2009). A more model-independent wayof constraining changes in the transit parameters with time is by measuring the transit duration.Where available, we use the quoted transit duration and error, and otherwise we calculate theTable 6. EPOCh secondary eclipse measurements Target Eclipse Depth Upper limit Implied A g HAT-P-4 − . ± . − . ± . . ± . . ± .
22 –Fig. 11.— Six EPOCh secondary eclipse observations of TrES-3, offset in relative flux for clarity.The error on each point is σ/ √ N , where σ is the scatter in the bin and N the number of points.The solid lines are the best fit eclipse model in each case.transit duration from the published parameters, using equation (4) from Charbonneau et al. (2006).Following the analytic approximation of Carter et al. (2008), we set the error on these calculatedtransit durations to twice the error in the measured transit times for each source. Although thiserror was originally derived for the transit duration from mid-ingress to mid-egress, as comparedto the transit duration from first to fourth contact, we find that for the EPOCh data the errorscalculated using this approximation and the errors measured from the data themselves are nearlyidentical (1.1 minutes and 1.0 minutes respectively). We plot the derived values in the lower panelof Figure 15, and we see no evidence of a change in the transit duration with time.In Section 2.2 we noted that in the process of calibrating the light curve, a long term variabilitywas evident. This variability is consistent with stellar variability due to spots. Using a v sin i of < − (O’Donovan et al. 2007), the rotational period of TrES-3 must be >
21 days, considerablylonger than our observation span of 12 days. We can therefore not place any additional constraintson the rotational period of TrES-3, however we note that if the variability is due to spots on thestellar surface rotating in and out of view then additional monitoring of TrES-3 may reveal therotational period. 23 –Fig. 12.— Six EPOCh secondary eclipse observations of TrES-2, offset in relative flux for clarity.The error on each point is σ/ √ N , where σ is the scatter in the bin and N the number of points.The solid lines are the best fit eclipse model in each case.For TrES-3, we calculate a new ephemeris of T c (BJD) = 2454538 . ± . . ± . E using the published transit times and the seven EPOCh transits presented in thispaper. Figure 16 shows the residuals to the new ephemeris. We see no evidence of the periodchanging with time or transit timing variations larger than 1 minute.Using the six EPOCh secondary eclipse observations of TrES-3, shown in Figure 11, we set a95% confidence upper limit on the eclipse depth of 0.062%. This indicates the planetary geometricalbedo must be A g < .
81 in the EPOCh bandpass. Winn et al. (2008) observed secondary eclipsesof TrES-3 in the i , z and R bands, and were able to put 99% confidence upper limits on theeclipse depths of 0.024%, 0.050% and 0.086% respectively. The EPOCh upper limit at 0.65 µ m isconsistent with the R band upper limit. de Mooij & Snellen (2009) observed the secondary eclipsein the K band and found a depth of 0.241 ± Spitzer
IRAC instrument, measuring depths of 0.356 ± ± ± ± σ/ √ N , where σ is the scatter in the bin and N the number of points.The solid lines are the best fit eclipse model in each case.Given the high levels of stellar irradiation, the atmosphere of TrES-3 was anticipated to hosta thermal inversion (Fortney et al. 2008; de Mooij & Snellen 2009). Using all data sets, however,Fressin et al. (2010) found the observations to be best fit with a dayside atmosphere model withouta thermal inversion.Our model spectra are computed using the exoplanet atmosphere model developed in Madhusudhan & Seager(2009). The model consists of a line-by-line radiative transfer model, with constraints of hydrostaticequilibrium and global energy balance, and coupled to a parametric pressure-temperature (P-T)structure and parametric molecular abundances (parametrized as deviations from thermochemicalequilibrium and solar abundances). Our modeling approach allows one to compute large ensemblesof models, and efficiently explore the parameter space of molecular compositions and temperaturestructure.We confirm previous findings that existing detections of day-side observations can be explainedto within the 1 σ uncertainties by models without thermal inversions. The black curve in Figure 17shows one such model spectrum, which has a chemical composition at thermochemical equilibrium 25 –Fig. 14.— The transit times of HAT-P-4. The open diamonds are the EPOCh transit times fromthis paper; the asterisk is the discovery epoch (Kovacs et al. 2007). Lower panel : An expandedview of the EPOCh transit times, with 1 σ errors of 48-71 seconds.and solar abundances for the elements. The model is also consistent with the EPOCh upper-limitat 0.65 microns, and with the upper-limits from Winn et al. (2008). The dark green dashed curveshows a 1600K blackbody spectrum of the planet, indicating that the data cannot be explainedby a pure blackbody. The model reported here has a day-night energy redistribution fraction of0.4, indicating very efficient redistribution. Therefore, based on previous studies and our currentfinding, existing data do not require the presence of a thermal inversion in TrES-3. However, adetailed exploration of the model parameter space would be needed to rule out thermal inversionswith a given statistical significance (Madhusudhan & Seager 2010). For TrES-2, we derive system parameters that are consistent at the 1.5 σ level with estimatespublished by O’Donovan et al. (2006), Sozzetti et al. (2007), and Holman et al. (2007), finding R p = 1 . ± . R Jup , R ⋆ = 0 . ± . R ⊙ , i = 84 . ± .
16 degrees and τ = 107 . ± . Upper panel : The estimates of the inclination for TrES-3 as a function of time.
Lowerpanel : The estimates of the TrES-3 transit durations.minutes.As discussed in Section 1, there is currently a debate as to whether the inclination of theplanetary orbit and duration of the TrES-2 transit are decreasing with time due to orbital precession.In the upper panel of Figure 18 we plot the estimates for the inclination as a function of time. For theinclination, the error bars of Mislis & Schmitt (2009), Mislis et al. (2010) and Scuderi et al. (2009)were calculated by fixing the stellar and planetary radii and allowing only the inclination and timeof center of transit to vary. The remainder of the inclination error bars were calculated allowingall of the geometric parameters to vary simultaneously, which explains why they are considerablylarger than the later results. Since the errors skew any weighted linear fit towards an unrealisticallylarge increase in the inclination with time, we instead plot an unweighted linear fit to guide theeye. We note that TrES-2 is in the
Kepler field and that any change in inclination with time willsoon be measured with exquisite precision.The inclination measured from a particular transit light curve will necessarily depend on thegeometric parameters and to some extent the choice of limb-darkening treatment. However, thetransit duration is directly measurable from the light curve and should not depend on the limb 27 –Fig. 16.— The times of transit of TrES-3. O’D07: O’Donovan et al. (2007); S09: Sozzetti et al.(2009); G09: Gibson et al. (2009); EPOXI: this paper.
Lower panel : An expanded view of theEPOCh transit times, with 1 σ errors of 28–35 seconds.darkening. The lower panel of Figure 18 shows the published transit durations as a function oftime. Where they were not given, we calculated the durations and errors as described for TrES-3.In this case, we perform a weighted linear fit and do see a formally significant decrease in thetransit duration with time. However, this conclusion is heavily dependent on one point, in thiscase the duration calculated from Holman et al. (2007). If this point is excluded from the fit, then dτ /dt = − . ± . Kepler to provide a clear answer to this question.Using the published transit times of TrES-2 and the nine transits observed by EPOCh pre-sented in this paper, we find a new weighted ephemeris of T c (BJD) = 24544664 . ± . . ± . E . The residuals to this ephemeris are shown in Figure 19. In the EPOChresiduals, we see no variations in the transit times above the level of 2 minutes; excluding theamateur data from the Exoplanet Transit Database due to the large error bars, the scatter in thefull set of residuals is less than 5 minutes. We see no evidence for long term drifts in the period. 28 –Fig. 17.— The optical and near-infrared secondary eclipse measurements of TrES-3. The EPOChupper limit of 0.062% is shown in blue at 0.65 microns. The remaining upper limits in the opticalare from Winn et al. (2008); the measurement at 2.2 microns is from de Mooij & Snellen (2009);and the four measurements from 3.6 to 8.0 microns are from Fressin et al. (2010). The solid blackline is a representative model from the set of models that fit the data to within 1 σ , and the dashedlined shows a black-body spectrum for a temperature of 1600K. The green circles represent themodel integrated to the Spitzer bandpasses. The inset is the temperature-pressure profile for themodel shown.We used six of the eight EPOCh secondary eclipses of TrES-2 to place a 95% confidence upperlimit on the eclipse depth of 0.16%. This corresponds to a planetary geometric albedo of A g = 6 . For WASP-3, we measure system parameters that are consistent with, and an improvementupon, previously published parameters from Pollacco et al. (2008) and Gibson et al. (2008), finding 29 –Fig. 18.—
Upper panel : The estimates of the inclination of TrES-2 as a function of time. Thedotted line is an unweighted linear fit. O’D07: (O’Donovan et al. 2007); H07: (Holman et al. 2007);R09: (Rabus et al. 2009); M09/10: (Mislis & Schmitt 2009; Mislis et al. 2010); S09: (Scuderi et al.2009); EPOXI: this paper.
Lower panel : The TrES-2 transit durations. In this case the dotted lineis a weighted linear fit. R p = 1 . ± . R Jup , R ⋆ = 1 . ± . R ⊙ , i = 84 . ± .
81 degrees and τ = 167 . ± . T c (BJD) = 2454686 . ± . . ± . E . The residualsto this ephemeris are shown in Figure 20.The phase-folded light curve of WASP-3 (Figure 9) shows correlated residuals in the latter halfof transit. Since the noise in the transit exceeds the noise out of transit, one conclusion could bespot activity on the surface of the star being eclipsed during transit. However, if we examine thetransits individually we observe that the correlated noise in the full light curve is not typically largerin transit than out of transit. The six transits used in the analysis are shown in Figure 21. In thetransits numbered 2, 3, 4, and 6 large deviations can be seen in the second half of the transit, whichleads to residuals in the phased light curve. If there were star spots producing correlated residualsin the transits, we would not necessarily expect them to occur at the same phase for each transit.The v sin i for WASP-3 has been measured by Simpson et al. (2009) to be 15 . +1 . − . km s − , which 30 –Fig. 19.— Upper panel : The transit times of TrES-2. O’D06: O’Donovan et al. (2006); H07:Holman et al. (2007); R09: Raetz et al. (2009); R09(ETD): Raetz et al. (2009) (from the ExoplanetTransit Database, http://var.astro.cz/ETD); EPOXI: this paper.
Lower panel : An expanded viewof the EPOCh transit times, with 1 σ errors of 24–44 seconds.corresponds to a rotational period for the star of 4.2 days. Transits of WASP-3 are spaced by 1.85days, so it is improbable for spot activity to appear at the same phase in successive transits. Giventhese constraints, we conclude that the alignment of signals with phase in the EPOCh transits ofWASP-3 are coincidental and are due to instrumental artifacts.We use four of the nine EPOCh secondary eclipse observations of WASP-3 to set a 95%confidence upper limit on the eclipse depth of 0.11%. This corresponds to a planetary geometricalbedo of A g = 2 .
6. Conclusion
We have presented time series photometry from the NASA
EPOXI
Mission of Opportunityfor four known transiting planet systems: HAT-P-4, TrES-3, TrES-2 and WASP-3. For each 31 –Fig. 20.— The transit times of WASP-3. P08: Pollacco et al. (2008); G08: Gibson et al. (2008);EPOXI: this paper.
Lower panel : An expanded view of the EPOXI transit times, with 1 σ errorsof 23–51 seconds.system we provided an updated set of system parameters and orbital period, and placed upperlimits on the secondary eclipse depth. For TrES-3, we see evidence of stellar variability over longtimescales. We combined the EPOCh secondary eclipse upper limit for TrES-3 with previouslypublished measurements and confirm that the data are best fit using an atmosphere model withno temperature inversion. For TrES-2, the EPOCh data weaken the claimed trends of decreasinginclination and transit duration (Mislis & Schmitt 2009; Mislis et al. 2010). We have also performeda search for additional transiting planets in the EPOCh photometry for these systems, which wewill present in a forthcoming paper.We are extremely grateful to the
EPOXI
Flight and Spacecraft Teams that made these difficultobservations possible. At the Jet Propulsion Laboratory, the Flight Team has included M. Abra-hamson, B. Abu-Ata, A.-R. Behrozi, S. Bhaskaran, W. Blume, M. Carmichael, S. Collins, J. Diehl,T. Duxbury, K. Ellers, J. Fleener, K. Fong, A. Hewitt, D. Isla, J. Jai, B. Kennedy, K. Klassen, G.LaBorde, T. Larson, Y. Lee, T. Lungu, N. Mainland, E. Martinez, L. Montanez, P. Morgan, R.Mukai, A. Nakata, J. Neelon, W. Owen, J. Pinner, G. Razo Jr., R. Rieber, K. Rockwell, A. Romero, 32 –Fig. 21.— The six EPOCh transits of WASP-3. The best fit model for the combined set of transitsis plotted in each case. The scatter around the model is not typically larger in transit than out oftransit, indicating that the in-transit residuals cannot be attributed to star spots.B. Semenov, R. Sharrow, B. Smith, R. Smith, L. Su, P. Tay, J. Taylor, R. Torres, B. Toyoshima,H. Uffelman, G. Vernon, T. Wahl, V. Wang, S. Waydo, R. Wing, S. Wissler, G. Yang, K. Yetter,and S. Zadourian. At Ball Aerospace, the Spacecraft Systems Team has included L. Andreozzi,T. Bank, T. Golden, H. Hallowell, M. Huisjen, R. Lapthorne, T. Quigley, T. Ryan, C. Schira, E.Sholes, J. Valdez, and A. Walsh.Support for this work was provided by the
EPOXI
Project of the National Aeronautics andSpace Administration’s Discovery Program via funding to the Goddard Space Flight Center, andto Harvard University via Co-operative Agreement NNX08AB64A, and to the Smithsonian Astro-physical Observatory via Co-operative Agreement NNX08AD05A. The authors acknowledge andare grateful for the use of publicly available transit modeling routines by Eric Agol and KaiseyMandel, and also the Levenberg-Marquardt least-squares minimization routine MPFITFUN byCraig Markwardt. This work has used data obtained by various observers collect in the ExoplanetTransit Database, http://var.astro.cz/ETD. 33 –
REFERENCES
Ballard, S., et al. 2010, ApJ, submitted, arXiv:0909.2875Borucki, W. J., et al. 2009, Science, 325, 709Carter, J. A., Yee, J. C., Eastman, J., Gaudi, B. S., & Winn, J. N. 2008, ApJ, 689, 499Charbonneau, D., et al. 2006, ApJ, 636, 445Christiansen, J. L., et al. 2010, ApJ, 710, 97Claret, A., 2000, A&A, 363, 1081de Mooij, E. J. W., & Snellen, I. A. G. 2009, A&A, 493, 35Fortney, J. J., Lodders, K., Marley, M. S., & Freedman, R. S. 2008, ApJ, 678, 1419Fressin, F., Knutson, H. A., Charbonneau, D., O’Donovan, F. T., Burrows, A., Deming, L. D.,Mandushev, G., & Spiegel, D. 2010, ApJ, 711, 374Gibson, N. P., et al. 2008, A&A, 492, 603Gibson, N. P., et al. 2009, ApJ, 700, 1078Hampton, D. L., Baer, J. W., Huisjen, M. A., Varner, C. C., Delamere, A., Wellnitz, D. D.,A’Hearn, M. F., & Klaasen, K. P. 2005, Space Science Reviews, 117, 43Holman, M. J., et al. 2007, ApJ, 664, 1185Klaasen, K. P., Carcich, B., Carcich, G., Grayzeck, E. J., & McLaughlin, S. 2005, Space ScienceReviews, 117, 335Kovacs, G., et al. 2007, ApJ, 670, 41Kurucz, R. 1994, Solar abundance model atmospheres for 0,1,2,4,8 km/s. Kurucz CD-ROMNo. 19. Cambridge, Mass.: Smithsonian Astrophysical Observatory, 1994., 19Kurucz, R. L. 2005, Memorie della Societa Astronomica Italiana Supplement, 8, 14Madhusudhan, N., & Seager, S. 2009, ApJ, 707, 24Madhusudhan, N., & Seager, S. 2010, ApJ, in press, arXiv:1010.4585Mandel, K., & Agol, E. 2002, ApJ, 580, L171Mislis, D., & Schmitt, J. H. M. M, 2009, A&A, 500, L45Mislis, D, Schr¨oter, S., Schmitt, J. H. M. M., Cordes, O., & Reif, K. 2007, A&A, 510, 107 34 –O’Donovan, F. T., et al. 2006, ApJ, 651, L61O’Donovan, F. T., et al. 2007, ApJ, 663, L37O’Donovan, F. T., Charbonneau, D., Harrington, J., Madhusudhan, N., Seager, S., Deming, L. D.& Knutson, H. A. 2010, ApJ, 710, 1551Pollacco, D., et al. 2008, MNRAS, 385, 1576Raetz, St., et al. 2009, AN, 330, 459Rabus, M, Deeg, H. J., Alonso, R., Belmonte, J. A., & Almenara, J. M. 2009, A&A, 508, 1011Scuderi, L. J., Dittman, J. A., Males, J. R, Green, E. M., & Close, L. M. 2009, ApJ, submitted,arXiv:0907.1685Simpson, E. K., et al. 2009, MNRAS, submitted, arXiv:0912.3643Sozzetti, A, et al. 2009, ApJ, 691, 1145Sozzetti, A., Torres, G., Charbonneau, D., Latham, D., Holman, M. J., Winn, J. N., Laird, J. B.,& O’Donovan, F. T. 2007, ApJ, 664, 1190Torres, G., Winn, J. N., & Holman, M. J. 2007, ApJ, 677, 1324Winn, J. N., et al. 2008, ApJ, 683, 1076