Observations of the WASP-2 System by the APOSTLE Program

0.8 MB·English

by  Andrew C. Becker

Draftversion January18,2013
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
OBSERVATIONS OF THE WASP–2 SYSTEM BY THE APOSTLE PROGRAM
Andrew C. Becker 1, Praveen Kundurthy 1, Eric Agol 1, Rory Barnes 1,2, Benjamin F. Williams 1, Amy E.
Rose 1
Draft version January 18, 2013
ABSTRACT
We present transit observations of the WASP–2 exoplanet system by the Apache Point Survey
3 of Transit Lightcurves of Exoplanets (APOSTLE) program. Model fitting to these data allows us
1 to improve measurements of the hot–Jupiter exoplanet WASP–2b and its orbital parameters by a
0 factor of ∼ 2 over prior studies; we do not find evidence for transit depth variations. We do find
2 reduced χ2 values greater than 1.0 in the observed minus computed transit times. A sinusoidal fit
to the residuals yields a timing semi–amplitude of 32 seconds and a period of 389 days. However,
n
random rearrangementsof the data provide similar quality fits, and we cannot with certainty ascribe
a
J the timing variations to mutual exoplanet interactions. This inconclusive result is consistent with
the lack of incontrovertible transit timing variations (TTVs) observed in other hot–Jupiter systems.
7
This outcome emphasizes that unique recognition of TTVs requires dense sampling of the libration
1
cycle (e.g. continuous observations from space-based platforms). However, even in systems observed

] with the Kepler spacecraft, there is a noted lack of transiting companions and TTVs in hot–Jupiter
P systems. Thisresultismoremeaningful,andindicatesthathot–Jupitersystems,whiletheyareeasily
E observable from the ground, do not appear to be currently configured in a manner favorable to the
. detection of TTVs. The future of ground–based TTV studies may reside in resolving secular trends,
h
and/or implementation at extreme quality observing sites to minimize atmospheric red noise.
p
- Subject headings: eclipses, stars: planetary systems, planets and satellites: fundamental parameters,
o individual: WASP-2b
r
t
s
a 1. INTRODUCTION stars and across observing epochs, with leading terms
[ including the structure function of clouds (Ivezi´c et al.
The transit technique is a highly efficient means of
2007), the time–rate of change of aerosols and water va-
1 searching for exoplanetary systems. The detection of
por in the atmosphere (Stubbs et al. 2007), and atmo-
v transiting systems requires a fortuitous observing geom-
spheric scintillation (Young et al. 1991). Space–based
5 etry during the experiment – the exoplanet must be ob-
observations by the Kepler spacecraft (Borucki et al.
5 served to traverse its host’s stellar disk, occurring for
9 ∼ 10% of viewing angles for hot Jupiters, but only 2010) set the gold–standard for relative photometry,
3 0.4% for Earth analogues – and a control of experi- reaching root–mean–square systematic variations of 20
1. mental systematics at or below the level of the tran- ppmontimescalesofseveralhours(Gilliland et al.2011).
As recognized by Agol et al. (2005) and
0 sit depth. For hot–Jupiter systems around Solar–type
3 stars, this may be as high as 1% (104 parts per mil- Holman & Murray (2005), the times of transits in
multi–planet systems may not be exactly periodic due
1 lion, ppm) of the out–of–transit depth; an Earth ana-
to mutual gravitational interactions of the planets.
: logue in the same system would cause a transit depth
v Multiple studies have been undertaken to search for
of only 85 ppm. Ground–based observations have been
i these transit timing variations (TTVs) in known tran-
X able to achieve per–exposure precisions of down to 211
siting exoplanet systems, using high–precisionfollow–up
ppm (Tregloan-Reed & Southworth 2012) to 250 ppm
r observations. The vast majority of follow–up has
a (Gilliland et al. 1993) for the brightest objects. More
been undertaken on systems originally discovered from
commonly, in transit follow–up efforts where measure-
the ground, which have been heavily biased towards
ments of faint stars in the field is not a priority, rela-
hot–Jupiter systems. The follow–up sampling of these
tive photometry at the 300–500 ppm level is achieved
transits is often irregular, due to weather, daytime,
through defocusing and precision tracking, which mini-
and seasonal effects. This makes detection of the
mize the sampling of the flat–field function, and allow
libration of transit times, expected to occur over the
the observer to accumulate more photons before sat-
timescales of months to years, difficult to recognize
uration (e.g. Southworth et al. 2009; Winn et al. 2009;
because the signal is undersampled. Bou´e et al. (2012)
Gillon et al. 2012; Lendl et al. 2012). Methods to model
outline the difficulties in resolving TTVs in Jovian
thenon–random(“red”)noiseinthedataarealsoshown
systems: they are mostly relevant for systems near
toimprovethe accuracyofphotometrictransitmeasure-
(but not exactly at) mean–motion resonance, and even
ments (Carter & Winn 2009). However, relative preci-
detected signals may yield degenerate solutions for
sioninground–baseddataisultimatelylimitedbyatmo-
the mass of the perturber. No unambiguous TTVs
spheric decoherence between the target and comparison
have yet been discovered in ground–based follow–up
1Astronomy Department, University of Washington, Seattle, (see however Tingley et al. 2011). In contrast, the
WA98195 Keplerspacecraftfollows–upits owndiscoveriesthrough
2VirtualPlanetaryLaboratory, USA
2
continuous lightcurve coverage. Several multi–planet
systemshavebeendiscoveredthroughKeplerTTVs(e.g.
Ford et al. 2012; Steffen et al. 2012a; Fabrycky et al.
2012), which have proven to be a powerful verification
and mass measurement technique for planet candidates
(Cochran et al. 2011).
2. APOSTLEPROGRAM
TheApachePointSurveyofTransitLightcurvesofEx-
oplanets (APOSTLE; Kundurthy et al. 2013b) program
was initiated as a systematic study of known transiting
exoplanet systems on the ARC 3.5m telescope + Agile
imager (Mukadam et al. 2011). The large aperture of
the system and frame–transfer capabilities of Agile al-
low us to obtain high–precision(500 ppm RMS) relative
photometry between R = 10.8th and R = 10.8th mag-
nitude stars (XO–2; Kundurthy et al. 2013a), decreas-
ing to 700 ppm at R = 12.2 vs. R = 12.9 (TrES–3;
Kundurthy et al. 2013b), and 1000 ppm at R = 13.8
Figure 1. Seven I-bandand threer-banddetrended lightcurves
vs. R = 13.6 (GJ 1214; Kundurthy et al. 2011). Im-
oftheWASP-2system. Theverticalaxisisinnormalizedfluxratio
portantly,these observationshappenat100%duty cycle units. Thehorizontalaxisshowstimefromthemid–transittimein
due toAgile’sframe–transfercapabilities. We makeuse days, computed by subtracting the appropriate mid–transit time
of the MultiTransitQuickmodeling programdescribed foreachtransitfromthebest–fitvaluesintheθMulti−Depthchain.
inKundurthy et al.(2013b),whichusesaMarkovChain
Reduced lightcurves were detrended and mod-
Monte Carlo (MCMC) analyzer alongside a lightcurve
eled using the MultiTransitQuick (MTQ) package
parameterization that minimizes degeneracies between
(Kundurthy et al. 2013b). We used MTQ in two modes:
fittedparameters,ensuringthattheMCMC proceedsef-
to fit for similar transit depths for data taken in a
ficiently and faithfully samples parameter space.
given filter (Multi-Filter model); and to fit each transit
This paper describes APOSTLE observations of the
depth individually (Multi-Depth). The set of parame-
WASP–2 (Cameron et al. 2007) system. The host star
WASP–2A is a R = 11.3, spectral type K1 dwarf, tersusedforMulti–FilterversionofMTQisθMulti−Filter =
{t ,t ,D ,v ,v ,T }, where t is
with an effective temperature of T = 5110± 60 in- T G j...NF 1,j...NF 2,j...NF i...NT T
eff transitdurationandt the limb–crossingduration. The
ferred from optical and infrared colors (Maxted et al. G
per–filter fit parameters, up to the number of filters
2011), T = 5150 ± 80K using photospheric fitting
eff N , include the transit depth D, and limb darkening
of spectroscopic data (Triaud et al. 2010), and metal- F
parameters v and v . Finally, the parameter set in-
licity of [Fe/H] = 0.08±0.08 (Triaud et al. 2010). In 1 2
cludes mid–transittimes T up to the number of transits
our modeling we included photometric data from pre- i
vious publications including Southworth et al. (2010) – NT. FortheMulti–DepthversionweusedθMulti−Depth =
{t ,t ,D ,v ,v ,T }, the main
who converted the timings from Cameron et al. (2007), T G i...NT 1,j...NF 2,j...NF i...NT
difference being we fit for each transit depth separately
Charbonneau et al. (2007), Hrudkov´a et al. (2009) into
(N ) instead of per–filter (N ).
the common time standard BJD(TDB) as outlined by T F
As outlined in Kundurthy et al. (2013b) and
Eastman et al.(2010)–aswellasonetransitepochfrom
Kundurthy et al. (2013a), we did not fit for the limb
Sada et al. (2012).
darkening coefficients as they result in poorly converged
Markovchains. Insteadwe keptthem fixedatvaluesde-
3. APOSTLEOBSERVATIONSOFWASP–2
termined using the Claret & Bloemen (2011) quadratic
The APOSTLE data reduction pipeline is described limb darkening models: u = 0.3926, u = 0.2166,
1,I 2,I
in prior publications, including our observational tech- u = 0.5541, u = 0.1594 (see Csizmadia et al.
1,r 2,r
niques, details of photometric extraction, detrending 2013, for cautions regarding this procedure). Our limb
of the lightcurves, and parameterization of the tran- darkening terms v ,v are linear combinations of the
1 2
sit model (Kundurthy et al. 2013b). Specifically to the Claret & Bloemen (2011) quadratic terms, v =u +u
1 1 2
WASP–2 system, we acquired 7 Cousins I–band and 3 and v =u −u .
2 1 2
r–band transit sequences between July 2007 and Octo- Figure 1 presents our detrended data, offset for clar-
ber 2010. The I–band images were fringe–corrected us- ity, with the best–fit model lightcurvesoverplotted. The
ingthetechniquesdescribedinKundurthy et al.(2013a). root–mean–square scatter about the model fits ranged
Observations were taken with a variety of instrumental from 472 ppm (2008-10-03) to 2252 ppm (2007-07-26),
settings, staring with 0.5s observations on the nights of withamedianof626ppmfortheI–banddata,and1146
2007-07-24 and 2007-07-26, and moving to longer defo- for the r–band data.
cussedexposuresstarting in 2010. For the analysis here, High resolution imaging of the system by
alldatawerebinnedtoequivalent–45sexposures. Forall Daemgen et al. (2009) reveals a faint companion
observationsweusedtheR=11.4comparisonstarTYC within the wings of the WASP–2 host star, which will
522-780-1. affect our conversion from D to R /R . This required
p ⋆
that we estimate the apparent I–band and r–band
4. MODELFITTING magnitudes of WASP–2A and the contaminating star
3
(named here WASP–2/C). Fitted–for and derived system parameters are pre-
′ ′
We converted the reported i and z magnitudes from sented in Table 1, along with their uncertainties. We
Daemgen et al. (2009) using the transformations pre- notethatthereportedtransitdepthsarefortheWASP–
sented in Rodgers et al. (2006) and Jordi et al. (2006), 2systemonly, after correctionfor WASP–2/C.For com-
as well as on the SDSS DR7 webpage 3. The final esti- parison, we present the results from Southworth et al.
mates yielded r = 11.68±0.11, I = 11.00±0.11, (2010, S10), who observed in Cousins R–band. Figure 2
2A 2A
r =17.05±0.20,I =15.39±0.20. The two domi- presents the joint probability distributions of fitted–for
2/C 2/C
nantuncertaintiesintheseconversionsare: theapparent (left) and derived parameters (right). The left panel
brightnesses reported by Daemgen et al. (2009), which shows a much smaller level of correlation between pa-
are uncertain to 0.1 magnitudes; and for WASP–2/C its rameters, making it an effective basis in which to per-
redder color, which leads to a larger uncertainty in each form MCMC. Final MTQ times of transits for each night
color–term. This result indicated that 0.7% of the stel- of observation are presented in the left–hand columns of
larfluxinther–bandcomesfromWASP–2/C,and1.7% Table 2.
in the I–band; the WASP–2b transit depth D increased To model the effects of correlated lightcurve noise on
proportionally. The change in the I–band depth was our transit times, we used the Transit Analysis Package
approximately four times the parameter uncertainty de- (TAP; Gazak et al. 2012), which is an implementation of
terminedbelow,makingthisanecessarycorrection. The the red–noise model of Carter & Winn (2009). Impor-
derived values of R /R increased by 0.3% and 0.8% in tantly, TAP models the amplitude of “white” (random)
p ⋆
the r–band and I–band, respectively. and “red” (correlated) noise on each night of observa-
Foreachparameterset(θMulti−Filter andθMulti−Depth), tions. We applied TAP using the period derived from
we ran two MCMC chains, each having 2×106 steps. MTQ, fixed limb darkening values, and zero eccentricity
These were cropped at the beginning of the chains, andargumentofperiastron. ForAPOSTLEobservations
where the step acceptance rate is lower than optimal of WASP–2, the median red (white) noise contributions
(Gelman et al. 2003), yielding approximately 1.8×106 were0.002(0.0006)magnitudesintheI–band,and0.006
steps per chain used in the subsequent analysis. These (0.0006) magnitudes in the r–band. This indicated that
chainswere comparedagainsteachother to evaluate the while the statistical noise in the two datasets is compa-
Gelman–RubinRˆ–static(Gelman & Rubin1992)andas- rable, the correlated noise dominates, and is larger in
the r–banddata. Thissuggeststhatthe correlatednoise
sure that the chains sufficiently sampled model space.
comes from intrinsic stellar variability (either of the tar-
Evaluation of our Multi–Depth fit indicated that the
getor comparisonstar),orperhaps thatthe nights ofr–
depths in the I–band were consistent at D = 0.0174±
I bandobservationhappenedtohavelargertime–variation
0.0003 magnitudes, while in the r–band the depth were
inatmosphericmolecularwaterabsorption(Stubbs et al.
also consistent (D = 0.017±0.001) but with a larger
r 2007). The TAP system parameters are included in Ta-
RMSduetohavingonly2completelysampledtransits4.
ble 1, and times of transit in the right–hand columns of
Wefoundnoevidencefortransitdepthvariationswithin
Table 2. While the TAPuncertainties are typically larger
these data, and present the Multi–Filter fits as our final
thanthose fromMTQ,inallcasesthe APOSTLEanalysis
results.
yields an improvement in precision over previous mea-
Fitted–for and derived Multi–Filter parameters are
surements.
presented in Table 1, with the joint–probability distri-
butions presented in Figure 2 for the fitted and derived
5.1. Transit Timing Analysis
parameters. Derivedparametersinclude: R /R ,thera-
p ⋆
diusoftheplanetinunitsofthehoststellarradius;a/R , Usingtheaboveanalysis,wefoundarevisedephemeris
⋆
the normalizedsemi–majoraxisa ofthe planetaryorbit; for WASP–2b of
thestellardensityρ ;planetimpactparameterb;orbital
⋆ P =2.152220976±0.000000305days
inclination i; and orbital period P. We found values of
theGelman–RubinRˆ–staticwithin10−3 of1.0forallfit- T0=2453991.5148944±0.0001232BJD
tedparameters,indicatingsufficientcoverageofthechain using APOSTLE results combined with Sada et al.
overparameterspace. Theshortesteffectivechainlength (2012) and the non–amateur results presented in
is for the time of transit on 2007-07-26 with a length Southworth et al. (2010), for 17 epochs overall. As Fig-
of 9419. This night had some of the largest photomet- ure 3 indicates, there is largescatter in the observedmi-
ric uncertainties, and largest overall uncertainty on the nus computed transit times (O–C diagram), with a re-
timeoftransit. Allotherparametershaveeffectivechain duced χ2 of 4.7 for the TAP results (7.0 for MTQ), but it
lengths largerthan 104, indicative of sufficientmixing in isdifficulttoclaimadetectionofcoherenttransittiming
the MCMC sample (e.g. Tegmark et al. 2004). Finally, variations due to the sparse sampling.
theχ2ofthebestmodelfittothedatais2822.93for2809 To quantify the significance of this signal, we per-
degreesoffreedom(reducedχ2 of1.005),indicatingthat formeda 3–parametersinusoidalfit (periodin days,am-
ourdata(andthereforeparameter)uncertaintiesarewell plitudeinseconds,andphaseoffsetasanuisanceparam-
understood. eter)totheO–CdataforboththeTAP(andMTQ)timings.
This yielded a ∆χ2 improvement of 28.2 (47.7), with
5. SYSTEMPARAMETERS
amplitudes of 32 (34) seconds and periods of 389 (437)
days. We next performed 105 random reassignments of
3http://www.sdss.org/dr7/algorithms/jeg photometric eq dr1.html
4Notethatthesedepthsweredeterminedbeforethecorrections the timing data to the epochs of observations (i.e. we
forWASP–2/Cwereapplied,andthusdifferfromthefinalMulti– keptthe APOSTLEtime samplingof anyputative TTV
FilterresultspresentedinTable1 signal, but shuffled the observedamplitudes). The fitter
4
Figure 2. Plots of the jointprobability distributions (JPD) of parameters from the Multi–Filter chains with fixed limbdarkening. The
leftpanelshowsthefitted–forparameters,whichareweaklycorrelated. Therightpanelsshowsthederivedparameters,whichtendtoshow
largercorrelations. Table1providestherelevantunitsforeachparameter set.
Table 1
WASP-2System Parameters
Parameter Value TAP S10 Unit
MTQ θMulti-Filter Parameters
tG 0.0161±0.0002 ··· ··· days
tT 0.0591±0.0001 ··· ··· days
D 0.0178±0.0001 ··· ··· -
(I)
D 0.0194+0.0002 ··· ··· -
(r’) −0.0003
v1(I) (0.6092) ··· ··· -
v2(I) (0.1760) ··· ··· -
v1(r’) (0.7135) ··· ··· -
v2(r’) (0.3947) ··· ··· -
Derived Parameters
(Rp/R⋆)(I) 0.1315±0.0003 0.1317±0.0004 ··· -
(Rp/R⋆)(r’) 0.1362+−00..00000079 0.1359±0.001 ··· -
(Rp/R⋆)(R) ··· ··· 0.1326±0.0007 -
a/R⋆ 8.06±0.04 7.99±0.06 8.08±0.12 -
ρ⋆ 2.14±0.03 2.08±0.05 2.15±0.09 g/cc
b 0.719±0.003 0.723±0.005 ··· -
i 84.89±0.05 84.81±0.08 84.81±0.17 o(deg)
P(2.1522 days +) 1812±26 ··· 1852±34 milli-sec
was initialized to the period corresponding to the peak level, the TAP results are more realistic given the cor-
of the shuffled–TTV periodogram,determined using the related noise in our data. Thus, these data provided
method of Zechmeister & Ku¨rster (2009). We then ex- only marginal evidence for transit timing variations in
amined what fraction of these random assignments al- the WASP–2 system.
loweda ∆χ2 equalto or largerthanthat observed. This
provided an estimate of the false alarm probability for 6. RESULTSANDCONCLUSIONS
any potential transit timing modulation. We found that We presented observations and analysis of 10 transit
42%(9.7%)ofthe randomshufflesyielded∆χ2 improve- timings of the WASP–2 system by the APOSTLE pro-
ments at an amplitude equal to or larger than that ob- gram. After an extensive treatment of the data to ad-
served. WhiletheMTQresultsweresignificantatthe1.7σ dress and model the intrinsic systematic errors, we un-
5
there is not incontrovertible evidence of coherent tran-
Table 2
APOSTLETransitTimesforWASP2 sit timing librations (e.g. Eibe et al. 2012; Sada et al.
2012; Hoyer et al. 2012). A primary reason for this is
Epoch T0(MTQ) σT0 T0(TAP) σT0 sparse sampling of transit epochs, due to weather, day-
2,400,000+ (BJD) (BJD) 2,400,000+ (BJD) (BJD) time, and seasonal considerations. In contrast, the con-
146 54305.73863 0.00035 54305.73862 0.00019 tinuous observations afforded by the Kepler spacecraft
147 54307.89212 0.00063 54307.89200 0.00065
providecompletesamplingoftheTTVsignal,withboth
185 54389.67652 0.00018 54389.67646 0.00024
high signal–to–noise per transit and a large number of
298 54632.87724 0.00010 54632.87720 0.00019
transits observed. ResolvedKepler TTVs have sufficient
336 54714.66135 0.00014 54714.66158 0.00018
overallsignal–to–noisetoverifyandweighplanetsinthe
349 54742.64007 0.00006 54742.64011 0.00009
362 54770.61909 0.00008 54770.61897 0.00016 system. Evenwithtight controlofexperimentalsystem-
646 55381.84717 0.00092 55381.84757 0.00072 atics,ground–basedobservationsareintrinsicallylimited
678 55450.72118 0.00024 55450.72108 0.00029 by the spatial and temporal stability of the Earth’s at-
691 55478.70099 0.00025 55478.70063 0.00044 mosphere;metrologyatthe levelrequiredto achievecal-
ibration at the level of Kepler is currently not available.
It is likely that the lack of TTVs being detected
from the ground is due to a fundamental property of
the systems that are being studied. The vast major-
ity of ground–based follow–up is focused on hot–Jupiter
systems, since resolving their transit depths is achiev-
able even with modest aperture telescopes and non–
photometric observing conditions. However, as outlined
by Steffen et al. (2012b), hot–Jupiter systems observed
by Kepler also fail to show detectable TTVs, or any ev-
idence for being in a multi–planet system. Their neigh-
borsinexoplanetparameterspace,looselytermedwarm–
Jupiters and hot–Neptunes, do show evidence for both
TTVs and transiting companions. What this suggests is
a unique dynamical pathway for the formation of con-
temporary hot–Jupiters,such as multi–planet scattering
(e.g. Beaug´e & Nesvorny´ 2012) leading to the ejection
of lesser bodies from the system. It is thus possible
that those systems that are most easily observable from
Figure 3. The observed minus computed transit times for
WASP–2b. Values from APOSTLEs MTQ analysis, TAP, and pre- the ground are also those that will fail to exhibit TTVs.
vious literature are plotted. The horizontal axis represents the Giventhelongevityofground–basedobservingresources
transitEpoch. Thezero-lineephemerisisdescribedinSection5.1. comparedtospace–basedones,itmaybenefitthefieldto
undertakelonger–termobservationsofsystemstoresolve
dertook a MCMC modeling analysis to understand the secular trends such as those arising from stellar binary
parameter uncertainties and correlations. As in previ- hosts(Ford et al.2000)ortidalorbitaldecay(Hut1981).
ous publications, a model analysis incorporating tran- TheresolutionofTTVsfromthegroundmayalsorequire
sit duration t , limb–crossing duration t , and tran- observations from sites designed for the minimization of
T G
sit depth D yielded weakly correlated parameters (Fig- aerosols and water vapor, such as Llano de Chajnantor
ure 2). We corrected for a previously reported object in the Atacama desert of Chile, to reduce atmospheric
within the photometric aperture of the WASP–2b host red noise and make resolving transits of other classes of
star (Daemgen et al. 2009) to yield the system param- exoplanet systems feasible.
eters reported in Table 1. The uncertainties on these While efforts to resolve TTVs from the ground have
parameters are smaller than those reported in previous beenlargelyunsuccessful,thedrivetofollow–updetected
studies (Southworth et al. 2010). We disentangled the exoplanet systems has enabled significant leaps in the
randomandcorrelatednoiseineachlightcurveusingthe understanding and application of high–precisionrelative
method of Gazak et al. (2012), and found that the red photometry. These advances are now extending to the
noise dominates scatter in the lightcurves, at a larger broad application of time–domain spectroscopy during
amplitude in the r–band than in the I–band. transitstomapoutexoplanetfeaturesinabsorption(e.g.
Thedepthsoftransitcomingfromthisanalysisdidnot Crossfield et al. 2011), and have overall been a boon to
showsignificanttime dependence. However,the timesof the field of time–domain astronomy.
transit shown in Figure 3 show scatter larger than the
uncertainties. While a basic sinusoidal fit to this signal ACKNOWLEDGMENTS
provided a significant improvement in χ2, we achieved a Based on observations obtained with the Apache
similar goodness of fit in 18% of random reassignments Point Observatory 3.5-meter telescope, which is owned
ofthetransittimingvariationstotheAPOSTLEepochs. and operated by the Astrophysical Research Consor-
Wethereforecannotconclusivelyreportevidenceoftran- tium. Funding for this work came from NASA Origins
sit timing variations in the WASP–2 system. grant NNX09AB32G and NSF Career grant 0645416.
Theseresultsmirrormanyofthosereportedinthefield RB acknowledges funding from the NASA Astrobi-
ofground–basedtransittimingmeasurements,wherethe ology Institute’s Virtual Planetary Laboratory lead
O–C diagrams show reduced χ2 larger than 1.0, but team, supportedby NASA under cooperativeagreement
6
NNH05ZDA001C.WewouldliketothanktheAPOStaff, Gelman,A.,&Rubin,D.1992,StatisticalScience, 7,457
APO Engineers, and R. Owen for helping the APOS- Gilliland,R.L.,etal.1993,AJ,106,2441
TLE program with its observations and A. Mukadam Gilliland,R.L.,etal.2011,ApJS,197,6
Gillon,M.,etal.2012,A&A,542,A4
for instrument characterization. We would like thank S.
Holman,M.J.,&Murray,N.W.2005,Science, 307,1288
L. Hawley for scheduling our observations on APO. We Hoyer,S.,Rojo,P.,&L´opez-Morales,M.2012, ApJ,748,22
thank N. Thomas for her help in the early analysis of Hrudkova´,M.,Skillen,I.,Benn,C.,Pollacco,D.,Gibson,N.,
the WASP–2 data. This work acknowledges the use of Joshi,Y.,Harmanec,P.,&Tulloch,S.2009,inIAU
parts of J. Eastman’s EXOFAST transit code as part of Symposium,Vol.253,IAUSymposium,446
Hut,P.1981, A&A,99,126
APOSTLE’s transit model MTQ. Ivezi´c,Zˇ.,etal.2007, AJ,134,973
Jordi,K.,Grebel,E.K.,&Ammon,K.2006,A&A,460,339
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