Transit Monitoring in the South (TraMoS) project: Discarding Transit Timing Variations in WASP-5b

3.4 MB·English

by  S. Hoyer

Transit Monitoring in the South (TraMoS) project: Discarding
Transit Timing Variations in WASP-5b
S. Hoyer1
2
1 [email protected]
0
2
P. Rojo1
n
a [email protected]
J
and
7
1

M. Lo´pez-Morales2,3
]
P
[email protected]
E
.
h
p
-
o
ABSTRACT
r
t
s We reportnine new transitepochsofthe extrasolarplanetWASP-5b,observedinthe Bessell
a I band with SOAR at the Cerro Pachon Observatory and with the SMARTS 1-m Telescope at
[
CTIO1 , between August 2008 and October 2009. The new transits have been combined with

1 all previously published transit data for this planet to provide a new Transit Timing Variations
v
(TTVs) analysis of its orbit. We find no evidence of TTVs RMS variations larger than 1 min
6
over a 3 year time span. This result discards the presence of planets more massive than about
1
6 5 M⊕ , 1 M⊕ and 2 M⊕ around the 1:2, 5:3 and 2:1 orbital resonances. These new detection
3 limits exceed by ∼5−30 times the limits imposed by currentradialvelocity observationsin the
. Mean Motion Resonances of this system. Our search for the variation of other parameters, such
1
0 asorbitalinclinationandtransitdepthalsoyieldsnegativeresultsoverthetotaltimespanofthe
2 transit observations. This result supports formation theories that predict a paucity of planetary
1 companions to Hot Jupiters.
:
v
Subject headings: exoplanets: general — transiting exoplanets: individual(WASP-5b)
i
X
1. Introduction omoons (Sartoretti & Schneider 1999; Kipping
r
a 2009), several observational groups have started
Once the method of Transit Timing Variations
to monitor the majority of the known transit-
(TTVs) was theoretical proposed as of great po-
ing planets. This monitoring aims at detecting
tential to detect additional exoplanets in tran-
changes in the predicted mid-time of the transits
siting systems (Miralda-Escud´e 2002; Agol et al.
to infer the presence of additional planets in the
2005; Holman & Murray 2005), and even ex-
system not detected previously by e.g. radial ve-
locities. Those data have also been used to detect
1AstronomyDepartment, UniversidaddeChile,Casilla
variations in other transit parameters (e.g. tran-
36-D,SantiagodeChile,Chile
2Institut deCi`encies de l’Espai(CSIC-IEEC), Campus sit depth and duration), that can be attributed
UAB,FacultatdeCiencies,TorreC5,parall,2apl,E-08193 to perturbations produced by unseen companions
Bellaterra,Barcelona,Spain (Miralda-Escud´e 2002).
3VisitingScientist,CarnegieInstitutionofWashington, In addition to having the potential of finding
Department ofTerrestrialMagnetism, 5241BroadBranch
planets in the Earth-like or smaller mass regime,
Rd. NW,Washington, D.C.20015, USA.
1
the detection (or non-detection) of companions of Gillon et al. (2009) was based on the divergence
transitingHotJupitersthroughTTVsalsocanim- of only one point out of six. Smith et al. (2009)
proveconstraintsonplanetformationmodels(e.g. searchedforsignaturesofadditionalplanetsinthe
Triaud et al. 2010; Naoz et al. 2011; Miguel et al. residualsofWASP lightcurvesafterremovingthe
2011, and references therein) and help discrimi- transits of WASP-5b, and found no evidence of a
nate between the different mechanisms proposed. transiting companion downto Saturn-size planets
In this way, TTVs become a powerful tool for the within periods of up to 20 days.
detection and study of multi-planet system archi- Otherrecentworkshavedeterminedandrefined
tectures (Latham et al. 2011; Ford et al. 2011). severalphysicalparametersofthesystem. Forex-
The firstunquestionableevidence ofTTVs was ample, Triaud et al. (2010) determined the angle
announced by Holman et al. (2010) in the double between the orbital plane of WASP-5b and the
Saturn-like transiting planetary system Kepler-9, spinaxis directionofits hoststar to be consistent
wherethecentraltimesoftransitvarywithampli- with zero (λ=12◦+10). This conclusion has been
−8
tudes of 4 and 39 minutes in timescales of about confirmedby the reanalysisofFukui et al.(2011),
19 and 40 days, respectively. Another extraordi- hereafter F11, who obtain λ=7.2◦±9.5.
nary confirmation of the TTVs effect came with F11 additionally searched for TTVs of WASP-
the discovery of Kepler-11 (Lissauer et al. 2011), 5busing sevennew transitepochs,combinedwith
a system with six transiting planets which shows all previously available observations. They find a
TTVs of amplitudes as large as tens of minutes RMS of about 68 seconds in their timing resid-
produced by the gravitational perturbations be- uals despite of having an average of 41 seconds
tween the planets. An additional remarkable re- uncertainty per epoch, and proposed that such a
sult of this later work has been the use of dynam- large deviation from a linear fit (χ2 = 32.2 for 9
ical orbital fits to determine directly the masses degreesoffreedom)canbeexplainedbyanorbital
of the transiting planets, dismissing the need of perturber. Using dynamical simulations F11 con-
radial velocities. strainedthe massesofthis hypotheticalperturber
In2008,theWASP-Southsurveyreportedtheir to 2 M⊕ in the 1:2 and 2:1 mean motion reso-
seconddetectionofanexoplanet,WASP-5b,tran- nances (MMRs) and set a mass of 43 M⊕ for a
siting a relatively bright star (V = 12.3) in the potential Trojan body.
SouthernHemisphere(Anderson et al.2008,here- Dragomir et al.(2011),hereafterD11,reported
afterA08). Thisdiscoverypaper,basedonWASP twonewtransitsofWASP-5bwithdataofthe1-m
photometryandtwoadditionaltransitepochsplus telescopeatCerroTololoInter-AmericanObserva-
radial velocities measurements, announced a Hot- tory.
JupiterplanetwithamassofM =1.58+0.13 M
P −0.08 J Inthisworkwepresentnineadditionaltransits
andadensityofρ =1.22+0.19ρ ,orbitingaG4V
p −0.24 J of WASP-5b, observed between August 2008 and
star with a period of P =1.62 days.
October 2009, and perform a new homogeneous
Gillon et al. (2009) did a reanalysis of the A08 timing analysis of all available epochs to further
datatoproducethefirsttimingstudyofWASP-5b confirm or rule out the TTV signals previously
and arrived to the conclusion of potential period proposed for this system.
variations,basedona∼2-minuteshiftinthetim-
In section 2 we describe the new observations
ing residuals of the most precise points.
andthedatareduction. Section3detailsthemod-
Southworth et al. (2009), hereafter S09, ob- elingofthelightcurvesandinsection4wepresent
served two new transits, for which they achieved the timing analysis. In Section 5 we discuss the
very high photometric precision by defocusing mass limits for a unseen perturber. Finally, we
the images at the 1.54-m Danish Telescope at present our conclusions in section 6.
La Silla Observatory, but at the expense of pro-
ducing only 3-minute cadence. They refined the 2. Observations and data reduction
linear ephemeris of the system and concluded the
high deviation of the timing residuals with re- In 2008 we started the Transit Monitoring in
spect to that straight line (χ2 = 5.7) found by theSouthProject,whichisamonitoringcampaign
red
oftransitingplanetsobservablefromtheSouthern
2
Hemisphere (Hoyer et al. 2011), following the ap- inparticularweusedthevalueoftheModified Ju-
proachofusinghigh-cadenceobservationsandthe lian Day (JD-2400000.5) field. In the SMARTS
same instruments and setups to try to minimize telescope, the time stamp recorded in the header
systematics and reduce uncertainties in the mid- ofeachframeis generatedby aIRIG-B GPS time
transit times, as well as other transit parameters. synchronization protocol connected to the com-
For the TraMoSprojectwe havealreadyobserved puters that control the instrument. The SOAR
more than 60 transits of over 20 exoplanets. telescope data use the time values provided by a
As part of TraMoS we observed a total of timeserviceconnectedtotheinstrument. Wecon-
nine transits of WASP-5b, between August 2008 firmedthatthesevalueshave∼1secondprecision.
and October 20092, with the Y4KCam on the Thetimevalueassignedtoeachframecorresponds
SMARTS 1-m Telecope at Cerro Tololo Inter- totheJulianDay atthestartoftheexposureplus
American Observatory (CTIO) and with the 1/2ofthe integrationtime ofeachimage(see sec-
SOAR Optical Imager (SOI) at the 4.2-meter tion 4 for details).
Southern Astrophysical Research (SOAR) tele- WASP-5 is located in a relative empty field,
scope in Cerro Pacho´n. whereboththetargetandseveralwellsuitedcom-
Y4KCamis a 4064×4064 CCD camera with a parison stars appear well isolated in our images.
Field of View (FoV) of 20×20 squared arcmin- Therefore, we extracted the flux from the target
utesandapixelscaleof0.289arcsecpixel−1. The and comparison stars via standard aperture pho-
standard readout time of the camera is 46 sec, tometry, and using our own python-based code.
which we reduce to ∼16 sec by binning 2x2. The Weusedarangeofstellaraperturesbetween8and
SOI detector is composed of two E2V mosaics of 12 pixels, and sky rings which extended between
4096 × 4096 pixels with a scale of 0.077 arcsec 25 and 35 pixels in radius.
pixel−1, givinga FoVof5.2×5.2squaredarcmin- For each sky-aperture combination, we gener-
utes. Theinstrumenthasa20.6secstandardread- ated differential light curves between the target
out, which becomes only ∼ 11 sec after binning andeachcomparisonstarto 1)optimize the aper-
2x2. turesand2)selectthebestcomparisonstars. The
All nine transits were observed using a Bessell criterium used in both cases was RMS minimiza-
I filter (λ = 8665 ˚A and FWHM=3914 ˚A) to tion for the out-of-transitand in-transit data (ex-
eff
reduce limb darkening effects in our light curves. cludingtheingressandegressportionsofthelight
Six of the transits were fully covered in phase. curves). The final light curves were generated
A fraction of the ingress of the 2008-11-03 tran- computing the ratiobetween target’sflux and the
sit was not observed because a telescope system best 2 to 5 comparison stars.
crashas illustratedin Figure 1. Nevertheless,this Finally, some systematics remaining after this
transit was treated as a complete transit. Two stepwereremovedbymeansoflinearorquadratic
other transits, 2009-08-05 and 2009-10-21, were regression fits to the out-of-transit light curve
only partially covered with data between phases points using X-Y pixel position, time and/or air-
−0.034 . φ . 0.01 and 0.12 . φ . 0.06, re- mass as free parameters. The final light curves
spectively. Two of our transits, 2008-08-29 and presentaveragephotometric dispersionsofthe or-
2008-09-21,coincide with the transit epochs pub- der of 0.2% - 0.45%.
lishedbyS09. Theobservinglogissummarizedin
Table 1. 3. Light Curve Modeling
The initial trimming, bias and flatfield correc-
3.1. Algorithm Comparison
tions of all the collected data were performed us-
ing custom-made pipelines specifically developed We performed a comparison between algo-
for each instrument. The times at the start of rithms that use different statistical uncertainty
the exposure are recorded in the image headers, estimation techniques to the transit’s parame-
ters, in order to test potential systematics be-
2In the remaining of the text we refer to each individual tween them. There are different approaches to do
transit by the UT date of mid-time of the transit, using thatstatisticalerrorestimationanalysis;forexam-
thefollowingnotation YYYY-MM-DD
3
ple, JKTEBOP3 (Southworth et al. 2004a,b) uses Figure 2 shows the distribution of each param-
the Levenberg-Marquardt Monte Carlo (LMMC) eter obtained using the LMMC and the MCMC
technique to compute errors (see e.g. Southworth techniqueswithdatafrom2008-08-21transit(sim-
2010; Hoyer et al. 2011), while severalother stud- ilar analysis was done with the other 6 complete
ieshavestartedtoimplementMonteCarloMarkov lightcurves). Fromthethreebottompanelsinthe
Chains (MCMC) techniques (e.g. Adams et al. Figure2itisevidentthatthe1σerrors(definedas
2010; Fulton et al. 2011). the 68% of a Gaussian fit to the parameter value
In Hoyer et al. (2011) we proposedthat the re- distributions) obtained with LMMC are generally
sults of both, the LMMC and MCMC algorithms smaller than those obtained using MCMC, since
are equivalent if the parameter space lacks of lo- the latter does a more exhaustive exploration of
cal minima, where LMMC minimization can be the parameter space and therefore performs bet-
trapped. Here we further test that proposal by ter error estimations. Also, from the top-panel
comparing the results of both algorithms on the of Figure 2, it can be seen that the LMMC re-
WASP-5b data used for this study. We compare sults for certain parameters can appear biased
the results of fitting a light curve of WASP-5b towards their initial input values. That is the
with JKTEBOP and the Transit Analysis Pack- case for the linear limb-darkening coefficient, for
age4 (TAP; Gazak et al. 2011), which implements which the value resulting from the LMMC anal-
the MCMC method for the estimation of errors ysis is µ1(I) = 0.22±0.12 (the initial value was
(more details in Fulton et al. 2011, and references 0.296). Ontheotherhand,thedistributionofval-
therein). uesforthisparameteronasingleepochasgivenby
MCMC does not appear Gaussian, revealing that
Among the parameters that JKTEBOP allows
the quality of a single transit in the current data
tofitare: the planet-to-starradiusratio(R /R ),
p s
does not allow to constrain the values of µ (I).
the inclination (i) and eccentricity (e) of the or- 1
Notice, however, that a Gaussian distribution is
bit,theout-of-transitbaselineflux(F ),themid-
oot
obtained when fitting several transits simultane-
time of transit (T ), the quadratic limb darkening
c
ously (see Figure 4 and section 3.2).
coefficients (µ and µ ), and the sum of the frac-
1 2
tional radii, R = R /a+R /a, where R and R From the test results above we conclude that
p s p s
are the absolute stellar and planetary radii, and the LMMC and MCMC techniques arriveto simi-
a is the orbital semi-major axis. TAP allows to lar parameter results. However, because the ap-
fit for all those parameters except for the latter, parent underestimation of the errors estimated
which is replaced by a/R . by LMMC we have opted for using TAP for our
s
analysis of the full WASP-5b transit dataset and
For the comparison we left free all the men-
the re-analysis of all the available data (see next
tioned parameters except a/Rs and R in TAP
section). This underestimation is due to lack of
andJKTEBOP,respectively,since they otherwise
multi-parameter uncertainty estimator and fail-
presented convergence problems. We also fixed
ure to account for red noise in the minimization
F = 1, e = 0 and µ (I) = 0 and the orbital
OOT 2
(Carter & Winn 2009) as TAP does. Other ad-
period to P = 1.62843142 days from F11 since
vantages of TAP include that the code can fit a
any variation in this parameter will be detected
later in our timing analysis. We used 104 itera- greater number of parameters like linear system-
tionsinJKTEBOPand10chainsof105stepseach atics in the datasets, and it allows a simultaneous
fitting of multiple transits.
in TAP. We discarded the first 10% iterations on
eachchaintocomputethefinalparameter’svalues
3.2. Final Modeling
and its respective errors. The results on each fit,
showninTable 2, revealthat the resultantfit val- We used TAP to fit the nine new transit light
ues of all parameters common to the JKTEBOP curvespresentedinthispaperandalltheavailable
andTAPalgorithmsagreewithintheerror,except light curves of the system (seven of F11, two of
for µ (I). D11, two of S09 and the two of A08).
1
First, we attempted to model each of the new
3http://www.astro.keele.ac.uk/ jkt/codes/jktebop.html light curves independently, but ran into several
4http://ifa.hawaii.edu/users/zgazak/ifA/TAP.html problems. TAP had difficulties fitting the incom-
4
plete light curves. Also, when fitting individual was fit simultaneously for all seven light curves,
lightcurves,parameterssuchasµ didnotclearly while for the other parameters we obtained one
1
convergetoasinglevalue,asalreadymentionedin valuepercurveandcombinethemafterwardviaa
section 3.1 and illustrated in Figure 2. To avoid weightedaverage. Theresultingaveragevaluesfor
these problems we fit the seven complete light eachparameterarelistedinTable3,togetherwith
curves simultaneously, leaving as free parameters their1σerrors. Asanexample,Figure4showsthe
µ (I), i, R /R , T , F ,inadditiontopossible resultantMCMCdistributionsofi,R /R ,andT
1 p s c OOT p s c
linear trends to the lightcurves, F , andwhite for the transit observed on 2008-08-29, while the
slope
(uncorrelated) and red (correlated) noise compo- distribution of µ (I) correspond to the results of
1
nents,σ andσ ,respectively. Theorbitalperiod, the simultaneous seven transits fit. This distribu-
w r
the eccentricity, and the longitude of the perias- tion is now clearly Gaussian in contrast with the
tron were fixed to the values P= 1.62843142days previously obtained.
(the value obtained by F11), e=0 and ω =0. Finally,weadoptedthevaluesofalltheparam-
We used a quadratic limb-darkening law, but eters that define the shape of the transit derived
found that the precision of the light curves was in the fit above and used them as fixed values in
notenoughtoreliablyfitthequadraticcoefficient, the two incomplete light curves (2008-10-22 and
sothatvaluewasalsofixedtoµ (I)=0.32,based 2009-08-06 transits) to derive their mid-times of
2
on the tabulated results in Claret (2000). transit, T . The F , F , σ and σ are still
c OOT slope w r
As mentioned in Section 2, we initially cor- left variable in this case.
rected for systematic trends in the light curves F11usedaprocedurebasedonχ2minimization
using linear or quadratic regression fits. Altough for modeling their light curves. We re-analyzed
slopes in the light curves are not clearly appar- their data to do an homogeneous study of all the
ent, we leave F and F as free parameters light curves, given that a multi-parameter mini-
OOT slope
toensurethatanysmallresidualsareproperlyfit. mizationbasedonMCMCisstatisticallymorero-
Thismightcreateconcernsaboutwheterthistwo- bust. We modeled the seven light curves of F115,
step fitting of systematics can affect the results of the two light curves of D11 (data provided by
the fits. To ensure we are not introducing any the author,private communication),the two light
biasonthedeterminationoftheplanetaryparam- curves of S096 and the two of A08 (data provided
eters, we fit the two sets of data (i.e. the light bytheauthor,privatecommunication)inasimilar
curves with and without systematics trends re- manner to our complete light curves above. The
moved) with TAP and arrive to consistent values F11 transits were observed with a Bessel I filter,
of all derived planetary parameters. the D11 and the S09 with a R filter, and the A08
We also searched for potential parameter cor- with R and SDSS i’ filter; therefore, we fit one
relations in the light curves using the fit results µ1(I)simultaneouslyforallF11curves,oneµ1(R)
ofthe2008-08-29transitdescribedintheprevious fortheD11curvesandonefortheS09curves,and
section, where allthe parameterswere let to vary. separate µ1(i) and µ1(R) for the A08 curves. We
Theresultantparametercorrelationsareshownin fixed µ2 =0.32 in all cases.
Figure 3. This figure reveals a strong correlation TheobtainedparametersaresummarizedTable
between a/R and i. There is also evidence of 3. The resultant models to all 22 light curves are
s
weakercorrelationsbetweenthosetwoparameters illustrated in Figure 1.
and Rp/Rs. Therefore, to minimize the impact We point out that the errors of the F11’s light
of those correlations in our results, we fixed a/Rs curvesestimatedbyusare,inaverage,70%larger
in all the light curves to 5.37 (from F11), while than the reported by F11. We checked that the
closely monitoring Rp/Rs and i for variations. origin of this difference was not due only by the
To fit the transits we ran 10 MCMC chains different red-noise estimator methods. Using the
of 105 links each, discarding the first 10% results
fromeachchaintoavoidbiastowardtheinitialin- 5The data isavailable inthe on-linematerial fromthe F11
put values of each fitted parameter. Because the publicationonPASJ
resulting MCMC distributions for µ (I) are not 6The data is available at the CDS
1
(http://cdsweb.u-strasbg.fr/)
Gaussian (see Figures 2 and 3), that parameter
5
same red-noise factor estimated by F11, we have trendcanbe explainedby the accumulationofer-
obtainederrorsconsistentwiththosewepresentin rors in the current orbital period and T of the
0
Table 3. Carter & Winn (2009) found that time transits over time, and therefore can be modeled
averaging and residual permutation methods un- out.
derestimated the errors by 15−30% compared ThislinearregressionofthepointsintheO−C
with the wavelet-based method (implemented by diagram has a χ2 = 1.22 (χ2 = 24.37 for 20 de-
red
TAP). grees of freedom), which is significantly smaller
Using the model results is possible to look for than the value obtained for F11 of χ2 = 3.66
red
variationsinthemostrelevantparameters,inpar- (χ2 = 32.2 for 9 degrees of freedom). Addition-
ticular i and R /R , that can reveal the presence ally, we confirmedthat with our results for the 11
p s
of an additional body in the system. In Figure 5, epochsincludedinF11’sanalysiswealsoobtained
we plot R /R and i as a function of the transit ansmallerχ2(χ2 =15.45thatyieldsχ2 =1.72).
p s red
epoch, based in the results of the twenty transit ThisresultliesinthefactthatourT uncertainties
c
fits (our two incomplete light curves were not in- are larger than those estimated by F11.
cluded). We do not see any significant variations Once the linear trend is removed the updated
in those parameters. The weightedaveragevalues ephemeris equation is:
ofiandR /R basedonallthelightcurvesresults
p s
are summarized in Table 4. We studied in detail
the timing of the transits in the next section. T =2454375.62459(23)[BJD ]+
c TT
1.62842888(78)×E,
4. Timing Analysis
where T is the central time of a transit in the
The times in our nine transit data and the c
epochE sincethereferencetimeT . Theerrorsof
D11 data were initially computed in Coordinated 0
the last digits are shown in parenthesis. The bot-
Universal Time (UTC) and then converted to
tom panel in Figure 6 shows the resulting O−C
Barycentric Julian Days, expressed in Terrestrial
values of all available transits using the updated
Time, BJD(TT), using the Eastman et al. (2010)
online calculator 7. The transit times of S09 and ephemeris equation. The resultant O − C dia-
gramis consistentwith a constantperiod, andwe
A08, which were initially expressed in HJD(UT)
conclude that the observed TTV residuals (with
havealsobeenconvertedtoBJD(TT).Noconver-
a RMS of ∼ 0.00073 days ≃ 63 seconds), are
sion was applied to the light curves reported by
most likely introduced by data uncertainties and
F11.
systematics rather than due by gravitational per-
The times of the common transits, 2008-08-29
turbations of an orbital companion. This newly
and 2008-09-21,derived from our light curves are
obtained precision permits to place strong con-
consistent within the errors in the values derived
straintsinthemassofanhypotheticalcompanion,
by us and also by F11 from S09 data.
particularly in MMR’s, as we discuss in the next
Using the F11’s ephemeris equation, we cal-
section.
culated the residuals of the mid-times of the 22
transits of WASP-5b analyzed in this work. The
5. Limits to additional planets
top panel in Figure 6, shows the Observed minus
Calculated(O−C)diagramforour nine transits. To place upper limits to the potential per-
In the middle panel of the figure we combine the turbers in the WASP-5 system based in the de-
O−C valuesofourninetransitswiththenewval- rived TTV RMS of about 60 sec we use Mercury
uesderivedfortheF11,D11,S09andA08(shown (Chambers 1999) N-body simulator. The input
as open circles). As illustrated in that figure, a parameters to Mercury include the mass and the
lineartrendwithaslopeof2.54×10−6 daysisob- radius of both the star andthe transiting planets,
served in the time residuals of all transits. That theplanet-to-starorbitalseparation,aswellasthe
inclination, eccentricity and periastron longitude
7http://astroutils.astronomy.ohio- of the system. The values for all these parame-
state.edu/time/utc2bjd.html
ters were adopted from S09. In addition, all the
6
initial relative angles between the perturber and Figure 7 thus shows that the perturber would
WASP-5b were set to zero. have been detected by RV measurements in all
We explored a wide range of perturber masses areas except around the 1:2, 5:3 and 2:1 MMRs,
between 1 M⊕ and 4000 M⊕ in initial steps of where it could have a maximum mass of 5, 1 and
50 M⊕, which are subsequently refined as de- 2 M⊕, respectively.
scribed below. For the semi-major axis distances
we explore a range between 0.001 and 1.2 AU in 6. Conclusions
steps of 0.001 AU, which was further reduce near
We present nine new transit light curves of
resonances. Thedensityoftheperturberwaskept
WASP-5b. We homogeneously model these light
constant to that of Earth for Mp ≤10M⊕ and to curves together with all available transit data of
that of Jupiter for MP ≥ 200M⊕, it was varied this system. Based in these fits we search for any
linearly for masses in between. Also, we assumed
variation in the timing of the transits.
theperturbertobeinacircularorbitandcoplanar
Using22transitepochsweupdatedtheephemeris
toWASP-5b,sincethis configurationprovidesthe
equationandwefindaTTVsRMS of63 seconds.
most strict limit to the amplitude of the TTVs
Allthetransittimesareconsistentwithaconstant
for a given perturber’s mass. Non-zero eccen-
orbital period within 2σ.
tricities and non-coplanar orbits produce larger
TTVsasalreadypointedoutbye.g. Bean(2009), Our linear fit of the transit times has a
Hoyer et al. (2011) and Fukui et al. (2011). For χ2 = 1.22, which is considerably lower than
reduce
each model configuration we let the system relax the value found by Fukui et al. (2011) used to
forfiveyears,andthenweusedthenextfiveyears implied the presence of an perturber body.
to obtain our fit results, which in total is more Despite obtaining a similar TTV RMS than
than 3 times the time span of the observations. Fukui et al.(2011)(∼1min),weconcludeamuch
These 5 years of relaxation time permits to mini- smaller significance to deviations from a constant
mize the effect ofanyinitialbias(e.g. the relative period due to our larger per-epoch uncertainties
angles). We found orbits between 0.02 and 0.035 as obtained by the MCMC algorithm.
AU to be unstable due to the presence of WASP-
If the system has an additional orbiting body,
5b. For all other (stable) orbits we recorded the
itsmasshastobelowerthan5,1and2M⊕,inthe
centraltimesofeachtransitofWASP-5bandcom-
2:1, 5:3 and 1:2 resonances. In any other location
puted the predicted TTVs for each configuration,
the perturber would have been detected by RVs.
assuming an average constant period. Addition-
We search for any trend in the depth of the
ally,we checkedthatthe fitted averageperiod did
transit and inclination of the orbit but we do not
not deviate by more than 3 σ from the obtained
see any clear evidence of variation with statistical
orbitalperiodofWASP-5b. Also,toensureagood
significance.
sampling ofthe potentialperturber’s mass,we re-
duced the steps in Mpert to 1M⊕ whenever the 7. Acknowledgements
TTVs approached60 sec.
The results of our model simulations is illus- The authors would like thank David Ander-
tratedinFigure7,whereweshowtheMpert (M⊕) son for providing WASP light curves and Di-
versusa(AU) diagramthat places the mass limits ana Dragomir and Stephen Kane for provid-
to potential perturbers in the system. The solid ing TERMS light curves. S.H. and P.R. ac-
line in the diagram indicates the derived upper knowledgementssupportfromBasalPFB06,Fon-
limits to the mass of the perturbers that would dap #15010003, and Fondecyt #11080271. Ad-
produce TTVs RMS of 60 sec at different orbital ditionally, S.H, recieved support from ALMA-
separation. The dashed line shows the perturber CONICYT FUND #31090030. We thanks the
mass upper limits imposed by the most recent ra- CTIOandSOARstaffforthehelpandcontinuous
dial velocity observations of the WASP-5 system, support during the numerous observing nights.
for which we have adopted a precision of 15 m/s
(A08 and Triaud et al. 2010, report RV precision
of 14 m/s and 12−18 m/s, respectively).
7
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8
Table 1
Observational information of each night.
TransitDate Telescope/Instrument Filter IntegrationTime[s] airmassrange Epoch
2008-08-21 SMARTS-1m/Y4KCam BessellI 13 1.7-1.01 199
2008-08-29a SMARTS-1m/Y4KCam BessellI 10 1.05-1.02-1.06 204
2008-09-21a SMARTS-1m/Y4KCam BessellI 10,7 1.9-1.01-1.07 218
2008-10-22b SOAR/SOI BessellI 7,5,3 1.12-1.02 237
2008-11-04 SOAR/SOI BessellI 3 1.07-1.02-1.4 245
2008-11-17 SMARTS-1m/Y4KCam BessellI 10 1.02-1.4 253
2009-06-22 SOAR/SOI BessellI 7,5,3 1.95-1.02 387
2009-08-06b SOAR/SOI BessellI 5,4 1.07-1.15 414
2009-10-25 SMARTS-1m/Y4KCam BessellI 15 1.06-1.02-1.97 463
aThistransitwasalsoobservedbySouthworthetal.(2009).
bThistransithasaincompletephasecoverage.
9
Table 2
Values obtained with Levenberg-Marquardt Monte Carlo (JKTEBOP) and Markov Chain
Monte Carlo (TAP) algorithms with data of the 2008-08-21 transit of WASP-5b.
Parameter JKTEBOP TAP
R /R 0.0988±0.0018 0.0988±0.0026
p s
i [◦] 83.4±1.5 83.7±2.3
µ (I) 0.22±0.12 0.45±0.11
1
T −2454699(UT) 0.67690±.00035 0.67697±0.00041
c
(R +R )/a 0.223±0.015 ···
p s
a/R ··· 5.01±0.48
s
10