Is there a circumbinary planet around NSVS 14256825?

1.7 MB·

by  Ilham Nasiroglu

DraftversionJanuary20,2017
TypesetusingLATEXtwocolumnstyleinAASTeX61
ISTHEREACIRCUMBINARYPLANETAROUNDNSVS14256825?
IlhamNasiroglu,1KrzysztofGoz´dziewski,2AgaSłowikowska,KrzysztofKrzeszowski,MichałZ˙ejmo,3StaszekZola,4HuseyinER,1
WaldemarOgłoza,MarekDro´z˙dz˙,5DorotaKoziel-Wierzbowska,BartlomiejDebski,6andNazliKaraman7
1DepartmentsofAstronomyandAstrophysics,AtaturkUniversityYakutiye,25240,Erzurum,Turkey
7
1 2CentreforAstronomy,FacultyofPhysics,AstronomyandAppliedInformatics,N.CopernicusUniversity,Grudziadzka5,87-100Torun´,Poland
0 3JanuszGilInstituteofAstronomy,UniversityofZielonaGo´ra,Prof.Szafrana2,65-516ZielonaGo´ra,Poland
2 4AstronomicalObservatory,JagiellonianUniversity,Orla171,30-244Krako´w,Poland
n 5Mt.SuhoraObservatory,PedegogicalUniversity,Podchorazych2,30-084Krako´w,Poland
a 6AstronomicalObservatory,JagiellonianUniversity,ul.Orla171,30-244Krako´w,Poland
J 7PhysicsDepartment,AdiyamanUniversityMerkez,02040,Adiyaman,Turkey

8
1 (ReceivedDecember7,2016;RevisedJanuary6,2017;AcceptedJanuary20,2017)

] SubmittedtoApJ
P
E
ABSTRACT
.
h The cyclic behaviour of (O–C) residuals of eclipse timings in the sdB+M eclipsing binary NSVS 14256825 was previously
p
- attributedtooneortwoJovian-typecircumbinaryplanets. Wereport83neweclipsetimingsthatnotonlyfillinthegapsinthose
o already published but also extend the time span of the (O–C) diagram by three years. Based on the archival and our new data
r
t spanningovermorethan17yearswere-examinedtheuptodatesystem(O–C).Thedatarevealedsystematic,quasi-sinusoidal
s
a variationdeviatingfromanolderlinearephemerisbyabout100s. Italsoexhibitsamaximuminthe(O-C)nearJD2,456,400
[ that was previously unknown. We consider two most credible explanations of the (O-C) variability: the light propagation

1 time due to the presence of an invisible companion in a distant circumbinary orbit, and magnetic cycles reshaping one of the
v binarycomponents,knownastheApplegateorLanza–Rodono´ effect. Wefoundthatthelattermechanismisunlikelyduetothe
1 insufficient energy budget of the M-dwarf secondary. In the framework of the third-body hypothesis, we obtained meaningful
1
constraintsontheKeplerianparametersofaputativecompanionanditsmass. Ourbest-fittingmodelindicatesthattheobserved
2
5 quasi-periodic(O-C)variabilitycanbeexplainedbythepresenceofabrowndwarfwiththeminimalmassof15Jupitermasses
0 ratherthanaplanet,orbitingthebinaryinamoderatelyellipticalorbit(e (cid:39)0.175)withtheperiodof∼10years. Ouranalysis
. rulesouttwoplanetsmodelproposedearlier.
1
0
7 Keywords: Stars: binaries: eclipsing - Stars: binaries: close - Stars: subdwarfs - Stars: individual: NSVS
1
14256825-Planetarysystems: detection.
:
v
i
X
r
a
Correspondingauthor:AgaSłowikowska
[email protected]
2 Nasirogluetal.
1. INTRODUCTION alongwithafeweclipsetimes. NSVS14256825isamem-
ber of the HW Vir family (PCEB) consisting of a OB sub–
The number of discovered exoplanets around binary sys-
dwarfandaMdwarfcompanion(sdOB+dM)(Almeidaetal.
tems increases rapidly. These discoveries have sparked a
2012). The following physical and geometrical parameters
rising interest on this subject among researchers, and con-
were obtained: i = 82.◦5 ± 0.◦3 (inclination of the system),
sequently,theydrivethedevelopmentofnewdetectiontech-
M =0.419±0.070M ,R =0.188±0.010R ,M =0.109
niques. Studies of circumbinary planets (CBPs) have taken 1 (cid:12) 1 (cid:12) 2
±0.023M R =0.162±0.008R (themassesandradiiof
usmuchclosertowardansweringthefundamentalquestions (cid:12) 2 (cid:12)
thecomponents),a=0.80±0.04R (separationbetweenthe
how such planets form and evolve. The properties of cir- (cid:12)
cumbinaryplanetsarelikelydifferentthantheseorbitingiso- components)fromthephotometricandspectroscopicobser-
vations(Almeidaetal.2012).
latedstars(Leeetal.2009).
TheeclipsetimesofNSVS14256825havebeenreported
The most remarkable discovery made with the transit
byWilsetal.(2007);Kilkenny&Koen(2012);Beuermann
method with the Kepler satellite is the discovery of a cir-
etal.(2012b);Almeidaetal.(2013)andLohretal.(2014).
cumbinaryplanettransitingacrossbothstarsoftheclosebi-
Qian et al. (2010) and Zhu et al. (2011) also argued for a
narysystemKepler-16(AB)(Doyleetal.2011). Thetransits
O–C cyclic variation, however they have not published any
in this system leave no doubt about the existence of planets
supporting data yet. Kilkenny & Koen (2012), reported
intheso-called“P-type”orbits,i.e. circumbinaryorbits. So
an increasing orbital period of this system with a rate of
farthelongest-periodtransitingCBPisKepler-1647withthe
∼ 1.1 × 10−10 ss−1. Beuermann et al. (2012b) detected
orbitalperiodof∼1100days(Kostovetal.2016b).
cyclicperiodchangesandsuggestedthepresenceofasingle
Even before the Kepler discoveries, timing observations
circumbinaryplanetof∼ 12M withaperiodof∼ 20yrs.
have provided evidence of planets orbiting binary systems. Jup
Almeidaetal.(2013)presentedafewadditionaleclipsetimes
Hints for such companions were reported by Deeg et al.
andarguedforthepresenceoftwocircumbinaryplanetswith
(2008) and Lee et al. (2009) for the eclipsing binaries CM
periodsof∼ 3.5yrsand∼ 6.7yrs, andmassesof∼ 3M
DraandHWVir,respectively. Thepresenceoftheseobjects Jup
areindicatedthroughtheLightTravelTime(LTT)effectin- and ∼ 8.0 MJup, respectively. Wittenmyer et al. (2013) pre-
sentedadynamicalanalysisoftheorbitalstabilityofthetwo
dicated by the variations in the timings of eclipse minima
planetmodelproposedbyAlmeidaetal.(2013). Theyfound
w.r.t. the linear ephemeris (O-C). Quasi-periodic variations
that this model is extremely unstable on time scale of less
ofthe(O-C)canresultfromthegravitationaltugduetodis-
than a thousand years. Moreover, Hinse et al. (2014) also
tant planets (companions), which leads to swinging of the
performed a detailed data analysis of the timing measure-
eclipsing binary, and causing the eclipses to appear slightly
earlierorlaterw.r.tthelinearephemeris. TheLTTeffectcan ments of this system. They concluded that the time span
of eclipse time variations is not long enough neither to ex-
bemeasuredwithahighaccuracyandusedtoinferthepres-
plainanyparticularone–planetmodelnorprovideaconvinc-
ence of planetary-mass companions around binary stars (Ir-
ing evidence for a second planetary companion. Recently,
win1952;Horneretal.2012;Goz´dziewskietal.2012,2015).
Lohretal.(2014)presentedmanyneweclipsetimesofNSVS
Incontrasttoothertechniques,thetimingmethodissensitive
14256825 from the SuperWASP archive. Their measure-
to massive extrasolar planets in long-period orbits. Futher-
more,forlow–massbinariestheamplitudeoftheLTTeffect ments obtained between 2006 and 2011 confirm the overall
trendalreadyseenintheO–Cdiagram.
increases(Ribas2005;Pribulla etal.2012).
In this study, we present 83 new mid-eclipse times of
Recently,anumberofplanetarymasscompanionsorbiting
NSVS 14256825 obtained between 2009-08-21 and 2016-
thecataclysmicvariables(CVs)andpost-commonenvelope
11-03thattogetherwiththeliteraturedatagive153eclipses
binaries(PCEBs)havebeenreported.Forinstance,twoplan-
over the time span of 17 years. We combined our new data
ets for NN Ser (Beuermann et al. 2010) and UZ For (Potter
with the previously published measurements to analyse the
et al. 2011), a single planet for DP Leo (Beuermann et al.
orbital period variations of this system. In Section 2 we
2011) and V470 Cam (Beuermann et al. 2012b) have been
presenttheobservationsanddatareductionprocesstogether
claimed. A long-term stable system of three planets hosted
withthemethodologyusedtoobtaintheeclipsetimes. Sec-
byHUAqr,withthemiddleonebeingonaretrogradeorbit,
tion 3 presents the procedure applied to examine the period
wasrecentlyproposedbyGoz´dziewskietal.(2015).
variations, while the results are gathered in Section 4. In
NSVS14256825wasdiscoveredthroughtheNorthernSky
Sections5and6wediscussandconcludeourfindings. We
Variability Survey (NSVS) (Woz´niak et al. 2004a). Wils
includesomeadditionalmaterialsintheon-lineAppendix.
etal.(2007)identifiedthissystemasaneclipsingbinarywith
an amplitude of variations in the range of 13.22–14.03 (V).
TheseauthorsalsopresentedthefirstB,V,I lightcurvesand
c
physicalparametersofthisbinary(P=0.110374230(2)days), 2. NEWPHOTOMETRYOFNSVS14256825
NSVS14256825andcircumbinaryplanet 3
WeperformedphotometricobservationsofNSVS14256825 aregivenaccordingtotheephemerisfromBeuermannetal.
between2009-08-21and2016-11-03withfivedifferenttele- (2012b). We would like to note that we have three pairs
scopes: the 1.3 m telescope at the Skinakas Observatory of simultaneous observations of NSVS 14256825 with the
(SKO, Creete, Greece), the 0.5 m telescope at the Astro- TUGandAdiyamantelescopes,i.e. theseforcyclenumbers:
nomical Observatory of the Jagiellonian University (KRK, 30669, 30670 and 30931. For each pair the difference be-
Krako´w, Poland), the 0.6 m telescope at the Mt. Suhora tween derived T agrees within their errors derived from
obs
Observatory (SUH, Koninki, Poland), the 0.6 m telescope thefit,i.e. lessthantwoseconds.
at the AdiyamanUniversity Observatory (ADYU60, Adiya-
man, Turkey) and with the 1 m telescope at the TUBITAK 3. LTTMODELSOFTHE(O–C)
NationalObservatory(TUG,Antalya,Turkey). To model the eclipses ephemeris with the presence of a
Between2009and2013,observationswereperformedus- hypotheticalthirdbodyweusedthefollowingformulae
ing the SKO, KRK and SUH telescopes, while these taken
between 2014 and 2016, with the ADYU60 and TUG tele- Teph(L)=t0+PbinL+γtb(L), (1)
scopes. WegathereddatawiththefollowingCCDcameras:
whereγ representstheLightTravelTime(LTT)term(Irwin
the Andor iKon DZ-936B-BV (KRK), the Andor DZ436 tb
1952). In our formulation this term is parametrised by the
(SKO), the Apoge Alta U47 (SUH), the Andor iKon-M934
Keplerian orbital elements of the third body companion in
(ADYU60) and the SI1100 (TUG). A summary of observa-
orbitaroundthemasscenterofthebinary(Goz´dziewskietal.
tions is given in Tab. 3, where the start observing date, the
2012):
cyclenumber,eclipsetype(primary–1,secondary–2),fil-
√
terused,exposuretimeandreadouttimearelisted. γ (t)= K[sinω(cosE(t)−e)+cosω 1−e2sinE(t)],
tb
The CCD data were reduced with the pipeline developed
usingPython,IRAFandSextractorsoftware. Theusualbias where K isthesemi-amplitudeoftheLTTsignal,e,ω, P,τ
anddarksubtractionaswellasflat-fieldcorrectionwereap- are the eccentricity, periastron argument, orbital period and
pliedtoallimages. ForAndorCCDsdarkcountswerenegli- thetimeofperiastronpassageoftherelativeorbitofthepu-
gibleandtherefore,onlybiassubtractionwasdone.Anearby tativecompanionw.r.t. thebinary. Wenotethat Pandτare
constant star in the field of view, comparable to the target introducedindirectlythroughtheKeplerequation
star in brightness and color, was chosen as the comparison
star. Sinceourmajorgoalwastoobtaindifferentialphotom- 2π(t−τ)= E−esinE.
etryonly,wedidnotobserveanyphotometricstandardstars. P
For each night a light curve was constructed consisting of Due to very different time scales of orbital motion, the
extracted magnitude differences and time in the form of JD binary is represented as a point with the total mass of both
UTC.Themid-exposuretimesweretaken. stellarcomponentsequalto0.528M (Almeidaetal.2012).
(cid:12)
We modelled the shapes of the eclipses with a modified Furthermore,toaccountforsmalleccentricity,weintroduce
andtruncatedinvertedGaussianG(τ)multipliedbyapolyno- Poincare´ elements (x ≡ ecosω,y ≡ esinω) which make
mial,asdescribedinSection2. ofBeuermannetal.(2012b). it possible to get rid of weakly constrained eccentricity and
The model involves 8 parameters, including eclipse mini- pericenterargumentωforquasi-circularandmoderatelyec-
mumtime(Tobs)denotedas p1 inBeuermannetal.(2012b). centricorbits.
The resulting parameters values and their respective uncer- Toexpressthe(O–C)variabilitythroughγ (L(t)),weop-
pl
tainties(includingσTobs)wereobtainedfromthefittingpro- timizethelikelihoodfunctionL,
cedure as a term of the resulting covariance matrix from
1 1(cid:88) 1
the nonlinear least squares fitting algorithm. Figs. 8 and logL(D|ξξξ)=− χ2− Nlogσ2− Nlog2π, (2)
9 show the observed light curves and model fits. The de- 2 2 i 2
i
rivedeclipsetimeswereconvertedtothebarycentricdynam-
ical time (BJD), using the FK5 sky coordinates of NSVS wheretheχ2function
14256825 (α = 20h20m00s.458, δ = +04◦37(cid:48)56(cid:48)(cid:48).50) and
(cid:88)N [O(D)−C(ξξξ)]2
thegeodeticcoordinatesofeachgivenobservatory,withthe χ2(D,ξξξ)= i (3)
helpofthenumericalproceduredevelopedbyEastmanetal. σ2
i i
(2010). The eclipse minimum times, together with their re-
dependsonmodelparametersthrough(O–C) ≡ (T (L)−
spective errors, obtained from our new measurements are i obs i
T (L)) and the measurements uncertainties σ, where i =
listedinTab.1,whilealltimings(includingthesepublished eph i i
1...,N (Goz´dziewskietal.2015). Here,(O–C) denotesthe
in the literature) are gathered in Tab. 4 (available in the on- i
deviationoftheobservedi-theclipsetime-markfromitsBJD
line version only). The cycle numbers in Tabs. 1 and 4
ephemeris(Eq.1)forcycleL ≡ L(t).Themodelparameters
i i
4 Nasirogluetal.
Table1.ListofnewNSVS14256825eclipsetimes.Cyclenumber, Table1.continued...
time of the minimum, its error, type of the eclipse (1 – primary,
Cycle BJD Error[days] EclipseType Ref
2 – secondary) and references are given. References are for the
observatories: (5)theAstronomicalObs. oftheJagiellonianUniv., 26331.0 2457180.469794 0.000026 1 9
(6)theMt. SuhoraObs.,(7)theSkinakasObs.,(8)theTUBITAK
26413.0 2457189.520546 0.000020 1 8
NationalObs.and(9)theAdiyamanUniv.Obs.
26422.0 2457190.513847 0.000010 1 8
Cycle BJD Error[days] EclipseType Ref
26422.5 2457190.569067 0.000075 2 8
7167.5 2455065.315208 0.000082 2 5
26648.0 2457215.458344 0.000012 1 9
7204.0 2455069.343870 0.000036 1 5
26683.0 2457219.321420 0.000012 1 8
7223.0 2455071.440996 0.000014 1 5
26684.0 2457219.431837 0.000013 1 8
7386.0 2455089.432002 0.000024 1 6
26730.0 2457224.509018 0.000014 1 9
7503.0 2455102.345843 0.000018 1 5
26846.0 2457237.312397 0.000017 1 9
7557.0 2455108.306027 0.000041 1 5
26911.0 2457244.486749 0.000012 1 9
7955.0 2455152.234856 0.000018 1 6
26937.5 2457247.411658 0.000056 2 8
9797.0 2455355.544034 0.000035 1 5
27009.0 2457255.303376 0.000015 1 9
10593.0 2455443.401924 0.000010 1 6
27073.0 2457262.367301 0.000016 1 9
10918.0 2455479.273564 0.000012 1 6
27082.0 2457263.360683 0.000034 1 9
14162.0 2455837.327516 0.000016 1 6
27099.0 2457265.237010 0.000020 1 9
16808.0 2456129.377577 0.000015 1 7
27154.0 2457271.307578 0.000031 1 9
16808.5 2456129.432822 0.000023 2 7
27408.0 2457299.342580 0.000028 1 9
16817.0 2456130.370981 0.000006 1 7
27543.0 2457314.243090 0.000010 1 9
16835.0 2456132.357723 0.000017 1 6
28004.0 2457365.125453 0.000022 1 9
16835.5 2456132.412907 0.000033 2 6
29411.5 2457520.476902 0.000061 2 8
17650.0 2456222.312685 0.000020 1 5
29412.0 2457520.532048 0.000015 1 8
17867.0 2456246.263846 0.000021 1 5
29611.0 2457542.496481 0.000012 1 9
19301.0 2456404.540320 0.000024 1 6
29620.0 2457543.489845 0.000014 1 9
19545.0 2456431.471682 0.000019 1 6
29647.0 2457546.469948 0.000039 1 9
19744.0 2456453.436075 0.000040 1 6
29956.0 2457580.575537 0.000013 1 8
19744.5 2456453.491275 0.000099 2 6
30135.0 2457600.332481 0.000014 1 9
20206.0 2456504.428991 0.000015 1 6
30163.0 2457603.422952 0.000012 1 9
20206.5 2456504.484030 0.000044 2 6
30172.0 2457604.416311 0.000011 1 9
20269.0 2456511.382498 0.000014 1 6
30180.0 2457605.299328 0.000013 1 9
20360.0 2456521.426538 0.000013 1 6
30397.0 2457629.250499 0.000009 1 8
20803.0 2456570.322299 0.000098 1 6
30399.0 2457629.471256 0.000020 1 8
20812.0 2456571.315608 0.000025 1 6
30408.0 2457630.464585 0.000006 1 8
20812.5 2456571.370781 0.000113 2 6
30660.0 2457658.278862 0.000008 1 9
20813.0 2456571.425973 0.000046 1 6
30669.0 2457659.272248 0.000008 1 9
20830.0 2456573.302321 0.000014 1 6
30669.0 2457659.272263 0.000014 1 8
20975.0 2456589.306568 0.000016 1 5
30670.0 2457659.382587 0.000009 1 8
23458.0 2456863.365367 0.000033 1 8
30670.0 2457659.382609 0.000015 1 9
23467.0 2456864.358634 0.000032 1 8
30705.0 2457663.245692 0.000008 1 9
24553.0 2456984.224844 0.000017 1 8
30714.0 2457664.239053 0.000010 1 9
26132.0 2457158.505405 0.000012 1 9
30904.0 2457685.210139 0.000012 1 9
26141.0 2457159.498659 0.000030 1 9
30931.0 2457688.190200 0.000015 1 8
26205.0 2457166.562708 0.000012 1 8
30931.0 2457688.190212 0.000011 1 9
26213.0 2457167.445649 0.000021 1 8
30941.0 2457689.293987 0.000027 1 9
31004.0 2457696.247504 0.000009 1 8
NSVS14256825andcircumbinaryplanet 5
vectorξξξ ≡(K,P,e,ω,τ,P ,t ,σ ),andN denotesthenum-
bin 0 f
berofmeasurementsencodedasdatasetD. Wenotethatall
50
parametersofT areoptimized. Thismoregeneralformof
eph
Lmakesitalsopossibletodeterminethefreeparameterσ
f 0
that scales the raw uncertainties σi in quadrature, such that nds]
σ2 →σ2+σ2 resultsinχ2 ≡χ2/(N−dimξξξ)∼1. co
i,Ot ptimiisationf ofthedynaνmicalmodelreliesoninvestigat- C[se −50
O-
ingthespaceof8freemodelparametersξξξ,throughsampling
100
the posterior probability distribution P(ξξξ|D) of the param- −
etersξξξ, given the data set D: P(ξξξ|D) ∝ P(ξξξ)P(D|ξξξ), where
P(ξξξ)istheprior,andthesamplingdatadistributionP(D|ξξξ)≡ −150
logL(D|ξξξ). Foralloftheseparameters,priorshavebeenset 50000 40000 30000 20000 10000 0 10000 20000
− − − − −
as uniform (or uniform improper) through imposing param- cyclenumberL
etersrangesavailablefortheexploration, i.e., K,P,τ > 0d, Figure 1. The (O–C) diagram w.r.t. the linear ephemeris for
σf > 0 d, and x,y ∈ [−0.71,0.71], Pbin ∈ [0.110,0.112] d, Dataset A, with all data available in the literature. Filled rectan-
and ∆t ∈ [−0.1,0.1] d which is for the displacement w.r.t. glesareforraw(unbinned)SuperWASPdata,filledcirclesanddi-
0
thecycleL=0fortheepochofT =BJD2455793.840061. amondsareforothermeasurementspriortoepochofAugust2012,
0
andpentagonsareforthenewtimingdatainthispaper(Tab.1).See
We sampled the posterior with the Markov Chain Monte
Carlo(MCMC)emceepackageoftheaffine-invariantensem- thetextfordetails.
ble sampler (Goodman & Weare 2010), kindly provided by
Foreman-Mackeyetal.(2013). 50
4. LTTMODELRESULTS
0
Duetothenon-homogeneoustimingdatawhicharegath-
ered across literature and in this manuscript, we consider ds]
n
threedatasets. DatasetAincludesallobservationsavailable eco −50
[s
to date, which encompasses CCD observations and 5 mea- C
O-
surementsfromtheNSVSandASASarchivesinBeuermann 100
−
et al. (2012b), SuperWASP-derived timing data (Lohr et al.
2014), as well as our new measurements listed in Table 1.
150
Duetoalargescatteranduncertainties,theSuperWASPmea- −
surementsarefinallyexcludedinDatasetB.InDatasetCwe 50000 40000 30000 20000 10000 0 10000 20000
− − − − −
alsoexcludedtheNSVSandASASmeasurementsduetoun- cyclenumberL
certainderivationofthesemeasurements,whichisdiscussed Figure 2. The (O–C) diagram w.r.t. the linear ephemeris for
in Sect. 5.1. Then we subsequently analysed Datasets A, B DatasetB.DarkbluediamondsarefortheNSVSandASASmea-
and C individually. These particular datasets are illustrated surements,filledcirclesarefordataintheup-todateliteratureex-
inthe(O–C)diagramsinFigs.1,2and3,respectively. cludingSuperWASPmeasurements, darkdiamondsareforNSVS
andASASdata,anddarkerpentagonsareforthenewmeasurements
Inallfiguresincludedinthissection,wemarkedwithgrey
inthispaper(Tab.1).Seethetextfordetails.
rectanglesthetimeintervalafterthelastepochin(Hinseetal.
2014). i.e. August2012, whichindicatesournewmeasure-
where T stands here for the linear ephemeris of the BJD
ments. We may expect that the orbital period of a putative eph
momentofthemid-eclipseofthecycleL. Wechosetheini-
thirdobjectmaybeconstrainedandthatchangesconclusions
tialepochT ofthecycleL =0roughlyinthemiddleofthe
ofHinseetal.(2014),whowereabletoseeonlyanincrease 0
observationalwindow,i.e.,T = BJD2455793.840061. Itis
ofthe(O–C). 0
clearthatthelinearephemerisisessentiallythesame,within
ParametersofthelinearephemerisforDatasetAare
the errors at the last significant digit marked in brackets.
Teph(L)=BJD2455793.84004(2)+L0.110374083(2), However,theSuperWASP,NSVSandASASpointsstrongly
deviatefromapparentlyaquasi-sinusoidalpatternformedby
forDatasetBthelinearephemerisisdescribedthrough
(O–C)derivedfrommoreaccuratemeasurements.
Teph(L)=BJD2455793.84005(3)+L0.110374082(3), Before sampling the posterior, which is determined
through the likelihood function (Eq. 2), we first found the
whilethatforDatasetCis
best-fitting parameters through maximising L with the ge-
T (L)=BJD2455793.84005(3)+L0.110374082(3), netic algorithm (Charbonneau 1995). Next we ran the
eph
6 Nasirogluetal.
savespace, wedonotquotethem. Wenotethatthetimeof
50 pericenter argument τ, the binary period P , and the time-
bin
shift∆t fromthecycleL = 0epocharerepresentedrelative
0
to the best-fitting parameters in Tab. 2, respectively, where
nds] 0 T0 =BJD2455793.840061. Theseparametersareveryclose
o
c totheinitialvaluesderivedwiththecommonmaximization
e
C[s ofthelikelihoodfunctionL.
O-
50 The posterior projections reveal relatively significant cor-
−
relations of particular model parameters, like (K,P) and
(P,τ). However, the posterior is uni-modal with a quite
100 strongpeak.ThisisillustratedinFig.7forafewselectedpa-
−
15000 10000 5000 0 5000 10000 15000 20000 rametersofthe(O-C)model. TheMCMCsamplingreveals
− − −
cyclenumberL theerrorfloorof(cid:39)2secondsformodelsoptimalinthesense
Figure 3. The (O–C) diagram w.r.t. the linear ephemeris for defined above. Without this correction, the “raw” reduced
Dataset C. Filled circles are for data in the up-to date literature χ2 ∼ 2 indicates underestimated uncertainties. The optimal
ν
excludingSuperWASP,NSVSandASASmeasurements,andpen- solution is represented with a red curve, and is overplotted
tagonsareforthenewtimingdatainthispaper(Tab.1),seethetext on 100 randomly selected model curves from the MCMC
fordetails.
sample. We found that the eccentricity of the best-fitting
orbit e (cid:39) 0.175, indicating a significantly skewed (O–C)
Table 2. Parameters of the third-body with linear ephemeris for curve, andarelativelylargesemi-amplitudeoftheLTTsig-
DatasetC(Figs.6and7).Parameter∆t isfortheshiftrelativetothe nal K (cid:39) 50 s, rule out pericenter precession of the orbit,
0
observationalmiddle-windowepochT = BJD2455793.840061. followingBeuermannetal.(2012b).
0
Totalmassofthebinaryis0.528M(cid:12)(Almeidaetal.2012),seethe Duetoapparentlyrandomresidualswitharms (cid:39) 10sec-
textfordetails.
onds, whichisalmostequaltothemeanoftherescaledun-
Parameter Value +σ −σ certainties,wedidnotanalysemodelswithadditionalparam-
eters,suchastheparabolicephemeris(Hinseetal.2014)or
K[s] 48.9 1.6 1.2
evenaputativesecondcompanion(Almeidaetal.2013).The
P[day] 3632.8 169.6 131.7
mostsimple,1-companionmodelwiththelinearephemeris,
x 0 0.045 0.042 does not exhibit systematic, long-term changes of the (O–
y 0.175 0.032 0.031 C) superimposed on the quasi-sinusoidal variation. Secular
changesoftheorbitalperiodshouldnotbeexpectedforsuch
τ[day] 7938.5 246.5 161.8
adetachedbinary(Beuermannetal.2012b).
P [day] 0.110374099 2×10−9 3×10−9
bin To infer the companion mass from the third-body model
∆t0[day] −5×10−5 2×10−5 2×10−5 parameters listed in Tab. 2, we used the stellar masses as
σf [s] 1.8 0.2 0.2 M1 = 0.419 M(cid:12) and M2 = 0.109 M(cid:12) for the primary and
thesecondary,respectively,followingAlmeidaetal.(2012).
mass[M ] 14.75 0.13 0.13
Jup
Thebest-fittingorbitalperiodof P (cid:39) 3600daysimpliesthe
a[au] 3.74 0.12 0.09
minimal mass of ∼ 15 Jupiter masses (when the orbits are
e 0.175 0.012 0.003 co-planar), that is in the brown dwarf. For the ratio of or-
ω[deg] 90.11 15.37 12.89 bital periods P/Pbin ∼ 4 × 104, the triple system is highly
hierarchical. Obviously, the brown dwarf has a stable or-
bit,whichistwoordersofmagnitudewiderthanthestability
MCMC sampler for 512 initial conditions inside a small
limit(cid:39) 0.2a (roughly∼ 0.01aufortheNSVS14256825
bin
ballcenteredonthissolution. Wetestedchainlengthsfrom
binary)expectedforcircumbinarycompanions,ifthebinary
32,000upto768,000samples. Thelatterverylargenumber
eccentricitye (cid:39)0(e.g.,Holman&Wiegert1999,theirTa-
bin
of samples may be considered redundant, given the accep-
ble 7). In such a case, the brown dwarf eccentricity ∼ 0.2
tance fraction of (cid:39) 0.35 indicating an optimal output from
hasanegligibleimpactonthestability.
theMCMCsampler(Foreman-Mackeyetal.2013).
The third-body parameters determined here substantially
The best-fitting models and their residuals are illustrated differ from previous estimates. For instance, Beuermann
in the top and bottom panels of Figs. 4, 5 and 6, for A,
et al. (2012b) reported the orbital period unconstrained be-
B and C datasets, respectively. The posterior distribution
tween20and70yearswitheccentricitye(cid:39)0.50fora20yrs
is illustrated only for Dataset C (Fig. 7), since the posteri-
orbit,sincetheirdatadidnotcoverthe(O–C)maximumre-
ors for Datasets A and B are very similar, and therefore, to
NSVS14256825andcircumbinaryplanet 7
50
50
0
0
ds] ds]
n n
o o
c c
e e
O-C[s −50 O-C[s −50
100
− 100
−
5000 4000 3000 2000 1000 0 1000 2000 3000 5000 4000 3000 2000 1000 0 1000 2000 3000
− − − − − − − − − −
time[daysw.r.t. cycle=0epochT0=BJD2455793.84006] time[daysw.r.t. cycle=0epochT0=BJD2455793.84006]
40
20
50
[s] [s] 0
C C
O- O- 20
0 −
als als
u u
d d 40
esi esi−
r r
60
50 −
−
80
−
5000 4000 3000 2000 1000 0 1000 2000 3000 5000 4000 3000 2000 1000 0 1000 2000
− − − − − − − − − −
time[daysw.r.t. cycle=0epochT0=BJD2455793.84006] time[daysw.r.t. cycle=0epochT0=BJD2455793.84006]
Figure4. Toppanel: thesyntheticcurveofthebest-fittingmodel Figure5. Toppanel: thesyntheticcurveofthebest-fittingmodel
(redcurve)toalltimingdata(DatasetA).Greycurvesillustrate100 (redcurve)toalldataexcludingSuperWASPdata(DatasetB).Grey
randomly selected parameter samples from the MCMC posterior. curvesillustrate100randomlyselectedparametersamplesfromthe
Bottompanel:residualstothebest-fittingsolution. MCMCposterior. Bottompanel: residualstothebest-fittingsolu-
tion.
vealed here. We determine the semi-amplitude of the LTT
downloaded the source light curves from the publicly avail-
signal being roughly twice larger than that stated in Hinse
able NSVS1 and ASAS2 archives. The NSVS light curve
et al. (2014). The amplitude of (O–C) is one of crucial pa-
spans epochs between 1999 and 2000, while the ASAS ob-
rameters needed to estimate the energy required to support
servations span over a few years between 2003 and 2008.
theApplegatecycles(e.g.,Vo¨lschowetal.2016).
ThephotometricNSVSmeasurementstimestampsaregiven
inMJDUTC,whiletheASASmeasurementsinHJDUTC.
5. DISCUSSION
Therefore we recomputed the observation moments to the
5.1. TheNSVSandASAStimingdata
standardSolarsystembarycenterBJDtime-scalewithapro-
Wewouldliketocommentonthefiveearliestpointsfrom cedure developed by Eastman et al. (2010). The data have
the literature, i.e. one timing measurement from the NSVS beendividedinto ∼ 1yearintervalsandphase-foldedwith
(Woz´niak et al. 2004b) survey and four measurements from theorbitalperiodofthebinaryderivedfromthemostrecent
the ASAS survey (Pojmanski 1997), all five presented by linear ephemeris. We know that this period is determined
Beuermannetal.(2012b). withanuncertaintytoafewpartsofmillisecond,andassum-
Itmaybeobservedthatthesedataexhibitlargeuncertain- ing that the linear ephemeris is valid, we may use this new,
tiesandtheystronglydeviatefromthemodelsshowninthis fixedestimate.
work.Theexposuretimeis80secondsforNSVSsurvey,and In the next step we attempted to fit the function repre-
aslongas180secondsfortheASASlightcurves. Moreover, senting primary eclipses, as proposed in Beuermann et al.
toderiveeclipses,onemustcollectmeasurementsbyfolding
photometricpointsspanningoverawholeyear.
1http://skydot.lanl.gov/
Therefore we decided to re-analyse the source photomet-
2http://www.astrouw.edu.pl/asas/
ric data to derive the timings in an independent way. We
8 Nasirogluetal.
60
C models derived for each of the three data-sets are simi-
40 lar. WebelievethatthefinalfitshowninTab.2,derivedfor
DatasetC,doesindeedrepresentareliablesolution.
20
ds] 5.2. TheApplegatemechanismofthe(O–C)
n 0
co Forcompactbinaries,likeNSVS14256825,magneticac-
e
O-C[s−20 tciyvcitlyesoafntdherelesshsapmeasthsieveincteormnaplonsetrnutcmtuareyotrfigtgheisr Sstoalrar(-el.igk.e,
40
− Applegate1992;Lanzaetal.1998;Brinkworthetal.2006).
60 This leads to changes of the mutual gravitational field and
−
oscillations of the orbital period. A common problem for
−803000 2000 1000 0 1000 2000 3000 thisoriginofthe(O–C)variationsisinsufficientenergybud-
− − −
time[daysw.r.t. cycle=0epochT0=BJD2455793.84006] get of the secondary required to change its quadrupole mo-
20 ment Q. Therefore, the Applegate cycles are usually dis-
missed in the literature as a possible explanation of cyclic
variations of the (O–C) observed in a number of PCEBs.
10
There are, however, more detailed and improved models of
C[s] theApplegatemechanism,whichmodifytheenergyrequire-
O- 0 ments (Lanza et al. 1998; Lanza 2006; Brinkworth et al.
uals 2006). Recently, Vo¨lschow et al. (2016) considered a few
d
esi variantsoftheBrinkworthetal.(2006)formulationthatgen-
r
10
− erally takes into account more realistic stellar density pro-
files.Theyanalysedasampleof15compact PCEBs,includ-
20 ingNSVS14256825,andfoundthatonlyforfoursystemsin
−
2000 1500 1000 500 0 500 1000 1500 2000 the sample, the magnetic cycles may be responsible for the
− − − −
time[daysw.r.t. cycle=0epochT0=BJD2455793.84006] (O–C) behaviour. For NSVS 14256825 the relative energy
∆E/E required to trigger the measured (O–C) should be
Figure6. Toppanel: thesyntheticcurveofthebest-fittingmodel sec
(red curve) to data without SuperWASP and NSVS/ASAS points between∼ 5.4forthe“classic”Applegatemodeland(cid:39) 100
(DatasetC).Greycurvesillustrate100randomlyselectedparameter foranadvancedmodelofthestellardensityprofile(foracon-
samplesfromtheMCMCposterior. Bottompanel: residualstothe stantdensityprofile,theratiois2ordersofmagnitudelarger,
best-fittingsolutiondisplayedinTab.2. ∼3000).
Theup-todate(O–C)analysedinthispaperimpliesasub-
(2012b). Weperformedtwoexperiments. Inthefirstone,we stantialchangeofthesemi-amplitudeKandthevariationpe-
fittedthewholesetofparameters. Inthesecondexperiment, riod,werecalculatedestimatesoftheenergybudget∆E/E
sec
weconstructedthemean,syntheticlight-curvefromthebest for NSVS 14256825 given in Vo¨lschow et al. (2016). We
71eclipsesderivedwiththestandardmethod. Thenwefitted recomputed thisvalue inaccord with theirEq. 7, following
onlysomeofthemodeleclipseparametersasfree. Tianetal.(2009),forcanonicalmodelsinApplegate(1992)
Unfortunately, all these experiments resulted in variable aswellforthemodifiedApplegatemechanisminLanzaetal.
mid-eclipses estimates spread over 90 seconds. Moreover, (1998); Lanza (2006, and references therein). We used also
fortheASASdata,theO-Cofourtimingmomentsaresys- dataforthesecondarycomponentfromtheirTab.1.
tematically∼60secondearlierthanthemeasurementslisted AdoptingthesecondaryradiusR =0.162R ,mass M =
2 (cid:12) 2
inBeuermannetal.(2012b). 0.109 M , orbital separation a = 0.80 R , and the effective
(cid:12) (cid:12)
Theobtainedformalerrorsfromthemodelcurvefitswere temperature T = 2550 K we found that ∆E/E (cid:39) 11. We
sec
on the level of ±35-42 seconds and are similar to the (O- computedtheperiodchangerelativetothebinaryperiod
C) deviations from the linear ephemeris. Also the folding
∆P K
ofphotometricdataforayear(whichisaround3300binary =4π (cid:39)2×10−6,
P P
cycles) introduces a systematic shift of the mid-eclipses, in bin
accord with the local (O–C) trend. It could be as large as with the semi-amplitude K (cid:39) 49 s and (O-C) oscillation
∼20−50seconds. P(cid:39)9.95yrs(modulationperiod)asdisplayedinTab.2. The
We conclude that the NSVS and ASAS mid-eclipse mea- quadrupoleperiodvariation∆Qneededtodrivethemodula-
surements are not very useful for the O-C analysis od such tionoftheorbitalperiod(Lanza&Rodono` 1999)is:
ashortperiodbinary. Fortunately, theparametersofourO- ∆P ∆Q
=−9 ,
P M a2
bin bin bin
NSVS14256825andcircumbinaryplanet 9
4
0.
3
0.
e 2
0.
1
0.
0
5
1
0
2
]◦ 1
ω[ 0
9
0
6
8
4.
4
u] 4.
a
[ 0
a 4.
6
3.
0
s] 0.
m
[n 0.8
Pbi −
∆ 6
1.
−
0
3.
4
s] 2.
[
σf 1.8
2
1.
5 0 5 0 1 2 3 4 0 0 0 0 6 0 4 8 6 8 0 2 8 4 0
14. 15. 15. 16.0. 0. 0. 0. 6 9 12 15 3. 4. 4. 4. 1. 0. 0. 1. 1. 2. 3.
− −
m [MJ] e ω[◦] a [au] ∆Pbin [ms] σf [s]
Figure7. One–andtwo–dimensionalprojectionsoftheposteriorprobabilitydistributionsofafewparametersinferredfromthe(O–C)model
forDatasetC(Tab.2andFig.6). Thereareillustrated32,000samplesfor512“walkers”initiatedinasmallballaroundthebest-fittingmodel
inTab.2. Weremovedaboutof10%initial,burn-outsamples. Subsequentparametersarethecompanionmassm,eccentricitye,periastron
argumentω,semi-majoraxisa,adeviationofthebinaryperiod∆P fromitsadoptedbestfittingvalue(inmilliseconds,seeTab.2),andthe
bin
measurementsuncertaintycorrectionfactorσ .Contoursareforthe16th,50thand84thpercentileofsamplesintheposteriordistribution.See
f
thetextfordetailsregardingparametrisationofthe(O–C)modelandimposedpriors.
where M anda arethebinarymassandthesemi-major lardensityprofiles,theApplegatemodulationsareevenless
bin bin
axis,respectively. ForNSVS14256825,weobtainthemag- probable, since the prescribed energy budget is then by 1-2
nitudeof∆Q(cid:39)1047gcm2. orders of magnitude too small, as shown in Vo¨lschow et al.
The updated ∆E/E is more than two times larger than (2016,theirTab.4).
sec
the value in Vo¨lschow et al. (2016) for the genuine Apple- InaccordwiththealternativegeneralisationoftheApple-
gatemodelwhich,inaccordwiththeiranalysis,tendstoun- gate mechanism by Lanza et al. (1998); Lanza (2006), tak-
derestimate the energy ratio. For other variants, based on ing into account additional factor of the Lorenz force, the
the Brinkworth et al. (2006) formulation, and realistic stel- magneticcyclesmayoperatewithafractionoftheenergyre-
10 Nasirogluetal.
quiredbytheoriginalApplegatemodel. Yetthelowerlimit Soker2014;Vo¨lschowetal.2014;Kostovetal.2016a;Veras
ofthecalculated∆E/E ∼ 11factorevenforthisscenario etal.2017). Inthefirstcase,thebest-fittingorbitalelements
sec
seems to be so large that one can safely conclude that the ofNSVS14256825maybeusedastheborderconditionsre-
Applegate mechanism and its generalizations proposed by quiredtoreconstructthebinaryevolution,asshownbyPorte-
Brinkworth et al. (2006), Lanza (2006) and Vo¨lschow et al. giesZwart(2013).
(2016)arenotacredibleexplanationsofthe(O–C)variabil- We do not analyse other possibilities of the (O–C) vari-
ityintheNSVS14256825binary. ability, like the mass transfer, orbital precession, magnetic
brakingorgravitationalradiation, whichareusuallyrefuted
forthisclassofbinaries.
6. CONCLUSIONS
Weshouldstress,however,that thethird-bodyhypothesis
Ournewsetoflight-curvesoftheNSVS14256825binary
investigated for a number of close and evolved PCEBs re-
substantiallyextendsthearchivedlistofeclipsetiming. For
ported in the literature, remains uncertain in most cases. A
thefirsttimeournewdatacoverthemaximumofthe(O–C)
very discouraging example of this kind is the Cataclysmic
w.r.t. the linear ephemeris, covering almost one full cycle
Variable(CV)polar,HUAqr(Schwopeetal.1993;Schwarz
of a quasi-sinusoidal modulation, and making it possible to
etal.2009;Qianetal.2011;Hinseetal.2012;Goz´dziewski
putconstrainsonprevious LTTmodelsaimedatexplaining
et al. 2012; Schwope & Thinius 2014; Bours et al. 2014;
the(O–C)behaviourofthissystem(Beuermannetal.2012b;
Goz´dziewski et al. 2015). The apparently quasi-sinusiodal
Almeidaetal.2013;Hinseetal.2014).
(O–C) variations with a full amplitude of ∼ 60 s observed
Inaccordwiththethird-bodyhypothesis,theobserved(O–
for almost 20 years till 2012, has changed to a strong, sec-
C)variationsintheNSVS14256825maybeexplainedbythe
ular trend that deviates by 180 s from the linear ephemeris
presence of a single companion with a minimal mass in the
to date. Two and three planet models of this system are
brown dwarf mass range (14.7 Jupiter masses), in a moder-
strongly unstable, unless we consider an exotic system of
ately eccentric orbit with eccentricity (cid:39) 0.2, and the orbital
three5−6M massplanets,withthemiddleonerevolving
periodof∼10years. Wefoundthatparametersofthisthird- Jup
inaretrogradeorbit. Suchasystemmaybestableforatleast
body within our best model are relatively well constrained
1 Gyr (Goz´dziewski et al. 2015). Similarly, the (O-C) of
throughthepresentdata. Theresidualsdonotindicate any
HW Vir interpreted through 5:2 MMR configuration of two
significantseculartrendswhichcouldappearduetodissipa-
Jovianplanets(Beuermannetal.2012a)arenotconstrained,
tive phenomena in the binary (like mass transfer, magnetic
regarding the outermost planet and its mass. The (O-C) for
braking and gravitational radiation). We note that Beuer-
otherPCEBs,likeNYVir(Qianetal.2012b;Leeetal.2014),
mann et al. (2012b) and Hinse et al. (2014) reported such
QSVir(Horneretal.2013),UZFor(Potteretal.2011)could
trendsduetomuchshorterobservationalwindowthatdidnot
beformallyexplainedwiththeresonant2-planetsystems,yet
coverthemaximumofthe(O–C)showninthiswork.
none of them has been found stable. An exception is the
Therefore,a1-companionmodelmaybethemostreliable
NNSerwithlow-mass,Jovianplanetscloseto2:1meanmo-
explanation of the NSVS 14256825 (O–C). Taking into ac-
tionresonance,whichiswelldocumentednadhaspassed so
count the updated amplitude of LTT of K (cid:39) 50 s and its
faralltestsoftheplanetarynatureofthe(O–C)(Beuermann
periodof(cid:39) 10yr,thealternativehypothesis–theApplegate
etal.2010;Marshetal.2014;Vo¨lschowetal.2014). Afew
mechanism–doesnotseemtobesufficientlyeffectivetopro-
otherPCEBs,likeV471Tau(Hardyetal.2015),V470Cam
ducesuchchanges. Inaccordwithaveryrecentanalysisby
(Qian et al. 2013), RR Cae (Qian et al. 2012a) might host
Vo¨lschowetal.(2016),theenergyrequiredtotriggertheAp-
single-companions,seeAlmeidaetal.(2013)andZorotovic
plegatecyclesinthesecondarycompanionshouldbe10–100
&Schreiber(2013)listingsuchbinarieswiththeirastrophys-
largerthanitsnuclearenergy. Moreover,therelativelylarge
icalcharacteristics.
K and the the shape of (O–C) yielding the third-body orbit
Observationsofthesesystemsisstilltimelysincethelong-
eccentricityof(cid:39) 0.17,ruleoutalsotheorbitalprecessionas
term,hardlypredictable(O-C)aretypicallyknownforafrac-
aplausible(O–C)variationsmechanism.
tion of the longest putative orbital periods. There are open
The presence of a massive companion in moderately ec-
problemsregardingthePCBEs,liketheformationofputative
centric orbit around the evolved, compact binary would be
companionsasfirst-orsecond-generationplanets,orbitalar-
not necessarily unusual on the grounds of the planet forma-
chitecturesandstabilityofhypotheticalmultiple-companion
tiontheory. Manyscenariosarepossible,regardingbothfirst
configurations,thepresenceofmechanismsalternativeorco-
generationplanets(companions)thatsurvivedtheCommon-
existing with the Applegate and Lanza-Rodono´ cycles and
Envelope (CE) phase, as well as emerged in a protoplane- the LTT effect. Therefore, while the planetary hypothesis
tary disc formed from the stellar matter ejected during the
of the (O–C) observed for NSVS 14256825 cannot be yet
CE phase, as second generation planets (e.g., Veras et al.
definite,ourobservationsandnewdatamaycontributemore
2011; Veras & Tout 2012; Portegies Zwart 2013; Bear &