Astronomy&Astrophysicsmanuscriptno.RSPup_pFactor_v3r0 (cid:13)cESO2017 January20,2017 Observational calibration of the projection factor of Cepheids III. The long-period Galactic Cepheid RSPuppis(cid:63) PierreKervella1,2,BorisTrahin1,2,HowardE.Bond3,AlexandreGallenne4,LaszloSzabados5,AntoineMérand4, JoanneBreitfelder2,4,JulienDailloux1,6,RichardI.Anderson7,8,PascalFouqué9,10,WolfgangGieren11, NicolasNardetto12,andGrzegorzPietrzyn´ski13 1 Unidad Mixta Internacional Franco-Chilena de Astronomía (CNRS UMI 3386), Departamento de Astronomía, Universidad de Chile,CaminoElObservatorio1515,LasCondes,Santiago,Chile,e-mail:[email protected]. 2 LESIA(UMR8109),ObservatoiredeParis,PSLResearchUniversity,CNRS,UPMC,Univ.Paris-Diderot,5PlaceJulesJanssen, 7 92195Meudon,France,e-mail:[email protected]. 1 3 DepartmentofAstronomy&Astrophysics,525DaveyLab.,PennsylvaniaStateUniversity,UniversityPark,PA16802USA. 0 4 EuropeanSouthernObservatory,AlonsodeCórdova3107,Casilla19001,Santiago19,Chile. 2 5 KonkolyObservatory,MTACSFK,KonkolyThegeM.út15-17,H-1121,Hungary. 6 InstitutSupérieurdel’Aéronautiqueetdel’Espace,10AvenueEdouardBelin,31400Toulouse,France n 7 PhysicsandAstronomyDepartment,TheJohnsHopkinsUniversity,3400N.CharlesSt,Baltimore,MD21218,USA a 8 ObservatoiredeGenève,UniversitédeGenève,51Ch.desMaillettes,1290Sauverny,Switzerland. J 9 IRAP,UMR5277,CNRS,UniversitédeToulouse,14av.E.Belin,F-31400Toulouse,France. 8 10 CFHTCorporation,65-1238MamalahoaHwy,Kamuela,Hawaii96743,USA 1 11 UniversidaddeConcepción,DepartamentodeAstronomía,Casilla160-C,Concepción,Chile. 12 LaboratoireLagrange,UMR7293,UniversitédeNiceSophia-Antipolis,CNRS,ObservatoiredelaCôted’Azur,Nice,France ] 13 NicolausCopernicusAstronomicalCenter,PolishAcademyofSciences,ul.Bartycka18,PL-00-716Warszawa,Poland. R S Received;Accepted . h p ABSTRACT - o Theprojectionfactor(p-factor)isanessentialcomponentoftheclassicalBaade-Wesselink(BW)technique,whichiscommonlyused r todeterminethedistancestopulsatingstars.Itisamultiplicativeparameterusedtoconvertradialvelocitiesintopulsationalvelocities. t s AstheBWdistancesarelinearlyproportionaltothe p-factor,itsaccuratecalibrationforCepheidsisofcriticalimportanceforthe a reliability of their distance scale. We focus on the observational determination of the p-factor of the long-period Cepheid RSPup [ (P=41.5days).ThisstarisparticularlyimportantasthisisoneofthebrightestCepheidsintheGalaxyandananalogoftheCepheids 1 usedtodetermineextragalacticdistances.Anaccuratedistanceof1910±80pc(±4.2%)hasrecentlybeendeterminedforRSPup v usingthelightechoespropagatinginitscircumstellarnebula.WecombinethisdistancewithnewVLTI/PIONIERinterferometric 2 angulardiameters,photometry,andradialvelocitiestoderivethe p-factorofRSPupusingthecodeSpectro-Photo-Interferometry 9 of Pulsating Stars (SPIPS). We obtain p = 1.250±0.064 (±5.1%), defined for cross-correlation radial velocities. Together with 1 measurements from the literature, the p-factor of RSPup confirms the good agreement of a constant p = 1.293±0.039 (±3.0%) 5 modelwiththeobservations.Weconcludethatthep-factorofCepheidsisconstantormildlyvariableoverabroadrangeofperiods 0 (3.7to41.5days). . 1 Key words. Stars: individual: RS Pup, Stars: variables: Cepheids, Techniques: interferometric, Techniques: photometric, Stars: 0 distances,Cosmology:distancescale. 7 1 v:1. Introduction Cepheids. This is complicated by the rarity of these massive i stars, and particularly the long-period oscillators, which re- XThe oscillation period of Cepheids is longer for more mas- sultsinlargedistancesbeyondthecapabilitiesoftrigonometric rsive, less dense, and more luminous stars. This cyclic change parallax measurements. The parallax-of-pulsation method, also ain radius, and its associated effective temperature modulation, known as the Baade-Wesselink (BW) technique, is a powerful is the physical basis of the empirical Leavitt law (the Period- technique to measure the distances to individual Galactic and Luminosity relation, Leavitt 1908; Leavitt & Pickering 1912). LMCCepheids.Thevariationoftheangulardiameterofthestar The calibration of the zero-point of the Leavitt law requires (from surface brightness-color relations or optical interferome- the independent measurement of the distances of a sample of try)iscomparedtothevariationofthelineardiameter(fromthe integration of the radial velocity). The distance of the Cepheid (cid:63) Based on observations collected at the European Organisation isthenobtainedbysimultaneouslyfittingthelinearandangular for Astronomical Research in the Southern Hemisphere under ESO amplitudes(see,e.g.,Stormetal.2011).Themainweaknessof programs093.D-0316(A),094.D-0773(B),096.D-0341(A)and098.D- the BW technique is that it uses a numerical factor to convert 0067(A).Basedinpartonobservationswiththe1.3mtelescopeoper- disk-integratedradialvelocitiesintophotosphericvelocities,the atedbytheSMARTSConsortiumatCerroTololoInteramericanObser- projectionfactor,or p-factor(Nardettoetal.2007,Barnes2009, vatory. Articlenumber,page1of17 A&Aproofs:manuscriptno.RSPup_pFactor_v3r0 Nardettoetal.2014b).Thisfactor,whoseexpectedvalueistyp- Table2.PIONIERobservationsofRSPup.Welistthemeanmodified Juliandate(MJD)ofeachobservingnight,thecalibratorstars,theuni- icallyaround1.3,simultaneouslycharacterizesthesphericalge- ometryofthepulsatingstar,thelimbdarkening,andthediffer- form disk diameter adjusted on the squared visibility measurements, anditsstatisticalandsystematic(calibration)uncertainties. ence in velocity between the photosphere and the line-forming regions. Owing to this intrinsic complexity, the p-factor is cur- UTDate MJD Cal. θ ±σ ±σ rently uncertain to 5-10%, and accounts for almost all the sys- UD stat. syst. tematicuncertaintiesofthenearbyCepheidBWdistances.This (mas) is the main reason why Galactic Cepheids were excluded from 2014-04-03 56750.0178 1,2 0.860±0.011±0.020 themeasurementofH byRiessetal.(2011). Recent observation0al efforts have produced accurate mea- 2014-05-08 56785.0009 1,2 0.801±0.007±0.020 surements of the p-factor of Cepheids (Mérand et al. 2005b; 2015-01-15 57037.3056 1,2 0.813±0.005±0.020 Pilecki et al. 2013; Breitfelder et al. 2015; Gieren et al. 2015; 2015-01-16 57038.3660 1,2 0.830±0.009±0.020 Breitfelderetal.2016),withtheobjectivetoreducethissource 2015-01-17 57039.3643 1,2 0.882±0.015±0.020 of systematic uncertainty. However, these p-factor calibrations 2015-02-14 57067.1757 1,2 0.916±0.005±0.020 up to now were essentially obtained on low-luminosity, rela- tively short-period Cepheids (P (cid:46) 10days) that are the most 2015-02-18 57071.0997 1,2 0.848±0.002±0.020 common in the Galaxy. The most important Cepheids for ex- 2015-02-21 57074.1467 1,2 0.827±0.010±0.020 tragalacticdistancedeterminationsarethelong-periodpulsators 2015-12-27 57383.1893 3,4 0.983±0.007±0.012 (P (cid:38) 10days),however.Acalibrationofthe p-factorofthein- 2015-12-31 57387.1858 3,4 0.956±0.005±0.012 trinsicallybrightestCepheidsisthereforehighlydesirable.The- 2016-02-21 57439.1475 3,4 0.933±0.011±0.012 oretical studies (e.g., Neilson et al. 2012) indicate that the p- factormayvarywiththeperiod,butthedependencediffersbe- tween authors (Nardetto et al. 2014a; Storm et al. 2011; Breit- mismatch of the beams. The raw data have been reduced us- felderetal.2016). ingthepndrsdatareductionsoftwareofPIONIER(LeBouquin We focus the present study on the long-period Cepheid RS et al. 2011), which produces calibrated squared visibilities and Pup (HD 68860, HIP 40233, SAO 198944). Its period of P = phaseclosures.TwoexamplesofthemeasuredRSPupsquared 41.5daysmakesitoneofthebrightestCepheidsofourGalaxy visibilities are presented in Fig. 1. The visibilities were classi- andthesecondnearestlong-periodpulsatorafter(cid:96)Carinae(HD cally converted into uniform disk (UD) angular diameters (see, 84810,P=35.55days).Kervellaetal.(2014)reportedanaccu- e.g.,Mozurkewichetal.2003andYoung2003)thatarelistedin ratemeasurementofthedistanceofRSPup,d = 1910±80pc, Table2. corresponding to a parallax π = 0.524 ± 0.022mas. This dis- tance was obtained from a combination of photometry and po- larimetry of the light echoes that propagate in its circumstellar 2.2. Photometry dustnebula.ItisinagreementwiththeGaia-TGASparallaxof π=0.63±0.26mas(GaiaCollaborationetal.2016a),whosesys- As the measurements available in the literature are of uneven tematicuncertaintyisestimatedto±0.3masbyLindegrenetal. qualityforRSPup,weobtainednewphotometryintheJohnson- (2016).Inthepresentwork,weemploythelightechodistanceof Kron-Cousins BVR system using the ANDICAM CCD camera RSPup,inconjunctionwithnewinterferometricangulardiame- on the SMARTS2 1.3 m telescope at Cerro Tololo Interameri- termeasurements,photometry,andarchivaldata(Sect.2)toap- canObservatory(CTIO).Atotalof277queue-scheduledobser- plytheSpectro-Photo-InterferometryofPulsatingStars(SPIPS) vations were made by service observers between 2008 Febru- modeling(Sect.3).Throughthisinverseversionoftheparallax- ary 28 and 2011 January 25. The exposure times were usually of-pulsationtechnique,wederiveits p-factorandcompareitto one second in each filter, but nevertheless, many of the V im- thevaluesobtainedfor(cid:96)CarandotherCepheids(Sect.4). agesandmostoftheRimagesweresaturated,especiallyaround maximum light, and had to be discarded. After standard flat- fieldcorrectionsoftheframes,wedetermineddifferentialmag- 2. Observations nitudesrelativetoanearbycomparisonstar.Inordertoconvert the relative magnitudes into calibrated values, the BVR magni- 2.1. Interferometry tudesofthecomparisonstarweredeterminedthroughobserva- tions of Landolt (1992) standard-star fields obtained on seven We observed RSPup between 2014 and 2016 using the Very photometric nights. The resulting BVR light curves are pre- Large Telescope Interferometer (Mérand et al. 2014) equipped sented in Fig. 2, phased with a period P = 41.5113days and with the PIONIER beam combiner (Berger et al. 2010; Le T [JD ] = 2455501.254. As discussed further in this section, Bouquin et al. 2011). This instrument is operating in the in- 0 (cid:12) frared H band (λ = 1.6µm) using a spectral resolution of thisperiodissuitableovertherangeoftheSMARTSobserving R = 40. The four relocatable 1.8meter Auxiliary Telescopes epochs(2008-2011).Thelistofmeasuredmagnitudesisgivenin TableA.2.Theassociateduncertaintyisestimatedto±0.03mag (ATs) were positioned at stations A1-G1-J3-K0 or A0-G1-J2- J31. These quadruplets offer the longest available baselines (up permeasurement(Wintersetal.2011). to 140m), which are necessary to resolve the apparent disk of We supplemented the new SMARTS photometric measure- RSPup(θ ≈0.9mas)sufficientlywell.ThepointingsofRSPup ments with archival visible light photometry from Moffett & were interspersed with observations of calibrator stars to esti- Barnes (1984), Berdnikov (2008), and Pel (1976). In order to matetheinterferometrictransferfunctionoftheinstrument(Ta- improve the coverage of the recent epochs, we also added a ble1).ThesecalibratorswereselectedcloseangularlytoRSPup set of accurate photoelectric measurements retrieved from the in order to minimize any possible bias caused by polarimetric 2 SMARTS is the Small & Moderate Aperture Research Telescope 1 https://www.eso.org/paranal/telescopes/vlti/configuration/ System;http://www.astro.yale.edu/smarts Articlenumber,page2of17 P.Kervellaetal.:Projectionfactorofthelong-periodCepheidRSPup Table1.CharacteristicsofthecalibratorsusedforthePIONIERobservationsofRSPup.TheywereselectedfromthecatalogsofLafrasseetal. (2010a,b)(1to3)andMérandetal.(2005a)(4).Forcalibrators1to3,weemployedthesurfacebrightnesscolorrelationscalibratedbyKervella etal.(2004)toestimatetheirangulardiameters. Number Name Sp.Type m m m m θ θ B V H K LD UDH (mas) (mas) 1 HD67977 G8III 7.10 6.21 4.29 4.06 0.738±0.020 0.713±0.020 2 HD69002 K2III 7.54 6.37 3.99 3.84 0.867±0.020 0.838±0.020 3 HD68978 G2V 7.33 6.71 5.37 5.27 0.374±0.008 0.361±0.008 4 HD73947 K2III 8.48 7.09 3.95 3.88 0.863±0.012 0.834±0.012 AAVSOdatabase3.TheserecentmeasurementsintheJohnsonV Juliandate) bandarelistedinTableA.3andplottedinFig.A.1.Theycover C = 2455501.3428±0.1756 the JD range 2456400 (April 2013) to 2457550 (June 2016), (cid:16) (cid:17) whichmatchesourPIONIERinterferometricobservationswell. + 41.491734±0.001404 ×E Finally, we also included in our dataset the near-infrared JHK (cid:16) (cid:17) bandphotometryfromLaney&Stobie(1992)andWelchetal. + 9.51510−5±1.73310−5 ×E2. (1) (1984). AstheE2 coefficientinthisequationispositive,theparabolain theO−C diagramtendstowardpositivevalues,thusindicating 2.3. Radialvelocities thattheperiodisincreasingwithtime.BoththeO−Cgraphand We included in our dataset the radial velocity measurements the parabolic fit are in good agreement with their counterpart fromAnderson(2014)thatprovideanexcellentcoverageofsev- obtained by Berdnikov et al. (2009), who find a secular period eral pulsation cycles of RSPup with a high accuracy. We com- change of 7.824 10−5 ±1.968 10−5 (quadratic term, expressed plementedthesedatawiththemeasurementsobtainedbyStorm infractionoftheperiodpercycle).Thesecularperiodincrease etal.(2004).AsdiscussedbyAnderson(2014),theradialveloc- thatwederivecorrespondstoalengtheningof+0.1675dayover ity curve of RSPup is not perfectly reproduced cycle-to-cycle. a century, or +144.7 s/year. This value is high, but not without ThisispotentiallyadifficultyfortheapplicationoftheBWtech- precedent among long-period classical Cepheids (Mahmoud & nique, which relies on observational datasets that are generally Szabados1980).Thisrateofsecularperiodchangecorresponds obtainedatdifferentepochsandthereforedifferentpulsationcy- totheexpectedvalueforathirdcrossingCepheidwithaperiod cles.Thisinducesanuncertaintyontheamplitudeofthelinear likeRSPup(Andersonetal.2016c). radius variation, and therefore on the derived parameters (dis- The erratic period changes superimposed on the monotonic tance or p-factor). Following the approach by Anderson et al. period variation of RSPup are clearly seen on the residuals of (2016b),weestimateinSect.3.1theuncertaintyinducedonthe the O−C fit in Fig. 3. In the bottom panels of this figure, the p-factor by separately fitting the different cycles monitored by parabola has been subtracted from the O −C values listed in Anderson(2014). TableA.1(asshownintheupperpanels).Therearethreeinter- valsinthisdiagramwherethepulsationperiodcanbeapproxi- matedwithaconstantvalue:between1995and2002as41.518± 2.4. Phasingofthedatasets 0.002days,between2003and2007as41.437±0.002days,and Wetookparticularcaretoproperlyphasethedifferentdatasets, between 2008 and 2013 as 41.512±0.002days. Kervella et al. a task that is complicated by the rapidly changing period of (2014)adoptedaperiod P = 41.5117daysfortheepochofthe RSPup.Thisisanimportantstepinthefittingprocess,however, HST/ACSobservations(2010)thatwereusedtoestimatethedis- as an incorrect phasing results in biases on the derived model tanceofRSPupthroughitslightechoes.Itisworthnotingthat parameters. thescatterbetweenthesubsequentdatapointscanbeintrinsicto Asafirst-orderapproach,thepulsationperiod Panditslin- thestellarpulsation:thisphenomenonisinterpretedasacycle- ear rate of variation have been determined with the classical to-cyclejitterinthepulsationperiod,asobservedinV1154Cyg, methodoftheO−Cdiagram(Sterken2005).Thediagramcon- the only Cepheid in the original Kepler field (Derekas et al. structed for the moments of the maximum brightness covering 2012). It was proposed by Neilson & Ignace (2014) that the morethanacenturyisshownintheleftpanelofFig.3.Therele- physical mechanism underlying the period jitter of V1154 Cyg vantdatausedforconstructingtheO−CdiagramarelistedinTa- is linked to the presence of convective hot spots on the photo- bleA.1.Thegeneraltrendoftheperiodvariationisanincrease, sphere of the star. This explanation may also apply to RSPup, with a superimposed oscillation exhibiting a pseudo-period on whose relatively low effective temperature could favor the ap- theorderofthreedecades.WhencalculatingtheO−Cvalues,the pearanceofsuchconvectivefeatures. referenceepoch E = 0wastakenasJD 2455501.254.Thisis The period changes that occurred in the past few decades (cid:12) thenormalmaximumdeterminedfromtheSMARTSlightcurve inducedavariabilityofthemaximumlightepochsof3to4days, showninFig.2.ThevariableEdesignatesthenumberofpulsa- thatis,upto0.10inphaseshift.Suchalargephaseshiftwould tion cycles that occurred since this reference epoch. The initial degradethequalityoftheSPIPScombinedfitoftheobservables, pulsationperiodwasarbitrarilytakenas41.49days.Thesecond- in particular the photometry that is spread over four decades. orderweightedleast-squaresfittotheO−Cresidualsisalsoplot- Totaketheperiodchangesintoaccount,weadoptapolynomial tedinFig.3.Theequationofthefittedparabolais(expressedin model of degree five. This relatively high degree allows us to fitthe observedepochsof maximumlightmuch betterthan the 3 https://www.aavso.org linear model, as shown in the residuals of the O −C diagram Articlenumber,page3of17 A&Aproofs:manuscriptno.RSPup_pFactor_v3r0 Fig.3.Leftcolumn:O−CdiagramforRSPup(toppanel)andresidualsofthemodel(bottompanel)foralinearperiodvariation(reddashedline andpoints)andafifth-degreepolynomialfunction(bluesolidlineandpoints).Thesizeoftheblackpointsintheupperpanelisproportionalto theirweightinthefit(TableA.1).Rightcolumn:enlargementoftheO−Cdiagramcoveringthelast400pulsationcyclesofRSPup. (Fig.3,bottompanels).Theperiodindaysasafunctionofthe Table3.ParametersoftheSPIPSmodelofRSPup.Theupperpartof thetableliststheprimarymodelparameters,andthelowerpartgives observing epoch T (expressed in modified Julian date) is given derivedphysicalparameters(meanvalueandminimum/maximumover bythepolynomialexpression thepulsationcycle). P(MJD)= (41.438138±0.00070)−3.42244×10−7(∆t) Parameter Value±σ ±σ stat syst +0.23085×10−8(∆t)2+0.13219×10−12(∆t)3 θ (mas)a 0.8490±0.0034±0.0120 0 −0.74919×10−16(∆t)4+0.42849×10−20(∆t)5, (cid:104)θ(cid:105)(mas)a 0.9305±0.0034±0.0120 (2) vγ (kms−1) 25.423±0.200 E(B−V) 0.4961±0.0060 with∆t = MJD−MJD thenumberofdayssincethereference 0 K excess 0.027±0.011 epochMJD =45838.0313.The+114.8s/yearlinearrateofthe 0 Hexcess 0.016±0.011 periodchangeoverthepast50yearsshowninFig.4iscloseto the value obtained from the fit of the complete dataset with a p-factor 1.250±0.034±0.054 linearlyvariableperiod(+144.7s/year). MJD 45838.0313±0.098 0 Period(days)b 41.438138±0.00070 Periodchange(s/year)c +114.8 3. AnalysisofRSPupusingSPIPS Distance(pc) 1910±80(fixed) TheSPIPSmodelingcode(Mérandetal.2015)considersapul- sating star as a sphere with a changing effective temperature Radius(R(cid:12)) 191(164/208) andradius,overwhichissuperimposedacombinationofatmo- Eff.temperature(K) 5060(4640/5850) spheric models from precomputed grids (ATLAS9). The pres- Bolom.luminosity(L ) 21700(14200/29500) (cid:12) ence of a circumstellar envelope emitting in the infrared K and Bolometricmagnitude −6.072(−6.434/−5.640) H bands is included in the model, as is the interstellar redden- ing. The best-fit SPIPS model of RSPup is presented in Fig. 5 Notes. a θ isthelimb-darkeneddisk(Rosseland)angulardiameterat 0 togetherwiththeobservationaldata,andthecorrespondingbest- phasezero,and(cid:104)θ(cid:105)thephase-averagemeanangulardiameteroverthe fitparametersarelistedinTable3.Thequalityofthefitisgen- pulsationcycle.bPeriodatthereferenceepochMJD0.cRateofperiod erally very good for all observing techniques, and the phasing changeasshowninFig.4. of the different datasets is satisfactory. The interpolation of the radialvelocitycurvewasachievedusingsplineswithoptimized node positions. We assume the distance d = 1910±80pc de- distancearefullydegenerateparameters,the±4.2%distanceer- termined by Kervella et al. (2014) as a fixed parameter in this ror bar directly translates into a σ = ±0.053 uncertainty on dist fit. p. As shown by Anderson (2014) and Anderson (2016), the cycle-to-cyclerepeatabilityofthevelocitycurveoflong-period 3.1. Projectionfactor Cepheids is imperfect. Anderson et al. (2016b) demonstrated Considering the complete radial velocity data set, we obtain a thatfor(cid:96)Car,variationsofthe p-factorof5%areobservedbe- projectionfactorof p=1.250withastatisticaluncertaintyfrom tween cycles. To quantify this effect for RSPup, we adjusted thefitofσ =±0.034. distinctSPIPSmodelsonthefourcyclessampledbyAnderson stat The primary source of systematic error on p is the uncer- (2014). The results are shown in Figs. B.1 to B.4. We observe taintyontheadoptedlightechodistance.Asthep-factorandthe astandarddeviationofσ = 0.028overthefour p-factorvalues Articlenumber,page4of17 P.Kervellaetal.:Projectionfactorofthelong-periodCepheidRSPup RS Pup (P~41.5d) p=1.250 d=1910.0pc E(B-V)=0.496 K =0.027mag H =0.016mag ex ex 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 6.0 50 VSVprγa=lidn2 e5m .N4oo3dd ekelm,s p/.st.p = 45.99km/s AStnodremrs+o n2 0200414Vrad χ2=4.90 1e3 K) 5555....2468 mSpolidneel Nodes s)40 T (eff445...680 km/30 9.5 Present Work χ2=0.76 Tycho χ2=1.95 y ( 7.5 cit 8.5 o20 el B_GCPD V_MVB_TYCHO v 7.5 6.5 10 0.8 0.0 P0e.l2+ 1907.64 0.6 χ0.28=2.15.20 7.6 0.0 A0A.V2SO 02.04160.6 χ02.=813.17.20 Berdnikov+ 2008 0.4 7.2 Moffett+ 1984 0 0.0 6.8 Present Work V_W V_GCPD 3 0.4 6.4 nσ 0 7.8 0.0 H0i.p2parc0o.s4 0.6 χ0.28=3.15.50 6.8 0.0 P0re.2sent0 W.4ork0.6 χ02.=810.17.20 3 7.4 6.4 7.0 1.00 HP_MVB_HIPPARCOS 6.0 R_JOHNSON 6.6 4.8 0.0 L0a.n2ey+0 1.49920.6 χ0.28=3.14.20 4.2 0.0 L0a.n2ey+0 1.49920.6 χ0.28=2.14.70 s)0.95 4.6 Welch+ 1984 4.0 Welch+ 1984 a no CSE m 4.4 3.8 m. (0.90 4.2 J_CTIO 3.6 H_CTIO dia 4.0 0.0 L0a.n2ey+0 1.49920.6 χ0.28=2.13.00 0.0 B0e.r2dnik0o.v4+ 2000.68 χ0.28=4.10.40 g. 3.8 Welch+ 1984 0.9 An0.85 no CSE 0.8 3.6 V_GCPD - 0.7 K_CTIO R_GCPD 0.80 model 3.4 0.6 UDH->θRoss χ2=1.2 1.7 0.0 B0e.r2dnik0o.v4+ 2000.68 χ0.28=2.14.10 0.0 0.2 0.4 0.6 0.8 1.0 3 1.5 σ 0 V_GCPD - n 3 1.3 I_GCPD 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 pulsation phase pulsation phase Fig.5.SPIPScombinedfitoftheobservationsofRSPup. derivedforthedifferentcyclesthatwetranslateintoasystematic Insummary,combiningthesystematicuncertaintiesthrough uncertaintyofσ =±0.014onthe p-factor.TheSPIPSmod- σ = (σ2 +σ2 )1/2 ,weobtainthe p-factorofRSPupfor cycle syst dist cycle els resultingfrom theseparate fitof theradial velocity datasets thecross-correlationradialvelocitymethod: of Storm et al. (2004) and Anderson (2014) are presented in Figs.B.5andB.6,respectively.Thederivedp-factorsfromthese twodatasetsdonotshowanysignificantbiasbeyondσ . cycle p=1.250±0.034±0.054=1.250±0.064(±5.1%). (3) We assumed in the SPIPS model that the p-factor is con- stant during the pulsation cycle of the star. This is a simpli- fication, as the p-factor is proportional to the limb darkening, 3.2. Colorexcessandcircumstellarenvelope which is known to change with the effective temperature of thestar.Theamplitudeofthe p-factorvariationinducedbythe We derive a color excess E(B−V) = 0.4961±0.0060, higher changing limb darkening is expected to be small. The effective than the value obtained by Fouqué et al. (2007), who list temperature of RSPup changes by 1300K during its pulsation E(B−V) = 0.457±0.009 for RSPup. The possible presence (4600−5900K, Fig. 5 and Table 3). Neilson & Lester (2013) of an excess emission in the infrared K (λ ≈ 2.2µm) and H presented predictions of the limb-darkening corrections appli- (λ≈1.6µm)bandsisadjustedasaparameterbytheSPIPScode. cable to interferometric angular diameter measurements based ForRSPup,wedetectamoderatelysignificantexcessemission onasphericalimplementationofKurucz’sATLASmodels.For of ∆m = 0.027 ± 0.011 in the K band, and marginal in the K the temperature range of RSPup considering logg ≈ 1.0 and H band (∆m = 0.016±0.011mag). This low level of excess H M ≈ 10M ), the listed correction factor k = θ /θ in the emission is in agreement with Kervella et al. (2009), who did (cid:12) UD LD V band(inwhichthespectroscopicmeasurementsareobtained) not detect a photometric excess in the K band, although a con- rangesfromk =0.9116(4600K)tok =0.9161(5900K)over siderableexcessfluxisfoundinthethermalinfrared(10µm)and V V the cycle. We consider here that this variation of 0.5% is neg- at longer wavelengths. We note that the best-fit infrared excess ligible compared to the other sources of systematic uncertainty values for the different pulsation cycles of RSPup (Fig. B.1 to (distanceandcycle-to-cyclevariations). B.6)areconsistentwithinafewmillimagnitudes. Articlenumber,page5of17 A&Aproofs:manuscriptno.RSPup_pFactor_v3r0 RS Pup - 2015-02-18 150 100 1.1 θUD = 0.848 ± 0.002 ± 0.020 mas 50 0 50 100 1.0 Squared visibility0.9 150150100 50 0 50 100150 0.8 0.7 0.6 ma) 3 χr2ed=0.34 Residual (sig 3101 Fig. 2. SMARTS light curves of RSPup in Johnson B, V, and Kron- 0 100 200 300 400 500 Spatial frequency (1/arcsec) CousinsR. RS Pup - 2015-12-31 150 100 1.1 θUD = 0.956 ± 0.005 ± 0.012 mas 50 41.50 RS Pup 0 +114.754 s/year 50 100 1.0 Squared visibility0.9 150150100 50 0 50 100150 y)4411..4468 a 0.8 d (d o eri p41.44 0.7 ma)0.63 χr2ed=0.99 41.42 Residual (sig 3101 41.4400000 42000 44000 46000 48000MJD50000 52000 54000 56000 58000 0 100 200 300 400 500 Spatial frequency (1/arcsec) Fig.4.PolynomialfitofthechangingperiodofRSPup.Thebluecurve Fig.1.ExamplesofPIONIERsquaredvisibilitiescollectedonRSPup isadegree-fivepolynomialfitoftheperiodvalues(blackpoints).The onthenightof18February2015,closetotheminimumangulardiam- blackdashedlinerepresentsthelineartrendoftheperiodchangeover eterphase(toppanel),andon31December2015,closetomaximum thepast50years. angulardiameter(bottompanel).Thesolidlineisthebest-fituniform disk visibility model, and the dashed lines represent the limits of the ±1σuncertaintydomainontheangulardiameter.The(u,v)planecov- plitude of the radial velocity of RSPup (Anderson 2014) may erageisshownintheupperrightsubpanels,withaxeslabeledinmeters. induce systematic uncertainties on the determination of the γ- velocity. This will particularly be the case if the radial veloc- ityphasecoverageisincomplete.Forthisreason,whiletheam- 3.3. Limitonthepresenceofcompanions plitude of the fluctuations appears significant, it is difficult to conclude that it is caused by a companion. It is interesting to We checked for the presence of a companion in the PIONIER notethattheγ-velocityvaluedependsonthetechniqueusedfor interferometric data using the companion analysis and non- the radial velocity measurement: Nardetto et al. (2008) find a detectionininterferometricdataalgorithm(CANDID,Gallenne γ-velocity of v = −25.7±0.2kms−1 for RSPup after correc- γ etal.2015).Theinterferometricobservablesareparticularlysen- tionoftheγ-asymmetryofitsspectrallines.Theγ-velocitycan sitivetothepresenceofcompanionsdowntohighcontrastratios alsodependonwhichlinesareincludedinthecross-correlation and small separations, as demonstrated, for instance, by Absil mask. et al. (2011), Gallenne et al. (2013) and Gallenne et al. (2014). Wedidnotdetectanysecondarysource,rulingoutthepresence 4. Discussion ofastellarcompanionwithacontrastintheHbandlessthanap- proximately 6magnitudes (flux ratio f/fCepheid = 0.4%) within Forareviewofthecurrentopenquestionsrelatedtothep-factor, 40masoftheCepheid(Fig.6). in particular in the context of the interferometric version of the The γ-velocity of RSPup measured using the cross- BWtechnique,werefertoBarnes(2009,2012). correlation technique is presented in Fig. 7, and the values are Asummaryoftheavailablepredictionsandmeasurementsof listedinTable4.Thecycle-to-cyclerandomvariationoftheam- the p-factorsof RSPup andofthe similarlong-periodCepheid Articlenumber,page6of17 P.Kervellaetal.:Projectionfactorofthelong-periodCepheidRSPup Table 5. Measured (top section) p-factor values of RSPup and (cid:96)Car andpredictionsfromperiod-p-factorrelations(bottomsection). Reference RSPup (cid:96)Car Breitfelderetal.(2016) − 1.23±0.12 Andersonetal.(2016b)c − 1.27±0.12 Presentwork 1.250±0.064 − Burkietal.(1982) 1.36 1.36 Hindsley&Bell(1986) 1.341 1.343 Gierenetal.(2005) 1.337±0.038 1.347±0.037 Groenewegen(2007)a 1.270±0.050 1.270±0.050 Laney&Joner(2009) 1.196±0.038 1.201±0.036 Stormetal.(2011) 1.249±0.105 1.262±0.101 Neilsonetal.(2012) 1.140±0.003 1.146±0.003 Groenewegen(2013) 1.112±0.030 1.128±0.030 Nardettoetal.(2014a) 1.181±0.019 1.186±0.018 Notes. a Constant p-factorvalue;b excludingFFAql;c averageofthe measuredvalues. (cid:96)CarispresentedinTable5.MostauthorsbasedtheirBWdis- tancedeterminationonthelinearperiod-p-factorrelationestab- Fig.6.Toppanel:Upperlimit(3σ)ofthefluxcontributionofcompan- lishedbyHindsley&Bell(1986,1989): p = 1.39−0.03logP. ionsofRSPupasafunctionoftheangularseparationfromtheCepheid. Owing to the weak dependence on period, the p-factors pre- ThelimitsobtainedusingtheapproachesofAbsiletal.(2011)andGal- dicted for RSPup and (cid:96)Car by this relation are both very lenneetal.(2015)areshownseparately.Bottompanel:mapoftheχ2 close to p = 1.34. The theoretical calibration of the period- ofthebestbinarymodelfit(left)andstatisticalsignificanceofthede- p-factor (Pp) relation by Neilson et al. (2012) gives a geomet- tection(right).Nosignificantsourceisfoundinthefieldofview. ric p-factor of p = [1.402±0.002]−[0.0440±0.0015]logP 0 Table4.γ-velocitiesofRSPupfromthecross-correlationtechnique. (V band, spherical model, linear law), to be multiplied by the period-dependentvelocitygradientanddifferentialvelocitycor- rections introduced by Nardetto et al. (2007). The recent work by Nardetto et al. (2014a) including δ Scuti stars confirms the MeanJD v (kms−1) Reference γ PprelationbyNardettoetal.(2009)andproposesacommonPp 2425612 21.1±2.0 Joy(1939) relationbetweenCepheidsandδScutistars(p=[1.31±0.01]− 2444913 22.5±1.2 Barnesetal.(1988) [0.08±0.01]logP). The Nardetto et al. (2014a) relation yields 2447090 25.8±0.5 Stormetal.(2004) p=1.181forRSPupand p=1.186for(cid:96)Car.Therelationfrom 2450563 24.8±0.5 Bersier(2002) Stormetal.(2011)ismuchsteeper(p=[1.550±0.04]−[0.186± 2453085 27.1±0.5 Nardettoetal.(2009) 0.06]logP).Groenewegen(2007)usedtheCepheidtrigonomet- 2456551 25.2±0.5 Anderson(2014) ricparallaxesfromBenedictetal.(2007)toderiveaPprelation of the form p = [1.28 ± 0.15] − [0.01 ± 0.16]logP, which is consistentwithaconstant p-factorwith p=1.27±0.05. Figure8givesanoverviewoftheavailablemeasurementsof p-factorsofCepheids,includingtheTypeIICepheidκPav(Bre- itfelder et al. 2015). We selected for this plot the p-factor val- ueswitharelativeaccuracybetterthan10%.Weremovedfrom the sample the binary Cepheid FFAql for which the HST/FGS distance is questionable (see the discussion, e.g., in Breitfelder et al. 2016 and Turner et al. 2013). As shown by Anderson et al. (2016a), the presence of a companion can bias the par- allax. The weighted average of the selected measurements is p = 1.293 ± 0.039, and the reduced χ2 of the measurements with respect to this constant value is χ2 = 0.9. If we include red FFAqlinthesample,weobtain p=1.285.Theuncertaintyof p wascomputedfromthecombinationoftheerrorbarsoftheinde- pendentmeasurementsof OGLE-LMC-CEP-0227(P = 3.80d, p = 1.21 ± 0.05, Pilecki et al. 2013), δCep (P = 5.37d, p = 1.288±0.054, Mérand et al. 2015), and the present mea- surement of RSPup (P = 41.5d, p = 1.250±0.064). We did notaveragetheerrorbarsofthedifferent p-factormeasurements Fig.7.Observedγ-velocityofRSPup. from the HST/FGS distances as the degree of correlation be- tween them and the possible associated systematics are uncer- Articlenumber,page7of17 A&Aproofs:manuscriptno.RSPup_pFactor_v3r0 tain.Forthesamereason,wedidnotaveragetheuncertaintiesof thetwo p-factormeasurementsofbinaryCepheidsintheLMC 1.5 from Pilecki et al. (2013) and Gieren et al. (2015), and we se- lected only the best p-factor of δCep derived by Mérand et al. (2015). In agreement with the present results, Breitfelder et al. 1.4 (2016)alsoconcludedfromafittothecompletesampleofmea- sured p-factors that a constant value of p = 1.324±0.024 (1σ or fromourvalue)reproducesthemeasurements. n fact1.3 The good agreement of the constant p-factor model p = ectio 1.293 ± 0.039 with the measurements indicates that this coef- Proj1.2 ficientismildlyvariableoverabroadrangeofCepheidperiods (3.0to41.5days).Thisresultcanbeexplainedbytherelatively wsnoahnrirco&hwLrereassuntelgtres(io2nf0a1e3ffm)eipcnrtoievrdevicattericmahtpaioenrngaetousfroethfaethniredlligimmrabbv-didtayarrkokefennCiniengpg.hNceoiedeifsl--, 1.1 LMC9009 CEP0227 Cepδ X SgrW Sgr Pav Dorβ Gemζ Car‘ RS Pup ficientk=θ /θ ofonlyafewpercentintheV bandoverthe 1.0 UD LD 0.4 0.2 0.0 0.2 0.4 0.6 0.8 fullrangeofclassicalCepheidproperties.Thedifferenceiseven Log(Period)-1 smaller at longer wavelengths. The spherical models in the V bandbytheseauthorsgivek = 0.9337forthehottestphaseofa Fig.8.Distributionofthemeasured p-factorsofCepheidswithbetter short-periodCepheid(7000K,logg=2.0,m=5M ),lessthan than 10% relative accuracy. The references for the different measure- (cid:12) 2.5% away from the value k = 0.9116 obtained for the coolest ments(exceptRSPup)arelistedinBreitfelderetal.(2016).Theblue phase of RSPup (4600K, logg = 1.0, m = 10M ). The mild pointsuseHST-FGSdistances(Benedictetal.2002,2007),theorange (cid:12) pointsaretheLMCeclipsingCepheids(Pileckietal.2013;Gierenetal. dependence of the p-factor on the period is consistent with the 2015).Thesolidlineandorangeshadedarearepresenttheweightedav- PprelationproposedbyGroenewegen(2007). eragep=1.293±0.039. The precision of the parallaxes of the first data release of Gaia-TGAS(Lindegrenetal.2016)istoolowtoaccuratelyde- termine the p-factor of nearby Cepheids (see, e.g., Casertano TheresearchleadingtotheseresultshasreceivedfundingfromtheEuropeanRe- searchCouncil(ERC)undertheEuropeanUnion’sHorizon2020researchand et al. 2016b). The availability in 2017 of the second Gaia data innovationprogramme(grantagreementNo695099).Thisresearchmadeuse release (Gaia Collaboration et al. 2016b) will provide very ac- ofAstropy4,acommunity-developedcorePythonpackageforAstronomy(As- curate parallaxes for hundreds of Galactic Cepheids, however, tropyCollaborationetal.2013).ThisworkhasmadeuseofdatafromtheEu- including RSPup, which will be among the longest periods in ropeanSpaceAgency(ESA)missionGaia(http://www.cosmos.esa.int/ the sample. The ongoing observations of a sample of 18 long- gaia),processedbytheGaiaDataProcessingandAnalysisConsortium(DPAC, http://www.cosmos.esa.int/web/gaia/dpac/consortium).Fundingfor period Cepheids by Casertano et al. (2016a) using the spatial theDPAChasbeenprovidedbynationalinstitutions,inparticulartheinstitutions scanning technique with the HST/WFC3 has started to provide participating in the Gaia Multilateral Agreement. We used the SIMBAD and accurateparallaxeswithaccuraciesof±30µsfortheserarepul- VIZIERdatabasesattheCDS,Strasbourg(France),andNASA’sAstrophysics sators. At a later stage, accurate broadband epoch photometry DataSystemBibliographicServices. willalsobeincludedintheGaiadatareleases(see,e.g.,Clemen- tini et al. 2016). Combining Gaia data with archival observa- tions,theSPIPStechniquewillenableaveryaccuratecalibration References of the Pp relation of Cepheids, and therefore of their distance Absil,O.,LeBouquin,J.-B.,Berger,J.-P.,etal.2011,A&A,535,A68 scale,whichisstilltodayanessentialingredientindetermining Anderson,R.I.2014,A&A,566,L10 thelocalvalueofH (Riessetal.2016).ForthenearestCepheids 0 Anderson,R.I.2016,MNRAS,463,1707 oftheGaiaandHST/WFC3samples,theavailabilityofinterfer- Anderson,R.I.,Casertano,S.,Riess,A.G.,etal.2016a,ApJS,226,18 ometricangulardiameterswillsignificantlyimprovethequality Anderson,R.I.,Mérand,A.,Kervella,P.,etal.2016b,MNRAS,455,4231 Anderson,R.I.,Saio,H.,Ekström,S.,Georgy,C.,&Meynet,G.2016c,A&A, ofthedeterminationoftheirparametersthankstotheresolution 591,A8 of the usual degeneracy between effective temperature and in- AstropyCollaboration,Robitaille,T.P.,Tollerud,E.J.,etal.2013,A&A,558, terstellarreddening.EvenfordistantCepheids,however,whose A33 angulardiameterscannotbemeasureddirectly,therobustnessof Barnes, T. G. 2009, in American Institute of Physics Conference Series, Vol. 1170,AIPConf.Ser.,ed.J.A.Guzik&P.A.Bradley,3–12 theSPIPSalgorithmwillenableanaccuratecalibrationoftheir Barnes,III,T.G.2012,JAAVSO,40,256 physicalproperties,includingthe p-factor,oncetheirparallaxes Barnes,III,T.G.,Moffett,T.J.,&Slovak,M.H.1988,ApJS,66,43 areknown. Benedict,G.F.,McArthur,B.E.,Feast,M.W.,etal.2007,AJ,133,1810 Benedict,G.F.,McArthur,B.E.,Fredrick,L.W.,etal.2002,AJ,124,1695 Acknowledgements. WewouldliketothankVelloTaburandStanleyWalkerfor Berdnikov,L.N.1995,inAstronomicalSocietyofthePacificConferenceSeries, sendingustheirunpublishedphotometricobservations,andMarcellaMarconi. Vol.83,IAUColloq.155:AstrophysicalApplicationsofStellarPulsation,ed. WeacknowledgewiththanksthevariablestarobservationsfromtheAAVSO R.S.Stobie&P.A.Whitelock,349 InternationalDatabasecontributedbyobserversworldwideandusedinthisre- Berdnikov,L.N.2008,VizieROnlineDataCatalog,2285,0 search.TheauthorsacknowledgethesupportoftheFrenchAgenceNationale Berdnikov, L. N., Henden, A. A., Turner, D. G., & Pastukhova, E. N. 2009, delaRecherche(ANR),undergrantANR-15-CE31-0012-01(projectUnlock- AstronomyLetters,35,406 Cepheids).PK,AG,andWGacknowledgesupportoftheFrench-Chileanex- Berger, J.-P., Zins, G., Lazareff, B., et al. 2010, in Society of Photo-Optical change program ECOS-Sud/CONICYT (C13U01). W.G. and G.P. gratefully InstrumentationEngineers(SPIE)ConferenceSeries,Vol.7734,Societyof acknowledgefinancial supportforthis workfromthe BASALCentrodeAs- Photo-OpticalInstrumentationEngineers(SPIE)ConferenceSeries trofisicayTecnologiasAfines(CATA)PFB-06/2007.W.G.alsoacknowledges Bersier,D.2002,ApJS,140,465 financial support from the Millenium Institute of Astrophysics (MAS) of the Breitfelder,J.,Kervella,P.,Mérand,A.,etal.2015,A&A,576,A64 IniciativaCientificaMileniodelMinisteriodeEconomia,FomentoyTurismo Breitfelder,J.,Mérand,A.,Kervella,P.,etal.2016,A&A,587,A117 deChile,projectIC120009.Weacknowledgefinancialsupportfromthe“Pro- Burki,G.,Mayor,M.,&Benz,W.1982,A&A,109,258 grammeNationaldePhysiqueStellaire"(PNPS)ofCNRS/INSU,France.LSz acknowledgessupportfromtheESTECContractNo.4000106398/12/NL/KML. 4 Availableathttp://www.astropy.org/ Articlenumber,page8of17 P.Kervellaetal.:Projectionfactorofthelong-periodCepheidRSPup Casertano,S.,Riess,A.G.,Anderson,J.,etal.2016a,ApJ,825,11 AppendixA: Photometricmeasurements Casertano, S., Riess, A. G., Bucciarelli, B., & Lattanzi, M. G. 2016b, ArXiv e-prints,1609.05175 Clementini,G.,Ripepi,V.,Leccia,S.,etal.2016,A&A,595,A133 Dean,J.F.,Cousins,A.W.J.,Bywater,R.A.,&Warren,P.R.1977,MmRAS, 83,69 Derekas,A.,Szabó,G.M.,Berdnikov,L.,etal.2012,MNRAS,425,1312 Eggen,O.J.,Gascoigne,S.C.B.,&Burr,E.J.1957,MNRAS,117,406 ESA,ed.1997,ESASpecialPublication,Vol.1200,TheHIPPARCOSandTY- CHOcatalogues.Astrometricandphotometricstarcataloguesderivedfrom theESAHIPPARCOSSpaceAstrometryMission Fouqué,P.,Arriagada,P.,Storm,J.,etal.2007,A&A,476,73 GaiaCollaboration,Brown,A.G.A.,Vallenari,A.,etal.2016a,A&A,595,A2 GaiaCollaboration,Prusti,T.,deBruijne,J.H.J.,etal.2016b,A&A,595,A1 Gallenne,A.,Mérand,A.,Kervella,P.,etal.2014,A&A,561,L3 Gallenne,A.,Mérand,A.,Kervella,P.,etal.2015,A&A,579,A68 Gallenne,A.,Monnier,J.D.,Mérand,A.,etal.2013,A&A,552,A21 Gerasimovic,B.P.1927,HarvardCollegeObservatoryBulletin,848,14 Gieren,W.,Pilecki,B.,Pietrzyn´ski,G.,etal.2015,ApJ,815,28 Gieren,W.,Storm,J.,Barnes,III,T.G.,etal.2005,ApJ,627,224 Groenewegen,M.A.T.2007,A&A,474,975 Groenewegen,M.A.T.2013,A&A,550,A70 Harris,H.C.1980,PhDthesis,WashingtonUniv.,Seattle. Hindsley,R.&Bell,R.A.1986,PASP,98,881 Hindsley,R.B.&Bell,R.A.1989,ApJ,341,1004 Innes,R.T.A.&Gill,D.1903,AnnalsoftheCapeObservatory,9,1 Irwin,J.B.1961,ApJS,6,253 Joy,A.H.1939,ApJ,89,356 Kervella,P.,Bond,H.E.,Cracraft,M.,etal.2014,A&A,572,A7 Kervella,P.,Mérand,A.,&Gallenne,A.2009,A&A,498,425 Kervella,P.,Thévenin,F.,DiFolco,E.,&Ségransan,D.2004,A&A,426,297 Lafrasse,S.,Mella,G.,Bonneau,D.,etal.2010a,VizieROnlineDataCatalog, 2300,0 Lafrasse, S., Mella, G., Bonneau, D., et al. 2010b, in Proc. SPIE, Vol. 7734, OpticalandInfraredInterferometryII,77344E–77344E–11 Landolt,A.U.1992,AJ,104,340 Laney,C.D.&Joner,M.D.2009,inAmericanInstituteofPhysicsConference Series,Vol.1170,AmericanInstituteofPhysicsConferenceSeries,ed.J.A. Guzik&P.A.Bradley,93–95 Laney,C.D.&Stobie,R.S.1992,A&AS,93,93 LeBouquin,J.-B.,Berger,J.-P.,Lazareff,B.,etal.2011,A&A,535,A67 Leavitt,H.S.1908,AnnalsofHarvardCollegeObservatory,60,87 Leavitt,H.S.&Pickering,E.C.1912,HarvardCollegeObservatoryCircular, 173,1 Lindegren,L.,Lammers,U.,Bastian,U.,etal.2016,A&A,595,A4 Madore,B.F.1975,ApJS,29,219 Mahmoud,F.&Szabados,L.1980,IBVS,1895,1 Mérand, A., Abuter, R., Aller-Carpentier, E., et al. 2014, in Proc. SPIE, Vol. 9146,OpticalandInfraredInterferometryIV,91460J Mérand,A.,Bordé,P.,&CoudéduForesto,V.2005a,A&A,433,1155 Mérand,A.,Kervella,P.,Breitfelder,J.,etal.2015,A&A,584,A80 Mérand,A.,Kervella,P.,CoudéduForesto,V.,etal.2005b,A&A,438,L9 Mitchell,R.I.,Iriarte,B.,Steinmetz,D.,&Johnson,H.L.1964,Boletindelos ObservatoriosTonantzintlayTacubaya,3,153 Moffett,T.J.&Barnes,III,T.G.1984,ApJS,55,389 Mozurkewich,D.,Armstrong,J.T.,Hindsley,R.B.,etal.2003,AJ,126,2502 Nardetto,N.,Gieren,W.,Kervella,P.,etal.2009,A&A,502,951 Nardetto,N.,Mourard,D.,Mathias,P.,Fokin,A.,&Gillet,D.2007,A&A,471, 661 Nardetto,N.,Poretti,E.,Rainer,M.,etal.2014a,A&A,561,A151 Nardetto,N.,Stoekl,A.,Bersier,D.,&Barnes,T.G.2008,A&A,489,1255 Nardetto, N., Storm, J., Gieren, W., Pietrzyn´ski, G., & Poretti, E. 2014b, in IAUSymposium,Vol.301,IAUSymposium,ed.J.A.Guzik,W.J.Chap- lin,G.Handler,&A.Pigulski,145–148 Neilson,H.R.&Ignace,R.2014,A&A,563,L4 Neilson,H.R.&Lester,J.B.2013,A&A,554,A98 Neilson,H.R.,Nardetto,N.,Ngeow,C.-C.,Fouqué,P.,&Storm,J.2012,A&A, 541,A134 Pel,J.W.1976,A&AS,24,413 Pilecki,B.,Graczyk,D.,Pietrzyn´ski,G.,etal.2013,MNRAS,436,953 Pojmanski,G.2002,ActaAstron.,52,397 Riess,A.G.,Macri,L.,Casertano,S.,etal.2011,ApJ,730,119 Riess,A.G.,Macri,L.M.,Hoffmann,S.L.,etal.2016,ApJ,826,56 Sterken,C.2005,inASPConf.Ser.,Vol.335,TheLight-TimeEffectinAstro- physics:CausesandcuresoftheO-Cdiagram,ed.C.Sterken,3 Storm,J.,Carney,B.W.,Gieren,W.P.,etal.2004,A&A,415,531 Storm,J.,Gieren,W.,Fouqué,P.,etal.2011,A&A,534,A94 Turner,D.G.,Kovtyukh,V.V.,Luck,R.E.,&Berdnikov,L.N.2013,ApJ,772, L10 Voûte,R.1939,AnnalsoftheBosschaObservatoryLembang(Java)Indonesia, 8,31 Walraven,T.,Muller,A.B.,&Oosterhoff,P.T.1958,Bull.Astron.Inst.Nether- lands,14,81 Welch,D.L.,Wieland,F.,McAlary,C.W.,etal.1984,ApJS,54,547 Westerlund,B.E.1963,MNRAS,127,71 Winters,J.G.,Henry,T.J.,Jao,W.-C.,etal.2011,AJ,141,21 Young,J.2003,inEASPublicationsSeries,Vol.6,EASPublicationsSeries,ed. G.Perrin&F.Malbet,181 Articlenumber,page9of17 A&Aproofs:manuscriptno.RSPup_pFactor_v3r0 TableA.1.O−C residualsforRSPuppis.JD(cid:12) istheheliocentricmo- JD(cid:12) E O−C W Reference mentofmaximumbrightness.Eistheepochnumberascalculatedfrom −2.4×106 [d] theephemerisC=2455501.254+41.49×E.Wistheweightassigned totheO−Cvalue(1,2,or3dependingonthequalityofthelightcurve). 53551.918 −47 0.694 2 Tabur∗ The∗symbolinthereferencesindicatesunpublisheddata. 53842.397 −40 0.743 2 AAVSO 53842.461 −40 0.807 3 Tabur∗ 53842.495 −40 0.841 2 Pojmanski(2002) 54091.419 −34 0.825 3 presentwork JD E O−C W Reference (cid:12) 54132.197 −33 0.113 3 AAVSO −2.4×106 [d] 54215.229 −31 0.165 3 Tabur∗ 15050.6 −977 85.1 1 Innes&Gill(1903) 54215.264 −31 0.200 3 Pojmanski(2002) 15424.6 −968 85.7 1 Gerasimovic(1927) 54505.241 −24 −0.253 3 Pojmanski(2002) 16830.1 −934 80.5 1 Gerasimovic(1927) 54546.574 −23 −0.410 3 Tabur∗ 18277.9 −899 76.2 1 Gerasimovic(1927) 54546.611 −23 −0.373 3 AAVSO 19723.4 −864 69.5 1 Gerasimovic(1927) 54588.094 −22 −0.380 2 presentwork 20963.2 −834 64.6 1 Gerasimovic(1927) 54837.503 −16 0.089 3 Pojmanski(2002) 22824.1 −789 58.5 1 Gerasimovic(1927) 54878.846 −15 −0.058 2 AAVSO 26006.61 −712 46.24 1 Voûte(1939) 55127.522 −9 −0.322 1 Pojmanski(2002) 26379.42 −703 45.64 1 Voûte(1939) 55252.067 −6 −0.247 2 AAVSO 26752.55 −694 45.36 1 Voûte(1939) 55252.640 −6 −0.241 3 Kervellaetal.(2014) 27042.15 −687 44.53 1 Voûte(1939) 55293.713 −5 −0.091 2 presentwork 27456.32 −677 43.80 1 Voûte(1939) 55335.074 −4 −0.220 3 presentwork 27828.94 −668 43.01 1 Voûte(1939) 55501.254 0 0.000 3 presentwork 28201.64 −659 42.30 1 Voûte(1939) 55625.868 3 0.144 2 AAVSO 34451.700 −508 27.366 1 Eggenetal.(1957) 56041.317 13 0.693 3 AAVSO 34533.607 −506 26.293 2 Walravenetal.(1958) 56373.179 21 0.635 3 AAVSO 34864.914 −498 25.680 2 Eggenetal.(1957) 35196.511 −490 25.357 1 Irwin(1961) 37513.865 −434 19.271 3 Westerlund(1963) 37638.297 −431 19.233 3 Mitchelletal.(1964) 40701.394 −357 12.070 3 Pel(1976) 40949.305 −351 11.041 3 Pel(1976) 41405.313 −340 10.659 1 Deanetal.(1977) 41735.214 −332 8.640 2 Madore(1975) 41776.643 −331 8.579 3 Deanetal.(1977) 42065.736 −324 7.242 3 Deanetal.(1977) 42438.472 −315 6.568 2 Deanetal.(1977) 44055.085 −276 5.071 2 Harris(1980) 44428.140 −267 4.716 1 Moffett&Barnes(1984) 44967.089 −254 4.295 3 Moffett&Barnes(1984) 47951.011 −182 0.937 3 ESA(1997) 48240.973 −175 0.469 3 ESA(1997) 48448.945 −170 0.991 3 ESA(1997) 48739.114 −163 0.730 3 ESA(1997) 49111.661 −154 −0.133 1 AAVSO 49360.599 −148 −0.135 1 Walker&Williams∗ 49527.027 −144 0.333 1 AAVSO 49817.467 −137 0.343 3 Berdnikov(1995,2008) 50108.216 −130 0.662 3 Bersier(2002) 50357.203 −124 0.709 3 Berdnikov(1995,2008) 50522.961 −120 0.507 3 Bersier(2002) 50564.680 −119 0.736 1 Berdnikov(1995,2008) 51270.917 −102 1.643 1 Berdnikov(1995,2008) 51644.316 −93 1.632 2 Berdnikov(1995,2008) 51976.659 −85 2.055 3 Berdnikov(1995,2008) 52350.347 −76 2.333 3 Berdnikov(1995,2008) 52640.475 −69 2.031 3 Berdnikov(1995,2008) 52681.984 −68 2.050 3 Pojmanski(2002) 53014.205 −60 2.351 2 Berdnikov(1995,2008) 53055.383 −59 2.039 3 Pojmanski(2002) 53096.193 −58 1.359 3 Berdnikov(1995,2008) Articlenumber,page10of17