Cepheids with giant companions. I. Revealing a numerous population of double-lined binary Cepheids
Bogumi? Pilecki, Grzegorz Pietrzy?ski, Richard I. Anderson, Wolfgang Gieren, Mónica Taormina, Weronika Narloch, Nancy R. Evans, Jesper Storm
aa r X i v : . [ a s t r o - ph . S R ] F e b Draft version February 24, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Cepheids with giant companions. I. Revealing a numerous population of double-lined binaryCepheids ∗† Bogumi l Pilecki, Grzegorz Pietrzy´nski, Richard I. Anderson,
2, 3
Wolfgang Gieren, M´onica Taormina, Weronika Narloch, Nancy R. Evans, and Jesper Storm Centrum Astronomiczne im. Miko laja Kopernika, PAN, Bartycka 18, 00-716 Warsaw, Poland Institute of Physics, Laboratory of Astrophysics, EPFL, Observatoire de Sauverny, 1290 Versoix, Switzerland European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching b. M¨unchen, Germany Universidad de Concepci´on, Departamento de Astronom´ıa, Casilla 160-C, Concepci´on, Chile Smithsonian Astrophysical Observatory, MS 4, 60 Garden St., Cambridge, MA 02138 Leibniz-Institut f¨ur Astrophysik Potsdam, An der Sternwarte 16, D-14482, Potsdam, Germany (Received January 20, 2021; Accepted February 17, 2021)
Submitted to ApJABSTRACTMasses of classical Cepheids of 3 to 11 M ⊙ are predicted by theory but those measured, clumpbetween 3.6 and 5 M ⊙ . As a result, their mass-luminosity relation is poorly constrained, impedingour understanding of basic stellar physics and the Leavitt Law. All Cepheid masses come from theanalysis of 11 binary systems, including only 5 double-lined and well-suited for accurate dynamical massdetermination. We present a project to analyze a new, numerous group of Cepheids in double-linedbinary (SB2) systems to provide mass determinations in a wide mass interval and study their evolution.We analyze a sample of 41 candidate binary LMC Cepheids spread along the P-L relation, that arelikely accompanied by luminous red giants, and present indirect and direct indicators of their binarity.In a spectroscopic study of a subsample of 18 brightest candidates, for 16 we detected lines of twocomponents in the spectra, already quadrupling the number of Cepheids in SB2 systems. Observationsof the whole sample may thus lead to quadrupling all the Cepheid mass estimates available now. Forthe majority of our candidates, erratic intrinsic period changes dominate over the light travel-timeeffect due to binarity. However, the latter may explain the periodic phase modulation for 4 Cepheids.Our project paves the way for future accurate dynamical mass determinations of Cepheids in the LMC,Milky Way, and other galaxies, which will potentially increase the number of known Cepheid masseseven 10-fold, hugely improving our knowledge about these important stars. Keywords: stars: variables: Cepheids - binaries: spectroscopic - stars: late-type INTRODUCTIONClassical Cepheids (hereafter also
Cepheids ) are per-haps the most important objects in astrophysics, crucialfor various fields of astronomy like stellar oscillationsand evolution of intermediate and massive stars, and
Corresponding author: Bogumi l [email protected] ∗ Based on observations collected at the European Southern Ob-servatory, Chile † This paper includes data gathered with the 6.5m Magellan ClayTelescope at Las Campanas Observatory, Chile. with enormous influence on modern cosmology. Sincethe discovery of the relationship between their pulsationperiod and luminosity over a century ago (the LeavittLaw, Leavitt & Pickering 1912), the Cepheids are exten-sively used to measure distances both inside and out-side of our Galaxy. The recent local Hubble constantdetermination accurate to 1.9% (Riess et al. 2019) thatshows a significant discrepancy with the value inferredfrom the Planck data (Planck Collaboration et al. 2018)highly depends on the aforementioned relation.Classical Cepheids are evolved intermediate and highmass, radially pulsating giants and supergiants. Theirwell defined position on the helium-burning loop (called
Pilecki et al. log T eff [K] l o g L [ L . ] MainsequenceSubgiant branch RedgiantbranchBlue loop AGBInstability strip 1O Fev. track (4.0 M . ⊙f ()t ove(tone (1O⊙fundamental (F⊙ Figure 1.
Hertzsprung-Russell diagram with the evolution-ary track for a star of 4 M ⊙ , which is typical for classicalCepheid variables. The instability strip for fundamental andfirst-overtone Cepheids is overplotted. Most Cepheids arefound on the blue loop, but they also appear during therapid stage of evolution on the subgiant branch. the blue loop ; see Fig. 1) makes them also a sensitiveprobe of various properties important for evolutionarystudies. The mass, metallicity, overshooting, mass lossand rotation affect significantly the shape and extent ofthe blue loop, determining the way and number the in-stability strip is penetrated. The Cepheids play also animportant role in testing and development of pulsationtheory (Buchler 2009).In the last decade the expected fraction of classicalCepheids in multiple systems has grown from about 30to 80% (Evans et al. 2015; Kervella et al. 2019), indicat-ing that we cannot ignore the multiplicity in our stud-ies of these variable stars. The light of a companiondirectly affects their observed brightness, but the tidaldeformation, mass transfer and the merger origin mayhave impact on their intrinsic brightness as well. Thebinary interactions, changing the stellar rotation, chem-ical composition, and mass may affect the evolution ofCepheids, and influence their pulsation characteristics.Apart from these complications, the multiplicitybrings also some opportunities. Since the first mea-surement (Pietrzy´nski et al. 2010) accurate masses of 6classical Cepheids in double-lined eclipsing binary sys-tems in the Large Magellanic Cloud (LMC) have beenobtained (Pilecki et al. 2013, 2018), helping in under- standing of the Cepheid mass discrepancy problem (between masses from evolution and pulsation theory;Cassisi & Salaris 2011) and serving to test the pulsationtheory models (Marconi et al. 2013). As only Cepheidsaccompanied by other giants (in a similar stage of evo-lution) were observed and analyzed, the measured massratios were mostly close to unity, but surprisingly forone system significantly different masses ( M /M ∼ visual wavelengths from ground observations.Although theoretical studies of Cepheids are quiteadvanced (Bono et al. 1999a, 2005; Caputo et al. 2005;Valle et al. 2009; Neilson et al. 2012; Vasilyev et al.2017), our observational data are still very limited. The-ory predicts masses of Cepheids in a range of 3-11 M ⊙ (Cox 1980; Bono et al. 1999b, 2001a; Anderson et al.2016) but their measured masses clump between 3.6 and5 M ⊙ , with only one higher but uncertain value of 6 M ⊙ (Pilecki et al. 2018; Gallenne et al. 2019; Evans et al.2018). This makes the mass-luminosity relation verypoorly constrained (Anderson et al. 2016), while it iscrucial for the theoretical understanding of the period-luminosity (P-L) relation and the basic stellar physicsregarding, e.g. the convection, mass-loss, and rotation.Moreover, the blue loops predicted by the evolution the- More information on the Cepheid mass discrepancy problem inGieren (1989); Bono et al. (2001b). epheids with giant companions. I. THE HYPOTHESISAs described above, there is a great need for an in-dependent source of Cepheids in binary systems thatare well-suited for mass determination. The most valu-able would be those in double-lined spectroscopic bi-naries, for which lines of both components are presentin the spectra. To meet these conditions, one has tofind Cepheids accompanied by stars of similar luminos-ity, and preferentially of late spectral types, i.e. at asubgiant or later stage of evolution. To identify them,we can consider at least three observable features causedby such companions: • the total observed brightness of a Cepheid shouldincrease significantly • its photometric pulsation amplitude (expressed inmagnitudes) should decrease • its color should be either similar or redder (we ex-pect companions mostly on the red giant branchor the blue loop) log T eff [K] l o g L [ L ⊙ ] CEP-0227CEP-4506CEP-2532CEP-1718BCEP-1718ACEP-1812CEP-4506B ev.⊙trac ⊙(4 M ⊙ ⊙e). (rac (3 M ⊙ ⊙e). (rac (5 M ⊙ ⊙IS for Cep-FIS for Cep-1Oeclipsing Cep-Feclipsing Cep-1Ocompanions Figure 2.
Positions of the components of known eclipsingbinary systems with Cepheids on the HR diagram. BaSTIevolutionary tracks for 3, 4, 5 M ⊙ , shifted by +0.15 in log L to match the measured Cepheid luminosities, are shown. It isevident that evolved companions can be mostly either similaror redder than Cepheids and of comparable brightness. We can test this assumptions looking at 5 similarSB2 eclipsing binary systems that were studied before(Pilecki et al. 2018). In Fig. 2 we can see their positionon the Hertzsprung-Russell diagram with overplottedBaSTI evolutionary tracks (Pietrinferni et al. 2004) us-ing canonical models for the LMC metallicity, and withthe mass loss efficiency η = 0 .
4. The tracks were shiftedby 0.15 in log L towards higher luminosities to match theCepheids with corresponding masses . The companionsto the Cepheids are either redder or similar in color.In general they have also a similar brightness, exceptfor the aforementioned OGLE-LMC-CEP-1812 system,which is probably of the merger origin. Its componentshave significantly different masses, yet they are foundat a similar evolutionary stage. But even in this casethe companion’s brightness is about 50% of that of theCepheid.Looking at the period-luminosity diagram for theLMC Cepheids (Fig. 3) one can see that all of the con-firmed eclipsing giant-giant SB2 systems with Cepheids(red circles) lie significantly above the corresponding P-L relation, being at least 50% (0.44 mag) brighter thana typical Cepheid for its period. After the subtractionof the companion’s light, these Cepheids move close tothe average P-L relation (empty circles). In the left Non-canonical models give higher luminosities but predict blueloops too short to reach the instability strip.
Pilecki et al. −0.50 −0.25 0.00 0.25 0.50 0.75 1.00 1.25 log(period) W I = I − . ( V − I ) Type IICepheids +200% 100%50%avg.1812 4506 022725321718A1718B ⊙ probablyAnom. Cepheid Pulsation periods of first-overtone (1O) modeCepheids were fundamentalized to matchthe P-L relation for the fundamental (F) mode.
Figure 3.
P-L relation for reddening free Wesenheit index. Filled red circles show known eclipsing binaries with Cepheids(OGLE catalog numbers), while empty circles mark their brightness without the companion light. Our candidates for binaryCepheids are ≥
50% brighter than an average Cepheid for its period. Note that their distribution parallel to the P-L relationadvocates strongly against blending by a random star. Outlying points below the P-L relation may be binary type-II Cepheidsand Anomalous Cepheids. panel of Fig. 4 (red circles and crosses) one can alsosee that their amplitude is about half of the typical one(red lines). The light dilution effect on the amplitude issmaller only for OGLE-LMC-CEP-1812 that has a sig-nificantly fainter companion. Note that there is a breakin the values of Cepheids amplitudes at a period of about10 days (Klagyivik & Szabados 2009).From the number of these eclipsing binary Cepheidswe can also try to estimate how many similar binaryCepheids exist, but have not been detected in the pho-tometric studies due to the lack of eclipses. The low-est inclination among the known eclipsing Cepheids is i = 83 ◦ (for OGLE-LMC-CEP-1718; Pilecki et al. 2018)at which the system shows a grazing eclipse. Assumingrandom inclinations, we can expect of the order of 50SB2 systems composed of a Cepheid and a giant com-panion in a range of periods similar to the one for eclips-ing Cepheids (i.e. 1-4 years).We investigated the P-L diagram for all the Cepheidsfrom the OGLE catalog (Soszynski et al. 2008) and weidentified 44 more Cepheids that lie 0.44 mag (4.7 σ )above the P-L relation, for which eclipses were not de-tected (Fig. 3). Virtually all Cepheids selected thisway have low amplitudes (left panel of Fig. 4) and col-ors redder than typical, on average by 0.12 mag in V-I (right panel). As stated above, these three features together clearly indicate that such overbright Cepheidshave luminous late-type giant companions. This, inturn, makes them perfect candidates for SB2 systemscomposed of giants, for which lines of all componentscan be easily detected and their radial velocities (RV)measured. In Fig. 3 periods of the first-overtone modeCepheids ( P O ) were fundamentalized to match the pe-riods of fundamental mode Cepheids ( P F ) using the fol-lowing formula: P F = P O ∗ (1 .
418 + 0 .
115 log P O ) . (1)This formula was derived by minimizing the scatter ofthe P-L relation for the combined set of all fundamen-tal and first-overtone Cepheids, using the period P F forboth and excluding the outliers.The distribution of our candidate Cepheids parallelto the P-L relation confirms the hypothesis of a simi-lar evolutionary stage of the companions and advocatesstrongly against blending which would statistically af-fect faint Cepheids more than the luminous ones. Also,blending would be rather random in colors, shifting starstoward redder (evolved companions) or bluer (main-sequence companions) colors, while practically all arered-shifted. Only for 1 of 41 objects there is a possibil-ity, that the shift in color is caused by a blue companion. epheids with giant companions. I. −0.50 −0.25 0.00 0.25 0.50 0.75 1.00 1.25 log(period) I - b a n d a m li t u d e V-I [mag] W I = I − . ( V − I ) Figure 4. left: Period-amplitude diagram for classicalCepheids. Red lines mark average amplitude for each modeas a function of period. Virtually all our candidates are atthe very low-amplitude end for their mode. right: Color-magnitude diagram. Red solid line marks a typical Cepheidcolor. As expected our selected objects are on average red-der, especially if we take into account the effect a same-color,same-luminosity companion would have on a brightness of aCepheid (red dashed line). Blue dashed line mark the ef-fect of a blue companion of a similar brightness. Cepheidsin known eclipsing binaries are marked with red circles andcrosses (F- and 1O-mode, respectively) in the left panel, andwith red circles in the right panel.
From that sample we excluded three objects, onethat is saturated (OGLE-LMC-CEP-0535) and one thatis marked as blended (OGLE-LMC-CEP-1583) in theOGLE catalog, as well as one object marked as pos-sibly spotted (rotating) star (OGLE-LMC-CEP-0016).For the latter the light curve changes are more complexand we could not obtain a good fit, even taking intoaccount the period change (see the next section). More- over, the distance inferred from the Gaia early Data Re-lease 3 (eDR3; Gaia Collaboration et al. 2020) parallaxis about 2650 +/- 130 pc, pointing to its Galactic origin.This was also confirmed by its radial velocity of about75 km/s, while values around 260 km/s are expected forLMC objects. Excluding these three stars we were leftwith 41 promising candidates for binary Cepheids (seealso Fig. 3).The Cepheids in this sample are spread all over theP-L relation from 0.26 to 10.5 days. Among them 20pulsate in the fundamental (F) mode and 21 in the first-overtone (1O) mode. Three of the latter are actuallydouble-mode Cepheids pulsating in the second-overtone(2O) as well. It is also interesting that in the groupselected this way there are two double Cepheids, i.e.objects where presence of two Cepheids is identified atthe exactly same coordinates. More details about theseinteresting and very valuable objects will be presentedin the next paper of the series (Paper II, Pilecki et al.,in prep.). DATA ANALYSIS3.1.
Periodicity
We looked for periodicity of all selected objectsusing all the available data sets from the OGLEproject (Soszynski et al. 2008; Soszy´nski et al. 2017;Udalski et al. 2015a), collected with both I and V-bandfilter. We analyzed all the data sets at the same time,excluding only those that did not have enough data for areliable fit with a Fourier series. For the same-band lightcurves from the OGLE-3 and OGLE-4 the amplitudeswere fitted separately (as they may differ in general) butwe kept the same phase coefficients. This way we limitedthe number of free parameters and we made sure thatthere is no phase shift between the datasets. This shiftis an effect of a non-linear period variability, which is notaveraged-out during the timespan of one dataset. Whenthe same-band constraints on phase coefficients are nottaken into account a sudden break may appear in thetransition from OGLE-3 to OGLE-4 data. The resultsof this analysis are presented in Table 1. For double-mode Cepheids the variabilities related to both modeswere first disentangled and data only for the strongerfirst-overtone mode are shown in the table. The anal-ysis and its results for two double Cepheids from thesample will be presented separately in Paper II. In thephotometric data of OGLE-LMC-CEP-3037 one eclipseis present, which suggest that this Cepheid may belongto an eclipsing binary system. The eclipse was removedbefore the periodicity analysis. This Cepheid is flaggedpECL in the table.
Pilecki et al.
Table 1.
Ephemeris time data for binary Cepheid candidates with giant companionsconstant P linear dP/dt OGLE ID mode T [days] period [days] period[days] dP/dt I [mag] flagsLMC-CEP-0973 F 6083.2990 10.46505(8) 10.46506(9) -6e-08 [0.2 σ ] 12.86 -LMC-CEP-0751 F 6001.1545 9.49519(8) 9.49531(10) -3.9e-07 [1.7 σ ] 12.99 QPOCLMC-CEP-1957 F 3178.7704 6.814157(5) 6.814157(5) -1.6e-12 [0.0 σ ] 13.63 -LMC-CEP-2096 F 5296.5907 5.971977(6) 5.971971(6) -1.7e-08 [2.2 σ ] 14.01 -LMC-CEP-0837 F 4688.8020 5.7773217(26) 5.777312(3) -1.4e-08 [4.3 σ ] 13.92 -LMC-CEP-0584 F 3361.7969 5.725339(19) 5.725344(19) -7.5e-08 [1.3 σ ] 13.79 -LMC-CEP-2999 F 5848.9308 5.406430(7) 5.406460(9) 4.3e-08 [4.9 σ ] 14.42 -LMC-CEP-1472 1O 4747.0853 4.871930(7) 4.871933(9) 3.5e-09 [0.5 σ ] 13.67 -LMC-CEP-1077 F 5228.0243 4.654260(3) 4.654257(4) -7e-09 [1.6 σ ] 14.51 QPOCLMC-CEP-0144 1O 6091.7275 4.61904(4) 4.61892(5) 5.8e-07 [4.4 σ ] 13.70 -LMC-CEP-1509 1O 4202.9424 4.533075(8) 4.533143(9) 1.3e-07 [14 σ ] 13.34 -LMC-CEP-2669 F 4965.1949 4.1099263(21) 4.1099228(31) -4.1e-09 [1.6 σ ] 14.30 -LMC-CEP-1369 F 5301.1134 4.0746625(12) 4.0746725(20) 8.2e-09 [6.4 σ ] 14.35 -LMC-CEP-0491 F 5432.4589 3.9792895(23) 3.9792634(30) -4.1e-08 [13 σ ] 14.47 -LMC-CEP-0224 F 5653.9554 3.779639(5) 3.779641(6) 3.4e-09 [0.6 σ ] 14.47 LTTELMC-CEP-2994 F 4945.5601 3.703564(4) 3.703560(4) -3.8e-08 [6.4 σ ] 14.47 -LMC-CEP-2208 F 4571.4092 3.5679932(16) 3.5679992(22) 7.2e-09 [3.8 σ ] 14.13 -LMC-CEP-0160 F 5529.5092 3.2012952(15) 3.2013016(19) 1.1e-08 [5.9 σ ] 14.77 -LMC-CEP-0889 F 4292.0659 3.1683767(12) 3.1683719(14) -1e-08 [7.0 σ ] 14.83 LTTELMC-CEP-0286 F 4829.1423 3.1335110(18) 3.1335111(18) 2.4e-09 [0.9 σ ] 15.04 LTTELMC-CEP-3037 1O 5096.1287 3.083785(5) 3.083809(6) 9.6e-08 [12 σ ] 14.54 pECLLMC-CEP-1711 F 4636.4767 2.9189493(15) 2.9189502(21) 1e-09 [0.6 σ ] 14.68 QPOCLMC-CEP-2605 1O 5294.9028 2.4194868(32) 2.419488(5) 1.2e-09 [0.3 σ ] 14.01 -LMC-CEP-0110 1O 5010.3116 2.1200434(20) 2.1200490(23) 1.7e-08 [5.3 σ ] 14.78 QPOCLMC-CEP-0231 1O 4909.8171 1.8993909(24) 1.8993917(25) 3.7e-09 [1.0 σ ] 14.57 -LMC-CEP-2237 1O 4440.6839 1.7933278(11) 1.7933269(11) 6.2e-09 [3.4 σ ] 14.74 -LMC-CEP-0334 1O 5631.8010 1.7219995(19) 1.7220008(24) 2.1e-09 [0.9 σ ] 14.75 -LMC-CEP-2748 1O 5007.4531 1.6514256(13) 1.6514072(18) -2.3e-08 [15 σ ] 15.13 -LMC-CEP-0397 1O 4882.8768 1.4772404(6) 1.4772401(6) -3.3e-09 [3.9 σ ] 15.23 -LMC-CEP-2590 1O 4509.3202 1.2057281(7) 1.2057368(7) 2.9e-08 [36 σ ] 15.72 -LMC-CEP-2471 1O 5353.4157 0.9605283(6) 0.9605283(7) 8.8e-12 [0.0 σ ] 16.24 -LMC-CEP-1347 1O/2O 4695.3526 0.69000824(17) 0.69001053(22) 3.2e-09 [16 σ ] 16.39 QPOCLMC-CEP-3287 1O/2O 3342.4313 0.6529152(10) 0.6529149(10) 1.1e-08 [3.5 σ ] 16.44 -LMC-CEP-1152 1O/2O 4063.8655 0.60684297(13) 0.60684260(14) -1.2e-09 [7.8 σ ] 16.36 -LMC-CEP-2123 1O 5306.5891 0.54304670(25) 0.54304476(32) -3.8e-09 [11 σ ] 16.65 LTTELMC-CEP-2583 1O 5356.1235 0.4103540(5) 0.4103536(6) -9.5e-10 [1.4 σ ] 17.63 -LMC-CEP-1662 1O 4063.3731 0.31516306(6) 0.31516315(6) 2.4e-10 [3.5 σ ] 17.48 -LMC-CEP-3370 1O 5078.2264 0.26924335(11) 0.26924375(13) 5.6e-10 [5.1 σ ] 18.01 -LMC-CEP-2705 1O 4816.0636 0.26454063(7) 0.26454191(10) 1.6e-09 [19 σ ] 17.21 - Note —Two ephemerides are presented, assuming either a constant period ( P ) or a linear period change ( dP/dt ).The same reference time ( T , maximum brightness at I-band for a constant P ) is used for both. Errors in thelast digits are given in parentheses. For dP/dt the significance in sigmas is given in brackets. In remarks:LTTE means a presence of a periodic light travel-time effect, QPOC - quasi-periodic cyclic variation in theO-C diagrams, pECL - probably an eclipsing system. epheids with giant companions. I. O-C analysis
The supposed orbital motion of our binary Cepheidcandidates should result in a slight change of its dis-tance from the observer. Due to the light-travel timeeffect (LTTE; Irwin 1959; Borkovits et al. 2015) such achange produces periodic phase shifts in the Cepheidpulsational variability (see examples in Udalski et al.2015b; Plachy et al. 2020). This effect can be describedas: ∆
LT T E = − a cep sin ic (1 − e ) sin( ν + ω )1 + e cos ν , where a cep is the semi-major axis of the Cepheid orbit, i is the orbit inclination, e the eccentricity, ν is the trueanomaly and ω the argument of periastron, and c is thespeed of light. The orbital period P orb and the referencetime T enters the equation through the true anomaly.In general, we could expect this kind of phase mod-ulation to be superimposed on a secular evolution-ary period variability, which can be easily describedwith a linear period change. Unfortunately, Cepheidsare known to show erratic period variations (Poleski2008; S¨uveges & Anderson 2018), which are interpreted,for example, as originating from the general instabil-ity of the light-curve shape (Derekas et al. 2012) ormore specifically, as an effect of convective hot spots(Neilson & Ignace 2014).Nevertheless, we performed the O-C analysis for allCepheids in our sample, calculating instantaneous phaseshifts along the collected photometric observational datain regard to the ephemeris from Table 1, both takingand not taking the linear period change into account.We then looked for any sign of the light-travel time effectdue to the supposed binary motion of Cepheids. As theamplitude of the phase variability in such analysis de-pends on the size of the projected orbit and the precisiondepends on the pulsation period, such study works wellonly for long orbital periods ( &
800 days) and Cepheidswith short pulsation periods ( . P orb from 700 to 1700 days) behaviorwas observed but with smaller amplitudes. The datafor all four systems are given in Table 2. The orbit ofOGLE-LMC-CEP-0889 seems almost circular and quiteextended. Its orbital period of about 7 years is proba- Table 2.
Orbital parameters from the O-C dataOGLE ID P orb T a cep sin( i ) ecc flags[days] [days] [ R ⊙ ]LMC-CEP-0224 1000 4710 350 ∼ ∼ ∼ Note —Parameters from the LTTE fit to the O-C data forCepheids with periodic phase variability. The full fit was madeonly for LMC-CEP-0889. For the rest, some parameters werefitted manually (M), because of the strong local O-C devia-tions. O - C [ d a y s ] Figure 5.
O-C diagram for OGLE-LMC-CEP-0889 ( P =3 . d ) using a non-linear ephemeris from Table 1. A clearLTTE modulation due to binary motion is present. Red lineis the best fit using the orbital parameters from Table 2. bly one of the longest in the sample. The orbits of theother three systems have rather eccentric orbits, but thequality of the fit does not permit to determine it quan-titatively. Their orbital periods are about 2, 3 and 5years. From the data obtained for OGLE-LMC-CEP-0889, we calculated the mass function f ( m ) = 1 . M ⊙ ,which suggests a rather high mass of the companion anda high inclination. Conservatively assuming the maxi-mum Cepheid mass of 4 . M ⊙ and the inclination of 90degrees, we obtain the minimum mass ratio of 1.27 forthis system. If our assumption of the similar evolution-ary stage stands, such a high mass ratio will point tothe companion being a merger, similar to OGLE-LMC-CEP-1812, but with the function of the components re-versed.For four objects more, we could detect a cyclic quasi-periodic (tentative periods from 1 to 4 years) behav-ior, but additional strong erratic changes make these Pilecki et al. detections more ambiguous. These objects are markedwith QPOC in Table 1. Moreover, for 25 objects we de-tected some cyclic variations in the O-C diagrams, whichhowever show strong deviations from periodicity acrossthe photometric data timespan. These can be eitherstochastic intrinsic period changes or a mixture of suchwith a weak effect of a binary motion. The O-C data forprobably eclipsing OGLE-LMC-CEP-3037 do not yieldconclusive results but we found a weak indication of aperiod of about 3000 days.From this analysis and from our knowledge onCepheids in eclipsing binary systems, for objects withno detection of LTTE we expect orbital periods from 1to 4 years unless very low orbital inclinations made theLTTE signal not detectable for longer period systems. SPECTROSCOPIC CONFIRMATIONThe first goal of our project was to confirm the hy-pothesis that all Cepheids selected as described in Sec-tion 2 are members of double-lined binaries by meansof spectroscopy. Such confirmation is not an easy task,however. The expected orbital periods are long and theorbits may be highly eccentric, meaning that for a signif-icant percentage of time the separation in radial veloci-ties is low. Comparing to Cepheids in eclipsing binaries,where inclinations are always between 80-90 degrees, inour case inclinations are scattered randomly between 0and 90 degrees, on average further decreasing the orbitalRV amplitudes. For the same reasons, the change of or-bital radial velocities during one observing season may,in general, also be not high enough to unambiguouslydetect the orbital motion given a very limited numberof spectra. This means that until we know the orbitalperiods, and are able to calculate when the separationsof component radial velocities is the highest, we haveto use other technique for confirmation of SB2 status ofour candidates.To check our hypothesis we selected a smaller sub-sample of 18 Cepheids brighter than 15.5 mag in theV-band, for which less observing effort is required. Four-teen of selected targets are fundamental mode Cepheidswith RV amplitudes of about 50 km/s. Depending onthe period their daily average RV change ranges from10 to 30 km/s. For the four first-overtone Cepheidsthat have lower RV amplitudes but also shorter peri-ods, the daily RV change ranges from 10 to 20 km/s.As a typical FWHM (full width at half maximum) ofa Cepheid line profile is 20 km/s, thanks to pulsationalvelocity changes, observations for a few consecutive daysshould guarantee detection of companions to most of theCepheids. Moreover, variable pulsation velocity allowsto separate the lines of components even for perfectly face-on orbits, where the orbital RV separation is zeroall the time.We have observed our targets for 4 consecutive nights,obtaining from 2 to 4 high-resolution spectra per objectwith the HARPS instrument mounted at 3.6-meter tele-scope at the La Silla observatory in Chile. For mostof the candidates one spectrum was also taken earlierusing a MIKE spectrograph mounted on the Magellantelescope at the Las Campanas observatory in Chile.We used the reduced HARPS data downloaded from theESO Archive , while the MIKE data were reduced us-ing Daniel Kelson’s pipeline available at the CarnegieObservatories Software Repository . For the identifica-tion of components in the spectra we used the Broad-ening Function (BF) technique (Rucinski 1992, 1999)implemented in the RaveSpan code (Pilecki et al. 2017).This technique provides narrower profiles than the cross-correlation function method, which helps in the separa-tion of components and increases the chance of detectingthe presence of a companion.We divided the analyzed objects in four groups, ofwhich three correspond to a positive detection. The neg-ative detection means that two components could not beidentified in any of the collected spectra. The objectswith a positive detection are those where the profiles ofthe components are clearly separated (SEP), where theprofiles are overlapping, but two peaks are seen (2P) andwhere the profiles are blended, but their shape can onlybe explained by a combination of two components (BP).In Fig. 6 we show one example for each of these groups.The final SB2 status of our sub-sample candidates forbinary Cepheid candidates is shown in Table 3. Thosethat belong to the first two positive detection groups(SEP and 2P) are marked as CLEAR cases, those be-longing to the third positive group (BP) are marked asHigh Probability (HProb) cases, and those with a neg-ative detection are marked as unconfirmed. In total wefound 16 out of 18 targets to be either clear (11), orhigh probability (5) cases, and only for two the sta-tus is yet unconfirmed. However, for these unconfirmedcases the data were taken unfortunately at very similarCepheid velocities. The reasons are that OGLE-LMC-CEP-0973 has the longest period in the sample (about10.5 days), while OGLE-LMC-CEP-2605 has the short-est one (about 2.4 days) and is a low-amplitude 1O-mode Cepheid. For neither of them the extrema of theRV curve were covered. Actually, in some spectra ofOGLE-LMC-CEP-0973 we detected profiles asymmetry http://archive.eso.org http://code.obs.carnegiescience.edu epheids with giant companions. I.
150 200 250 300 350 400
RV [km/s] b r o a d e n i n g f un c t i o n
175 200 225 250 275 300 325 350
RV [km/s] b r o a d e n i n g f un c t i o n
175 200 225 250 275 300 325 350 375
RV [km/s] b r o a d e n i n g f un c t i o n Figure 6.
Broadening Function profiles for one example ofeach class of SB2 status of Cepheids (see Table 3). Left:separated profiles (SEP), middle: 2 peaks visible (2P), right:blended profiles (BP). (ASM) that can be interpreted as coming from a com-panion, but we prefer to be conservative in this regard.As explained in Section 2, the possibility of an unde-tected blend is rather excluded for a great majority ofthese stars. Moreover the detection of lines of a secondcomponent for 90% of stars confirms that virtually allcompanions are red, evolved stars. It would be highlyimprobable that there are practically no Cepheids thatare blended with bright early-type main sequence stars.The above result is thus almost a decisive evidence thateven all our candidates may be not only binaries, butvery valuable SB2 systems as well. Although, as wenoted, we did not expect to detect the orbital motion ofCepheids during one season, for two objects in spectrataken 2 months apart we detected a slight but significantvelocity change of the companion, that with high prob-ability can be interpreted as its orbital variation. Thesetwo Cepheids have an additional cORB flag in Table 3.
Table 3.
SB2 status of binary Cepheid candidatesOGLE ID mode P F [d] status flagsLMC-CEP-0973 F 10.47 unconf. ASMLMC-CEP-0751 F 9.495 HProb BPLMC-CEP-1472 1O 7.294 ∗ CLEAR 2PLMC-CEP-0144 1O 6.903 ∗ CLEAR SEP,cORBLMC-CEP-1957 F 6.814 HProb BPLMC-CEP-1509 1O 6.770 ∗ HProb BPLMC-CEP-2096 F 5.972 HProb BPLMC-CEP-0837 F 5.777 CLEAR SEP,cORBLMC-CEP-0584 F 5.725 CLEAR 2PLMC-CEP-2999 F 5.406 CLEAR 2PLMC-CEP-1077 F 4.654 CLEAR SEPLMC-CEP-0835 F 4.563 CLEAR 2PLMC-CEP-2669 F 4.110 CLEAR 2PLMC-CEP-1369 F 4.075 CLEAR 2PLMC-CEP-0491 F 3.979 CLEAR SEPLMC-CEP-0224 F 3.780 CLEAR 2PLMC-CEP-2208 F 3.568 HProb BPLMC-CEP-2605 1O 3.537 ∗ unconf. - Note — P F is the pulsation period in case of F-modeCepheids and fundamentalized period (marked with aster-isk) for 1O-mode ones.5. CONCLUSIONS AND FUTURE WORKIn this first paper of the series we presented and provedour hypothesis regarding the double-lined status of over-bright Cepheids selected as described in Section 2. Upto now we have confirmed this status spectroscopicallyfor 16 out of 18 Cepheids of the sample that are brighterthan V=15.5 mag, but the two unconfirmed candidatescan still turn to be SB2 binaries once more observa-tions are collected. Orbital motion was also detected forcompanions to two Cepheids further strengthening ourconclusions about their status. For these two systemsrather short orbital periods can be expected. With the16 confirmed candidates, we have already quadrupledthe number of Cepheids in spectroscopic double-linedbinaries. In Fig. 7 one can see that most of these newCepheids have periods longer than those of known SB2Cepheids, spreading up to almost 10 days. The extrap-olation of the number of confirmed cases to the wholesample suggests that at least 36 new Cepheids in SB2systems can be expected once all 41 selected objects arestudied. This would mean a huge 7-fold increase in thenumber of this type of systems.For four objects (including one already confirmed asSB2) we also found a periodic variability in the O-C0
Pilecki et al. log(period) W I = I − . ( V − I ) Periods of 1O-mode Cepheidswere fundamentalized here. new SB2 Cepheids (1O)new SB2 Cepheids (F)known SB2 Cepheids
Figure 7.
Similar to Fig. 3 but for periods longer than1.15 days and showing the newly confirmed Cepheids in SB2systems. Almost all of them have periods longer than theknown SB2 Cepheids, spreading up to about 10 days. diagrams. From these diagrams the first-guess orbitalperiods of the Cepheids can be derived. Although futureobservations will be necessary to confirm it, the initialperiods will help considerably in establishing the finalones with lower number of spectra collected. The same istrue for the Cepheid for which one eclipse was observed.For that system we can also expect the inclination closeto 90 degrees, which will further simplify the analysis.If periods of all four objects showing significant LTTE(due to binary motion) are confirmed, we can learnfrom them to what extent the stochastic variation ofthe Cepheid period may affect the LTTE. This mayhelp in the identification of less clear cases and to con-firm those where cyclic yet not 100% periodic behav-ior was detected (marked QPOC). For one system wecould estimate the minimum mass ratio, which pointsto a merger scenario for the companion. This will stillhave to be confirmed spectroscopically but it suggeststhat more such interesting cases can be expected in thewhole sample.The full project dedicated to the LMC sample willtake several years to be completed. We decided that itis important to publish these preliminary results as theyalready have important implications for the interpreta-tion of period-luminosity relations and for our generalknowledge of Cepheids and their evolution. For exam-ple, we have now a strong clue that overbright Cepheids,that were often being rejected as P-L relation outliers,are just Cepheids with red, luminous (giant) compan-ions. These conclusions can be likely extended to other pulsating stars with well-defined P-L relations like, forexample, Type-II Cepheids or RR Lyrae stars.5.1.
Future work
The next step will be to check the double-lined statusfor the whole sample of 41 Cepheids and to confirm theorbital motion for those that are already identified asSB2. Although already there is very little chance thatthe candidates showing lines of two components are twounrelated stars, the detection of the Cepheid and com-panion orbital motion will be the ultimate proof and afirm base for the future mass determination.In the meantime, once enough data is collected, we willstart characterizing the components. We will measurethe spectroscopic light ratios and analyze their spectrathat will provide first estimates of their temperatures,metallicities and surface gravities.We then plan to monitor these systems with the aim tomeasure the exact orbital period and obtain the full or-bital solution, including the measurement of the mass ra-tio for them. We expect to be able to do so for the greatmajority of Cepheids within 5 years from now, whileseveral systems will possibly need a few years more tobe analyzed. Note that to have good mass ratios, mea-surements around quadratures are needed, which meansthat on average 3/4 of the orbital cycle have to be cov-ered (assuming starting observations at random orbitalphase). Knowing the mass ratios will already tell us alot about the evolution, original multiplicity and occur-rence of mergers in multiple systems of intermediate-mass stars. Moreover, for non-eclipsing SB2 systemslower mass limits ( M sin i ) can also be derived directly.While for a single system such knowledge has a limitedvalue, a statistically significant sample brings a multi-tude of possibilities.We can also use prior knowledge to put much strongerconstraints on masses. The best way would be to usethe distance to the system (from the accurate distanceto the LMC; Pietrzy´nski et al. 2019) and the expectedbrightness of the Cepheid (from the P-L relation) orthe spectroscopic light ratio, to calculate the luminos-ity of both components. Using temperatures obtainedfrom colors or spectra we can then determine the radiiand use the period-mass-radius relation or directly thepulsation theory to determine the mass of the Cepheid(Pilecki et al. 2017, 2018). Having the mass ratio, amass of the companion can also be calculated, providingthe full characterization of the system.In the long run our study will bring firm mass esti-mates for a large sample of Cepheids (about 4 timesmore numerous than available today), including long-period, high-mass Cepheids for which lack of data is the epheids with giant companions. I. The research leading to these results has received fund-ing from the European Research Council (ERC) underthe European Union’s Horizon 2020 research and innova-tion program (grant agreement No 695099) and from thePolish National Science Center grant MAESTRO UMO-2017/26/A/ST9/00446. We also acknowledge the grantMNiSW DIR/WK/2018/09. W.G. and G.P. gratefully ac-knowledge support from the BASAL Centro de Astrof´ısicay Tecnolog´ıas Afines (CATA) AFB-170002. W.G. also ac-knowledges support from the Millenium Institute of As-trophysics (MAS) of the Iniciativa Cientifica Milenio delMinisterio de Economia, Fomento y Turismo de Chile,project IC120009. M.T. acknowledges financial supportfrom the Polish National Science Centre grant PRELUDIUM2016/21/N/ST9/03310.This work is based on observations collected at theEuropean Southern Observatory under ESO programme106.21GB.003. We also thank Carnegie, and the CNTAC forthe allocation of observing time for this project. We wouldlike to thank the support staff at the ESO La Silla obser-vatory and at the Las Campanas Observatory for their helpin the remote observations. This research has made use ofNASA’s Astrophysics Data System Service.
Software:
RaveSpan (Pilecki et al. 2017,https://users.camk.edu.pl/pilecki/ravespan/)REFERENCES