Eclipsing binaries in the open cluster Ruprecht 147. III: The triple system EPIC 219552514 at the main-sequence turnoff
Guillermo Torres, Andrew Vanderburg, Jason L. Curtis, Adam L. Kraus, Aaron C. Rizzuto, Michael J. Ireland
aa r X i v : . [ a s t r o - ph . S R ] A p r Accepted for publication in The Astrophysical Journal
Preprint typeset using L A TEX style emulateapj v. 12/16/11
ECLIPSING BINARIES IN THE OPEN CLUSTER RUPRECHT 147. III: THE TRIPLE SYSTEMEPIC 219552514 AT THE MAIN-SEQUENCE TURNOFF
Guillermo Torres , Andrew Vanderburg , Jason L. Curtis , Adam L. Kraus , Aaron C. Rizzuto , and MichaelJ. Ireland Accepted for publication in The Astrophysical Journal
ABSTRACTSpectroscopic observations are reported for the 2.75 day, double-lined, detached eclipsing binaryEPIC 219552514 located at the turnoff of the old nearby open cluster Ruprecht 147. A joint analysisof our radial velocity measurements and the K2 light curve leads to masses of M = 1 . +0 . − . M ⊙ and M = 0 . +0 . − . M ⊙ for the primary and secondary, along with radii of R = 2 . +0 . − . R ⊙ and R = 0 . +0 . − . R ⊙ , respectively. The effective temperatures are 6180 ±
100 K for the F7 primaryand 4010 ±
170 K for the late K secondary. The orbit is circular, and the stars’ rotation appears to besynchronized with the orbital motion. This is the third eclipsing system analyzed in the same cluster,following our earlier studies of EPIC 219394517 and EPIC 219568666. By comparison with stellarevolution models from the PARSEC series, we infer an age of 2 . +0 . − . Gyr that is consistent with theestimates for the other two systems. EPIC 219552514 is a hierarchical triple system, with the periodof the slightly eccentric outer orbit being 463 days. The unseen tertiary is either a low-mass M dwarfor a white dwarf. INTRODUCTION
Eclipsing binaries that are members of star clus-ters are particularly valuable objects for Astrophysics.When they happen to be double-lined, classical spectro-scopic and lightcurve analysis techniques can yield ac-curate, model-independent masses and radii with pre-cisions reaching a few percent in favorable cases (see,e.g., Andersen 1991; Torres 2010). For detached binaries,such measurements provide stringent constraints on stel-lar evolution theory in a population whose age, metallic-ity, and distance can be determined independently based,e.g., on spectroscopic observations and studies of theircolor-magnitude diagrams.In recent work, we reported results for the eclipsingbinaries EPIC 219394517 (Torres et al. 2018, hereafterPaper I) and EPIC 219568666 (Torres et al. 2019, Pa-per II) in the nearby old open cluster Ruprecht 147(NGC 6774). Its members are slightly metal-rich com-pared to the Sun ([Fe / H] = +0 .
10; Curtis et al. 2018),and are located some 300 pc away. Both binaries gaveconsistent ages near 2.7 Gyr from a comparison withmodels of stellar evolution. While EPIC 219394517 (or-bital period P = 6 .
53 days) is composed of very similarearly G-type stars, the components of EPIC 219568666( P = 11 .
99 days) are considerably different in mass (F8and K5), and therefore provide greater leverage for test-ing theory.In this paper, we present an analysis of a third, shortperiod (2.75 days) but well detached eclipsing binary sys- Center for Astrophysics | Harvard & Smithsonian, 60 Gar-den St., Cambridge, MA 02138, USA; [email protected] Department of Astronomy, The University of Texas atAustin, Austin, TX 78712, USA NASA Sagan Fellow American Museum of Natural History, Central Park West,New York, NY, USA Research School of Astronomy and Astrophysics, AustralianNational University, Canberra, ACT 2611, Australia tem in the same cluster, EPIC 219552514. This objectwas observed by NASA’s K2 mission, the successor to the Kepler mission, during Campaign 7 (late 2015). Aliasesinclude TYC 6296-1893-1, 2MASS J19162232 − Gaia /DR2catalog (Gaia Collaboration et al. 2018), as reported byOlivares et al. (2019), and also by its systemic radial ve-locity located at the peak of the distribution of mea-sures for other cluster members (see Curtis et al. 2013;Yeh et al. 2019). EPIC 219552514 is quite bright ( Kp =10 . V = 10 . K2 light curve is de-scribed in Section 3. The results are then used to inferthe absolute properties of EPIC 219552514 in Section 4.Rotation and activity are discussed in Section 4.1, andSection 5 deals with a comparison of the masses, radii,and temperatures against current models of stellar evo-lution in order to infer the age. Concluding remarks arefound in Section 6. OBSERVATIONS
Torres et al.
Table 1
Detrended K2 Photometry ofEPIC 219552514HJD(2,400,000+) Residual flux57301.4866 0.9994772757301.5070 0.9993946057301.5275 0.9993835657301.5479 0.9994641957301.5683 0.99970927
Note . — K2 photome-try after removal of instru-mental effects and long-termdrifts. (This table is available inits entirety in machine-readableform.) Photometry
EPIC 219552514 was observed by the K2 mission dur-ing its Campaign 7, as part of a large super-aperturetargeting the core of Ruprecht 147. The observationswere made in long cadence mode, once every 29.4 min-utes. We downloaded the superstamp observations fromthe Mikulski Archive for Space Telescopes (MAST) ,extracted light curves for cluster members followingVanderburg & Johnson (2014) and Vanderburg et al.(2016), and initially identified EPIC 219552514 as aneclipsing binary. A total of 30 primary eclipses and 29secondary eclipses are included in the 81 days of photo-metric coverage. Because the object is in a fairly crowdedregion of the sky, we re-extracted a raw light curve fol-lowing the procedure from previous papers in our se-ries (Torres et al. 2018, 2019) using a circular movingaperture with a radius of 15 . ′′
8, in order to ensure thatthe third-light contamination in the lightcurve is con-stant (and not dependent on the roll of the K2 space-craft). We used a first pass systematics correction asin Vanderburg & Johnson (2014) and Vanderburg et al.(2016), and then took this as a starting point for a si-multaneous fit of the K2 Spectroscopy
EPIC 219552514 was monitored spectroscopically atthe Center for Astrophysics for three years begin-ning in 2016 September, with the fiber-fed, bench-mounted Tillinghast Reflector Echelle Spectrograph(TRES; Szentgyorgyi & F˝ur´esz 2007; F˝ur´esz 2008) at-tached to the 1.5m Tillinghast reflector at the FredL. Whipple Observatory on Mount Hopkins (Arizona,USA). We collected a total of 43 spectra, at a resolvingpower of R ≈ ,
000 and covering the wavelength re-gion 3800–9100 ˚A in 51 orders. For the order centeredat ∼ I b triplet, the signal-to-noise ratios range from 46 to 100 per resolution elementof 6.8 km s − . http://archive.stsci.edu/ While visual examination shows the spectra to be onlysingle-lined, the radial velocity of the very weak sec-ondary lines can be measured in most cases using TOD-COR, a two-dimensional cross-correlation technique in-troduced by Zucker & Mazeh (1994). Templates match-ing the properties of each component were taken froma pre-computed library of synthetic spectra that arebased on model atmospheres by R. L. Kurucz, and aline list tuned to better match the spectra of real stars(see Nordstr¨om et al. 1994; Latham et al. 2002). Thesetemplates cover a limited wavelength region of ∼
300 ˚Acentered around 5187 ˚A.The effective temperature ( T eff ) and projected rota-tional velocity ( v sin i ) of the primary star were deter-mined following the procedure described by Torres et al.(2002), by running grids of one-dimensional cross-correlations of the observed spectra against syntheticspectra over broad ranges in those two parameters. Weignored the presence of the faint secondary, as it doesnot affect the results. We then selected the combi-nation of parameters giving the highest value of thecross-correlation coefficient averaged over all 43 spectra,weighted by the strength of each exposure. We repeatedthis for fixed values of the surface gravity (log g ) of 3.5and 4.0, bracketing the final values reported below inSection 4, and for metallicities [Fe/H] of 0.0 and +0.5 oneither side of the known cluster abundance. By interpo-lation we obtained T eff = 6180 K and v sin i = 49 km s − ,with estimated uncertainties of 100 K and 3 km s − , re-spectively. These errors are based on the scatter fromthe individual spectra, conservatively increased to ac-count for possible systematic errors. The correspondingspectral type for the primary is approximately F7. Forthe radial velocity determinations of this star, we usedtemplate parameters of 6250 K and 50 km s − , whichare the nearest in our grid, along with log g = 4 . / H] = 0 . T eff = 4000 K appropriate for star of its mass as deter-mined later (spectral type late K). In Section 4 belowwe provide an empirical estimate of the secondary tem-perature that supports this choice. For the rotation, weadopted v sin i = 12 km s − assuming that its spin issynchronized with the orbital motion, and using a typi-cal radius for a star of this type. The metallicity for thesecondary template was kept at the solar value as for theprimary, and log g was set to 4.5.Each of the 43 spectra yielded a precise radial ve-locity measurement for the primary, but the secondarylines were clearly visible in only 31 of them. The he-liocentric velocities for both stars in EPIC 219552514are presented in Table 2, along with their formal un-certainties. The secondary velocities are much poorerbecause of its faintness. Using TODCOR we estimatedthe average secondary-to-primary flux ratio at the meanwavelength of our observations (5187 ˚A) to be only ℓ /ℓ = 0 . ± . clipsing binary in Ruprecht 147 Table 2
Heliocentric Radial-velocity Measurements of EPIC 219552514HJD RV RV Inner Outer(2,400,000+) (km s − ) (km s − ) Phase Phase57647.6200 − . ± . · · · − . ± .
33 182 . ± .
51 0.6978 0.519157857.9907 90 . ± . − . ± .
39 0.1544 0.527757863.9704 94 . ± . − . ± .
89 0.3260 0.540657878.9624 − . ± .
22 169 . ± .
67 0.7706 0.573057879.9634 87 . ± . − . ± .
46 0.1341 0.575157885.9000 100 . ± . · · · − . ± . · · · . ± . · · · . ± . − . ± .
01 0.2887 0.635457908.8536 2 . ± .
23 128 . ± .
08 0.6260 0.637457910.8995 88 . ± . − . ± .
54 0.3690 0.641957914.9432 − . ± .
26 165 . ± .
22 0.8375 0.650657919.8292 6 . ± .
22 144 . ± .
79 0.6120 0.661157932.9240 88 . ± . − . ± .
60 0.3675 0.689457965.7724 102 . ± . − . ± .
04 0.2969 0.760358001.6828 96 . ± . · · · − . ± .
24 170 . ± .
58 0.7024 0.839958020.6379 104 . ± . · · · . ± . · · · − . ± .
23 151 . ± .
08 0.6499 0.910958037.5873 86 . ± . − . ± .
51 0.3775 0.915258050.5881 78 . ± . − . ± .
68 0.0990 0.943358056.5695 102 . ± . − . ± .
34 0.2712 0.956258060.5644 − . ± .
22 181 . ± .
83 0.7220 0.964858068.5504 0 . ± .
28 134 . ± .
66 0.6222 0.982058259.9510 82 . ± . − . ± .
60 0.1321 0.395058276.8394 99 . ± . · · · − . ± .
24 147 . ± .
36 0.6510 0.433758279.8654 84 . ± . · · · . ± . − . ± .
69 0.3618 0.461758301.8394 89 . ± . − . ± .
44 0.3445 0.485458331.9025 101 . ± . − . ± .
71 0.2624 0.550258386.7016 95 . ± . − . ± .
32 0.1635 0.668558594.9671 − . ± . · · · . ± . − . ± .
85 0.3408 0.132958621.9451 2 . ± .
27 122 . ± .
59 0.5956 0.176058628.8947 75 . ± . − . ± .
28 0.1194 0.191058634.9162 91 . ± . − . ± .
10 0.3062 0.204058660.8715 − . ± .
27 172 . ± .
36 0.7323 0.260058674.8176 − . ± .
30 169 . ± .
50 0.7970 0.290158693.7778 − . ± . · · · . ± . · · · Note . — Orbital phases for the inner orbit are counted fromthe reference time of primary eclipse, and those for the outerorbit from the corresponding time of periastron passage. Thefinal velocity uncertainties for our analysis result from scalingthe values listed here for the primary and secondary by the near-unity factors f and f , respectively, from our global analysisdescribed in Section 3. residuals of the primary star, with a peak-to-peak am-plitude of about 10 km s − . This indicates the presenceof a third component in the system. However, carefulexamination of our spectra with TRICOR, an extensionof TODCOR to three dimensions (Zucker et al. 1995),showed no sign of a third set of lines. This suggests thatthe tertiary must be even fainter than the secondary,possibly a mid or late M dwarf.A preliminary fit to the velocities was performed toserve as a starting point for the analysis of Section 3, solv-ing for the elements of the inner and outer orbits simul-taneously assuming they are represented by independentKeplerian trajectories. The outer orbit is slightly eccen-tric ( e ≈ .
19) and has a period of about 463 days that iscovered more than twice by our observations. The innerorbit for the eclipsing pair, on the other hand, shows nosignificant eccentricity.
Figure 1.
Radial-velocity measurements for EPIC 219552514,with our adopted model for the inner orbit from Section 3. Pri-mary and secondary measurements are represented with filled andopen circles, respectively, and have the motion in the outer or-bit removed. The dotted line marks the center-of-mass velocityof the triple system. Error bars for the primary are too small tobe visible. They are seen in the lower panels, which display theresiduals. Phases are counted from the reference time of primaryeclipse (Table 4).
Figure 1 displays the velocities of the primary and sec-ondary in the inner (2.75 day) orbit after subtracting themotion in the outer orbit, as described below. Our finalmodel is also shown. The motion of the primary starin the outer orbit is illustrated in Figure 2, in which wehave removed the short-period motion in the inner orbit.
Imaging
The aperture we used to extract the photometry ofEPIC 219552514 appears fairly clear of any intrudingstars bright enough to add significant flux to the lightcurve and bias the results of our analysis below. Thisis shown in Figure 3, which is a seeing-limited imagein a bandpass similar to Sloan r (close to Kepler ’s Kp bandpass) taken in 2008 by Curtis et al. (2013) with theMegaCam instrument (Hora et al. 1994) on the Canada-France-Hawaii Telescope (CFHT). The positions of allnumbered stars in or near the aperture, their separations ρ from the target, and their brightness in the CFHT gri filters , are given in Table 3 when bright enough to mea-sure. We include also J - and K -band brightness mea-surements based on UKIRT/WFCAM imaging (Curtis2016), which reaches deeper. We additionally reportthe G -band magnitude and trigonometric parallax, whenavailable, for the few companions that have entries inthe Gaia /DR2 catalog (Gaia Collaboration et al. 2018).None appear to be members of the cluster. All com-panions within the aperture are very faint and have noeffect on our analysis. Even the two brighter ones thatare slightly outside the aperture ( Torres et al.
Figure 2.
Radial-velocity measurements for the primary ofEPIC 219552514 in the outer orbit, as a function of time (top)and orbital phase counted from periastron passage (bottom). Mo-tion in the inner orbit has been removed. The secondary has muchlarger scatter and is not shown, for clarity. The solid line is our finalmodel from Section 3, and the dotted line represents the center-of-mass velocity of the triple. contribute significantly: they are more than 6 magni-tudes fainter than the target in the near infrared, theyare fairly red (SpT ∼ K3 and K5, respectively) and willtherefore appear even fainter in the Kp band, and only asmall fraction of their flux would be inside the aperturegiven the Kepler pixel scale of 3 . ′′
98 pix − .In order to search for blended stellar companions toEPIC 219552514 inside the inner working angle of theseeing-limited imaging, we used the 10m Keck II tele-scope with the NIRC2 facility adaptive optics (AO) im-ager to obtain natural guide star adaptive optics imag-ing and non-redundant aperture mask interferometry(NRM). These observations were made in the K ′ filter( λ = 2 . µ m) on 2016 June 16 UT, and followed thestandard observing strategy described by Kraus et al.(2016) and previously reported for Ruprecht 147 tar-gets by Torres et al. (2018) and Torres et al. (2019).For EPIC 219552514, we obtained a short sequence of6 images and 8 interferograms in vertical angle mode.In both cases, calibrators were drawn from the otherRuprecht 147 members observed on the same night.The images were analyzed following the methods de-scribed by Kraus et al. (2016). To summarize, the pri-mary star point spread function (PSF) was subtractedusing both an azimuthal median profile and the cali-brator that most closely matches the speckle pattern.Within each image, the residual fluxes as a function of EPIC 219552514
20 10 0 -10 -20 ∆ Right Ascension (arcseconds)-20-1001020 ∆ D e c li na t i on ( a r cs e c ond s ) NE12 34 56 789 1011121314 151617 1819 20212223 24
Figure 3.
CFHT r -band image of the field of EPIC 219552514,with the 15 . ′′ K2 pho-tometry indicated with a circle. Nearby companions are numberedas in Table 3. position were measured in apertures of radius 40 milli-arcseconds (mas), centered on each pixel, and the noise wasestimated from the RMS of fluxes within concentric ringsaround the primary star. Finally, the detections and de-tection limits were estimated from the flux-weighted sumof the detection significances in the stack of all images,and any location with a total significance greater than6 σ was visually inspected to determine if it was a resid-ual speckle or cosmic ray. No candidates remained afterthis visual inspection. The observations yielded contrastlimits of ∆ K ′ = 5 . ρ = 150 mas, ∆ K ′ = 7 . ρ = 500 mas, and ∆ K ′ = 9 . ρ > K ′ = 0 .
13 mag at ρ = 20–40 mas,∆ K ′ = 1 .
22 mag at ρ = 40–80 mas, and ∆ K ′ = 0 .
73 magat ρ = 80–160 mas. ANALYSIS
For the analysis of the K2 light curve, we adoptedthe Nelson-Davis-Etzel binary model (Etzel 1981;Popper & Etzel 1981) as implemented in the eb code ofIrwin et al. (2011). This model approximates the starshapes as biaxial spheroids for calculating proximity ef-fects, and is adequate for well-detached systems in whichthe stars are nearly spherical, as is the case here (see clipsing binary in Ruprecht 147 Table 3
Close Neighbors of EPIC 219552514R.A. Dec. P.A. ρ J K σ JK g r i σ gri G π
Gaia ′′ ) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mag) (mas)1 19:16:22.01 − · · · · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · · · · − · · · · · · · · · · · · · · · · · ·
10 19:16:21.69 − · · · · · · · · · · · · · · ·
11 19:16:21.96 − · · · · · · · · · · · · · · · · · ·
12 19:16:21.93 − · · · · · · · · · · · · · · · · · ·
13 19:16:21.80 − · · · · · · · · · · · · · · · · · ·
14 19:16:21.96 − · · · · · · · · · · · · · · · · · ·
15 19:16:21.42 − · · · · · ·
16 19:16:23.22 − . ± . − · · · · · · · · · · · · · · · · · ·
18 19:16:21.34 − . ± . − · · · · · ·
20 19:16:21.24 − . ± . − · · · · · · · · · · · · − . ± . − · · · · · · · · · · · · · · · · · ·
23 19:16:23.15 − . ± . − . ± . Note . — Coordinates based on UKIRT images (see Curtis 2016). Average uncertainties σ JK and σ gri are listed for the corre-sponding magnitude measurements. below). The main adjustable parameters we consideredfor the inner binary are as follows: the orbital period( P in ), a reference epoch of primary eclipse ( T , which isstrictly the time of inferior conjunction in this code), thecentral surface brightness ratio in the Kepler bandpass( J ≡ J /J ), the sum of the relative radii normalized bythe semimajor axis ( r + r ) and their ratio ( k ≡ r /r ),the cosine of the inclination angle (cos i ), the eccentricityparameters e in cos ω in and e in sin ω in , with e in being theeccentricity and ω in the longitude of periastron for theprimary, and an out-of-eclipse brightness level in magni-tude units ( m ). We adopted a quadratic limb-darkeninglaw for this work, with coefficients u and u for the pri-mary and a corresponding set for the secondary. Thereflection albedos ( A , A ) were included as additionalvariables. Gravity darkening coefficients for the Kepler band were adopted from the theoretical calculations byClaret & Bloemen (2011), interpolated to the metallic-ity of Ruprecht 147, the temperatures indicated earlier,and the final log g values reported below. They wereheld fixed at the values y = 0 .
306 for the primary and y = 0 .
460 for the secondary. Even though there is no evidence of significant fluxfrom neighboring stars in the photometric aperture, asa precaution we included the third light parameter ℓ asan additional adjustable parameter because the unseentertiary (presumably a very red star) may be brighter inthe Kepler band (centered around 6000 ˚A) than in ourspectroscopic window ( ∼ ℓ + ℓ + ℓ = 1, and the values for theprimary and secondary for this normalization correspondto the light at first quadrature. Note that these are bandpass-specific coefficients , not to beconfused with the bolometric gravity darkening exponents used inother eclipsing binary modeling programs (see Torres et al. 2017).
To avoid biases, the finite integration time of the K2 long-cadence observations was accounted for by oversam-pling the model light curve and then integrating over the29.4-minute duration of each cadence prior to the com-parison with the observations (see Gilliland et al. 2010;Kipping 2010).The radial velocities were included in the analysis alongwith the photometry, and the spectroscopic elements forthe inner and outer orbits were solved simultaneouslyas done in Section 2.2. This introduces the followingadditional elements: the primary and secondary velocitysemiamplitudes ( K and K ), the center-of-mass velocityof the triple system ( γ ), the outer orbital period ( P out ),a reference time of periastron passage for the outer orbit( T peri ), the velocity semiamplitude of the inner binary inthe outer orbit ( K out ), and the eccentricity parameters e out cos ω out and e out sin ω out , where ω out corresponds tothe longitude of periastron of the inner binary. We pointout here that a mismatch between our cross-correlationtemplates and the real stars can potentially introduce aspurious systematic offset between the measured primaryand secondary velocities. Because the template param-eters adopted for the secondary, particularly v sin i , aremerely educated guesses, we allowed for such an offset(∆RV) that we added to the list of free parameters.Light travel time in the outer orbit will cause theeclipses to arrive slightly earlier or later than they wouldin the absence of the tertiary. Over the ∼
80 days of the K2 observations the effect varies between − . − . T below. Con-sequently, we accounted for this effect during the analy-sis. This was done by appropriately adjusting all timesof observation based on a estimate of those correctionsfrom a preliminary model that used the radial velocitiesalone. Torres et al. -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6Orbital Phase0.980.991.001.01 R e l a t i v e B r i gh t ne ss -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6Orbital Phase0.980.991.001.01 R e l a t i v e B r i gh t ne ss -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6Days from Midtransit0.9850.9900.9951.0001.0051.010 R e l a t i v e B r i gh t ne ss -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6Orbital Phase0.9850.9900.9951.0001.0051.010 R e l a t i v e B r i gh t ne ss Figure 4.
Phase-folded photometry of EPIC 219552514, color-coded by date to show the evolution of lightcurve distortions pre-sumably caused by spots. Red points correspond to earlier data,and purple points to later data. The bottom panel has the eclipsesremoved, and reveals what appears to be a spot-crossing event(bump) during the primary eclipse in the early observations (red),which gradually disappears and is no longer seen in the later data(purple).
Our method of solution used the emcee codeof Foreman-Mackey et al. (2013), which is a Pythonimplementation of the affine-invariant Markov chainMonte Carlo (MCMC) ensemble sampler proposed byGoodman & Weare (2010). We used 100 walkers withchain lengths of 15,000 each, after discarding the burn-in. Uniform (non-informative) or log-uniform priors oversuitable ranges were adopted for most adjustable param-eters (see below), and convergence was verified by ex-amining the chains visually and by requiring a Gelman-Rubin statistic of 1.05 or smaller for each parameter(Gelman & Rubin 1992). For more efficient samplingof parameter space, and to reduce the correlation be-tween them, the traditional quadratic limb-darkening co-efficients u and u for each star were recast as q and q following Kipping (2013), where q = ( u + u ) and q = 0 . u / ( u + u ).The relative weighting between the photometry andradial velocity measurements was handled by introduc-ing additional free parameters in the form of multiplica-tive scale factors for the observational errors. Thesescale factors ( f K2 for the photometry, and f and f for the primary and secondary velocities) were solvedfor self-consistently and simultaneously with the otherorbital quantities (see Gregory 2005). The initial errorassumed for the photometric measurements is 1.6 milli-magnitudes (mmag), which is approximately the out-of-eclipse scatter, and the initial errors for the velocities arethose listed in Table 2. The large scatter in the phase-folded photometry compared to the typical precision ofthe K2 instrument (roughly 50 parts per million per half-hour integration for a non-variable star of this brightness)is caused by obvious distortions presumably due to spots,which appear to be changing on very short timescales ofdays. This is illustrated in Figure 4, and discussed fur-ther below.Initial tests showed that the second-order limb-darkening coefficients q were essentially unconstrainedfor both stars, likely because of the light curve distortionsjust mentioned. We therefore held those coefficients fixedat their theoretical values for the Kepler band according http://dan.iel.fm/emcee to Claret & Bloemen (2011), selecting the ones based onATLAS model atmospheres and the least-squares fittingprocedure favored by those authors. The tabulated u values in the standard quadratic limb-darkening formu-lation are 0.305 and 0.182 for the primary and secondary.For the linear coefficients q we adopted Gaussian priorsfrom theory with a standard deviation of 0.1 (see Ta-ble 4). We also found that while the albedo for the sec-ondary was well constrained, the one for the primary wasnot. We chose to impose weak Gaussian priors on both,with a mean of 0.5 (appropriate for convective stars) anda standard deviation of 0.3. Finally, all our tests indi-cated a negligible eccentricity for the inner orbit, consis-tent with the findings from the spectroscopy. To reducethe already large number of free parameters, we set theeccentricity to zero for the remainder of this work.The results of our analysis for EPIC 219552514 are re-ported in Table 4, in which the values given correspondto the mode of the posterior distributions. The distribu-tions of the derived quantities listed in the bottom sectionof the table were constructed directly from the MCMCchains of the adjustable parameters involved. Includedamong these is J ave , the surface brightness ratio aver-aged over the stellar disk, and the flux ratio ℓ /ℓ in the Kepler band. Both stars in the inner binary are foundto be nearly spherical, justifying the use of this binarymodel. We calculate the oblateness of the primary staras defined by Binnendijk (1960) to be 0.008, which is wellbelow the safe limit for this binary model (0.04; see, e.g.,Popper & Etzel 1981). The oblateness of the secondaryis an order of magnitude smaller.The observations and final model are shown in Fig-ure 5. As noted earlier, we attribute the considerablescatter of the residuals (just under 1.6 mmag) to pho-tometric modulation from spots rotating in and out ofview. The nature of this scatter is highly correlated(“red”) noise, which raises at least two concerns. Onthe one hand, it could introduce possibly significant bi-ases in the results. On the other, it will generally causethe formal uncertainties from our MCMC analysis to beunderestimated. We now address each of these issues inturn.To gain an understanding of the extent to which thesedistortions may affect the fitted parameters, we dividedthe complete K2 data set into 29 separate cycles eachcontaining one primary and one secondary eclipse (for anaverage of 125 data points per cycle), with the last cy-cle including an extra primary eclipse. We repeated theanalysis independently for each cycle in the same way asabove, except that we added a 4-term Fourier series tothe model (9 extra parameters) in order to at least par-tially account for the distortions, and we used only thephotometry for computational expediency. The funda-mental period was kept fixed at the orbital period, whichalong with the mass ratio was adopted from our modelresults in Table 4. The median value for each parameterover the 29 data segments, and the corresponding 68.3%confidence intervals, are given in Table 5. Comparisonwith the values in Table 4 indicates very good agreementfor the geometric parameters r + r , k , and cos i , whichare the most relevant here. From this we conclude thatany detrimental effect of the lightcurve distortions seemsto average out over the 29 cycles, at least in this par-ticular case. The agreement is in fact also good for all clipsing binary in Ruprecht 147 Figure 5. K2 observations of EPIC 219552514 along with our adopted model. Enlargements of the eclipses are shown at the bottom.Residuals in magnitude units are displayed on an expanded scale below each panel. other parameters in Table 5 except for the limb darken-ing coefficient of the secondary, and to a lesser degree itsalbedo. These may well be biased in Table 4, but haveno influence on any other results. The addition of the4-term Fourier series to the model for each cycle clearlyimproves the solutions considerably, reducing the typicalscatter by a factor of more than 6 compared to our origi-nal fit, from about 1.6 mmag to ∼ u and 0.05 for y and y . We repeated this 100 times, and adopted the scat-ter (standard deviation) of the resulting distribution foreach fitted parameter as a more realistic measure of theuncertainty. These numbers were added quadraticallyto the internal errors from our original MCMC analysis,resulting in the final uncertainties reported in Table 4.The parameters that had their internal errors inflatedthe most are J , k , q for the primary, and the albedo A for the secondary, by factors typically ranging from 3 toabout 7. In other cases, the extra error is similar to orsmaller than the internal errors. ABSOLUTE DIMENSIONS
The physical properties we infer for the componentsof EPIC 219552514 are presented in Table 6, in whichthe values listed correspond to the mode of the poste-rior distributions calculated by directly combining thechains of adjusted parameters in the top section of Ta-ble 4. The uncertainties represent the 68.3% confidenceintervals. The precision in the absolute masses is 4.2%for the primary and 2.3% for the secondary, while theradii have errors of 1.2% and 2.0%, respectively. Includedamong the physical parameters are the luminosities, theabsolute bolometric and visual magnitudes, and the dis-tance to the system (determined to about 7.7%). For de-rived quantities involving external information, those ex-ternal quantities (effective temperatures, bolometric cor-rections, interstellar reddening, and the apparent visualmagnitude of the system; see below) were assumed to bedistributed normally and independently for combiningthem with the chains of adjusted parameters.In Section 2.2 we derived an estimate of the primarytemperature directly from our spectra (6180 ±
100 K),but had to use an adopted value for the much fainter sec-ondary (4000 K) for the radial-velocity determinations.Our analysis of the light curve now provides an accu-rate way to measure the temperature ratio (or difference,∆ T eff ) between the components, through the central sur-face parameter J (or the disk-integrated value J ave ; Ta-ble 4). This, then, allows the secondary temperatureto be inferred. Such estimates are often quite accuratebecause J is closely related to the difference in depthbetween the eclipses, which can be measured accurately.We obtain ∆ T eff = 2170 ±
140 K, with which the sec-ondary temperature becomes 4010 ±
170 K. This is es-sentially the same as the value adopted in Section 2.2 forthe radial-velocity determinations, justifying that choicea posteriori. We adopt this as the final temperature of
Torres et al.
Table 4
Results from our Combined MCMC Analysis forEPIC 219552514Parameter Value Prior P in (days). . . . . . . . . . . . . . . . 2 . +0 . − . [2, 3] T (HJD − . +0 . − . [57356, 57358] J . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . [0.02, 1.0] r + r . . . . . . . . . . . . . . . . . . . 0 . +0 . − . [0.01, 0.50] k . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . [0.1, 1.0]cos i . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . [0, 1] m (mag) . . . . . . . . . . . . . . . . 10 . +0 . − . [9, 11]Primary q . . . . . . . . . . . . . . . 0 . +0 . − . G (0 . , . q . . . . . . . . . . . . . 0 . +0 . − . G (0 . , . A . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . G (0 . , . A . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . G (0 . , . ℓ . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . [ −
10, 0]* γ (km s − ) . . . . . . . . . . . . . . . +41 . +0 . − . [30, 50] K (km s − ) . . . . . . . . . . . . . 58 . +0 . − . [1, 180] K (km s − ) . . . . . . . . . . . . . 137 . +2 . − . [1, 180]∆RV (km s − ) . . . . . . . . . . . − . +1 . − . [ −
10, 10] P out (days) . . . . . . . . . . . . . . 463 . +2 . − . [200, 800] T peri (HJD − . +5 . − . [57900, 58600] K out (km s − ) . . . . . . . . . . . 5 . +0 . − . [1, 180] √ e out cos ω out . . . . . . . . . . . . − . +0 . − . [ −
1, 1] √ e out sin ω out . . . . . . . . . . . . +0 . +0 . − . [ −
1, 1] f K . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . [ −
5, 1]* f . . . . . . . . . . . . . . . . . . . . . . . . 1 . +0 . − . [ −
5, 5]* f . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . [ −
5, 5]*Derived quantities r . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . · · · r . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . · · · i (degree) . . . . . . . . . . . . . . . . 89 . +0 . − . · · · Eclipse duration (hour) . . 6 . +0 . − . · · · Primary u . . . . . . . . . . . . . . 0 . +0 . − . · · · Secondary u . . . . . . . . . . . . 0 . +0 . − . · · · J ave . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . · · · ℓ /ℓ . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . · · · e out . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . · · · ω out (degree). . . . . . . . . . . . . 92 . +4 . − . · · · Note . — The values listed correspond to the mode of the re-spective posterior distributions, and the uncertainties representthe 68.3% credible intervals. Priors in square brackets are uni-form over the specified ranges, except those for ℓ , f K2 , f , and f (marked with asterisks), which are log-uniform. For the firstorder limb-darkening coefficients and the albedos the priors wereGaussian, indicated above as G (mean , σ ). the secondary, and list it in Table 6.The component temperatures may be used to derivean estimate of the reddening, as done in our earlier stud-ies of Paper I and Paper II. We refer the reader to thosesources for the details. Briefly, we gathered standardphotometry for the combined light of EPIC 219552514 in Table 5
Results from our cycle-by-cycle MCMCAnalysis for EPIC 219552514 with the additionof a 4-term Fourier series to the modelParameter Value J . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . r + r . . . . . . . . . . . . . . . . . . . 0 . +0 . − . k . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . cos i . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . Primary q . . . . . . . . . . . . . . . 0 . +0 . − . Secondary q . . . . . . . . . . . . . 0 . +0 . − . A . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . A . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . ℓ . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . f K . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . Derived quantities r . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . r . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . i (degree) . . . . . . . . . . . . . . . . 89 . +0 . − . Primary u . . . . . . . . . . . . . . 0 . +0 . − . Secondary u . . . . . . . . . . . . 0 . +0 . − . J ave . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . ℓ /ℓ . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . Note . — The values listed correspond to themedian of the results for the 29 independentorbital cycles. The uncertainties represent the68.3% credible intervals. the Tycho-2, Johnson, Sloan, 2MASS, and
Gaia systems(Høg et al. 2000; Henden et al. 2015; Skrutskie et al.2006; Gaia Collaboration et al. 2018) and we constructed14 non-independent color indices. We then usedcolor/temperature calibrations by Casagrande et al.(2010), Huang et al. (2015), and Stassun et al. (2019) toderive an average photometric temperature for a rangeof reddening values, adjusting all color indices appro-priately at each value of E ( B − V ). Our adopted red-dening estimate is the one that provides a match to theluminosity-weighted average temperature of the binarysystem. We ignored the presence of the tertiary, as it isfaint enough that it will not affect the results. We ob-tained E ( B − V ) = 0 . ± .
025 mag, corresponding to A V = 0 . ± .
078 mag for a ratio of total to selectiveextinction of R V = 3 .
1. Very similar values were foundfor the other two eclipsing binaries studied previously inthe cluster.A consistency check on our effective temperaturesand radii may be obtained by comparing our measuredflux ratios with predicted values from synthetic spec-tra. Figure 6 shows the predictions as a function ofwavelength, using spectra by Husser et al. (2013) basedon PHOENIX model atmospheres for temperatures of6200 K and 4000 K, near our best estimates for thebinary components. The normalization of the ratio ofthe spectra was carried out with the radius ratio derivedfrom our light curve analysis, k = 0 . K2 photom-etry show very good agreement with the expected val- clipsing binary in Ruprecht 147 Table 6
Physical Properties of EPIC 219552514Parameter Primary Secondary M ( M N ⊙ ) . . . . . . . . . . . . . . . 1 . +0 . − . . +0 . − . R ( R N ⊙ ) . . . . . . . . . . . . . . . . 2 . +0 . − . . +0 . − . log g (dex) . . . . . . . . . . . . . . 3 . +0 . − . . +0 . − . q ≡ M /M . . . . . . . . . . . . 0 . +0 . − . a ( R N ⊙ ) . . . . . . . . . . . . . . . . . 10 . +0 . − . T eff (K) . . . . . . . . . . . . . . . . 6180 ±
100 4010 ± L ( L ⊙ ) . . . . . . . . . . . . . . . . . 8 . +0 . − . . +0 . − . M bol (mag). . . . . . . . . . . . . 2 . +0 . − . . +0 . − . BC V (mag) . . . . . . . . . . . . − . ± . − . ± . M V (mag). . . . . . . . . . . . . . 2 . +0 . − . . +0 . − . v sync sin i (km s − ) a . . . . 46 . +0 . − . . +0 . − . v sin i (km s − ) b . . . . . . . . 49 ± E ( B − V ) (mag). . . . . . . . 0.119 ± A V (mag) . . . . . . . . . . . . . . 0.369 ± . +0 . − . Distance (pc) . . . . . . . . . . . 291 +22 − π (mas) . . . . . . . . . . . . . . . . 3 . +0 . − . π Gaia/
DR2 (mas) c . . . . . . 3 . ± . Note . — The masses, radii, and semimajor axis a are ex-pressed in units of the nominal solar mass and radius ( M N ⊙ , R N ⊙ ) as recommended by 2015 IAU Resolution B3 (see Prˇsa et al.2016), and the adopted solar temperature is 5772 K (2015 IAUResolution B2). Bolometric corrections are from the work ofFlower (1996), with conservative uncertainties of 0.1 mag, andthe bolometric magnitude adopted for the Sun appropriate forthis BC V scale is M ⊙ bol = 4 .
732 (see Torres 2010). See text forthe source of the reddening. For the apparent visual magnitudeof EPIC 219552514 out of eclipse we used V = 10 . ± . a Synchronous projected rotational velocity assuming spin-orbitalignment. b Measured projected rotational velocity for the primary. c A global parallax zero-point correction of +0 .
029 mas has beenadded to the parallax (Lindegren et al. 2018a), and 0.021 masadded in quadrature to the internal error (see Lindegren et al.2018b). ues, supporting the accuracy of our determinations forEPIC 219552514.The measured projected rotational velocity for the pri-mary star, v sin i = 49 ± − , agrees with the pre-dicted value v sync sin i listed in Table 6, which assumessynchronous rotation and spin-orbit alignment. Giventhe ∼ M ⊙ .If it is a main sequence star, the lack of detection in ourspectra implies a mass that can be no larger than that ofthe secondary, or ∼ M ⊙ . This, in turn, gives a lowerlimit for the inclination angle of the outer orbit of about Figure 6.
Comparison of the predicted flux ratio between thecomponents of EPIC 219552514 and our ℓ /ℓ values measuredspectroscopically and from the light curve analysis. Squares rep-resent the calculated flux ratio integrated over the correspond-ing spectroscopic and K2 bandpasses, and the measurements areshown as circles with error bars. The calculated curve is based onmodel spectra by Husser et al. (2013) for solar metallicity, normal-ized using our measured radius ratio k = 0 . T eff = 6200 K and log g = 4 .
0, and for the secondary T eff = 4000 K and log g = 4 . ◦ . Alternatively, the tertiary may be a white dwarf. Rotation and activity
Oscillations in the K2 photometry of EPIC 219552514are obvious in the residuals from our light curve analy-sis, and are seen as a function of time in the top panel ofFigure 7. The oscillations are rather irregular (see alsoFigure 4), and display a peak-to-peak amplitude close to10 mmag. This amplitude is in line with those seen inother late F dwarfs, as reported by Giles et al. (2017).A Lomb-Scargle periodogram of the residuals shows amain peak at a period of 2 . ± .
04 days (bottom panelof Figure 7), which we interpret as a rotational signaturecaused by one or more spots or spot regions. The uncer-tainty was estimated from the half width of the peak athalf maximum. This period is marginally longer than the2.75-day orbital period of the binary, which could implysubsynchronous rotation, or may also be a consequenceof solar-like differential rotation, with spots located atintermediate or high latitudes rotating more slowly thanthe equator. In view of the spectroscopic evidence ( v sin i of the primary) presented earlier for spin-orbit synchro-nization, we are inclined to favor the latter interpreta-tion. The spots are most likely located on the primarystar, as assuming that they are on the secondary wouldimply a rather unusual intrinsic amplitude exceeding onemagnitude, because of the large brightness dilution fac-tor ( ℓ /ℓ ≈ . II Hand K emission, or variable H α equivalent widths. This isperhaps consistent with the relatively small amplitude ofthe photometric variations. We note also that, as far aswe can tell, the object does not appear to have been de-tected as an X-ray source (e.g., by ROSAT ; Voges et al.1999) or as a source of ultraviolet radiation (
GALEX ;Bianchi et al. 2011). It would not be surprising if the0
Torres et al.
Figure 7.
Residuals from our best fit to the K2 photometry ofEPIC 219552514 showing modulations presumably due to spots.The corresponding periodogram shown at the bottom features adominant peak at a period of P rot = 2 . ± .
04 days. faint secondary star were somewhat active as well, de-spite the old age of the system, given its moderatelylarge expected rotational velocity of about 12 km s − (Table 4). COMPARISON WITH THEORY
The masses, radii, and temperatures of the binary com-ponents of EPIC 219552514 are compared in Figure 8against models of stellar evolution from the PARSECv1.2S series by Chen et al. (2014). Isochrones in both themass-radius and mass-temperature diagrams are shownfor the age range 2.0–3.2 Gyr in steps of 0.2 Gyr, with theheavy dashed line representing the best fit. The corre-sponding age is 2 . +0 . − . Gyr, in which the uncertainty isdominated by the error in the primary mass. Uncertain-ties in the adopted chemical composition of Ruprecht 147([Fe / H] = +0 . ± .
04; see Curtis et al. 2018) contributean additional 0.13 Gyr to the error budget for the age.Because the age determination for EPIC 219552514 isonly sensitive to the radius of the primary star (the sec-ondary evolves too slowly), the best-fit isochrone matches R precisely. The secondary radius appears slightlylarger than predicted (by 3.7%), although the deviationis less than twice its uncertainty and may not be sig-nificant. On the other hand, the effective temperaturesof both components are consistent with predictions fromtheory. Many cool main sequence stars such as the sec-ondary have shown discrepancies with standard stellarevolution models that are believed to be caused by stel-lar activity (see, e.g., Torres 2013). They tend to belarger and cooler than predicted. However, in this casea reasonably good agreement between the [ R , T eff ] mea-surements for the secondary and these particular modelsis expected a priori because the PARSEC v1.2S modelshave been adjusted by changing the temperature-opacityrelation in such a way as to match the average measuredproperties of low-mass stars (see Chen et al. 2014).The above age determination for EPIC 219552514 Figure 8.
Physical properties of EPIC 219552514 com-pared against model isochrones from the PARSEC v1.2S series(Chen et al. 2014) for the metallicity of the cluster, [Fe / H] =+0 .
10. The dotted lines in both panels represent isochrones forages between 2.0 and 3.2 Gyr in steps of 0.2 Gyr, and the heavydashed line corresponds to an age of 2.67 Gyr that fits the mea-sured masses and radii best. Results for the two eclipsing binariesstudied previously in Paper I and Paper II are shown as well. agrees well with our estimates for the eclipsing binariesEPIC 219394517 and EPIC 219568666 from our earlierstudies (Paper I and Paper II), whose physical proper-ties are also shown in the figure. The ages we reportedfor those two objects using the same PARSEC modelsas above are 2 . ± .
25 and 2 . ± .
61 Gyr. Othermodels with different physical ingredients lead to slightlydifferent ages. For example, using the MIST models ofChoi et al. (2016), we obtain a marginally younger agefor EPIC 219552514 of 2.51 Gyr.The evolved status of the primary star places it atthe very end of the main sequence for the cluster. Thismay be seen in the color-magnitude diagram of Figure 9,which shows other member stars from the
Gaia /DR2 cat-alog along with the 2.67 Gyr PARSEC isochrone cor-rected for reddening and extinction. The absolute mag-nitudes for the other members were calculated using theirindividual parallaxes. The two previously studied bina-ries in Ruprecht 147 are marked on the isochrone as well,at the locations expected from their measured masses. FINAL REMARKS
EPIC 219552514 is special for being located near theturnoff of Ruprecht 147, making it the system most sen-sitive to age among the known eclipsing binaries in the As discussed in Paper II, the individual component radii forEPIC 219568666 were reported to be slightly affected by system-atic errors in the radius ratio k , although the age could still bedetermined accurately using instead the sum of the radii, which isunaffected. clipsing binary in Ruprecht 147 Figure 9.
Color-magnitude diagram for Ruprecht 147 based onthe measured G magnitudes, G BP − G RP colors, and parallaxesfrom the Gaia /DR2 catalog. Also shown is a model isochrone fromthe PARSEC series (Chen et al. 2014) for the metallicity of thecluster and the age that best fits the properties of EPIC 219552514(Figure 8). Reddening and extinction corrections have been appliedto the model (reddening vector indicated with an arrow). Thesame symbols as in Figure 8 are used to mark the locations on themain sequence of the stars in EPIC 219552514 and the other twoeclipsing binaries in the cluster studied previously. cluster. Our accurate mass and radius determinationshave allowed an accurate age to be inferred for the binary(2 . +0 . − . Gyr) based on the PARSEC models. This isin excellent agreement with estimates for the two previ-ously studied eclipsing systems in the cluster that usedthe same models. The weighted average of the three de-terminations is 2 . ± .
21 Gyr. The precision of our cur-rent age for EPIC 219552514 is limited by the uncertaintyin the mass of the primary star (4.2%), which in turn iscaused mostly by the reduced precision of the radial ve-locities of the secondary star on account of its faintness( σ RV ∼ − , on average). Additional spectra withhigher signal-to-noise ratios would help to reduce thesestatistical errors.Our distance estimate for EPIC 219552514 is sim-ilar to those inferred in Paper I and Paper II, andimplies a parallax (3 . +0 . − . mas) that is marginallylower than the one reported in the Gaia /DR2 catalog(3 . ± .
051 mas), although still consistent within theerrors. It is possible that part of the difference is dueto the fact that the system is found here to be triple,whereas
Gaia has so far been treating the object as a sin-gle star. The discovery that EPIC 219552514 is a triplesystem is in fact not surprising, as it has been found thatthe vast majority of spectroscopic binaries with periodsunder 3 days have additional companions (96%, accord-ing to Tokovinin et al. 2006).The nature of the third component, i.e., whether itis a main-sequence star or a white dwarf, is undeter-mined from the present data. In either case, this distantcompanion may play a role in the dynamical evolutionof the system, modulating the eccentricity of the innereclipsing binary (which we currently find to be consis-tent with having a circular orbit) as well as modulat- ing the relative inclination angle between the inner andouter orbital planes (Kozai-Lidov oscillations; see, e.g.,Naoz 2016). The latter can potentially change the eclipsedepths, or temporarily cause them to cease altogether.This would be expected to occur on timescales that aremuch longer than the orbital periods. We find the sys-tem to be dynamically stable according to the criteriaof Eggleton & Kiseleva (1995) and Mardling & Aarseth(2001), for any reasonable mass of the third star and anyrelative inclination of the orbital planes.If the tertiary is a white dwarf, constraints on its massand that of its progenitor may be obtained from the samePARSEC isochrone used earlier for the age and metal-licity of Ruprecht 147. We find a lower limit for theprogenitor mass of 1.59 M ⊙ , and a corresponding lowerlimit for the present-day white dwarf mass of 0.60 M ⊙ .This would imply significant mass loss from the thirdcomponent, which may have left some observable traceon the system. One possiblity would be chemical polu-tion of the eclipsing binary components. This could bepursued through a detailed spectroscopic analysis of theprimary star.We estimate the angular size of the outer orbit to beabout 5.7 mas at the distance of Ruprecht 147, which isinside the reach of our NRM observations described inSection 2.3. While Gaia cannot spatially resolve the ter-tiary, in principle it should be capable of detecting themotion of the eclipsing binary in the outer orbit witha period of 463 days. We estimate this motion shouldhave a semimajor axis between 0.8 and 1.3 mas, depend-ing on the outer inclination angle, assuming the tertiarycontributes negligibly to the total light. Disappointingly,the
Gaia /DR2 data for this system show no sign of excessastrometric noise (which could otherwise be an indicationof unmodeled motion), although it is still possible thatthe 463 day signal may emerge or be recoverable by theend of the mission, particularly with the knowledge wenow have. In that case,
Gaia should be able to measurethe inclination angle of the outer orbit. When combinedwith the elements of our spectroscopic orbit, this anglewould then immediately allow a determination of the dy-namical mass of the tertiary component.The spectroscopic observations of EPIC 219552514were gathered with the help of P. Berlind, M. Calkins,and G. Esquerdo. J. Mink is thanked for maintaining theCfA echelle database. The anonymous referee providedhelpful comments on the original manuscript. G.T. ac-knowledges partial support from NASA’s AstrophysicsData Analysis Program through grant 80NSSC18K0413,and to the National Science Foundation (NSF) throughgrant AST-1509375. J.L.C. is supported by the NSF As-tronomy and Astrophysics Postdoctoral Fellowship un-der award AST-1602662, and by NASA under grantNNX16AE64G issued through the K2 Guest ObserverProgram (GO 7035). The research has made use of theSIMBAD and VizieR databases, operated at the CDS,Strasbourg, France, and of NASA’s Astrophysics DataSystem Abstract Service. The work has also made useof data from the European Space Agency (ESA) mis-sion
Gaia ( ), pro-cessed by the Gaia
Data Processing and Analysis Con-sortium (DPAC, Torres et al. gaia/dpac/consortium ). Funding for the DPAC hasbeen provided by national institutions, in particular theinstitutions participating in the
Gaia
Multilateral Agree-ment. The computational resources used for this researchinclude the Smithsonian Institution’s “Hydra” High Per-formance Cluster. REFERENCES
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