ECLIPSING BINARIES IN OPEN CLUSTERS John Southworth Dr Pierre Maxted Dr Barry Smalley Astrophysics Group Keele University

EBs are good tests of theoretical stellar models –EBs in clusters have known age and metal abundance –EBs in clusters are even better tests of theoretical models EBs are good distance indicators –Find distance to cluster without using MS fitting Eclipsing binaries in open clusters Two EBs in one cluster: –four stars with same age and chemical composition –excellent test of models –find metal and helium abundance of cluster –2004, MNRAS, 349, 547

HD in the Pleiades AO Vp (Si) + Am Period 2.46 days m V = 5.9 mag Shallow eclipses discovered by Torres (2003) Munari et al (2004) distance: ± 2.1 pc

Distance to the Pleiades Possible solution: Pleiades is metal-poor –Castellani et al. (2002): Fit for Z = –But Boesgaard & Friel (1990): [Fe/H] = ± 0.02 Possible solution: Hipparcos parallaxes correlated –(Pinsonneault et al. 1998; Makarov 2002) ‘Long’ distance scale: 132 ± 3 pc –MS fitting (e.g., Percival et al. 2003) –HD (Munari et al. 2004) –Interferometric binary Atlas (Zwahlen et al. 2004) `Short’ distance scale: 120 ± 3 pc –Hipparcos (van Leeuwen et al. 2004)

HD light curves B and V light curves from Munari et al. (2004) –We analysed them using EBOP –Theoretical limb darkening and gravity darkening –Formal errors very optimistic

Monte Carlo analysis Used Monte Carlo simulations to find light curve uncertainties –Limb darkening coefficients perturbed –r A = ± r B = ± Problem: B and V solutions inaccurate and don’t agree well –Solution: spectroscopic light ratio (Torres 2003) –r A = ± r B = ± Monte Carlo analysis results for HD without spectroscopic light ratio

HD effective temperatures Compare observations to ATLAS 9 spectra: –Temperatures: 9750 ± 250 K 7600 ± 400 K uvbyβ photometry + Moon & Dworetsky (1985) calibration: –9200 K for system 9870 K for primary only Infrared Flux Method: 9620 ± 280 K 7510 ± 430 K

Pleiades is not metal-poor HD 23642: –M A = 2.19 ± 0.02 –M B = 1.55 ± 0.02 –R A = 1.83 ± 0.03 –R B = 1.55 ± 0.04 Compare to Granada models: –Z ≈ 0.02 –Pleiades distance scales cannot be reconciled with low metal abundance Granada theoretical models 125 Myr Z =

Distance to the Pleiades Distance from luminosity + bolometric correction: –L = 4 π R 2 σ T eff 4  M bol –M bol + BC + V  M V + V  distance Problems: –BCs depend on theoretical model atmospheres –Fundamental effective temperatures are needed –Consistent solar M bol and luminosity values needed Girardi et al. (2000) BCs: (V filter):139.8 ± 5.3 pc (K filter):138.8 ± 3.3 pc –Bessell et al. (1998) BCs give same results –BCs better in the infrared: reddening less important metallicity less important BCs less dependent on T eff

Distance from surface brightness Calibrations of surface brightness vs. colour index –S V = surface brightness in V filter –Φ = angular diameter (mas) –R = linear radius of star (R  ) –S V = m V - 5 log Φ –distance = (R / Φ) parsecs Distance to HD23642: 138 ± 19 pc –Use Di Benedetto (1998) calibration of S V against (B - V) Problems: –HD B and V light ratios are inaccurate –B filter is sensitive to metallicity –(B - V) is not very sensitive to surface brightness –Reddening is important

Surface brightness from temperature Use zeroth-magnitude angular diameter Φ (m=0) –S V = V log Φ so Φ (m=0) = Φ 10 (0.2 m) = 0.2 S V –Kervella et al (2004) give Φ (m=0) - log T eff calibrations Use 2MASS JHK photometry: IR relations better –Distance : ± 3.5 pc –Individual uncertainties: Effective temperatures:0.7 pc1.4 pc Stellar radii:1.4 pc1.5 pc Apparent K magnitude:1.9 pc `Cosmic’ scatter in calibration:1.4 pc

The Pleiades distance is....? Long distance scale: 132 ± 3 pc –main sequence fitting –study of astrometric binary Atlas Short distance scale: 120 ± 3 pc –Hipparcos parallaxes Distance to HD 23642: 139 ± 4 pc –only weakly dependent on temperatures and radii The Pleiades is not metal-poor –from comparison between the masses and radii and theoretical evolutionary models Southworth, Maxted & Smalley, astro-ph/

W W Aurigae A4 m + A5 m Period 2.52 days m V = 5.9 mag Discovered by Solviev (1918) and Schwab (1918) Hipparcos distance: 84.3 ± 7.3 pc

WW Aur spectral characteristics Both components are Am stars –spectra show strong lines of both components

WW Aur spectroscopic orbit TODCOR: two-dimensional cross-correlation –Cross-correlate against many observed template spectra –Fit spectroscopic orbits using SBOP –Choose which sets of spectra give good orbits –Average good orbits to find best orbit RV semiamplitudes: K A = ± 0.23 km/s K B = ± 0.32 km/s –Uncertainty is standard deviation of the results from each good orbit –SBOP uncertainties agree very well

WW Aur light curves 1 UBV light curves from Kiyokawa & Kitamura (1975) –3037 datapoints scanned from paper

WW Aur light curves 2 uvby light curves from Etzel (1975) Master’s Thesis –3748 datapoints on a nine-track magnetic tape

WW Aur light curve analysis UBV and uvby light curves fitted using EBOP –Limb darkening coefficients adjusted Uncertainties from Monte Carlo analysis –Good agreement with variation between the seven light curves: –r A = ± –r B = ± HD WW Aur

WW Aur effective temperatures Am stars so spectral analysis unreliable Hipparcos parallax gives distance 84.3 ± 7.3 pc Get bolometric flux –UV fluxes from TD-1 satellite –UBVRI magnitudes –2MASS JHK magnitudes Convert to separate fluxes using V light ratio Temperatures: –T eff (A) = 7960 ± 420 K –T eff (B) = 7670 ± 410 K –almost no dependence on model atmospheres

WW Aur results Masses from cross-correlation against observed spectra: M A = ± M  M B = ± M  Radii from EBOP geometrical analysis: –Gravity darkening unimportant –Limb darkening fitted R A = ± R  R B = ± R  Effective temperatures from Hipparcos parallax and UV-optical-IR fluxes: T eff (A) = 7960 ± 420 K T eff (B) = 7670 ± 410 K

Assume common age and chemical composition for both stars in WW Aur Problem: no published theoretical stellar models fit the masses and the radii Comparison with theoretical models

Solution: Z = 0.06 Claret (2004) models fit for Z = 0.06 age 77  107 Myr

Metallic-lined eclipsing binaries

Conclusions EBs are excellent distance indicators –HD gives Pleiades distance 139 ± 4 pc –Agrees with MS fitting but not Hipparcos Distance from surface brightness is good –Avoids bolometric corrections from model atmospheres –Best in the infrared (reddening, T eff dependence) Eclipsing binaries in open clusters are very useful WW Aur seems to be very metal-rich –Masses and radii found to accuracies of 0.4%, 0.6% –T eff s from Hipparcos parallax and UV-optical-IR fluxes –Metal abundance of Z ≈ 0.06 not connected to Am spectra

John Southworth Keele University, UK