1. HIGH-PRECISION PHOTOMETRY OF ECLIPSING BINARY STARS John Southworth + Hans Bruntt + Pierre Maxted + many others

2. Eclipsing binary stars: why bother?

3. Light curve and radial velocity analysis: get masses and radii of two stars to 1% –where else could we get this from?

4. Eclipsing binary stars: why bother? Light curve and radial velocity analysis: get masses and radii of two stars to 1% –where else could we get this from? Accurate mass, radius, T eff, luminosity –use as high-precision distance indicators –check that theoretical models work

5. Eclipsing binary stars: why bother? Light curve and radial velocity analysis: get masses and radii of two stars to 1% –where else could we get this from? Accurate mass, radius, T eff, luminosity –use as high-precision distance indicators –check that theoretical models work Comparison with theoretical models –get metal abundance and age –investigate overshooting, mixing length, helium abundance, diffusion

6. Eclipsing binary stars: how? WW Aurigae – Southworth et al. (2005)

7. Eclipsing binary stars: how? Light curve analysis gives: –r A r B radii as fraction of orbital separation –e ωorbital eccentricity and periastron longitude –P i orbital period and inclination

8. Eclipsing binary stars: how? WW Aurigae – Southworth et al. (2005)

9. Eclipsing binary stars: how? Light curve analysis gives: – r A r B e ω P i Radial velocity analysis gives: P e ω –M A sin 3 iminimum mass of star A –M B sin 3 iminimum mass of star B –a sin iprojected orbital separation

10. Eclipsing binary stars: how? Light curve analysis gives: – r A r B e ω P i Radial velocity analysis gives: –M A sin 3 i M B sin 3 i a sin i P e ω Combine quantities: –M A M B R A R B log g A log g B –get the masses and radii of both stars

11. Eclipsing binary stars: how? Light curve analysis gives: – r A r B e ω P i Radial velocity analysis gives: –M A sin 3 i M B sin 3 i a sin i P e ω Combine quantities: –M A M B R A R B log g A log g B –get the masses and radii of both stars Spectral modelling or photometric colours: –get effective temperatures –get luminosities –get distance

12. The WIRE satellite Launched in 1999 for an IR galaxy survey –electronics problem caused loss of coolant

13. The WIRE satellite Launched in 1999 for an IR galaxy survey –electronics problem caused loss of coolant Star tracker used since 1999 as a high-speed photometer –aperture: 5 cm –cadence: 2 Hz –5 targets at once

14. Eclipsing binaries with WIRE. I. ψ Centauri V = 4.0 spectral type = B9 V + A2 V Known spectroscopic binary WIRE light curve: 41 000 points with 2 mmag scatter

15. Interlude 1: JKTEBOP Based on EBOP model (Paul Etzel, 1975) –stars treated as biaxial spheroids –numerical integration includes LD and GD

16. Interlude 1: JKTEBOP Based on EBOP model (Paul Etzel, 1975) –stars treated as biaxial spheroids –numerical integration includes LD and GD JKTEBOP retains original model –new input / output –Levenberg-Marquardt optimisation algorithm –bootstrapping and Monte Carlo simulations to find parameter uncertainties http://www.astro.keele.ac.uk/~jkt/codes.htmlFORTRAN77

17. JKTEBOP fit to the eclipses Eclipsing binaries with WIRE. I. ψ Centauri

18. Best fit and Monte Carlo simulation results: –r A = 0.043984 ± 0.000045 –r B = 0.021877 ± 0.000032 –e = 0.55408 ± 0.00024 –P = 38.81252 ± 0.00029 And limb darkening too: –u A = 0.256 ± 0.009 –u B = 0.362 ± 0.041 Eclipsing binaries with WIRE. I. ψ Centauri

19. Best fit and Monte Carlo simulation results: –r A = 0.043984 ± 0.000045 –r B = 0.021877 ± 0.000032 –e = 0.55408 ± 0.00024 –P = 38.81252 ± 0.00029 And limb darkening too: –u A = 0.256 ± 0.009 –u B = 0.362 ± 0.041 See Bruntt et al. (2006, A&A, 456, 651) We are currently working on new spectroscopy Eclipsing binaries with WIRE. I. ψ Centauri

20. P = 6.07 days B4 V + A6 V V = 4.9 –variation at primary star rotation period –several pulsation frequencies Eclipsing binaries with WIRE. II. AR Cas

21. V = 1.9 P = 3.960 d ays A1m + A1m First known double-lined binary: 1889 (Maury) First known double-lined eclipsing binary: Stebbins (1911) WIRE light curve: 30 000 po ints; 0.3 mmag scatter Eclipsing binaries with WIRE. III. β Aurigae

22. Interlude 2: more JKTEBOP Problem: linear limb darkening law too simple –Solution: add log, sqrt, quad, cubic LD laws

23. Interlude 2: more JKTEBOP Problem: linear limb darkening law too simple –Solution: add log, sqrt, quad, cubic LD laws Problem: ratio of the radii poorly determined –Solution: allow spectroscopic light ratio to be included directly as another observation http://www.astro.keele.ac.uk/~jkt/codes.htmlFORTRAN77

24. Interlude 2: more JKTEBOP Problem: linear limb darkening law too simple –Solution: add log, sqrt, quad, cubic LD laws Problem: ratio of the radii poorly determined –Solution: allow spectroscopic light ratio to be included directly as another observation Problem: difficult to get good times of minimum light from the WIRE data –Solution: include old times of minimum light directly as additional observations http://www.astro.keele.ac.uk/~jkt/codes.htmlFORTRAN77

25. r A = 0.1569 ± 0.0008P = 3.96004673 (17) r B = 0.1460 ± 0.0008e = 0.0018 ± 0.0004 Eclipsing binaries with WIRE. III. β Aurigae

26. Combine light curve result with spectroscopic orbit of Smith (1948): –M A = 2.376 ± 0.027 M  –M B = 2.291 ± 0.027 M  –R A = 2.762 ± 0.017 R  –R B = 2.568 ± 0.017 R  Eclipsing binaries with WIRE. III. β Aurigae

27. Combine light curve result with spectroscopic orbit of Smith (1948): –M A = 2.376 ± 0.027 M  –M B = 2.291 ± 0.027 M  –R A = 2.762 ± 0.017 R  –R B = 2.568 ± 0.017 R  Distance to system: –Hipparcos parallax:25.2 ± 0.5 pc –Orbital parallax:24.8 ± 0.8 pc –Surface brightness:25.0 ± 0.4 pc –Bolometric corrections:24.8 ± 0.3 pc Southworth, Bruntt & Buzasi (2007, A&A, 467, 1215) Eclipsing binaries with WIRE. III. β Aurigae

28. Eclipsing binaries: why bother? Get mass and radius to 1% –accurate distance indicators –compare to theoretical models: get precise age and metal abundance

29. Eclipsing binaries: why bother? Get mass and radius to 1% –accurate distance indicators –compare to theoretical models: get precise age and metal abundance Now apply to EBs in open clusters –get accurate distance –get precise age and metallicity –no need for MS fitting

30. Eclipsing binaries: why bother? Get mass and radius to 1% –accurate distance indicators –compare to theoretical models: get precise age and metal abundance Now apply to EBs in open clusters –get accurate distance –get precise age and metallicity –no need for MS fitting Combined study of cluster and binary –stronger test of theoretical models

31. Eclipsing binaries in open clusters. I. V615 and V618 Per Both members of the young h Per cluster –have same age and chemical composition –compare all four stars to models using a mass-radius diagram h Per has low metal abundance: Z = 0.01

32. Eclipsing binaries in open clusters. II. V453 Cyg Member of sparse young cluster NGC 6871 Comparison to theoretical models: –age = 10.0 ± 0.2 Myr –metal abundance Z ≈ 0.01 (half solar – maybe)

33. Eclipsing binaries in open clusters. III. The distance to the Pleiades Surface brightness method gives good results –Use zeroth-magnitude angular diameter Φ (m=0) –Kervella et al (2004) give Φ (m=0) - T eff calibrations –Just need R A and R B and apparent magnitudes See Southworth, Maxted & Smalley (2005, A&A, 429, 645)

34. V = 6.8 P = 2.46 AO Vp (Si) + Am Light curves from Munari et al. (2004) We find distance = 139.1 ± 3.5 pc Eclipsing binaries in open clusters. III. HD 23642 in the Pleiades

35. Eclipsing binaries in open clusters: what next? V1481 Cyg and V2263 Cyg in NGC 7128 –14 nights of INT / WFC photometry –7 nights of INT / IDS spectroscopy –watch this space

36. JKTEBOP and HD 209458 JKTEBOP very good for transiting exoplanets –fast and accurate –lots of different limb darkening laws

37. JKTEBOP and HD 209458 JKTEBOP very good for transiting exoplanets –fast and accurate –lots of different limb darkening laws Results for HD 209458 –r A = 0.11405 ± 0.00042 –r B = 0.01377 ± 0.00008 –g B = 9.28 ± 0.15 m s -2 Southworth et al. (2007, MNRAS, 379, L)

38. Extrasolar planet surface gravity The known transiting extrasolar planets have a significant correlation between orbital period and suface gravity –the closer planets are more bloated Southworth et al. (2007, MNRAS, 379, L)

39. John Southworth jkt@astro.keele.ac.uk University of Warwick, UK