6. Detached eclipsing binaries

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1 Rolf Kudritzki SS Detached eclipsing binaries 50% of all stars live in binary systems and some of them are eclipsing 1

2 Rolf Kudritzki SS 2015 classification of binary systems by geometry of equipotential surfaces center of gravity (x, y, z) = G M 1 r 1 G M 2 r 2 1 2!2 s 2 contribution by centrifugal force potential in coordinate system rotating with orbital period Roche potential 2

3 Rolf Kudritzki SS 2015 equipotential surfaces close to centers of M 1, M 2 : spherical further out deviation from spherical symmetry Roche-surface: surfaces touch each other at inner Lagrange point L 1, where forces are zero inside Roche-surface: matter bound to either 1 or 2 3

4 Rolf Kudritzki SS 2015 surfaces light curves detached semi-detached contact 4

5 Rolf Kudritzki SS 2015 detached eclipsing binaries (DEBs): radii smaller than Roche-surfaces stars are nicely round, no stellar surface effects through deformation (changes of T eff, log g over surface) light curves are regular with well defined eclipses accurate constraints on radii and masses from light curve and radial velocity curve spectral analysis with standard model atmospheres reliable 5

6 Eclipsing binaries Joel D. Hartman, CfA

7 Rolf Kudritzki SS 2015 v 1 = 2 a 1 P diagnostics of DEBs for simplicity: circular orbits, sin i =1 a 1 M 1 = a 2 M 2 a 3 P 2 = v 2 = 2 a 2 P a = a 1 + a 2 Kepler law G 4 2 (M 1 + M 2 ) M 2 = a 1 = v 1 M 1 a 2 v 2 a = P 2 (v 1 + v 2 ) M 1 + M 2 = P 2 (v 1 + v 2 ) 3 G masses from v rad!!! 7

8 Rolf Kudritzki SS 2015 Eclipse analysis (circular orbits) t 4 t 1 P t 3 t 2 P = 2R 1 +2R 2 l = 2R 1 2R 2 l l =2 a = P (v 1 + v 2 ) eclipse duration minimum duration orbit length star 2 around star 1 radii from eclipse!!! 8

9 Rolf Kudritzki SS 2015 total flux S tot = d 2 R2 1F 1 + R 2 2F 2 = R1 d 2 F 1 [1 + R2 2 R 2 1 F 2 F 1 ] 1 st eclipse flux 2 S 1st R1 = F 1 d 2 nd eclipse flux S 2nd = d 2 R2 1F 1 R 2 2F 2 + R 2 2F 2 = R1 d 2 F 1 [1 R2 2 R1 2 (1 F 2 F 1 )] F 2 < F 1 à S λ 1st > S λ 2nd = = > < depth of eclipses constraints flux ratio or temperature ratio 9

10 DEB distance d 2 = π R 1 2 F 1 [1 + (R 2 /R 1 ) 2 F 2 /F 1 ] / S λ primary surface brightness T 1, F 1 (T 1 ), model atmospheres or (V-K) 1, F 1 (V-K) empirical surface brightness- color relationship de-reddened observed flux S λ intrinsic (B-V) 0, SED E(B-V), R λ

11 Example A new distance to M33 from an eclipsing O-star binary Bonanos, Stanek, Kudritzki et al., 2006, ApJ 652,313

12 HST WFPC2 U&B-images

13 Lightcurve V

14 Radial velocity curve Keck ESI Gemini GMOS

15 Spectral fit of composite spectrum at quadrature model spectra for star 1 log g 1 = 3.78, v 1 (rad) star 2 log g 2 = 4.03, v 2 (rad) free parameter : T 1 (F 1 /F 2 à T 2 ) spectrum star 1: shift by v 1 (rad), weight R 1 2 F 1 star 2 : v 2 (rad) R 2 2 F 2 add weighted and shifted spectra

16 A crucial test Balmer lines model atmospheres depend strongly on log g log g 1 = 3.78 log g 2 = 4.03 do models reproduce observed Balmer lines??

17 H4 Star 1 Star 2 H β T 1 = 35, 37, 39 kk

18 HeI 4026 HeII 5412 HeI and HeII lines à T eff HeI 4471 HeII 4542 HeI 4922 HeII 4200

19 HeI 4922 Star 1 Star 2 HeI λ4922 T 1 = 35, 37, 39 kk

20 HeII 5412 Star 2 Star 1 HeII λ5412 T 1 = 35, 37, 39 kk

21 m-m = ± 0.1 mag T 1 = ± 1500 K R V = 3.5 T 1 = K

22 IfA 2013 An O-type DEB in the LMC P = 4.25d R 1 = 15.1±0.2 R sun R 2 = 11.9±0.2 R sun M 1 = 30.9±1.0 M sun M 2 = 13.0±0.7 M sun Bonanos, Castro, Macri, Kudritzki, 2011, ApJ 729, L9

23 H γ as test of gravity log g at quadrature 1 2 log g 1 = 3.54 ± 0.02 log g 2 = 3.40 ± 0.03

24 HeI/II at quadrature à T 1 and T T 1 = ± 1000 K T 2 = ± 1000 K

25 SED fit à E(B-V), A V and distance a 3% distance however

26 Problem with early type DEB distances d 2 = π R 1 2 F 1 [1 + (R 2 /R 1 ) 2 F 2 /F 1 ] / S λ F 1 (T 1 ) surface flux from NLTE model atmosphere!!! (almost) no astronomer trusts such complicated models!!! Systematic uncertainties difficult!!!

27 IfA 2013 LMC B-type DEBs: Villanova Group Guinan+, 1998 Fitzpatrick+, 2002, 2003 Ribas+, 2000, 2002 d[kpc] HV ±2.2 HV ±1.2 E ±1.8 HV ±1.8 Problem: no spectral lines for T but SED à degeneracy with E(B-V), A V

28 8 binaries late type Dec Nature

29 Problem with early type DEB distances d 2 = π R 1 2 F 1 [1 + (R 2 /R 1 ) 2 F 2 /F 1 ] / S λ F 1 (T 1 ) surface flux from NLTE model atmosphere!!! (almost) no astronomer trusts such complicated models!!! Systematic uncertainties difficult!!!

30 IfA 2013 Alternative: late spectral type DEBs Pietrzynsky et al. 2009, ApJ 697,862 Pietrzynsky et al. 2013, Nature 495, 76

31 The alternative: late type DEB distances Interferometry à obs. surface brightness color relationship SBCR late type giants G, K, M σ ~ 0.03 mag DiBenedetto, 1998,2005 Groenewegen, 2004 Kervella, 2004

32 Late type DEBs in LMC OGLE à monitoring 35 million LMC stars over 14 years Pietrzynski et al., 2013 Nature, 495, 76 8 well detached eclipsing late type giants periods days observations over the last 8 years spectra: Magellan/MIKE echelle ESO 3.6m HARPS photometry: OGLE II/III/IV (B,V,I) CTIO 1.3 m (B,V,I) ESO NTT (J,K)

33 object close to line of nodes and dynamical center of LMC à inclination and geometrical structure of LMC negligible Pietrzynski et al., 2013

34 Δv rad < 200 m/s ΔK < 0.5% Δ(R 1 +R 2 ) < 1.5% Pietrzynski et al., 2013

35 DEB distances S[mag] = (V-K) (V-K) 0 2 SBCR σ = 0.03 mag φ[mas] = 100.2(S V) angular diameter d[pc] = R[R sun ]/φ[mas] distance

36 SBCR angular diameter DEB distances and errors S[mag] = (V-K) (V-K) 0 2 distance stochastic errors φ = 100.2(S V) d ~ R/φ σ SBCR = 0.03 mag ΔR/R < 1.5 % dominates Reddening maps, T 1,2 à E(B-V) ΔE(B-V) almost cancels in S-V systematic errors σ SBCR dominates à Δd/d ~ 1.5% V,K z.p mag à 1.0 total à 1.8%

37 individual distances vs. angular distance from center Pietrzynski et al., 2013

38 LMC distance d [kpc] = ± 0.19 (statistical) ± 1.11 (systematic) m-m = ± (statistical) ± (systematic) firm base for 3% H 0 improvement of σ SBCR with VLTI: % LMC distance possible further improvement of H 0

39 4 binaries 1 binary 8 binaries Dec Nature

40 Observed objects à solid circles future objects à open circles

41 Δv rad < 500 m/s ΔK < 0.5% Δ(R 1 +R 2 ) < 1.5%

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45 individual distances vs. RA

46 Upper left part of SMC known to be closer

47 SMC distance m-m = ± (statistical) ± (systematic) canonical distance modulus m-m = ± 0.07 LMC distance m-m = ± 0.045

48 Rolf Kudritzki SS 2015 Cepheids in binary systems OGLE-LMC-CEP-0227: best studied system so far Pilecki et al. 2013, MNRAS, 436, 953 orbit: P = 309d pulsation: P = 3.8d Gieren, 2014 MIAPP 48

49 Rolf Kudritzki SS 2015 OGLE-LMC-CEP-0227: out-of-eclipse light curves Pilecki et al.,

50 Rolf Kudritzki SS 2015 OGLE-LMC-CEP-0227: best studied system so far (Pilecki et al. 2013, MNRAS, 436, 953) Results: Masses to 0.7%, radii to 1%, p-factor to 3% Optical limb darkening of Cepheid much higher than theory predictions! Gieren, 2014 MIAPP 50

51 Rolf Kudritzki SS 2015 OGLE-LMC-CEP-0227: radial velocity pulsation curve Gieren, 2014 MIAPP 51

52 Rolf Kudritzki SS 2015 Code of Pilecki et al., applied to Cep-0227 photometric data yields very accurate fits to the observed light curve eclipses Gieren, 2014 MIAPP 52

53 Rolf Kudritzki SS 2015 eclipse fits: a closer look Gieren, 2014 MIAPP 53

54 Rolf Kudritzki SS 2015 OGLE-LMC-CEP-0227: Pilecki et al.,

55 Rolf Kudritzki SS 2015 OGLE-LMC-CEP-0227: Cepheid variable radius indicated Pilecki et al.,

56 Rolf Kudritzki SS 2015 Distance of OGLE-LMC-CEP-0227! 2 methods for the same object: Baade-Wesselink (IRSB) technique Binary distance (expected ±1.5%)! Unique opportunity to improve calibration of IRSB method (p-factor!)! Work in progress (waiting for more K-band data covering light curve eclipses) Gieren, 2014 MIAPP 56

57 A second Cepheid in a LMC EB system: OGLE-LMC-CEP-1812 Pietrzynski, Thompson, Gieren et al. 2011, ApJ, 742, L20 P orb : 552 d, P pul : 1.31 d, M cep = ( M o ), M giant = 2.64 M o Rolf Kudritzki SS 2015 Gieren, 2014 MIAPP 57

58 OGLE-LMC-CEP-1718, the first known double-cepheid binary system Rolf Kudritzki SS 2015 Primary component: a classical Cepheid pulsating with P=1.96 d (filled circles), the secondary Cepheid pulsates with P=2.48 days. The orbital period is 413 days (Gieren et al. 2014, ApJ 786, 80) Gieren, 2014 MIAPP 58

59 Rolf Kudritzki SS 2015 The disentangled pulsational radial velocity curve of the shorterperiod primary Cepheid in CEP-1718 Gieren, 2014 MIAPP 59

60 Rolf Kudritzki SS 2015 The disentangled pulsational radial velocity curve of the longerperiod secondary Cepheid in CEP-1718 Gieren, 2014 MIAPP 60

61 Rolf Kudritzki SS 2015 The disentangled pulsational I-band light curve of the primary Cepheid in CEP-1718, based on 1535 OGLE observations Gieren, 2014 MIAPP 61

62 Rolf Kudritzki SS 2015 The disentangled pulsational I-band light curve of the secondary Cepheid in CEP-1718 Gieren, 2014 MIAPP 62

63 Rolf Kudritzki SS 2015 Gieren, 2014 MIAPP 63

64 Rolf Kudritzki SS