Relative stellar chronology and secular evolution.

1. Relative stellar chronology and secular evolution. Nathan Mayne Exeter University.

2. Structure: • Background • Motivation/Context for research • Stellar chronology Research • Empirical Isochrones • The R-C (Radiative-Convective) gap • 2 Distances • Extinctions (Q-method v1.1) • Fitting • Relative age ladder • Conclusions • Summary • Future work Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

3. Motivation: • Secular Evolution. • *Large timescales and no experimental design. • Compare properties of clusters, groups etc • Assume an evolutionary sequence (given chronological order) • Constrain models using derived parameters • Current state-Half-full. • Data precise (~1%), ubiquitous • Models sophisticated input physics. • Half-empty. • Ages model dependent, uncertain to a factor two. • Low resolution on timescales <5Myrs • Local environment effects missed? • Population mixing • Model and data need an equal footing! • Example: • Fig: Haisch et al (2001) showing disc indicator against age, t1/2disc~5Myrs. • Age uncertainties change ordering • No local effects. • Robust relative ages better Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

4. Stellar Chronology: • Isochronal fitting: • Model stellar interior & atmospheres • Isochrones in Colour-Magnitude Diagram (CMD). • Fit ‘by eye’ to a sequence. • Problems: • Derived quantities model dependent e.g. mass and age. • - Geneva, Padova, Siess & Dufour, Baraffe and D’AM. • Shape, Main-Sequence (MS)-Pre-Main-Sequence (PMS) not seen in data. • - Bonatto et al (2004), Pinsonneault et al (2004) and Mayne et al (2007) • Inconsistent across bands. • - Naylor et al (2002) • Intrinsic degeneracy’s of age with distance or extinction. • Selection of a (~)coeval data sequence. • - Unresolved distinct populations, Jeffries et al (2006) • - Capture of field stars Pflamm-Altenberg and Kroupa (2007) Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

5. Empirical Isochrones: • Why: • Alternative to theoretical isochrones. • Necessarily fit the data better. • Compared to provide relative ages. • Construction: • Select (~)coeval members. • Use averaging filter. • Fit Cubic spline to points. • Apply distance and extinction. • Compare on age ladder plot. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

6. Photometry

7. Photometry • Members • X-ray sources

8. Photometry • Members • X-ray sources • Periodic variables

9. Photometry • Members • X-ray sources • Periodic variables • Spectroscopic members

10. Photometry • Members • X-ray sources • Periodic variables • Spectroscopic members • H sources

11. Photometry • Members • X-ray sources • Periodic variables • Spectroscopic members • H sources • Isochrone • Isolate members

12. Photometry • Members • X-ray sources • Periodic variables • Spectroscopic members • H sources • Isochrone • Isolate members • Photometric cut • Fit cubic spline

13. Empirical Isochrones-Results: • Problems: • Heterogenous photometry. • PMS degeneracy with distance. • Distances large source of uncertainty. • Discoveries: • Age order of several fiducial cluster. • Local environment effects? • R-C gap Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

14. Relative age order: ~1Myr (the ONC, NGC6530 and IC5146), ~3Myrs (Cep OB3b, NGC2362,  Ori and NGC2264 and ~4-5Myrs ( Ori and IC348) • Updated Disc lifetime: • New age order. • Second-order effects achievable. • IC348, no O stars, local environment effects. R-C gap? Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

15. R-C gap: • Distance independent age indicator. • Shape factor. • Size of gap is a function of age. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

16. R-C gap, Physics: • Using Siess and Dufour (2000) mass tracks. Radiative-Convective gap. • 1, 3 and 13Myr isochrones. • 1 and 3Msol evolution shown (red). • Star from Convective (Hayashi) track to radiative track. • Moves fast in CMD space. • Leads to paucity of stars. • Older clusters R-C gap at lower masses, closer to MS. • Noted in the literature, Stolte et al (2004), not utilised. Calibration required! Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

17. Calibration: • 2 fitting: • Statistically meaningful uncertainties. • Objective fitting statistic. • Binary stars included. • Consistent method. • By eye fitting: • Subjective. • Uncertainties not well defined. • Binaries neglected. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8]2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

18. 2 Distances: • Generalised 2 fitting with uncertainties in two-dimensions. • Massive jump in statistical sophistication, provides first statistically robust uncertainties. • Use for MS stars to find distances. • Model dependent, okay for relative ages. • Extinction dependency for HM fitting. • 2, extremely sensitive to data, utilise the ~1% photometry. • Initial Problems: • Normalisation causing numerical instability? • Post-MS stars falling outside area of fit, altering 2 • Extinctions from Q-method of spectral types, former inconsistent. • Filter response?! Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

19. Extinctions, Q-method: • Johnson & Morgan (1953). • Remarkable piece of work • From NGC2362, the Pleiades and the Praesepe with nearby stars. • U-B vs B-V CMD used to calculate extinctions. • Empirically derived ‘reddening independent’ relationship: • Using: E(U-B)/E(B-V)=0.72±0.03 (empirically derived) • (B-V)0=0.337Q-0.009. • Valid for -0.80<Q<-0.05 • For B stars in their sample. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

20. Q-method V1.1: • Problems: • Implies intrinsic straight-line Pseudo-MS in U-B vs B-V. • Binarity effects ignored. • E(U-B)/E(B-V)=CONST. • Filter response? • Figure: • Geneva 1Myr isochrone. • Intrinsic Q-method Pseudo-MS line. • Empirical Extinction vector. Using AV=3.1E(B-V), can lead to an error of ~0.07. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

21. Q-method V1.1: • Problems: • Implies intrinsic straight-line Pseudo-MS in U-B vs B-V. • Binarity effects ignored. • E(U-B)/E(B-V)=CONST. • Filter response? • Figure: • Geneva isochrone 50% binary fraction. • Q-method implicit line. • Extinction vector. Can Lead to an error of AV~0.1. Errors smaller in the B star range. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

22. Q-method V1.1: • Problems: • Implies intrinsic straight-line Pseudo-MS in U-B vs B-V. • Binarity effects ignored. • E(U-B)/E(B-V)=CONST. • Filter response? • Bessels (1998) provides extinction as a function of colour: • AV=(3.26+0.22(B-V)0)*E(B-V) • E(U-B)/E(B-V)=0.71+0.24(B-V)0 • (based on E(B-V)~0.3) • Over range of Q→-0.279<(B-V)0<-0.0259 •  Error in AV~0.05 Therefore summed error so far: In B range: AV~0.2 Errors in different sense. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

23. Q-method V1.1: • Applied Bessels Extinction functions. • Limit to binarity E(B-V)<0.03. • Use Bessels (1998) Col-Teff relation (logg=4.5). • If AV decereases use a smaller range of B stars. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

24. Fitting: • Use Q-method or spectral types for extinctions. • Use 2 to find distances. • Filter response: • Previously used Col-Teff conversion of Flower (1996). • Updated to Bessels (1998), now consistent. • Check photometry! • Naked eye fitting cannot detect the details, and uncertainties meaningless. Next: Spot the Difference! Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

25. 11.81<dm<11.84

26. 11.84<dm<11.9

27. NGC2264: • 9.35<dm<9.54 • Updated Q • Extinction=f(B-V) • Bessels (1998) Col-Teff

28. Spectral types: • The ONC: • 8.04<dm<8.16 • Taken Log Teff • Used Geneva Isochrones for (V-I)0 • Derived E(V-I),  AV • Apply to V. • Refit using: • E(V-I)=F(V-I) and AV=F(V-I). • Use Bessels (1998) Col-Teff relation. • Check filter responses for data.

29. Age ladder: • ZAMS isochrone from Siess and Dufour (2000) • h and  Per, NGC2264 and the ONC. • Straight line fits to PMS. • Stop fit at base of R-C gap. • Distances from 2. • Substract the ZAMS colour at each magnitude. • Relative age order clear. • R-C gap size in colour. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

30. Summary: • Developed technique to derive robust relative ages using empirical isochrones. • Discovery of R-C gap. • Derived improved distances to fiducial clusters. • New method of deriving extinctions. • Guinea pig for 2-improvements. Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

31. Future Work: • WHT dataset to calibrate the R-C gap. • INT (ugri’z), empirical isochrones with homogenous dataset. • Use 2 to fit gap? • Rinse and repeat/automation. • GAIA? • But First…. • Write Thesis • Get a Post-Doc Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].