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

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

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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, t 1/2 disc ~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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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) Stellar Chronology: Intro: [1 2 3] Empirical Isochrones: [3 4 5] R-C gap: [6 7 8] 2 distances: [9] Extinctions: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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Photometry

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Members X-ray sources Photometry

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Members X-ray sources Periodic variables

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Photometry Members X-ray sources Periodic variables Spectroscopic members

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Members X-ray sources Periodic variables Spectroscopic members H sources Photometry

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Members X-ray sources Periodic variables Spectroscopic members H sources Isochrone Isolate members

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

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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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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R-C gap, Physics: Using Siess and Dufour (2000) mass tracks. Radiative-Convective gap. 1, 3 and 13Myr isochrones. 1 and 3M sol 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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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

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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. 2 Distances: 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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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 Valid for -0.80

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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? Q-method V1.1: Figure: Geneva 1Myr isochrone. Intrinsic Q-method Pseudo- MS line. Empirical Extinction vector. Using A V =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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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 A V ~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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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: A V =( (B-V) 0 )*E(B-V) E(U-B)/E(B-V)= (B-V) 0 (based on E(B-V)~0.3) Over range of Q→-0.279<(B-V) 0 < Error in A V ~0.05 Therefore summed error so far: In B range: A V ~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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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Q-method V1.1: Applied Bessels Extinction functions. Limit to binarity E(B-V)<0.03. Use Bessels (1998) Col-T eff relation (logg=4.5). If A V 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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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Fitting: Use Q-method or spectral types for extinctions. Use 2 to find distances. Filter response: Previously used Col-T eff 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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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11.81

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11.84

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NGC2264: 9.35

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The ONC: 8.04

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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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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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: [ ] Fitting [15] Relative ages [16] Summary [17] Future Work [18].

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

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