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

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

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].

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].

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].

Photometry

Members X-ray sources Photometry

Members X-ray sources Periodic variables

Photometry Members X-ray sources Periodic variables Spectroscopic members

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

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

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

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].

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].

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].

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].

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].

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].

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

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].

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].

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].

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].

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].

11.81<dm<11.84

11.84<dm<11.9

NGC2264: 9.35<dm<9.54 Updated Q Extinction=f(B-V) Bessels (1998) Col-T eff

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

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].

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].

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].