Relative stellar chronology and Relative stellar chronology and secular evolution.secular evolution.

Nathan MayneNathan Mayne

Exeter University.Exeter University.

Research• Empirical Isochrones

• The R-C (Radiative-Convective) gap 2 Distances

• Extinctions (Q-method v1.1)

• Fitting

• Relative age ladder

Structure:Structure:

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].

Background• Motivation/Context for research • Stellar chronology

Conclusions

• Summary

• Future work

Motivation: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 parametersCurrent 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, t1/2

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: [10 11 12 13 14] 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:Stellar Chronology:

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].

Empirical Isochrones: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].

Photometry

Members

• X-ray sources

Photometry

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

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: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].

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].

R-C gap: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].

R-C gap, Physics: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].

Calibration: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: [10 11 12 13 14] 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 2 Distances: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?!

dcdmmcmmccU iNi ii ),(),(ln2,1

2

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].

Extinctions, Q-method: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].

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:Q-method V1.1:

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].

Q-method V1.1: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].

Q-method V1.1: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].

Q-method V1.1: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].

Fitting: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].

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-Teff

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.

Spectral types:Spectral types:

Refit using:

• E(V-I)=F(V-I) and AV=F(V-I).

• Use Bessels (1998) Col-Teff relation.

• Check filter responses for data.

Age ladder: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].

Summary: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].

Future Work: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: [10 11 12 13 14] Fitting [15] Relative ages [16] Summary [17] Future Work [18].