# a new technique to measure Δ y/ Δ z

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A New Technique to Measure Δ Y/ Δ Z. Main collaborators: J. R. de Medeiros (UFRN)M. Catelan (PUC). A. A. R. Valcarce (UFRN). XXXVII SAB meeting Águas de Lindóia, Brazil , Oct 16 th , 2012. Outline. Introduction Determination of Y Theoretical models (PGPUC ) - PowerPoint PPT PresentationTRANSCRIPT

A New Technique to Measure ΔY/ΔZ

A. A. R. Valcarce (UFRN)

Main collaborators:J. R. de Medeiros (UFRN) M. Catelan (PUC)

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Outline

• Introduction

• Determination of Y– Theoretical models (PGPUC)– Method– Comparison

• Application

• Summary

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Outline

• Introduction

• Determination of Y– Theoretical models (PGPUC)– Method– Comparison

• Application

• Summary

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

IntroductionThe helium-metallicity relation (Y-Z relation) is the keystone to understand the formation and evolution of stars and all the objects related to them.

This relation reads:Y = Yp + ΔY/ΔZ x Z

The importance of the Y-Z relation:One can know a free parameter (Y) and then assume that the differences between theory and observations are only associated to differences in ages, masses and/or other free parameters.

Yp: primordial helium abundance

ΔY/ΔZ: helium-to-metal enrichment ratio

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Effects of Y on Evolutionary Tracks

Evolutionary tracks are different if they have the same [Fe/H], [α/Fe] and mass, but a different He abundance (Y).

Some effects include:• Variations in luminosity (L),

effective temperatures (Teff), and surface gravity (g).

• Faster evolution for higher Y.

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Effects of Y on Evolutionary Tracks

Evolutionary tracks are different if they have the same [Fe/H], [α/Fe] and mass, but a different He abundance (Y).

Some effects include:• Variations in luminosity (L),

effective temperatures (Teff), and surface gravity (g).

• Faster evolution for higher Y.

The problem is that maybe Y ≠ Yp + ΔY/ΔZ x Z

as happens in some globular clusters.

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Y ≠ Yp + ΔY/ΔZ x ZThe CMD of some GCs show they are not simple stellar populations. In some cases implying Y ≠ Yp + ΔY/ΔZ x Z .

NGC 2808 (Piotto et al. 2007)

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Outline

• Introduction

• Determination of Y– Theoretical models (PGPUC)– Method– Comparison

• Application

• Summary

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Theoretical Models

For more information see:Valcarce, Catelan, & Sweigart (2012, ArXiv:astro-ph/1208.5127)

PGPUC stellar evolutionary code: updated version of the code of Sweigart (1971 – 1998), that is a highly modified version of the code created by Schwarzschild & Härm (1965).

Evolutionary Tracks:Grevesse & Sauval (1998) chemical composition.7 masses ( 0.5 ≤ M/Mʘ ≤ 1.1 )7 helium abundances ( 0.230 ≤ Y ≤ 0.370 )12 metallicities ( -2.00 ≤ [Fe/H] ≤ 0.75 )2 alpha-elements distributions ( [α/Fe]=0.0, 0.3 )

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Method for Determining Y

For a star with a given chemical composition only one evolutionary track reproduces Mbol and Teff at the same time.

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Method for Determining Y

For a star with a given chemical composition only one evolutionary track reproduces Mbol and Teff at the same time.

However, if Y is unknown several evolutionary tracks with the same [Fe/H] pass through the same point.

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Method for Determining Y

→ Another observable is required to solve this mathematical problem.

For a star with a given chemical composition only one evolutionary track reproduces Mbol and Teff at the same time.

However, if Y is unknown several evolutionary tracks with the same [Fe/H] pass through the same point.

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Since the stellar mass (M) is different for each Y at the same Mbol—Teff, the spectroscopic surface gravity (g) can be used to determine Y.

If Y is known, it is straightforward to determine the other stellar properties (Z, M, Age).

However, the precision in the measurement of g have to be really high to constrain them.

Method for Determining Y

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Method for Determining Y

Since the stellar mass (M) is different for each Y at the same Mbol—Teff, the spectroscopic surface gravity (g) can be used to determine Y.

If Y is known, it is straightforward to determine the other stellar properties (Z, M, Age).

However, the precision in the measurement of g have to be really high to constrain them.

log g = 4.53 ± 0.06

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Because this method require 3 parameters (Mbol , Teff, and log g), we

use the observational results listed in Casagrande et al. (2006).

Low-mass MS stars • -2.0 ≤ [Fe/H] ≤ +0.4

with σ[Fe/H] ≤ ±0.15 dex• 4400 ≤ Teff[K] ≤ 6400

with σTeff ≤ ±100 K• 4.1 ≤ log g ≤ 5.0

with σlog g ≤ ±0.20 dex

Comparison: Observational Data

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Because this method require 3 parameters (Mbol , Teff, and log g), we

use the observational results listed in Casagrande et al. (2006).

Low-mass MS stars • -2.0 ≤ [Fe/H] ≤ +0.4

with σ[Fe/H] ≤ ±0.15 dex• 4400 ≤ Teff[K] ≤ 6400

with σTeff ≤ ±100 K• 4.1 ≤ log g ≤ 5.0

with σlog g ≤ ±0.20 dex

Comparison: Observational Data

Yp

Casagrande et al. (2007)

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Comparison: ΔY/ΔZ from nearby stars

Casagrande et al. (2007) determined Y assuming all stars are 5 Gyr old.

Y=0.245 + ΔY/ΔZ x Z with ΔY/ΔZ=2.0

Yp

If we assume all stars are 5 Gyr old, we also find helium abundances below the primordial value.

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Comparison: ΔY/ΔZ from nearby stars

Casagrande et al. (2007) determined Y assuming all stars are 5 Gyr old.

Y=0.245 + ΔY/ΔZ x Z with ΔY/ΔZ=2.0

t < 13.5 Gyr t > 13.5 GyrInterpolated Extrapolated

However, when we use our method (age is not constant) metal poor stars show more realistic Y values.

Yp

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Comparison: ΔY/ΔZ from nearby stars

Casagrande et al. (2007) determined Y assuming all stars are 5 Gyr old.

Y=0.245 + ΔY/ΔZ x Z with ΔY/ΔZ=2.0

t < 13.5 Gyr t > 13.5 GyrInterpolated Extrapolated

Mass Limit ≈ 0.75 Mʘdue to the “classic radius problem” of low mass stars (e.g., Feiden & Chaboyer 2012).

Yp

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Outline

• Introduction

• Determination of Y– Theoretical models (PGPUC)– Method– Comparison

• Application

• Summary

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Application

Baumann et al. (2010)

Baumann et al. (2010) study the lithium abundances in nearby stars with solar properties.

• -0.4 ≤ [Fe/H] ≤ +0.3 with σ[Fe/H] ≤ ±0.025 dex

• 5600 ≤ Teff[K] ≤ 6100 with σTeff ≤ ±40 K

• 4.0 ≤ log g ≤ 4.6 with σlog g ≤ ±0.06 dex

They determined stellar masses and ages using the theoretical Teff vs log g diagram together with Y2 isochrones (Y=0.23+0.20xZ, Yi et al. 2001).

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

We use our method (Y ≠ Yp +ΔY/ΔZ x Z) to determine the fundamental properties of the stars of Baumann et al. (2010): Y, Z, M, and age.

Application

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

When a Y-Z relation is used instead of assuming an unknown Y, there are differences in masses and ages around ≈ 0.02 Mʘ and ≈ 2 Gyr.

TW: This work with Y ≠ Yp +ΔY/ΔZ x Z

B10: Baumann et al. (2010) with Y = Yp +ΔY/ΔZ x Z

Application

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

www2.astro.puc.cl/pgpuc/

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Outline

• Introduction

• Determination of Y– Theoretical models (PGPUC)– Method

• Testing the Method– Observational Data– ΔY/ΔZ from nearby stars

• Summary

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

Summary

We present a new method to determine the He abundance in nearby stars using Mbol, Teff, and g, that can be used to determine ΔY/ΔZ.

However, this method has mass limit around 0.75 Mʘ.

We show that assuming all stars are 5 Gyr old is not a good approximation (specially for metal poor stars), inducing an error Y determination.

When a Y-Z relation is assumed instead of a variable Y value, there will be differences of |ΔM|≈0.02 Mʘ and |ΔAge|≈2 Gyr.

Finally, we present the PGPUC online database for theoretical models for a wide range of M, Y, and Z (and soon [α/Fe]).

www2.astro.puc.cl/pgpuc/

XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012