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A New Technique to Measure Δ Y/ Δ Z

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 )

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A New Technique to Measure Δ Y/ Δ Z

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  1. A New Technique to Measure ΔY/ΔZ Main collaborators: J. R. de Medeiros (UFRN) M. Catelan (PUC) A. A. R. Valcarce (UFRN) XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  2. Outline • Introduction • Determination of Y • Theoretical models (PGPUC) • Method • Comparison • Application • Summary XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  3. Outline • Introduction • Determination of Y • Theoretical models (PGPUC) • Method • Comparison • Application • Summary XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  4. Introduction The 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

  5. 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

  6. 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

  7. Y ≠Yp + ΔY/ΔZ x Z The 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

  8. Outline • Introduction • Determination of Y • Theoretical models (PGPUC) • Method • Comparison • Application • Summary XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  9. Theoretical Models 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 ) For more information see: Valcarce, Catelan, & Sweigart (2012, ArXiv:astro-ph/1208.5127) XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  10. 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

  11. 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

  12. 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. → Another observable is required to solve this mathematical problem. XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

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

  14. Method for Determining Y log g = 4.53 ± 0.06 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. XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  15. Comparison: Observational Data 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 XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  16. Comparison: Observational Data 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 Yp Casagrande et al. (2007) XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  17. Comparison: ΔY/ΔZ from nearby stars Y=0.245 + ΔY/ΔZ x Z with ΔY/ΔZ=2.0 Casagrande et al. (2007) determined Y assuming all stars are 5 Gyr old. 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

  18. Comparison: ΔY/ΔZ from nearby stars Y=0.245 + ΔY/ΔZ x Z with ΔY/ΔZ=2.0 Casagrande et al. (2007) determined Y assuming all stars are 5 Gyr old. Yp t < 13.5 Gyr Interpolated Extrapolated t > 13.5 Gyr However, when we use our method (age is not constant) metal poor stars show more realistic Y values. XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  19. Comparison: ΔY/ΔZ from nearby stars Y=0.245 + ΔY/ΔZ x Z with ΔY/ΔZ=2.0 Casagrande et al. (2007) determined Y assuming all stars are 5 Gyr old. Yp t < 13.5 Gyr Interpolated Extrapolated t > 13.5 Gyr Mass Limit ≈ 0.75 Mʘ due to the “classic radius problem” of low mass stars (e.g., Feiden & Chaboyer 2012). XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  20. Outline • Introduction • Determination of Y • Theoretical models (PGPUC) • Method • Comparison • Application • Summary XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  21. Application 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). Baumann et al. (2010) XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

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

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

  24. www2.astro.puc.cl/pgpuc/ XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16th, 2012

  25. 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

  26. 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

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