1. 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 16 th, 2012

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

3. Outline Introduction Determination of Y –Theoretical models (PGPUC) –Method –Comparison Application Summary XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 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 = Y p + 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. Y p : primordial helium abundance ΔY/ΔZ: helium-to-metal enrichment ratio XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 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 (T eff ), and surface gravity (g). Faster evolution for higher Y. XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 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 (T eff ), and surface gravity (g). Faster evolution for higher Y. The problem is that maybe Y ≠ Y p + ΔY/ΔZ x Z as happens in some globular clusters. XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

7. Y ≠ Y p + ΔY/ΔZ x Z The CMD of some GCs show they are not simple stellar populations. In some cases implying Y ≠ Y p + ΔY/ΔZ x Z. NGC 2808 (Piotto et al. 2007) XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

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

9. 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/M ʘ ≤ 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 16 th, 2012

10. Method for Determining Y For a star with a given chemical composition only one evolutionary track reproduces M bol and T eff at the same time. XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

11. Method for Determining Y For a star with a given chemical composition only one evolutionary track reproduces M bol and T eff 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 16 th, 2012

12. 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 M bol and T eff 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 16 th, 2012

13. Since the stellar mass (M) is different for each Y at the same M bol —T eff, 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 16 th, 2012

14. Method for Determining Y Since the stellar mass (M) is different for each Y at the same M bol —T eff, 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 16 th, 2012

15. Because this method require 3 parameters (M bol, T eff, 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 ≤ T eff [K] ≤ 6400 with σ Teff ≤ ±100 K 4.1 ≤ log g ≤ 5.0 with σ log g ≤ ±0.20 dex Comparison: Observational Data XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

16. Because this method require 3 parameters (M bol, T eff, 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 ≤ T eff [K] ≤ 6400 with σ Teff ≤ ±100 K 4.1 ≤ log g ≤ 5.0 with σ log g ≤ ±0.20 dex Comparison: Observational Data YpYp Casagrande et al. (2007) XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

17. 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 YpYp 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 16 th, 2012

18. 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 Gyrt > 13.5 Gyr InterpolatedExtrapolated However, when we use our method (age is not constant) metal poor stars show more realistic Y values. YpYp XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

19. 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 Gyrt > 13.5 Gyr InterpolatedExtrapolated Mass Limit ≈ 0.75 M ʘ due to the “classic radius problem” of low mass stars (e.g., Feiden & Chaboyer 2012). YpYp XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

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

21. 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 ≤ T eff [K] ≤ 6100 with σ Teff ≤ ±40 K 4.0 ≤ log g ≤ 4.6 with σ log g ≤ ±0.06 dex They determined stellar masses and ages using the theoretical T eff vs log g diagram together with Y 2 isochrones (Y=0.23+0.20xZ, Yi et al. 2001). XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

22. We use our method (Y ≠ Y p +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 16 th, 2012

23. When a Y-Z relation is used instead of assuming an unknown Y, there are differences in masses and ages around ≈ 0.02 M ʘ and ≈ 2 Gyr. TW: This work with Y ≠ Y p +ΔY/ΔZ x Z B10: Baumann et al. (2010) with Y = Y p +ΔY/ΔZ x Z Application XXXVII SAB meeting Águas de Lindóia, Brazil, Oct 16 th, 2012

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

26. Summary We present a new method to determine the He abundance in nearby stars using M bol, T eff, and g, that can be used to determine ΔY/ΔZ. However, this method has mass limit around 0.75 M ʘ. 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 M ʘ 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 16 th, 2012