On the Helium-Metal Fraction Slope &Delta Y/&Delta Z

Eric Mamajek (UR)

Last updated: 2 November 2010

Summary

Based on a literature search of published helium-metal fraction ratios (&Delta Y/&Delta Z or dY/dZ), it appears that the mean value of this parameter is determined to roughly ~10%. The value &Delta Y/&Delta Z = 2.2 ± 0.2 is consistent with the majority of published estimates, and more importantly with several recent independent estimates which depend on very different samples (nearby K dwarfs, eclipsing binaries, and extragalactic HII regions).

Data

I am not an expert on efforts to measure the helium-metal fraction slope (&Delta Y/&Delta Z), but I am now interested in this parameter as my AST 565 class is producing stellar evolutionary tracks using the TYCHO stellar evolution code. As main sequence lifetimes for stars are ultimately set by how much helium is in their cores, the helium-metals ratio is important for determining the ages of stellar populations.
If one assumes a linear relation between the helium and metal content of a star, then:

&Delta Y / &Delta Z = (Y - Yp)/Z

Y(Z) = Yp + (Z/ZSun)(YSun - Yp)

then Y, Yp, and YSun are the stellar, primordial (Big Bang), and protosolar (initial solar) helium abundances, respectively. Z and ZSun are the stellar and protosolar (initial solar) metal mass fractions, respectively (see discussion in Lebreton et al. 1999). Note that "metallicity" [Fe/H] is connected to these terms by:

[Fe/H] = log(Z/X) - log(Z/X)Sun
In all honesty, I was surprised to see how poorly constrained the parameter &Delta Y/&Delta Z is. Here I tabulate the published values of &Delta Y/&Delta Z that I was able to find in the literature (at least back to ~1990). The table is ordered by published &Delta Y/&Delta Z estimates. "Yp" indicates the adopted primordial helium abundance used by the authors (if given). Links are provided to the bibliographic information for the papers using ADS. Particularly interesting or useful studies (for their class of target) are highlighted green.

&Delta Y/&Delta Z Reference Notes
1.1 ± 1.4 Fukugita & Kawasaki 2006 reanalysis of Izotov-Thuan extragal. HII region data
1.33 ± 0.36 Peimbert 2003 30 Dor (Yp = 0.2475)
1.41 ± 0.62 Balser 2006 Two galactic HII regions: M17 & S206 (radio recombination lines)
1.46 ± 0.60 Peimbert, Carigi & Peimbert 2001 reanalysis of Thuan & Izotov 1998 data
1.64 ± 0.56 Peimbert 2003 Sun-to-primordial (Yp=0.2475)
1.7 ± 0.9 Izotov et al. 1997 27 supergiant HIII regions in 23 low-z compact blue galaxies
~1.7-2.2 (1.95?) Serenelli & Basu 2010 helioseismology constraints + WMAP Big Bang primordial Yp
1.97 ± 0.41 Carigi & Peimbert 2008 M17 - z-rich Galactic HII region
~2.0 Lacy et al. 2000 eclipsing binary FS Mon
2 ± 1 Chaboyer et al. 1999 NGC 6791
2.1 ± 0.4 Jimenez et al. 2003 Hipparcos K dwarfs with spectroscopic metallicities.
2.1 ± 0.9 Casagrande et al. 2007 nearby K dwarfs (mostly same authors as Jimenez et al. 2003)
2.15 ± 0.45 Peimbert & Peimbert 2002 not listed in abstract, but quoted in Peimbert 2003 (Yp=0.2475)
2.19 ± 0.39 Izotov et al. 2007 86 low-z extragalactic HII regions (Yp=0.2472, 0.2516 for two HeI emissivities); using Porter et al. emissivities
2.2 ± 0.8 Ribas et al. 2000 eclipsing binaries (Yp = 0.225 ± 0.013)
2.38 ± 0.45 Izotov et al. 2007 86 low-z extragalactic HII regions (Yp=0.2472, 0.2516 for two HeI emissivities); using Benjamin et al. 2002 emissivities
2.3 ± 1.0
2.4 ± 1.0
2.4 ± 1.0
 Thuan & Izotov 1998
Izotov & Thuan 1999
Thuan & Izotov 2002		 seems like same abstract and sample over and over... (combined into one entry) 54 supergiant HII regions in 50 low-z blue compact galaxies. Presumably Izotov & Thuan 2004 has obsoleted these values?
2.5 Peimbert 1993 M8, M17, M42
2.66 ± 0.78 Peimbert et al. 2000
Peimbert et al. 2002		 NGC 346; value attributed to both by Peimbert 2003 (Yp=0.2475)
2.8 ± 0.5 Izotov & Thuan 2004 82 HII regions in 76 blue compact galaxies
3 ± 2 Pagel & Portinari 1998 fine structure in the MS of nearby Hipparcos stars
>3 Chiappini & Maciel 1994 PN, Gal & extragal HII regions, blue compact galaxies
4 ± 1 Pagel et al. 1992 "HII galaxies"
5.8 ± (4.4 or 1.7) Izotov et al. 1994 10 low-z blue compact galaxies. presumably this value is outdated by the later Izotov-Thuan papers.

Executive Summary

For the 23 published values, the true median is 2.19 ± 0.12 (error in median; Gott et al. 2001), the mean is 2.22 ± 0.13 (error in mean), and the "probit" mean is 2.21 (Lutz & Upgren 1980). Note that not all of the published estimates can be considered independent (the Izotov-Thuan papers alone, and reanalysis by other authors accounts for at least 10 of the references!) so the uncertainty in the mean/median is not really a useful metric of uncertainty. Notably, all published &Delta Y/&Delta Z values since 2000 lie between 1 and 3, so at least a mean can be quoted to better than ±1.

Arguably, the best modern estimates come from analyses of large samples of: nearby K dwarfs (2.1 ± 0.4, 2.1 ± 0.9; Jimenez et al. 2003, Casagrande et al. 2007), low-z extrgalactic HII regions (2.19 ± 0.39, 2.38 ± 0.45; same sample, different assumed emissivities; Izotov et al. 2007), and eclipsing binaries (2.2 ± 0.8; Ribas et al. 2000). These values are independent, and agree very well with one another -- all in the range 2.1-2.38.