The Helium Abundance of NGC 6791 from Modeling of Stellar Oscillations

TL;DR

This study uses detailed asteroseismology of Kepler data to precisely determine the helium abundance and age of the old, metal-rich open cluster NGC 6791, providing new insights into stellar evolution.

Contribution

It introduces a method to constrain helium abundance and age of cluster stars using individual mode frequencies from Kepler data, improving upon previous global parameter approaches.

Findings

Helium abundance of Y0=0.297±0.003 for NGC 6791

Cluster age determined to be 8.2±0.3 Gyr

Enhanced precision in stellar parameter estimation

Abstract

The helium abundance of stars is a strong driver of evolutionary timescales, however it is difficult to measure in cool stars. We conduct an asteroseismic analysis of NGC 6791, an old, metal rich open cluster that previous studies have indicated also has a high helium abundance. The cluster was observed by Kepler and has unprecedented lightcurves for many of the red giant branch stars in the cluster. Previous asteroseismic studies with Kepler data have constrained the age through grid based modeling of the global asteroseismic parameters ($\Delta\nu$ and $\nu_{\mathrm{max}}$). However, with the precision of Kepler data, it is possible to do detailed asteroseismology of individual mode frequencies to better constrain the stellar parameters, something that has not been done for these cluster stars as yet. In this work, we use the observed mode frequencies in 27 hydrogen shell burning red giants to better constrain initial helium abundance ($Y_0$) and age of the cluster. The distributions of helium abundance and age for each individual red giant are combined to create a final probability distribution for age and helium abundance of the entire cluster. We find a helium abundance of $Y_0=0.297\pm0.003$ and a corresponding age of $8.2\pm0.3$ Gyr.

Tables

Table 1. Table 1 Binary star parameters

	V18	V18	V20	V20
	Primary	Secondary	Primary	Secondary
Mass [$M_{\odot }$]	0.9955$\pm$0.0033	0.9293$\pm$0.0032	1.0868$\pm$0.0039	0.8276$\pm$0.0022
Radius [$R_{\odot }$]	1.1011$\pm$0.0068	0.9708$\pm$0.0089	1.397$\pm$0.013	0.7813$\pm$0.0053
Teff [K]	5600$\pm$95	5430$\pm$125	5645$\pm$95	4860$\pm$125
$\left[\text{Fe/H}\right]$	0.31$\pm$0.06	0.22$\pm$0.10	0.26$\pm$0.06	$\cdots$

Table 2. Table 2 Global asteroseismic and spectroscopic properties of target red giants.

KIC	${\nu }_{\text{text}max}$	$\Delta \nu$	$T_{\mathrm{eff}}$	[Fe/H]a	RVa
	$\mu \text{Hz}$	$\mu \text{Hz}$	K	dex	km/s
2436814	25.56$\pm$0.04	3.11$\pm$0.03	4289$\pm$100
2436824	34.26$\pm$0.13	3.85$\pm$0.04	4324$\pm$100
2436900	35.67$\pm$0.18	4.02$\pm$0.04	4403$\pm$78	0.40$\pm$0.02	-48.37
2436458	35.87$\pm$0.24	4.14$\pm$0.03	4340$\pm$100
2435987	36.26$\pm$0.20	4.19$\pm$0.04	4434$\pm$100	0.38$\pm$0.02	-43.75
2436097	40.53$\pm$0.22	4.54$\pm$0.04	4365$\pm$100
2437240	45.58$\pm$0.22	4.87$\pm$0.05	4440$\pm$100
2437402	46.09$\pm$0.26	4.82$\pm$0.05	4414$\pm$100
2570518	46.48$\pm$0.16	4.94$\pm$0.05	4496$\pm$71	0.38$\pm$0.02	-48.88
2569618	56.01$\pm$0.16	5.68$\pm$0.07	4479$\pm$81	0.40$\pm$0.02	-46.12
2436540	57.31$\pm$0.28	5.82$\pm$0.07	4492$\pm$83	0.41$\pm$0.02	-48.60
2436209	57.62$\pm$0.24	5.76$\pm$0.08	4498$\pm$83	0.43$\pm$0.02	-48.31
2438333	61.07$\pm$0.14	6.11$\pm$0.08	4522$\pm$80	0.43$\pm$0.02	-48.10
2438038	62.56$\pm$0.21	6.13$\pm$0.07	4450$\pm$100
2437488	65.30$\pm$0.19	6.31$\pm$0.09	4452$\pm$100
2570094	68.39$\pm$0.25	6.45$\pm$0.08	4485$\pm$100
2438140	71.37$\pm$0.24	6.72$\pm$0.10	4543$\pm$100
2437653	74.20$\pm$0.26	6.96$\pm$0.10	4588$\pm$83	0.42$\pm$0.02	-46.89
2570172	74.33$\pm$0.28	7.00$\pm$0.09	4536$\pm$85	0.44$\pm$0.02	-47.24
2436688	76.06$\pm$0.39	7.22$\pm$0.10	4537$\pm$86	0.43$\pm$0.02	-47.89
2437972	84.66$\pm$0.29	7.84$\pm$0.13	4543$\pm$100
2437781	85.15$\pm$0.29	7.74$\pm$0.16	4456$\pm$100
2437976	89.83$\pm$0.35	8.16$\pm$0.15	4525$\pm$100
2437957	92.71$\pm$0.38	8.36$\pm$0.20	4602$\pm$100
2437325	93.50$\pm$0.35	8.45$\pm$0.21	4557$\pm$100
2570244	106.31$\pm$0.33	9.17$\pm$0.27	4559$\pm$100
2437933	107.72$\pm$0.33	9.39$\pm$0.32	4610$\pm$100

Table 3. Table 3 Stellar model parameters

Parameter	Range	Step size
Main sequence models
$M$	0.8 $\to$ 1.12	0.003 $\to$ 0.02
$Y$	0.26 $\to$ 0.34	0.005, 0.01
Fe/H	0.15 $\to$ 0.55	0.05
$\alpha$	1.6 $\to$ 2.2	0.1
Red giant models
$M$	1.1 $\to$ 1.25	0.01
$Y$	0.28 $\to$ 0.32	0.005, 0.01
Fe/H	0.25 $\to$ 0.45	0.05
$\alpha$	1.7 $\to$ 2.1	0.1

Equations

$$B(\nu )=\sum _{i=1}^3\frac{\xi {\sigma }_i^2/{\nu }_{0,i}}{1+(\nu /{\nu }_{0,i}{)}^4}+W,$$

$$G(\nu )=H_0\exp \left[-\frac{(\nu -{\nu }_{\max }{)}^2}{2{\sigma }_g^2}\right],$$

$$P(\nu )=\frac{A^2/(\pi \Gamma )}{1+4/{\Gamma }^2(\nu -{\nu }_0{)}^2},$$

$${\chi }^2={\chi }_M^2+{\chi }_R^2+{\chi }_{T_{\mathrm{eff}}}^2+{\chi }_{[Fe/H]}^2,$$

$${\chi }^2=\frac{1}{3}\left({\chi }_{\mathrm{ast}}^2+{\chi }_{T_{\mathrm{eff}}}^2+{\chi }_{[Fe/H]}^2\right),$$

$${\chi }_{\mathrm{ast}}^2=\frac{1}{N}\sum _i\frac{({\nu }_{\mathrm{obs},i}-{\nu }_{\mathrm{model},i}{)}^2}{{\sigma }_i^2},$$

Full text

1. Introduction

As the second most abundant element, helium provides valuable insight into many astrophysical situations. The helium abundance of stars has a direct link to age, such that stars evolve more quickly, and at a higher temperature and luminosity, with a larger helium abundance. This leads to a red giant branch that is hotter than one with lower helium content (Salaris et al., 2006). The study of helium can also allow us some insight into chemical evolution in the galaxy. Helium abundance is particularly difficult to measure in stars cooler than 12000 K, where the lines are very weak. Helioseismic measurements of helium abundance for the Sun (Däppen et al., 1991; Vorontsov et al., 1991; Basu & Antia, 1995, 2004), 16 Cyg (Verma et al., 2014), and HD176465 (Gai et al., 2018) are the only individual stellar measurements of helium abundance in cooler stars, although a few others have been analyzed (Verma et al., submitted).

Stellar clusters are a unique setting in which all members share the same age and composition. This enables us to study many individual stars to determine cluster properties with better precision. NGC 6791 is an old ($\sim 8$ Gyr) and metal rich ([Fe/H]$\sim+0.4$) open cluster. The combination of old age and high metallicity makes it a very interesting place to study the helium abundance. There have been many studies of the cluster and extensive work has been done to study the age of the cluster through various techniques including isochrone fitting (Harris & Canterna, 1981; Anthony-Twarog & Twarog, 1985; Stetson et al., 2003), binaries (Brogaard et al., 2011, 2012, hereafter B2012), white dwarfs (Bedin et al., 2005, 2008; García-Berro et al., 2010), and asteroseismology (Basu et al., 2011), however, not much has been done regarding helium specifically. Brogaard et al. (2011), as part of their analysis, had noted that the helium abundance of the cluster from their isochrones was likely super-solar, with a value of $Y_{0}\sim 0.30$.

Asteroseismology is a unique tool to study the interiors of stars and derive fundamental parameters, such as mass and radius, with very high precision. In conjunction with a set of reasonable stellar models, we are able to determine the properties of stars, including ages, to very high precision using the information contained in the oscillations. Thus, asteroseismic modeling of stars in clusters provides an ideal method to examine the helium abundance of the cluster in detail, especially for cool stars where traditional methods such as spectroscopy are limited.

In NGC 6791 specifically, Hekker et al. (2011a) examined the global properties of giants in the cluster, such as the mass and radius distributions, through an asteroseismic analysis of the red giants, using only the global asteroseismic parameters. By using some of the extra information contained in individual frequencies, Corsaro et al. (2012) determined the period spacing of observed modes as a way to distinguish between red clump and red giant branch stars. However, there as yet are no studies that approach the cluster by modeling the oscillations of individual stars directly.

Modeling of the individual oscillation modes in stars across the HR diagram is not a new idea, however until recently the observational data did not exist. With new space-based satellites such as CoRoT (Baglin et al., 2006) and Kepler (Borucki et al., 2010), solar-like oscillations were exposed in thousands of red giants (Hekker et al., 2009; Kallinger et al., 2010b, a; Bedding et al., 2010; Huber et al., 2010; Hekker et al., 2011b). The potential for the discovery of many more oscillating stars exists with current and forthcoming missions such as TESS (Ricker et al., 2015) and PLATO (Rauer et al., 2014). Solar-like oscillations arise in stars with outer convective layers. The oscillations are stochastically driven by the turbulent convection in the outer layers. There are several examples of asteroseismic modeling applied to main sequence stars (Miglio & Montalbán, 2005; Lebreton & Goupil, 2014; Metcalfe et al., 2014; Appourchaux et al., 2015; Roxburgh, 2016; Silva Aguirre et al., 2017; Creevey et al., 2017; White et al., 2017; Bazot et al., 2018), and recently to several red giants (Miglio et al., 2010; Pérez Hernández et al., 2016; Triana et al., 2017; Ball et al., 2018).

In this work we examine the helium abundance in NGC 6791 through two different approaches. First, we model the eclipsing binaries of B2012, taking into account a wide range of initial helium abundances in a thorough search through a fine grid of stellar evolution models. And secondly, with an asteroseismic study of the red giants in the cluster. The subgiants and main sequence stars of NGC 6791 are too faint for asteroseismic detections with Kepler. We fitted the oscillation frequencies of 27 red giants and match them to frequencies computed from stellar evolution models. Finally, we use the fact that as cluster members, all stars should have the same age and initial composition to do a joint analysis of both helium abundance and age.

The rest of our paper is organized as follows: In Section 2 we layout our target selection as well as describe the global asteroseismic parameter determination and the individual frequency fitting. In Section 3 we explain the range of parameters and choice of physics included in our models. Section compares our models along the main sequence to the results obtained by B2012 and we discuss our results obtained from the red giants. We conclude with a short summary in Section 5.

2. Data & Target Selection

2.1. Eclipsing Binaries

We used the two eclipsing binary star systems in the cluster previously studied by B2012 to test our models and confirm their results. They span a large range of masses along the main sequence up to the turnoff; their properties are summarized from B2012 in Table 1. The secondary star in V20 does not have an independently measured metallicity, so we assumed [Fe/H]$=0.26$, the same as the primary. There is no asteroseismic data for these stars, however, as we shall show, the dynamical and spectroscopic parameters are sufficient to constrain the helium abundance.

2.2. Red giant data

2.2.1 Asteroseismic data

NGC 6791 was observed for four years with the Kepler satellite, which has provided remarkable light curves for many of the stars in the field. We retrieved long cadence (30 min) light curves for Q1-Q17 from the Kepler Asteroseismic Science Operations Center (KASOC)111http://kasoc.phys.au.dk/ which produces light curves and power spectra that have been processed for asteroseismology specifically (Handberg & Lund, 2014). From the red giants previously identified in the cluster (Stello et al., 2011), we chose stars with a good signal-to-noise ratio and clearly visible modes in the power spectrum. The stars chosen for this study are highlighted in Fig. 1, which shows a color-magnitude diagram of the cluster with the photometry of Stetson et al. (2003). Their global asteroseismic parameters and available spectroscopic data are listed in Table 2.2.1. We considered only stars on the red giant branch.