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1. Introduction
The Gaia benchmark stars is a sample suitable for calibrating and validating automated pipelines, and their Teff, [Fe/H], and log g have been carefully estimated (Jofré et al. 2014; Heiter et al. 2015). Recently, we supplemented the work on the Gaia benchmark stars with an investigation of their ages (Sahlholdt et al. 2019).
Here we extend our work to include the solar-type subgiant star μ Herculis. For its parameters, we adopt Teff = 5560 ± 80 K and [Fe/H] = 0.28 ± 0.07 dex from spectrosocpy (Jofré et al. 2015) with uncertainties taken from Grundahl et al. (2017). This temperature is not based on the angular diameter and bolometric flux like for the Gaia benchmark sample; however, the temperature obtained by combining the interferometric radius with the photometric luminosity is consistent with the spectroscopic value (Grundahl et al. 2017). We adopt log g = 4.01 ± 0.02 dex from asteroseismic modeling of individual frequencies (Grundahl et al. 2017). We take the Hipparcos parallax of ϖ = 120.33 ± 0.16 mas (van Leeuwen 2007) and V = 3.42 ± 0.02. We estimate the age based on Bayesian isochrone fitting to either Teff, [Fe/H], and log g or to Teff, [Fe/H], parallax, and V. Additionally, we have searched the literature for age estimates dating back to 1997.
2. Results
All of the ages compiled and derived in this work are shown in Figure 1. We find no significant differences between the ages we derive using the magnitude or log g for a given set of isochrones. Between isochrones, our age estimates vary from about 7.5 to 8.5 Gyr. This is consistent with our previous finding that the lower limit on the accuracy of the age of a turn-off star is about 1 Gyr (for stars older than about 2 Gyr) (Sahlholdt et al. 2019).
Figure 1. Ages and HR diagrams for the star μ Her (HD 161797). (a) Ages collected from the literature (top panel), and ages determined in this work (bottom panel). Uncertainties on the ages are plotted when available; in some cases they are smaller than the symbol size. The vertical dashed line indicates the age of the universe. (b) Location of the star in (Teff, log g)-space (star symbol) with MIST isochrones of the given metallicity and ages (from left to right) of 0.5, 1, 3, 6, 10, and 15 Gyr. (c) The same as (b), but in (Teff, distance modulus)-space (for details see Sahlholdt et al. 2019).
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We found ages in the literature based on model fitting (Mallik et al. 2003; Valenti & Fischer 2005; Takeda 2007; Takeda et al. 2007; Ramírez et al. 2012; da Silva et al. 2015; Brewer et al. 2016; Baines et al. 2018; Deka-Szymankiewicz et al. 2018), chromochronology (Wright et al. 2004; Marsden et al. 2014), and asteroseismology (Yang & Meng 2010; Grundahl et al. 2017; Li et al. 2019). Estimates based on model fitting generally agree with those determined in this work. For the chromochronology estimates, Marsden et al. (2014) measured a lower activity level than Wright et al. (2004) leading to different ages. The asteroseismic estimate by Yang & Meng (2010) stands out because they misidentified the oscillation frequencies as shown by Grundahl et al. (2017) who had a longer time series. Li et al. (2019) used the same data as Grundahl et al. (2017) but considered more sources of systematic errors leading to a larger uncertainty.
In conclusion, based on current stellar models, the most likely age of μ Herculis is slightly below 8 Gyr in agreement with the latest asteroseismic analysis. We define a benchmark age for μ Herculis in the same manner as for the Gaia benchmark stars in Sahlholdt et al. (2019). We recommend using the range 7–8.5 Gyr as a benchmark age which is consistent with both the asteroseismic estimates and the estimates made in this work based on stellar surface parameters and different sets of stellar isochrones.
The authors were supported by the grant 2016-03412 from the Swedish Research Council. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.