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The Age-Mass-Metallicity-Activity Relation for Solar-Type Stars: Comparisons with Asteroseismology and the NGC 188 Open Cluster D

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The Age-Mass-Metallicity-Activity Relation for Solar-Type Stars: Comparisons with Asteroseismology and the NGC 188 Open Cluster D A&A 594, L3 (2016) Astronomy DOI: 10.1051/0004-6361/201629233 & c ESO 2016 Astrophysics Letter to the Editor The age-mass-metallicity-activity relation for solar-type stars: comparisons with asteroseismology and the NGC 188 open cluster D. Lorenzo-Oliveira1, G. F. Porto de Mello1, and R. P. Schiavon2 1 Universidade Federal do Rio de Janeiro, Observatório do Valongo, Ladeira do Pedro Antonio 43, CEP: 20080-090 Rio de Janeiro, RJ, Brazil e-mail: [diego;gustavo]@astro.ufrj.br 2 Astrophysics Research Institute, Liverpool John Moores University, Liverpool, L3 5RF, UK e-mail: [email protected] Received 3 July 2016 / Accepted 21 September 2016 ABSTRACT 0 Context. The Mount Wilson Ca ii index log(RHK) is the accepted standard metric of calibration for the chromospheric activity versus age relation for FGK stars. Recent results claim its inability to discern activity levels, and thus ages, for stars older than ∼2 Gyr, which would severely hamper its application to date disk stars older than the Sun. Aims. We present a new activity-age calibration of the Mt. Wilson index that explicitly takes mass and [Fe/H] biases into account; these biases are implicit in samples of stars selected to have precise ages, which have so far not been appreciated. Methods. We show that these selection biases tend to blur the activity-age relation for large age ranges. We calibrate the Mt. Wilson index for a sample of field FGK stars with precise ages, covering a wide range of mass and [Fe/H], augmented with data from the Pleiades, Hyades, M 67 clusters, and the Ursa Major moving group. 0 Results. We further test the calibration with extensive new Gemini/GMOS log(RHK) data of the old, solar [Fe/H] clusters, M 67 and NGC 188. The observed NGC 188 activity level is clearly lower than M 67. We correctly recover the isochronal age of both clusters and establish the viability of deriving usable chromospheric ages for solar-type stars up to at least ∼6 Gyr, where average errors are ∼0.14 dex provided that we explicitly account for the mass and [Fe/H] dimensions. We test our calibration against asteroseismological ages, finding excellent correlation (ρ = +0:89). We show that our calibration improves the chromospheric age determination for a wide range of ages, masses, and metallicities in comparison to previous age-activity relations. Key words. stars: late-type – stars: activity – stars: chromospheres – open clusters and associations: individual: M 67 – open clusters and associations: individual: NGC 188 1. Introduction of the Galactic disk, thereby negating its usefulness as a tool to investigate Galactic evolution. Here we analyze the presence, in Stellar ages are fundamental parameters in our understanding of the CA-age relation, of mass and metallicity ([Fe=H]) biases that the chemo-dynamical evolution of the Galaxy and other stel- are implicit in conventional methods of selecting solar-type stars lar systems as well as exoplanetary systems. Ages, which are with precise isochronal ages. We show that these biases have very difficult to gauge, are usually only estimated through meth- masked structural complexity in the CAR and present a new cal- ods optimized to restricted classes of stars since these are in- ibration explicitly relating age, activity, mass, and [Fe=H]. We direct parameters inferred from the time evolution of a range test this calibration against asteroseismological ages and new 0 of observational quantities that do not uniquely characterize Gemini data on the log(RHK) indexes of the M 67 and NGC 188 this range. Strong spectral lines are useful indicators of stel- clusters (ages 4.0 and 6.0 Gyr, respectively). As an extension of lar chromospheric activity (CA) that is physically linked to MH08 CAR, we provide the activity distribution expected for the efficiency of angular momentum evolution. The stellar ro- 6 Gyr solar metallicity stars anchored on 49 NGC 188 members tation and CA in single main-sequence stars decay monoton- (16× the M08 sample for NGC 188), constraining the activity ically with time, under the action of the torque produced by average and dispersion beyond the solar age. the magnetized stellar wind, as it is a potential indicator of age (Soderblom et al. 1991). The Mount Wilson (MW) project 2. Biases in the age-chromospheric activity relation (Baliunas et al. 1995) has been monitoring the widely used S in- The authors of MH08 pointed out a slight positive trend of CA dex, which is the ratio of the flux in the line cores of the Ca ii with color index (B − V) in the sense that hotter (more massive) H & K lines and two nearby continuum regions; this S index stars appear less active than cooler ones; yet it was not clear can be converted into the log(R0 ) index, which is defined as HK that this trend extended beyond the Hyades age. Also, it was the absolute line excess flux (line flux − photospheric flux) nor- proposed that the M 67 cluster presented the opposite trend of malized to the bolometic flux (Linsky et al. 1979; Noyes et al. that observed in younger clusters, suggesting that evolutionary 1984). The log(R0 ) is the standard metric in the literature to HK effects on color indices might affect the gauging of CA levels. retrieve stellar ages through CA-age relations (hereafter CAR, Indeed, as solar-type stars age away from the Zero Age Main e.g., Mamajek & Hillenbrand 2008, hereafter MH08). Sequence (ZAMS), Teff swings in the Hertzsprung-Russell (HR) Recent claims that the evolution of CA fluxes cannot be diagram are bound to introduce biases into the flux calibration of traced beyond ∼2 Gyr (Pace 2013) imply that the derivation of the CAR. The inclusion by MH08 of an explicit color correction CA ages is severely hampered for most of the age dispersion in their CAR hints at the presence of such degeneracy, possibly Article published by EDP Sciences L3, page 1 of4 A&A 594, L3 (2016) making standard age-activity calibrations not uniquely adequate for different levels CA. However, even though mass and/or color terms may be ex- plicitly incorporated into the CAR, a deeper reason for these cor- rections lies in their effects in the convective efficiency, which es- tablishes the theoretical connection between chromospheric and rotational evolution and is usually represented by the Rossby number (Barnes & Kim 2010). Noyes et al.(1984) found a strong correlation between the Rossby number (defined as the ratio of the rotational period and the convective overturn time 0 τC) and log(RHK) in FGK stars. Empirically, metallicity is ex- pected to affect τC, since stars that are more metal rich have deeper convection zones and thus longer τC, other parameters being equal. This structural connection was already hinted at by Lyra & Porto de Mello(2005) in their analysis of H α fluxes and Fig. 1. Upper panels: comparison of asteroseismological with chro- ages. However, such structural effects cannot be separated for the mospheric ages from our calibration (black circles) and MH08 (red case of the Ca ii lines from the intrinsic observed profile which, squares) for a sample of stars spanning a wide interval in age, mass, unlike Hα (Fuhrmann et al. 1993), responds directly to metal- and metallicity. The dashed line is the 1:1 relation. Lower panels: dif- licity. Thus metal-poor stars have shallower Ca ii profiles that ference between the age estimates ∆log(t) (log(tastero) − log(tchrom)) as a mimic high levels of chromospheric fill-in, and thus appear more function of [Fe/H]. The dashed lines stand for ±1σ chromospheric age uncertainty. active and younger than metal-rich stars at a given Teff, or mass (Rocha-Pinto & Maciel 1998). The selection of stars with precise ages automatically packs variety of sources, where the main sources are Arriagada(2011), these biases into stellar samples. Pace(2013, hereafter P13) se- Duncan et al.(1991), Gray et al.(2003), Gray et al.(2006), Henry et al.(1996), Isaacson & Fischer(2010), Jenkins et al. lected stars with small age uncertainties (<2 Gyr or σage/age <30%), from the Geneva-Copenhagen survey (GCS) of photo- (2011), Schröder et al.(2009), and Wright et al.(2004). Ages metric atmospheric parameters (Casagrande et al. 2011), in ad- and masses were inferred from the Yale isochrones (Kim et al. dition to data from clusters spanning from 0.5 to 6 Gyr. Pace 2002). 0 The age-mass-metallicity-activity relation (hereafter AM- crossed this sample with log(RHK) indices and reported the ab- sence of CA evolution beyond ∼2 Gyr. The difficulty in build- MAR) was derived from an iterated, re-weighted least-squares ing a sample of stars with precise ages is not only dependent on regression, yielding the quality of the atmospheric parameters. Demanding precise 0 log(t) = β0 + β1 log(RHK) + β2[Fe=H] ages implies that most stars in such a sample are more massive 0 2 than the Sun because of the need for a sizable detachment from + β3 log(M=M ) + β4 log(RHK) ; (1) the ZAMS to enable a reliable age determination. Besides, such where β0 = −56.01 ± 4.74; β1 = −25.81 ± 1.97; β2 = −0.44 ± a sample necessarily has a large metallicity range: young stars 0.06; β3 = −1.26 ± 0.25; and β4 = −2.53 ± 0.21. The standard are preferably more metal rich because of the age-metallicity deviation of the relation is ∼0.14 dex in log(age in years). Ac- relation, and possess deeper H & K profiles, thereby mimick- tivity is the most significant variable in the regression (>12σ) ing a more subdued CA.
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