J/ApJ/780/159 Rotation-mass-age relationship of old field stars (Epstein+, 2014) ================================================================================ How good a clock is rotation? The stellar rotation-mass-age relationship for old field stars. Epstein C.R., Pinsonneault M.H. =2014ApJ...780..159E ================================================================================ ADC_Keywords: Clusters, open ; Stars, ages ; Stars, masses ; Effective temperatures Keywords: stars: evolution - stars: late-type - stars: rotation Abstract: The rotation-mass-age relationship offers a promising avenue for measuring the ages of field stars, assuming the attendant uncertainties to this technique can be well characterized. We model stellar angular momentum evolution starting with a rotation distribution from open cluster M37. Our predicted rotation-mass-age relationship shows significant zero-point offsets compared to an alternative angular momentum loss law and published gyrochronology relations. Systematic errors at the 30% level are permitted by current data, highlighting the need for empirical guidance. We identify two fundamental sources of uncertainty that limit the precision of rotation-based ages and quantify their impact. Stars are born with a range of rotation rates, which leads to an age range at fixed rotation period. We find that the inherent ambiguity from the initial conditions is important for all young stars, and remains large for old stars below 0.6M_{sun}_. Latitudinal surface differential rotation also introduces a minimum uncertainty into rotation period measurements and, by extension, rotation-based ages. Both models and the data from binary star systems 61 Cyg and {alpha} Cen demonstrate that latitudinal differential rotation is the limiting factor for rotation-based age precision among old field stars, inducing uncertainties at the ~2Gyr level. We also examine the relationship between variability amplitude, rotation period, and age. Existing ground-based surveys can detect field populations with ages as old as 1-2Gyr, while space missions can detect stars as old as the Galactic disk. In comparison with other techniques for measuring the ages of lower main sequence stars, including geometric parallax and asteroseismology, rotation-based ages have the potential to be the most precise chronometer for 0.6-1.0M_{sun}_stars. Description: The rotation-mass-age relationship offers a promising avenue for measuring the ages of field stars. We model stellar angular momentum evolution starting with a rotation distribution from open cluster M37. File Summary: -------------------------------------------------------------------------------- FileName Lrecl Records Explanations -------------------------------------------------------------------------------- ReadMe 80 . This file table2.dat 80 456 Median gyrochronology with uncertainties for a modified Kawaler (1988ApJ...333..236K) and Reiners & Mohanty (2012ApJ...746...43R) wind law -------------------------------------------------------------------------------- See also: J/ApJ/747/51 : Lagoon Nebula stars. I. Rotation periods (Henderson+, 2012) J/MNRAS/424/11 : Rotation of field stars from CoRoT data (Affer+, 2012) J/ApJ/743/48 : Stellar rotation per. and X-ray luminosities (Wright+, 2011) J/ApJ/733/L9 : Stellar rotation for 71 NGC 6811 members (Meibom+, 2011) J/MNRAS/413/2218 : Stellar rotation in Hyades and Praesepe (Delorme+, 2011) J/MNRAS/408/475 : HATNet Pleiades Rotation Period Catalogue (Hartman+, 2010) J/ApJ/695/679 : Stellar rotation in M35 (Meibom+, 2009) J/ApJ/691/342 : griBVI photometry in M37 (Hartman+, 2009) J/ApJ/687/1264 : Age estimation for solar-type dwarfs (Mamajek+, 2008) J/ApJ/675/1233 : gri photometry in M37 (NGC 2099) (Hartman+, 2008) J/A+A/446/267 : Stellar latitudinal differential rotation (Reiners+, 2006) J/A+A/397/147 : Activity-rotation relationship in stars (Pizzolato+ 2003) J/PAZh/25/115 : A study of the open cluster NGC 6811 (Glushkova+, 1999) J/A+A/331/81 : Hyades membership (Perryman+ 1998) J/ApJS/91/625 : ROSAT survey of the Pleiades (Stauffer+ 1994) Byte-by-byte Description of file: table2.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 5 F5.2 Gyr Age [0.55/10] Age (M37 to main sequence turnoff, or the age of the Galactic disk, assumed to be t=10Gyr) (1) 7- 10 F4.2 Msun M [0.45/1.1] Star mass (2) 12- 15 F4.2 mag (B-V)0 [0.59/1.54] YREC isochrone (B-V) color index (3) 17- 20 I4 K Teff [3641/6008] YREC isochrone effective temperature (3) 22- 26 F5.2 d P10K [0.58/63.32] Modified Kawaler (1988ApJ...333..236K) law 10th percentile rotation period (4) 28- 32 F5.2 d P25K [0.77/65.05] Modified Kawaler (1988ApJ...333..236K) law 25th percentile rotation period (4) 34- 38 F5.2 d P50K [2.09/71.85] Modified Kawaler (1988ApJ...333..236K) law 50th percentile rotation period (4) 40- 44 F5.2 d P75K [7.04/81.08] Modified Kawaler (1988ApJ...333..236K) law 75th percentile rotation period (4) 46- 50 F5.2 d P90K [7.81/83.54] Modified Kawaler (1988ApJ...333..236K) law 90th percentile rotation period (4) 52- 56 F5.2 d P10RM [0.58/41.06] Reiners & Mohanty (2012ApJ...746...43R) law 10th percentile rotation period (4) 58- 62 F5.2 d P25RM [0.77/41.07] Reiners & Mohanty (2012ApJ...746...43R) law 25th percentile rotation period (4) 64- 68 F5.2 d P50RM [2.09/41.1] Reiners & Mohanty (2012ApJ...746...43R) law 50th percentile rotation period (4) 70- 74 F5.2 d P75RM [7.04/41.11] Reiners & Mohanty (2012ApJ...746...43R) law 75th percentile rotation period (4) 76- 80 F5.2 d P90RM [7.81/41.13] Reiners & Mohanty (2012ApJ...746...43R) law 90th percentile rotation period (4) -------------------------------------------------------------------------------- Note (1): We model stellar angular momentum evolution starting with a rotation distribution from open cluster M37 (NGC 2099). The vast majority of field stars will be older than 500Myr, which makes this simpler approach attractive for examining field star rotation studies. We selected M37 because it is the cluster with the largest homogeneous set of measured rotation periods spanning a wide color range in the intermediate age range. For our base case, we adopt a modified Kawaler (1988ApJ...333..236K) angular momentum loss model. We distill the M37 distribution into a mass-dependent median rotation period and use the interquartile region to measure of the period uncertainty due to the spread of initial rotation rates. We evolve the smoothed 25^th^ and 75^th^ percentile curves (defined in Section 3.1.1) forward in time until we reach either the age of the Galactic disk, which we take to be t=10Gyr, or when a model corresponding to that mass leaves the main sequence. The main sequence turnoff is defined as the point when the core hydrogen abundance drops below X_C_=10^-3^. Note (2): The old open clusters have sparse data at the low mass end. We therefore restrict our calculations to the mass range of 0.4<=M/M_{sun}<=1.2M, sampled in equally spaced 0.05M_{sun}_. Stars in M37 (used to define the initial rotation distribution; Section 2.1.1) are excluded if their mass lies outside of this restricted range where our angular momentum loss model is valid. Note (3): (B-V) and T_eff_ are computed at fixed mass using a YREC isochrone of the appropriate age and [Fe/H]=+0.045. Note (4): To simulate stellar angular momentum loss, we adopt as our preferred model a modified Kawaler wind law (Kawaler 1988ApJ...333..236K; Chaboyer et al., 1995ApJ...441..865C; Sills et al., 2000ApJ...534..335S; see Eq.(1) in section 2.3.1 for details about this law). Reiners & Mohanty (2012ApJ...746...43R) present a new braking law that pivots on two major deviations from the modified Kawaler law (see Eq.(3) in section 2.3.2 for details about this law). As we have two predictions for how M37's rotation distribution evolves in time, we need to characterize their median trend and range. To quantify the width of the rotation distribution, we adopt the interquartile range in period: the middle 50% of stars in the observed M37 cluster mass-rotation distribution lie within the interquartile band shown in Figure 4 and we use this to characterize the spread between fast and slow rotators. For comparison, we also consider the 10^th^ and 90^th^ percentile rotation periods because they set much broader bounds than the interquartile region, but are not overly sensitive to outliers in the rotation distribution. -------------------------------------------------------------------------------- History: From electronic version of the journal ================================================================================ (End) Greg Schwarz [AAS], Sylvain Guehenneux [CDS] 30-Jan-2015