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.
<Astrophys. J., 780, 159 (2014)>
=2014ApJ...780..159E 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☉. 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 α 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☉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 1988ApJ...333..236K) and
Reiners & Mohanty (2012ApJ...746...43R 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 1988ApJ...333..236K)
law 10th percentile rotation period (4)
28- 32 F5.2 d P25K [0.77/65.05] Modified Kawaler (1988ApJ...333..236K 1988ApJ...333..236K)
law 25th percentile rotation period (4)
34- 38 F5.2 d P50K [2.09/71.85] Modified Kawaler (1988ApJ...333..236K 1988ApJ...333..236K)
law 50th percentile rotation period (4)
40- 44 F5.2 d P75K [7.04/81.08] Modified Kawaler (1988ApJ...333..236K 1988ApJ...333..236K)
law 75th percentile rotation period (4)
46- 50 F5.2 d P90K [7.81/83.54] Modified Kawaler (1988ApJ...333..236K 1988ApJ...333..236K)
law 90th percentile rotation period (4)
52- 56 F5.2 d P10RM [0.58/41.06] Reiners & Mohanty (2012ApJ...746...43R 2012ApJ...746...43R)
law 10th percentile rotation period (4)
58- 62 F5.2 d P25RM [0.77/41.07] Reiners & Mohanty (2012ApJ...746...43R 2012ApJ...746...43R)
law 25th percentile rotation period (4)
64- 68 F5.2 d P50RM [2.09/41.1] Reiners & Mohanty (2012ApJ...746...43R 2012ApJ...746...43R)
law 50th percentile rotation period (4)
70- 74 F5.2 d P75RM [7.04/41.11] Reiners & Mohanty (2012ApJ...746...43R 2012ApJ...746...43R)
law 75th percentile rotation period (4)
76- 80 F5.2 d P90RM [7.81/41.13] Reiners & Mohanty (2012ApJ...746...43R 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 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 25th and 75th 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 XC=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_☉≤1.2M, sampled in equally spaced 0.05M☉. 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 Teff 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 1988ApJ...333..236K; Chaboyer
et al., 1995ApJ...441..865C 1995ApJ...441..865C; Sills et al., 2000ApJ...534..335S 2000ApJ...534..335S; see
Eq.(1) in section 2.3.1 for details about this law). Reiners & Mohanty
(2012ApJ...746...43R 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 10th and
90th 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