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correcting a few typos before posting to ArXiv
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RuthAngus committed Aug 20, 2019
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43 changes: 24 additions & 19 deletions paper/master.tex
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Expand Up @@ -153,7 +153,7 @@
rotational behavior of stars whose rotation periods do not lengthen with the
square-root of time, and parts of the Hertzsprung-Russell diagram where
gyrochronology has not been calibrated.
This publication is accompanied by an open source {\it Python} package (\sd)
This publication is accompanied by an open source {\it Python} package, \sd,
for inferring the ages of main-sequence and subgiant FGKM stars from rotation
periods, spectroscopic parameters and/or apparent magnitudes and parallaxes.
\end{abstract}
Expand All @@ -173,7 +173,7 @@ \section{Introduction}
On the MS, isochrones are tightly spaced and, even with very precise
measurements of effective temperature and luminosity, the position of a MS
star on the HRD may be consistent with range of isochrones spanning several
billion years.
billion years \citep[see][for a review of stellar ages]{soderblom2010}.
At the main-sequence turnoff however, isochrones are spread further apart, so
that sufficiently precisely measured temperatures and luminosities can yield
ages that are extremely precise (with minimum statistical uncertainties on the
Expand Down Expand Up @@ -389,12 +389,14 @@ \subsection{A new empirical gyrochronology relation}
In order to fit a relation to Praesepe, we removed rotational outliers bluer
than \gcolor\ = 2.7 via sigma-clipping and fit a 5th-order polynomial to the
remaining FGK and early M stars.
\racomment{We found that a 5th order polynomial provided a substantially
% \racomment{
We found that a 5th order polynomial provided a substantially
better fit than lower-order polynomials, which were not able to capture the
sharp `elbow’ in the rotation period-color relation. Additional orders
provided either a worse
fit, tending towards extreme values at the boundaries, or diminishing returns
in goodness-of-fit.}
in goodness-of-fit.
% }
We also fit a straight line to the late M dwarfs (\gcolor\ $>$ 2.7), to
capture the mass-dependent initial rotation periods of low mass stars
\citep{somers2017}.
Expand Down Expand Up @@ -812,7 +814,7 @@ \subsection{Test 1: simulated stars}
& D \sim U(10, 1000)~\mathrm{[pc]} \\
& A_V \sim U(0, 0.1).
\end{eqnarray}
\teff, \logg, \fhat, parallax, and apparent magnitudes $B$, $V$, $J$, $H$, $K$,
\teff, \logg, [Fe/H], parallax, and apparent magnitudes $B$, $V$, $J$, $H$, $K$,
\gaia\ $G$, $G_{BP}$ and $G_{RP}$ were generated from these
stellar parameters using the MIST stellar evolution models.
We added a small amount of noise to the `observed' stellar properties in order
Expand Down Expand Up @@ -969,7 +971,7 @@ \subsection{Test 1: simulated stars}

An important caveat associated with these results is that they strongly depend
on the uncertainties adopted for all observables used in the analysis: \teff,
\feh, \logg, $G$, $G_BP$, $G_RP$, $J$, $H$, $K$, $B$, $V$, and rotation
\feh, \logg, $G$, $G_{BP}$, $G_{RP}$, $J$, $H$, $K$, $B$, $V$, and rotation
period.
Changing the uncertainties on these observables will affect the uncertainties
on inferred ages in different ways.
Expand Down Expand Up @@ -1101,7 +1103,7 @@ \subsection{Test 2: Open clusters}
cluster and figure \ref{fig:NGC6819_results} shows the results of inferring
the ages of individual cluster members using a combination of gyrochronology
and isochrone fitting (via \sd) and isochrone fitting alone.
The ages of F stars in this cluster (\gcolor\ $\sim$ 5.5-6.5) were relatively
The ages of F stars in this cluster (\gcolor\ $\sim$ 0.5-0.75) were relatively
precisely constrained by isochrone fitting alone because, at 2.5 Gyr, they are
approaching the MS turnoff.
For these hot stars, ages inferred with gyrochronology and isochrones were
Expand Down Expand Up @@ -1201,7 +1203,8 @@ \subsection{Test 2: Open clusters}
functions do not provide them.
% In general, formal rotation period uncertainties should probably be calculated
% empirically via simulations as in the \citet{aigrain2015} study.
\racomment{Ideally, rotation period uncertainties should capture {\it both} the
% \racomment{
Ideally, rotation period uncertainties should capture {\it both} the
measurement precision, {\it and} the physical uncertainty introduced by the
latitudinal movement of star spots on the surface of a differentially rotating
star.
Expand All @@ -1223,10 +1226,12 @@ \subsection{Test 2: Open clusters}
measurement uncertainty and physical variation, affect stellar ages via
gyrochronology is key to understanding the power of gyrochronology as an
age-dating method.
For now, we leave this exploration for a future study.}
For now, we leave this exploration for a future study.
% }

\subsection{Test 3: Kepler asteroseismic stars}
\racomment{In order to test our method in the regime where both isochrone
% \racomment{
In order to test our method in the regime where both isochrone
fitting and gyrochronology become important, we recovered the ages of the 21
asteroseismic stars analysed in \citet{vansaders2016}.
These 21 stars were observed in \kepler's short cadence mode and are a mixture
Expand Down Expand Up @@ -1269,9 +1274,9 @@ \subsection{Test 3: Kepler asteroseismic stars}
The white circles show ages inferred from isochrones only.
Dashed lines connect the three different age measurements for the same
stars.
}
% }

\racomment{
% \racomment{
Although the ages of all 21 stars shown in figure \ref{fig:astero} were
inferred with a joint isochronal and gyrochronal model, most (all but 8) were
either too evolved, too metal poor, or too metal rich for gyrochronology to
Expand All @@ -1285,9 +1290,9 @@ \subsection{Test 3: Kepler asteroseismic stars}
relatively hot.
% Isochrones are information-rich for these hot and old stars, and this is
% exactly where gyrochronology is at its most information-poor.
}
% }

\racomment{
% \racomment{
In general, there is relatively poor agreement between the asteroseismic ages
and the ages inferred using \sd.
Much of this discrepancy is driven by differences in the isochronal ages,
Expand All @@ -1302,9 +1307,9 @@ \subsection{Test 3: Kepler asteroseismic stars}
between the two sets of models can be as large as 1-2 billion years.
The MIST isochrones lie above the BaSTI isochrones on the HR diagram, leading
to a systematic underprediction of ages.
}
% }

\racomment{
% \racomment{
The gyrochronal ages, where gyrochronology is applicable, do not show
excellent agreement with the asteroseismic ages either.
The four hot stars to the left in figure \ref{fig:astero} are rotating more
Expand All @@ -1330,7 +1335,7 @@ \subsection{Test 3: Kepler asteroseismic stars}
It is the only clear SB1 in the \citet{vansaders2016} sample, although some
others do have binary companions with long orbital periods, for which tidal
interactions are not expected to be strong.
}
% }

\begin{figure}
\caption{ A comparison of stellar ages inferred using
Expand Down Expand Up @@ -1382,7 +1387,7 @@ \section{Conclusions}
Although V-band extinction is marginalized over during inference, correcting
photometry for dust-extinction before analysis, or including it as a
prior can improve the accuracy of stellar ages measured with \sd.
\racomment{
% \racomment{
We also tested \sd\ on a set of 21 \kepler\ asteroseismic stars
\citep{vansaders2016}.
We found that discrepancies between ages measured with \sd\ and ages measured
Expand All @@ -1397,7 +1402,7 @@ \section{Conclusions}
period depends on age, mass, metallicity, surface gravity, etc), many stars
with precise ages, spanning a range of properties, are still needed to
reliably calibrate them.
}
% }

In cases where gyrochronology predicts inaccurate stellar ages it is either
because models are not correctly calibrated, because the rotation periods or
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6 changes: 1 addition & 5 deletions paper/ms.tex
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Expand Up @@ -80,14 +80,10 @@
\newcommand{\Eep}{Equivalent evolutionary point}

% \newcommand{\racomment}[1]{{\color{blue}#1}}
\newcommand{\racomment}[1]{{\bf #1}}
% \newcommand{\racomment}[1]{{\bf #1}}

\begin{document}

% \title{Inferring stellar ages by combining isochrone fitting with
% gyrochronology}
% \title{A new age-dating model for cool main sequence stars that combines
% isochrone fitting with gyrochronology}
\title{Towards precise stellar ages: combining isochrone fitting with
empirical gyrochronology}

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