# Modelling stellar variability in archival HARPS data: I - Rotation and
activity properties with multi-dimensional Gaussian Processes

Haochuan Yu1, Suzanne Aigrain1, Baptiste Klein1, Oscar Barragán1, Annelies
Mortier2, Niamh K. O’Sullivan1, and Michael Cretignier1
1Sub-department of Astrophysics, Department of Physics, University of Oxford,
Oxford, OX1 3RH, UK
2School of Physics & Astronomy, University of Birmingham, Edgbaston,
Birmingham B15 2TT, UK<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Although instruments for measuring the radial velocities (RVs) of stars now
routinely reach sub-meter per second accuracy, the detection of low-mass
planets is still very challenging. The rotational modulation and evolution of
spots and/or faculae can induce variations in the RVs at the level of a few
m/s in Sun-like stars. To overcome this, a multi-dimensional Gaussian Process
framework has been developed to model the stellar activity signal using
spectroscopic activity indicators together with the RVs. A recently published
computationally efficient implementation of this framework, S+LEAF 2, enables
the rapid analysis of large samples of targets with sizeable data sets. In
this work, we apply this framework to HARPS observations of 268 well-observed
targets with precisely determined stellar parameters. Our long-term goal is to
quantify the effectiveness of this framework to model and mitigate activity
signals for stars of different spectral types and activity levels. In this
first paper in the series, we initially focus on the activity indicators
(S-index and Bisector Inverse Slope), and use them to a) measure rotation
periods for 49 slow rotators in our sample, b) explore the impact of these
results on the spin-down of middle-aged late F, G & K stars, and c) explore
indirectly how the spot to facular ratio varies across our sample. Our results
should provide valuable clues for planning future RV planet surveys such as
the Terra Hunting Experiment or the PLATO ground-based follow-up observations
program, and help fine-tune current stellar structure and evolution models.

###### keywords:

exoplanets - planets and satellites: detection - stars: low-mass - stars:
rotation - stars: magnetic fields - techniques: radial velocities

††pubyear: 2024††pagerange: Modelling stellar variability in archival HARPS
data: I - Rotation and activity properties with multi-dimensional Gaussian
Processes–B

##  1 Introduction

Since the groundbreaking detection of the first exoplanet orbiting a sun-like
star, 51 Peg b (Mayor & Queloz, 1995), using the radial velocity (RV) method,
numerous techniques have been developed and campaigns initiated to discover
exoplanets with the ultimate goal of finding another habitable world. The RV
method continues to be one of the most promising techniques for detecting
Earth-like planets, thanks to the development of optical ultra-stable high-
resolution échelle spectrographs such as High Accuracy Radial Velocity Planet
Searcher (HARPS; Mayor et al., 2003), HARPS-N (Cosentino et al., 2012),
ESPRESSO (Pepe et al., 2021), EXPRES (Jurgenson et al., 2016), NEID (Schwab et
al., 2018) and the upcoming KPF (Gibson et al., 2016) and HARPS-3 (Thompson et
al., 2016). These new instruments can achieve extreme precision down to 0.3
$\rm{ms^{-1}}$ (e.g., Suárez Mascareño et al., 2020; Faria et al., 2022) and
even beyond.

However, despite the sub-meter-per-second accuracy achieved by RV instruments,
the detection of Earth analogues remains a significant challenge, primarily
attributed to stellar activity. For example, in our own solar system, the
amplitude of Earth’s RV signal is a mere 0.1 m/s, yet RV fluctuations caused
by solar activity can exceed several m/s (e.g., Meunier et al., 2010a; Haywood
et al., 2022). As a result, signals from small, moderately distant planets,
similar to Earth, could easily be obscured by the activity of their host star.
Accurate modelling of these activity signals is crucial for the successful
detection of such planets.

Variations in the RV time-series can arise from a variety of stellar activity
processes, often manifesting across different timescales. Predominantly, these
fluctuations are the consequence of the magnetic field of the star interplay
with the convection. In the following, we discuss several mechanisms believed
to be most crucial in inducing variations in the RVs.

On short timescales, the surface of an FGKM star consists of cells where local
convection occurs, a phenomenon known as granulation. In each cell, material
heated up rises to the surface, causing a blueshift in the lines, while cooler
material sinks, causing a redshift. Since the hotter material is generally
brighter than the cooler material, averaging the line profiles over the
stellar surface produces an asymmetric line profile, resulting in a net
blueshift when measuring the line centers. As these cells, or granules, evolve
stochastically on the stellar surface, this effect can induce RV variations at
the m/s level, with timescales ranging from a few minutes to several hours
(e.g., Dumusque et al., 2011a; Meunier et al., 2015; Meunier & Lagrange, 2019;
Cegla et al., 2013, 2018, 2019). On even shorter timescales, surface
granulation and magnetic events can excite oscillations of the star at
characteristic frequencies (acoustic modes), known as pressure-mode (p-mode)
oscillations (e.g., Kjeldsen & Bedding, 1995; Arentoft et al., 2008). For sun-
like stars, p-mode oscillations can induce RV variations with a period of
several minutes and an amplitude of around 0.1 to 1 m/s (Strassmeier et al.,
2018; Cegla, 2019). Given that the timescales of these effects are normally
short compared to the orbital period of the planet of interest, such effects
can be filtered out by either extending the exposure time (e.g., Chaplin et
al., 2019), or binning the data to a lower time resolution.

On moderate timescales, effects caused by active regions on the stellar
surface become significant. These regions are shaped by magnetic fields, which
can interfere with the convection on the stellar surface in two ways. First,
when the magnetic field suppresses the local heat transport, it results in
dark regions known as spots. Second, if the magnetic field is not strong
enough to entirely suppress the heat transport, it alters local opacity which
produces brighter regions, often referred to as faculae or plages. These
active regions can induce RV variations through two primary mechanisms: the
photometric effect, marked by a localized flux alteration, and the inhibition
of the convective blueshift effect, characterized by a reduced blueshift on
the local line profile. Therefore, disk-integrated line profiles exhibit
distortion due to these localized changes, manifesting as shifts in the RV. As
these active regions rotate with the surface of the star, the induced RV
signal is modulated by such rotation, resulting in a signal with quasi-
periodic variations. Meunier et al. (2010b) found that, for the Sun, the
amplitude of such variation in the RV is around 0.4 to 1.4 m/s and is
dominated by the convective blueshift effect. The challenge lies in the fact
that the rotation periods of Sun-like stars can be of the same order of
magnitudes as the orbital period of exoplanets. This similarity led to a few
early claims being subsequently refuted (e.g., Rajpaul et al., 2016).

Several techniques have been developed to mitigate such activity signals. One
straightforward approach is to compare the Lomb-Scargle periodograms of RV and
spectroscopic activity indicators to visually distinguish between stellar and
planetary periods. This method is only effective when the data is relatively
regular-sampled and the stellar signal remains less evolved. An alternative
approach is to employ Stacked Bayesian General Lomb-Scargle periodograms
(Mortier & Collier Cameron, 2017), which provides a way to assess the
stability of signals over time. Stellar signals can be identified as they are
unstable and incoherent, in contrast to planetary signals which are consistent
and stable. A more advanced approach is to use a multi-dimensional Gaussian
Process framework, which models the RV together with the activity indicators
(e.g., Aigrain et al., 2012; Rajpaul et al., 2015; Barragán et al., 2022). We
will delve deeper into this approach in section 3. Besides, there are
techniques that conduct activity mitigation at earlier stages. For instance,
some start from cross-correlation function (CCF) (e.g., Donati et al., 2014;
Collier Cameron et al., 2021; John et al., 2022; Zhao et al., 2022b; de Beurs
et al., 2022), while others focus on the spectrum level mitigation (e.g.,
Davis et al., 2017; Jones et al., 2017; Cretignier et al., 2021, 2022). For
more details on existing activity mitigation techniques, we refer readers to
Zhao et al. (2022a) for an overview.

On longer timescales of several years, the influence of magnetic activity
cycles becomes prominent. Solar-type stars exhibit cycles of magnetic activity
spanning several years, which can potentially affect all the above activity
signals. Such cycles have been linked to long-term RV fluctuations over the
years (Dumusque et al., 2011b). This means the RV signals attributed to these
cycles can be easily confounded with the RV signals from long-period planets.
Meunier et al. (2019) demonstrated that such effects can be substantially
reduced by decorrelating the RV from chromospheric emissions. In addition to
the long-term baseline variations, magnetic activity cycles can alter the
characteristic period of signals induced by active regions over time. This is
because the distribution of active regions across latitudes changes throughout
the magnetic activity cycle (e.g., the butterfly diagram of the Sun) (e.g.,
Foing, 1988). If the surface rotation rate varies from equator to pole
(differential rotation), the rotation period inferred from the modulation of
surface heterogeneities (whether in photometry or spectroscopic indicators)
will vary along the magnetic cycle. For a Sun-like differential rotation and
butterfly pattern, the active regions move from higher to lower latitudes as
the cycle progresses, and their rotation period decreases.

Since 2003, the high-resolution spectrograph HARPS has been observing
thousands of stars. The rich archival, high-quality data from HARPS provides a
unique opportunity to test and apply state-of-the-art methods for activity
modelling and mitigation. In this paper, we apply the multi-dimensional
Gaussian Process framework to HARPS observations of 268 well-observed targets.
We discuss sample selection, data reduction and pre-processing, as well as the
basic properties of the sample in section 2. We then briefly introduce the
multi-dimensional GP framework and detail its implementation in section 3. We
discuss results regarding stellar rotation in section 4, and facular to spot
ratio in section 5. We summarize our key conclusions and outline future work
in section 6.

##  2 The HARPS Sample

###  2.1 Sample selection

We utilized archived data from the HARPS, accessible via the ESO science
archive 111http://archive.eso.org/scienceportal/home.

We retrieved all publicly available HARPS spectra using the ESO’s astroquery
222https://github.com/astropy/astroquery (Ginsburg et al., 2019) package. For
every observation and each target, we cross-matched the stellar name and
position with their respective counterparts in the simbad database (Wenger et
al., 2000). This step ensured the removal of potential misclassifications from
the ESO archive and close-in binary systems from our data set. Polarimetric
data, which only constitute a minor portion of the HARPS archive, have been
discarded as they were not reduced automatically by the standard pipeline. We
did not implement cuts based on the signal-to-noise ratio (SNR) of the
spectra, or cuts based on whether the simultaneous calibration has been
applied. We anticipated that these factors would manifest themselves through
the uncertainties of the pipeline products, which would be taken into account
statistically by our Bayesian framework introduced later. Our preliminary
target set included a total of 1438 targets with spectral types spanning from
F to M. Their effective temperatures ($T_{\rm{eff}}$) approximately ranged
between 2800 K and 7500 K.

To guarantee a sufficient observation duration for our targets, we excluded
those that had less than 40 daily-binned observations. In pursuit of
homogeneity in the determination of the stellar parameters, e.g., effective
temperature $T_{\rm{eff}}$, surface gravity $\rm{log}\ g$, we restricted our
sample to stars listed in the catalogue published in Gomes da Silva et al.
(2021), and used the parameters listed in that catalogue throughout our paper.
Our final sample contains 268 targets, with spectral types spanning from F to
K. Figure 1 shows our sample selection in an Hertzsprung-Russell (HR) diagram,
with $\rm{log}\ g$ versus $T_{\rm{eff}}$ from GAIA DR2 (Gaia Collaboration et
al., 2016, 2018). The grey points show the 1438 targets on our initial list,
while the selected 268 targets in our final sample are highlighted in orange.

Figure 1: Our sample selection in an HR diagram, with $\rm{log}\ g$ versus
$T_{\rm{eff}}$ from GAIA DR2 (Gaia Collaboration et al., 2016, 2018). The grey
points show the 1438 targets on our initial list. The selected 268 targets in
our final sample are highlighted in orange.

###  2.2 Data reduction and pre-processing

The raw data underwent automatic reduction using version 3.5 and/or 3.8 of the
HARPS Data Reduction Software (DRS). For each target, cross-correlation
functions (CCFs) were computed by correlating the reduced spectra with a line
mask that matches the spectral type of the star. CCF proxies, namely RV and
bisector inverse slopes (BIS), were then measured from the CCFs within the
DRS. Additionally, we computed a chromospheric emission metric, $S$-index,
from the Ca II H and K lines (resp. 3968.47 and 3933.66 Å) in the S1D spectra,
employing the ACTIN333https://github.com/gomesdasilva/ACTIN (Gomes da Silva et
al., 2018) package.

For each time-series, we calculated the median absolute deviation (MAD)
metric, which is considered a more reliable measure of statistical dispersion
than the often-employed standard deviation, especially in the presence of
outliers. Data points exceeding three times the MAD value were identified as
outliers and subsequently excluded. Any time-series extending beyond
BJD=2457161.5 was partitioned into two sections for the purpose of outlier
removal, given the expectation of two separate baselines resulting from the
HARPS fibre upgrade. Finally, we binned each time-series to a maximum of one
data point per day.

###  2.3 Basic properties of the sample

We showcase the basic properties of the 268 targets in our sample using HR
diagrams in Figure 2. The colours of the points in the left, middle, and right
panels represent the number of data points in the pre-processed time-series,
the mean SNR per pixel (in échelle order 50) of the acquired spectra, and the
mean $\log R_{\rm{HK}}^{\prime}$ of the star, using values from the catalogue
provided by Gomes da Silva et al. (2021), respectively. We can see that the
numbers of data points in our sample vary, ranging from 40 to over 400, though
the majority fall between 40 and 100. The mean SNR spans from 50 to above 300.
The mean $\log R_{\rm{HK}}^{\prime}$ for the majority of the targets are below
-4.4, suggesting that they are predominantly inactive stars. This aligns with
expectations, given that the primary goal of HARPS is exoplanet detection,
leading the survey to prioritize low-activity stars.

In Figure 3, we show the normalized root mean square (RMS) of the time-series
for both $S$-index and BIS, plotted against the mean $\log
R_{\rm{HK}}^{\prime}$. The RMS values serve as direct metrics of variability
in the activity indicators, and as such, they are anticipated to correlate
more intimately with the challenges of activity mitigation. We find, however,
no clear correlation between the overall RMS values and the mean $\log
R_{\rm{HK}}^{\prime}$, even though there appears to be a tentative positive
correlation between the RMS’s upper envelope and the mean $\log
R_{\rm{HK}}^{\prime}$. For instance, at a mean $\log R_{\rm{HK}}^{\prime}$
value of approximately -4.9, the corresponding RMS for either $S$-index or BIS
can fluctuate by an order of magnitude. Therefore, we deduce that relying
solely on the mean $\log R_{\rm{HK}}^{\prime}$ is inadequate as an activity
metric within the context of activity mitigation. We recommend that future
survey target selections consider additional metrics alongside mean $\log
R_{\rm{HK}}^{\prime}$.

Figure 2: The figure shows the basic properties of the 268 targets in our
sample. The targets are displayed in HR diagrams, and the colours of the
points in the left, middle, and right panels represent the number of data
points in the pre-processed time-series, the mean signal-to-noise ratio (SNR)
of the acquired spectra, and the mean $\log R_{\rm{HK}}^{\prime}$ of the star,
respectively. Figure 3: The figure shows the normalized root mean square (RMS)
of the time-series for both $S$-index and BIS versus the mean $\log
R_{\rm{HK}}^{\prime}$.

##  3 Model for stellar activity

Different processes of stellar activity, e.g., p-mode oscillations,
granulation, active regions, and magnetic activity cycles, can induce
variations in the time-series of RV and spectroscopic activity indicators at
various timescales. In this section, we focus on modelling the variations
induced by the active regions — notably the effects of faculae/plages and
spots. This is primarily because such activity signal is modulated by the
rotation of the star, and the associated timescales (i.e., tens of days) are
closest to the orbital periods of the planets. In the following, we introduce
the multi-dimensional GP framework to model such activity-induced signals in
section 3.1, with the aim of measuring the rotation period of the stars. We
then detail the implementation of the framework to activity indicators in
section 3.2.

###  3.1 Multi-dimensional Gaussian Processes framework

GPs are commonly used in recent years as a tool to model stellar activity,
given their ability to model the data by parameterising its covariance matrix
to constrain the characteristics of the data, e.g., period, evolution
timescale. This avoids the necessity of knowing the exact deterministic form
of the underlying physical processes, which can be extremely hard in the case
of modelling stellar activity as it is expected to be stochastic. For
comprehensive descriptions of GPs, we refer readers to specialised literature,
e.g., Rasmussen & Williams (2006), Roberts et al. (2017) and Aigrain &
Foreman-Mackey (2023).

At its core, a GP model is characterized by a mean function and a kernel
function, the latter parameterizing the covariance matrix. Parameters within
these kernel functions, termed hyper-parameters, shape the characteristics of
the modelled data rather than its exact form. For example, a frequent choice
for modelling stellar activity is the Quasi-Periodic (QP) kernel,

$k_{QP}\left(t,t^{\prime}\right)=A\exp\left[-\Gamma\sin^{2}\left(\frac{\pi\left(t-t^{\prime}\right)}{P}\right)-\frac{\left(t-t^{\prime}\right)^{2}}{2l^{2}}\right]\mathrm{,}$
(1)

where $A$ is the amplitude representing the overall scale of the variation
from the mean function, $P$ is the characteristic period of the variation,
$\Gamma$ is the harmonic complexity, which in simpler terms indicates how much
the variation strays from a pure sine oscillation within a given period. $l$
is the ’evolution timescale’, which scales with the maximum distance of two
data points that are strongly correlated.

Aiming to maximise the usage of information from the spectroscopic time-series
in modelling the stellar activity, we want to model the activity signals from
the RVs together with a set of selected spectroscopic activity indicators,
i.e., $S$-index and BIS. Following Aigrain et al. (2012); Rajpaul et al.
(2015); Barragán et al. (2022); Delisle et al. (2022), we assume a set of N
observable time-series, $Y_{i=1,\ldots,N}(t)$, which can be time-series of RV
and activity indicators, and each time-series $Y_{i}$ follows

$Y_{i}(t)=f_{i}(t)+[a_{i}G(t)+b_{i}\dot{G}(t)]+\epsilon_{i}(t)\mathrm{,}$ (2)

where $f_{i}(t)$ is the deterministic part of the model. For RV, it is where
the mean function and planet-induced RV are incorporated. For activity
indicators, it is simply the mean function. $\epsilon_{i}(t)$ is the
measurement ’white’ noise, which normally includes photon noise, calibration
noise, etc. Every $Y_{i}(t)$ has a shared entity, $G(t)$. We interpret this as
a latent GP variable, approximating the proportion of the visible stellar disc
blanketed by active regions. Commonly, a GP with a quasi-periodic (QP) kernel
is the modelling choice for this variable. $\dot{G}(t)$ is the first temporal
derivative of $G(t)$ and remains a GP, roughly representing how the active
regions evolve in time on the stellar disc. Coefficients $a_{i}$ and $b_{i}$
are free parameters that harmonise the interplay between the latent GP
variables, $G$ and $\dot{G}$, and various observable time-series, $Y_{i}$.

Building on this framework, a fully parameterised covariance matrix
$\mathbf{K}$ for the N time-series $Y_{i=1,\ldots,N}(t)$ can be established.
With a known mean function $\mathbf{m}$ and covariance matrix $\mathbf{K}$,
the likelihood function can be written in analytic expression as

$\mathcal{L}=\frac{1}{\sqrt{2\pi|\mathbf{K}|}}\exp\left(-\frac{1}{2}(\mathbf{y}-\mathbf{m})^{\mathrm{T}}\mathbf{K}^{-1}(\mathbf{y}-\mathbf{m})\right),$
(3)

where $\mathbf{y}$ encompasses the vector of N observed time-series
$Y_{i}(t)$. Full Bayesian frameworks, such as Monte Carlo Markov Chain (MCMC)
or nested sampling, can be implemented with $\mathcal{L}$ to explore the
posterior distributions of free parameters in the model. We direct readers to
Rajpaul et al. (2015) and Barragán et al. (2022) for details.

For $G(t)$, the traditional approach involving a quasi-periodic (QP) kernel,
as outlined in Equation 1, faces the drawback of computational costs that rise
cubically in relation to the size of the dataset. An alternative option is to
use a fast approximated kernel, such as a Matern 3/2 exponential periodic
(MEP) kernel facilitated in S+LEAF 2444https://gitlab.unige.ch/Jean-
Baptiste.Delisle/spleaf (Delisle et al., 2022), of which the computational
cost only scales linearly. Such efficiency becomes indispensable when tasked
with analysing expansive datasets for a large volume of targets without
straining computational resources. We refer readers to Delisle et al. (2022)
for details on the MEP kernel.

###  3.2 Implementation

We implemented the multi-dimensional GP framework on every target in our
sample. As we initially focused on the activity indicators in the present
work, the exact form of the framework we used can be outlined as follows

$\displaystyle\mathrm{BIS}(t)=f_{\mathrm{BIS}}(t)+a_{\mathrm{BIS}}G(t)+b_{\mathrm{BIS}}\dot{G}(t)+\epsilon_{\mathrm{BIS}}(t)\mathrm{,}$
(4) $\displaystyle
S\mathrm{-index}(t)=f_{S\mathrm{-index}}(t)+a_{S\mathrm{-index}}G(t)+\epsilon_{S\mathrm{-index}}(t)\mathrm{,}$

where

$\displaystyle f_{\mathrm{BIS}}(t)=\overline{\mathrm{BIS}(t)}\mathrm{,}$ (5)
$\displaystyle
f_{S\mathrm{-index}}(t)=\overline{S\mathrm{-index}(t)}\mathrm{,}$

and $\epsilon(t)$ are white noise models containing measurement noise and
jitter terms. BIS is proved to be interlinked with both $G(t)$ and its
derivative $\dot{G}(t)$, while S-index is exclusively related to $G(t)$ (e.g.,
Isaacson & Fischer, 2010; Dumusque et al., 2014; Thompson et al., 2017). Hence
we exclude $\dot{G}(t)$ term for $S$-index. In terms of choices of kernels for
$G(t)$, we opted for MEP kernels available in S+LEAF introduced earlier, which
is a faster approximation of the QP kernel. To explore the posterior of free
parameters, we used nested sampling through
PolyChord555https://github.com/PolyChord/PolyChordLite (Handley et al., 2015a,
b), with all priors on the free parameters set as uninformative. This nested
sampling approach is favoured here as it demonstrates better performance when
compared to MCMC approaches, especially in datasets exhibiting multi-modality.

Figure 4: Demonstration of multi-dimensional GP fit on the * 61 Vir (HD
115617) dataset. In the left panel, the black markers show the time-series of
$S$-index and BIS, and their associated uncertainties. The coloured (blue and
coral) lines show the GP predictions over the observations, and the
corresponding shaded areas of the lines show one $\sigma$ uncertainty of
predicted distributions. The horizontal dashed grey lines show the means of
the time-series. The grey extensions on the errorbars show the jitter terms.
The right panel show posterior distributions of selected model parameters,
including period, evolution timescale and harmonic complexity.

We show an example of implementing the framework using the * 61 Vir dataset.
In Table 1, we show the inferred values of the free parameters in the model
based on the posterior distributions, alongside the priors designated for the
parameters during the sampling. The inferred values are the median of the
posterior distributions, and the statistical uncertainties are given by the
16th to 84th percentile range.

Table 1: Priors and inferred value of selected parameters in the model for the
example on the * 61 Vir (HD 115617) dataset.

Parameter | Prior ∗ | Inferred value
---|---|---
$\rm{Period}\ P\ (\mathrm{d})$ | $\mathcal{U}[0.1,60.0]$ | $32.1_{-0.2}^{+0.2}$
$\rm{Evolution\ timescale}\ l\ (\mathrm{d})$ | $\mathcal{U}[1,5000]$ | $186_{-50}^{+78}$
$\rm{Harmonic\ complexity}\ \Gamma$ | $\mathcal{U}[0.01,5.00]$ | $0.68_{-0.12}^{+0.16}$
$a_{\mathrm{BIS}}(\mathrm{~{}m}\mathrm{~{}s}^{-1})$ | $\mathcal{U}[\rm{-rms(BIS)},\rm{rms(BIS)}]$ | $0.55_{-0.08}^{+0.15}$
$b_{\mathrm{BIS}}(\mathrm{~{}m}\mathrm{~{}s}^{-1}\mathrm{~{}d}^{-1})$ | $\mathcal{U}[\rm{-10*rms(BIS)},\rm{10*rms(BIS)}]$ | $-3.5_{-0.9}^{+0.7}$
$a_{S\mathrm{-index}}(\mathrm{~{}d}^{-1})$ | $\mathcal{U}[\rm{-rms(S-index)},\rm{rms(S-index)}]$ | $0.0013_{-0.0002}^{+0.0003}$

* $\mathcal{U}$[a,b] refers to a uniform prior between a and b.

Figure 4 shows a multi-dimensional GP fits to the time-series of * 61 Vir (HD
115617) dataset. In the left panel, the black markers show the time-series of
$S$-index and BIS, and their associated uncertainties. The coloured (blue and
coral) lines show the GP predictions over the observations, and the
corresponding shaded areas of the lines show one $\sigma$ uncertainty of
predicted distributions. The horizontal dashed grey lines show the means of
the time-series. The grey extensions on the errorbars show the jitter terms.
The right panel show posterior distributions of selected model parameters,
including period, evolution timescale and harmonic complexity.

##  4 Stellar rotation

###  4.1 Rotation period measurement

Figure 5: HR diagram of our sample with the coloured points showing the
measured rotation period for the 49 targets which passed our vetting
procedure. The grey markers denote the other targets for which the rotation
periods were not recovered or were not considered sufficiently robust to
include in subsequent analysis. The dotted line at $\rm{log}\ g=4.1$
approximately separates main-sequence stars from evolved stars, i.e., sub-
giants.

The variations induced by active regions in activity indicators, modulated by
the rotation of the star, are believed to closely represent the star’s true
rotation period (e.g., Angus et al., 2018; Nicholson & Aigrain, 2022). As
such, the rotation period is captured by the hyper-parameter ’period’ in our
multi-dimensional GP model when the activity-induced signal is well-modelled.

We applied the multi-dimensional GP framework with a MEP kernel to each star
in our sample. To determine whether the period is securely detected, on a
separate analysis, we applied the same framework but used a Matern 3/2 kernel
instead with GP, representing an aperiodic model in comparison to the above
periodic model (with the MEP kernel). The evidence $Z$ of each model is
estimated through nested sampling to calculate $\rm{\Delta ln}\ Z=\rm{ln}\
Z_{periodic}-\rm{ln}\ Z_{aperiodic}$. A positive value indicated that the
periodic model is preferred. We then used $\Delta\rm{ln}\ Z$ as our starting
criterion to select targets where the periodic model is preferred.
Additionally, we rejected cases through visual inspection where the
$\Delta\rm{ln}\ Z$ was unreliable because of two possible scenarios. Firstly,
in cases where neither model fits well, the $\Delta\rm{ln}\ Z$ criterion could
be biased as the Bayesian model comparison is only meaningful when both models
adequately fit the data. Secondly, the MEP kernel (or the quasi-periodic
kernel in general) we employed has regions in the parameter space that could
behave aperiodically. In such cases, even if the periodic model appears
preferable based on evidence difference, secure detection of the period is not
guaranteed. Upon thorough vetting, we identified 49 targets for which we
believe the model adequately captured the activity-induced variations,
resulting in an accurate recovery of their true rotation periods.

We also want to emphasize that in comparison to conventional methods, such as
periodograms or the autocorrelation function (ACF), the GP approach displays
greater resilience against harmonic misdetection when determining rotation
periods (e.g., Angus et al., 2018). This robustness arises from the
utilization of the MEP or QP kernel, where potential harmonic components are
inherently considered, i.e., the ’harmonic complexity’ hyperparameter serves
as an approximate gauge of the harmonic contribution. This ensures the
algorithm finds the true rotation period which is associated with the lowest
base frequency.

The selected 49 targets are shown in an HR diagram in Figure 5, with the
colour of the markers representing their recovered rotation periods. All other
targets of which the periods have not been successfully recovered are denoted
with grey markers. The dotted line at $\rm{log}\ g=4.1$ approximately
separates main-sequence stars from evolved stars, i.e., sub-giants. Notably,
we find that the rotation period broadly decreases as effective temperature
rises (or for earlier spectral types), although there is a considerable amount
of scatter at any given temperature. This is broadly consistent with both
theoretical expectations (e.g., Skumanich, 1972a) and preceding rotation
period surveys (e.g., McQuillan et al., 2014). Further insights on age-
activity-rotation relations are discussed in section 4.3.

Regarding the detection rate, there are approximately 23% of main-sequence G
and K stars of which the rotation period is well recovered. However, this rate
decreases significantly for earlier type stars such as F stars, and for sub-
giants. The rapid rotation of F stars, typically with periods under 10 days,
necessitates denser time sampling than what is currently available to
accurately determine their rotation periods. In the case of sub-giants, their
evolving nature results in diminished or altered activity patterns, deviating
from the assumption of our activity model and thus reducing the detection
rate. It is important to note that the detection rate for the rotation period
can be considered as an indirect measure of the model’s efficacy at mitigating
activity signals across different stellar types. In this context, the model
demonstrates the best performance for G and K stars. For F stars, the model’s
efficacy could be enhanced with optimized sampling, tailored to capture their
rapid rotation. However, it is essential to recognize that effective activity
modelling does not necessarily equate to a target’s appropriateness for planet
detection. For example, challenges in modelling activity could arise due to a
lack of pronounced active regions on the stellar surface. In such cases, the
amplitude of the activity signal remains minimal and as such the star could
still possibly be an attractive candidate for exoplanet detection.

Last but not least, it is important to highlight that compared to traditional
methods like the Lomb-Scargle periodogram, the GP method holds an advantage in
determining the signal’s period when the rotational modulation signal evolves
over time (Angus et al., 2018). Additionally, with the multi-GP method used in
this work, we search for and identify common periodic signatures among
multiple time-series, thereby increasing the confidence in the measured
rotation period. Moreover, the multi-GP framework offers insights beyond just
the rotation periods of the stars. Specifically, it provides a quantitative
understanding of the covariance structure of the activity signals. Such
information can be integrated into statistical frameworks to disentangle
activity from planetary signals in the RVs. This can be achieved through
either simple linear regression models, or a more complex framework that
explicitly takes the covariance structure into account, such as the L1
periodogram of Hara et al. (2017). We defer further exploration of this
potential to future work.

###  4.2 Rossby number

Figure 6: As Figure 5, but the colour scale now shows the Rossby number.

The Rossby number $\rm{Ro}$, which is given by the ratio of the rotation
period $P_{\mathrm{rot}}$ to the convective turnover timescale
$\tau_{\mathrm{c}}$:

$\rm{Ro}=P_{\mathrm{rot}}/\tau_{\mathrm{c}},$ (6)

is a key parameter of the dynamo process that gives rise to large-scale
magnetic fields among the stars we are considering in this study. Numerous
empirical studies have shown that $\rm{Ro}$ is a key parameter for the angular
momentum evolution, as well as for magnetic field strength and topography of
late-type stars (see e.g. Noyes et al., 1984). To first order, it is an
indicator of the activity level of the star: the lower the Rossby number, the
more active the star.

We evaluated the Rossby number for the stars in our sample with rotation
period measurements, using the empirical relations from Cranmer & Saar (2011)
to calculate $\tau_{\mathrm{c}}$:

$\displaystyle\tau_{\mathrm{c}}\left(T_{\text{eff }}\right)=$ $\displaystyle
314.24\exp\left[-\left(\frac{T_{\text{eff
}}}{1952.5\mathrm{~{}K}}\right)-\left(\frac{T_{\text{eff
}}}{6250\mathrm{~{}K}}\right)^{18}\right]$ (7) $\displaystyle+0.002.$

.

The Rossby number of the sample is shown in the right panel of Figure 6. The
coloured points show the selected 49 targets from the visual vetting. Most of
the stars in our sample have a relatively high Rossby number, i.e., ${\rm
Ro}>1.0$, and are thus inactive stars. This is unsurprising, as most archival
HARPS observations were taken as part of planet surveys, which tend to avoid
active stars. Unlike $\log R_{\rm{HK}}^{\prime}$, the correlation between the
Rossby number and the effective temperature is relatively weak, and can be
explained mostly by the fact that the hotter stars in our sample are starting
to evolve off the main sequence.

###  4.3 Implications for spin-down of middle-aged stars

Sun-like stars are expected to undergo spin-down following a simple power law
(e.g., Skumanich, 1972b) to the first order during their main sequence stage.
This spin-down emerges from the continuous loss of angular momentum, a
consequence of torques generated from interactions between the star’s surface
magnetic field and its stellar wind. However, subsequent observations from
open clusters spanning a wide age range challenged the Skumanich-like spin-
down. Specifically, these results have brought to light two phases in a star’s
evolution where the spin-down process appears to ‘stall’ (Meibom et al., 2009;
Agüeros et al., 2018; Douglas et al., 2019).

To account for these stalling effects, several scenarios have been proposed.
The two main hypotheses are the core-envelope coupling (e.g., Spada et al.,
2011; Lanzafame & Spada, 2015; Spada & Lanzafame, 2020; Johnstone et al.,
2021) happening at a few Myrs to a Gyr, and the weakened magnetic breaking
(e.g., van Saders et al., 2016) happening at a few Gyrs. The former suggests
angular momentum can be transferred from the radiative core to the convective
envelope due to internal differential rotation, attenuating the spin-down of
the envelope. The latter indicates that magnetic braking is substantially
weakened once the star achieves a critical Rossby number, possibly due to a
change in the magnetic field’s morphology. This alteration – shifting from a
dipole field to a quadrupole field or an even more intricate configuration –
makes it less effective at shedding angular momentum (Réville et al., 2015).

Gaps in the rotation period versus effective temperature diagram have been
found with Kepler stars (e.g., McQuillan et al., 2013, 2014; Gordon et al.,
2021). These gaps can potentially be explained by the aforementioned stalling
effects. David et al. (2022) provide stronger evidence by combining the
_Kepler_ rotation periods with more accurate spectroscopic effective
temperatures from, e.g., the Large Sky Area Multi-Object Fiber Spectroscopic
Telescope (LAMOST) (Cui et al., 2012; Zhao et al., 2012). Their findings
indicate two prominent pile-ups in the period–effective temperature diagram.
The short-period pile-up is attributed to the core-envelope coupling
mechanism, while the long-period pile-up is linked to the phenomenon of
weakened magnetic braking. This latter association is primarily because it
aligns seamlessly with a consistent Rossby number curve.

We constructed a similar diagram, by combining rotation periods measured in
_Kepler_ data by McQuillan et al. (2014) with effective temperatures from
LAMOST. This resulted in a blue Kernel Density Estimation (KDE) plot,
displayed in the background of Figure 7, generated with the codes
666https://github.com/trevordavid/rossby-ridge provided by David et al.
(2022). Empirical cluster sequences of different ages are shown in grey lines,
derived from Curtis et al. (2020). The purple lines correspond to constant
Rossby numbers, following

$P_{\rm{rot}}\left(\rm{Ro},T_{\rm{eff}}\right)=\rm{Ro}\times\tau_{\rm{c}}\left(T_{\rm{eff}}\right),$
(8)

with convective turnover timescales from Cranmer & Saar (2011) as Equation 7.

In the KDE, the long-period pile-up is visible below the ${\rm Ro}=1.45$
curve, while the short-period pile-up appears above the ${\rm Ro}=0.4$ curve.
The Sun is shown as a reference in red, with $T_{\text{eff},\odot}=5772\
\rm{K}$ (Prša et al., 2016) and $P_{\text{rot},\odot}=27\pm 2\ \rm{d}$
estimated from Snodgrass & Ulrich (1990). We have overlaid the asteroseismic
sample from Hall et al. (2021), depicted in grey, and our HARPS sample of 49
well-determined rotation periods (detailed in section 4.1) in orange. Both
samples clearly occupy a distinct period-temperature space to the much larger
_Kepler_ , predominantly located above the long-period pile-up. We interpret
this primarily as a consequence of the different selection effects for the
three samples. The _Kepler_ sample, while much larger and benefiting from
tight, regular time sampling, relies on detecting the rotational modulation of
active regions in broad-band optical light curves. This becomes increasingly
difficult for less active stars as the fraction of the stellar disk covered by
active regions drops, and for slower rotators as the rotation period becomes
comparable to both the lifetime of the active regions and the duration of
individual _Kepler_ ‘quarters’. The asteroseismic sample uses $p$-modes to
measure internal and surface rotation rates, and is strongly biased towards
hotter and lower gravity (evolved) stars, for which the amplitude of the
$p$-modes is larger and their frequencies lower than for later type main-
sequence stars. The HARPS sample spans a longer baseline and uses
spectroscopic activity indicators rather than broad-band photometry to detect
the rotational modulation of active regions. It is reasonable to expect that
targetted indicators should be more sensitive to active regions than
photometry, particularly as the active regions decrease in size and number and
the rotation slows. A possible additional contributing factor is the fact
that, while dark spots dominate the activity patterns for active stars, less
active stars tend to be more faculae-dominated (Meunier et al., 2010a). The
photometric signatures of faculae are rather subtle, whereas they have strong
chromospheric signatures, which are probed by spectroscopic indicators such as
$\log R^{\prime}_{\rm HK}$ and also have a strong signature in line-shape
indicators such as the BIS via their local dampening effect on convective
flows. A more in-depth discussion on this topic can be found in section 5.

Figure 7: Rotation period versus effective temperature for our sample,
compared to previous results from the literature. The blue shading in the
background represents a kernel density estimate of the _Kepler_ /LAMOST
period-temperature results. Empirical cluster sequences of different ages are
shown in grey lines, derived from Curtis et al. (2020). Lines of constant
Rossby number are shown in purple. The asteroseismic sample of Hall et al.
(2021) is plotted in grey and our new results based on HARPS data are plotted
in orange. Figure 8: As Figure 7, but the points now show our sample colour-
coded according to Rossby number.

Considering the combined HARPS and asteroseismic samples, we see that two
distinct populations emerge. The first is composed of hotter stars (with
$T_{\rm eff}\geq 5700$ K), mostly from the asteroseismic sample, though with a
handful of HARPS measurements. This population follows a very steep period-
temperature relation, consistent with the rapid spin-down expected as stars
leave the main sequence and start to evolve towards the red giant branch.

The second population, predominantly from our sample, consists of cooler
(mid-G to mid-K) main-sequence stars. It follows a shallower period-
temperature relation, and its upper envelope corresponds to the ${\rm Ro}=2$
curve. This second population could possibly be the extension of the long-
period pile-up observed in the _Kepler_ sample, but skewed towards cooler
stars. In the _Kepler_ sample, the long-period pile-up is less pronounced at
cooler temperatures, but this could be a selection effect: at lower
temperatures, the pile-up moves to longer periods, which correspond to lower
photometric amplitudes, and the stars also become intrinsically fainter. In
Figure 8, we show the Rossby numbers computed for our sample compared to the
KDE of the _Kepler_ sample. They fall in the range of 1.5–2.5, consistent with
the critical Rossby number inferred from the photometric long-period pile-up.
A slight discrepancy between this tail and the anticipated long-period pile-up
extension might arise from biases in effective temperature measurements from
different sources, as argued in David et al. (2022) in the context of the
asteroseismic sample.

##  5 Faculae-to-spots ratio

Figure 9: The left panel shows the RMS ratio $A/B$ (a proxy for the faculae-
to-spot ratio) versus the Rossby number ${\rm Ro}$ (more magnetically active
stars have smaller Ro). The error bars show the derived statistical
uncertainties, and the colour scheme indicates the effective temperature. The
dotted grey line indicates ${\rm Ro}=1.9$, and the orange line shows the
linear fit to the data within the range of ${\rm Ro}<1.9$. The right panel
shows the estimated Spearman correlation coefficient between $A/B$ and ${\rm
Ro}$, as well as the slope of the linear fit to $\rm{log}(A/B)$ as a function
of ${\rm Ro}$. The two proxies are plotted against the cut-off value of ${\rm
Ro}$ ranging from 1.6 to 4.1. The blue and orange lines show the analysis of
the full data, while the thinner purple and coral lines show the analysis
excluding the data point at ${\rm Ro}\approx 0.5$ for comparison.

Spots and faculae (or their chromospheric counterpart, plages) are the two
main types of active regions that are expected to induce variations in the RVs
and activity indicators used in planet searches. These variations are induced
by two simultaneous processes. The first, known as the photometric effect, is
thought to be mainly induced by dark spots, which locally reduce (or even
suppress entirely) the local flux emerging from the stellar surface. The other
is due to the fact that convective up-flows are suppressed in regions of
enhanced magnetic flux density, which includes both spots and faculae. This
results in a local reduction in the net blue-shift caused by convective flows
relative to the "clear" photosphere, known as the Inhibition of Convective
Blueshift (ICB) effect. Both processes cause distortions to the disk-
integrated line profiles, resulting in variations the RV, FWHM and BIS, while
chromospheric activity indicators such as the $S$-index or $\log
R^{\prime}_{\rm HK}$ are sensitive to the fractional coverage of the active
regions themselves.

The differentiating factor between spots and faculae lies in the processes
through which they induce variations. While spots cause variations via both
these processes, faculae primarily influence the ICB effect (e.g., Dumusque et
al., 2014). Within the context of our multi-dimensional GP framework, the
terms $aG(t)$ and $b\dot{G}(t)$ distinctively represent these two effects
(e.g., Aigrain et al., 2012; Rajpaul et al., 2015). Hence, the ratio of the
RMS values of these two terms, $\mathrm{{RMS}[}aG(t)\mathrm{]}\ /\
\mathrm{{RMS}[}b\dot{G}(t)\mathrm{]}$, which we denote as $A/B$ in the
following text, can be interpreted as an approximate representation of the
relative faculae-to-spots ratio. This potentially offers an interesting way to
measure the faculae-to-spots ratio in the sample of stars where we consider
the results of the GP modelling to be sufficiently robust.

In turn, doing this would allow us, in principle, to test the widely held
paradigm that more magnetically active stars are more spot-dominated, while
quieter stars have fewer spots and more faculae (e.g., Meunier et al., 2010b;
Amazo-Gómez et al., 2020). Of course, direct measurements of the star’s
magnetic field necessitate polarimetric observations, and few stars in our
sample have such observations. However, the Rossby number ${\rm Ro}$ derived
in Section 4.2 is known to correlate strongly with the strength of the
magnetic field $\rm{<B>}$ (e.g., Reiners et al., 2014; Vidotto et al., 2014;
Reiners et al., 2022), with an exception for very inactive stars (i.e., ${\rm
Ro}>2$).

For the targets of which we have detected their rotation periods securely, we
examined the relationship between the RMS ratio $A/B$ and the derived Rossby
number ${\rm Ro}$ in the left panel of Figure 9. The error bars show the
propagated statistical uncertainties, and the colour scheme indicates the
effective temperature of the stars. We excluded samples exhibiting
uncertainties in the $A/B$ exceeding 200$\%$.

To evaluate the monotonic relationship between the $A/B$ and the ${\rm Ro}$,
we calculated the Spearman correlation coefficient, considering an upper cut-
off value for ${\rm Ro}$ in the range of 1.6 to 4.0. The result is shown in
the right panel of Figure 9. We found that the Spearman coefficient peaks
between $1.8<{\rm Ro}<2.0$ with a value of 0.62, after which the value drops
rapidly. In addition, we conducted linear fits to $\rm{log}(A/B)$ as a
function of ${\rm Ro}$, and showed the slope of the fit versus the ${\rm Ro}$
cut-off value in the same panel. We found that the slope also peaks between
$1.8<{\rm Ro}<2.0$, behaving similarly to the Spearman coefficient. Both
proxies indicate a relatively strong positive correlation between $A/B$ and
${\rm Ro}$ until $\rm Ro\approx 1.9$, after which the correlation
significantly weakens.

Additionally, we conducted analyses to assess the impact of the data point at
${\rm Ro}\approx 0.5$ by excluding it from the correlation analysis. The
results are represented as thinner lines in the same panel, labelled as ${\rm
Ro}>0.6$. Both the Spearman coefficient and the slope showed behaviors
remarkably similar to those observed in the full analysis. This similarity
suggests that the overall results are not predominantly influenced by this
single data point. Despite this, we assert that the detection at ${\rm
Ro}\approx 0.5$ is robust. The lack of data in the $0.5<{\rm Ro}<1.0$ range is
likely attributed to the HARPS sample’s bias towards inactive stars.

The relationship between $A/B$ and ${\rm Ro}$ is aligned with theoretical
predictions: a lower ${\rm Ro}$ implies a stronger magnetic field and
consequently, a star that is more spot-dominated. This leads to a decreased
facular-to-spot ratio, mirrored by a lower $A/B$, which is exactly the trend
we have seen in the ${\rm Ro}<1.9$ regime. However, when ${\rm Ro}>1.9$, the
correlation disappears, and there is no longer any obvious relationship
between the $A/B$ and the Rossby number. We speculate that the disappearance
of the correlation might arise from a morphological transition in the stellar
magnetic field beyond ${\rm Ro}\approx 1.9$, away from a predominantly dipolar
configuration. If the $B$-field structure becomes more complex, the
correlation between $B$-field strength and Rossby number would not be expected
to persist.

Intriguingly, the Rossby number at which the correlation with the $A/B$
disappears, ${\rm Ro}\approx 1.9$, is close to the ${\rm Ro}$ that marks the
upper envelope of the _Kepler_ main-sequence rotation period-temperature
distribution in Figures 7 and 8. It also corresponds approximately to the
critical Rossby number in the range $1.4\leq{\rm Ro}\leq 2.0$ postulated in
stellar spin-down theories (e.g., van Saders et al., 2016, 2019; David et al.,
2022), where the efficiency of stellar angular momentum dissipation is
expected to drop significantly due to the same alterations in magnetic field
morphology.

A more detailed investigation of the faculae-to-spot ratio and its dependence
on magnetic field strength would certainly be valuable, but would likely
require more sophisticated activity indicators that can help disentangle the
contributions of the different types of active regions (see e.g. Crétignier et
al. 2023) as well as a larger sample of stars with direct, polarimetric
magnetic field measurements, and is therefore beyond the scope of this work.

##  6 Conclusions

This paper presents the first results from an ongoing study of the activity
properties of F, G and K stars using archival HARPS data. We applied the
multi-dimensional GP framework developed by Rajpaul et al. (2015) and Barragán
et al. (2022) for activity mitigation in RV planet searches to activity
indicators extracted from HARPS spectra of 268 well-observed targets with
precisely determined stellar parameters. Applying the GP framework to such a
large dataset was made possible by using the efficient implementation of our
framework provided by Delisle et al. (2022). While we do plan to perform a
joint analysis of the activity indicators and the RVs in the future, this is
made challenging by the presence in the RV time-series of residual systematic
effects and an unknown number of planetary signals. A new version of the HARPS
Data Reduction Software is under development (Dumusque et al. priv. comm.),
which is expected to lead to significantly reduced systematics and has already
allowed new planet candidates to be identified (with further HARPS
observations being gathered to confirm them, ESO program 1110.C-4043, PI
Hara). In the mean time, applying the multi-dimensional GP framework to the
activity indicators alone already reveals a wealth of useful information. Our
key findings are as follows.

We successfully recovered rotation periods for 49 slow rotators in our sample.
We found that the rotation period decreases as effective temperature rises,
i.e. for earlier spectral types, which is broadly consistent with both
theoretical expectations (e.g., Skumanich, 1972a) and preceding rotation
period surveys (e.g., McQuillan et al., 2014). One limitation of our approach
is that we do not consider the effects of differential rotation, primarily due
to the sparse sampling of the majority of the targets in our sample. A
possible extension of this work would be to analyse the data season by season
and investigate seasonal variations in the period as well as in the other
parameters of the model.

We placed our results in the context of existing, photometric estimates of
field star rotation periods from Kepler, and discussed their implications for
the age-activity-rotation relations of F, G & K stars. Our samples typically
have longer periods than those derived from photometry, with the exception of
the asteroseismic sample. We ascribe this to two factors. First, spectroscopic
surveys like HARPS have a much longer baseline compared to photometric
surveys. This allows for multi-seasonal monitoring, increasing sensitivity to
slow rotators. Second, spectroscopic indicators are more sensitive to active
regions, particularly the faculae that tend to dominate in slowly-rotating,
magnetically inactive stars, than broad-band optical photometry.

Taken together with the pre-existing asteroseismic sample, our new sample of
slowly-rotating ($P>\approx 30$ d) FGK stars consists of two, distinct sub-
populations. One is a potential extension of the long-period pileup towards
cooler stars, with Rossby numbers in the range $1.4<{\rm Ro}<2.0$. The other
consists of ‘hot slow rotators’ with $T_{\rm eff}>5700$ K which we interpret
as sub-giants which are rapidly spinning down as they start to expand.

Overall, our results broadly agree with the findings of David et al. (2022),
but this is the first time that the population of late G and K-type slow
rotators is observed so clearly, above the ‘critical’ Rossby number of ${\rm
Ro}\approx 1.5$ that marks the upper envelope of the period-temperature
distributions for _Kepler_ stars with photometrically derived surface rotation
periods. We infer that angular momentum loss via a magnetised wind continues
beyond this critical value, which instead marks the point where the active
region covering fraction becomes too low to allow for photometric rotation
period estimates.

We also explored indirectly how the ratio of faculae to spots in active
regions varies across our sample, using the RMS ratio of $aG(t)$ to
$b\dot{G}(t)$ as a proxy. We find that this ratio is positively correlated
with the Rossby number up to ${\rm Ro}\approx 1.9$, in accordance with
theoretical expectations, since a lower ${\rm Ro}$ implies a stronger magnetic
field and consequently, a more spot-dominated star. The correlation disappears
for larger values of ${\rm Ro}$, indicating a possible transition in the
stars’ magnetic field morphology away from large-scale, predominantly dipolar
fields that give rise to clearly detectable rotational modulation in the
activity indicators.

Thus, both our rotation period measurements and the relative contribution of
higher-order versus lower-order behaviour in the activity indicator time-
series are consistent with the idea that a significant transition in magnetic
field morphology occurs around a critical Rossby number in the range
$1.4\leq{\rm Ro}\leq 2.0$. Notably, this transition aligns well with the
critical ${\rm Ro}$ values suggested in stellar spin-down theories.

This paper demonstrates that rich information can be extracted from
spectroscopic activity indicators, which sheds light on the structure and
evolution of stars. Our intention is to extend this methodology to the RV once
there is existing progress on the systemic correction and strategy for a
thorough search of planetary signals. We note that the covariance structure of
the activity signals learnt from this work can be effectively used to separate
stellar and planetary components in the RVs.

The longer-term behaviour of the activity indicators analysed in this work can
also be used to search for activity cycles in our targets. This will be the
topic of the next paper in our series (Crétignier et al. in prep.). In the
longer term, we also plan to incorporate the RV time-series, as well as other
activity indicators, into our modelling, in order to improve our understanding
of the strengths and limitations of the multi-dimensional GP framework for
activity mitigation in RV planet searches, as a function of the stellar
properties.

## Acknowledgements

H.Y., S.A., B.K., O.B., N.K.O.S. acknowledge funding from the European
Research Council under the European Union’s Horizon 2020 research and
innovation programme (grant agreement No 865624, GPRV). N.K.O.S thanks the
LSSTC Data Science Fellowship Program, which is funded by LSSTC, NSF
Cybertraining Grant #1829740, the Brinson Foundation, and the Moore
Foundation; her participation in the program has benefited this work. M.C.
acknowledges the SNSF support under grant P500PT_211024. Based on observations
made with ESO Telescopes at the La Silla Paranal Observatory under the HARPS
Guaranteed Time Observations (GTO) programme. This research has made use of
the SIMBAD database operated at CDS, Strasbourg (France).

## Data Availability

This work was based entirely on publicly available data download from the ESO
archive. Tables and are available in electronic format.

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##  Appendix A Confirmed rotation period measurements

Table Data Availability shows the measured rotation periods $\rm{P_{rot}}$ for
the selected 49 targets. In addition to $\rm{P_{rot}}$, we have provided
information about the time span of the data $\rm{T_{span}}$, as well as all
other hyperparameters from our model, including the evolution timescale
$\rm{l}$ and the harmonic complexity $\rm{\Gamma}$. We have also included the
derived Rossby number $\rm{Ro}$ and the $\mathrm{{RMS}[}aG(t)\mathrm{]}\ /\
\mathrm{{RMS}[}b\dot{G}(t)\mathrm{]}$ ($\rm{A/B}$; representing the facular-
to-spot ratio). All values, except for $\rm{T_{span}}$, come with associated
uncertainties.

##  Appendix B Basic properties of the sample

Table Data Availability shows the basic properties of all 268 targets in the
sample, including the effective temperature $T_{\rm{eff}}$, surface gravity
$\rm{log}\ g$, and mean $\log R_{\rm{HK}}^{\prime}$ from the catalogue
provided by Gomes da Silva et al. (2021), with associated uncertainties.
Additionally, we have included details about the temporal coverage of
observations, denoted as $\rm{T_{range}}$, as well as the temporal span of the
data processed using DRS 3.5. Any temporal span not covered by the DRS 3.5
processed data is filled by the DRS 3.8 processed data.

Table 2: Confirmed rotation period measurements of 49 targets. Simbad name |  $\rm{T_{span}}$ [yr] |  $\rm{P_{rot}}$ [d] |  $\rm{l}$ [d] | $\rm{\Gamma}$ | $\rm Ro$ | $\rm{A/B}$
---|---|---|---|---|---|---
BD-08 2823 | $2.42$ | $27.0_{-0.4}^{+0.4}$ | $966_{-462}^{+559}$ | $1.86_{-0.64}^{+0.91}$ | $0.94_{-0.02}^{+0.02}$ | $1.5_{-1.0}^{+1.0}$
HD 104067 | $2.38$ | $30.3_{-0.8}^{+0.8}$ | $386_{-230}^{+379}$ | $1.21_{-0.51}^{+0.66}$ | $1.25_{-0.03}^{+0.03}$ | $0.7_{-0.6}^{+0.6}$
HD 109200 | $7.24$ | $39.6_{-8.3}^{+8.3}$ | $57_{-38}^{+32}$ | $0.76_{-0.12}^{+0.34}$ | $1.72_{-0.36}^{+0.36}$ | $1.8_{-0.5}^{+0.5}$
HD 115617 | $7.49$ | $32.1_{-0.2}^{+0.2}$ | $186_{-50}^{+78}$ | $0.68_{-0.12}^{+0.16}$ | $1.99_{-0.02}^{+0.02}$ | $1.2_{-0.7}^{+0.7}$
HD 125072 | $7.44$ | $40.8_{-0.8}^{+0.8}$ | $482_{-227}^{+455}$ | $1.14_{-0.32}^{+0.47}$ | $1.52_{-0.03}^{+0.03}$ | $1.9_{-1.5}^{+1.5}$
HD 125184 | $9.38$ | $43.9_{-2.0}^{+2.0}$ | $200_{-78}^{+151}$ | $0.59_{-0.14}^{+0.19}$ | $3.06_{-0.14}^{+0.14}$ | $1.8_{-1.2}^{+1.2}$
HD 125595 | $3.44$ | $37.1_{-0.5}^{+0.5}$ | $804_{-410}^{+485}$ | $2.82_{-1.33}^{+1.78}$ | $1.27_{-0.02}^{+0.02}$ | $1.2_{-1.0}^{+1.0}$
HD 13060 | $0.39$ | $34.3_{-3.8}^{+3.8}$ | $538_{-272}^{+420}$ | $3.91_{-1.75}^{+3.06}$ | $1.68_{-0.19}^{+0.19}$ | $0.8_{-0.7}^{+0.7}$
HD 136713 | $9.49$ | $36.4_{-1.6}^{+1.6}$ | $395_{-231}^{+527}$ | $0.87_{-0.35}^{+0.48}$ | $1.52_{-0.07}^{+0.07}$ | $0.3_{-0.3}^{+0.3}$
HD 13808 | $8.08$ | $38.0_{-0.3}^{+0.3}$ | $379_{-106}^{+197}$ | $1.20_{-0.20}^{+0.28}$ | $1.62_{-0.01}^{+0.01}$ | $3.1_{-2.0}^{+2.0}$
HD 144628 | $9.44$ | $38.5_{-1.1}^{+1.1}$ | $184_{-64}^{+135}$ | $1.59_{-0.38}^{+0.64}$ | $1.63_{-0.05}^{+0.05}$ | $3.5_{-2.7}^{+2.7}$
HD 15337 | $10.94$ | $37.1_{-0.8}^{+0.8}$ | $1330_{-513}^{+456}$ | $5.43_{-2.48}^{+2.72}$ | $1.73_{-0.04}^{+0.04}$ | $3.0_{-2.5}^{+2.5}$
HD 154088 | $5.25$ | $30.7_{-1.7}^{+1.7}$ | $150_{-38}^{+66}$ | $1.53_{-0.35}^{+0.54}$ | $1.64_{-0.09}^{+0.09}$ | $14.7_{-12.8}^{+12.8}$
HD 154577 | $7.44$ | $34.3_{-1.0}^{+1.0}$ | $104_{-30}^{+42}$ | $1.00_{-0.14}^{+0.17}$ | $1.32_{-0.04}^{+0.04}$ | $1.7_{-0.5}^{+0.5}$
HD 157172 | $5.40$ | $35.4_{-10.6}^{+10.6}$ | $498_{-247}^{+478}$ | $4.23_{-2.16}^{+2.96}$ | $2.00_{-0.60}^{+0.60}$ | $4.7_{-3.4}^{+3.4}$
HD 157830 | $2.56$ | $25.4_{-5.4}^{+5.4}$ | $566_{-332}^{+722}$ | $3.46_{-1.48}^{+2.45}$ | $1.55_{-0.33}^{+0.33}$ | $0.8_{-0.4}^{+0.4}$
HD 161098 | $9.43$ | $27.5_{-0.2}^{+0.2}$ | $323_{-94}^{+163}$ | $1.00_{-0.22}^{+0.37}$ | $1.71_{-0.01}^{+0.01}$ | $1.6_{-1.2}^{+1.2}$
HD 16417 | $3.33$ | $33.0_{-6.1}^{+6.1}$ | $102_{-38}^{+90}$ | $0.83_{-0.23}^{+0.51}$ | $2.81_{-0.52}^{+0.52}$ | $1.3_{-1.4}^{+1.4}$
HD 168863 | $2.36$ | $32.0_{-7.8}^{+7.8}$ | $1000_{-529}^{+605}$ | $2.58_{-1.28}^{+2.71}$ | $1.19_{-0.29}^{+0.29}$ | $2.0_{-2.5}^{+2.5}$
HD 171587 | $2.56$ | $24.7_{-3.3}^{+3.3}$ | $650_{-390}^{+583}$ | $2.76_{-1.18}^{+1.95}$ | $1.35_{-0.18}^{+0.18}$ | $1.3_{-0.9}^{+0.9}$
HD 172513 | $1.18$ | $24.0_{-0.6}^{+0.6}$ | $276_{-127}^{+173}$ | $1.14_{-0.34}^{+0.40}$ | $1.41_{-0.03}^{+0.03}$ | $1.0_{-0.6}^{+0.6}$
HD 176986 | $10.06$ | $34.8_{-0.8}^{+0.8}$ | $95_{-24}^{+34}$ | $0.65_{-0.11}^{+0.12}$ | $1.48_{-0.03}^{+0.03}$ | $1.1_{-0.4}^{+0.4}$
HD 183658 | $3.40$ | $28.4_{-8.2}^{+8.2}$ | $803_{-460}^{+535}$ | $3.57_{-2.03}^{+2.85}$ | $2.300_{-0.66}^{+0.66}$ | –
HD 189567 | $9.04$ | $41.7_{-11.7}^{+11.7}$ | $75_{-62}^{+52}$ | $0.64_{-0.11}^{+0.89}$ | $3.06_{-0.86}^{+0.86}$ | $6.5_{-2.3}^{+2.3}$
HD 192310 | $7.23$ | $41.0_{-0.9}^{+0.9}$ | $222_{-64}^{+175}$ | $1.23_{-0.21}^{+0.37}$ | $1.81_{-0.04}^{+0.04}$ | $2.5_{-2.8}^{+2.8}$
HD 202206 | $1.29$ | $50.0_{-5.1}^{+5.1}$ | $918_{-352}^{+406}$ | $5.54_{-2.04}^{+2.27}$ | $3.810_{-0.39}^{+0.39}$ | –
HD 208704 | $2.28$ | $32.2_{-7.8}^{+7.8}$ | $878_{-507}^{+615}$ | $3.10_{-1.47}^{+2.29}$ | $2.69_{-0.65}^{+0.65}$ | $2.0_{-2.1}^{+2.1}$
HD 215152 | $8.10$ | $38.0_{-0.8}^{+0.8}$ | $182_{-42}^{+70}$ | $2.59_{-0.59}^{+0.86}$ | $1.43_{-0.03}^{+0.03}$ | $4.7_{-3.1}^{+3.1}$
HD 216770 | $9.26$ | $37.4_{-4.7}^{+4.7}$ | $314_{-149}^{+221}$ | $1.57_{-0.51}^{+0.81}$ | $2.07_{-0.26}^{+0.26}$ | $1.0_{-1.0}^{+1.0}$
HD 21693 | $5.47$ | $32.0_{-0.7}^{+0.7}$ | $321_{-119}^{+294}$ | $0.84_{-0.17}^{+0.31}$ | $1.78_{-0.04}^{+0.04}$ | $3.4_{-2.8}^{+2.8}$
HD 21749 | $0.39$ | $38.3_{-4.9}^{+4.9}$ | $382_{-222}^{+353}$ | $1.45_{-0.47}^{+0.60}$ | $1.32_{-0.17}^{+0.17}$ | $0.4_{-0.3}^{+0.3}$
HD 22049 | $0.23$ | $11.2_{-0.1}^{+0.1}$ | $128_{-56}^{+74}$ | $1.70_{-0.58}^{+0.58}$ | $0.48_{-0.01}^{+0.01}$ | $0.1_{-0.1}^{+0.1}$
HD 223171 | $12.48$ | $37.2_{-11.2}^{+11.2}$ | $85_{-64}^{+163}$ | $0.98_{-0.38}^{+2.82}$ | $3.170_{-0.95}^{+0.95}$ | –
HD 26965 | $12.41$ | $35.6_{-16.0}^{+16.0}$ | $51_{-40}^{+52}$ | $1.64_{-0.77}^{+3.74}$ | $1.560_{-0.70}^{+0.70}$ | –
HD 27894 | $13.56$ | $48.2_{-8.0}^{+8.0}$ | $827_{-635}^{+762}$ | $3.34_{-1.60}^{+2.80}$ | $1.968_{-0.32}^{+0.32}$ | –
HD 36003 | $11.21$ | $50.2_{-2.0}^{+2.0}$ | $214_{-78}^{+129}$ | $0.85_{-0.15}^{+0.22}$ | $1.74_{-0.07}^{+0.07}$ | $2.4_{-1.3}^{+1.3}$
HD 40307 | $7.42$ | $42.5_{-0.5}^{+0.5}$ | $494_{-139}^{+273}$ | $1.21_{-0.20}^{+0.29}$ | $1.76_{-0.02}^{+0.02}$ | $2.5_{-1.6}^{+1.6}$
HD 45184 | $15.01$ | $20.0_{-0.1}^{+0.1}$ | $278_{-78}^{+115}$ | $1.22_{-0.21}^{+0.27}$ | $1.78_{-0.01}^{+0.01}$ | $5.6_{-3.0}^{+3.0}$
HD 4915 | $13.33$ | $25.2_{-11.7}^{+11.7}$ | $180_{-163}^{+326}$ | $2.49_{-1.28}^{+2.46}$ | $1.72_{-0.80}^{+0.80}$ | $2.3_{-1.9}^{+1.9}$
HD 51608 | $7.43$ | $37.1_{-1.8}^{+1.8}$ | $845_{-527}^{+762}$ | $1.60_{-0.52}^{+1.10}$ | $1.95_{-0.10}^{+0.10}$ | $3.1_{-2.8}^{+2.8}$
HD 63765 | $12.33$ | $25.5_{-9.1}^{+9.1}$ | $95_{-42}^{+82}$ | $3.20_{-1.59}^{+3.15}$ | $1.42_{-0.51}^{+0.51}$ | $1.6_{-1.5}^{+1.5}$
HD 65277A | $2.43$ | $42.9_{-5.8}^{+5.8}$ | $1368_{-501}^{+426}$ | $5.28_{-2.04}^{+2.56}$ | $1.52_{-0.20}^{+0.20}$ | $0.7_{-0.9}^{+0.9}$
HD 68978 | $8.24$ | $16.8_{-0.8}^{+0.8}$ | $63_{-20}^{+30}$ | $0.73_{-0.13}^{+0.20}$ | $1.75_{-0.08}^{+0.08}$ | $2.2_{-1.1}^{+1.1}$
HD 69830 | $7.50$ | $33.7_{-1.0}^{+1.0}$ | $234_{-106}^{+418}$ | $1.31_{-0.31}^{+0.63}$ | $1.83_{-0.06}^{+0.06}$ | $2.5_{-1.8}^{+1.8}$
HD 71835 | $7.47$ | $29.7_{-0.5}^{+0.5}$ | $1123_{-595}^{+583}$ | $2.06_{-0.70}^{+1.80}$ | $1.66_{-0.03}^{+0.03}$ | $5.0_{-4.2}^{+4.2}$
HD 78429 | $13.37$ | $43.4_{-14.8}^{+14.8}$ | $19_{-8}^{+58}$ | $0.84_{-0.33}^{+5.90}$ | $3.32_{-1.13}^{+1.13}$ | $4.4_{-1.5}^{+1.5}$
HD 89454 | $1.43$ | $16.4_{-1.9}^{+1.9}$ | $327_{-187}^{+278}$ | $1.07_{-0.36}^{+0.47}$ | $1.21_{-0.14}^{+0.14}$ | $0.6_{-0.5}^{+0.5}$
HD 93083 | $10.26$ | $44.6_{-6.2}^{+6.2}$ | $321_{-213}^{+448}$ | $1.75_{-0.66}^{+1.06}$ | $1.92_{-0.27}^{+0.27}$ | $2.1_{-1.9}^{+1.9}$
HD 96700 | $5.33$ | $43.6_{-2.3}^{+2.3}$ | $194_{-72}^{+177}$ | $0.79_{-0.21}^{+0.46}$ | $3.73_{-0.20}^{+0.20}$ | $6.3_{-11.6}^{+11.6}$

Table 3: Basic properties of all 268 targets in the sample. Simbad name |  $T_{\rm{eff}}$ [K] |  $T_{\rm{eff}}$ err [K] | $\rm{log}\ g$ |  $\rm{log}\ g$ err | Mean $\log R_{\rm{HK}}^{\prime}$ | Mean $\log R_{\rm{HK}}^{\prime}$ err | $\rm{T_{range}}$ |  $\rm{T_{range}}$ (DRS 3.5)
---|---|---|---|---|---|---|---|---
BD-08 2823 | 4672.0 | 105.0 | 4.61 | 0.26 | -4.6944 | 0.0039 | 2004-01 to 2018-04 | 2004-01 to 2010-01
CD-23 395 | 4673.0 | 175.0 | 4.52 | 0.47 | -4.8528 | 0.0040 | 2004-07 to 2016-10 | 2004-07 to 2013-01
CD-24 10619 | 4574.0 | 155.0 | 4.68 | 0.44 | -4.5766 | 0.0036 | 2005-06 to 2021-02 | 2005-06 to 2011-07
CD-26 2288 | 4924.0 | 94.0 | 4.51 | 0.28 | -4.6539 | 0.0037 | 2004-01 to 2019-10 | 2004-01 to 2011-12
HD 10180 | 5911.0 | 19.0 | 4.19 | 0.03 | -4.9957 | 0.0043 | 2003-11 to 2017-08 | 2003-11 to 2015-01
HD 101930 | 5164.0 | 61.0 | 4.49 | 0.11 | -5.0048 | 0.0033 | 2004-02 to 2016-06 | 2004-02 to 2015-05
HD 102117 | 5657.0 | 24.0 | 4.21 | 0.04 | -5.1215 | 0.0050 | 2004-01 to 2016-05 | 2004-01 to 2015-05
HD 102365 | 5629.0 | 29.0 | 4.35 | 0.03 | -4.9489 | 0.0030 | 2003-11 to 2017-05 | 2003-11 to 2015-05
HD 103197 | 5250.0 | 60.0 | 4.51 | 0.11 | -5.0796 | 0.0059 | 2004-02 to 2018-04 | 2004-02 to 2010-04
HD 103720 | 5017.0 | 88.0 | 4.58 | 0.16 | -4.4493 | 0.0038 | 2005-02 to 2021-02 | 2005-02 to 2015-05
HD 103774 | 6732.0 | 56.0 | 4.29 | 0.06 | -4.7718 | 0.0073 | 2004-12 to 2018-04 | 2004-12 to 2013-02
HD 104067 | 4969.0 | 72.0 | 4.64 | 0.13 | -4.7370 | 0.0017 | 2004-02 to 2010-04 | 2004-02 to 2010-04
HD 104800 | 5697.0 | 25.0 | 4.35 | 0.02 | -4.8877 | 0.0058 | 2004-02 to 2015-01 | 2004-02 to 2015-01
HD 105690 | 5666.0 | 38.0 | 4.53 | 0.07 | -4.3063 | 0.0012 | 2009-04 to 2017-06 | 2009-04 to 2014-07
HD 106116 | 5680.0 | 15.0 | 4.28 | 0.03 | -5.0317 | 0.0041 | 2004-02 to 2017-06 | 2004-02 to 2015-05
HD 10647 | 6218.0 | 20.0 | 4.30 | 0.04 | -4.7431 | 0.0024 | 2003-11 to 2020-01 | 2003-11 to 2012-01
HD 10700 | 5310.0 | 17.0 | 4.49 | 0.03 | -4.9773 | 0.0025 | 2003-09 to 2012-10 | 2003-10 to 2012-10
HD 107094 | 5562.0 | 17.0 | 4.48 | 0.03 | -4.8283 | 0.0055 | 2004-01 to 2021-02 | 2004-01 to 2015-03
HD 109200 | 5056.0 | 33.0 | 4.50 | 0.08 | -4.9542 | 0.0027 | 2004-02 to 2018-05 | 2004-02 to 2015-05
HD 109271 | 5783.0 | 18.0 | 4.13 | 0.02 | -4.9963 | 0.0074 | 2005-02 to 2018-04 | 2005-02 to 2014-07
HD 111232 | 5460.0 | 21.0 | 4.41 | 0.03 | -4.9832 | 0.0041 | 2004-02 to 2021-03 | 2004-02 to 2015-05
HD 111515 | 5398.0 | 18.0 | 4.47 | 0.02 | -4.9528 | 0.0043 | 2004-02 to 2017-07 | 2004-02 to 2009-03
HD 111777 | 5666.0 | 19.0 | 4.36 | 0.03 | -4.9115 | 0.0048 | 2004-02 to 2018-06 | 2004-02 to 2014-05
HD 11397 | 5564.0 | 26.0 | 4.40 | 0.04 | -4.8975 | 0.0047 | 2003-10 to 2019-09 | 2003-10 to 2014-08
HD 114076 | 5066.0 | 25.1 | 4.47 | 0.07 | -4.9911 | 0.0058 | 2004-02 to 2015-04 | 2004-02 to 2015-04
HD 114613 | 5729.0 | 17.0 | 3.84 | 0.02 | -5.1529 | 0.0041 | 2004-01 to 2019-04 | 2004-01 to 2015-05
HD 114729 | 5844.0 | 12.0 | 4.02 | 0.02 | -5.0046 | 0.0044 | 2004-02 to 2021-03 | 2004-02 to 2014-08
HD 114853 | 5705.0 | 14.0 | 4.32 | 0.02 | -4.9435 | 0.0037 | 2004-01 to 2017-08 | 2004-01 to 2015-05
HD 115617 | 5559.0 | 17.0 | 4.30 | 0.03 | -5.0132 | 0.0029 | 2004-01 to 2021-03 | 2004-01 to 2015-05
HD 117207 | 5667.0 | 21.0 | 4.22 | 0.04 | -5.0881 | 0.0045 | 2004-02 to 2021-03 | 2004-02 to 2015-05
HD 117618 | 5990.0 | 13.0 | 4.18 | 0.02 | -4.9790 | 0.0040 | 2004-02 to 2019-08 | 2004-02 to 2010-05
HD 119173 | 5779.0 | 44.0 | 4.11 | 0.04 | -4.8290 | 0.0050 | 2006-02 to 2020-02 | 2006-02 to 2014-03
HD 11964 | 5326.0 | 19.0 | 3.90 | 0.04 | -5.1763 | 0.0037 | 2003-10 to 2018-11 | 2003-10 to 2015-01
HD 119949 | 6359.0 | 36.0 | 4.10 | 0.04 | -4.9050 | 0.0046 | 2004-02 to 2014-01 | 2004-02 to 2014-01
HD 124292 | 5443.0 | 22.0 | 4.35 | 0.04 | -5.0128 | 0.0037 | 2004-02 to 2017-08 | 2004-02 to 2015-05
HD 125072 | 4794.0 | 102.0 | 4.51 | 0.24 | -4.9238 | 0.0018 | 2004-02 to 2017-08 | 2004-02 to 2015-05
HD 125184 | 5680.0 | 30.0 | 3.99 | 0.05 | -5.0952 | 0.0039 | 2004-02 to 2017-08 | 2004-02 to 2015-05
HD 125595 | 4636.0 | 83.9 | 4.50 | 0.26 | -4.7575 | 0.0030 | 2004-05 to 2019-08 | 2004-05 to 2010-02
HD 125612A | 5913.0 | 17.0 | 4.23 | 0.03 | -4.8988 | 0.0083 | 2004-02 to 2021-03 | 2004-02 to 2015-03
HD 125881 | 6036.0 | 17.0 | 4.24 | 0.03 | -4.8726 | 0.0036 | 2004-02 to 2013-05 | 2004-02 to 2013-05
HD 126525 | 5638.0 | 13.0 | 4.28 | 0.02 | -4.9978 | 0.0045 | 2004-06 to 2019-05 | 2004-06 to 2015-05
HD 126793 | 5904.0 | 33.0 | 4.23 | 0.03 | -4.8659 | 0.0048 | 2004-05 to 2015-02 | 2004-05 to 2015-02
HD 126803 | 5470.0 | 18.0 | 4.45 | 0.04 | -4.9348 | 0.0050 | 2004-02 to 2019-08 | 2004-02 to 2014-05
HD 129642 | 4919.0 | 65.0 | 4.54 | 0.16 | -5.0077 | 0.0037 | 2004-02 to 2017-08 | 2004-02 to 2015-05
HD 13060 | 5255.0 | 45.0 | 4.40 | 0.09 | -4.8547 | 0.0051 | 2003-10 to 2016-09 | 2003-10 to 2015-01
HD 131653 | 5324.0 | 26.0 | 4.57 | 0.04 | -4.9976 | 0.0077 | 2004-05 to 2015-07 | 2004-05 to 2015-05
HD 131664 | 5901.0 | 26.0 | 4.30 | 0.03 | -4.8432 | 0.0076 | 2004-05 to 2021-02 | 2004-05 to 2014-07
HD 132569 | 4967.0 | 44.7 | 4.64 | 0.11 | -4.6443 | 0.0043 | 2004-05 to 2011-08 | 2004-05 to 2011-08
HD 133633 | 5571.0 | 19.0 | 4.41 | 0.04 | -4.9437 | 0.0053 | 2005-05 to 2018-07 | 2005-05 to 2014-05
HD 134060 | 5966.0 | 14.0 | 4.21 | 0.03 | -4.9983 | 0.0038 | 2004-02 to 2017-05 | 2004-02 to 2015-05
HD 134088 | 5675.0 | 22.0 | 4.35 | 0.03 | -4.8092 | 0.0041 | 2004-05 to 2015-06 | 2004-05 to 2015-04
HD 134606 | 5633.0 | 28.0 | 4.29 | 0.05 | -5.1077 | 0.0042 | 2004-07 to 2017-05 | 2004-07 to 2015-05
HD 134987 | 5740.0 | 23.0 | 4.17 | 0.04 | -5.1106 | 0.0043 | 2004-02 to 2016-04 | 2004-02 to 2015-05
HD 135625 | 6003.0 | 14.0 | 4.08 | 0.04 | -5.0250 | 0.0087 | 2004-02 to 2021-03 | 2004-02 to 2015-05
HD 136352 | 5664.0 | 14.0 | 4.29 | 0.02 | -4.9412 | 0.0031 | 2004-05 to 2017-08 | 2004-05 to 2015-05
HD 136713 | 4994.0 | 74.0 | 4.61 | 0.14 | -4.7748 | 0.0020 | 2005-05 to 2016-09 | 2005-05 to 2015-05
HD 137388 | 5240.0 | 53.0 | 4.48 | 0.11 | -4.8949 | 0.0040 | 2005-07 to 2016-08 | 2005-07 to 2014-06
HD 137676 | 5253.0 | 18.0 | 3.99 | 0.03 | -5.1132 | 0.0044 | 2004-02 to 2018-06 | 2004-02 to 2011-08
HD 13808 | 5033.0 | 38.0 | 4.50 | 0.08 | -4.8921 | 0.0034 | 2003-12 to 2016-02 | 2003-12 to 2015-01
HD 1388 | 5954.0 | 10.0 | 4.19 | 0.02 | -4.9714 | 0.0038 | 2003-10 to 2017-09 | 2003-10 to 2014-12
HD 141624 | 5871.0 | 30.0 | 4.22 | 0.03 | -4.9127 | 0.0050 | 2005-05 to 2018-08 | 2005-05 to 2014-07
HD 142709 | 4728.0 | 65.0 | 4.70 | 0.18 | -4.9360 | 0.0023 | 2004-07 to 2016-04 | 2004-07 to 2015-02
HD 143361 | 5503.0 | 36.0 | 4.32 | 0.06 | -5.1130 | 0.0072 | 2007-05 to 2020-03 | 2007-05 to 2014-09
HD 144628 | 5022.0 | 26.0 | 4.58 | 0.08 | -4.9259 | 0.0025 | 2004-07 to 2019-04 | 2004-07 to 2015-05
HD 145377 | 6054.0 | 16.0 | 4.27 | 0.03 | -4.6128 | 0.0051 | 2005-06 to 2011-04 | 2005-06 to 2011-04
HD 145417 | 4953.0 | 48.4 | 4.98 | 0.08 | -4.8971 | 0.0032 | 2004-05 to 2014-08 | 2004-05 to 2014-08
HD 14745 | 6290.0 | 39.0 | 4.37 | 0.04 | -4.8876 | 0.0073 | 2003-11 to 2021-02 | 2003-11 to 2014-03
HD 148156 | 6251.0 | 25.0 | 4.18 | 0.05 | -4.9315 | 0.0087 | 2005-04 to 2019-07 | 2005-04 to 2013-07
HD 148211 | 5948.0 | 22.0 | 4.15 | 0.02 | -4.9037 | 0.0050 | 2004-05 to 2016-04 | 2004-05 to 2015-03
HD 148303 | 4829.0 | 84.0 | 4.66 | 0.22 | -4.6532 | 0.0022 | 2004-07 to 2013-05 | 2004-07 to 2013-05
HD 149396 | 5657.0 | 23.0 | 4.37 | 0.03 | -4.6836 | 0.0056 | 2004-09 to 2016-05 | 2004-09 to 2013-07
HD 150177 | 6216.0 | 28.0 | 3.86 | 0.03 | -4.8915 | 0.0041 | 2004-05 to 2013-07 | 2004-05 to 2013-07
HD 150433 | 5665.0 | 12.0 | 4.33 | 0.02 | -4.9512 | 0.0038 | 2005-08 to 2017-08 | 2005-08 to 2014-09
HD 15337 | 5179.0 | 44.0 | 4.48 | 0.09 | -4.9226 | 0.0039 | 2003-12 to 2019-09 | 2003-12 to 2015-01
HD 153950 | 6074.0 | 15.0 | 4.13 | 0.03 | -4.9721 | 0.0082 | 2005-05 to 2018-03 | 2005-05 to 2014-07
HD 154088 | 5374.0 | 43.0 | 4.38 | 0.07 | -5.0718 | 0.0029 | 2006-04 to 2017-08 | 2006-04 to 2015-05
HD 154577 | 4847.0 | 35.0 | 4.69 | 0.07 | -4.8699 | 0.0022 | 2004-05 to 2017-08 | 2004-05 to 2015-05
HD 156098 | 6517.0 | 44.0 | 3.76 | 0.05 | -4.7816 | 0.0045 | 2005-05 to 2021-03 | 2005-05 to 2015-05
HD 15612 | 5256.0 | 34.0 | 4.55 | 0.06 | -4.5080 | 0.0044 | 2003-11 to 2018-02 | 2003-11 to 2014-03
HD 156411 | 5910.0 | 16.0 | 3.79 | 0.01 | -5.1400 | 0.0096 | 2005-05 to 2019-07 | 2005-05 to 2013-07
HD 157172 | 5451.0 | 27.0 | 4.37 | 0.05 | -5.0040 | 0.0037 | 2005-07 to 2017-03 | 2005-07 to 2015-05
HD 157347 | 5676.0 | 16.0 | 4.27 | 0.03 | -5.0213 | 0.0038 | 2006-03 to 2019-08 | 2006-03 to 2015-05
HD 157830 | 5540.0 | 16.0 | 4.43 | 0.02 | -4.7868 | 0.0030 | 2004-05 to 2012-09 | 2004-05 to 2012-09
HD 1581 | 5951.0 | 13.0 | 4.28 | 0.03 | -4.9174 | 0.0031 | 2003-10 to 2020-12 | 2003-10 to 2014-12
HD 16008 | 5770.0 | 14.0 | 4.33 | 0.03 | -4.8465 | 0.0049 | 2003-10 to 2021-03 | 2003-10 to 2015-01
HD 161098 | 5560.0 | 15.0 | 4.40 | 0.02 | -4.9240 | 0.0037 | 2006-04 to 2017-09 | 2006-04 to 2015-05
HD 161566 | 6230.0 | 24.0 | 3.88 | 0.04 | -4.9879 | 0.0077 | 2005-06 to 2019-07 | 2005-06 to 2013-03
HD 16160 | 4796.0 | 109.0 | 4.62 | 0.27 | -4.8649 | 0.0020 | 2003-10 to 2008-09 | 2003-10 to 2008-09
HD 16280 | 4677.0 | 83.5 | 4.58 | 0.31 | -4.6712 | 0.0039 | 2003-10 to 2021-03 | 2003-10 to 2014-12
HD 16417 | 5841.0 | 17.0 | 3.99 | 0.02 | -5.1028 | 0.0043 | 2003-11 to 2017-09 | 2003-11 to 2015-01
HD 165131 | 5870.0 | 15.0 | 4.27 | 0.03 | -4.9658 | 0.0086 | 2006-05 to 2021-03 | 2006-05 to 2015-05
HD 166724 | 5099.0 | 36.0 | 4.55 | 0.09 | -4.7253 | 0.0033 | 2004-05 to 2011-09 | 2004-05 to 2011-09
HD 167677 | 5474.0 | 20.0 | 4.40 | 0.03 | -4.9899 | 0.0074 | 2005-05 to 2019-08 | 2005-05 to 2015-05
HD 168863 | 4782.0 | 80.0 | 4.52 | 0.23 | -4.7762 | 0.0041 | 2006-07 to 2021-03 | 2006-07 to 2014-07
HD 170493 | 4751.0 | 108.0 | 4.49 | 0.25 | -4.8776 | 0.0024 | 2005-07 to 2015-09 | 2005-07 to 2015-05
HD 171028 | 5671.0 | 16.0 | 3.73 | 0.03 | -5.1098 | 0.0071 | 2004-10 to 2017-09 | 2004-10 to 2011-03
HD 171587 | 5412.0 | 15.0 | 4.58 | 0.02 | -4.7553 | 0.0035 | 2004-11 to 2014-08 | 2004-11 to 2014-08
HD 172513 | 5500.0 | 18.0 | 4.37 | 0.03 | -4.7730 | 0.0025 | 2004-05 to 2007-05 | 2004-05 to 2007-05
HD 172568 | 5728.0 | 22.0 | 4.45 | 0.03 | -4.9046 | 0.0051 | 2005-05 to 2018-08 | 2005-05 to 2013-10
HD 175607 | 5392.0 | 17.0 | 4.51 | 0.03 | -4.9298 | 0.0052 | 2004-07 to 2015-04 | 2004-07 to 2015-04
HD 176354 | 5271.0 | 40.0 | 3.89 | 0.07 | -5.0505 | 0.0052 | 2006-05 to 2019-07 | 2006-05 to 2011-09
HD 176986 | 5018.0 | 59.0 | 4.60 | 0.11 | -4.8283 | 0.0028 | 2004-07 to 2017-08 | 2004-07 to 2015-04
HD 177565 | 5627.0 | 19.0 | 4.30 | 0.03 | -4.9085 | 0.0027 | 2003-10 to 2017-09 | 2003-10 to 2015-05
HD 17865 | 5877.0 | 24.0 | 4.13 | 0.03 | -4.9272 | 0.0051 | 2003-11 to 2014-09 | 2003-11 to 2014-09
HD 17970 | 5038.0 | 31.0 | 4.53 | 0.06 | -5.0043 | 0.0037 | 2003-10 to 2017-09 | 2003-10 to 2015-01
HD 181433 | 4962.0 | 134.0 | 4.54 | 0.27 | -5.1290 | 0.0036 | 2003-10 to 2017-08 | 2003-10 to 2015-05
HD 181720 | 5792.0 | 17.0 | 4.10 | 0.02 | -4.9792 | 0.0051 | 2005-05 to 2017-11 | 2005-05 to 2014-08
HD 183658 | 5803.0 | 17.0 | 4.24 | 0.02 | -4.9407 | 0.0043 | 2005-08 to 2019-05 | 2005-08 to 2015-05
HD 185283 | 4746.0 | 79.3 | 4.53 | 0.20 | -4.9514 | 0.0046 | 2005-07 to 2019-09 | 2005-07 to 2015-05
HD 189567 | 5726.0 | 15.0 | 4.28 | 0.01 | -4.9120 | 0.0031 | 2003-10 to 2017-08 | 2003-10 to 2015-05
HD 190248 | 5644.0 | 30.0 | 4.12 | 0.05 | -5.1315 | 0.0034 | 2003-10 to 2016-10 | 2003-10 to 2015-05
HD 190647 | 5639.0 | 24.0 | 4.09 | 0.04 | -5.1613 | 0.0064 | 2004-09 to 2021-03 | 2004-09 to 2014-10
HD 190984 | 6007.0 | 25.0 | 3.78 | 0.03 | -5.0626 | 0.0073 | 2004-05 to 2013-08 | 2004-05 to 2013-08
HD 191797 | 5037.0 | 48.5 | 4.61 | 0.11 | -4.3751 | 0.0037 | 2004-07 to 2019-08 | 2004-07 to 2014-07
HD 192310 | 5087.0 | 48.0 | 4.42 | 0.10 | -4.9509 | 0.0019 | 2003-11 to 2016-10 | 2003-11 to 2014-10
HD 19467 | 5720.0 | 10.0 | 4.18 | 0.01 | -5.0079 | 0.0040 | 2003-10 to 2017-10 | 2003-10 to 2015-01
HD 195145 | 5625.0 | 20.0 | 4.32 | 0.03 | -4.9820 | 0.0081 | 2006-07 to 2018-06 | 2006-07 to 2013-07
HD 19641 | 5806.0 | 14.0 | 4.23 | 0.02 | -4.9734 | 0.0082 | 2003-11 to 2021-01 | 2003-11 to 2014-12
HD 197027 | 5694.0 | 28.0 | 4.09 | 0.04 | -5.0001 | 0.0067 | 2009-05 to 2019-05 | 2009-05 to 2014-11
HD 197197 | 5812.0 | 16.0 | 4.04 | 0.02 | -5.0203 | 0.0061 | 2003-11 to 2018-10 | 2003-11 to 2015-04
HD 199288 | 5765.0 | 19.0 | 4.36 | 0.02 | -4.8868 | 0.0033 | 2003-11 to 2019-11 | 2003-11 to 2015-05
HD 199289 | 5928.0 | 37.0 | 4.43 | 0.03 | -4.8466 | 0.0050 | 2003-11 to 2018-08 | 2003-11 to 2014-10
HD 199604 | 5817.0 | 22.0 | 4.18 | 0.03 | -4.9118 | 0.0057 | 2003-11 to 2018-10 | 2003-11 to 2010-11
HD 199847 | 5763.0 | 20.0 | 4.08 | 0.02 | -5.0033 | 0.0067 | 2003-11 to 2018-10 | 2003-11 to 2014-09
HD 20003 | 5494.0 | 27.0 | 4.37 | 0.05 | -4.9891 | 0.0050 | 2003-12 to 2017-08 | 2003-12 to 2015-01
HD 200538 | 6042.0 | 18.0 | 4.13 | 0.03 | -5.0017 | 0.0085 | 2004-09 to 2017-04 | 2004-09 to 2012-09
HD 202206 | 5757.0 | 25.0 | 4.33 | 0.03 | -4.7434 | 0.0028 | 2004-05 to 2019-06 | 2004-05 to 2012-06
HD 202871 | 6055.0 | 16.0 | 4.28 | 0.04 | -4.7825 | 0.0075 | 2005-06 to 2012-09 | 2005-06 to 2012-09
HD 20407 | 5866.0 | 14.0 | 4.32 | 0.01 | -4.8786 | 0.0034 | 2003-10 to 2017-11 | 2003-10 to 2015-02
HD 204313 | 5776.0 | 22.0 | 4.23 | 0.02 | -5.0384 | 0.0046 | 2006-05 to 2017-09 | 2006-05 to 2014-10
HD 204941 | 4997.0 | 36.0 | 4.52 | 0.10 | -4.9275 | 0.0034 | 2004-12 to 2016-09 | 2004-12 to 2014-10
HD 205294 | 6370.0 | 32.0 | 3.92 | 0.04 | -4.8884 | 0.0072 | 2003-10 to 2018-09 | 2003-10 to 2011-08
HD 205536 | 5442.0 | 23.0 | 4.36 | 0.04 | -5.0377 | 0.0036 | 2003-10 to 2020-11 | 2003-10 to 2009-11
HD 206998 | 5822.0 | 26.0 | 4.08 | 0.03 | -4.9271 | 0.0058 | 2003-11 to 2018-10 | 2003-11 to 2014-10
HD 2071 | 5719.0 | 14.0 | 4.35 | 0.02 | -4.9186 | 0.0036 | 2003-10 to 2017-10 | 2003-10 to 2014-11
HD 207129 | 5937.0 | 13.0 | 4.28 | 0.02 | -4.8853 | 0.0030 | 2003-10 to 2020-11 | 2003-10 to 2015-05
HD 20781 | 5256.0 | 29.0 | 4.43 | 0.05 | -5.0498 | 0.0043 | 2003-12 to 2017-09 | 2003-12 to 2015-02
HD 20782 | 5774.0 | 14.0 | 4.22 | 0.01 | -4.9044 | 0.0036 | 2003-10 to 2017-10 | 2003-10 to 2015-01
HD 207832 | 5718.0 | 27.0 | 4.33 | 0.04 | -4.7324 | 0.0052 | 2003-10 to 2019-09 | 2003-10 to 2013-10
HD 207869 | 5527.0 | 21.0 | 4.45 | 0.05 | -4.9486 | 0.0060 | 2003-11 to 2017-08 | 2003-11 to 2013-08
HD 20807 | 5824.0 | 15.0 | 4.29 | 0.03 | -4.8720 | 0.0029 | 2003-10 to 2021-02 | 2003-10 to 2015-02
HD 208487 | 6146.0 | 19.0 | 4.19 | 0.03 | -4.9230 | 0.0038 | 2004-09 to 2019-09 | 2004-09 to 2007-06
HD 20868 | 4720.0 | 91.0 | 4.50 | 0.22 | -4.9930 | 0.0050 | 2003-11 to 2019-08 | 2003-11 to 2008-08
HD 208704 | 5826.0 | 11.0 | 4.21 | 0.01 | -4.9438 | 0.0037 | 2004-07 to 2017-10 | 2004-07 to 2014-11
HD 210918 | 5755.0 | 12.0 | 4.21 | 0.02 | -5.0101 | 0.0037 | 2003-10 to 2019-12 | 2003-10 to 2014-09
HD 211038 | 4974.0 | 17.0 | 3.84 | 0.05 | -5.1615 | 0.0030 | 2003-11 to 2017-08 | 2003-11 to 2014-10
HD 21132 | 6243.0 | 34.0 | 4.27 | 0.05 | -4.8531 | 0.0058 | 2004-02 to 2020-01 | 2004-02 to 2015-01
HD 21209 | 4671.0 | 65.0 | 4.59 | 0.15 | -4.7945 | 0.0026 | 2003-10 to 2016-09 | 2003-10 to 2015-01
HD 215152 | 4803.0 | 52.0 | 4.49 | 0.15 | -4.8599 | 0.0022 | 2003-12 to 2016-09 | 2003-12 to 2014-08
HD 215456 | 5789.0 | 15.0 | 3.95 | 0.03 | -5.1311 | 0.0049 | 2003-10 to 2017-05 | 2003-10 to 2014-10
HD 215497 | 5003.0 | 103.0 | 4.41 | 0.26 | -5.0695 | 0.0050 | 2004-10 to 2018-08 | 2004-10 to 2009-11
HD 216770 | 5424.0 | 51.0 | 4.37 | 0.07 | -4.9645 | 0.0031 | 2003-10 to 2019-09 | 2003-10 to 2013-11
HD 21693 | 5430.0 | 26.0 | 4.36 | 0.04 | -4.9244 | 0.0035 | 2003-10 to 2017-09 | 2003-10 to 2015-01
HD 21749 | 4640.0 | 100.0 | 4.91 | 0.07 | -4.6899 | 0.0019 | 2003-11 to 2016-12 | 2003-11 to 2009-12
HD 218504 | 5962.0 | 29.0 | 4.12 | 0.03 | -4.9327 | 0.0045 | 2003-11 to 2014-09 | 2003-11 to 2014-09
HD 219828 | 5888.0 | 14.0 | 4.01 | 0.02 | -5.1190 | 0.0064 | 2005-05 to 2015-08 | 2005-05 to 2013-11
HD 220339 | 4938.0 | 32.0 | 4.60 | 0.08 | -4.8213 | 0.0024 | 2003-10 to 2020-12 | 2003-10 to 2014-12
HD 22049 | 5049.0 | 48.0 | 4.59 | 0.09 | -4.4937 | 0.0007 | 2003-11 to 2020-01 | 2003-11 to 2007-08
HD 220507 | 5698.0 | 17.0 | 4.17 | 0.03 | -5.0747 | 0.0049 | 2003-10 to 2017-10 | 2003-10 to 2014-12
HD 221580 | 5322.0 | 24.0 | 2.71 | 0.04 | -5.4860 | 0.0158 | 2003-11 to 2007-10 | 2003-11 to 2007-10
HD 222669 | 5894.0 | 17.0 | 4.27 | 0.02 | -4.8376 | 0.0038 | 2003-12 to 2016-10 | 2003-12 to 2014-12
HD 223171 | 5841.0 | 18.0 | 4.03 | 0.02 | -5.0245 | 0.0042 | 2003-10 to 2018-11 | 2003-10 to 2014-12
HD 224685 | 5504.0 | 30.0 | 4.43 | 0.06 | -4.9248 | 0.0064 | 2004-12 to 2018-08 | 2004-12 to 2014-12
HD 224817 | 5894.0 | 22.0 | 4.17 | 0.02 | -4.9232 | 0.0052 | 2003-11 to 2015-07 | 2003-11 to 2014-11
HD 22879 | 5857.0 | 27.0 | 4.28 | 0.02 | -4.8791 | 0.0035 | 2003-10 to 2017-10 | 2003-10 to 2015-01
HD 23249 | 5035.0 | 39.0 | 3.80 | 0.08 | -5.1648 | 0.0024 | 2003-10 to 2017-03 | 2003-10 to 2015-01
HD 24062 | 6107.0 | 60.0 | 4.34 | 0.06 | -5.0123 | 0.0086 | 2003-11 to 2021-03 | 2003-11 to 2013-11
HD 24633 | 5276.0 | 43.0 | 4.41 | 0.07 | -4.9850 | 0.0071 | 2003-11 to 2021-03 | 2003-11 to 2013-12
HD 25171 | 6160.0 | 24.0 | 4.13 | 0.03 | -4.9322 | 0.0068 | 2003-11 to 2020-12 | 2003-11 to 2015-02
HD 26965 | 5072.0 | 53.0 | 4.58 | 0.19 | -4.9495 | 0.0022 | 2003-10 to 2021-02 | 2003-10 to 2015-01
HD 27063 | 5767.0 | 14.0 | 4.30 | 0.03 | -4.7496 | 0.0029 | 2003-11 to 2008-02 | 2003-11 to 2008-02
HD 27894 | 4952.0 | 105.0 | 4.56 | 0.20 | -4.9392 | 0.0065 | 2003-10 to 2019-03 | 2003-10 to 2013-11
HD 28254A | 5653.0 | 33.0 | 4.05 | 0.05 | -5.1685 | 0.0094 | 2003-10 to 2021-03 | 2003-10 to 2014-09
HD 28471 | 5745.0 | 14.0 | 4.24 | 0.01 | -4.9963 | 0.0043 | 2003-11 to 2018-01 | 2003-11 to 2013-01
HD 297396 | 4622.0 | 114.0 | 4.58 | 0.36 | -4.8059 | 0.0039 | 2004-01 to 2021-02 | 2004-01 to 2015-05
HD 31103 | 6078.0 | 16.0 | 4.23 | 0.02 | -4.6294 | 0.0055 | 2003-11 to 2020-11 | 2003-11 to 2013-11
HD 31128 | 6096.0 | 67.0 | 4.63 | 0.06 | -4.8146 | 0.0057 | 2003-11 to 2015-04 | 2003-11 to 2015-04
HD 31527 | 5898.0 | 13.0 | 4.26 | 0.02 | -4.9395 | 0.0038 | 2003-10 to 2017-08 | 2003-10 to 2015-02
HD 31822 | 6042.0 | 16.0 | 4.32 | 0.03 | -4.8204 | 0.0035 | 2003-10 to 2016-03 | 2003-10 to 2015-02
HD 3220 | 5846.0 | 15.0 | 4.34 | 0.02 | -4.8183 | 0.0079 | 2003-11 to 2010-11 | 2003-11 to 2010-11
HD 32564 | 5533.0 | 29.0 | 4.31 | 0.06 | -5.0305 | 0.0052 | 2009-11 to 2016-03 | 2009-11 to 2015-01
HD 330075 | 4958.0 | 52.0 | 4.41 | 0.13 | -4.9777 | 0.0041 | 2004-02 to 2015-04 | 2004-02 to 2012-02
HD 35854 | 4928.0 | 56.0 | 4.64 | 0.11 | -4.8052 | 0.0021 | 2003-10 to 2018-05 | 2003-10 to 2015-02
HD 36003 | 4647.0 | 88.0 | 4.60 | 0.21 | -4.8609 | 0.0016 | 2003-12 to 2016-03 | 2003-12 to 2015-03
HD 36379 | 6030.0 | 14.0 | 4.05 | 0.02 | -4.9482 | 0.0040 | 2003-10 to 2017-04 | 2003-10 to 2015-03
HD 3823 | 6022.0 | 14.0 | 4.07 | 0.02 | -4.9692 | 0.0039 | 2003-10 to 2017-09 | 2003-10 to 2015-01
HD 38858 | 5733.0 | 12.0 | 4.38 | 0.01 | -4.9051 | 0.0029 | 2003-10 to 2019-01 | 2003-10 to 2015-02
HD 39091 | 6003.0 | 17.0 | 4.18 | 0.03 | -4.9815 | 0.0037 | 2003-12 to 2020-12 | 2003-12 to 2015-01
HD 39194 | 5205.0 | 23.0 | 4.61 | 0.05 | -4.9628 | 0.0041 | 2003-11 to 2017-08 | 2003-11 to 2015-02
HD 3964 | 5729.0 | 19.0 | 4.37 | 0.04 | -4.8328 | 0.0073 | 2003-11 to 2020-12 | 2003-11 to 2014-09
HD 40307 | 4977.0 | 59.0 | 4.63 | 0.16 | -4.9389 | 0.0021 | 2003-10 to 2019-04 | 2003-10 to 2015-02
HD 40397 | 5527.0 | 20.0 | 4.34 | 0.04 | -5.0316 | 0.0037 | 2003-10 to 2016-09 | 2003-10 to 2015-04
HD 40865 | 5719.0 | 16.0 | 4.38 | 0.03 | -4.9144 | 0.0053 | 2003-10 to 2017-12 | 2003-10 to 2014-12
HD 41248 | 5713.0 | 21.0 | 4.37 | 0.03 | -4.8806 | 0.0053 | 2003-10 to 2017-12 | 2003-10 to 2014-01
HD 4308 | 5644.0 | 16.0 | 4.28 | 0.03 | -4.9553 | 0.0035 | 2003-10 to 2021-01 | 2003-10 to 2015-01
HD 43197 | 5449.0 | 42.0 | 4.28 | 0.08 | -5.0857 | 0.0070 | 2003-12 to 2021-03 | 2003-12 to 2013-03
HD 44219 | 5766.0 | 18.0 | 4.06 | 0.03 | -5.0551 | 0.0083 | 2003-11 to 2021-03 | 2003-11 to 2013-03
HD 45184 | 5869.0 | 14.0 | 4.29 | 0.02 | -4.9011 | 0.0031 | 2003-10 to 2021-03 | 2003-10 to 2015-03
HD 45364 | 5434.0 | 20.0 | 4.37 | 0.03 | -4.9753 | 0.0041 | 2003-12 to 2017-09 | 2003-12 to 2015-02
HD 457 | 6089.0 | 23.0 | 4.16 | 0.03 | -5.0230 | 0.0085 | 2003-10 to 2020-11 | 2003-10 to 2014-12
HD 47186 | 5675.0 | 21.0 | 4.25 | 0.04 | -5.0712 | 0.0043 | 2003-12 to 2017-09 | 2003-12 to 2015-04
HD 48115 | 5825.0 | 12.0 | 4.31 | 0.02 | -4.7526 | 0.0070 | 2004-01 to 2020-11 | 2004-01 to 2011-01
HD 48265 | 5798.0 | 29.0 | 3.79 | 0.14 | -5.1912 | 0.0063 | 2007-09 to 2021-03 | 2007-09 to 2015-02
HD 4915 | 5658.0 | 13.0 | 4.42 | 0.03 | -4.7879 | 0.0025 | 2003-10 to 2020-12 | 2003-10 to 2008-09
HD 51608 | 5358.0 | 22.0 | 4.38 | 0.05 | -5.0082 | 0.0043 | 2003-12 to 2017-09 | 2003-12 to 2015-04
HD 52265 | 6136.0 | 31.0 | 4.07 | 0.03 | -4.9915 | 0.0043 | 2004-02 to 2021-02 | 2004-02 to 2010-04
HD 5388 | 6311.0 | 33.0 | 3.89 | 0.03 | -4.9165 | 0.0082 | 2003-11 to 2019-07 | 2003-11 to 2010-01
HD 56274 | 5734.0 | 22.0 | 4.38 | 0.03 | -4.8320 | 0.0034 | 2003-11 to 2015-04 | 2003-11 to 2015-04
HD 59468 | 5618.0 | 20.0 | 4.30 | 0.03 | -5.0095 | 0.0034 | 2003-10 to 2018-05 | 2003-10 to 2015-05
HD 59711A | 5722.0 | 13.0 | 4.33 | 0.02 | -4.9295 | 0.0041 | 2003-10 to 2017-11 | 2003-10 to 2015-01
HD 60532 | 6273.0 | 37.0 | 3.68 | 0.04 | -5.0976 | 0.0050 | 2006-02 to 2011-06 | 2006-02 to 2011-06
HD 61051 | 5363.0 | 27.0 | 4.38 | 0.05 | -5.0692 | 0.0079 | 2004-01 to 2021-01 | 2004-01 to 2015-03
HD 61383 | 5716.0 | 14.0 | 4.08 | 0.02 | -5.0179 | 0.0088 | 2003-12 to 2021-03 | 2003-12 to 2015-03
HD 61986 | 5725.0 | 20.0 | 4.35 | 0.04 | -4.8898 | 0.0045 | 2003-12 to 2017-05 | 2003-12 to 2010-12
HD 63765 | 5432.0 | 19.0 | 4.41 | 0.03 | -4.7358 | 0.0026 | 2003-12 to 2019-04 | 2003-12 to 2010-04
HD 65277A | 4701.0 | 57.0 | 4.57 | 0.16 | -5.0334 | 0.0025 | 2003-12 to 2017-01 | 2003-12 to 2015-05
HD 65907A | 5945.0 | 16.0 | 4.31 | 0.02 | -4.9009 | 0.0032 | 2003-10 to 2021-01 | 2003-10 to 2015-04
HD 68146 | 6427.0 | 44.0 | 4.12 | 0.04 | -4.8606 | 0.0033 | 2006-02 to 2014-05 | 2006-02 to 2014-05
HD 68284 | 5933.0 | 26.0 | 3.87 | 0.03 | -5.0952 | 0.0062 | 2003-11 to 2015-01 | 2003-11 to 2015-01
HD 68607 | 5215.0 | 45.0 | 4.48 | 0.08 | -4.7254 | 0.0027 | 2003-12 to 2007-04 | 2003-12 to 2007-04
HD 68978 | 5965.0 | 22.0 | 4.26 | 0.02 | -4.8548 | 0.0029 | 2003-10 to 2016-03 | 2003-10 to 2015-05
HD 69611 | 5762.0 | 25.0 | 4.17 | 0.03 | -4.9562 | 0.0045 | 2003-11 to 2017-04 | 2003-11 to 2015-01
HD 69830 | 5402.0 | 28.0 | 4.40 | 0.04 | -4.9989 | 0.0027 | 2003-10 to 2019-12 | 2003-10 to 2015-05
HD 70642 | 5668.0 | 22.0 | 4.30 | 0.04 | -5.0217 | 0.0046 | 2003-12 to 2021-03 | 2003-12 to 2015-03
HD 71334 | 5694.0 | 13.0 | 4.26 | 0.03 | -4.9853 | 0.0045 | 2003-12 to 2017-02 | 2003-12 to 2015-01
HD 71835 | 5438.0 | 22.0 | 4.37 | 0.04 | -4.9417 | 0.0037 | 2003-12 to 2017-05 | 2003-12 to 2015-05
HD 7199 | 5386.0 | 45.0 | 4.34 | 0.08 | -4.9891 | 0.0037 | 2003-11 to 2017-09 | 2003-11 to 2015-01
HD 72659 | 5926.0 | 12.0 | 4.03 | 0.01 | -4.9963 | 0.0086 | 2004-02 to 2021-03 | 2004-02 to 2014-06
HD 72673 | 5243.0 | 22.0 | 4.52 | 0.04 | -4.9259 | 0.0022 | 2003-12 to 2019-04 | 2003-12 to 2015-05
HD 73267 | 5373.0 | 30.0 | 4.38 | 0.05 | -5.0939 | 0.0067 | 2004-01 to 2021-03 | 2004-01 to 2015-05
HD 73524 | 6017.0 | 13.0 | 4.19 | 0.03 | -4.9962 | 0.0040 | 2003-12 to 2019-04 | 2003-12 to 2015-05
HD 73583 | 4597.0 | 69.0 | 4.57 | 0.28 | -4.4603 | 0.0032 | 2004-02 to 2020-03 | 2004-02 to 2005-12
HD 7449 | 6024.0 | 13.0 | 4.27 | 0.03 | -4.8206 | 0.0032 | 2003-11 to 2016-01 | 2003-11 to 2015-01
HD 74698 | 5783.0 | 19.0 | 4.12 | 0.02 | -5.0331 | 0.0090 | 2004-02 to 2021-03 | 2004-02 to 2015-05
HD 74957 | 5915.0 | 20.0 | 4.34 | 0.03 | -4.9276 | 0.0081 | 2004-01 to 2021-03 | 2004-01 to 2015-02
HD 76151 | 5788.0 | 23.0 | 4.33 | 0.02 | -4.7266 | 0.0022 | 2003-11 to 2021-02 | 2003-11 to 2012-11
HD 77110 | 5717.0 | 20.0 | 4.36 | 0.02 | -4.9256 | 0.0050 | 2004-01 to 2017-05 | 2004-01 to 2014-02
HD 77338 | 5440.0 | 52.0 | 4.34 | 0.11 | -5.0587 | 0.0047 | 2004-12 to 2019-06 | 2004-12 to 2013-09
HD 78429 | 5760.0 | 19.0 | 4.19 | 0.02 | -4.9518 | 0.0037 | 2003-12 to 2017-06 | 2003-12 to 2015-05
HD 79601 | 5825.0 | 25.0 | 4.15 | 0.03 | -4.9291 | 0.0047 | 2004-01 to 2015-02 | 2004-01 to 2015-02
HD 82342 | 4470.0 | 21.0 | 4.96 | 0.05 | -4.9746 | 0.0030 | 2003-12 to 2016-05 | 2003-12 to 2015-05
HD 82516 | 5041.0 | 57.0 | 4.61 | 0.12 | -4.9816 | 0.0031 | 2003-12 to 2017-07 | 2003-12 to 2015-05
HD 82943 | 5989.0 | 20.0 | 4.20 | 0.02 | -4.9623 | 0.0034 | 2004-01 to 2017-06 | 2004-01 to 2015-05
HD 8389A | 5283.0 | 64.0 | 4.41 | 0.12 | -5.0311 | 0.0028 | 2003-11 to 2020-12 | 2003-11 to 2013-09
HD 8535 | 6158.0 | 13.0 | 4.12 | 0.02 | -4.9292 | 0.0081 | 2003-11 to 2019-08 | 2003-11 to 2014-10
HD 85390 | 5135.0 | 45.0 | 4.42 | 0.12 | -4.9666 | 0.0037 | 2003-12 to 2017-05 | 2003-12 to 2015-05
HD 85725 | 5986.0 | 26.0 | 3.72 | 0.04 | -5.2147 | 0.0093 | 2004-02 to 2021-02 | 2004-02 to 2015-05
HD 87838 | 6118.0 | 33.0 | 4.19 | 0.03 | -4.8489 | 0.0045 | 2004-01 to 2017-07 | 2004-01 to 2015-05
HD 88218 | 5878.0 | 14.0 | 3.97 | 0.02 | -5.0915 | 0.0045 | 2003-12 to 2016-05 | 2003-12 to 2015-05
HD 8828 | 5403.0 | 25.0 | 4.46 | 0.03 | -5.0145 | 0.0042 | 2003-10 to 2017-09 | 2003-10 to 2015-01
HD 88725 | 5654.0 | 17.0 | 4.39 | 0.03 | -4.8848 | 0.0039 | 2004-02 to 2015-06 | 2004-02 to 2014-12
HD 89454 | 5728.0 | 17.0 | 4.34 | 0.03 | -4.6977 | 0.0024 | 2004-01 to 2008-01 | 2004-01 to 2008-01
HD 89839 | 6314.0 | 24.0 | 4.13 | 0.06 | -4.9294 | 0.0080 | 2004-02 to 2021-02 | 2004-02 to 2015-05
HD 90156 | 5599.0 | 12.0 | 4.40 | 0.02 | -4.9509 | 0.0034 | 2004-01 to 2017-07 | 2004-01 to 2015-05
HD 91889 | 6140.0 | 22.0 | 4.03 | 0.03 | -4.8652 | 0.0031 | 2006-02 to 2011-02 | 2006-02 to 2011-02
HD 92719 | 5824.0 | 16.0 | 4.34 | 0.03 | -4.8249 | 0.0027 | 2004-01 to 2016-05 | 2004-01 to 2015-04
HD 93083 | 5048.0 | 66.0 | 4.46 | 0.16 | -4.9899 | 0.0031 | 2004-01 to 2017-07 | 2004-01 to 2015-04
HD 93385 | 5977.0 | 18.0 | 4.19 | 0.02 | -4.9714 | 0.0043 | 2003-12 to 2017-05 | 2003-12 to 2015-04
HD 94151 | 5583.0 | 19.0 | 4.31 | 0.02 | -4.9724 | 0.0038 | 2003-12 to 2019-04 | 2003-12 to 2013-03
HD 94771 | 5631.0 | 21.0 | 3.94 | 0.03 | -5.2218 | 0.0090 | 2004-02 to 2021-03 | 2004-02 to 2015-05
HD 95456 | 6276.0 | 22.0 | 4.01 | 0.04 | -4.9432 | 0.0038 | 2003-12 to 2017-06 | 2003-12 to 2015-05
HD 95542 | 5984.0 | 15.0 | 4.29 | 0.03 | -4.6653 | 0.0068 | 2004-01 to 2020-12 | 2004-01 to 2015-03
HD 9578 | 6055.0 | 14.0 | 4.26 | 0.03 | -4.5938 | 0.0055 | 2003-11 to 2020-11 | 2003-11 to 2012-11
HD 96423 | 5711.0 | 18.0 | 4.23 | 0.02 | -5.0486 | 0.0042 | 2003-12 to 2019-05 | 2003-12 to 2015-01
HD 96700 | 5845.0 | 13.0 | 4.22 | 0.02 | -4.9378 | 0.0035 | 2004-01 to 2017-07 | 2004-01 to 2015-04
HD 97037 | 5883.0 | 14.0 | 4.15 | 0.02 | -4.9815 | 0.0039 | 2004-01 to 2017-02 | 2004-01 to 2015-01
HD 97343 | 5410.0 | 20.0 | 4.39 | 0.03 | -5.0374 | 0.0033 | 2004-01 to 2018-05 | 2004-01 to 2015-05
HD 98281 | 5381.0 | 23.0 | 4.43 | 0.04 | -4.9154 | 0.0029 | 2004-01 to 2016-03 | 2004-01 to 2015-03