# Constraints on Magnetic Braking from the G8 Dwarf Stars 61 UMa and τ Cet

Travis S Metcalfe, Klaus G Strassmeier, Ilya V Ilyin, Jennifer L van Saders, Thomas R Ayres, Adam J Finley, Oleg Kochukhov, Pascal Petit, Victor See, Keivan G Stassun, et al.

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Travis S Metcalfe, Klaus G Strassmeier, Ilya V Ilyin, Jennifer L van Saders, Thomas R Ayres, et al. Constraints on Magnetic Braking from the G8 Dwarf Stars 61 UMa and τ Cet. The Astrophysical journal letters, 2023, 948 (1), pp.L6. 10.3847/2041-8213/acce38. hal-04169468

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# Constraints on Magnetic Braking from the G8 Dwarf Stars 61 UMa and τ Cet

Travis S. Metcalfe<fnref n="1" />, Klaus G. Strassmeier<fnref n="2" />, Ilya V. Ilyin<fnref n="2" />, Jennifer L. van Saders<fnref n="3" />, Thomas R. Ayres<fnref n="4" />,
Adam J. Finley<fnref n="5" />, Oleg Kochukhov<fnref n="6" />, Pascal Petit<fnref n="7" />, Victor See<fnref n="8" />, Keivan G. Stassun<fnref n="9" />, Sandra V. Jeffers<fnref n="10" />,
Stephen C. Marsden<fnref n="11" />, Julien Morin<fnref n="12" />, and Aline A. Vidotto<fnref n="13" />

Received 2023 February 27; revised 2023 April 18; accepted 2023 April 19; published 2023 April 28

## Abstract

During the first half of their main-sequence lifetimes, stars rapidly lose angular momentum to their magnetized winds, a process known as magnetic braking. Recent observations suggest a substantial decrease in the magnetic braking efficiency when stars reach a critical value of the Rossby number, the stellar rotation period normalized by the convective overturn timescale. Cooler stars have deeper convection zones with longer overturn times, reaching this critical Rossby number at slower rotation rates. The nature and timing of the transition to weakened magnetic braking have previously been constrained by several solar analogs and two slightly hotter stars. In this Letter, we derive the first direct constraints from stars cooler than the Sun. We present new spectropolarimetry of the old G8 dwarf τ Cet from the Large Binocular Telescope, and we reanalyze a published Zeeman Doppler image of the younger G8 star 61 UMa, yielding the large-scale magnetic field strengths and morphologies. We estimate mass-loss rates using archival X-ray observations and inferences from Lyα measurements, and we adopt other stellar properties from asteroseismology and spectral energy distribution fitting. The resulting calculations of the wind braking torque demonstrate that the rate of angular momentum loss drops by a factor of 300 between the ages of these two stars (1.4–9 Gyr), well above theoretical expectations. We summarize the available data to help constrain the value of the critical Rossby number, and we identify a new signature of the long-period detection edge in recent measurements from the Kepler mission.

*Unified Astronomy Thesaurus concepts: Spectropolarimetry (1973); Stellar evolution (1599); Stellar magnetic fields (1610); Stellar rotation (1629); Stellar winds (1636)*

## 1. Introduction

Seven years after the suggestion that weakened magnetic braking (WMB) might explain the anomalously rapid rotation of old Kepler field stars (van Saders et al. 2016), the debate has shifted from whether this transition actually occurs to the specific physical mechanisms that might drive it. Although the original sample included just 21 stars, the analysis was subsequently extended (van Saders et al. 2019) to reproduce the properties of 34,000 Kepler field stars with measured rotation periods (McQuillan et al. 2014). The truncated distribution of rotation periods that led to the WMB hypothesis has now been confirmed using a sample of 94 stars with rotation rates measured from asteroseismology (Hall et al. 2021), and the predicted overdensity of stars with a range of ages near the long-period edge of the distribution has been confirmed (David et al. 2022) using more than 10,000 stars

with precise effective temperatures from LAMOST spectra (Xiang et al. 2019).

Evidence quickly surfaced that the interruption to stellar rotational evolution was probably caused by an underlying transition in stellar magnetism. The influence of magnetic morphology on the rate of angular momentum loss from stellar winds (Garraffo et al. 2015; Réville et al. 2015) led to the initial suggestion that WMB could be driven by a shift from a simple dipole to higher-order fields (van Saders et al. 2016). Preliminary support for this interpretation was identified (Metcalfe et al. 2016) in measurements of the large-scale magnetic field strength and morphology from Zeeman Doppler imaging (Petit et al. 2008) and was reinforced by the associated changes in stellar activity cycles (Metcalfe & van Saders 2017). Targeted observations for an evolutionary sequence of two stars slightly hotter than the Sun (Metcalfe et al. 2019, 2021), followed by a sequence of several solar analogs (Metcalfe et al. 2022), provided the first direct evidence of a magnetic morphology shift in older solar-type stars and placed new constraints on the relative importance of various contributions to the overall reduction in the wind braking torque. Such

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Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹ White Dwarf Research Corporation, 9020 Brumm Trail, Golden, CO 80403, USA; travis@wdrc.org</footnote>

<footnote n="2">² Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany</footnote>

<footnote n="3">³ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA</footnote>

<footnote n="4">⁴ Center for Astrophysics and Space Astronomy, 389 UCB, University of Colorado, Boulder, CO 80309, USA</footnote>

<footnote n="5">⁵ Department of Astrophysics-AIM, University of Paris-Saclay and University of Paris, CEA, CNRS, Gif-sur-Yvette Cedex F-91191, France</footnote>

<footnote n="6">⁶ Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden</footnote>

<footnote n="7">⁷ Université de Toulouse, CNRS, CNES, 14 avenue Edouard Belin, F-31400, Toulouse, France</footnote>

<footnote n="8">⁸ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands</footnote>

<footnote n="9">⁹ Vanderbilt University, Department of Physics & Astronomy, 6301 Stevenson Center Lane, Nashville, TN 37235, USA</footnote>

<footnote n="10">¹⁰ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-weg 3, D-37077, Göttingen, Germany</footnote>

<footnote n="11">¹¹ Centre for Astrophysics, University of Southern Queensland, Toowoomba, Queensland, 4350, Australia</footnote>

<footnote n="12">¹² Centre national de la recherche scientifique (CNRS), Université de Montpellier, Place Eugène Bataillon, F-34095, Montpellier, France</footnote>

<footnote n="13">¹³ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA, Leiden, The Netherlands</footnote>
constraints may ultimately help to identify a corresponding transition in the stellar dynamo.

In this Letter, we present the first direct constraints on the nature and timing of WMB from stars that are cooler than the Sun. In Section 2, we describe spectropolarimetric observations for an evolutionary sequence of two G8 dwarf stars, and we adopt other stellar properties largely from published sources. In Section 3, we use the prescription of Finley & Matt (2018) to estimate the wind braking torque for each star, confirming a dramatic decrease in the rate of angular momentum loss as seen previously for solar analogs and slightly hotter stars. Finally, we summarize the available constraints, and we identify a new signature of the long-period detection edge in recent measurements from the Kepler mission.

## 2. Observations

### 2.1. Spectropolarimetry

We observed $\tau$Cet on 2022 September 18 from the 2 × 8.4 m Large Binocular Telescope (LBT) using the Potsdam Echelle Polarimetric and Spectroscopic Instrument (Strassmeier et al. 2015). The instrumental setup and data reduction methods were identical to those described in Metcalfe et al. (2019), and we employed the least-squares deconvolution (LSD) technique (Kochukhov et al. 2010) to derive precise mean intensity and polarization profiles. We obtained the line data required for the LSD analysis from the VALD database (Ryabchikova et al. 2015), adopting stellar atmospheric parameters from Brewer et al. (2016) and $v \sin i = 0.4$ km s$^{-1}$ from Saar & Osten (1997). Because $\tau$Cet has a 50 yr record of constant chromospheric activity (Baum et al. 2022) and appears to have a nearly pole-on orientation that minimizes rotational modulation (Gray & Baliunas 1994), we assume that our snapshot observation is representative of the mean stellar activity level. The value of $\log R'_{HK}$ for $\tau$Cet is above recent solar minimum levels (Egeland et al. 2017) although the actual value may be slightly lower due to its subsolar metallicity (Saar & Testa 2012). There is no observational evidence to suggest that the low activity level of $\tau$Cet represents a magnetic grand minimum; it appears similar to other constant-activity stars like $\rho$CrB and 16 Cyg A & B.

By combining the information from 1463 metal lines deeper than 5% of the continuum, we obtained a mean Stokes V profile with an uncertainty of 5.8 ppm (see Figure 1). The data yielded a statistically marginal detection of the circular polarization signature for $\tau$Cet, with a mean longitudinal magnetic field $\langle B_z \rangle = -0.37 \pm 0.08$ G. Following Metcalfe et al. (2019) we modeled the line profile assuming an axisymmetric dipole magnetic field with the inclination fixed at $i=20^{\circ}$ (see Section 2.2), yielding a formal best fit $B_d = -0.77 \pm 0.31$ G. Note that the derived magnetic field strength does not depend strongly on the inclination (e.g., $B_d = -0.73$ G for $i=5^{\circ}$).

To complement the new LBT observations with another star along an evolutionary sequence, we reanalyzed a Zeeman Doppler imaging (ZDI) map for the younger G8 star 61 UMa (See et al. 2019), which was obtained near the minimum of its 4 yr activity cycle. This ZDI map was based on 21 Stokes V measurements obtained in 2008 with the NARVAL spectropolarimeter on the 2.03 m Telescope Bernard Lyot. Folsom et al. (2018) provide details of the ZDI inversion procedure, while Jardine et al. (2013) discuss the connection between the resulting magnetic fields at the surface and in the corona. The

<figure><img src="image_5.png" /><figcaption>**Figure 1.** Stokes V polarization profile for $\tau$Cet from LBT observations on 2022 September 18. The mean profile is shown as a black line with uncertainties indicated by the gray shaded area. The dashed blue line is an axisymmetric model profile assuming dipole morphology with the inclination fixed at $i=20^{\circ}$.</figcaption></figure>

<table><caption>**Table 1**
Stellar Properties of 61 UMa and $\tau$Cet</caption><thead><tr><th></th><th>61 UMa</th><th>τ Cet</th><th>Sources</th></tr></thead><tbody><tr><td>T<sub>eff</sub> (K)</td><td>5502 ± 78</td><td>5333 ± 78</td><td>1</td></tr><tr><td>[M/H] (dex)</td><td>-0.07 ± 0.07</td><td>-0.44 ± 0.07</td><td>1</td></tr><tr><td>log g (dex)</td><td>4.52 ± 0.08</td><td>4.60 ± 0.08</td><td>1</td></tr><tr><td>B - V (mag)</td><td>0.72</td><td>0.72</td><td>2</td></tr><tr><td>log R'<sub>HK</sub> (dex)</td><td>-4.546</td><td>-4.958</td><td>2</td></tr><tr><td>P<sub>rot</sub> (days)</td><td>17</td><td>34</td><td>2</td></tr><tr><td>|B<sub>d</sub>| (G)</td><td>11.5</td><td>0.77</td><td>3</td></tr><tr><td>|B<sub>q</sub>| (G)</td><td>12.0</td><td>...</td><td>3</td></tr><tr><td>|B<sub>o</sub>| (G)</td><td>6.12</td><td>...</td><td>3</td></tr><tr><td>L<sub>X</sub> (10<sup>27</sup> erg s<sup>-1</sup>)</td><td>26.9 ± 0.6</td><td>0.49 ± 0.10</td><td>4</td></tr><tr><td>Mass-loss rate (M<sub>☉</sub>)</td><td>9.6 ± 0.6</td><td>&lt;0.1</td><td>4, 5</td></tr><tr><td>Mass (M<sub>☉</sub>)</td><td>0.94 ± 0.06</td><td>0.783 ± 0.012</td><td>4, 6</td></tr><tr><td>Radius (R<sub>☉</sub>)</td><td>0.845 ± 0.015</td><td>0.816 ± 0.012</td><td>4, 7</td></tr><tr><td>Luminosity (L<sub>☉</sub>)</td><td>0.588 ± 0.007</td><td>0.473 ± 0.011</td><td>4</td></tr><tr><td>Age (Gyr)</td><td>1.4 ± 0.2</td><td>9.0 ± 1.0</td><td>8, 9</td></tr><tr><td>Torque (10<sup>30</sup> erg)</td><td>7.7</td><td>&lt;0.026</td><td>10</td></tr></tbody></table>

**References.** (1) Brewer et al. (2016), (2) Baliunas et al. (1996), (3) Section 2.1, (4) Section 2.2, (5) Wood (2018), (6) Teixeira et al. (2009), (7) von Braun & Boyajian (2017), (8) Barnes (2007), (9) Tang & Gai (2011), (10) Section 3.

wind braking prescription of Finley & Matt (2018) requires the polar strengths of axisymmetric dipole, quadrupole, and octupole magnetic fields ($B_d$, $B_q$, $B_o$) as input, but the observed ZDI map contains both axisymmetric and nonaxisymmetric components. We followed the procedure described in Metcalfe et al. (2022) to calculate the equivalent polar field strengths for use with the wind braking prescription. This procedure captures the radial dependence of the magnetic flux for all components of the field, which is what matters for angular momentum loss. The results of this analysis for 61 UMa are shown in Table 1. There may be slight inconsistencies between the observed ZDI map and the equivalent polar field strengths derived in this way, but Jardine et al. (2013) demonstrated that the differences arise from nonradial components of the field, which induce near-surface magnetic stresses without altering the source
surface of the stellar wind. Consequently, they are unimportant
for our estimation of the wind braking torque.

## 2.2. Stellar Properties

In addition to the magnetic field strength and morphology,
the wind braking prescription of Finley & Matt (2018) also
depends on the mass-loss rate ($\dot{M}$), the rotation period ($P_{\text{rot}}$),
and the stellar radius and mass ($R, M$). For $\tau$ Cet we adopted the
upper limit on the mass-loss rate from Wood (2018), which was
obtained directly from Ly$\alpha$ measurements. The rotation period
was determined from time series observations of chromo-
spheric activity by Baliunas et al. (1996), while the radius was
inferred from interferometry (von Braun & Boyajian 2017) and
the mass was adopted from asteroseismology (Teixeira et al.
2009). The stellar age was derived from an analysis of these
same asteroseismic observations by Tang & Gai (2011). Our
estimate of the inclination $i = 20^\circ$ in Section 2.1 was calculated
from the values of $v \sin i$, $P_{\text{rot}}$, and $R$.

For 61 UMa, we determined the X-ray luminosity ($L_X$) from
the ROSAT All-Sky Bright Source Catalog (Boller et al. 2016),
following the approach described in Ayres & Buzasi (2022).
When combined with the radius inferred from the spectral
energy distribution (SED), following the procedures described
in Stassun et al. (2017, 2018), this led to an X-ray flux per unit
surface area that could be used to estimate the mass-loss rate
from the empirical relation $\dot{M} \propto F_X^{0.77}$ (Wood et al. 2021). The
rotation period of 61 UMa was determined from chromospheric
activity measurements (Baliunas et al. 1996), while the mass
was estimated from the SED radius using the empirical mass-
radius relation from eclipsing binaries (Torres et al. 2010). The
age of 61 UMa was determined from the gyrochronology
relation of Barnes (2007), which remains valid for younger
stars.

## 3. Wind Braking Torque

We now have all of the observational inputs that are required
to estimate the wind braking torque using the prescription of
Finley & Matt (2018).<fnref n="14" /> For 61 UMa we have the equivalent
polar field strengths ($B_d$, $B_q$, $B_o$) from our reanalysis of
the published ZDI map. For $\tau$ Cet we have the snapshot
observation from LBT, which we model with an axisymmetric
dipole field inclined at $i = 20^\circ$ (below, in this Section, we
assess the influence of adopting a different inclination or
morphology). We estimate the mass-loss rate ($\dot{M}$) from the
X-ray flux for 61 UMa, but we infer it directly from Ly$\alpha$
measurements for $\tau$ Cet (below we assess the influence of the
higher mass-loss rate estimated from the X-ray flux for $\tau$ Cet).
The remaining parameters ($P_{\text{rot}}$, $R$, $M$) do not produce
substantial uncertainties in the torque. Using the parameter
values listed in Table 1 for our fiducial models, we find that the
wind braking torque decreases by a factor of 300 between the
ages of 61 UMa and $\tau$ Cet (1.4–9 Gyr).

By changing the wind braking prescription one parameter at
a time between the values for 61 UMa and $\tau$ Cet, we can
evaluate the relative importance of various contributions to the
overall decrease in the torque. We find almost equal
contributions from the evolutionary change in mass-loss rate
(–92%) and the difference in magnetic field strength and
morphology (–91%), with smaller contributions from the

evolutionary change in rotation period (–50%) and differences
in the stellar radius (–10%) and mass (+4%). Rotational
evolution models use the Rossby number (Ro) to scale the
mass-loss rate as $\dot{M} \sim Ro^{-2}$ and the magnetic field strength as
$B \sim P_{\text{phot}}^{0.5}/Ro$, where $P_{\text{phot}}$ is the photospheric pressure (van
Saders & Pinsonneault 2013), but they do not directly account
for changes in magnetic morphology. Considering either WMB
or standard spin down, these models predict a decrease in the
wind braking torque of less than a factor of 15, with a smaller
contribution from the evolutionary change in the mass-loss rate
(–70% to –82%) and a difference from the change in magnetic
field strength (–40% to –52%) that suggests a substantial
contribution from a shift in magnetic morphology.

The large decrease in wind braking torque between the ages
of 61 UMa and $\tau$ Cet is robust against changes to our
assumptions about the magnetic field and mass-loss rate. For
example, $\tau$ Cet has a debris disk with a measured inclination
($i = 35^\circ \pm 10^\circ$; Lawler et al. 2014). If we assume that the
rotation axis of $\tau$ Cet shares this same inclination, the inferred
dipole field would be slightly stronger ($B_d = –0.89$ G) and
produce a corresponding increase in the wind braking torque
(0.029 $\times 10^{30}$ erg, +14%). If we keep $i = 20^\circ$ but model the
Stokes V profile as an axisymmetric quadrupole or octupole
field, enhanced geometric cancellation would lead us to infer a
stronger field ($B_q = –2.94$ G or $B_o = –118.9$ G). For a
quadrupole field, this ultimately leads to a lower wind braking
torque (0.023 $\times 10^{30}$ erg; –11%) because the stronger field
does not compensate for the shorter effective lever arm. By
contrast, the much stronger octupole field would ultimately
produce a higher torque (0.043 $\times 10^{30}$ erg, +67%) despite the
much shorter effective lever arm although this scenario is
incompatible with the measured chromospheric activity level.
Finally, if we use the X-ray flux of $\tau$ Cet to estimate its mass-
loss rate (0.46 $\dot{M}_{\odot}$) following the same approach as for 61
UMa, the wind braking torque would more than double
(0.058 $\times 10^{30}$ erg, +129%). However, even if we adopt both
the octupole field and the higher mass-loss rate for $\tau$ Cet
(contradicting the actual measurements of $\log R'_{\text{HK}}$ and $\dot{M}$
shown in Table 1), the wind braking torque would still be 50
times weaker than for 61 UMa.

We can assess the empirical value of the critical Rossby
number (Ro$_{crit}$) by plotting the available estimates of wind
braking torque on a common scale. We use the asteroseismic
calibration of Corsaro et al. (2021) for the convective overturn
timescale to calculate Ro for each star in our sample based on
the Gaia $G_{BP} – G_{RP}$ color. The results are shown in Figure 2
with points grouped by Gaia color, corresponding to solar
analogs (yellow circles) and hotter (blue triangles) or cooler
stars (red squares). Our empirical constraint on the critical
value of Ro on this scale (Ro$_{crit} = 0.457 \pm 0.006$) is shown
with a vertical dashed line. Our new estimates of the wind
braking torque for 61 UMa and $\tau$ Cet extend the range of Ro
sampled by our spectropolarimetric targets and show the
highest and lowest torques of the ensemble. By construction,
the more active stars in our sample (61 UMa, 88 Leo,
HD 76151) are all below Ro$_{crit}$, while the less active stars
(16 Cyg A & B, $\rho$ CrB, 18 Sco, $\tau$ Cet) are all above it. The
Rossby numbers of HD 76151 (Ro = 0.451) and 16 Cyg A
(Ro = 0.463) currently define the empirical constraint on the
value of Ro$_{crit}$ shown above, falling slightly below the solar
value (Ro$_{\odot} = 0.496$) where we plot the solar wind braking
torque determined by Finley et al. (2018).

<footnote n="14">¹⁴ https://github.com/travismetcalfe/FinleyMatt2018</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 2.** Evolution of the wind braking torque with Ro from the calibration of Corsaro et al. (2021). Points are grouped by Gaia color, corresponding to solar analogs (yellow circles) and hotter (blue triangles) or cooler stars (red squares). The empirical constraint for $Ro_{crit}$ on this scale is shown with a vertical dashed line.</figcaption></figure>

## 4. Discussion

Using spectropolarimetric constraints on the large-scale magnetic field, we have demonstrated that the rate of angular momentum loss due to stellar winds decreases by a factor of 300 between the ages of two stars that are cooler than the Sun, dominated by contributions from both the mass-loss rate and the magnetic field strength and morphology. Relative to previous comparisons for solar analogs and slightly hotter stars, there is a larger evolutionary gap between 61 UMa and $\tau$ Cet, which would naturally lead to a more substantial decrease in the strength of magnetic braking across $Ro_{crit}$. On the other hand, the estimated wind braking torque for $\tau$ Cet could be even smaller because the mass-loss rate from Wood (2018) is an upper limit. For the solar analogs 16 Cyg A & B, Metcalfe et al. (2022) estimated a factor of 15–16 decrease in the wind braking torque relative to HD 76151, while for the slightly hotter star $\rho$ CrB, Metcalfe et al. (2021) estimated a factor of 13 decrease relative to 88 Leo. However, these estimates all adopted upper limits on the magnetic field strengths from statistical nondetections of the Stokes V signatures, so the actual decreases could be larger. Our marginal detection of the Stokes V signature for $\tau$ Cet was facilitated by lower noise levels and by the nearly pole-on orientation, which minimizes geometric cancellation for an axisymmetric dipole magnetic field.

From a sample of 40,000 Kepler targets with measured rotation periods, Corsaro et al. (2021) plotted a photometric proxy for stellar activity ($S_{ph}$; Mathur et al. 2014) against the newly calibrated values of Ro (see Figure 3). Despite the vertical dispersion at all values of Ro due to activity cycles and inclination effects, the highest density of stars in their sample (yellow and green) appears at Ro slightly below the solar value, showing a broad range of stellar activity levels (Santos et al. 2019, 2021) at nearly constant Ro. This feature may correspond to the long-period edge of the Kepler sample (McQuillan et al. 2014; van Saders et al. 2019), where stellar activity gradually declines with age at roughly constant rotation period during the second half of main-sequence lifetimes (Metcalfe et al. 2016; Metcalfe & van Saders 2017). However, the relatively uniform distribution of bright asteroseismic targets (red circles) across

<figure><img src="image_7.png" /><figcaption>**Figure 3.** Rotation–activity relation for stars published in Corsaro et al. (2021), with the critical value of Ro from Section 3 shown as a vertical dashed line. Bright asteroseismic targets are shown with red circles. The highest density of stars (yellow and green) exhibit a broad range of activity levels at nearly constant Ro, which may correspond to the long-period edge of the Kepler sample.</figcaption></figure>

our empirical value of $Ro_{crit}$ and toward low values of $S_{ph}$ suggests that the detection of rotational modulation may simply be less efficient at higher Ro and lower $S_{ph}$ (van Saders et al. 2019; Masuda 2022).

Future spectropolarimetry promises to extend our measurements to even cooler K-type stars and provide additional constraints on the empirical value of $Ro_{crit}$. Snapshot observations at LBT are already planned for HD 103095 and HD 166620. Although HD 103095 is an early K-type star, its extremely low metallicity ([M/H] = -1.16; Valenti & Fischer 2005) gives it the shallower convection zone of a late G-type star similar to $\tau$ Cet. With an activity cycle of 7.3 yr and a measured rotation period of 31 days (Baliunas et al. 1995, 1996), it will sample intermediate conditions ($Ro = 0.542$) between 61 UMa and $\tau$ Cet and probe how the driving mechanisms of WMB change over time. Observations of HD 166620 will complement our existing measurements of the active star 40 Eri, probing the magnetic morphology of a K-type star that recently entered a grand magnetic minimum (Baum et al. 2022; Luhn et al. 2022). Archival ZDI maps of younger K-type stars like $\epsilon$ Eri (Jeffers et al. 2014) and 61 Cyg A (Boro Saikia et al. 2016) from the BCool collaboration will provide additional context for our understanding of how magnetic braking shapes the lives of other Sun-like stars.

Special thanks to Steve Saar, Ângela Santos, and Brian Wood for helpful exchanges. T.S.M. acknowledges support from the U.S. National Science Foundation (AST-2205919). A. J.F. and A.A.V. have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreements No 810218 WHOLESUN, and No 817540 ASTROFLOW). O.K. acknowledges support by the Swedish Research Council (project 2019-03548) and the Royal Swedish Academy of Sciences. V.S. acknowledges support from the European Space Agency (ESA) as an ESA Research Fellow. The LBT is an international collaboration among institutions in the United States, Italy and Germany. LBT Corporation partners are: The University of Arizona on behalf of the Arizona Board of
Regents; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, The Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; The Ohio State University, and The Research Corporation, on behalf of The University of Notre Dame, University of Minnesota and University of Virginia.

## ORCID iDs

Travis S. Metcalfe https://orcid.org/0000-0003-4034-0416

Klaus G. Strassmeier https://orcid.org/0000-0002-6192-6494

Ilya V. Ilyin https://orcid.org/0000-0002-0551-046X

Jennifer L. van Saders https://orcid.org/0000-0002-4284-8638

Thomas R. Ayres https://orcid.org/0000-0002-1242-5124

Adam J. Finley https://orcid.org/0000-0002-3020-9409

Oleg Kochukhov https://orcid.org/0000-0003-3061-4591

Pascal Petit https://orcid.org/0000-0001-7624-9222

Victor See https://orcid.org/0000-0001-5986-3423

Keivan G. Stassun https://orcid.org/0000-0002-3481-9052

Sandra V. Jeffers https://orcid.org/0000-0003-2490-4779

Stephen C. Marsden https://orcid.org/0000-0001-5522-8887

Julien Morin https://orcid.org/0000-0002-4996-6901

Aline A. Vidotto https://orcid.org/0000-0001-5371-2675

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