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There is now a large sample of stars observed by the Kepler satellite with measured rotation periods and photometric activity index $S_{\rm ph}$. We use this data, in conjunction with stellar interiors models, to explore the interplay of magnetism, rotation, and convection. Stellar activity proxies other than $S_{\rm ph}$ are correlated with the Rossby number, $Ro$, or ratio of rotation period to convective overturn timescale. We compute the latter using the Yale Rotating Evolution Code stellar models. We observe different $S_{\rm ph}$-$Ro$ relationships for different stellar spectral types. Though the overall trend of decreasing magnetic activity versus $Ro$ is recovered, we find a localized dip in $S_{\rm ph}$ around $Ro/Ro_{\odot} \sim$\,0.3 for the G and K dwarfs. F dwarfs show little to no dependence of $S_{\rm ph}$ on $Ro$ due to their shallow convective zones; further accentuated as $T_{\rm eff}$ increases. The dip in activity for the G and K dwarfs corresponds to the intermediate rotation period gap, suggesting that the dip in $S_{\rm ph}$ could be associated with the redistribution of angular momentum between the core and convective envelope inside stars. For G-type stars, we observe enhanced magnetic activity above solar $Ro$. Compared to other Sun-like stars with similar effective temperature and metallicity, we find that the Sun's current level of magnetic activity is comparable to its peers and lies near the transition to increasing magnetic activity at high $Ro$. We confirm that metal-rich stars have a systematically larger $S_{\rm ph}$ level than metal-poor stars, which is likely a consequence of their deeper convective zones., Comment: 21 pages, 10 figures, including 7 pages of Appendix. Accepted for publication in ApJ

There is an intricate relationship between the organization of large-scale magnetic fields by a stellar dynamo and the rate of angular momentum loss due to magnetized stellar winds. An essential ingredient for the operation of a large-scale dynamo is the Coriolis force, which imprints organizing flows on the global convective patterns and inhibits the complete cancellation of bipolar magnetic regions. Consequently, it is natural to expect a rotational threshold for large-scale dynamo action and for the efficient angular momentum loss that it mediates through magnetic braking. Here we present new observational constraints on magnetic braking for an evolutionary sequence of six early K-type stars. To determine the wind braking torque for each of our targets, we combine spectropolarimetric constraints on the large-scale magnetic field, Ly-alpha or X-ray constraints on the mass-loss rate, as well as uniform estimates of the stellar rotation period, mass, and radius. As identified previously from similar observations of hotter stars, we find that the wind braking torque decreases abruptly by more than an order of magnitude at a critical value of the stellar Rossby number. Given that all of the stars in our sample exhibit clear activity cycles, we suggest that weakened magnetic braking may coincide with the operation of a subcritical stellar dynamo., Comment: 14 pages including 5 figures and 1 table. Under second review at AAS Journals

During the solar cycle, the Sun's magnetic field polarity reverses due to the emergence, cancellation, and advection of magnetic flux towards the rotational poles. Flux emergence events occasionally cluster together, although it is unclear if this is due to the underlying solar dynamo or simply by chance. Regardless of the cause, we aim to characterise how the reversal of the Sun's magnetic field and the structure of the solar corona are influenced by nested flux emergence. From the spherical harmonic decomposition of the Sun's photospheric magnetic field, we identify times when the reversal of the dipole component stalls for several solar rotations. Using observations from sunspot cycle 23 to present, we locate the nested active regions responsible for each stalling and explore their impact on the coronal magnetic field using potential field source surface extrapolations. Nested flux emergence has a more significant impact on the topology of the coronal magnetic field than isolated emergences as it produces a coherent (low spherical harmonic order) contribution to the photospheric magnetic field. The heliospheric current sheet (HCS), that separates oppositely directed coronal magnetic field, can become anchored above these regions due to the formation of strong opposing magnetic fluxes. Further flux emergence, cancellation, differential rotation, and diffusion, then effectively advects the HCS and shifts the dipole axis. Nested flux emergence can restrict the evolution of the HCS and impede the reversal of the coronal magnetic field. The sources of the solar wind can be more consistently identified around nested active regions as the magnetic field topology remains self-similar for multiple solar rotations. This highlights the importance of identifying nested active regions to guide the remote-sensing observations of modern heliophysics missions., Comment: Accepted to A&A. 7 Pages + Appendix. 5 Figures + 2 Appendix Figures

For Sun-like stars, the generation of toroidal magnetic field from poloidal magnetic field is an essential piece of the dynamo mechanism powering their magnetism. Previous authors have estimated the net toroidal flux generated in each hemisphere of the Sun by exploiting its conservative nature. This only requires observations of the surface magnetic field and differential rotation. We explore this approach using a 3D magnetohydrodynamic dynamo simulation of a cool star, for which the magnetic field generation is known throughout the entire star. Changes to the net toroidal flux in each hemisphere were evaluated using a closed line integral bounding the cross-sectional area of each hemisphere, following the application of Stokes-theorem to the induction equation; the individual line segments corresponded to the stellar surface, base, equator, and rotation axis. The influence of the large-scale flows, the fluctuating flows, and magnetic diffusion to each of the line segments was evaluated, along with their depth-dependence. In the simulation, changes to the net toroidal flux via the surface line segment typically dominate the total line integral surrounding each hemisphere, with smaller contributions from the equator and rotation axis. The bulk of the toroidal flux is generated deep inside the convection zone, with the surface observables capturing this due to the conservative nature of the net flux. Surface magnetism and rotation can therefore be used to estimate the net toroidal flux generated in each hemisphere, allowing us to constrain the reservoir of magnetic flux for the next magnetic cycle. However, this methodology cannot identify the physical origin, nor the location, of the toroidal flux generation. In addition, not all dynamo mechanisms depend on the net toroidal field produced in each hemisphere, meaning this method may not be able to characterise every magnetic cycle., Comment: Accepted to A&A. 8 Pages + Appendix. 6 Figures + 2 Appendix Figures

The consistently low activity level of the old solar analog 51 Peg not only facilitated the discovery of the first hot Jupiter, but also led to the suggestion that the star could be experiencing a magnetic grand minimum. However, the 50 year time series showing minimal chromospheric variability could also be associated with the onset of weakened magnetic braking (WMB), where sufficiently slow rotation disrupts cycling activity and the production of large-scale magnetic fields by the stellar dynamo, thereby shrinking the Alfven radius and inhibiting the efficient loss of angular momentum to magnetized stellar winds. In this Letter, we evaluate the magnetic evolutionary state of 51 Peg by estimating its wind braking torque. We use new spectropolarimetric measurements from the Large Binocular Telescope to reconstruct the large-scale magnetic morphology, we reanalyze archival X-ray measurements to estimate the mass-loss rate, and we detect solar-like oscillations in photometry from the Transiting Exoplanet Survey Satellite, yielding precise stellar properties from asteroseismology. Our estimate of the wind braking torque for 51 Peg clearly places it in the WMB regime, driven by changes in the mass-loss rate and the magnetic field strength and morphology that substantially exceed theoretical expectations. Although our revised stellar properties have minimal consequences for the characterization of the exoplanet, they have interesting implications for the current space weather environment of the system., Comment: ApJ Letters (accepted), 6 pages including 4 figures and 1 table. Data available at https://doi.org/10.5281/zenodo.8381444

The strength and morphology of the Sun's magnetic field evolves significantly during the solar cycle, with the overall polarity of the Sun's magnetic field reversing during the maximum of solar activity. Long-term changes are also observed in sunspot and geomagnetic records, however systematic magnetic field observations are limited to the last four cycles. We investigate the long-term evolution of the Sun's magnetic field, and the influence this has on the topology and rotation of the solar corona. The Sun's photospheric magnetic field was decomposed into spherical harmonics using synoptic Carrington magnetograms from 1) WSO, 2) MDI onboard the SOHO, and 3) HMI onboard the SDO. The time-evolution of the spherical harmonic coefficients was used to explore the variation of the Sun's magnetic field, focusing on the large-scale modes. PFSS extrapolations of the photospheric field were computed to follow topological changes in the corona. The footpoints of the Sun's open magnetic field vary between the polar coronal holes and activity driven features such as active regions, and equatorial coronal holes. Consequently, the mean rotation rate of the solar wind is modulated during each cycle by the latitudinal variation of open field footpoints, with slower rotation during minima and faster (Carrington-like) rotation during maxima. Thisc variation is sensitive to cycle to cycle differences in the polar field strengths and hemispherical flux emergence rates, with the ratio of quadrupole to dipole energy following a similar variation. Cycle 23 maintained a larger fraction of quadrupolar energy in the declining phase, which kept the sources of open magnetic flux closer to the equator, extending the period of faster equator-ward connectivity. The ratio of quadrupole to dipole energy could be a useful proxy when examining the impact of differential rotation on the coronae of other Sun-like stars., Comment: Accepted to A&A. 13 Pages + Appendix. 11 Figures + 7 Appendix Figures

The bright star $\lambda$ Ser hosts a hot Neptune with a minimum mass of 13.6 $M_\oplus$ and a 15.5 day orbit. It also appears to be a solar analog, with a mean rotation period of 25.8 days and surface differential rotation very similar to the Sun. We aim to characterize the fundamental properties of this system, and to constrain the evolutionary pathway that led to its present configuration. We detect solar-like oscillations in time series photometry from the Transiting Exoplanet Survey Satellite (TESS), and we derive precise asteroseismic properties from detailed modeling. We obtain new spectropolarimetric data, and we use them to reconstruct the large-scale magnetic field morphology. We reanalyze the complete time series of chromospheric activity measurements from the Mount Wilson Observatory, and we present new X-ray and ultraviolet observations from the Chandra and Hubble space telescopes. Finally, we use the updated observational constraints to assess the rotational history of the star and to estimate the wind braking torque. We conclude that the remaining uncertainty on stellar age currently prevents an unambiguous interpretation of the properties of $\lambda$ Ser, and that the rate of angular momentum loss appears to be higher than for other stars with similar Rossby number. Future asteroseismic observations may help to improve the precision of the stellar age., Comment: 19 pages including 9 figures and 6 tables. Astronomical Journal, accepted

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 has 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 $\tau$ 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 Ly$\alpha$ 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., Comment: ApJ Letters (accepted), 6 pages including 3 figures and 1 table. Python code is available at https://github.com/travismetcalfe/FinleyMatt2018

Sun-like stars shed angular momentum due to the presence of magnetised stellar winds. Magnetohydrodynamic models have been successful in exploring the dependence of this "wind-braking torque" on various stellar properties, however the influence of surface differential rotation is largely unexplored. As the wind-braking torque depends on the rotation rate of the escaping wind, the inclusion of differential rotation should effectively modulate the angular momentum-loss rate based on the latitudinal variation of wind source regions. In order to quantify the influence of surface differential rotation on the angular momentum-loss rate of the Sun, we exploit the dependence of the wind-braking torque on the effective rotation rate of the coronal magnetic field. This quantity is evaluated by tracing field lines through a Potential Field Source Surface (PFSS) model, driven by ADAPT-GONG magnetograms. The surface rotation rates of the open magnetic field lines are then used to construct an open-flux weighted rotation rate, from which the influence on the wind-braking torque can be estimated. During solar minima, the rotation rate of the corona decreases with respect to the typical solid-body rate (the Carrington rotation period is 25.4 days), as the sources of the solar wind shift towards the slowly-rotating poles. With increasing activity, more solar wind emerges from the Sun's active latitudes which enforces a Carrington-like rotation. The effect of differential rotation on the Sun's current wind-braking torque is found to be small. The wind-braking torque is ~10-15% lower during solar minimum, than assuming solid body rotation, and a few percent larger during solar maximum. For more rapidly-rotating Sun-like stars, differential rotation may play a more significant role, depending on the configuration of the large-scale magnetic field., Comment: Accepted to A&A. 12 Pages + Appendix. 9 Figures + 4 Appendix Figures

Current models of the solar wind must approximate (or ignore) the small-scale dynamics within the solar atmosphere, however these are likely important in shaping the emerging wave-turbulence spectrum and ultimately heating/accelerating the coronal plasma. The Bifrost code produces realistic simulations of the solar atmosphere that facilitate the analysis of spatial and temporal scales which are currently at, or beyond, the limit of modern solar telescopes. For this study, the Bifrost simulation is configured to represent the solar atmosphere in a coronal hole region, from which the fast solar wind emerges. The simulation extends from the upper-convection zone (2.5 Mm below the photosphere) to the low-corona (14.5 Mm above the photosphere), with a horizontal extent of 24 Mm x 24 Mm. The twisting of the coronal magnetic field by photospheric flows, efficiently injects energy into the low-corona. Poynting fluxes of up to $2-4$ kWm$^{-2}$ are commonly observed inside twisted magnetic structures with diameters in the low-corona of 1 - 5 Mm. Torsional Alfv\'en waves are favourably transmitted along these structures, and will subsequently escape into the solar wind. However, reflections of these waves from the upper boundary condition make it difficult to unambiguously quantify the emerging Alfv\'en wave-energy flux. This study represents a first step in quantifying the conditions at the base of the solar wind using Bifrost simulations. It is shown that the coronal magnetic field is readily braided and twisted by photospheric flows. Temperature and density contrasts form between regions with active stirring motions and those without. Stronger whirlpool-like flows in the convection, concurrent with magnetic concentrations, launch torsional Alfv\'en waves up through the magnetic funnel network, which are expected to enhance the turbulent generation of magnetic switchbacks in the solar wind., Comment: Accepted to A&A. 22 Pages + Appendix. 20 Figures + 5 Appendix Figures

The rotation rates of main-sequence stars slow over time as they gradually lose angular momentum to their magnetized stellar winds. The rate of angular momentum loss depends on the strength and morphology of the magnetic field, the mass-loss rate, and the stellar rotation period, mass, and radius. Previous observations suggested a shift in magnetic morphology between two F-type stars with similar rotation rates but very different ages (88 Leo and rho CrB). In this Letter, we identify a comparable transition in an evolutionary sequence of solar analogs with ages between 2-7 Gyr. We present new spectropolarimetry of 18 Sco and 16 Cyg A & B from the Large Binocular Telescope, and we reanalyze previously published Zeeman Doppler images of HD 76151 and 18 Sco, providing additional constraints on the nature and timing of this transition. We combine archival X-ray observations with updated distances from Gaia to estimate mass-loss rates, and we adopt precise stellar properties from asteroseismology and other sources. We then calculate the wind braking torque for each star in the evolutionary sequence, demonstrating that the rate of angular momentum loss drops by more than an order of magnitude between the ages of HD 76151 and 18 Sco (2.6-3.7 Gyr) and continues to decrease modestly to the age of 16 Cyg A & B (7 Gyr). We suggest that this magnetic transition may represent a disruption of the global dynamo arising from weaker differential rotation, and we outline plans to probe this phenomenon in additional stars spanning a wide range of spectral types., Comment: 6 pages including 2 figures and 1 table. ApJ Letters (accepted June 16)

On the main sequence, low-mass and solar-like stars are observed to spin-down over time, and magnetized stellar winds are thought to be predominantly responsible for this significant angular momentum loss. Previous studies have demonstrated that the wind torque can be predicted via formulations dependent on stellar properties, such as magnetic field strength and geometry, stellar radius and mass, wind mass-loss rate, and stellar rotation rate. Although these stars are observed to experience surface differential rotation, torque formulations so far have assumed solid-body rotation. Surface differential rotation is expected to affect the rotation of the wind and thus the angular momentum loss. To investigate how differential rotation affects the torque, we use the PLUTO code to perform 2.5D magnetohydrodynamic, axisymmetric simulations of stellar winds, using a colatitude-dependent surface differential rotation profile that is solar-like (i.e., rotation is slower at the poles than the equator). We demonstrate that the torque is determined by the average rotation rate in the wind, so that the net torque is less than that predicted by assuming solid-body rotation at the equatorial rate. The magnitude of the effect is essentially proportional to the magnitude of the surface differential rotation, for example, resulting in a torque for the Sun that is $\sim 20 \%$ smaller than predicted by the solid-body assumption. We derive and fit a semi-analytic formulation that predicts the torque as a function of the equatorial spin rate, magnitude of differential rotation, and wind magnetization (depending on the dipolar magnetic field strength and mass-loss rate, combined)., Comment: 15 pages, 7 figures

During the first half of main-sequence lifetimes, the evolution of rotation and magnetic activity in solar-type stars appears to be strongly coupled. Recent observations suggest that rotation rates evolve much more slowly beyond middle-age, while stellar activity continues to decline. We aim to characterize this mid-life transition by combining archival stellar activity data from the Mount Wilson Observatory with asteroseismology from the Transiting Exoplanet Survey Satellite (TESS). For two stars on opposite sides of the transition (88 Leo and $\rho$ CrB), we independently assess the mean activity levels and rotation periods previously reported in the literature. For the less active star ($\rho$ CrB), we detect solar-like oscillations from TESS photometry, and we obtain precise stellar properties from asteroseismic modeling. We derive updated X-ray luminosities for both stars to estimate their mass-loss rates, and we use previously published constraints on magnetic morphology to model the evolutionary change in magnetic braking torque. We then attempt to match the observations with rotational evolution models, assuming either standard spin-down or weakened magnetic braking. We conclude that the asteroseismic age of $\rho$ CrB is consistent with the expected evolution of its mean activity level, and that weakened braking models can more readily explain its relatively fast rotation rate. Future spectropolarimetric observations across a range of spectral types promise to further characterize the shift in magnetic morphology that apparently drives this mid-life transition in solar-type stars., Comment: 11 pages of text including 6 figures and 2 tables. ApJ accepted

Aims: We present the first measurements of the solar-wind angular-momentum (AM) flux recorded by the Solar Orbiter spacecraft. Our aim is the validation of these measurements to support future studies of the Sun's AM loss. Methods: We combine 60-minute averages of the proton bulk moments and the magnetic field measured by the Solar Wind Analyser (SWA) and the magnetometer (MAG) onboard Solar Orbiter. We calculate the AM flux per solid-angle element using data from the first orbit of the mission's cruise phase during 2020. We separate the contributions from protons and from magnetic stresses to the total AM flux. Results: The AM flux varies significantly over time. The particle contribution typically dominates over the magnetic-field contribution during our measurement interval. The total AM flux shows the largest variation and is typically anti-correlated with the radial solar-wind speed. We identify a compression region, potentially associated with a co-rotating interaction region or a coronal mass ejection, that leads to a significant localised increase in the AM flux, yet without a significant increase in the AM per unit mass. We repeat our analysis using the density estimate from the Radio and Plasma Waves (RPW) instrument. Using this independent method, we find a decrease in the peaks of positive AM flux but otherwise consistent results. Conclusions: Our results largely agree with previous measurements of the solar-wind AM flux in terms of amplitude, variability, and dependence on radial solar-wind bulk speed. Our analysis highlights the potential for future, more detailed, studies of the solar wind's AM and its other large-scale properties with data from Solar Orbiter. We emphasise the need to study the radial evolution and latitudinal dependence of the AM flux in combination with data from Parker Solar Probe and assets at heliocentric distances of 1 au and beyond., Comment: 10 pages, 9 figures. Accepted for publication in A&A

An accurate assessment of the Sun's angular momentum (AM) loss rate is an independent constraint for models that describe the rotation evolution of Sun-like stars. In-situ measurements of the solar wind taken by Parker Solar Probe (PSP), at radial distances of $\sim 28-55R_{\odot}$, are used to constrain the solar wind AM-loss rate. For the first time with PSP, this includes a measurement of the alpha particle contribution. The mechanical AM flux in the solar wind protons (core and beam), and alpha particles, is determined as well as the transport of AM through stresses in the interplanetary magnetic field. The solar wind AM flux is averaged over three hour increments, so that our findings more accurately represent the bulk flow. During the third and fourth perihelion passes of PSP, the alpha particles contain around a fifth of the mechanical AM flux in the solar wind (the rest is carried by the protons). The proton beam is found to contain $\sim 10-50\%$ of the proton AM flux. The sign of the alpha particle AM flux is observed to correlate with the proton core. The slow wind has a positive AM flux (removing AM from the Sun as expected), and the fast wind has a negative AM flux. As with previous works, the differential velocity between the alpha particles and the proton core tends to be aligned with the interplanetary magnetic field. In future, by utilising the trends in the alpha-proton differential velocity, it may be possible to estimate the alpha particle contribution when only measurements of the proton core are available. Based on the observations from this work, the alpha particles contribute an additional $10-20\%$ to estimates of the solar wind AM-loss rate which consider only the proton and magnetic field contributions. Additionally, the AM flux of the proton beam can be just as significant as the alpha particles, and so should not be neglected in future studies., Comment: 12 pages + 8 figures, accepted for publication in A&A

The long-term evolution of the Sun's rotation period cannot be directly observed, and is instead inferred from trends in the measured rotation periods of other Sun-like stars. Assuming the Sun spins-down as it ages, following rotation rate $\propto$ age$^{-1/2}$, requires the current solar angular momentum-loss rate to be around $6\times 10^{30}$erg. Magnetohydrodynamic models, and previous observations of the solar wind (from the Helios and Wind spacecraft), generally predict a values closer to $1\times 10^{30}$erg or $3\times 10^{30}$erg, respectively. Recently, the Parker Solar Probe (PSP) observed tangential solar wind speeds as high as $\sim50$km/s in a localized region of the inner heliosphere. If such rotational flows were prevalent throughout the corona, it would imply that the solar wind angular momentum-loss rate is an order of magnitude larger than all of those previous estimations. In this letter, we evaluate the angular momentum flux in the solar wind, using data from the first two orbits of PSP. The solar wind is observed to contain both large positive (as seen during perihelion), and negative angular momentum fluxes. We analyse two solar wind streams that were repeatedly traversed by PSP; the first is a slow wind stream whose average angular momentum flux fluctuates between positive to negative, and the second is an intermediate speed stream containing a positive angular momentum flux (more consistent with a constant flow of angular momentum). When the data from PSP is evaluated holistically, the average equatorial angular momentum flux implies a global angular momentum-loss rate of around $2.6-4.2\times 10^{30}$ erg (which is more consistent with observations from previous spacecraft)., Comment: 11 pages + 6 figures, accepted for publication to ApJL

Reconnection between pairs of solar magnetic flux elements, one open and the other a closed loop, is theorised to be a crucial process for both maintaining the structure of the corona and producing the solar wind. This 'interchange reconnection' is expected to be particularly active at the open-closed boundaries of coronal holes (CHs). Previous analysis of solar wind data at 1AU indicated that peaks in the flux of suprathermal electrons at slow-fast stream interfaces may arise from magnetic connection to the CH boundary, rather than dynamic effects such as compression. Further, offsets between the peak and stream interface locations are suggested to be the result of interchange reconnection at the source. As a preliminary test of these suggestions, we analyse two solar wind streams observed during the first Parker Solar Probe (PSP) perihelion encounter, each associated with equatorial CH boundaries (one leading and one trailing with respect to rotation). Each stream features a peak in suprathermal electron flux, the locations and associated plasma properties of which are indicative of a solar origin, in agreement with previous suggestions from 1AU observations. Discrepancies between locations of the flux peaks and other features suggest these peaks may too be shifted by source region interchange reconnection. Our interpretation of each event is compatible with a global pattern of open flux transport, although random footpoint motions or other explanations remain feasible. These exploratory results highlight future opportunities for statistical studies regarding interchange reconnection and flux transport at CH boundaries with modern near-Sun missions.

Observations of stellar rotation show that low-mass stars lose angular momentum during the main sequence. We simulate the winds of Sun-like stars with a range of rotation rates, covering the fast and slow magneto-rotator regimes, including the transition between the two. We generalize an Alfv\'en-wave driven solar wind model that builds on previous works by including the magneto-centrifugal force explicitly. In this model, the surface-averaged open magnetic flux is assumed to scale as $B_\ast f^{\rm open}_\ast \propto {\rm Ro}^{-1.2}$, where $f^{\rm open}_\ast$ and ${\rm Ro}$ are the surface open-flux filling factor and Rossby number, respectively. We find that, 1. the angular momentum loss rate (torque) of the wind is described as $\tau_w \approx 2.59 \times 10^{30} {\rm \ erg} \ \left( \Omega_\ast / \Omega_\odot \right)^{2.82}$, yielding a spin-down law $\Omega_\ast \propto t^{-0.55}$. 2. the mass-loss rate saturates at $\dot{M}_w \sim 3.4 \times 10^{-14} M_\odot {\rm \ yr^{-1}}$, due to the strong reflection and dissipation of Alfv\'en waves in the chromosphere. This indicates that the chromosphere has a strong impact in connecting the stellar surface and stellar wind. Meanwhile, the wind ram pressure scales as $P_w \propto \Omega_\ast^{0.57}$, which is able to explain the lower-envelope of the observed stellar winds by Wood et al. 3. the location of the Alfv\'en radius is shown to scale in a way that is consistent with 1D analytic theory. Additionally, the precise scaling of the Alfv\'en radius matches previous works which used thermally-driven winds. Our results suggest that the Alfv\'en-wave driven magnetic rotator wind plays a dominant role in the stellar spin-down during the main-sequence., Comment: accepted for publication in The Astrophysical Journal

Numerous attempts to estimate the rate at which low-mass stars lose angular momentum over their lifetimes exist in the literature. One approach is to use magnetic maps derived from Zeeman-Doppler imaging (ZDI) in conjunction with so-called "braking laws". The use of ZDI maps has advantages over other methods because it allows information about the magnetic field geometry to be incorporated into the estimate. However, ZDI is known to underestimate photospheric field strengths due to flux cancellation effects. Recently, Lehmann et al. (2018) conducted synthetic ZDI reconstructions on a set of flux transport simulations to help quantify the amount by which ZDI underestimates the field strengths of relatively slowly rotating and weak activity solar-like stars. In this paper, we evaluate how underestimated angular momentum-loss rate estimates based on ZDI maps may be. We find that they are relatively accurate for stars with strong magnetic fields but may be underestimated by a factor of up to $\sim$10 for stars with weak magnetic fields. Additionally, we re-evaluate our previous work that used ZDI maps to study the relative contributions of different magnetic field modes to angular momentum-loss. We previously found that the dipole component dominates spin-down for most low-mass stars. This conclusion still holds true even in light of the work of Lehmann et al. (2018)., Comment: 8 pages, 3 figures, 1 table, accepted for publication by ApJ

The rate at which the solar wind extracts angular momentum from the Sun has been predicted by theoretical models for many decades, and yet we lack a conclusive measurement from in-situ observations. In this letter we present a new estimate of the time-varying angular momentum flux in the equatorial solar wind, as observed by the \textit{Wind} spacecraft from 1994-2019. We separate the angular momentum flux into contributions from the protons, alpha particles, and magnetic stresses, showing that the mechanical flux in the protons is $\sim$3 times larger than the magnetic field stresses. We observe the tendency for the angular momentum flux of fast wind streams to be oppositely signed to the slow wind streams, as noted by previous authors. From the average total flux, we estimate the global angular momentum loss rate of the Sun to be $3.3\times10^{30}$erg, which lies within the range of various MHD wind models in the literature. This angular momentum loss rate is a factor of $\sim$2 weaker than required for a Skumanich-like rotation period evolution ($\Omega_*\propto $ stellar age$^{-1/2}$), which should be considered in studies of the rotation period evolution of Sun-like stars., Comment: 10 pages + 2 figures, accepted for publication to ApJL

Main sequence low-mass stars are known to spin-down as a consequence of their magnetised stellar winds. However, estimating the precise rate of this spin-down is an open problem. The mass-loss rate, angular momentum-loss rate and the magnetic field properties of low-mass stars are fundamentally linked making this a challenging task. Of particular interest is the stellar magnetic field geometry. In this work, we consider whether non-dipolar field modes contribute significantly to the spin-down of low-mass stars. We do this using a sample of stars that have all been previously mapped with Zeeman-Doppler imaging. For a given star, as long as its mass-loss rate is below some critical mass-loss rate, only the dipolar fields contribute to its spin-down torque. However, if it has a larger mass-loss rate, higher order modes need to be considered. For each star, we calculate this critical mass-loss rate, which is a simple function of the field geometry. Additionally, we use two methods of estimating mass-loss rates for our sample of stars. In the majority of cases, we find that the estimated mass-loss rates do not exceed the critical mass-loss rate and hence, the dipolar magnetic field alone is sufficient to determine the spin-down torque. However, we find some evidence that, at large Rossby numbers, non-dipolar modes may start to contribute., Comment: 15 pages, 6 figures, 3 tables, accepted to ApJ

The Sun and Sun-like stars lose angular momentum to their magnetised stellar winds. This braking torque is coupled to the stellar magnetic field, such that changes in the strength and/or geometry of the field modifies the efficiency of this process. Since the space-age, we have been able to directly measure solar wind properties using in-situ spacecraft. Furthermore, indirect proxies such as sunspot number, geomagnetic indices, and cosmogenic radionuclides, constrain the variation of solar wind properties on centennial, and millennial timescales. We use near-Earth measurements of the solar wind plasma and magnetic field to calculate the torque on the Sun throughout the space-age. Then, reconstructions of the solar open magnetic flux are used to estimate the time-varying braking torque during the last nine millennia. We assume a relationship for the solar mass loss rate based on observations during the space-age which, due to the weak dependence of the torque on mass loss rate, does not strongly affect our predicted torque. The average torque during the last nine millennia is found to be $2.2\times10^{30}$erg, which is comparable to the average value from the last two decades. Our dataset includes grand minima (such as the Maunder Minimum), and maxima in solar activity, where the torque varies from $\sim1-5\times10^{30}$erg (averaged on decadal timescales), respectively. We find no evidence for any secular variation of the torque on timescales of less than $9000$ years., Comment: 13 pages + 3 figures, accepted for publication to ApJ

The magnetic fields of low-mass stars are observed to be variable on decadal timescales, ranging in behaviour from cyclic to stochastic. The changing strength and geometry of the magnetic field should modify the efficiency of angular momentum loss by stellar winds, but this has not been well quantified. In Finley et al. (2018) we investigated the variability of the Sun, and calculated the time-varying angular momentum loss rate in the solar wind. In this work, we focus on four low-mass stars that have all had their surface magnetic fields mapped for multiple epochs. Using mass loss rates determined from astrospheric Lyman-$\alpha$ absorption, in conjunction with scaling relations from the MHD simulations of Finley & Matt (2018), we calculate the torque applied to each star by their magnetised stellar winds. The variability of the braking torque can be significant. For example, the largest torque for $\epsilon$ Eri is twice its decadal averaged value. This variation is comparable to that observed in the solar wind, when sparsely sampled. On average, the torques in our sample range from 0.5-1.5 times their average value. We compare these results to the torques of Matt et al. (2015), which use observed stellar rotation rates to infer the long-time averaged torque on stars. We find that our stellar wind torques are systematically lower than the long-time average values, by a factor of ~3-30. Stellar wind variability appears unable to resolve this discrepancy, implying that there remain some problems with observed wind parameters, stellar wind models, or the long-term evolution models, which have yet to be understood., Comment: 15 pages + 8 figures, accepted for publication to ApJ

Low-mass stars are known to have magnetic fields that are believed to be of dynamo origin. Two complementary techniques are principally used to characterise them. Zeeman-Doppler imaging (ZDI) can determine the geometry of the large-scale magnetic field while Zeeman broadening can assess the total unsigned flux including that associated with small-scale structures such as spots. In this work, we study a sample of stars that have been previously mapped with ZDI. We show that the average unsigned magnetic flux follows an activity-rotation relation separating into saturated and unsaturated regimes. We also compare the average photospheric magnetic flux recovered by ZDI, $\langle B_V\rangle$, with that recovered by Zeeman broadening studies, $\langle B_I\rangle$. In line with previous studies, $\langle B_V\rangle$ ranges from a few % to $\sim$20% of $\langle B_I\rangle$. We show that a power law relationship between $\langle B_V\rangle$ and $\langle B_I\rangle$ exists and that ZDI recovers a larger fraction of the magnetic flux in more active stars. Using this relation, we improve on previous attempts to estimate filling factors, i.e. the fraction of the stellar surface covered with magnetic field, for stars mapped only with ZDI. Our estimated filling factors follow the well-known activity-rotation relation which is in agreement with filling factors obtained directly from Zeeman broadening studies. We discuss the possible implications of these results for flux tube expansion above the stellar surface and stellar wind models., Comment: 8 pages (main text), 3 additional pages (appendix), 4 figures, 2 tables

The rotational evolution of cool stars is governed by magnetised stellar winds which slow the stellar rotation during their main sequence lifetimes. Magnetic variability is commonly observed in Sun-like stars, and the changing strength and topology of the global field is expected to affect the torque exerted by the stellar wind. We present three different methods for computing the angular momentum loss in the solar wind. Two are based on MHD simulations from Finley & Matt (2018), with one using the open flux measured in the solar wind, and the other using remotely-observed surface magnetograms. Both methods agree in the variation of the solar torque seen through the solar cycle and show a 30-40% decrease from cycle 23 to 24. The two methods calculate different average values, $2.9\times10^{30}$erg (open flux) and $0.35\times10^{30}$erg (surface field). This discrepancy results from the already well-known difficulty with reconciling the magnetograms with observed open flux, which is currently not understood, leading to an inability to discriminate between these two calculated torques. The third method is based on the observed spin-rates of Sun-like stars, which decrease with age, directly probing the average angular momentum loss. This method gives $6.2\times10^{30}$erg for the solar torque, larger than the other methods. This may be indicative of further variability in the solar torque on timescales much longer than the magnetic cycle. We discuss the implications for applying the formula to other Sun-like stars, where only surface field measurements are available, and where the magnetic variations are ill-constrained., Comment: 16 pages + 4 figures, accepted for publication to ApJ

During the lifetime of sun-like or low mass stars a significant amount of angular momentum is removed through magnetised stellar winds. This process is often assumed to be governed by the dipolar component of the magnetic field. However, observed magnetic fields can host strong quadrupolar and/or octupolar components, which may influence the resulting spin-down torque on the star. In Paper I, we used the MHD code PLUTO to compute steady state solutions for stellar winds containing a mixture of dipole and quadrupole geometries. We showed the combined winds to be more complex than a simple sum of winds with these individual components. This work follows the same method as Paper I, including the octupole geometry which increases the field complexity but also, more fundamentally, looks for the first time at combining the same symmetry family of fields, with the field polarity of the dipole and octupole geometries reversing over the equator (unlike the symmetric quadrupole). We show, as in Paper I, that the lowest order component typically dominates the spin down torque. Specifically, the dipole component is the most significant in governing the spin down torque for mixed geometries and under most conditions for real stars. We present a general torque formulation that includes the effects of complex, mixed fields, which predicts the torque for all the simulations to within 20% precision, and the majority to within ~5%. This can be used as an input for rotational evolution calculations in cases where the individual magnetic components are known., Comment: 18 pages + 15 figures, accepted for publication to ApJ

Cool stars with outer convective envelopes are observed to have magnetic fields with a variety of geometries, which on large scales are dominated by a combination of the lowest order fields such as the dipole, quadrupole and octupole modes. Magnetised stellar wind outflows are primarily responsible for the loss of angular momentum from these objects during the main sequence. Previous works have shown the reduced effectiveness of the stellar wind braking mechanism with increasingly complex, but singular, magnetic field geometries. In this paper, we quantify the impact of mixed dipolar and quadrupolar fields on the spin-down torque using 50 MHD simulations with mixed field, along with 10 of each pure geometries. The simulated winds include a wide range of magnetic field strength and reside in the slow-rotator regime. We find that the stellar wind braking torque from our combined geometry cases are well described by a broken power law behaviour, where the torque scaling with field strength can be predicted by the dipole component alone or the quadrupolar scaling utilising the total field strength. The simulation results can be scaled and apply to all main-sequence cool stars. For Solar parameters, the lowest order component of the field (dipole in this paper) is the most significant in determining the angular momentum loss., Comment: 15 pages + 9 figures (main), 3 pages + 1 figure (appendix), accepted for publication to ApJ