Angular Momentum Loss Rate Research Articles

The Solar Wind Angular Momentum Flux as Observed by Parker Solar Probe

Abstract 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 ∝ age−1/2, requires the current solar angular momentum (AM) loss rate to be around 6 × 1030 erg. Magnetohydrodynamic models, and previous observations of the solar wind (from the Helios and Wind spacecraft), generally predict a values closer to 1 × 1030 erg or 3 × 1030 erg, respectively. Recently, the Parker Solar Probe (PSP) observed tangential solar wind speeds as high as ∼50 km s−1 in a localized region of the inner heliosphere. If such rotational flows were prevalent throughout the corona, it would imply that the solar wind AM-loss rate is an order of magnitude larger than all of those previous estimations. In this Letter, we evaluate the AM 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 AM fluxes. We analyze two solar wind streams that were repeatedly traversed by PSP; the first is a slow wind stream whose average AM flux fluctuates between positive and negative values, and the second is an intermediate speed stream that contains a positive AM flux (more consistent with a constant flow of AM). When the data from PSP are evaluated holistically, the average equatorial AM flux implies a global AM-loss rate of around (2.6–4.2) × 1030 erg (which is more consistent with observations from previous spacecraft).

Alfvén-wave-driven Magnetic Rotator Winds from Low-mass Stars. I. Rotation Dependences of Magnetic Braking and Mass-loss Rate

Abstract Observations of stellar rotation show that low-mass stars lose angular momentum during the main sequence. We simulate the winds of sunlike stars with a range of rotation rates, covering the fast and slow magneto-rotator regimes, including the transition between the two. We generalize an Alfvén-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 , where and 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 , yielding a spin-down law . (2) The mass-loss rate saturates at , due to the strong reflection and dissipation of Alfvén 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 , which is able to explain the lower envelope of the observed stellar winds by Wood et al. (3) The location of the Alfvén radius is shown to scale in a way that is consistent with one-dimensional analytic theory. Additionally, the precise scaling of the Alfvén radius matches previous works, which used thermally driven winds. Our results suggest that the Alfvén-wave-driven magnetic rotator wind plays a dominant role in the stellar spin-down during the main sequence.

How Much Do Underestimated Field Strengths from Zeeman–Doppler Imaging Affect Spin-down Torque Estimates?

Abstract Numerous attempts to estimate the rate at which low-mass stars lose angular momentum over their lifetimes fill 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. 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 ∼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.

The solar wind from a stellar perspective

Context.Due to the effects that they can have on the atmospheres of exoplanets, stellar winds have recently received significant attention in the literature. Alfvén-wave-driven 3D magnetohydrodynamic models, which are increasingly used to predict stellar wind properties, contain unconstrained parameters and rely on low-resolution stellar magnetograms.Aims.In this paper, we explore the effects of the input Alfvén wave energy flux and the surface magnetogram on the wind properties predicted by the Alfvén Wave Solar Model (AWSoM) model for both the solar and stellar winds.Methods.We lowered the resolution of two solar magnetograms during solar cycle maximum and minimum using spherical harmonic decomposition. The Alfvén wave energy was altered based on non-thermal velocities determined from a far ultraviolet spectrum of the solar twin 18 Sco. Additionally, low-resolution magnetograms of three solar analogues, 18 Sco, HD 76151, and HN Peg, were obtained using Zeeman Doppler imaging and used as a proxy for the solar magnetogram. Finally, the simulated wind properties were compared to Advanced Composition Explorer (ACE) observations.Results.AWSoM simulations using well constrained input parameters taken from solar observations can reproduce the observed solar wind mass loss and angular momentum loss rates. The simulated wind velocity, proton density, and ram pressure differ from ACE observations by a factor of approximately two. The resolution of the magnetogram has a small impact on the wind properties and only during cycle maximum. However, variation in Alfvén wave energy influences the wind properties irrespective of the solar cycle activity level. Furthermore, solar wind simulations carried out using the low-resolution magnetogram of the three stars instead of the solar magnetogram could lead to an order of a magnitude difference in the simulated solar wind properties.Conclusions.The choice in Alfvén energy has a stronger influence on the wind output compared to the magnetogram resolution. The influence could be even stronger for stars whose input boundary conditions are not as well constrained as those of the Sun. Unsurprisingly, replacing the solar magnetogram with a stellar magnetogram could lead to completely inaccurate solar wind properties, and should be avoided in solar and stellar wind simulations. Further observational and theoretical work is needed to fully understand the complexity of solar and stellar winds.

LBT/PEPSI Spectropolarimetry of a Magnetic Morphology Shift in Old Solar-type Stars*

Abstract Solar-type stars are born with relatively rapid rotation and strong magnetic fields. Through a process known as magnetic braking, the rotation slows over time as stellar winds gradually remove angular momentum from the system. The rate of angular momentum loss depends sensitively on the magnetic morphology, with the dipole field exerting the largest torque on the star. Recent observations suggest that the efficiency of magnetic braking may decrease dramatically in stars near the middle of their main-sequence lifetimes. One hypothesis to explain this reduction in efficiency is a shift in magnetic morphology from predominantly larger to smaller spatial scales. We aim to test this hypothesis with spectropolarimetric measurements of two stars that sample chromospheric activity levels on opposite sides of the proposed magnetic transition. As predicted, the more active star (HD 100180) exhibits a significant circular polarization signature due to a nonaxisymmetric large-scale magnetic field, while the less active star (HD 143761) shows no significant signal. We identify analogs of the two stars among a sample of well-characterized Kepler targets, and we predict that the asteroseismic age of HD 143761 from future Transiting Exoplanet Survey Satellite observations will substantially exceed the age expected from gyrochronology. We conclude that a shift in magnetic morphology likely contributes to the loss of magnetic braking in middle-aged stars, which appears to coincide with the shutdown of their global dynamos.

Do Non-dipolar Magnetic Fields Contribute to Spin-down Torques?

Abstract Main-sequence low-mass stars are known to spin down as a consequence of their magnetized stellar winds. However, estimating the precise rate of this spin-down is an open problem. The mass-loss rate, angular momentum loss rate, and 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; 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.

Direct Detection of Solar Angular Momentum Loss with the Wind Spacecraft

Abstract The rate at which the solar wind extracts angular momentum (AM) 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 AM flux in the equatorial solar wind, as observed by the Wind spacecraft from 1994 to 2019. We separate the AM flux into contributions from the protons, alpha particles, and magnetic stresses, showing that the mechanical flux in the protons is ∼3 times larger than the magnetic field stresses. We observe the tendency for the AM 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 AM loss rate of the Sun to be 3.3 × 1030 erg, which lies within the range of various magnetohydrodynamic wind models in the literature. This AM loss rate is a factor of ∼2 weaker than required for a Skumanich-like rotation period evolution ( stellar age−1/2), which should be considered in studies of the rotation period evolution of Sun-like stars.

The Effect of Magnetic Variability on Stellar Angular Momentum Loss. II. The Sun, 61 Cygni A, ϵ Eridani, ξ Bootis A, and τ Bootis A

Abstract The magnetic fields of low-mass stars are observed to be variable on decadal timescales, ranging in behavior 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 Lyα absorption, in conjunction with scaling relations from the MHD simulations of Finley & Matt (2018), we calculate the torque applied to each star by their magnetized stellar winds. The variability of the braking torque can be significant. For example, the largest torque for ϵ 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 to 1.5 times their average value. We compare these results to the torques of Matt et al. (2015), who 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-averaged 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.

The evolutionary status of Cataclysmic Variables: eclipse modelling of 15 systems

We present measurements of the component masses in 15 Cataclysmic Variables (CVs) - 6 new estimates and 9 improved estimates. We provide new calibrations of the relationship between superhump period excess and mass ratio, and use this relation to estimate donor star masses for 225 superhumping CVs. With an increased sample of donor masses we revisit the implications for CV evolution. We confirm the high mass of white dwarfs in CVs, but find no trend in white dwarf mass with orbital period. We argue for a revision in the location of the orbital period minimum of CVs to $79.6 \pm 0.2$ min, significantly shorter than previous estimates. We find that CV donors below the gap have an intrinsic scatter of only 0.005 R$_{\odot}$ around a common evolutionary track, implying a correspondingly small variation in angular momentum loss rates. In contrast to prior studies, we find that standard CV evolutionary tracks - without additional angular momentum loss - are a reasonable fit to the donor masses just below the period gap, but that they do not reproduce the observed period minimum, or fit the donor radii below 0.1 M$_{\odot}$.

MOVES – II. Tuning in to the radio environment of HD189733b

ABSTRACT We present stellar wind modelling of the hot Jupiter host HD189733, and predict radio emission from the stellar wind and the planet, the latter arising from the interaction of the stellar wind with the planetary magnetosphere. Our stellar wind models incorporate surface stellar magnetic field maps at the epochs 2013 June/July, 2014 September, and 2015 July as boundary conditions. We find that the mass-loss rate, angular momentum loss rate, and open magnetic flux of HD189733 vary by 9 per cent, 40 per cent, and 19 per cent over these three epochs. Solving the equations of radiative transfer, we find that from 10 MHz–100 GHz the stellar wind emits fluxes in the range of 10−3–5 μJy, and becomes optically thin above 10 GHz. Our planetary radio emission model uses the radiometric Bode’s law, and neglects the presence of a planetary atmosphere. For assumed planetary magnetic fields of 1–10 G, we estimate that the planet emits at frequencies of 2–25 MHz, with peak flux densities of 102 mJy. We find that the planet orbits through regions of the stellar wind that are optically thick to the emitted frequency from the planet. As a result, unattenuated planetary radio emission can only propagate out of the system and reach the observer for 67 per cent of the orbit for a 10 G planetary field, corresponding to when the planet is approaching and leaving primary transit. We also find that the plasma frequency of the stellar wind is too high to allow propagation of the planetary radio emission below 21 MHz. This means a planetary field of at least 8 G is required to produce detectable radio emission.

Can the Friction of the Nova Envelope Account for the Extra Angular Momentum Loss in Cataclysmic Variables?

It has been shown that the rate of angular momentum loss (AML) in cataclysmic variables (CVs) below the period gap is about 2.47 times that caused by gravitational radiation, suggesting extra AML mechanism besides gravitational radiation. Several potential mechanisms have been proposed but none of them has been verified. In this work we examine whether AML caused by friction between the expanding nova envelope and the donor star can account for the required AML rate. By adopting various expanding velocities of the envelope, we have calculated the evolution of CVs with typical initial parameters. Our results show that this friction interaction unlikely solve the extra AML problem unless the expanding velocities are extremely low. Thus there should be a more efficient AML mechanism that plays a role in the CV evolution.

Low-mass X-ray binaries: the effects of the magnetic braking prescription

We present a population study of low- and intermediate-mass X-ray binaries (LMXBs) with neutron star accretors, performed using the detailed 1D stellar evolution code MESA. We identify all plausible Roche-lobe overflowing binaries at the start of mass transfer, and compare our theoretical mass transfer tracks to the population of well-studied Milky Way LMXBs. The mass transferring evolution depends on the accepted magnetic braking (MB) law for angular momentum loss. The most common MB prescription ("Skumanich MB") originated from observations of the time-dependence of rotational braking of Sun-type stars, where the angular momentum loss rate depends on the donor mass $M_d$, donor radius $R_d$, and rotation rate $\Omega$, $\dot{J} \propto M_d R_d^{\gamma} \Omega^3$. The functional form of the Skumanich MB can be also obtained theoretically assuming a radial magnetic field, isotropic isothermal winds, and boosting of the magnetic field by rotation. Here we show that this simple form of the Skumanich MB law gives mass transfer rates an order of magnitude too weak to explain most observed persistent LMXBs. This failure suggests that the standard Skumanich MB law should not be employed to interpret Galactic, or extragalactic, LMXB populations, with either detailed stellar codes or rapid binary population synthesis codes. We investigate modifications for the MB law, and find that including a scaling of the magnetic field strength with the convective turnover time, and a scaling of MB with the wind mass loss rate, can reproduce persistent LMXBs, and does a better job at reproducing transient LMXBs.

The Solar Wind in Time II: 3D stellar wind structure and radio emission

In this work, we simulate the evolution of the solar wind along its main sequence lifetime and compute its thermal radio emission. To study the evolution of the solar wind, we use a sample of solar mass stars at different ages. All these stars have observationally-reconstructed magnetic maps, which are incorporated in our 3D magnetohydrodynamic simulations of their winds. We show that angular-momentum loss and mass-loss rates decrease steadily on evolutionary timescales, although they can vary in a magnetic cycle timescale. Stellar winds are known to emit radiation in the form of thermal bremsstrahlung in the radio spectrum. To calculate the expected radio fluxes from these winds, we solve the radiative transfer equation numerically from first principles. We compute continuum spectra across the frequency range 100 MHz - 100 GHz and find maximum radio flux densities ranging from 0.05 - 8.3 $\mu$Jy. At a frequency of 1 GHz and a normalised distance of d = 10 pc, the radio flux density follows 0.24 $(\Omega/\Omega_{\odot})^{0.9}$ (d/[10pc])$^2$ $\mu$Jy, where $\Omega$ is the rotation rate. This means that the best candidates for stellar wind observations in the radio regime are faster rotators within distances of 10 pc, such as $\kappa^1$ Ceti (2.83 $\mu$Jy) and $\chi^1$ Ori (8.3 $\mu$Jy). These flux predictions provide a guide to observing solar-type stars across the frequency range 0.1 - 100 GHz in the future using the next generation of radio telescopes, such as ngVLA and SKA.

The life cycles of Be viscous decretion discs: The case of ω CMa

We analyzed V-band photometry of the Be star {\omega} CMa, obtained during the last four decades, during which the star went through four complete cycles of disc formation and dissipation. The data were simulated by hydrodynamic models based on a time-dependent implementation of the viscous decretion disc (VDD) paradigm, in which a disc around a fast-spinning Be star is formed by material ejected by the star and driven to progressively larger orbits by means of viscous torques. Our simulations offer a good description of the photometric variability during phases of disc formation and dissipation, which suggests that the VDD model adequately describes the structural evolution of the disc. Furthermore, our analysis allowed us to determine the viscosity parameter {\alpha}, as well as the net mass and angular momentum (AM) loss rates. We find that {\alpha} is variable, ranging from 0.1 to 1.0, not only from cycle to cycle but also within a given cycle. Additionally, build-up phases usually have larger values of {\alpha} than the dissipation phases. Furthermore, during dissipation the outward AM flux is not necessarily zero, meaning that {\omega} CMa does not experience a true quiescence but, instead, switches between a high to a low AM loss rate during which the disc quickly assumes an overall lower density but never zero. We confront the average AM loss rate with predictions from stellar evolution models for fast-rotating stars, and find that our measurements are smaller by more than one order of magnitude.

The Solar Wind Environment in Time

Abstract We use magnetograms of eight solar analogs of ages 30 Myr–3.6 Gyr obtained from Zeeman Doppler Imaging and taken from the literature, together with two solar magnetograms, to drive magnetohydrodynamical wind simulations and construct an evolutionary scenario of the solar wind environment and its angular momentum loss rate. With observed magnetograms of the radial field strength as the only variant in the wind model, we find that a power-law model fitted to the derived angular momentum loss rate against time, t, results in a spin-down relation Ω ∝ t −0.51, for angular speed Ω, which is remarkably consistent with the well-established Skumanich law Ω ∝ t −0.5. We use the model wind conditions to estimate the magnetospheric standoff distances for an Earth-like test planet situated at 1 au for each of the stellar cases, and to obtain trends of minimum and maximum wind ram pressure and average ram pressure in the solar system through time. The wind ram pressure declines with time as , amounting to a factor of 50 or so over the present lifetime of the solar system.

The life cycles of Be viscous decretion discs: fundamental disc parameters of 54 SMC Be stars

Be stars are main-sequence massive stars with emission features in their spectrum, which originates in circumstellar gaseous discs. Even though the viscous decretion disc (VDD) model can satisfactorily explain most observations, two important physical ingredients, namely the magnitude of the viscosity ($\alpha$) and the disk mass injection rate, remain poorly constrained. The light curves of Be stars that undergo events of disc formation and dissipation offer an opportunity to constrain these quantities. A pipeline was developed to model these events that uses a grid of synthetic light curves, computed from coupled hydrodynamic and radiative transfer calculations. A sample of 54 Be stars from the OGLE survey of the Small Magellanic Cloud (SMC) was selected for this study. Because of the way our sample was selected (bright stars with clear disc events), it likely represents the densest discs in the SMC. Like their siblings in the Galaxy, the mass of the disc in the SMC increases with the stellar mass. The typical mass and angular momentum loss rates associated with the disk events are of the order of $\sim$$10^{-10}\, M_\odot\,\mathrm{yr^{-1}}$ and $\sim$$5\times 10^{36}\, \mathrm{g\, cm^{2}\, s^{-2}}$, respectively. The values of $\alpha$ found in this work are typically of a few tenths, consistent with recent results in the literature and with the ones found in dwarf novae, but larger than current theory predicts. Considering the sample as a whole, the viscosity parameter is roughly two times larger at build-up ($\left\langle\alpha_\mathrm{bu}\right\rangle = 0.63$) than at dissipation ($\left\langle\alpha_\mathrm{d}\right\rangle = 0.26$). Further work is necessary to verify whether this trend is real or a result of some of the model assumptions.

Wind-accelerated orbital evolution in binary systems with giant stars

Using 3D radiation-hydrodynamic simulations and analytic theory, we study the orbital evolution of asymptotic-giant-branch (AGB) binary systems for various initial orbital separations and mass ratios, and thus different initial accretion modes. The time evolution of binary separations and orbital periods are calculated directly from the averaged mass loss rate, accretion rate and angular momentum loss rate. We separately consider spin-orbit synchronized and zero spin AGB cases. We find that the the angular momentum carried away by the mass loss together with the mass transfer can effectively shrink the orbit when accretion occurs via wind-Roche-lobe overflow. In contrast, the larger fraction of mass lost in Bondi-Hoyle-Lyttleton accreting systems acts to enlarge the orbit. Synchronized binaries tend to experience stronger orbital period decay in close binaries. We also find that orbital period decay is faster when we account for the nonlinear evolution of the accretion mode as the binary starts to tighten. This can increase the fraction of binaries that result in common envelope, luminous red novae, Type Ia supernovae and planetary nebulae with tight central binaries. The results also imply that planets in the the habitable zone around white dwarfs are unlikely to be found.

Studying stellar spin-down with Zeeman–Doppler magnetograms

Magnetic activity and rotation are known to be intimately linked for low-mass stars. Understanding rotation evolution over the stellar lifetime is therefore an important goal within stellar astrophysics. In recent years, there has been increased focus on how the complexity of the stellar magnetic field affects the rate of angular momentum-loss from a star. This is a topic that Zeeman-Doppler imaging (ZDI), a technique that is capable of reconstructing the large-scale magnetic field topology of a star, can uniquely address. Using a potential field source surface model, we estimate the open flux, mass loss-rate and angular momentum-loss rates for a sample of 66 stars that have been mapped with ZDI. We show that the open flux of a star is predominantly determined by the dipolar component of its magnetic field for our choice of source surface radius. We also show that, on the main sequence, the open flux, mass- and angular momentum-loss rates increase with decreasing Rossby number. The exception to this rule is stars less massive than $0.3M_{\odot}$. Previous work suggests that low mass M dwarfs may possess either strong, ordered and dipolar fields or weak and complex fields. This range of field strengths results in a large spread of angular momentum-loss rates for these stars and has important consequences for their spin down behaviour. Additionally, our models do not predict a transition in the mass-loss rates at the so called wind dividing line noted from Ly$\alpha$ studies.

The missing magnetic morphology term in stellar rotation evolution

This study examines the relationship between magnetic field complexity and mass and angular momentum losses. Observations of open clusters have revealed a bimodal distribution of the rotation periods of solar-like stars that has proven difficult to explain under the existing rubric of magnetic braking. Recent studies suggest that magnetic complexity can play an important role in controlling stellar spin-down rates. However, magnetic morphology is still neglected in most rotation evolution models due to the difficulty of properly accounting for its effects on wind driving and angular momentum loss. Using state-of-the-art magnetohydrodynamical magnetized wind simulations we study the effect that different distributions of the magnetic flux at different levels of geometrical complexity have on mass and angular momentum loss rates. Angular momentum loss rates depend strongly on the level of complexity of the field but are independent of the way this complexity is distributed. We deduce the analytical terms representing the magnetic field morphology dependence of mass and angular momentum loss rates. We also define a parameter that best represents complexity for real stars. As a test, we use these analytical methods to estimate mass and angular momentum loss rates for $8$ stars with observed magnetograms and compare them to the simulated results. Magnetic field complexity provides a natural physical basis for stellar rotation evolution models requiring a rapid transition between weak and strong spin-down modes.

Estimating stellar wind parameters from low-resolution magnetograms

Abstract Stellar winds govern the angular momentum evolution of solar-like stars throughout their main-sequence lifetime. The efficiency of this process depends on the geometry of the star's magnetic field. There has been a rapid increase recently in the number of stars for which this geometry can be determined through spectropolarimetry. We present a computationally efficient method to determine the 3D geometry of the stellar wind and to estimate the mass-loss rate and angular momentum loss rate based on these observations. Using solar magnetograms as examples, we quantify the extent to which the values obtained are affected by the limited spatial resolution of stellar observations. We find that for a typical stellar surface resolution of 20o–30o, predicted wind speeds are within 5 per cent of the value at full resolution. Mass-loss rates and angular momentum loss rates are within 5–20 per cent. In contrast, the predicted X-ray emission measures can be underestimated by one-to-two orders of magnitude, and their rotational modulations by 10–20 per cent.