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Register a new userEstimating magnetic filling factors from Zeeman-Doppler magnetograms
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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, $langle B_Vrangle$, with that recovered by Zeeman broadening studies, $langle B_Irangle$. In line with previous studies, $langle B_Vrangle$ ranges from a few % to $sim$20% of $langle B_Irangle$. We show that a power law relationship between $langle B_Vrangle$ and $langle B_Irangle$ 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.
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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.
State of the art radial velocity (RV) exoplanet searches are limited by the effects of stellar magnetic activity. Magnetically active spots, plage, and network regions each have different impacts on the observed spectral lines, and therefore on the apparent stellar RV. Differentiating the relative coverage, or filling factors, of these active regions is thus necessary to differentiate between activity-driven RV signatures and Doppler shifts due to planetary orbits. In this work, we develop a technique to estimate feature-specific magnetic filling factors on stellar targets using only spectroscopic and photometric observations. We demonstrate linear and neural network implementations of our technique using observations from the solar telescope at HARPS-N, the HK Project at the Mt. Wilson Observatory, and the Total Irradiance Monitor onboard SORCE. We then compare the results of each technique to direct observations by the Solar Dynamics Observatory (SDO). Both implementations yield filling factor estimates that are highly correlated with the observed values. Modeling the solar RVs using these filling factors reproduces the expected contributions of the suppression of convective blueshift and rotational imbalance due to brightness inhomogeneities. Both implementations of this technique reduce the overall activity-driven RMS RVs from 1.64 m/s to 1.02 m/s, corresponding to a 1.28 m/s reduction in the RMS variation. The technique provides an additional 0.41 m/s reduction in the RMS variation compared to traditional activity indicators.
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 stars 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 20$^{rm o}$-30$^{rm o}$, predicted wind speeds are within 5$%$ of the value at full resolution. Mass loss rates and angular momentum loss rates are within 5-20$%$. In contrast, the predicted X-ray emission measures can be under-estimated by 1-2 orders of magnitude, and their rotational modulations by 10-20$%$.
We are reaching the point where spectropolarimetric surveys have run for long enough to reveal solar-like magnetic activity cycles. In this paper we investigate what would be the best strategy to identify solar-like magnetic cycles and ask which large-scale magnetic field parameters best follow a solar-type magnetic cycle and are observable with the Zeeman-Doppler-Imaging (ZDI) technique. We approach these questions using the 3D non-potential flux transport simulations of cite{Yeates2012} modelling the solar vector magnetic field over 15 years (centred on solar cycle 23). The flux emergence profile was extracted from solar synoptic maps and used as input for a photospheric flux transport model in combination with a non-potential coronal evolution model. We synthesise spectropolarimetric data from the simulated maps and reconstruct them using ZDI. The ZDI observed solar cycle is set into the context of other cool star observations and we present observable trends of the magnetic field topology with time, sunspot number and S-index. We find that the axisymmetric energy fraction is the best parameter of the ZDI detectable large-scale field to trace solar-like cycles. Neither the surface averaged large-scale field or the total magnetic energy is appropriate. ZDI seems also to be able to recover the increase of the toroidal energy with S-index. We see further that ZDI might unveil hints of the dynamo modes that are operating and of the global properties of the small-scale flux emergence like active latitudes.
Zeeman Doppler Imaging is a powerful tool for characterizing the strength and topology of stellar magnetic fields. In this research note, we present a new way to visualize the typical results from ZDI for an ensemble of stars, addressing some of the concerns with the standard `confusogram approach to illustrating the data. Our publically available plotting methods further enable an accessible means to consider variability in the inferred magnetic field topologies from repeated observations, as we demonstrate with the literature ZDI data on M dwarfs.
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