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Register a new userIdentifying solar-like magnetic cycles with Zeeman-Doppler-Imaging (ZDI)
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Added by
Lisa Theres Lehmann
Publication date
2020
fields
Physics
and research's language is
English
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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.
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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.
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.
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 stellar magnetic field plays a crucial role in the star internal mechanisms, as in the interactions with its environment. The study of starspots provides information about the stellar magnetic field, and can characterise the cycle. Moreover, the analysis of solar-type stars is also useful to shed light onto the origin of the solar magnetic field. The objective of this work is to characterise the magnetic activity of stars. Here, we studied two solar-type stars Kepler-17 and Kepler-63 using two methods to estimate the magnetic cycle length. The first one characterises the spots (radius, intensity, and location) by fitting the small variations in the light curve of a star caused by the occultation of a spot during a planetary transit. This approach yields the number of spots present in the stellar surface and the flux deficit subtracted from the star by their presence during each transit. The second method estimates the activity from the excess in the residuals of the transit lightcurves. This excess is obtained by subtracting a spotless model transit from the lightcurve, and then integrating all the residuals during the transit. The presence of long term periodicity is estimated in both time series. With the first method, we obtained $P_{rm cycle}$ = 1.12 $pm$ 0.16 yr (Kepler-17) and $P_{rm cycle}$ = 1.27 $pm$ 0.16 yr (Kepler-63), and for the second approach the values are 1.35 $pm$ 0.27 yr and 1.27 $pm$ 0.12 yr, respectively. The results of both methods agree with each other and confirm their robustness.
The periods of magnetic activity cycles in the Sun and solar-type stars do not exhibit a simple or even single trend with respect to rotation rate or luminosity. Dynamo models can be used to interpret this diversity, and can ultimately help us understand why some solar-like stars do not exhibit a magnetic cycle, whereas some do, and for the latter what physical mechanisms set their magnetic cycle period. Three-dimensional non-linear magnetohydrodynamical simulations present the advantage of having only a small number of tunable parameters, and produce in a dynamically self-consistent manner the flows and the dynamo magnetic fields pervading stellar interiors. We conducted a series of such simulations within the EULAG-MHD framework, varying the rotation rate and luminosity of the modeled solar-like convective envelopes. We find decadal magnetic cycles when the Rossby number near the base of the convection zone is moderate (typically between 0.25 and 1). Secondary, shorter cycles located at the top of the convective envelope close to the equator are also observed in our numerical experiments, when the local Rossby number is lower than 1. The deep-seated dynamo sustained in these numerical experiments is fundamentally non-linear, in that it is the feedback of the large-scale magnetic field on the large-scale differential rotation that sets the magnetic cycle period. The cycle period is found to decrease with the Rossby number, which offers an alternative theoretical explanation to the variety of activity cycles observed in solar-like stars.
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