Night‐time science with large solar telescopes: The magnetic Sun through time

Today the Sun has a regular magnetic cycle driven by a dynamo action. But how did this regular cycle develop? How do basic parameters such as rotation rate, age, and differential rotation affect the generation of magnetic fields? Zeeman Doppler imaging (ZDI) is a technique that uses high‐resolution observations in circularly polarised light to map the surface magnetic topology on stars. Utilising the spectropolarimetric capabilities of future large solar telescopes it will be possible to study the evolution and morphology of the magnetic fields on a range of Sun‐like stars from solar twins through to rapidly‐rotating active young Suns and thus study the solar magnetic dynamo through time. In this article I discuss recent results from ZDI of Sun‐like stars and how we can use night‐time observations from future solar telescopes to solve unanswered questions about the origin and evolution of the Sun's magnetic dynamo (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation of cool active stars: the case of intermediate rotators

In this paper, we present a new method for measuring the surface differential rotation of cool stars with rotation periods of a few days, for which the sparse phase coverage achievable from single-site observations generally prevents the use of more conventional techniques. The basic idea underlying this new analysis is to obtain the surface differential rotation pattern that minimizes the information content of the reconstructed Doppler image through a simultaneous fit of all available data.
Simulations demonstrate that the performance of this new method in the case of cool stars is satisfactory for a variety of observing strategies. Differential rotation parameters can be recovered reliably as long as the total data set spans at least 4 per cent of the time for the equator to lap the pole by approximately one complete cycle. We find in particular that these results hold for potentially complex spot distributions (as long as they include a mixture of low- and high-latitude features), and for various stellar inclination angles and rotation velocities. Such measurements can be obtained from either unpolarized or polarized data sets, provided their signal-to-noise ratio is larger than approximately 500 and 5000 per 2 km s⁻¹ spectral bin, respectively.
This method should therefore be very useful for investigating differential rotation in a much larger sample of objects than what has been possible up to now, and should hence give us the opportunity of studying how differential rotation reacts to various phenomena operating in stellar convective zones, such as tidal effects or dynamo magnetic field generation.     

The exceptional Herbig Ae star HD 101412: The first detection of resolved magnetically split lines and the presence of chemical spots in a Herbig star

In our previous search for magnetic fields in Herbig Ae stars, we pointed out that HD 101412 possesses the strongest magnetic field among the Herbig Ae stars and hence is of special interest for follow‐up studies of magnetism among young pre‐main‐sequence stars. We obtained high‐resolution, high signal‐to‐noise UVES and a few lower quality HARPS spectra revealing the presence of resolved magnetically split lines. HD 101412 is the first Herbig Ae star for which the rotational Doppler effect was found to be small in comparison to the magnetic splitting and several spectral lines observed in unpolarized light at high dispersion are resolved into magnetically split components. The measured mean magnetic field modulus varies from 2.5 to 3.5kG, while the mean quadratic field was found to vary in the range of 3.5 to 4.8 kG. To determine the period of variations, we used radial velocity, equivalent width, line width, and line asymmetry measurements of variable spectral lines of several elements, as well as magnetic field measurements. The period determination was done using the Lomb‐Scargle method. The most pronounced variability was detected for spectral lines of He I and the iron peak elements, whereas the spectral lines of CNO elements are only slightly variable. From spectral variations and magnetic field measurements we derived a potential rotation period P_rot = 13.86 d, which has to be proven in future studies with a larger number of observations. It is the first time that the presence of element spots is detected on the surface of a Herbig Ae/Be star. Our previous study of Herbig Ae stars revealed a trend towards stronger magnetic fields for younger Herbig Ae stars, confirmed by statistical tests. This is in contrast to a few other (non‐statistical) studies claiming that magnetic Herbig Ae stars are progenitors of the magnetic Ap stars. New developments in MHD theory show that the measured magnetic field strengths are compatible with a current‐driven instability of toroidal fields generated by differential rotation in the stellar interior. This explanation for magnetic intermediate‐mass stars could be an alternative to a frozen‐in fossil field (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation on rapidly rotating stars

Theories of meridional circulation and differential rotation in stellar convective zones predict trends in surface flow patterns on main-sequence stars that are amenable to direct observational testing. Here I summarise progress made in the last few years in determining surface differential rotation patterns on rapidly-rotating young main-sequence stars of spectral types F, G, K and M. Differential rotation increases strongly with increasing effective temperature along the main sequence. The shear rate appears to increase with depth in the sub-photospheric layers. Tidal locking in close binaries appears to suppress differential rotation, but better statistics are needed before this conclusion can be trusted. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation in F stars

Differential rotation can be detected in single line profiles of stars rotating more rapidly than about v sin i = 10km s-1 with the Fourier transform technique. This allows to search for differential rotation in large samples to look for correlations between differential rotation and other stellar parameters. I analyze the fraction of differentially rotating stars as a function of color, rotation, and activity in a large sample of F-type stars. Color and rotation exhibit a correlation with differential rotation in the sense that more stars are rotating differentially in the cooler, less rapidly rotating stars. Effects of rotation and color, however, cannot be disentangled in the underlying sample. No trend with activity is found. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling the time variation of the surface differential rotation in AB Doradus and LQ Hydrae

Sequences of Doppler images of the young, rapidly rotating late-type stars AB Dor and LQ Hya show that their equatorial angular velocity and the amplitude of their surface differential rotation vary versus time. Such variations can be modelled to obtain information on the intensity of the azimuthal magnetic stresses within stellar convection zones. We introduce a simple model in the framework of the mean-field theory and discuss briefly the results of its application to those solar-like stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The eclipsing binary PV Cas: a case of strong differential rotation in depth

In this study, we show that only models with differential rotation, as opposed to non-rotation or solid-body rotation for the components of PV Cas, are in satisfactory agreement with the observations (including constraints on the apsidal advance rate and the synchronous rotation of the components in addition to their luminosities and radii). Internal rotation profiles found for solar and metal-rich chemical compositions are similar to each other in that only a small part of the outermost regions is rotating very slowly  ( v _eq∼ 65 km s ⁻¹)  and the rest is rotating very rapidly. Confirmation of Ap-like variations in the light curve of the system leads us to search for a connection between this type (and similar types) of internal rotation and chemically peculiar stars. The temperature difference between the blue sides of the main sequence for the normal and for the magnetic Ap stars may arise from such a connection, since we find a similar difference between the models with this kind of rotation and the non-rotating models of somewhat lower mass.     

Spots on FK Com: active longitudes and “flip‐flops”

We have earlier investigated the surface structures of a late‐type, single, giant FK Com for the years 1994–1998 using Doppler imaging. These surface temperature maps revealed long‐lived active regions at high latitudes. Long‐term photometric observations also show that these active regions tend to occur at two permanent active longitudes which are 180 degrees apart from each other, and that the activity switches the longitude with an average period of about 3 years (the “flip‐flop” phenomenon). In this work we present new Doppler maps of FK Com obtained 1998‐2003 and light‐curve maps obtained 2002–2003. These new maps are investigated together with the earlier temperature maps and light‐curve maps, with an aim of further studying the active longitudes, “flip‐flop” phenomenon and surface differential rotation on FK Com. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Long‐term photometry of the ultra‐fast rotator LO Peg

LO Peg is a young main‐sequence star of spectral type K3. With its equatorial rotation velocity of 65 km s^–1 it is amongst the ultra‐fast rotators. Its high equatorial rotation velocity and rapidly changing surface activity features make it an important object in terms of both stellar activity and the evolution of stellar rotation and angular momentum. Since its discovery as a variable star, it has mostly been subject to spectral surface mapping studies such as Doppler Imaging, while there have been very few photometric studies on it. This paper aims to present the first long‐term photometric observations and its results covering the years between 2003 and 2009. The UBVR Johnson wide band photometric data showed that the surface activity structures of LO Peg vary in timescales changing between days and months, and parallel to this, the mean, maximum and minimum brightness and amplitudes change dramatically between years and sometimes even within the same observation season. Long‐term changes in system brightness and colours, both characteristic features of active stars, were also seen in this ultra‐fast young star. The active longitudes, which has a life time of ∼1.3 years and an activity cycle period of ∼4.8 years for LO Peg were estimated (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the time dependence of differential rotation in young late-type stars

A model for the angular momentum transfer within the convection zone of a rapidly rotating star is introduced and applied to the analysis of recent observations of temporal fluctuations of the differential rotation on the young late-type stars AB Doradus (AB Dor) and LQ Hydrae (LQ Hya). Under the hypothesis that the mean magnetic field produced by the stellar dynamo rules the angular momentum exchanges and that the angular velocity depends only on the distance s from the rotation axis and the time, the minimum azimuthal Maxwell stress  | B_sB _φ|  , averaged over the convection zone, is found to range from ∼0.04 to  ∼0.14 T²  . If the poloidal mean magnetic field   B _s   is of the order of 0.01 T, as indicated by the Zeeman–Doppler imaging maps of those stars, then the azimuthal mean field   B _φ  can reach an intensity of several teslas, which significantly exceeds equipartition with the turbulent kinetic energy. Such strong fields can account also for the orbital period modulation observed in cataclysmic variables and RS Canum Venaticorum systems with a main-sequence secondary component. Moreover, the model allows us to compute the kinetic energy dissipation rate during the maintenance of the differential rotation. Only in the case of the largest surface shear observed on LQ Hya may the dissipated power exceed the stellar luminosity, but the lack of a sufficient statistic on the occurrence of such episodes of large shear does not allow us to estimate their impact on the energy budget of the convection zone.     

Stellar surface imaging: mapping brightness and magnetic fields

Rapidly rotating late‐type stars typically display signs of magnetic activity that exceed those seen on the Sun by over two orders of magnitude. The techniques of Doppler imaging and Zeeman Doppler imaging have been instrumental in unveiling magnetic activity patterns at the photospheres of these active stars. Essentially, these techniques work by inverting time‐series of high resolution spectra to produce temperature, brightness and/or magnetic field maps at the surfaces of stars. I will describe how these techniques work and review what they have taught us about the nature of magnetic activity in rapid rotators over the last 20 years. Finally, I will conclude by outlining the capabilities of these techniques in light of new instrumentation that is now becoming available. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of magnetic fields in stars across the upper main sequence: II. Observed distribution of the magnetic field geometry

We re‐discuss the evolutionary state of upper main sequence magnetic stars using a sample of Ap and Bp stars with accurate Hipparcos parallaxes and definitely determined longitudinal magnetic fields. We confirm our previous results obtained from the study of Ap and Bp stars with accurate measurements of the mean magnetic field modulus and mean quadratic magnetic fields that magnetic stars of mass M < 3 M_⊙ are concentrated towards the centre of the main‐sequence band. In contrast, stars with masses M > 3 M_⊙ seem to be concentrated closer to the ZAMS. The study of a few known members of nearby open clusters with accurate Hipparcos parallaxes confirms these conclusions. Stronger magnetic fields tend to be found in hotter, younger and more massive stars, as well as in stars with shorter rotation periods. The longest rotation periods are found only in stars which spent already more than 40% of their main sequence life, in the mass domain between 1.8 and 3 M_⊙ and with log g values ranging from 3.80 to 4.13. No evidence is found for any loss of angular momentum during the main‐sequence life. The magnetic flux remains constant over the stellar life time on the main sequence. An excess of stars with large obliquities β is detected in both higher and lower mass stars. It is quite possible that the angle β becomes close to 0. in slower rotating stars of mass M > 3 M_⊙ too, analog to the behaviour of angles β in slowly rotating stars of M < 3 M_⊙. The obliquity angle distribution as inferred from the distribution of r ‐values appears random at the time magnetic stars become observable on the H‐R diagram. After quite a short time spent on the main sequence, the obliquity angle β tends to reach values close to either 90. or 0. for M < 3 M_⊙. The evolution of the obliquity angle β seems to be somewhat different for low and high mass stars. While we find a strong hint for an increase of β with the elapsed time on the main sequence for stars with M > 3 M_⊙, no similar trend is found for stars with M < 3 M_⊙. However, the predominance of high values of β at advanced ages in these stars is notable. As the physics governing the processes taking place in magnetised atmospheres remains poorly understood, magnetic field properties have to be considered in the framework of dynamo or fossil field theories. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotation,activity, and lithium abundance in cool binary stars

We have used two robotic telescopes to obtain time‐series high‐resolution optical echelle spectroscopy and VI and/or by photometry for a sample of 60 active stars, mostly binaries. Orbital solutions are presented for 26 double‐lined systems and for 19 single‐lined systems, seven of them for the first time but all of them with unprecedented phase coverage and accuracy. Eighteen systems turned out to be single stars. The total of 6609 R = 55000 échelle spectra are also used to systematically determine effective temperatures, gravities, metallicities, rotational velocities, lithium abundances and absolute Hα‐core fluxes as a function of time. The photometry is used to infer unspotted brightness, V – I and/or b – y colors, spot‐induced brightness amplitudes and precise rotation periods. An extra 22 radial‐velocity standard stars were monitored throughout the science observations and yield a new barycentric zero point for our STELLA/SES robotic system. Our data are complemented by literature data and are used to determine rotation‐temperature‐activity relations for active binary components. We also relate lithium abundance to rotation and surface temperature. We find that 74% of all known rapidly‐rotating active binary stars are synchronized and in circular orbits but 26% (61 systems) are rotating asynchronously of which half have P_rot > P_orb and e > 0. Because rotational synchronization is predicted to occur before orbital circularization active binaries should undergo an extra spin‐down besides tidal dissipation. We suspect this to be due to a magnetically channeled wind with its subsequent braking torque. We find a steep increase of rotation period with decreasing effective temperature for active stars, P_rot α T^–7_eff, for both single and binaries, main sequence and evolved. For inactive, single giants with P_rot > 100 d, the relation is much weaker, P_rot α T^‐1.12_eff. Our data also indicate a period‐activity relation for Hα of the form R_Hα α P_0.24^rot for binaries and R_Hα α P_‐0.14^rot for singles. Its power‐law difference is possibly significant. Lithium abundances in our (field‐star) sample generally increase with effective temperature and are paralleled with an increase of the dispersion. The dispersion for binaries can be 1–2 orders of magnitude larger than for singles, peaking at an absolute spread of 3 orders of magnitude near T_eff ≈ 5000 K. On average, binaries of comparable effective temperature appear to exhibit 0.25 dex less surface lithium than singles, as expected if the depletion mechanism is rotation dependent. We also find a trend of increased Li abundance with rotational period of form log n (Li) α –0.6 log P_rot but again with a dispersion of as large as 3‐4 orders of magnitude (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotation and activity in the solar-type stars of NGC 2547

We present high-resolution spectroscopy of a sample of 24 solar-type stars in the young (15–40 Myr), open cluster NGC 2547. We use our spectra to confirm cluster membership in 23 of these stars, to determine projected equatorial velocities and chromospheric activity, and to search for the presence of accretion discs. We find examples of both fast ( v _e sin  i >50 km s⁻¹) and slow ( v _e sin  i <10 km s⁻¹) rotators, but no evidence for active accretion in any of the sample. The distribution of projected rotation velocities is indistinguishable from the slightly older IC 2391 and IC 2602 clusters, implying similar initial angular momentum distributions and circumstellar disc lifetimes. The presence of very slow rotators indicates either that long (10–40 Myr) disc lifetimes or internal differential rotation are needed, or that NGC 2547 (and IC 2391/2602) were born with more slowly rotating stars than are presently seen in even younger clusters and associations. The solar-type stars in NGC 2547 follow a similar rotation–activity relationship to that seen in older clusters. X-ray activity increases until a saturation level is reached for v _e sin  i >15–20 km s⁻¹. We are unable to explain why this saturation level, of log( L _x L _bol)≃−3.3, is a factor of 2 lower than in other clusters, but rule out anomalously slow rotation rates or uncertainties in X-ray flux calculations.     

Zonal Model of Starspots. Application to RS CVn Systems

Model results on starspots in 15 chromospherically active type RS CVn binary systems are presented. The dependences of the parameters of the spots on the principal characteristics of the stars (spectral class, luminosity class, rotation, Rossby number) are examined. Latitudinal drift of the spots, cycles in the spot activity, and differential rotation are found in 9 of the stars. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 535–552 (November 2005).     

Differential rotation of giant stars

From a set of high-resolution spectral observations of late type giant stars we used Doppler imaging to derive time-series temperature maps of the stellar surfaces. Using these temperature maps, it is possible to track the temporal changes of the spot features and derive estimates of the strength and sign of the differential surface rotation of these stars. Looking into the latitudinal changes of the surface maps, it is also possible to derive meridional flows on these stars. But due to the lower accuracy of the latitudes of the reconstructed spot features, the data requirements are higher than for the detection of differential rotation. Nevertheless, a correlation between the differential rotation and meridional flow estimates is suggested. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A search for magnetic fields in cool sdB stars

Hot cluster horizontal branch (HB) stars and field subdwarf B (sdB) stars are core helium burning stars that exhibit abundance anomalies that are believed to be due to atomic diffusion. Diffusion can be effective in these stars because they are slowly rotating. In particular, the slow rotation of the hot HB stars (T_eff > 11000 K), which show abundance anomalies, contrasts with the fast rotation of the cool HB stars, where the observed abundances are consistent with those of red giants belonging to the same cluster. The reason why sdB stars and hot HB stars are rotating slowly is unknown. In order to assess the possible role of magnetic fields on abundances and rotation, we investigated the occurrence of such fields in sdB stars with T_eff < 30 000 K, whose temperatures overlap with those of the hot HB stars. We conclude that large‐scale organised magnetic fields of kG order are not generally present in these stars but at the achieved accuracy, the possibility that they have fields of a few hundred Gauss remains open. We report the marginal detection of such a field in SB 290; further observations are needed to confirm it (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new look at the relationship between activity, dynamo number and Rossby number in late-type stars

The correlation between stellar activity, as measured by the indicator Δ R _HK, and the Rossby number Ro in late-type stars is revisited in light of recent developments in solar dynamo theory. Different stellar interior models, based on both mixing-length theory and the full spectrum of turbulence, are used in order to see to what extent the correlation of activity with Rossby number is model dependent, or otherwise can be considered universal. Although we find some modest model dependence, we find that the correlation of activity with Rossby number is significantly better than with rotation period alone for all the models we consider. Dynamo theory suggests that activity should scale with the dynamo number. A current model of the solar dynamo, the so-called interface dynamo, proposes that the amplification of the toroidal magnetic field by differential rotation (the ω -effect) and the production of the poloidal magnetic field from toroidal by helical turbulence (the α -effect) take place in different, adjacent layers near the base of the convection zone. A new scale analysis based on the interface dynamo shows that the appropriate dynamo number does not depend on the Rossby number alone, but also depends on an additional dimensionless factor related to the differential rotation. This leads to a new interpretation of the correlation between activity and Rossby number, which in turn leads to some conclusions about the magnitude of differential rotation in the dynamo layers of late-type main-sequence stars.     

Rapid rotation,active nests of convection and global-scale flows in solar-likestars

In the solar convection zone, rotation couples with intensely turbulent convection to build global-scale flows of differential rotation and meridional circulation. Our sun must have rotated more rapidly in its past, as is suggested by observations of many rapidly rotating young solar-type stars. Here we explore the effects of more rapid rotation on the patterns of convection in such stars and the global-scale flows which are self-consistently established. The convection in these systems is richly time dependent and in our most rapidly rotating suns a striking pattern of spatially localized convection emerges. Convection near the equator in these systems is dominated by one or two patches of locally enhanced convection, with nearly quiescent streaming flow in between at the highest rotation rates. These active nests of convection maintain a strong differential rotation despite their small size. The structure of differential rotation is similar in all of our more rapidly rotating suns, with fast equators and slower poles. We find that the total shear in differential rotation, as measured by latitudinal angular velocity contrast, ΔΩ, increases with more rapid rotation while the relative shear, ΔΩ/Ω, decreases. In contrast, at more rapid rotation the meridional circulations decrease in both energy and peak velocities and break into multiple cells of circulation in both radius and latitude. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Imaging the cool stars in the interacting binaries AE Aqr,BV Cen and V426 Oph

It is well known that magnetic activity in late‐type stars increases with increasing rotation rate. Using inversion techniques akin to medical imaging, the rotationally broadened profiles from such stars can be used to reconstruct ‘Doppler images’ of the distribution of cool, dark starspots on their stellar surfaces. Interacting binaries, however, contain some of the most rapidly rotating late‐type stars known and thus provide important tests of stellar dynamo models. Furthermore, magnetic activity is thought to play a key role in their evolution, behaviour and accretion dynamics. Despite this, we know comparatively little about the magnetic activity and its influence on such binaries. In this review we summarise the concepts behind indirect imaging of these systems, and present movies of the starspot distributions on the cool stars in some interacting binaries. We conclude with a look at the future opportunities that such studies may provide. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)