Stellar Differential Rotation Research Articles

Long-term monitoring of active stars

As part of an extensive program focused on the global properties and evolution of active stars, high-precision UBV ( RI ) c and UBV photometry of 18 selected stars is presented. UBV ( RI ) c observations were collected at the European Southern Observatory over the intervals 21–28 September 1994 and 25 November–05 December 1994. Additional UBV photometry obtained late in 1994 by Catania Astrophysical Observatory Automatic Photoelectric Telescope is also presented. Significant evolution of the light curves, period variations and evidence for long-term variability of the global degree of spottedness are found. Some spectral classifications are revised and photometric parallaxes are compared, whenever possible, with the values measured by the Hipparcos satellite. These observations are finalized to the construction of an extended photometric database, which can give important clues on topics such as the stability of spotted areas, differential stellar rotation, solar-like activity cycles and the correlation between inhomogeneities at different atmospheric levels.

Wavelet analysis of stellar differential rotation

Future space projects like KEPLER will deliver a vast quantity of high precision light curves of stars. This paper describes a test concerning the observability of rotation and even dierential rotation of slowly rotating stars from such data. Two published light curves of solar total irradiance measures are investigated: the Nimbus-7 Earth Radiation Budget (ERB) observations between 1978 and 1993 and the Active Cavity Radiometer Irradiance Monitor I (ACRIM I) measurements between 1980 and 1989. Light curve analysis show that oscillations on time-scales comparable to solar rotation but of a complex pattern are visible. Neither Fourier analysis nor time-frequency Wavelet analysis yield the true rotation period during the more active phases of the solar cycle. The true rotation period dominates only for a short time during solar minimum. In the light of this study even space-born broad band photometry may turn out an inappropriate instrument to study stellar butterfly diagrams of stars rotating as slow as the Sun. However, it was shown in Papers I and II of this series that chromospheric tracers like Lyman, Mg II h+k and CaII H+K are appropriate instruments to perform this task.

On Stellar Dynamo Processes and Differential Rotation

Many stars exhibit strong magnetic fields, some of which are thought to be of primordial origin and others a sign of magnetic dynamo processes. We briefly review the results of observational studies of solar-type stars seeking to evaluate the linkage between rotation rate and possible magnetic cycles of activity. Clearly turbulent convection and rotation within spherical shell geometries provide ingredients essential for dynamo action. However, intensive efforts over several decades in solar research have demonstrated that it is no easy matter to achieve cyclic magnetic activity that is in accord with observations. Helioseismology has revealed that an essential element for the global solar dynamo is the presence of a tachocline of shear at the base of the solar convection zone, leading to the likely operation of an interface dynamo. We review the crucial elements for achieving a cyclic magnetic activity. We then discuss some of our current 3-D MHD simulations of solar turbulent convection in spherical shells that yield differential rotation profiles which make good contact with some of the helioseismic findings. We show that such turbulent motions can amplify and sustain magnetic field in the bulk of the convective zone whose strength are sufficient to feed back both upon the convection and its global circulations.

Can star spots mimic differential rotation?

The search for stellar differential rotation in Fourier-transformed profiles utilizes subtle deviations from the standard rotation profile. We investigate the influence of stellar spots on the results obtained with the Fourier Transform Method. Different spot configurations, especially polar spots, are examined, and their influence on Fourier-transformed line profiles studied. We found that polar spots cannot mimic solar-like differential rotation and are thus not critical for the use of the Fourier Transform Method. Although not indicated by Doppler imaging, other configurations may occur on stellar surfaces and their influence on the analysis is discussed. A symmetric distribution of spots in an activity belt leads - in a small region of the parameter space - to line profiles that are very similar to the signatures produced by differential rotation.

Wavelet analysis of stellar differential rotation

Among the several methods to study differential rotation on stellar surfaces the observation of a stellar butterfly diagram, i.e. monitoring the rotation period over a complete activity cycle, is the only method which canbe applied to stars rotating as slow as the Sun. However, the method requires active belts on the stellar surface which are moving continously in stellar latitude during a cycle. In addition, an appropriate activity tracer showing rotational modulation is needed. Tracers which even work for slowly rotating, i.e. weakly active, stars are the emission cores of certain spectral lines. However, the question is whether surface differential rotation can be determined from this kind of observations and furthermore, which method of analysis is best suited to yield a correct result. We investigate observations of the Sun as a star, i.e. disk-integrated measurements, to answer these questions. In a Paper I it was demonstrated that time-frequency analysis using the wavelet transform is possibly a suitable method for monitoring the stellar butterfly diagram. It was also shown that - in comparison with Fourier analysis - wavelet analysis of disk-integrated solar Ca II K line core emission measures yield a much more realistic pattern of the solar differential rotation. In this Paper II disk-integrated solar measures in Mg II h+k and Lyman a taken from public UARLS Solstice data are analysed using the same methods as in Paper I. In these data solar rotational modulation is much more pronounced than in earlier Ca II K time-series. Wavelet analysis yields the following results: from the beginning of the time-series in 1991 until the end of solar cycle 22 the period of rotational modulation remains stable at 26.9-27.0 days. It is followed by a jump to 27.6 days when the new cycle 23 starts. Then the period rapidly decreases to 26.9 days again until the end of the time-series in 1999. However, the analysis is hampered by frequent period splitting into two modes. It can be shown that this kind of splitting results from phase jumps in the time-series coming from active region growth and decay at 180° shifted solar longitudes.

On the feasibility of the detection of differential rotation in stellar absorption profiles

Stellar differential rotation invokes subtle effects on line absorption profiles which can be best studied in the Fourier domain. Detailed calculations of the behavior of Fourier transformed profiles with respect to varying differential rotation, limb darkening and inclination angles are presented. The zero positions of the Fourier transform are found to be very good tracers of differential rotation. The ratio of the first two zero positions σ 2 /σ 1 can be easily measured and is a reliable parameter to deduce the amount of differential rotation. It is shown that solar-like differential rotation (equatorial regions have larger angular velocity then polar regions) has an unambigious signature in the Fourier domain and that in certain cases it can easily be distinguished from limb darkening effects. A simple procedure is given allowing the determination of the amount of differential rotation by the knowledge of the first two zero positions of a line profile's Fourier transform alone (i.e., without the need for thorough atmospheric modelling), under the assumption of a linear limb darkening law with a limb darkening coefficient of e = 0.6.

Stellar differential rotation from direct star-spot tracking

On the Sun, the rotation periods of individual sunspots not only trace the latitude-dependence of the surface rotation rate, but also provide clues as to the amount of subsurface fluid shear. In this paper we present the first measurements of stellar differential rotation made by tracking the rotation of individual star-spots with sizes comparable to the largest sunspots. To achieve this we re-analyse four sequences of densely sampled, high signal-to-noise ratio echelle spectra of AB Doradus spanning several stellar rotations in 1996 December. Using spectral subtraction, least-squares deconvolution and matched-filter analysis, we demonstrate that it is possible to measure directly the velocity amplitudes and rotation periods of large numbers of individual star-spots at low to intermediate latitude. We derive values for the equatorial rotation rate and the magnitude of the surface differential rotation, both of which are in excellent agreement with those obtained by Donati & Collier Cameron from cross-correlation of Doppler images derived a year earlier in 1995 December, and with a re-analysis of the 1996 data by the Χ 2 landscape method. The differences between the rotation rates of individual spots and the fitted differential rotation law are substantially greater than the observational errors. The smaller spots show a greater scatter about the mean relation than the larger ones, which suggests that buffeting by turbulent supergranular flows could be responsible.

A Central Engine for Cosmic Gamma‐Ray Burst Sources

One of a family previously proposed engines for cosmic gamma-ray burst sources is considered in some detail. A steadily accreting 106 G magnetic white dwarf should ultimately collapse to a strongly differentially rotating, millisecond-rotation-period neutron star for a wide range of steady accretion rates and initial masses if the accreting white dwarf has an evolved O-Ne-Mg composition. A similar neutron star could also result from an initial C-O white dwarf but only for more constrained accretion rates. Because the collapsing white dwarf begins as a γ = polytrope, the final neutron star's spin rate increases strongly with cylindrical radius. A stable windup of the neutron star's poloidal magnetic field then produces buoyant magnetic toroids which grow, break loose, rise, and partly penetrate the neutron star surface to form a transient, B ≈ 1017 G millisecond-spin-period pulsar with a powerful pulsar wind. This pulsar wind emission is then rapidly suppressed by the surface shear motion from the strong stellar differential rotation. This windup and transient pulsar formation can occur at other times on different cylinders and/or repeat on the same one, with (re-)windup and surface penetration timescales hugely longer than the neutron star's millisecond spin period. In this way, differential rotation both opens and closes the doors which allow neutron star spin energy to be emitted in powerful bursts of pulsar wind. Predictions of this model compare favorably to needed central engine properties of gamma-ray burst sources (total energy, birth rate, duration, subburst fluctuations and timescales, variability among burst events, and baryon loading).

The magnetic field of the nearest cool starA Paradigm for Stellar Activity

Looking at the Sun forges the framework within which we try to interpret stellar observations. The stellar counterparts of spots, plages, flux tubes, chromospheres, coronae, etc., are readily invoked when attempting to interpret stellar data. This review discusses a selection of solar phenomena that are crucial to understand stellar atmospheric activity. Topics include the interaction of magnetic fields and flows, the relationships between fluxes from different temperature regimes in stellar atmospheres, the photospheric flux budget and its impact on the measurement of the dynamo strength, and the measurement of stellar differential rotation.

The solar surface differential rotation from disk-integrated chromospheric fluxes

Disk-integrated solar chromospheric Caii K-line (3933.68 A) fluxes have been measured almost daily at Sacramento Peak Observatory since 1977. Using observing windows selected to mimic seasonal windows for chromospheric measurements of lower Main-Sequence stars such as those observed by Mount Wilson Observatory's HK Project, we have measured the solar rotation from the modulation of the Caii K-line flux. We track the change of rotation period from the decline of cycle 21 through the maximum of cycle 22. This variation in rotation period is shown to behave as expected from the migration of active regions in latitude according to Maunder's ‘butterfly diagram’, including an abrupt change in rotation period at the transition from cycle 21 to cycle 22. These results indicate the successful detection of solar surface differential rotation from disk-integrated observations. We argue that the success of our study compared to previous investigations of the solar surface differential rotation from disk-integrated fluxes lies primarily with the choice of the length of the time-series window. Our selection of 200 days is shorter than in previous studies whose windows are typically on the order of one year. The 200-day window is long enough to permit an accurate determination of the rotation period, yet short enough to avoid complications arising from active region evolution. Thus, measurements of the variation of rotation period in lower Main-Sequence stars, especially those that appear to be correlated with long-term changes in chromospheric activity (i.e., cycles), are probably evidence for stellar surface differential rotation.

MEAN MAGNETIC FIELD AS A TRACER OF DIFFERENTIAL ROTATION IN LATE-TYPE DWARFS

ABSTRACT Subsets of the solar mean-magnetic-field measurements have been studied to determine the conditions for which a solar-type differential rotation signal may be seen in stellar observations. Stellar differential rotation may be detected from mean-magnetic-field measurements if: (1) the number of observations is relatively high; (2) the noise level is less than roughly 25 percent of the maximum field strength value; and (3) the sign of the magnetic field has been determined. The combination of synoptic polarization measurements with those of Zeeman broadening may permit the detection of stellar differential rotation.

ON THE DETERMINATION OF STELLAR ROTATION AND DIFFERENTIAL ROTATION FROM CHROMOSPHERIC ACTIVITY DATA

ABSTRACT Methods of determining stellar rotation and differential rotation from data sets of chromospheric activity indicators are discussed from the point of view of establishing required properties of the time series. Problems inherent in determining differential rotation and partial solutions to these difficulties are addressed. Detection and characterization of stellar differential rotation is a difficult, but approachable goal, and requires a better signal-to-noise ratio in the observations than the problem of rotation period determination. A solar data set of plage areas from the summer of 1982 is used to illustrate the technique.

Is stellar differential rotation observable?

Daily measures of the disk integral 2.8 GHz solar flux from the years 1947 through 1982 are analyzed to determine the detectability of stellar differential rotation using the tracer method. Autocorrelation and power spectral analyses of 1 yr data sets yield rotation periods whose scatter about the mean period is too large to permit detection of the expected differential rotation signal. The principal noise source is the random appearance of tracer regions on the solar surface, in time and longitude. Criteria are given for optimizing stellar observations and analyses to detect differential rotation.

A quest for differential stellar rotation in A stars

A quest for differential stellar rotation in A stars