Measurements Of Differential Rotation Research Articles

Asteroseismic measurement of core and envelope rotation rates for 2006 red giant branch stars

Context. Tens of thousands of red giant stars in the Kepler data exhibit solar-like oscillations. The mixed-mode characteristics of their oscillations enable us to study the internal physics from the core to the surface, such as differential rotation. However, envelope rotation rates have only been measured for about a dozen red giant branch (RGB) stars so far. This limited the theoretical interpretation of angular momentum transport in post-main sequence phases. Aims. We report the measurements of g-mode properties and differential rotation in the largest sample of Kepler RGB stars. Methods. We applied a new approach to calculate the asymptotic frequencies of mixed modes, which accounts for so-called near-degeneracy effects (NDEs) and leads to improved measurements of envelope rotation rates. By fitting these asymptotic expressions to the observations, we obtained measurements of the properties of g modes (period spacing, ΔΠ1, coupling factor, q, g-mode offset term, εg, small separation, δν01) and the internal rotation (mean core, Ωcore, and envelope, Ωenv, rotation rates). Results. Among 2495 stars with clear mixed-mode patterns, we found that 800 show doublets and 1206 show triplets, while the remaining stars do not show any rotational splittings. We measured core rotation rates for 2006 red giants, doubling the size of pre-existing catalogues. This led us to discover an over-density of stars that are narrowly distributed around a well-defined ridge in the plane, showing core rotation rate versus evolution along the RGB. These stars could experience a different angular momentum transport compared to other red giants. With this work, we also increased the sample of stars with measured envelope rotation rates by two orders of magnitude. We found a decreasing trend between envelope rotation rates and evolution, implying that the envelopes slow down with expansion, as expected. We found 243 stars whose envelope rotation rates are significantly larger than zero. For these stars, the core-to-envelope rotation ratios are around Ωcore/Ωenv ∼ 20 and show a large spread with evolution. Several stars show extremely mild differential rotations, with core-to-surface ratios between 1 and 2. These stars also have very slow core rotation rates, suggesting that they go through a peculiar rotational evolution. We also discovered more stars located below the ΔΠ1–Δν degeneracy sequence, which presents an opportunity to study the history of plausible stellar mergers.

Measurement of Solar Differential Rotation by Absolutely Calibrated Iodine-Cell Spectroscopy

Measurement of Solar Differential Rotation by Absolutely Calibrated Iodine-Cell Spectroscopy

The Sun’s Large-Scale Flows I: Measurements of Differential Rotation & Torsional Oscillation

We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.

Single-shot vector magnetic measurements using synchronous coherent population trapping resonance in a feedback compensation system

We demonstrate a real-time, single-shot vector magnetic measurement technique using synchronous coherent population trapping (SCPT) in an apparatus consisting of a small rubidium vapor cell. Vector modality of our magnetometer is enabled by designing a feedback system based on performing a peak-lock on a particularly strong 2ΩL magnetic resonance produced in the SCPT spectrum and compensating the external magnetic field via a three-axis field coil. With its current design, this magnetometer exhibits high sensitivities of approximately 155, 129, and 57pT/Hz in measuring the magnetic field vector components along the (x,y,z) axes. Sensitivities closer to the shot-noise limit can be achieved in the future by reducing the technical noise of our equipment and by employing a differential detection and polarization rotation measurement scheme in our system.

Determining the spin wave exchange constant of ferromagnets using canted high-order exchange magnons

We propose an alternative method for obtaining the spin wave exchange constant of a ferromagnetic material. This involves generating and detecting canted high-order magnons in Co films using a time-resolved magneto-optical Kerr effect instrument, which enables the extraction of the spin wave exchange constant in a single film thickness in a reliable manner. To enhance the sensitivity of high-order magnon detection, we perform simultaneous measurements of differential Kerr rotation and ellipticity on both sides of the film. This method will be particularly useful in practical situations where the magnetic properties of a material vary with thickness or where it is not feasible to produce films of the same quality.

10 Years of Stellar Activity for GJ 1243

Abstract The flaring M4 dwarf GJ 1243 has become a benchmark for studying stellar flare and starspot activity thanks to the exceptional photometric monitoring archive from the Kepler mission. New light curves from the Transiting Exoplanet Survey Satellite (TESS) mission for this star allow precise stellar activity characterization over more than a decade timescale. We have carried out the first flare and starspot analysis of GJ 1243 from over 50 days of data from TESS Sectors 14 and 15. Using 133 flare events detected in the 2 minute cadence TESS data, we compare the cumulative flare frequency distributions, and find the flare activity for GJ 1243 is unchanged between the Kepler and TESS epochs. Two distinct starspot groups are found in the TESS data, with the primary spot having the same rotational period and phase as seen in Kepler. The phase of the secondary spot feature is consistent with the predicted location of the secondary starspot and measurement of weak differential rotation, suggesting this secondary spot may be long-lived and stable in both latitude and longitude. As expected for this highly active star, the constant spot and flare activity reveal no sign of solar-like activity cycles over 10 yr. However, we highlight the unique ability for Kepler and TESS to use flare rates to detect activity cycles.

New Suns in the Cosmos. V. Stellar Rotation and Multifractality in Active Kepler Stars

Abstract In the present study, high-precision time series photometry for the active Kepler stars is described in the language of multifractals. We explore the potential of using the rescaled-range analysis (R/S) and multifractal detrended moving average analysis methods to characterize the multiscale structure of the observed time series from a sample of ∼40,000 active stars. Among these stars, 6486 have surface differential rotation measurement, whereas 1846 have no signature of differential rotation. As a result, the Hurst exponent (H) derived from both methods shows a strong correlation with the period derived from rotational modulation. In addition, the variability range R var reveals how this correlation follows a high activity “line.” We also verify that the H-index is an able parameter for distinguishing the different signs of stellar rotation that can exist between the stars with and without differential rotation. In summary, the results indicate that the Hurst exponent is a promising index for estimating photometric magnetic activity.

The Measurement of Solar Differential Rotation from Proper Motion of Individual Sunspots

The differential rotation is the result of the interaction between rotation and convection and causes dynamo circulation that affect the cycle of solar activity. Tracer method using features in the photosphere such as sunspot is a simple method to measure the differential rotation. In this study, 98 individual sunspots on January 8 - 22, 2013 and August 25 - September 7, 2013 were used to measure the differential rotation of the Sun. The Sun’s continuum images were obtained from HMI (Helioseismic Magnetic Imager) instrument at SDO (Solar Dynamic Observatory). Coordinate and area of sunspot were measured using ImageJ software and converted to Carrington coordinates. From the measurement, we derived the differential rotation equation, the relation of velocity and area of sunspot, and the relation of sunspot’s velocity and Zurich classification. The differential rotation equation obtained in this study is ω (B) = (14.376 ± 0.04) + (0.6 ± 0.38) sin2B (°/day). For the relation between velocity and area of sunspot, we got the sidereal rotation rate of sunspots with area < 100 pixels2 is about 0.8% higher than sunspots with area > 100 pixels2.

Latitudinal differential rotation in the solar analogues 16 Cygni A and B

Context.Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT andKeplerspace missions. The latter is now yielding the first measurements of latitudinal differential rotation obtained directly from oscillation frequencies. Differential rotation is a fundamental mechanism of the stellar dynamo effect.Aims.Our goal is to measure the amount of differential rotation in the solar analogues 16 Cyg A and B, which are the components of a binary system. These stars are the brightest observed byKeplerand have therefore been extensively observed, with exquisite precision on their oscillation frequencies.Methods.We modelled the acoustic power spectrum of 16 Cyg A and B using a model that takes into account the contribution of differential rotation to the rotational frequency splitting. The estimation was carried out in a Bayesian setting. We then inverted these results to obtain the rotation profile of both stars under the assumption of a solar-like functional form.Results.We observe that the magnitude of latitudinal differential rotation has a strong chance of being solar-like for both stars, their rotation rates being higher at the equator than at the pole. The measured latitudinal differential rotation, defined as the difference of rotation rate between the equator and the pole, is 320 ± 269 nHz and 440−383+363nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are 535 ± 75 nHz and 565−129+150nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry.Conclusions.We present the first conclusive measurement of latitudinal differential rotation for solar analogues. Their rotational profiles are very close to those of the Sun. These results depend weakly on the uncertainties of the stellar parameters.

Differential rotation of Kepler-71 via transit photometry mapping of faculae and starspots

Knowledge of dynamo evolution in solar-type stars is limited by the difficulty of using active region monitoring to measure stellar differential rotation, a key probe of stellar dynamo physics. This paper addresses the problem by presenting the first ever measurement of stellar differential rotation for a main-sequence solar-type star using starspots and faculae to provide complementary information. Our analysis uses modelling of light curves of multiple exoplanet transits for the young solar-type star Kepler-71, utilizing archival data from the Kepler mission. We estimate the physical characteristics of starspots and faculae on Kepler-71 from the characteristic amplitude variations they produce in the transit light curves and measure differential rotation from derived longitudes. Despite the higher contrast of faculae than those in the Sun, the bright features on Kepler-71 have similar properties such as increasing contrast towards the limb and larger sizes than sunspots. Adopting a solar-type differential rotation profile (faster rotation at the equator than the poles), the results from both starspot and facula analysis indicate a rotational shear less than about 0.005 rad d-1, or a relative differential rotation less than 2 per cent, and hence almost rigid rotation. This rotational shear contrasts with the strong rotational shear of zero-age main-sequence stars and the modest but significant shear of the modern-day Sun. Various explanations for the likely rigid rotation are considered.

Surprisingly different star-spot distributions on the near equal-mass equal-rotation-rate stars in the M dwarf binary GJ 65 AB

We aim to understand how stellar parameters such as mass and rotation impact the distribution of starspots on the stellar surface. To this purpose, we have used Doppler imaging to reconstruct the surface brightness distributions of three fully convective M dwarfs with similar rotation rates. We secured high cadence spectral time series observations of the 5.5 AU separation binary GJ 65, comprising GJ 65A (M5.5V, Prot = 0.24 d) and GJ 65B (M6V, Prot = 0.23 d). We also present new observations of GJ 791.2A (M4.5V, Prot = 0.31 d). Observations of each star were made on two nights with UVES, covering a wavelength range from 0.64 - 1.03 microns. The time series spectra reveal multiple line distortions, which we interpret as cool starspots and which are persistent on both nights suggesting stability on the timescale of 3 days. Spots are recovered with resolutions down to 8.3 degs at the equator. The global spot distributions for GJ 791.2A are similar to observations made a year earlier. Similar high latitude and circumpolar spot structure is seen on GJ791.2A and GJ 65A. However, they are surprisingly absent on GJ 65B, which instead reveals more extensive, larger, spots concentrated at intermediate latitudes. All three stars show small amplitude latitude-dependent rotation that is consistent with solid body rotation. We compare our measurements of differential rotation with previous Doppler imaging studies and discuss the results in the wider context of other observational estimates and recent theoretical predictions.

Variations in the Solar Coronal Rotation with Altitude – Revisited

Here we report in depth reanalysis of a paper by Vats et al. (2001) [Astrophys. J. 548, L87] based on the measurements of differential rotation with altitude as a function of observing frequencies (as lower and higher frequencies indicate higher and lower heights, respectively) in the solar corona. The radial differential rotation of the solar corona is estimated from daily measurements of the disc-integrated solar radio flux at 11 frequencies: (275, 405, 670, 810, 925, 1080, 1215, 1350, 1620, 1755 MHz and 2800 MHz). We use the same data as were used in Vats et al. (2001), but instead of the 12th maxima of autocorrelograms used there, we use the 1st secondary maxima to derive the synodic rotation period. We estimate synodic rotation by Gaussian fit of the 1st secondary maxima. Vats et al. (2001) reported that the sidereal rotation period increases with increasing frequency. The variation found by them was from 23.6 to 24.15 days in this frequency range with a difference of only 0.55 days. The present study finds that sidereal rotation period increases with decreasing frequency. The variation range is from 24.4 to 22.5 days and difference is about three times larger (1.9 days). However, at 925 MHz both studies give similar rotation period. In Vats et al. (2001) the Pearson factor with trend line was 0.86 whereas present analysis obtained a ~ 0.97 Pearson factor with the trend line. Our study shows that the solar corona rotates slower at higher altitudes, which is in contradiction to the findings reported in Vats et al. (2001). Key words: Solar radio flux- flux modulation method- Gaussian fit- sidereal rotation period.

Measurements of Solar Differential Rotation and Meridional Circulation from Tracking of Photospheric Magnetic Features

Abstract Long-lived rotational and meridional flows are important ingredients of the solar cycle. Magnetic field images have typically been used to measure these flows on the solar surface by cross-correlating thin longitudinal strips or square patches across sufficiently long time gaps. Here, I use 1 month of SDO/HMI line-of-sight magnetic field observations, combined with the Southwest Automatic Magnetic Identification Suite magnetic feature-tracking code to measure the motion of individual features in these magnetograms. By controlling for perturbations due to short-lived flows and due to false motions from feature interactions, I effectively isolate the long-lived flows traced by the magnetic features. This allows me to produce high-resolution (2° bins) differential rotation measurements with well-characterized variances and covariances of the fit parameters. I find a sidereal rotational profile of (14.296 ± 0.006) + (−1.847 ± 0.056)sin2 b + (−2.615 ± 0.093) sin4 b, with units of deg day−1, and a large covariance σ BC 2 = −4.87 × 10−3(deg day−1)2. I also produce measurements of the much weaker meridional flow that are broadly consistent with previous results. These measurements exhibit a peak flow of 16.7 ± 0.6 m s−1 at latitude b = 45° but are insufficiently characterized at higher latitudes to ascertain whether the chosen functional form is appropriate. This work demonstrates that measuring the motions of individual features in photospheric magnetograms can produce high-precision results in relatively short time spans, and suggests that high-resolution non-longitudinally averaged photospheric velocity residual measurements could be produced to compare with coronal results and to provide other diagnostics of the solar dynamo.

Data compression for local correlation tracking of solar granulation

Context. Several upcoming and proposed space missions, such as Solar Orbiter, will be limited in telemetry and thus require data compression. Aims. We test the impact of data compression on local correlation tracking (LCT) of time-series of continuum intensity images. We evaluate the effect of several lossy compression methods (quantization, JPEG compression, and a reduced number of continuum images) on measurements of solar differential rotation with LCT. Methods. We apply the different compression methods to tracked and remapped continuum intensity maps obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We derive 2D vector velocities using the local correlation tracking code FLCT and determine the additional bias and noise introduced by compression to differential rotation. Results. We find that probing differential rotation with LCT is very robust to lossy data compression when using quantization. Our results are severely affected by systematic errors of the LCT method and the HMI instrument. The sensitivity of LCT to systematic errors is a concern for Solar Orbiter.

ON THE DIFFERENTIAL ROTATION OF MASSIVE MAIN-SEQUENCE STARS

To date, asteroseismology has provided core to surface differential rotation measurements in eight main-sequence stars. These stars, ranging in mass from $\sim$1.5-9$M_\odot$, show rotation profiles ranging from uniform to counter-rotation. Although they have a variety of masses, these stars all have convective cores and overlying radiative regions, conducive to angular momentum transport by internal gravity waves (IGW). Using two-dimensional (2D) numerical simulations we show that angular momentum transport by IGW can explain all of these rotation profiles. We further predict that should high mass, faster rotating stars be observed, the core to envelope differential rotation will be positive, but less than one.

SUN-LIKE MAGNETIC CYCLES IN THE RAPIDLY ROTATING YOUNG SOLAR ANALOG HD 30495

A growing body of evidence suggests that multiple dynamo mechanisms can drive magnetic variability on different timescales, not only in the Sun but also in other stars. Many solar activity proxies exhibit a quasi-biennial ($\sim$2 year) variation, which is superimposed upon the dominant 11 year cycle. A well-characterized stellar sample suggests at least two different relationships between rotation period and cycle period, with some stars exhibiting long and short cycles simultaneously. Within this sample, the solar cycle periods are typical of a more rapidly rotating star, implying that the Sun might be in a transitional state or that it has an unusual evolutionary history. In this work, we present new and archival observations of dual magnetic cycles in the young solar analog HD 30495, an $\sim$1 Gyr-old G1.5V star with a rotation period near 11 days. This star falls squarely on the relationships established by the broader stellar sample, with short-period variations at $\sim$1.7 years and a long cycle of $\sim$12 years. We measure three individual long-period cycles and find durations ranging from 9.6-15.5 years. We find the short-term variability to be intermittent, but present throughout the majority of the time series, though its occurrence and amplitude are uncorrelated with the longer cycle. These essentially solar-like variations occur in a Sun-like star with more rapid rotation, though surface differential rotation measurements leave open the possibility of a solar equivalence.

Starspots on Young Solar-Type Stars

AbstractDoppler Imaging of starspots on young solar analogues is a way to investigate the early history of solar magnetic activity by proxy. Doppler images of young G-dwarfs have yielded the presence of large polar spots, extending to moderate latitudes, along with measurements of the surface differential rotation. The differential rotation measurement for one star (RX J0850.1-7554) suggests it is possibly the first example of a young G-type dwarf whose surface rotates as almost a solid body, in marked contrast to the differential rotation of other rapidly rotating young G-dwarfs and the present-day Sun. Overall, our Doppler imaging results show that the young Sun possessed a fundamentally different dynamo to today.

Stellar differential rotation in theory and observation

AbstractStellar differential rotation is intimately related to the stellar magnetic dynamo and, thus, to stellar activity. In recent years, significant progress in the measurement of differential rotation on the basis of Doppler imaging techniques and the availability of space‐based long‐term photometry has been achieved. Similarly, simulations incorporate ever more details of the complexity of convective zones. While some aspects of solar and stellar differential rotation can be explained now, several important questions remain open or controversial. In this splinter session, we discussed the latest observational and theoretical progress in the field of differential rotation. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Helioseismic measurements of differential rotation and meridional flow

AbstractSolar interior differential rotation and meridional flow play important roles in dynamo models. In this review, I briefly review results in interior rotational profiles and zonal flows obtained from helioseismology studies. Due to the new developments in recent years in interior meridional flow studies, this review focuses more on results on meridional flow. I describe new developments in the shallower poleward meridional flow, and the temporal evolution of these flows. Then I introduce a newly identified center-to-limb variation effect in helioseismology studies, and present recent results in the search of equatorward meridional flows. I also discuss how these results will effect the dynamo models.

New measurements of rotation and differential rotation in A-F stars: are there two populations of differentially rotating stars?

We present projected rotational velocities and new measurements of the rotational profile of some 180 nearby stars with spectral types A-F. The overall broadening profile is derived analysing spectral line shape from hundreds of spectral lines by the method of least-squares deconvolution. Rigid and differential rotation can be distinguished in 56 cases. Ten stars with significant differential rotation rates are identified. As of now, 33 differential rotators detected by line profile analysis have been confirmed. The frequency of differential rotators decreases towards high effective temperature and rapid rotation. There is evidence for two populations of differential rotators with a gap in between at spectral type early-F. The gap can only partly be explained by an upper bound found for the horizontal shear of F stars. Apparently, the physical conditions of differential rotation change at early-F spectral types.