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Register a new userAnti-solar differential rotation on the active sub-giant HU Virginis
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Measuring surface differential rotation (DR) on different types of stars is important when characterizing the underlying stellar dynamo. It has been suggested that anti-solar DR laws can occur when strong meridional flows exist. We aim to investigate the differential surface rotation on the primary star of the RS CVn binary HU Vir by tracking its starspot distribution as a function of time. We also aim to recompute and update the values for several system parameters of the triple system HU Vir (close and wide orbits). Time-series high-resolution spectroscopy for four continuous months was obtained with the 1.2-m robotic STELLA telescope. Nine consecutive Doppler images were reconstructed from these data, using our line-profile inversion code iMap. An image cross-correlation method was applied to derive the surface differential-rotation law for HU Vir. New orbital elements for the close and the wide orbits were computed using our new STELLA radial velocities (RVs) combined with the RV data available in the literature. Photometric observations were performed with the Amadeus Automatic Photoelectric Telescope (APT), providing contemporaneous Johnson-Cousins $V$ and $I$ data for approximately 20 years. This data was used to determine the stellar rotation period and the active longitudes. We confirm anti-solar DR with a surface shear parameter $alpha$ of -0.029 $pm$ 0.005 and -0.026 $pm$ 0.009, using single-term and double-term differential rotation laws, respectively. The best fit is achieved assuming a solar-like double-term law with a lap time of $approx$ 400 d. Our orbital solutions result in a period of 10.387678 $pm$ 0.000003 days for the close orbit and 2726 $pm$ 7 d ($approx$ 7.5 yr) for the wide orbit. A Lomb-Scarge (L-S) periodogram of the pre-whitened $V$-band data reveals a strong single peak providing a rotation period of 10.391 $pm$ 0.008 d.
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We demonstrate the power of the local correlation tracking technique on stellar data for the first time. We recover the spot migration pattern of the long-period RS CVn-type binary $sigma$ Gem from a set of six Doppler images from 3.6 consecutive rotation cycles. The resulting surface flow map suggests a weak anti-solar differential rotation with $alphaapprox-0.0022pm0.0016$, and a coherent poleward spot migration with an average velocity of $220pm10$ m s$^{-1}$. This result agrees with our recent findings from another study and could also be confirmed theoretically.
We re-investigate UZ Librae spectra obtained at KPNO in 1998 and 2000. From the 1998 data we compose 11 consecutive Doppler images using the Ca I-6439, Fe I-6393 and Fe I-6411 lines. Applying the method of average cross-correlation of contiguous Doppler images we find anti-solar differential rotation with a surface shear of alpha ~ -0.03. The pilot application of the local correlation tracking technique for the same data qualitatively confirms this result and indicates complex flow pattern on the stellar surface. From the cross-correlation of the two available Doppler images in 2000 we also get anti-solar differential rotation but with a much weaker shear of alpha ~ -0.004.
Solar-cycle related variation of differential rotation is investigated through analyzing the rotation rates of magnetic fields, distributed along latitudes and varying with time at the time interval of August 1976 to April 2008. More pronounced differentiation of rotation rates is found to appear at the ascending part of a Schwabe cycle than at the descending part on an average. The coefficient $B$ in the standard form of differential rotation, which represents the latitudinal gradient of rotation, may be divided into three parts within a Schwabe cycle. Part one spans from the start to the $4^{th}$ year of a Schwabe cycle, within which the absolute $B$ is approximately a constant or slightly fluctuates. Part two spans from the $4^{th}$ to the $7^{th}$ year, within which the absolute $B$ decreases. Part three spans from the $7^{th}$ year to the end, within which the absolute $B$ increases. Strong magnetic fields repress differentiation of rotation rates, so that rotation rates show less pronounced differentiation, but weak magnetic fields seem to just reflect differentiation of rotation rates. The solar-cycle related variation of solar differential rotation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation of rotation rates.
The latitudinal distributions of the yearly mean rotation rates measured respectively by Suzuki in 1998 and 2012 and Pulkkinen $&$ Tuominen in 1998 are utilized to investigate internal-cycle variation of solar differential rotation. The rotation rate at the solar Equator seems to decrease since cycle 10 onwards. The coefficient $B$ of solar differential rotation, which represents the latitudinal gradient of rotation, is found smaller in the several years after the minimum of a solar cycle than in the several years after the maximum time of the cycle, and it peaks several years after the maximum time of the solar cycle. The internal-cycle variation of the solar rotation rates looks similar in profile to that of the coefficient $B$. A new explanation is proposed to address such a solar-cycle related variation of the solar rotation rates. Weak magnetic fields may more effectively reflect differentiation at low latitudes with high rotation rates than at high latitudes with low rotation rates, and strong magnetic fields may more effectively repress differentiation at relatively low latitudes than at high latitudes. The internal-cycle variation is inferred to the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity to differentiation.
We present a simple diagnostic that can be used to constrain the location of the differential rotation in red giants with measured mixed mode rotational splittings. Specifically, in red giants with radii $sim 4R_odot$, the splittings of p-dominated modes (sound wave dominated) relative to those of g-dominated modes (internal gravity wave dominated) are sensitive to how much of the differential rotation resides in the outer convection zone versus the radiative interior of the red giant. An independently measured surface rotation rate significantly aids breaking degeneracies in interpreting the measured splittings. We apply our results to existing observations of red giants, particularly those of Kepler-56, and find that most of the differential rotation resides in the radiative region rather than in the convection zone. This conclusion is consistent with results in the literature from rotational
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