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Register a new userMagnetic activity cycles in solar-like stars: The cross-correlation technique of p-mode frequency shifts
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Aims. We aim studying the use of cross-correlation techniques to infer the frequency shifts induced by changing magnetic fields in the p-mode frequencies and provide precise estimation of the error bars. Methods. This technique and the calculation of the associated errors is first tested and validated on the Sun where the p-mode magnetic behaviour is very well known. These validation tests are performed on 6000-day time series of Sun-as-a-star observations delivered by the SoHO spacecraft. Errors of the frequency shifts are quantified through Monte Carlo simulations. The same methodology is then applied to three solar-like oscillating stars: HD 49933, observed by CoRoT, as well as KIC 3733735 and KIC 7940546 observed by Kepler. Results. We first demonstrate the reliability of the error bars computed with the Monte Carlo simulations using the Sun. From the three analyzed stars we confirm the presence of a magnetic activity cycle with this methodology in HD 49933 and we unveil seismic signature of on going magnetic variations in KIC 3733735. Finally, the third star, KIC 7940546, seems to be in a quiet regime.
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The variations of the frequencies of the low-degree acoustic oscillations in the Sun induced by magnetic activity show a dependence with radial order. The frequency shifts are observed to increase towards higher-order modes to reach a maximum of about 0.8 muHz over the 11-yr solar cycle. A comparable frequency dependence is also measured in two other main-sequence solar-like stars, the F-star HD49933, and the young 1-Gyr-old solar analog KIC10644253, although with different amplitudes of the shifts of about 2 muHz and 0.5 muHz respectively. Our objective here is to extend this analysis to stars with different masses, metallicities, and evolutionary stages. From an initial set of 87 Kepler solar-like oscillating stars with already known individual p-mode frequencies, we identify five stars showing frequency shifts that can be considered reliable using selection criteria based on Monte Carlo simulations and on the photospheric magnetic activity proxy Sph. The frequency dependence of the frequency shifts of four of these stars could be measured for the l=0 and l=1 modes individually. Given the quality of the data, the results could indicate that a different physical source of perturbation than in the Sun is dominating in this sample of solar-like stars.
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.
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 correlation coefficients of the linear regression of six solar indices versus F10,7 were analyzed in solar cycles 21, 22 and 23. We also analyzed the interconnection between these indices and F10,7 with help of the approximation by the polynomials of second order. The indices weve studied in this paper are: Wolf numbers - W, 530,3 nm coronal line flux - F530, the total solar irradiance - TSI, Mg II UV-index 280 nm core-to-wing ratio, Flare Index - FI and Counts of flares. In the most cases the regressions of these solar indices versus F10,7 are close to linear except the moments of time near to the minimums and maximums of 11-year activity. For the linear regressions we found that the values of correlation coefficients Kcorr(t) for the indices versus F10,7 and W show the cyclic variations with periods approximately equal to the to half length of 11-year cycle - 5,5 years approximately.
The atmospheric activity of the Sun and solar-type stars is analysed involving observations from HK-project at the Mount Wilson Observatory, the California and Carnegie Planet Search Program at the Keck and Lick Observatories, and the Magellan Planet Search Program at the Las Campanas Observatory. We show that for stars of F, G and K spectral classes, the cyclic activity, similar to the 11-yr Solar cycles, is different: it becomes more prominent in K-stars. Comparative study of solar-type stars with different levels of the chromospheric and coronal activity confirms that the Sun belongs to stars with the low level of the chromospheric activity and stands apart among these stars by the minimum level of the coronal radiation and minimum flux variations of the photospheric radiation.
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