From CoRoT 102899501 to the Sun
P. GondoinD. GandolfiM. FridlundA. FrascaE. W. GuentherA. P. HatzesH. J. DeegH. ParviainenPhilipp EigmüllerM. Deleuil
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Using a model based on the rotational modulation of the visibility of active regions, we analyse the high-accuracy CoRoT lightcurve of the active young star CoRoT102899501. Spectroscopic follow-up observations are used to derive its fundamental parameters. We compare its chromospheric activity level with a model of chrosmospheric activity evolution established by combining relationships between the R'HK index and the Rossby number with a recent model of stellar rotation evolution on the main sequence. We measure the spot coverage of the stellar surface as a function of time, and find evidence for a tentative increase from 5-14% at the beginning of the observing run to 13-29% 35 days later. A high level of magnetic activity on CoRoT102899501 is corroborated by a strong emission in the Balmer and Ca II HK lines (logR'HK ~ -4). The starspots used as tracers of the star rotation constrain the rotation period to 1.625+/-0.002 days and do not show evidence for differential rotation. The effective temperature (Teff=5180+/-80 K), surface gravity (logg=4.35+/-0.1), and metallicity ([M/H]=0.05+/-0.07 dex) indicate that the object is located near the evolutionary track of a 1.09+/-0.12 M_Sun pre-main sequence star at an age of 23+/-10 Myrs. This value is consistent with the "gyro-age" of about 8-25 Myrs, inferred using a parameterization of the stellar rotation period as a function of colour index and time established for the I-sequence of stars in stellar clusters. We conclude that the high magnetic activity level and fast rotation of CoRoT102899501 are manifestations of its stellar youth consistent with its estimated evolutionary status and with the detection of a strong Li I 6707.8 A absorption line in its spectrum. We argue that a magnetic activity level comparable to that observed on CoRoT102899501 could have been present on the Sun at the time of planet formation.Keywords:
Starspot
Rotation period
Stellar rotation
Effective temperature
Surface gravity
Rossby number
Balmer series
Abstract Temperature contrasts and magnetic field strengths of sunspot umbrae broadly follow the thermal-magnetic relationship obtained from magnetohydrostatic equilibrium. Using a compilation of recent observations, especially in molecular bands, of temperature contrasts of starspots in cool stars, and a grid of Kurucz stellar model atmospheres constructed to cover layers of sub-surface convection zone, we examine how the above relationship scales with effective temperature ( T eff ), surface gravity g and the associated changes in opacity of stellar photospheric gas. We calculate expected field strengths in starpots and find that a given relative reduction in temperatures (or the same darkness contrasts) yield increasing field strengths against decreasing T eff due to a combination of pressure and opacity variations against T eff .
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Abstract We use Doppler imaging techniques to determine the dependence of starspot rotation rates on latitude in an homogeneous sample of young, rapidly rotating solar analogues. A solar-like differential rotation law is used, where the rotation depends on sin2θ, where θ is the stellar latitude. By including this term in the image reconstruction process, using starspots as tracers, we are able to determine the magnitude of the shear over more than one rotation cycle. We also consider results from matched filter starspot tracking techniques, where individual starspot rotation rates are determined. In addition we have re-analysed published results and present a new measurement for the K3 dwarf Speedy Mic. A total of 10 stars of spectral type G2—M2 are considered. We find a trend towards decreasing surface differential rotation with decreasing effective temperature. The implied approach to solid body rotation with increasing relative convection zone depth implies that the dynamo mechanism operating in low-mass stars may be substantially different from that in the Sun.
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Differential rotation is a key ingredient in theories of stellar magnetic field generation. The solar surface differential rotation was initially discovered via the simple method of tracking the rotation rates of individual starspots at different latitudes. Today, the same technique can be applied to rapidly rotating stars, using sequences of Doppler images spanning several stellar rotations. Early results suggest that solar-like differential rotation patterns prevail on rapidly rotating dwarf stars, but much remains to be done in tracing global flow patterns on pre-main sequence stars, giants, and tidally-locked binary components. I outline the relative merits of the three main methods that have so far been used to track the latitude dependence of starspot rotation rates, and discuss the validity of the physical assumptions that underpin them.
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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.
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Using high-precision photometry from the \textit{Kepler} mission, we investigate patterns of spot activity on the K1-type subgiant component of KIC 11560447, a short-period late-type eclipsing binary. We tested the validity of maximum entropy reconstructions of starspots by numerical simulations. Our procedure successfully captures up to three large spot clusters migrating in longitude. We suggest a way to measure a lower limit for stellar differential rotation, using slopes of spot patterns in the reconstructed time-longitude diagram. We find solar-like differential rotation and recurrent spot activity with a long-term trend towards a dominant axisymmetric spot distribution during the period of observations.
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In the first part of this work, the empirical correlation of stellar surface brightness FV with (Ic — K) broad-band colour is investigated by using a sample of stars cooler than the Sun. A bilinear correlation is found to represent well the brightness of G, K and M giant stars. The change in slope occurs at (Ic — K)∼2.1 or at about the transition from K to M spectral types. The same relationship is also investigated for dwarf stars and found to be distinctly different from that of the giants. The dwarf star correlation differs by an average of −0.4 in (Ic-K) or by a maximum in Fv of ∼−0.1, positioning it below that of the giants, with both trends tending towards convergence for the hotter stars in our sample. The flux distribution derived from the Fv — (Ic — K) relationship for the giant stars, together with that derived from an FV — (V — K) relationship and the blackbody flux distribution, is then utilized to compute synthetic light V and colour (V — R)c, (V — I)c and (V — K) curves of cool spotted stars. We investigate the effects on the amplitudes of the curves by using these FV -colour relations and by assuming the effective gravity of the spots to be lower than the gravity of the unspotted photosphere. We find that the amplitudes produced by using the FV — (Ic — K) relationship are larger than those produced by the other two brightness correlations, meaning smaller and/or warmer spots.
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Quasi-periodic modulations of the stellar light curve may result from dark spots crossing the visible stellar disc. Due to differential rotation, spots at different latitudes generally have different rotation periods. Hence, by studying spot-induced modulations, one can learn about stellar surface (differential) rotation and magnetic activity. Recently, Reinhold & Arlt (2015) proposed a method based on the Lomb-Scargle periodogram of light curves to identify the sign of the differential rotation at the stellar surface. Our goal is to understand how the modulation of the stellar light curve due to the presence of spots and the corresponding periodogram are affected by both the stellar and spot properties. We generate synthetic light curves of stars with different properties (inclination angle, limb darkening, and rotation rate) and spot configurations (number of spots, latitude, intensity contrast, and size). By analysing their Lomb-Scargle periodograms, we compute the ratio between the heights of the second and first harmonics of the rotation period (peak-height-ratio). We find that the peak-height ratios are essentially a function of a single parameter, the fraction of time the spot is visible, which is related to the sinusoidality of the spot modulation. We identify the conditions under which the periodogram analysis can actually provide an estimate of the spot latitudes and/or the stellar inclination angle. We also identify possible sources of error in the identification of the sign of the differential rotation.
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Stellar rotation is crucial for studying stellar evolution since it provides information about age, angular momentum transfer, and magnetic fields of stars. In the case of the Sun, due to its proximity, detailed observation of sunspots at various latitudes and longitudes allows the precise estimate of the solar rotation period and its differential rotation. Here, we present for the first time an analysis of stellar differential rotation using starspot transit mapping as a means of detecting differential shear in solar-type and M stars. The aim of this study is to investigate the relationship between rotational shear, $\Delta\Omega$, with both the star's effective temperature ($T_{\text{eff}}$) and average rotation period ($P_{\text{r}}$). We present differential rotation profiles derived from previously collected spot transit mapping data for 13 slowly rotating stars ($P_{\text{rot}} \geq 4.5$ days), with spectral types ranging from M to F, which were observed by the Kepler and CoRoT satellites. Our findings reveal a significant negative correlation between rotational shear and the mean period of stellar rotation (correlation coefficient of -0.77), which may be an indicator of stellar age. On the other hand, a weak correlation was observed between differential rotation and the effective temperature of the stars. Overall, the study provides valuable insights into the complex relationship between stellar parameters and differential rotation, which may enhance our understanding of stellar evolution and magnetic dynamos.
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We present the results of numerical experiments to assess degeneracies in lightcurve models of starspots. Using synthetic lightcurves generated with the Cheetah starspot modeling code, we explore the extent to which photometric light curves constrain spot model parameters, including spot latitudes and stellar inclination. We also investigate the effects of spot parameters and differential rotation on one's ability to correctly recover rotation periods and differential rotation in the Kepler lightcurves. We confirm that in the absence of additional constraints on the stellar inclination, such as spectroscopic measurements of vsini or occultations of starspots by planetary transits, the spot latitude and stellar inclination are difficult to determine uniquely from the photometry alone. We find that for models with no differential rotation, spots that appear on opposite hemispheres of the star may cause one to interpret the rotation period to be half of the true period. When differential rotation is included, the changing longitude separation between spots breaks the symmetry of the hemispheres and the correct rotation period is more likely to be found. The dominant period found via periodogram analysis is typically that of the largest spot. Even when multiple spots with periods representative of the star's differential rotation exist, if one spot dominates the lightcurve the signal of differential rotation may not be detectable from the periodogram alone. Starspot modeling is applicable to stars with a wider range of rotation rates than other surface imaging techniques (such as Doppler imaging), allows subtle signatures of differential rotation to be measured, and may provide valuable information on the distribution of stellar spots. However, given the inherent degeneracies and uncertainty present in starspot models, caution should be exercised in their interpretation.
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