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Register a new userActivity time series of old stars from late F to early K. IV. Limits of the correction of radial velocities using chromospheric emission
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Inhibition of the convective blueshift in active regions is a major contribution to the radial velocity variations, at least for solar-like stars. A common technique to correct for this component is to model the RV as a linear function of chromospheric emission, because both are strongly correlated with the coverage by plages. This correction is not perfect: the aim of the present study is to understand the limits of this correction and to improve it. We investigate these questions by analysing a large set of synthetic time series corresponding to old main sequence F6-K4 stars modelled using a consistent set of parameters. We focus here on the analysis of the correlation between time series, in particular between RV and chromospheric emission on different timescales. We also study the temporal variation for each time series. Inclination strongly impacts these correlations, as well as additional signals (granulation and supergranulation). Although RV and LogRHK are often well correlated, a combination of geometrical effects (butterfly diagrams related to dynamo processes and inclination) and activity level variations over time create an hysteresis pattern during the cycle, which produces a departure from an excellent correlation: for a given activity level, the RV is higher or lower during the ascending phase compared to the descending phase of the cycle depending on inclination, with a reversal for inclinations about 60 deg from pole-on. This hysteresis is also observed for the Sun and other stars. This property is due to the spatio-temporal distribution of the activity pattern and to the difference in projection effects of the RV and chromospheric emission. These results allow us to propose a new method which significantly improves the correction for long timescales, and could be crucial to improving detection rates of planets in the habitable zone around F6-K4 stars.
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Solar simulations and observations show that the detection of long-period Earth-like planets is expected to be very difficult with radial velocity techniques in the solar case because of activity. The inhibition of the convective blueshift in active regions (which is then dominating the signal) is expected to decrease toward lower mass stars, which would provide more suitable conditions. In this paper we build synthetic time series to be able to precisely estimate the effects of activity on exoplanet detectability for stars with a wide range of spectral type (F6-K4) and activity levels (old main-sequence stars). We simulated a very large number of realistic time series of radial velocity, chromospheric emission, photometry, and astrometry. We built a coherent grid of stellar parameters that covers a wide range in the (B-V, LogRHK) space based on our current knowledge of stellar activity, to be able to produce these time series. We describe the model and assumptions in detail. We present first results on chromospheric emission. We find the average LogRHK to correspond well to the target values that are expected from the model, and observe a strong effect of inclination on the average LogRHK (over time) and its long-term amplitude. This very large set of synthetic time series offers many possibilities for future analysis, for example, for the parameter effect, correction method, and detection limits of exoplanets.
High-precision time series have recently become available for many stars as a result of data from CoRoT, Kepler, and TESS and have been widely used to study stellar activity. They provide information integrated over the stellar disk, hence many degeneracies between spots and plages or sizes and contrasts. Our aim is to understand how to relate photometric variability to physical parameters in order to help the interpretation of these observations. We computed a large number of synthetic time series of brightness variations for old MS stars within the F6-K4 range, using consistent modeling for radial velocity, astrometry, and LogRHK. We analyzed these time series to study the effect of the star spectral type on brightness variability, the relationship between brightness variability and LogRHK, the interpretation of brightness variability as a function of spot and plage properties, and the spot-dominated or plage-dominated regimes. Within our range of activity levels, the brightness variability increases toward low-mass stars, as suggested by Kepler results. Brightness variability roughly correlates to LogRHK level, but with a large dispersion, caused by spot contrast and inclination. It is also directly related to the number of structures, and we show that it cannot be interpreted solely in terms of spot sizes. In the activity range of old main-sequence stars, we can obtain both spot or plage dominated regimes, as in observation. The same star can be observed in both regimes depending on inclination. Only strong correlations between LogRHK and brightness variability are significant. Our realistic time series proves to be extremely useful when interpreting observations and understanding their limitations, most notably in terms of activity interpretation. Inclination is crucial and affects many properties, such as amplitudes and the respective role of spots and plages.
The effect of stellar activity on RV appears to be a limiting factor in detecting Earth-mass planets in the habitable zone of a star similar to the Sun in spectral type and activity level. It is crucial to estimate if this conclusion remain true for other stars with current correction methods. We built realistic time series in RV and chromospheric emission for old main-sequence F6-K4 stars. The stellar parameters are spectral type, activity level, rotation period, cycle period and amplitude, latitude coverage, and spot constrast, which we chose to be in ranges that are compatible with our current knowledge. This very large set of synthetic time series allowed us to study the effect of the parameters on the RV jitter and how the different contributions to the RV are affected in this first analysis of the data set. The RV jitter was used to provide a first-order detection limit for each time series and different temporal samplings. We find that the coverage in latitude of the activity pattern and the cycle amplitudes have a strong effect on the RV jitter, as has stellar inclination. RV jitter trends with B-V and LogRHK are similar to observations, but activity cannot be responsible for RV jitter larger than 2-3 m/s for very quiet stars: this observed jitter is therefore likely to be due to other causes. We show that based on the RV jitter that is associated with each time series and using a simple criterion, a planet with one Earth mass and a period of one to two years probably cannot be detected with current analysis techniques, except for the lower mass stars in our sample, but many observations would be required. The effect of inclination is critical. The results are very important in the context of future RV follow-ups of transit detections of such planets. A significant improvement of analysis techniques and/or observing strategies must be made to reach such low detection limits.
Stellar activity strongly affects and may prevent the detection of Earth-mass planets in the habitable zone of solar-type stars with radial velocity technics. Astrometry is in principle less sensitive to stellar activity because the situation is more favourable: the stellar astrometric signal is expected to be fainter than the planetary astrometric signal compared to radial velocities. We quantify the effect of stellar activity on high-precision astrometry when Earth-mass planets are searched for in the habitable zone around old main-sequence solar-type stars. We used a very large set of magnetic activity synthetic time series to characterise the properties of the stellar astrometric signal. We then studied the detectability of exoplanets based on different approaches: first based on the theoretical level of false positives derived from the synthetic time series, and then with blind tests for old main-sequence F6-K4 stars. The amplitude of the signal can be up to a few times the solar value depending on the assumptions made for activity level, spectral type, and spot contrast. The detection rates for 1 MEarth planets are very good, however, with extremely low false-positive rates in the habitable zone for stars in the F6-K4 range at 10 pc. The standard false-alarm probability using classical bootstrapping on the time series strongly overestimates the false-positive level. This affects the detection rates. We conclude that if technological challenges can be overcome and very high precision is reached, astrometry is much more suitable for detecting Earth-mass planets in the habitable zone around nearby solar-type stars than radial velocity, and detection rates are much higher for this range of planetary masses and periods when astrometric techniques are used than with radial velocity techniques.
We present a catalogue of homogeneous determined chromospheric emission (CE), stellar atmospheric parameters and ages for 1,674 FGK main sequence (MS), subgiant, and giant stars. The analysis of CE level and variability is also performed. We measured CE in the CaII lines using more than 180,000 high-resolution spectra from the HARPS spectrograph, as compiled in the AMBRE project, obtained between 2003 and 2019. We converted the fluxes to bolometric and photospheric corrected chromospheric emission ratio, $R_text{HK}$. Stellar atmospheric parameters $T_text{eff}$, $log g$, and [Fe/H] were retrieved from the literature or determined using an homogeneous method. $M_star$, $R_star$, and ages were determined from isochrone fitting. We analysed the CE distribution for the different luminosity classes and spectral types and confirmed the existence of the very inactive stars (VIS) and very active stars (VAS) populations at $log R_text{HK}< -5.1$ and $> -4.2$ dex, respectively. We found indications that the VIS population is composed mainly of subgiant and giant stars and that $log R_text{HK}= -5.1$ dex marks a transition in stellar evolution. There appears to be at least three regimes of variability, for inactive, active and very active stars, with the inactive and active regimes separated by a diagonal Vaughan-Preston gap. We show that stars with low activity levels do not necessarily have low variability. In the case of K dwarfs which show high CE variability, inactive and active stars have similar levels of activity variability. This means that activity levels alone are not enough to infer about the activity variability of a star. We also explained the shape of the VP gap observed in the distribution of CE by using the CE variability-level diagram. In the CE variability-level diagram, the Sun is located in the high variability region of the inactive MS stars zone. (Abridged)
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