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Connecting SOLar and stellar Variabilities

Periodic Reporting for period 4 - SOLVe (Connecting SOLar and stellar Variabilities)

Reporting period: 2021-07-01 to 2021-12-31

Cool stars, to which the Sun belongs, show various manifestations of activity, such as spectroscopic and brightness variations, chromospheric Ca II and coronal X-ray emission and its variations. Essentially all these phenomena are driven by magnetic fields emerging from below the stellar surface and evolving due to the dynamic interaction between matter and magnetic flux. The interest in solar and stellar activity is by far not limited to the solar and stellar astrophysics. Solar activity affects the Earth system and its space environment, while stellar activity is a limiting factor for detecting and studying exoplanets and can also affect their habitability. Despite such a broad interest, a comprehensive understanding of the link between the magnetic fields and the resulting phenomena is still missing. In this context, the main research directions of SOLVe have been:

a. Explaining and modelling various manifestations of magnetic activity in cool stars. The main idea behind the approach taken by SOLVe was to build on the methods and numerical codes originally developed for the Sun. Namely, we have extended and utilised radiative transfer, magnetohydrodynamic (MHD), and surface magnetic flux transfer codes to understand and model spectral, photometric, and astrometric effects caused by stellar magnetism;

b. Understanding how typical the Sun is as an active star. We have developed a number of new approaches for a quantitative comparison of the Sun to its peers, making significant progress in understanding the solar-stellar connection.

The scientific impact of SOLVe goes well beyond solar and stellar physics since better understanding of solar and stellar variability will, in turn, foster progress in understanding the solar-terrestrial and stellar-planetary connections
1. We have simulated small-scale magnetic features on stars with different metallicity values. These simulations have being used in various applications, e.g. modelling photometric variability of stars, modelling stellar radial velocity jitter, studying the impact of stellar magnetism on stellar limb darkening and colours.

2. We have developed an efficient and flexible radiative transfer code called Merged Parallelised Simplified ATLAS (MPS-ATLAS) which implements improved opacity distribution functions. We have used the code for creating a new extensive library of stellar model atmospheric structures as well as the stellar limb darkening curves. The MPS-ATLAS code in combination with the MURaM simulations have allowed us to study the effect of magnetic activity on stellar spectra for stars with a broad range of fundamental parameters.

3. We have employed the Surface Flux Transport Model for simulating diffusive-advective evolution of the radial field at solar and stellar surfaces. We have employed the model to explain the observed dependence of stellar variability on the rotation period, which is one of the most important dependences in the field of stellar activity.

4. Combining calculations with MURAM code and SATIRE code for modelling solar brightness variations, we have shown that the surface magnetic field and granulation can together precisely explain solar noise (that is, solar variability excluding oscillations) on timescales from minutes to decades, accounting for all timescales that have so far been resolved or covered by irradiance measurements (see figure). Our finding that solar brightness variations can be replicated in detail with just two well-known sources greatly simplifies modelling of stellar brightness variations.

5. We have used NESSY and MPS-ATLAS codes for improving the SATIRE model of solar variability. In particular, we have removed one of the most shortcomings of SATIRE: the need for the empirical correction of the SATIRE output below 300 nm. This made SATIRE UV results much more realistic.

6. We calculate the amplitude of the solar spectral irradiance variability over the course of the solar activity cycle as a function of solar age. Our calculations show that the young Sun was significantly more variable than the present Sun. For example, the amplitude of the solar-cycle Total Solar Irradiance (TSI) variability of the 600 Myr old Sun was about 10 times larger than that of the present Sun.

7. We have shown that even a small change (e.g. within the observational error range) of metallicity or effective temperature significantly affects the photometric brightness change compared to the Sun. In particular, we found that for Sun-like stars, the amplitude of the brightness variations obtained for Strömgren (b + y)/2 reaches a local minimum for fundamental stellar parameters close to the solar metallicity and effective temperature.

8. We have explained the low success rates in determining rotational periods of stars with near-solar ages and effective temperatures from photometric time series by short lifetime of spots in comparison to the stellar rotation period as well as the interplay between spot and facular contributions to brightness variations. We have shown that the rotation period can still be determined by measuring the period where the concavity of the power spectrum of brightness variations plotted in the log-log scale changes sign, i.e. by identifying the position of the inflection point. Such a novel method for determining rotational periods of stars has been tested against the Sun and stars with known rotational periods. It has been applied for creating the most accurate database of solar-like stars (i.e. stars with near-solar fundamental parameters and rotation periods).

9. We have investigated the effect of metallicity on the detectability of rotation periods. We find that the success rate for recovering the rotation signal has a minimum close to the solar metallicity value.

10. We have studied the effect of active-region nesting on photometric variability in solar-like stars. We found that a combination of increased nesting degree and 50% increase of solar activity level can explain the full range of observed variabilities of solar-like stars.

11. We have simulated the action of small-scale dynamo (SSD) in the near-surface layers of stars with various metallicities and have shown that SSD can significantly modify stellar radiative output (in particular, stellar limb darkening and profiles of spectral lines).

12. Combining 4-year high-precision time series of the Kepler space telescope with astrometric distances of the Gaia mission, we measure photometric variabilities of solar-like stars with near-solar rotational periods and ages to estimate the potential range of solar activity. We find that the distribution of the strength of magnetic activity of these stars peaks at low levels, but displays an exponential tail towards high activity. Based on the obtained distribution, we estimate that the Sun must spend about 10% of its time in a more active state than observed over the past century.
SOLVe lead to a major progress in understanding and modelling various manifestations of magnetic activity in cool stars. In particular, we have simulated and studied small-scale magnetic fields as well as magnetic features on stars with various metallicity values. We have developed a novel approach for the solar-stellar comparison and showed that stellar data indicate that the Sun could become substantially more active than it was over the past century.
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