Skip to main content

Connecting SOLar and stellar Variabilities

Periodic Reporting for period 3 - SOLVe (Connecting SOLar and stellar Variabilities)

Reporting period: 2020-01-01 to 2021-06-30

The Sun is an unusual star - even when compared to those, which resemble it in size, luminosity, and magnetic properties. Investigations of the past years show that the Sun’s brightness variations are markedly weaker than those of most comparable stars. One of the main goals of SOLVe is to investigate the reasons for this difference and to look for the link between the Sun and stars. Why do these bodies behave so similarly and yet so differently? And can findings from solar research be transferred to distant stars? More specifically SOLVe aims at answering following questions:

- How typical is the Sun as an active star?

- What does stellar data tell us about the possible range of solar variability and consequently solar contribution to historical climate change?

- How do stellar photometric variabilities depend on the main stellar parameters (e.g. age, effective temperature, metallicity)?

- How can one determine the basic properties of stellar magnetic cycles from the records of stellar brightness variations (e.g. from the Kepler and CoRoT data)?

Answering these questions has far-reaching implications that go well beyond solar and stellar physics. Intrinsic stellar brightness variation is a limiting factor for exoplanet characterisation via transit photometry. Similarly, solar brightness variability is one of the main natural forcings of Earth’s climate system.

In SOLVe we employ newest magnetohydrodynamic (MHD) and radiative transfer codes to extend models of solar irradiance variability to other stars and to analyze photometric data of Sun-like stars. Such a synergy of solar and stellar research simultaneously allows constraining solar models over a much wider space of stellar parameters and gaining more insights into the physical causes of stellar variability. In turn, better understanding of solar and stellar variability will help us to identify the role of the Sun in climate change and to develop new methods for exoplanet detection and characterization.
1. Combining calculations with MURAM 3D radiation magnetohydrodynamic 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. We demonstrate that no other sources of variability are required to explain the data (see Fig. 1). Our finding that solar brightness variations can be replicated in detail with just two well-known sources greatly simplifies modelling of stellar brightness variations.

2. We have extended the SATIRE model to stars with different fundamental parameters. 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.

3. The NESSY and MPS-ATLAS codes have been employed to develop a time-efficient algorithm for taking into account the line blanketing effect from millions of atomic and molecular lines. In particular, we have removed the need for the empirical correction of the SATIRE output below 300 nm, making SATIRE UV results much more realistic.

4. We have explained the low success rates in determining rotational periods of stars with near-solar ages and effective temperatures from photometric time series (e.g. obtained by the Kepler space telescope) 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. Currently we are working on determining rotational periods of stars with previously unknown periods.

5. 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.

6. We have employed the Surface Flux Transport Model for simulating diffusive-advective evolution of the radial field at solar and stellar surfaces. This allowed us to model the rotational variability of the Sun at different inclinations, i.e. as it would be measured by space-borne telescopes (see Fig. 2). The model is currently being employed for calculating the rotational variability of stars more active than the Sun.

7. 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.

8. We have updated the opacities and equation of state in the MURaM code for simulating solar magneto-convection. This allowed us to run the code for stars with different metallicity. We have made a number of test runs with the updated code and we are have currently running simulations for a set of stars with different parameters. We expect to have first scientific results very soon.

9. We calculate the amplitude of the SSI and TSI variability over the course of the solar activity cycle as a function of solar age by filling the solar surface with an incasing amount of active regions. Our calculations show that the young Sun was significantly more variable than the present Sun. 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.

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 developed an efficient and flexible radiative transfer code called Merged Parallelised Simplified ATLAS (MPS-ATLAS) which implements improved opacity distribution functions. We have extensively tested the performance of the code for calculating stellar spectra.

12. We have simulated the action of small-scale dynamo (SSD) in the near-surface layers of stars with various metallicities and show that SSD can significantly modify stellar radiative output.
Based on the current status of the project we expect that all scientific objectives of project will be fulfilled.
Fig 1 with caption (taken from Shapiro et al. 2017 Nat. Astron.)
Fig 2 with caption taken from the paper in preparation