Abstract: The stellar Rossby number (Ro) is a dimensionless quantity that is used in the description of fluid flows. It characterizes the relative importance of Coriolis forces on convective motions, which is central to understanding magnetic stellar evolution. Here we present an expanded sample of Kepler asteroseismic targets to help calibrate the relation between Ro and Gaia color, and we extend the relation to redder colors using observations of the mean activity levels and rotation periods for a sample of brighter stars from the Mount Wilson survey. Our quadratic fit to the combined sample is nearly linear between 0.55 < G_BP-G_RP < 1.2, and can be used to estimate Ro for stars with spectral types between F5 and K3. The strong deviation from linearity in the original calibration may reflect an observational bias against the detection of solar-like oscillations at higher activity levels for the coolest stars.

Abstract: The first adiabatic exponent profile, noted $\Gamma_1$, computed along adiabatic coordinates $(T, \rho)$ is in the focus of our study. Under conditions of almost fully ionized hydrogen and helium, the $\Gamma_1$ profile is quite sensitive to heavy elements ionization. $\Gamma_1$ decreases in regions where an element is partially ionized. The recent helioseismic structural inversion is obtained with an accuracy better than $10^{-4}$ in the most of the adiabatic convective zone that allows to study ionization variations. The aim is to determine the major heavy elements content in the solar convective zone. The method of our research is synthesis of the $\Gamma_1$ profile which is based on a linear combination of the contributions of individual heavy elements. The idea of the approach was proposed and justified by Baturin et al. (Astron. Astrophys., 660, A125, 2022). We find the best approximation of the inverted profile $\Gamma_1$ adjusting the abundances of major elements (C, N, O, Ne), meanwhile the abundances of elements heavier than neon are fixed. We synthesize the theoretical $\Gamma_1$ profile using the SAHA-S equation of state, and are able to reproduce the inverted profiles with an accuracy of $(1-2)\cdot 10^{-5}$. Total mass fraction of heavy elements found by this method is $Z=0.0148\pm 0.0004$. The oxygen logarithmic abundance is $8.70\pm 0.03$, carbon $8.44\pm 0.04$, nitrogen $8.12\pm 0.08$, and neon $8.17\pm 0.09$. The obtained estimations of oxygen and carbon agree with spectroscopic abundances by Asplund et al. (Astron. Astrophys., 653, A141, 2021).

Abstract: Solar irradiance variations across various timescales, from minutes to centuries, represents a potential natural driver of past regional and global climate cold phases. To accurately assess the Sun's effect on climate, particularly during periods of exceptionally low solar activity known as grand minima, an accurate reconstruction of solar forcing is essential. While direct measurements of Total Solar Irradiance (TSI) only began in the late 1970s with the advent of space radiometers, indirect evidence from various historical proxies suggests that the Sun's magnetic activity has undergone possible significant fluctuations over much longer timescales. Employing diverse and independent methods for TSI reconstruction is essential to gaining a comprehensive understanding of this issue. This study employs a semi-empirical model to reconstruct TSI over the past millennium. Our approach uses an estimated open solar magnetic field ($F_{o}$), derived from cosmogenic isotope data, as a proxy for solar activity. We reconstruct the cyclic variations of TSI, due to the solar surface magnetic features, by correlating $F_{o}$ with the parameter of active region functional form. Instead, we obtain the long-term TSI trend by applying the Empirical Mode Decomposition (EMD) algorithm to the reconstructed $F_{o}$ to filter out the 11-year and 22-year solar variability. We prepare a reconstructed TSI record, spanning 971 to 2020 CE. The estimated departure from modern TSI values occurred during the Spörer Minimum (around 1400 CE), with a decrease of approximately 2.3 $W m^{-2}$. A slightly smaller decline of 2.2 $W m^{-2}$ is reported during the Maunder Minimum, between 1645 and 1715 CE.

Abstract: The first adiabatic exponent profile, noted $\Gamma_1$, computed along adiabatic coordinats $(T, \rho)$ is in the focus of our study. Under conditions of almost fully ionized hydrogen and helium, the $\Gamma_1$ profile is quite sensitive to heavy elements ionization. $\Gamma_1$ decreases in regions where an element is partially ionized. The recent helioseismic structural inversion is obtained with an accuracy better than $10^{-4}$ in the most of the adiabatic convective zone that allows to study ionization variations. The aim is to determine the major heavy elements content in the solar convective zone. The method of our research is synthesis of the $\Gamma_1$ profile which is based on a linear combination of the contributions of individual heavy elements. The idea of the approach was proposed and justified by Baturin et al. (Astron. Astrophys., 660, A125, 2022). We find the best approximation of the inverted profile $\Gamma_1$ adjusting the abundances of major elements (C, N, O, Ne), meanwhile the abundances of elements heavier than neon are fixed. We synthesize the theoretical $\Gamma_1$ profile using the SAHA-S equation of state, and are able to reproduce the inverted profiles with an accuracy of $(1-2)\cdot 10^{-5}$. Total mass fraction of heavy elements found by this method is $Z=0.0148\pm 0.0004$. The oxygen logarithmic abundance is $8.70\pm 0.03$, carbon $8.44\pm 0.04$, nitrogen $8.12\pm 0.08$, and neon $8.17\pm 0.09$. The obtained estimations of oxygen and carbon agree with spectroscopic abundances by Asplund et al. (Astron. Astrophys., 653, A141, 2021).

Abstract: We examine 4 years of Kepler 30-min data, and 5 Sectors of TESS 2-min data for the dM3 star KIC-8507979/TIC-272272592. This rapidly rotating (P=1.2 day) star has previously been identified as flare active, with a possible long-term decline in its flare output. Such slow changes in surface magnetic activity are potential indicators of Solar-like activity cycles, which can yield important information about the structure of the stellar dynamo. We find that while TIC-272272592 shows evidence for both short and long timescale variations in its flare activity, it is unlikely physically motivated. Only a handful of stars have been subjected to such long baseline point-in-time flare studies, and we urge caution in comparing results between telescopes due to differences in bandpass, signal to noise, and cadence. In this work, we develop an approach to measure variations in the flare frequency distributions over time, which is quantified as a function of the observing baseline. For TIC-272272592, we find a $2.7\sigma$ detection of a Sector which has a flare deficit, therefore indicating the short term variation could be a result of sampling statistics. This quantifiable approach to describing flare rate variation is a powerful new method for measuring the months-to-years changes in surface magnetic activity, and provides important constraints on activity cycles and dynamo models for low mass stars.

Abstract: In this work we aim to determine the atmospheric survivability of the TRAPPIST-1 planets by modelling the response of the upper atmosphere to incoming stellar high-energy radiation. Through this case study, we also aim to learn more about rocky planet atmospheres in the habitable zone around low-mass M dwarfs. We simulated the upper atmospheres using the Kompot code, a self-consistent thermo-chemical code. Specifically, we studied the atmospheric mass loss due to Jeans escape induced by stellar high-energy radiation. This was achieved through a grid of models that account for the differences in planetary properties, irradiances, and atmospheric properties, allowing the exploration of the different factors influencing atmospheric loss. The present-day irradiance of the TRAPPIST-1 planets would lead to the loss of an Earth's atmosphere within just some 100 Myr. Taking into account the much more active early stages of a low-mass M dwarf, the planets undergo a period of even more extreme mass loss, regardless of planetary mass or atmospheric composition. This indicates that it is unlikely that any significant atmosphere could survive for any extended amount of time around any of the TRAPPIST-1 planets. The assumptions used here allow us to generalise the results, and we conclude that the results tentatively indicate that this conclusion applies to all Earth-like planets in the habitable zones of low-mass M dwarfs.

Abstract: PLATO will begin observing stars in its Southern Field (LOPS2) after its launch in late 2026. By this time, TESS will have observed the stars in LOPS2 for at least four years. We find that by 2025, on average each star in the PLATO field will have been monitored for 330 days by TESS, with a subset of stars in the TESS continuous viewing zone having over 1000 days of monitoring. There are currently 96 known transiting exoplanets in the LOPS2 field, with 33 of these residing in multiplanet systems. The LOPS2 field also contains around 500 TESS planet candidate systems, over 1000 bright (V<13) eclipsing binary systems, 6 transiting brown dwarf systems, and 2 bright white dwarfs (G<13). We calculate TESS and PLATO sensitivities to detecting transits for the bright FGK stars that make up the PLATO LOPS2 P1 sample. We find that TESS should have discovered almost all transiting giant planets out to approximately 30 d within the LOPS2 field, and out to approximately 100 d for the regions of the LOPS2 field within the TESS CVZ ($\sim$20 per cent of the LOPS2 field). However, we find that for smaller radius planets in the range 1$-$4 R$_\oplus$ PLATO will have significantly better sensitivity, and these are likely to make up the bulk of new PLATO discoveries.

Abstract: The detection of stellar variability often relies on the measurement of selected activity indicators such as coronal emission lines and non-thermal emissions. On the flip side, the effective stellar temperature is normally seen as one of the key fundamental parameters (with mass and radius) to understanding the basic physical nature of a star and its relation with its environment (e.g., planetary instellation). We present a novel approach for measuring disk-averaged temperature variations to sub-Kelvin accuracy inspired by algorithms developed for precision radial velocity. This framework uses the entire content of the spectrum, not just pre-identified lines, and can be applied to existing data obtained with high-resolution spectrographs. We demonstrate the framework by recovering the known rotation periods and temperature modulation of Barnard star and AU Mic in datasets obtained in the infrared with SPIRou at CHFT and at optical wavelengths on $\epsilon$ Eridani with HARPS at ESO 3.6-m telescope. We use observations of the transiting hot Jupiter HD189733\,b, obtained with SPIRou, to show that this method can unveil the minute temperature variation signature expected during the transit event, an effect analogous to the Rossiter-McLaughlin effect but in temperature space. This method is a powerful new tool for characterizing stellar activity, and in particular temperature and magnetic features at the surfaces of cool stars, affecting both precision radial velocity and transit spectroscopic observations. We demonstrate the method in the context of high-resolution spectroscopy but the method could be used at lower resolution.

Abstract: The grand minimum in the Sun's activity is a distinctive mode characterized by a magnetic lull that almost completely lacks the emergence of sunspots on the solar surface for an extended duration. The factors driving this transition of an otherwise magnetically active star into a quiescent phase, the processes occurring within the solar interior and across the heliosphere during this period, and the mechanisms leading to the eventual resurgence of surface magnetic activity remain enigmatic. However, there have been sustained efforts in the past few decades to unravel these mysteries by employing a combination of observation, reconstruction and simulation of solar magnetic variability. Here, we summarize recent research on the solar grand minimum and highlight some outstanding challenges - both intellectual and practical - that necessitate further investigations.

Abstract: Stellar evolution theory predicts that the Sun was fainter in the past, which can pose difficulties for understanding Earth's climate history. One proposed solution to this Faint Young Sun problem is a more luminous Sun in the past. In this paper, we address the robustness of the solar luminosity history using the YREC code to compute solar models including rotation, magnetized winds, and the associated mass loss. We present detailed solar models, including their evolutionary history, which are in excellent agreement with solar observables. Consistent with prior standard models, we infer a high solar metal content. We provide predicted X-ray luminosities and rotation histories for usage in climate reconstructions and activity studies. We find that the Sun's luminosity deviates from the standard solar model trajectory by at most 0.5% during the Archean (corresponding to a radiative forcing of 0.849 W m$^{-2}$). The total mass loss experienced by solar models is modest because of strong feedback between mass and angular momentum loss. We find a maximum mass loss of $1.35 \times 10^{-3} M_\odot$ since birth, at or below the level predicted by empirical estimates. The associated maximum luminosity increase falls well short of the level necessary to solve the FYS problem. We present compilations of paleotemperature and CO$_2$ reconstructions. 1-D "inverse" climate models demonstrate a mismatch between the solar constant needed to reach high temperatures (e.g. 60-80 $^{\circ}$C) and the narrow range of plausible solar luminosities determined in this study. Maintaining a temperate Earth, however, is plausible given these conditions.

Abstract: Stellar evolution theory predicts that the Sun was fainter in the past, which can pose difficulties for understanding Earth's climate history. One proposed solution to this Faint Young Sun problem is a more luminous Sun in the past. In this paper, we address the robustness of the solar luminosity history using the YREC code to compute solar models including rotation, magnetized winds, and the associated mass loss. We present detailed solar models, including their evolutionary history, which are in excellent agreement with solar observables. Consistent with prior standard models, we infer a high solar metal content. We provide predicted X-ray luminosities and rotation histories for usage in climate reconstructions and activity studies. We find that the Sun's luminosity deviates from the standard solar model trajectory by at most 0.5% during the Archean (corresponding to a radiative forcing of 0.849 W m$^{-2}$). The total mass loss experienced by solar models is modest because of strong feedback between mass and angular momentum loss. We find a maximum mass loss of $1.35 \times 10^{-3} M_\odot$ since birth, at or below the level predicted by empirical estimates. The associated maximum luminosity increase falls well short of the level necessary to solve the FYS problem. We present compilations of paleotemperature and CO$_2$ reconstructions. 1-D "inverse" climate models demonstrate a mismatch between the solar constant needed to reach high temperatures (e.g. 60-80 $^{\circ}$C) and the narrow range of plausible solar luminosities determined in this study. Maintaining a temperate Earth, however, is plausible given these conditions.

Abstract: After leaving the Sun's corona, the solar wind continues to accelerate and cools, but more slowly than expected for a freely expanding adiabatic gas. We use in situ measurements from the Parker Solar Probe and Solar Orbiter spacecrafts to investigate a stream of solar wind as it traverses the inner heliosphere. The observations show heating and acceleration of the the plasma between the outer edge of the corona and near the orbit of Venus, in connection to the presence of large amplitude Alfvén waves. Alfvén waves are perturbations in the interplanetary magnetic field that transport energy. Our calculations show the damping and mechanical work performed by the Alfvén waves is sufficient to power the heating and acceleration of the fast solar wind in the inner heliosphere.

Abstract: The solar-type subgiant $\beta$ Hyi has long been studied as an old analog of the Sun. Although the rotation period has never been measured directly, it was estimated to be near 27 days. As a southern hemisphere target it was not monitored by long-term stellar activity surveys, but archival International Ultraviolet Explorer data revealed a 12 year activity cycle. Previous ground-based asteroseismology suggested that the star is slightly more massive and substantially larger and older than the Sun, so the similarity of both the rotation rate and the activity cycle period to solar values is perplexing. We use two months of precise time-series photometry from the Transiting Exoplanet Survey Satellite (TESS) to detect solar-like oscillations in $\beta$ Hyi and determine the fundamental stellar properties from asteroseismic modeling. We also obtain a direct measurement of the rotation period, which was previously estimated from an ultraviolet activity-rotation relation. We then use rotational evolution modeling to predict the rotation period expected from either standard spin-down or weakened magnetic braking (WMB). We conclude that the rotation period of $\beta$ Hyi is consistent with WMB, and that changes in stellar structure on the subgiant branch can reinvigorate the large-scale dynamo and briefly sustain magnetic activity cycles. Our results support the existence of a "born-again" dynamo in evolved subgiants -- previously suggested to explain the cycle in 94 Aqr Aa -- which can best be understood within the WMB scenario.