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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 Sp\"{o}rer 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.

The solar activity, which is driven by a variable magnetic field, exhibits changes along several time scales, the 11-year being the most known. In addition to the SunSpot Number, the Ca II K index and the Mg II index are indices widely employed among those proposed to quantify the solar activity, also because of their ability to trace the solar UV emission. In this work, we compare the Ca II K 0.1nm emission index to the Mg II index over the time interval 1978-2017, which covers almost four solar cycles. We show that they are strongly correlated across each solar cycle (r$\geq$0.94), providing the corresponding linear regression fit parameters. The Hilbert-Huang Transform is then used to decompose such indices into their intrinsic mode of oscillation. By studying how their components are correlated over the different time scales, it is found that the maximum correlation is observed at the 11-year scale, while the correlation is less strong going to smaller time scales.

The Earth's magnetosphere extension is controlled by the solar activity level via solar wind properties. Understanding such a relation in the Solar System is important for predicting also the condition of exoplanetary magnetospheres near Sun-like stars. We use measurements of a chromospheric proxy, the Ca II K index, and solar wind OMNI parameters to connect the solar activity variations, on the decennial time scales, to the solar wind properties. The data span over the time interval 1965-2021, which almost entirely covers the last 5 solar cycles. Using both cross-correlation and mutual information analysis, a 3.2-year lag of the solar wind speed with respect to the Ca II K index is found. Analogously, a 3.6-year lag is found once considering the dynamic pressure. A correlation between the solar wind dynamic pressure and the solar UV emission is found and used to derive the Earth's magnetopause standoff distance. Moreover, the advantage of using a chromospheric proxy, such as the Ca II K index, opens the possibility to extend the relation found for the Sun to Sun-like stars, by linking stellar variability to stellar wind properties. The model is applied to a sample of Sun-like stars as a case study, where we assume the presence of an Earth-like exoplanet at 1 AU. Finally, we compare our results with previous estimates of the magnetosphere extension for the same set of Sun-like stars., Comment: 11 pages, 6 figures

Solar variability occurs over a broad range of spatial and temporal scales, from the Sun's brightening over its lifetime to the fluctuations commonly associated with magnetic activity over minutes to years. The latter activity includes most prominently the 11-year sunspot solar cycle and its modulations. Space weather events, in the form of solar flares, solar energetic particles, coronal mass ejections, and geomagnetic storms, have long been known to approximately follow the solar cycle occurring more frequently at solar maximum than solar minimum. These events can significantly impact our advanced technologies and critical infrastructures, making the prediction for the strength of future solar cycles particularly important. Several methods have been proposed to predict the strength of the next solar cycle, cycle 25, with results that are generally not always consistent. Most of these methods are based on the international sunspot number time series, or other indicators of solar activity. We present here a new approach that uses more than 100 years of measured fractional areas of the visible solar disk covered by sunspots and plages and an empirical relationship for each of these two indices of solar activity in even-odd cycles. We anticipate that cycle 25 will peak in 2024 and will last for about 12 years, slightly longer than cycle 24. We also found that, in terms of sunspot and plage areas coverage, the amplitude of cycle 25 will be substantially similar or slightly higher than cycle 24., Comment: 7 pages, 6 figures. Accepted on ApJL

Modeling of planets' climate and habitability requires as fundamental input the UV emission of the hosting star. \citet{lovric2017} employed SORCE/SOLSTICE solar observations to introduce a UV color index which is a descriptor of the UV radiation that modulates the photochemistry of planets atmospheres. After correcting the SOLSTICE data for residual instrumental effects that produced asymmetric signals during different phases of the cycles analyzed, the authors found that the UV color index is linearly correlated with the Mg II index.In this paper we employ an irradiance reconstruction technique to synthetize the UV color and Mg II index with the purpose of investigating whether the correction applied by \citet{lovric2017} to SORCE/SOLSTICE data might have compensated for solar variations, and to investigate the physical mechanisms that produce such a strong correlation between the UV color index and the solar activity. Reconstructed indices reproduce very well the observations and present the same strong linear dependence. Moreover our reconstruction, which extends back to 1989, shows that the UV color - Mg II index relation can be described by the same linear relation for almost three cycles, thus ruling out an overcompensation of SORCE/SOLTICE data in the analysis of \citet{lovric2017}. We suggest that the strong correlation between the indices results from the fact that most of the Far- and Middle- UV radiation originates in the chromosphere, where atmosphere models of quiet and magnetic features present similar temperature and density gradients., Comment: Accepted in ApJ

The investigation of dynamics of the small scale magnetic field on the Sun photosphere is necessary to understand the physical processes occurring in the higher layers of solar atmosphere due to the magnetic coupling between the photosphere and the corona. We present a simulation able to address these phenomena investigating the statistics of magnetic loops reconnections. The simulation is based on N-body model approach and is divided in two computational layers. We simplify the convection problem, interpreting the larger convective scale, mesogranulation, as the result of the collective interaction of convective downflow of granular scale. The N-body advection model is the base to generate a synthetic time series of nanoflares produced by interacting magnetic loops. The reconnection of magnetic field lines is the result of the advection of the magnetic footpoints following the velocity field generated by the interacting downflows. The model gives a quantitative idea of how much energy is expected to be released by the reconfiguration of magnetic loops in the quiet Sun., Comment: 6 pages, 2 figures. To be published in "Journal of Physics: Conference Series" as part of the proceedings of the sixth edition of the Young Researcher Meeting (YRM), 12-14 October 2015, L'Aquila, Italy. http://www.yrmr.it/

In the second paper of this series we pursue two objectives. First, in order to make the code more sensitive to small effects, we remove many approximations made in Paper I. Second, we include turbulence and rotation in the two-dimensional framework. The stellar equilibrium is described by means of a set of five differential equations, with the introduction of a new dependent variable, namely the perturbation to the radial gravity, that is found when the non-radial effects are considered in the solution of the Poisson equation; following the scheme of the first paper, we write the equations in such a way that the two-dimensional effects can be easily disentangled. The key concept introduced in this series is the equipotential surface. We use the underlying cause-effect relation to develop a recurrence relation to calculate the equipotential surface functions for uniform rotation, differential rotation, rotation-like toroidal magnetic fields and turbulence. We also develop a more precise code to numerically solve the two-dimensional stellar structure and evolution equations based on the equipotential surface calculations. We have shown that with this formulation we can achieve the precision required by observations by appropriately selecting the convergence criterion. Several examples are presented to show that the method works well. Since we are interested in modeling the effects of a dynamo-type field on the detailed envelope structure and global properties of the Sun, the code has been optimized for short timescales phenomena (down to 1 yr). The time dependence of the code has so far been tested exclusively to address such problems., Comment: 56 pages, 8 figures, submitted to ApJS