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Register a new userHow faculae and network relate to sunspots, and the implications for solar and stellar brightness variations
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How global faculae and network coverage relates to that of sunspots is relevant to the brightness variations of the Sun and Sun-like stars. We extend earlier studies that found the facular-to-sunspot-area ratio diminishes with total sunspot coverage. Chromospheric indices and the total magnetic flux enclosed in network and faculae, referred to here as facular indices, are modulated by the amount of facular and network present. We probed the relationship between various facular and sunspot indices through an empirical model that takes into account how active regions evolve. This model was incorporated into a total solar irradiance (TSI) model. The model presented here replicates most of the observed variability in the facular indices, and is better at doing so than earlier models. Contrary to recent studies, we found the relationship between the facular and sunspot indices to be stable over the past four decades. The model indicates that, like the facular-to-sunspot-area ratio, the ratio of the variation in chromospheric emission and total network and facular magnetic flux to sunspot area decreases with the latter. The TSI model indicates the ratio of the TSI excess from faculae and network to the deficit from sunspots also declines with sunspot area, with the consequence being that TSI rises with sunspot area more slowly than if the two quantities were linearly proportional to one another. The extrapolation of the TSI model to higher activity levels indicates that in the activity range where Sun-like stars are observed to switch from growing brighter with increasing activity to becoming dimmer instead, the activity-dependence of TSI exhibits a similar transition as sunspot darkening starts to rise more rapidly with activity than facular brightening. This bolsters the interpretation of this behavior of Sun-like stars as the transition from a faculae-dominated to a spot-dominated regime.
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We aim to gain insight into the effect of network and faculae on solar irradiance from their apparent intensity. Taking full-disc observations from the Solar Dynamics Observatory, we examined the intensity contrast of network and faculae in the continuum and core of the Fe I 6173 {AA} line and 1700 {AA}, including the variation with magnetic flux density, distance from disc centre, nearby magnetic fields, and time. The brightness of network and faculae is believed to be suppressed by nearby magnetic fields from its effect on convection. The difference in intensity contrast between the quiet-Sun network and active region faculae, noted by various studies, arises because active regions are more magnetically crowded and is not due to any fundamental physical differences between network and faculae. These results highlight that solar irradiance models need to include the effect of nearby magnetic fields on network and faculae brightness. We found evidence that suggests that departures from local thermal equilibrium (LTE) might have limited effect on intensity contrast. This could explain why solar irradiance models that are based on the intensity contrast of solar surface magnetic features calculated assuming LTE reproduce the observed spectral variability even where the LTE assumption breaks down. Certain models of solar irradiance employ chromospheric indices as direct indications of the effect of network and faculae on solar irradiance. Based on past studies of the Ca II K line and on the intensity contrast measurements derived here, we show that the fluctuations in chromospheric emission from network and faculae are a reasonable estimate of the emission fluctuations in the middle photosphere, but not of those in the lower photosphere. The data set, which extends from 2010 to 2018, indicates that intensity contrast was stable to about 3% in this period.
Comparing solar and stellar brightness variations is hampered by the difference in spectral passbands used in observations as well as by the possible difference in the inclination of their rotation axes from the line of sight. We calculate the rotational variability of the Sun as it would be measured in passbands used for stellar observations. In particular, we consider the filter systems used by the CoRoT, $Kepler$, TESS, and $Gaia$ space missions. We also quantify the effect of the inclination of the rotation axis on the solar rotational variability. We employ the Spectral And Total Irradiance REconstructions (SATIRE) model to calculate solar brightness variations in different filter systems as observed from the ecliptic plane. We then combine the simulations of the surface distribution of the magnetic features at different inclinations using a surface flux transport model (SFTM) with the SATIRE calculations to compute the dependence of the variability on the inclination. For an ecliptic-bound observer, the amplitude of the solar rotational variability, as observed in the total solar irradiance (TSI) is 0.68 mmag (averaged over solar cycles 21-24). We obtained corresponding amplitudes in the $Kepler$ (0.74 mmag), CoRoT (0.73 mmag), TESS (0.62 mmag), $Gaia~ $ (0.74 mmag), $Gaia~ G_{RP}$ (0.62 mmag), and ), $Gaia~ G_{BP}$ (0.86 mmag) passbands. Decreasing the inclination of the rotation axis decreases the rotational variability. For a sample of randomly inclined stars, the variability is on average 15% lower in all filter systems considered in this work. This almost compensates for the difference in the amplitudes of the variability in TSI and $Kepler$ passbands, making the amplitudes derived from the TSI records an ideal representation of the solar rotational variability for comparison to $Kepler$ stars with unknown inclinations.
Context. Comparison studies of Sun-like stars with the Sun suggest an anomalously low photometric variability of the Sun compared to Sun-like stars with similar magnetic activity. Comprehensive understanding of stellar variability is needed, to find a physical reasoning for this observation. Aims. We investigate the effect of metallicity and effective temperature on the photometric brightness change of Sun-like stars seen at different inclinations. The considered range of fundamental stellar parameters is sufficiently small so the stars, investigated here, still count as Sun-like or even as solar twins. Methods. To model the brightness change of stars with solar magnetic activity, we extend a well established model of solar brightness variations, SATIRE (which stands for Spectral And Total Irradiance Reconstruction), which is based on solar spectra, to stars with different fundamental parameters. For that we calculate stellar spectra for different metallicities and effective temperature using the radiative transfer code ATLAS9. Results. We show 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. We find that for Sun-like stars, the amplitude of the brightness variations obtained for Stromgren (b + y)/2 reaches a local minimum for fundamental stellar parameters close to the solar metallicity and effective temperature. Moreover, our results show that the effect of inclination decreases for metallicity values greater than the solar metallicity. Overall, we find that an exact determination of fundamental stellar parameters is crucially important for understanding stellar brightness changes.
Oscillation properties in two sunspots and two facular regions are studied using Solar Dynamics Observatory (SDO) data and ground-based observations in the SiI 10827 and HeI 10830 lines. The aim is to study different-frequency spatial distribution characteristics above sunspots and faculae and their dependence on magnetic-field features and to detect the oscillations that reach the corona from the deep photosphere most effectively. We used Fast-Fourier-Transform and frequency filtration of the intensity and Doppler-velocity variations with Morlet wavelet to trace the wave propagating from the photosphere to the chromosphere and corona. Spatial distribution of low-frequency (1-2 mHz) oscillations outlines well the fan-loop structures in the corona (the Fe IX 171 line) above sunspots and faculae. High-frequency oscillations (5-7 mHz) are concentrated in fragments inside the photospheric umbra boundaries and close to facular-region centers. This implies that the upper parts of most coronal loops, which transfer low-frequency oscillations from the photosphere, sit in the Fe IX 171 line-formation layer. We used dominant frequency vs. distance from barycenter relations to estimate magnetic-tube inclination angle in the higher layers, which poses difficulties for direct magnetic-field measurements. According to our calculations, this angle is about 40 degrees in the transition region around umbra borders. Phase velocities measured in the coronal loops upper parts in the Fe IX 171 line-formation layer reach 100-150 km/s for sunspots and 50-100 km/s for faculae.
The solar brightness varies on timescales from minutes to decades. Determining the sources of such variations, often referred to as solar noise, is of importance for multiple reasons: a) it is the background that limits the detection of solar oscillations, b) variability in solar brightness is one of the drivers of the Earths climate system, c) it is a prototype of stellar variability which is an important limiting factor for the detection of extra-solar planets. Here we show that recent progress in simulations and observations of the Sun makes it finally possible to pinpoint the source of the solar noise. We utilise high-cadence observations from the Solar Dynamic Observatory and the SATIRE model to calculate the magnetically-driven variations of solar brightness. The brightness variations caused by the constantly evolving cellular granulation pattern on the solar surface are computed with the MURAM code. We find that surface magnetic field and granulation can together precisely explain solar noise on timescales from minutes to decades, i.e. ranging over more than six orders of magnitude in the period. This accounts 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. Recent measurements of Sun-like stars by CoRoT and Kepler uncovered brightness variations similar to that of the Sun but with much wider variety of patterns. Our finding that solar brightness variations can be replicated in detail with just two well-known sources will greatly simplify future modelling of existing CoRoT and Kepler as well as anticipated TESS and PLATO data.
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