Context. Stellar spectral variability on timescales of a day and longer, arising from magnetic surface features such as dark spots and bright faculae, is an important noise source when characterising extra-solar planets. Current 1D models of faculae do not capture the geometric properties and fail to reproduce observed solar facular contrasts. Magnetoconvection simulations provide facular contrasts accounting for geometry. Aims. We calculate facular contrast spectra from magnetoconvection models of the solar photosphere with a view to improve (a) future parameter determinations for planets with early G type host stars and (b) reconstructions of solar spectral variability. Methods. Regions of a solar twin (G2, log g = 4.44) atmosphere with a range of initial average vertical magnetic fields (100 to 500 G) were simulated using a 3D radiation-magnetohydrodynamics code, MURaM, and synthetic intensity spectra were calculated from the ultraviolet (149.5 nm) to the far infrared (160000 nm) with the ATLAS9 radiative transfer code. Nine viewing angles were investigated to account for facular positions across most of the stellar disc. Results. Contrasts of the radiation from simulation boxes with different levels of magnetic flux relative to an atmosphere with no magnetic field are a complicated function of position, wavelength and magnetic field strength that is not reproduced by 1D facular models. Generally, contrasts increase towards the limb, but at UV wavelengths a saturation and decrease are observed close to the limb. Contrasts also increase strongly from the visible to the UV; there is a rich spectral dependence, with marked peaks in molecular bands and strong spectral lines. At disc centre, a complex relationship with magnetic field was found and areas of strong magnetic field can appear either dark or bright, depending on wavelength. Spectra calculated for a wide variety of magnetic fluxes will also serve to improve total and spectral solar irradiance reconstructions.
The variation in the radiative output of the Sun, described in terms of solar irradiance, is important to climatology. A common assumption is that solar irradiance variability is driven by its surface magnetism. Verifying this assumption has, however, been hampered by the fact that models of solar irradiance variability based on solar surface magnetism have to be calibrated to observed variability. Making use of realistic three-dimensional magnetohydrodynamic simulations of the solar atmosphere and state-of-the-art solar magnetograms from the Solar Dynamics Observatory, we present a model of total solar irradiance, TSI that does not require any such calibration. In doing so, the modelled irradiance variability is entirely independent of the observational record.(The absolute level is calibrated to the TSI record from the Total Irradiance Monitor, TIM). The model replicates 95% of the observed variability between April 2010 and July 2016, leaving little scope for alternative drivers of solar irradiance variability at least over the timescales examined (days to years).
This corrects the article DOI: 10.1103/PhysRevLett.119.091102.
Variability observed in photometric lightcurves of late-type stars (on timescales longer than a day) is a dominant noise source in exoplanet surveys and results predominantly from surface manifestations of stellar magnetic activity, namely faculae and spots. The implementation of faculae in lightcurve models is an open problem, with scaling typically based on spectra equivalent to hot stellar atmospheres or assuming a solar-derived facular contrast. We modelled rotational (single period) lightcurves of active G2, K0, M0 and M2 stars, with Sun-like surface distributions and realistic limb-dependent contrasts for faculae and spots. The sensitivity of lightcurve variability to changes in model parameters such as stellar inclination, feature area coverage, spot temperature, facular region magnetic flux density and active band latitudes is explored. For our lightcurve modelling approach we used actress, a geometrically accurate model for stellar variability. actress generates 2-sphere maps representing stellar surfaces and populates them with user-prescribed spot and facular region distributions. From this, lightcurves can be calculated at any inclination. Quiet star limb darkening and limb-dependent facular contrasts were derived from MURaM 3D magnetoconvection simulations using ATLAS9. 1D stellar atmosphere models were used for the spot contrasts. We applied actress in Monte Carlo simulations, calculating lightcurve variability amplitudes in the Kepler band. We found that, for a given spectral type and stellar inclination, spot temperature and spot area coverage have the largest effect on variability of all simulation parameters. For a spot coverage of $1{{\ \rm per\ cent}}$, the typical variability of a solar-type star is around 2 parts-per-thousand. The presence of faculae clearly affects the mean brightness and lightcurve shape, but has relatively little influence on the variability.
<p>Stellar variability is a dominant noise source in exoplanet surveys and results largely from the presence of photospheric faculae and spots. The implementation of faculae in lightcurve models is an open problem, with scaling based on spectra equivalent to hot stellar atmospheres or assuming a solar-derived facular contrast. We model the lightcurves of active late-type stars as they rotate, using emergent intensity spectra calculated from 3D magnetoconvection simulations of G, K and M-type stellar atmosphere regions at different viewing angles to reproduce centre-to-limb brightness variations. We present mean expected variability levels for several cases and compare with solar and stellar observations. We also investigate the wavelength dependence of variability.</p> <p>&#160;</p> <p><img src="data:image/jpeg;base64, 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
Magnetic features on the surface of stars, such as spots and faculae, cause stellar spectral variability on time-scales of days and longer. For stars other than the Sun, the spectral signatures of faculae are poorly understood, limiting our ability to account for stellar pollution in exoplanet transit observations. Here we present the first facular contrasts derived from magnetoconvection simulations for K0, M0 and M2 main-sequence stars and compare them to previous calculations for G2 main-sequence stars. We simulate photospheres and immediate subsurface layers of main-sequence spectral types between K0 and M2, with different injected vertical magnetic fields (0 G, 100 G, 300 G and 500 G) using MURaM, a 3D radiation-magnetohydrodynamics code. We show synthetic spectra and contrasts from the UV (300 nm) to the IR (10 000 nm) calculated using the ATLAS9 radiative transfer code. The calculations are performed for nine viewing angles to characterise the facular radiation across the disc. The brightness contrasts of magnetic regions are found to change significantly across spectral type, wavelength and magnetic field strength, leading to the conclusion that accurate contrasts cannot be found by scaling solar values. This is due to features of different size, apparent structure and spectral brightness emerging in the presence of a given magnetic field for different spectral types.
No abstract
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