arXiv subjects

L. Gizon

Publications and source records attributed to L. Gizon.

At least 55 records · Page 3Linked to original sources

arXiv2021

Radiative transfer with opacity distribution functions: Application to narrow band filters

Modelling of stellar radiative intensities in various spectral pass-bands plays an important role in stellar physics. At the same time the direct calculations of the high-resolution spectrum and then integrating it over the given spectral pass-band is computationally demanding due to the vast number of atomic and molecular lines. This is particularly so when employing three-dimensional (3D) models of stellar atmospheres. To accelerate the calculations, one can employ approximate methods, e.g., the use of Opacity Distribution Functions (ODFs). Generally, ODFs provide a good approximation of traditional spectral synthesis i.e., computation of intensities through filters with strictly rectangular transmission function. However, their performance strongly deteriorates when the filter transmission noticeably changes within its pass-band, which is the case for almost all filters routinely used in stellar physics. In this context, the aims of this paper are a) to generalize the ODFs method for calculating intensities through filters with arbitrary transmission functions; b) to study the performance of the standard and generalized ODFs methods for calculating intensities emergent from 3D models of stellar atmosphere. For this purpose we use the newly-developed MPS-ATLAS radiative transfer code to compute intensities emergent 3D cubes simulated with the radiative magnetohydrodynamics code MURaM. The calculations are performed in the 1.5D regime, i.e., along many parallel rays passing through the simulated cube. We demonstrate that generalized ODFs method allows accurate and fast syntheses of spectral intensities and their centre-to-limb variations.

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arXiv2020

Power spectrum of turbulent convection in the solar photosphere

The solar photosphere provides us with a laboratory for understanding turbulence in a layer where the fundamental processes of transport vary rapidly and a strongly superadiabatic region lies very closely to a subadiabatic layer. Our tools for probing the turbulence are high-resolution spectropolarimetric observations such as have recently been obtained with the two sunrise missions, and numerical simulations. Our aim is to study photospheric turbulence with the help of Fourier power spectra that we compute from observations and simulations. We also attempt to explain some properties of the photospheric overshooting flow with the help of its governing equations and simulations. We find that quiet-Sun observations and smeared simulations exhibit a power-law behavior in the subgranular range of their Doppler velocity power spectra with an index of$~\approx -2$. The unsmeared simulations exhibit a power-law index of$~\approx -2.25$. The smearing considerably reduces the extent of the power-law-like portion of the spectra. Therefore, the limited spatial resolution in some observations might eventually result in larger uncertainties in the estimation of the power-law indices. The simulated vertical velocity power spectra as a function of height show a rapid change in the power-law index from the solar surface to $300$~km above it. A scale-dependent transport of the vertical momentum occurs. At smaller scales, the vertical momentum is more efficiently transported sideways than at larger scales. This results in less vertical velocity power transported upward at small scales than at larger scales and produces a progressively steeper vertical velocity power law below $180$ km. Above this height, the gravity work progressively gains importance at all scales, making the atmosphere progressively more hydrostatic and resulting in a gradually less steep power law.

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arXiv2020

Acoustic wave propagation through solar granulation: Validity of effective-medium theories, coda waves

Context. The frequencies, lifetimes, and eigenfunctions of solar acoustic waves are affected by turbulent convection, which is random in space and in time. Since the correlation time of solar granulation and the periods of acoustic waves ($\sim$5 min) are similar, the medium in which the waves propagate cannot a priori be assumed to be time independent. Aims. We compare various effective-medium solutions with numerical solutions in order to identify the approximations that can be used in helioseismology. For the sake of simplicity, the medium is one dimensional. Methods. We consider the Keller approximation, the second-order Born approximation, and spatial homogenization to obtain theoretical values for the effective wave speed and attenuation (averaged over the realizations of the medium). Numerically, we computed the first and second statistical moments of the wave field over many thousands of realizations of the medium (finite-amplitude sound-speed perturbations are limited to a 30 Mm band and have a zero mean). Results. The effective wave speed is reduced for both the theories and the simulations. The attenuation of the coherent wave field and the wave speed are best described by the Keller theory. The numerical simulations reveal the presence of coda waves, trailing the coherent wave packet. These late arrival waves are due to multiple scattering and are easily seen in the second moment of the wave field. Conclusions. We find that the effective wave speed can be calculated, numerically and theoretically, using a single snapshot of the random medium (frozen medium); however, the attenuation is underestimated in the frozen medium compared to the time-dependent medium. Multiple scattering cannot be ignored when modeling acoustic wave propagation through solar granulation.

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arXiv2020

The Solar Orbiter Science Activity Plan: translating solar and heliospheric physics questions into action

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate? (2) How do solar transients drive heliospheric variability? (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere? (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission's science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit's science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans (SOOPs), resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime.

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arXiv2020

Effect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorial $β$ plane

Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near $20^\circ$-$30^\circ$, and decrease at higher latitudes. We search for an explanation that takes into account solar latitudinal differential rotation. In the equatorial $β$ plane, we study the propagation of linear Rossby waves (phase speed $c <0$) in a parabolic zonal shear flow, $U = - \overline{U}\ ξ^2<0$, where $\overline{U} = 244$ m/s and $ξ$ is the sine of latitude. In the inviscid case, the eigenvalue spectrum is real and continuous and the velocity stream functions are singular at the critical latitudes where $U = c$. We add eddy viscosity in the problem to account for wave attenuation. In the viscous case, the stream functions are solution of a fourth-order modified Orr-Sommerfeld equation. Eigenvalues are complex and discrete. For reasonable values of the eddy viscosity corresponding to supergranular scales and above (Reynolds number $100 \le Re \le 700$), all modes are stable. At fixed longitudinal wavenumber, the least damped mode is a symmetric mode with a real frequency close to that of the classical Rossby mode, which we call the R mode. For $Re \approx 300$, the attenuation and the real part of the eigenfunction is in qualitative agreement with the observations (unlike the imaginary part of the eigenfunction, which has a larger amplitude in the model. Conclusion: Each longitudinal wavenumber is associated with a latitudinally symmetric R mode trapped at low latitudes by solar differential rotation. In the viscous model, R modes transport significant angular momentum from the dissipation layers towards the equator.

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arXiv2020

Predicting frequency changes of global-scale solar Rossby modes due to solar cycle changes in internal rotation

Context. Large-scale equatorial Rossby modes have been observed on the Sun over the last two solar cycles. Aims. We investigate the impact of the time-varying zonal flows on the frequencies of Rossby modes. Methods. A first-order perturbation theory approach is used to obtain an expression for the expected shift in the mode frequencies due to perturbations in the internal rotation rate. Results. Using the time-varying rotation from helioseismic inversions we predict the changes in Rossby mode frequencies with azimuthal orders from m = 1 to m = 15 over the last two solar cycles. The peak-to-peak frequency change is less than 1 nHz for the m = 1 mode, grows with m, and reaches 25 nHz for m = 15. Conclusions. Given the observational uncertainties on mode frequencies due to the finite mode lifetimes, we find that the predicted frequency shifts are near the limit of detectability.

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arXiv2020

Rossby modes in slowly rotating stars: depth dependence in distorted polytropes with uniform rotation

Large-scale Rossby waves have recently been discovered from measurements of horizontal surface and near-surface solar flows (Löptien at al. 2018). We are interested in understanding why only the sectoral modes are seen in the observations and also in modelling the radial structure of the observed modes. To do so, we characterise here the radial eigenfunctions of r modes for slowly-rotating polytropes in uniform rotation. We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density, r modes can only exist for $\ell=m$ spherical harmonics in the inviscid case, and we compute their depth dependence and frequencies to leading order. For quasi-adiabatic stratification the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales as $r^m$. For all r modes except the zero radial order sectoral ones, non-adiabatic stratification plays a crucial role in the radial force balance. The lack of quasi-toroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the statement that the system needs to be in both horizontal and radial force balance. In the absence of super- or subadiabatic stratification and viscosity, both the horizontal and radial force balances independently determine the pressure perturbation. The only quasi-toroidal cases in which the two determinations of the pressure perturbation are consistent are the special cases where $\ell=m$, and the horizontal displacement scales with $r^m$.

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arXiv2020

Exploring the latitude and depth dependence of solar Rossby waves using ring-diagram analysis

Global-scale Rossby waves have recently been unambiguously identified on the Sun. Here we study the latitude and depth dependence of the Rossby wave eigenfunctions. By applying helioseismic ring-diagram analysis and granulation tracking to SDO/HMI observations, we compute maps of the radial vorticity of flows in the upper solar convection zone (down to depths of more than $16$ Mm). We use a Fourier transform in longitude to separate the different azimuthal orders m in the range $3 \le m \le 15$. At each $m$ we obtain the phase and amplitude of the Rossby waves as a function of depth using the helioseismic data. At each $m$ we also measure the latitude dependence of the eigenfunctions by calculating the covariance between the equator and other latitudes. We then study the horizontal and radial dependences of the radial vorticity eigenfunctions. The horizontal eigenfunctions are complex. As observed previously, the real part peaks at the equator and switches sign near $\pm 30^\circ$, thus the eigenfunctions show significant non-sectoral contributions. The imaginary part is smaller than the real part. The phase of the radial eigenfunctions varies by only roughly $\pm 5^\circ$ over the top $15$ Mm. The amplitude of the radial eigenfunctions decreases by about $10\%$ from the surface down to $8$ Mm (the region where ring-diagram analysis is most reliable, as seen by comparing with the rotation rate measured by global-mode seismology). The radial dependence of the radial vorticity eigenfunctions deduced from ring-diagram analysis is consistent with a power-law down to $8$ Mm and is unreliable at larger depths. However, the observations provide only weak constraints on the power-law exponents. For the real part, the latitude dependence of the eigenfunctions is consistent with previous work (using granulation tracking). The imaginary part is smaller than the real part but significantly nonzero.

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arXiv2019

The Polarimetric and Helioseismic Imager on Solar Orbiter

This paper describes the Polarimetric and Helioseismic Imager on the Solar Orbiter mission (SO/PHI), the first magnetograph and helioseismology instrument to observe the Sun from outside the Sun-Earth line. It is the key instrument meant to address the top-level science question: How does the solar dynamo work and drive connections between the Sun and the heliosphere? SO/PHI will also play an important role in answering the other top-level science questions of Solar Orbiter, as well as hosting the potential of a rich return in further science. SO/PHI measures the Zeeman effect and the Doppler shift in the FeI 617.3nm spectral line. To this end, the instrument carries out narrow-band imaging spectro-polarimetry using a tunable LiNbO_3 Fabry-Perot etalon, while the polarisation modulation is done with liquid crystal variable retarders (LCVRs). The line and the nearby continuum are sampled at six wavelength points and the data are recorded by a 2kx2k CMOS detector. To save valuable telemetry, the raw data are reduced on board, including being inverted under the assumption of a Milne-Eddington atmosphere, although simpler reduction methods are also available on board. SO/PHI is composed of two telescopes; one, the Full Disc Telescope (FDT), covers the full solar disc at all phases of the orbit, while the other, the High Resolution Telescope (HRT), can resolve structures as small as 200km on the Sun at closest perihelion. The high heat load generated through proximity to the Sun is greatly reduced by the multilayer-coated entrance windows to the two telescopes that allow less than 4% of the total sunlight to enter the instrument, most of it in a narrow wavelength band around the chosen spectral line.

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arXiv2019

Latitudinal differential rotation in the solar analogues 16 Cyg A and B

Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT and Kepler space missions. The latter is now yielding the first measurements of latitudinal differential rotation obtained directly from oscillation frequencies. Differential rotation is a fundamental mechanism of the stellar dynamo effect. Our goal is to measure the amount of differential rotation in the solar analogues 16 Cyg A and B, which are the components of a binary system. These stars are the brightest observed by Kepler and have therefore been extensively observed, with exquisite precision on their oscillation frequencies. We modelled the acoustic power spectrum of 16 Cyg A and B using a model that takes into account the contribution of differential rotation to the rotational frequency splitting. The estimation was carried out in a Bayesian setting. We then inverted these results to obtain the rotation profile of both stars under the assumption of a solar-like functional form. We observe that the magnitude of latitudinal differential rotation has a strong chance of being solar-like for both stars, their rotation rates being higher at the equator than at the pole. The measured latitudinal differential rotation, defined as the difference of rotation rate between the equator and the pole, is $320\pm269$ nHz and $440^{+363}_{-383}$ nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are $535\pm75$ nHz and $565_{-129}^{+150}$ nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry. We present the first conclusive measurement of latitudinal differential rotation for solar analogues. Their rotational profiles are very close to those of the Sun. These results depend weakly on the uncertainties of the stellar parameters.

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arXiv2019

Sectoral r modes and periodic RV variations of Sun-like stars

Radial velocity (RV) measurements are used to search for planets orbiting late-type main-sequence stars and confirm the transiting planets. The most advanced spectrometers are approaching a precision of $\sim 10$ cm/s that implies the need to identify and correct for all possible sources of RV oscillations intrinsic to the star down to this level and possibly beyond. The recent discovery of global-scale equatorial Rossby waves in the Sun, also called r modes, prompted us to investigate their possible signature in stellar RV measurements. R modes are toroidal modes of oscillation whose restoring force is the Coriolis force and propagate in the retrograde direction in a frame that corotates with the star. The solar r modes with azimuthal orders $3 \leq m \lesssim 15$ were identified unambiguously because of their dispersion relation and their long e-folding lifetimes of hundreds of days. Here we simulate the RV oscillations produced by sectoral r modes with $2 \leq m \leq 5$ assuming a stellar rotation period of 25.54 days and a maximum amplitude of the surface velocity of each mode of 2 m/s. This amplitude is representative of the solar measurements, except for the $m=2$ mode which has not yet been observed. Sectoral r modes with azimuthal orders $m=2$ and $3$ would produce RV oscillations with amplitudes of 76.4 and 19.6 cm/s and periods of 19.16 and 10.22 days, respectively, for a star with an inclination of the rotation axis $i=60^{\circ}$. Therefore, they may produce rather sharp peaks in the Fourier spectrum of the radial velocity time series that could lead to spurious planetary detections. Sectoral r~modes may represent a source of confusion in the case of slowly rotating inactive stars that are preferential targets for RV planet search. The main limitation of the present investigation is the lack of observational constraint on the amplitude of the $m=2$ mode on the Sun.

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arXiv2018

Starspot rotation rates vs. activity cycle phase: Butterfly diagrams of Kepler stars are unlike the Sun's

During the solar magnetic activity cycle the emergence latitudes of sunspots change, leading to the well-known butterfly diagram. This phenomenon is poorly understood for other stars as starspot latitudes are generally unknown. The related changes in starspot rotation rates caused by latitudinal differential rotation can however be measured. Using the set of 3093 Kepler stars with activity cycles identified by Reinhold et al. (2017), we aim to study the temporal change in starspot rotation rates over magnetic activity cycles, and how this relates to the activity level, mean rotation rate, and effective temperature of the star. We measure the photometric variability as a proxy for the magnetic activity and the spot rotation rate in each quarter over the duration of the Kepler mission. We phase-fold these measurements with the cycle period. We perform averages over stars with comparable mean rotation rates and effective temperature at fixed activity-cycle phases. We detect a clear correlation between the variation of activity level and the variation of the starspot rotation rate. The sign and amplitude of this correlation depends on the mean stellar rotation and, to a lesser extent, on the effective temperature. For slowly rotating stars (with periods between 15-28 days) the starspot rotation rates are clearly anti-correlated with the level of activity during the activity cycles. A transition is seen at periods of 10-15 days, where stars with effective temperature above 4200K instead show positive correlation. Our results can be interpreted in terms of a stellar "butterfly diagram", but these appear different from the Sun's as the starspot rotation rates are either in phase or anti-phase with the activity level. Alternatively, the activity cycles seen by Kepler are short (around 2.5 years) and may therefore be secondary cycles, perhaps analogous to the solar quasi-biennial oscillations.

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arXiv2018

Butterfly diagram of a Sun-like star observed using asteroseismology

Stellar magnetic fields are poorly understood but are known to be important for stellar evolution and exoplanet habitability. They drive stellar activity, which is the main observational constraint on theoretical models for magnetic field generation and evolution. Starspots are the main manifestation of the magnetic fields at the stellar surface. In this study we measure the variation of their latitude with time, called a butterfly diagram in the solar case, for the solar analogue HD 173701 (KIC 8006161). To that effect, we use Kepler data, to combine starspot rotation rates at different epochs and the asteroseismically determined latitudinal variation of the stellar rotation rates. We observe a clear variation of the latitude of the starspots. It is the first time such a diagram is constructed using asteroseismic data.

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arXiv2018

Asteroseismic detection of latitudinal differential rotation in 13 Sun-like stars

The differentially rotating outer layers of stars are thought to play a role in driving their magnetic activity, but the underlying mechanisms that generate and sustain differential rotation are poorly understood. We report the measurement of latitudinal differential rotation in the convection zones of 40 Sun-like stars using asteroseismology. For the most significant detections, the stars' equators rotate approximately twice as fast as their mid-latitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations.

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arXiv2018

Probing sunspots with two-skip time-distance helioseismology

Previous helioseismology of sunspots has been sensitive to both the structural and magnetic aspects of sunspot structure. We aim to develop a technique that is insensitive to the magnetic component so the two aspects can be more readily separated. We study waves reflected almost vertically from the underside of a sunspot. Time-distance helioseismology was used to measure travel times for the waves. Ray theory and a detailed sunspot model were used to calculate travel times for comparison. It is shown that these large distance waves are insensitive to the magnetic field in the sunspot. The largest travel time differences for any solar phenomena are observed. With sufficient modeling effort, these should lead to better understanding of sunspot structure.

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arXiv2018

Evolution and wave-like properties of the average solar supergranule

Solar supergranulation presents us with many mysteries. For example, previous studies in spectral space found that supergranulation has wave-like properties. Here we study, in real space, the wave-like evolution of the average supergranule over a range of spatial scales (from 10 to 80 Mm). We complement this by characterizing the evolution of the associated network magnetic field. We use one year of data from the Helioseismic and Magnetic Imager (HMI) to measure horizontal near-surface flows near the solar equator by applying time-distance helioseismology on Dopplergrams and granulation tracking on intensity images. The average supergranule outflow (or inflow) is constructed by averaging over 10000 individual outflows (or inflows). The contemporaneous evolution of the magnetic field is studied with HMI line-of-sight observations. We confirm and extend previous measurements of the supergranular wave dispersion relation to angular wavenumbers in the range 50 120. In real space, larger supergranules undergo oscillations with longer periods and lifetimes than smaller cells. We find excellent agreement between TD and LCT and obtain wave properties that are independent of the tracking rate. The observed network magnetic field follows the oscillations of the supergranular flows with a six-hour time lag. This behavior can be explained by computing the motions of corks carried by the supergranular flows. Signatures of supergranular waves in surface horizontal flows near the solar equator can be observed in real space. These oscillatory flows control the evolution of the network magnetic field, in particular they explain the recently discovered east-west anisotropy of the magnetic field around the average supergranule. Background flow measurements that we obtain from Doppler frequency shifts do not favor shallow models of supergranulation.

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arXiv2018

Asymmetry of line profiles of stellar oscillations measured by Kepler for ensembles of solar-like oscillators: impact on mode frequencies and dependence on effective temperature

Oscillation properties are usually measured by fitting symmetric Lorentzian profiles to the power spectra of Sun-like stars. However the line profiles of solar oscillations have been observed to be asymmetrical for the Sun. The physical origin of this line asymmetry is not fully understood, although it should depend on the depth dependence of the source of wave excitation (convective turbulence) and details of the observable (velocity or intensity). For oscillations of the Sun, it has been shown that neglecting the asymmetry leads to systematic errors in the frequency determination. This could subsequently affects the results of seismic inferences of the solar internal structure. Using light curves from the {\it Kepler} spacecraft we have measured mode asymmetries in 43 stars. We confirm that neglecting the asymmetry leads to systematic errors that can exceed the $1σ$ confidence intervals for seismic observations longer than one year. Therefore, the application of an asymmetric Lorentzian profile is to be favoured to improve the accuracy of the internal stellar structure and stellar fundamental parameters. We also show that the asymmetry changes sign between cool Sun-like stars and hotter stars. This provides the best constraints to date on the location of the excitation sources across the Hertzsprung-Russel diagram.

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arXiv2017

Maximum Entropy Limit of Small-scale Magnetic Field Fluctuations in the Quiet Sun

The observed magnetic field on the solar surface is characterized by a very complex spatial and temporal behavior. Although feature-tracking algorithms have allowed us to deepen our understanding of this behavior, subjectivity plays an important role in the identification and tracking of such features. In this paper, we continue studies Gorobets, A. Y., Borrero, J. M., & Berdyugina, S. 2016, ApJL, 825, L18 of the temporal stochasticity of the magnetic field on the solar surface without relying either on the concept of magnetic features or on subjective assumptions about their identification and interaction. We propose a data analysis method to quantify fluctuations of the line-of-sight magnetic field by means of reducing the temporal field's evolution to the regular Markov process. We build a representative model of fluctuations converging to the unique stationary (equilibrium) distribution in the long time limit with maximum entropy. We obtained different rates of convergence to the equilibrium at fixed noise cutoff for two sets of data. This indicates a strong influence of the data spatial resolution and mixing-polarity fluctuations on the relaxation process. The analysis is applied to observations of magnetic fields of the relatively quiet areas around an active region carried out during the second flight of the Sunrise/IMaX and quiet Sun areas at the disk center from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory satellite.

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