arXiv subjects

Laurent Gizon

Publications and source records attributed to Laurent Gizon.

At least 109 records · Page 6Linked to original sources

arXiv2017

Comparison of acoustic travel-time measurement of solar meridional circulation from SDO/HMI and SOHO/MDI

Time-distance helioseismology is one of the primary tools for studying the solar meridional circulation. However, travel-time measurements of the subsurface meridional flow suffer from a variety of systematic errors, such as a center-to-limb variation and an offset due to the P-angle uncertainty of solar images. Here we apply the time-distance technique to contemporaneous medium-degree Dopplergrams produced by SOHO/MDI and SDO/HMI to obtain the travel-time difference caused by meridional circulation throughout the solar convection zone. The P-angle offset in MDI images is measured by cross-correlating MDI and HMI images. The travel-time measurements in the south-north and east-west directions are averaged over the same observation period for the two data sets and then compared to examine the consistency of MDI and HMI travel times after correcting the systematic errors. The offsets in the south-north travel-time difference from MDI data induced by the P-angle error gradually diminish with increasing travel distance. However, these offsets become noisy for travel distances corresponding to waves that reach the base of the convection zone. This suggests that a careful treatment of the P-angle problem is required when studying a deep meridional flow. After correcting the P-angle and the removal of the center-to-limb effect, the travel-time measurements from MDI and HMI are consistent within the error bars for meridional circulation covering the entire convection zone. The fluctuations observed in both data sets are highly correlated and thus indicate their solar origin rather than an instrumental origin. Although our results demonstrate that the ad hoc correction is capable of reducing the wide discrepancy in the travel-time measurements from MDI and HMI, we cannot exclude the possibility that there exist other systematic effects acting on the two data sets in the same way.

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arXiv2016

The amplitude of the cross-covariance function of solar oscillations as a diagnostic tool for wave attenuation and geometrical spreading

Context. In time-distance helioseismology, wave travel times are measured from the two-point cross-covariance function of solar oscillations and are used to image the solar convection zone in three dimensions. There is, however, also information in the amplitude of the cross-covariance function, for example about seismic wave attenuation. Aims. Here we develop a convenient procedure to measure the amplitude of the cross-covariance function of solar oscillations. Methods. In this procedure, the amplitude of the cross-covariance function is linearly related to the cross-covariance function and can be measured even for high levels of noise. Results. As an example application, we measure the amplitude perturbations of the seismic waves that propagate through the sunspot in active region NOAA 9787. We can recover the amplitude variations due to the scattering and attenuation of the waves by the sunspot and associated finite-wavelength effects. Conclusions. The proposed definition of cross-covariance amplitude is robust to noise, can be used to relate measured amplitudes to 3D perturbations in the solar interior under the Born approximation, and will provide independent information from the travel times.

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arXiv2016

Shape of a slowly rotating star measured by asteroseismology

Stars are not perfectly spherically symmetric. They are deformed by rotation and magnetic fields. Until now, the study of stellar shapes has only been possible with optical interferometry for a few of the fastest-rotating nearby stars. We report an asteroseismic measurement, with much better precision than interferometry, of the asphericity of an A-type star with a rotation period of 100 days. Using the fact that different modes of oscillation probe different stellar latitudes, we infer a tiny but significant flattening of the star's shape of $ΔR/R = (1.8 \pm 0.6) \times 10^{-6}$. For a stellar radius $R$ that is $2.24$ times the solar radius, the difference in radius between the equator and the poles is $ΔR = 3 \pm 1$ km. Because the observed $ΔR/R$ is only one-third of the expected rotational oblateness, we conjecture the presence of a weak magnetic field on a star that does not have an extended convective envelope. This calls to question the origin of the magnetic field.

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arXiv2016

Computational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows

Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is `embarrassingly parallel', with each frequency and each azimuthal order solved independently on a computer cluster. We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.

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arXiv2016

A Tale of Two Emergences: Sunrise II Observations of Emergence Sites in a Solar Active Region

In June 2013, the two scientific instruments onboard the second Sunrise mission witnessed, in detail, a small-scale magnetic flux emergence event as part of the birth of an active region. The Imaging Magnetograph Experiment (IMaX) recorded two small (~5 arcsec) emerging flux patches in the polarized filtergrams of a photospheric Fe I spectral line. Meanwhile, the Sunrise Filter Imager (SuFI) captured the highly dynamic chromospheric response to the magnetic fields pushing their way through the lower solar atmosphere. The serendipitous capture of this event offers a closer look at the inner workings of active region emergence sites. In particular, it reveals in meticulous detail how the rising magnetic fields interact with the granulation as they push through the Sun's surface, dragging photospheric plasma in their upward travel. The plasma that is burdening the rising field slides along the field lines, creating fast downflowing channels at the footpoints. The weight of this material anchors this field to the surface at semi-regular spatial intervals, shaping it in an undulatory fashion. Finally, magnetic reconnection enables the field to release itself from its photospheric anchors, allowing it to continue its voyage up to higher layers. This process releases energy that lights up the arch-filament systems and heats the surrounding chromosphere.

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arXiv2016

Solar-cycle variation of the rotational shear near the solar surface

Helioseismology has revealed that the angular velocity of the Sun increases with depth in the outermost 35 Mm of the Sun. Recently, we have shown that the logarithmic radial gradient ($\rm d\lnΩ/\rm d\ln r $) in the upper 10~Mm is close to $-1$ from the equator to $60^\circ$ latitude.We aim to measure the temporal variation of the rotational shear over solar cycle 23 and the rising phase of cycle 24 (1996-2015). We used f mode frequency splitting data spanning 1996 to 2011 from the Michelson Doppler Imager (MDI) and 2010 to 2015 from the Helioseismic Magnetic Imager (HMI). In a first for such studies, the f mode frequency splitting data were obtained from 360-day time series. We used the same method as in our previous work for measuring $\rm d\lnΩ/d\ln r $ from the equator to $80^\circ$ latitude in the outer 13~Mm of the Sun. Then, we calculated the variation of the gradient at annual cadence relative to the average over 1996 to 2015. We found the rotational shear at low latitudes ($0^\circ$ to $30^\circ$) to vary in-phase with the solar activity, varying by $\sim \pm 10$\% over the period 1996 to 2015. At high latitudes ($60^\circ$ to $80^\circ$), we found rotational shear to vary in anti-phase with the solar activity. By comparing the radial gradient obtained from the splittings of the 360-day and the corresponding 72-day time series of HMI and MDI data, we suggest that the splittings obtained from the 72-day HMI time series suffer from systematic errors. We provide a quantitative measurement of the temporal variation of the outer part of the near surface shear layer which may provide useful constraints on dynamo models and differential rotation theory.

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arXiv2016

A low upper limit on the subsurface rise speed of solar active regions

Magnetic field emerges at the surface of the Sun as sunspots and active regions. This process generates a poloidal magnetic field from a rising toroidal flux tube, it is a crucial but poorly understood aspect of the solar dynamo. The emergence of magnetic field is also important because it is a key driver of solar activity. We show that measurements of horizontal flows at the solar surface around emerging active regions, in combination with numerical simulations of solar magnetoconvection, can constrain the subsurface rise speed of emerging magnetic flux. The observed flows imply that the rise speed of the magnetic field is no larger than 150 m/s at a depth of 20 Mm, that is, well below the prediction of the (standard) thin flux tube model but in the range expected for convective velocities at this depth. We conclude that convective flows control the dynamics of rising flux tubes in the upper layers of the Sun and cannot be neglected in models of flux emergence.

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arXiv2016

Statistics of the two-point cross-covariance function of solar oscillations

Context: The cross-covariance of solar oscillations observed at pairs of points on the solar surface is a fundamental ingredient in time-distance helioseismology. Wave travel times are extracted from the cross-covariance function and are used to infer the physical conditions in the solar interior. Aims: Understanding the statistics of the two-point cross-covariance function is a necessary step towards optimizing the measurement of travel times. Methods: By modeling stochastic solar oscillations, we evaluate the variance of the cross-covariance function as function of time-lag and distance between the two points. Results: We show that the variance of the cross-covariance is independent of both time-lag and distance in the far field, i.e., when they are large compared to the coherence scales of the solar oscillations. Conclusions: The constant noise level for the cross-covariance means that the signal-to-noise ratio for the cross-covariance is proportional to the amplitude of the expectation value of the cross-covariance. This observation is important for planning data analysis efforts.

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arXiv2016

Sensitivity Kernels for Flows in Time-Distance Helioseismology: Extension to Spherical Geometry

We extend an existing Born approximation method for calculating the linear sensitivity of helioseismic travel times to flows from Cartesian to spherical geometry. This development is necessary for using the Born approximation for inferring large-scale flows in the deep solar interior. In a first sanity check, we compare two $f-$mode kernels from our spherical method and from an existing Cartesian method. The horizontal and total integrals agree to within 0.3 %. As a second consistency test, we consider a uniformly rotating Sun and a travel distance of 42 degrees. The analytical travel-time difference agrees with the forward-modelled travel-time difference to within 2 %. In addition, we evaluate the impact of different choices of filter functions on the kernels for a meridional travel distance of 42 degrees. For all filters, the sensitivity is found to be distributed over a large fraction of the convection zone. We show that the kernels depend on the filter function employed in the data analysis process. If modes of higher harmonic degree ($90\lesssim l \lesssim 170$) are permitted, a noisy pattern of a spatial scale corresponding to $l\approx 260$ appears near the surface. When mainly low-degree modes are used ($l\lesssim70$), the sensitivity is concentrated in the deepest regions and it visually resembles a ray-path-like structure. Among the different low-degree filters used, we find the kernel for phase-speed filtered measurements to be best localized in depth.

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arXiv2015

Asteroseismic inversions for radial differential rotation of Sun-like stars: ensemble fits

Radial differential rotation is an important parameter for stellar dynamo theory and for understanding angular momentum transport. We investigate the potential of using a large number of similar stars simultaneously to constrain their average radial differential rotation gradient: we call this 'ensemble fitting'. We use a range of stellar models along the main sequence, each with a synthetic rotation profile. The rotation profiles are step functions with a step of -350 nHz, which is located at the base of the convection zone. These models are used to compute the rotational splittings of the p modes and to model their uncertainties. We then fit an ensemble of stars to infer the average step size. All the uncertainties on the inferred step size for individual stars are of the order 1 micro Hz. Using 15 stellar models in an ensemble fit, we show that the uncertainty on the average step size is reduced to less than the input step size, which allows us to constrain the sign of the radial differential rotation. We show that a solar-like step size (approximately 30 nHz) can be constrained by an ensemble fit of thousands of main-sequence stars. Observing the number of stars required to successfully exploit the ensemble fitting method will be possible with future asteroseismology missions, such as PLATO. We demonstrate the potential of ensemble fitting by showing that any systematic differences in the average step size between F, G, and K-type stars larger than 100 nHz can be detected.

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arXiv2015

Data compression for local correlation tracking of solar granulation

Context. Several upcoming and proposed space missions, such as Solar Orbiter, will be limited in telemetry and thus require data compression. Aims. We test the impact of data compression on local correlation tracking (LCT) of time-series of continuum intensity images. We evaluate the effect of several lossy compression methods (quantization, JPEG compression, and a reduced number of continuum images) on measurements of solar differential rotation with LCT. Methods. We apply the different compression methods to tracked and remapped continuum intensity maps obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We derive 2D vector velocities using the local correlation tracking code FLCT and determine the additional bias and noise introduced by compression to differential rotation. Results. We find that probing differential rotation with LCT is very robust to lossy data compression when using quantization. Our results are severely affected by systematic errors of the LCT method and the HMI instrument. The sensitivity of LCT to systematic errors is a concern for Solar Orbiter.

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arXiv2015

Interpretation of Helioseismic Travel Times - Sensitivity to Sound Speed, Pressure, Density, and Flows

Time-distance helioseismology uses cross-covariances of wave motions on the solar surface to determine the travel times of wave packets moving from one surface location to another. We review the methodology to interpret travel-time measurements in terms of small, localized perturbations to a horizontally homogeneous reference solar model. Using the first Born approximation, we derive and compute 3D travel-time sensitivity (Fréchet) kernels for perturbations in sound-speed, density, pressure, and vector flows. While kernels for sound speed and flows had been computed previously, here we extend the calculation to kernels for density and pressure, hence providing a complete description of the effects of solar dynamics and structure on travel times. We treat three thermodynamic quantities as independent and do not assume hydrostatic equilibrium. We present a convenient approach to computing damped Green's functions using a normal-mode summation. The Green's function must be computed on a wavenumber grid that has sufficient resolution to resolve the longest lived modes. The typical kernel calculations used in this paper are computer intensive and require on the order of 600 CPU hours per kernel. Kernels are validated by computing the travel-time perturbation that results from horizontally-invariant perturbations using two independent approaches. At fixed sound-speed, the density and pressure kernels are approximately related through a negative multiplicative factor, therefore implying that perturbations in density and pressure are difficult to disentangle. Mean travel-times are not only sensitive to sound-speed, density and pressure perturbations, but also to flows, especially vertical flows. Accurate sensitivity kernels are needed to interpret complex flow patterns such as convection.

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arXiv2015

Rotation, differential rotation, and gyrochronology of active Kepler stars

The high-precision photometry from the CoRoT and Kepler satellites has led to measurements of surface rotation periods for tens of thousands of stars. Our main goal is to derive ages of thousands of field stars using consistent rotation period measurements in different gyrochronology relations. Multiple rotation periods are interpreted as surface differential rotation (DR). We re-analyze the sample of 24,124 Kepler stars from Reinhold et al. (2013) using different approaches based on the Lomb-Scargle periodogram. Each quarter (Q1-Q14) is treated individually using a prewhitening approach. Additionally, the full time series, and different segments thereof are analyzed. For more than 18,500 stars our results are consistent with the rotation periods from McQuillan et al. (2014). Thereof, more than 12,300 stars show multiple significant peaks, which we interpret as DR. Gyrochronology ages between 100 Myr and 10 Gyr were derived for more than 17,000 stars using different gyrochronology relations. We find a bimodal age distribution for Teff between 3200-4700 K. The derived ages reveal an empirical activity-age relation using photometric variability as stellar activity proxy. Additionally, we found 1079 stars with extremely stable (mostly short) periods. Half of these periods may be associated with rotation stabilized by non-eclipsing companions, the other half might be due to pulsations. The derived gyrochronology ages are well constrained since more than 93.0 % of the stars seem to be younger than the Sun where calibration is most reliable. Explaining the bimodality in the age distribution is challenging, and limits accurate stellar age predictions. The existence of cool stars with almost constant rotation period over more than three years of observation might be explained by synchronization with stellar companions, or a dynamo mechanism keeping the spot configurations extremely stable.

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arXiv2015

Simulating acoustic waves in spotted stars

Acoustic modes of oscillation are affected by stellar activity, however it is unclear how starspots contribute to these changes. Here we investigate the nonmagnetic effects of starspots on global modes with angular degree $\ell \leq 2$ in highly active stars, and characterize the spot seismic signature on synthetic light curves. We perform 3D time-domain simulations of linear acoustic waves to study their interaction with a model starspot. We model the spot as a 3D change in the sound speed stratification with respect to a convectively stable stellar background, built from solar Model S. We perform a parametric study by considering different depths and perturbation amplitudes. Exact numerical simulations allow the investigation of the wavefield-spot interaction beyond first order perturbation theory. The interaction of the axisymmetric modes with the starspot is strongly nonlinear. As mode frequency increases, the frequency shifts for radial modes exceed the value predicted by linear theory, while the shifts for the $\ell=2, m=0$ modes are smaller than predicted by linear theory, with avoided-crossing-like patterns forming between the $m=0$ and $m=1$ mode frequencies. The nonlinear behavior increases with increasing spot amplitude and/or decreasing depth. Linear theory still reproduces the correct shifts for nonaxisymmetric modes. In the nonlinear regime the mode eigenfunctions are not pure spherical harmonics, but rather a mixture of different spherical harmonics. This mode mixing, together with the frequency changes, may lead to misidentification of the modes in the observed acoustic power spectra.

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arXiv2015

Seismic Sounding of Convection in the Sun

Our Sun, primarily composed of ionized hydrogen and helium, has a surface temperature of 5777~K and a radius $R_\odot \approx 696,000$ km. In the outer $R_\odot/3$, energy transport is accomplished primarily by convection. Using typical convective velocities $u\sim100\,\rm{m\,s^{-1}}$ and kinematic viscosities of order $10^{-4}$ m$^{2}$s$^{-1}$, we obtain a Reynolds number $Re \sim 10^{14}$. Convection is thus turbulent, causing a vast range of scales to be excited. The Prandtl number, $Pr$, of the convecting fluid is very low, of order $10^{-7}$\,--\,$10^{-4}$, so that the Rayleigh number ($\sim Re^2 Pr$) is on the order of $10^{21}\,-\,10^{24}$. Solar convection thus lies in extraordinary regime of dynamical parameters, highly untypical of fluid flows on Earth. Convective processes in the Sun drive global fluid circulations and magnetic fields, which in turn affect its visible outer layers ("solar activity") and, more broadly, the heliosphere ("space weather"). The precise determination of the depth of solar convection zone, departures from adiabaticity of the temperature gradient, and the internal rotation rate as a function of latitude and depth are among the seminal contributions of helioseismology towards understanding convection in the Sun. Contemporary helioseismology, which is focused on inferring the properties of three-dimensional convective features, suggests that transport velocities are substantially smaller than theoretical predictions. Furthermore, helioseismology provides important constraints on the anisotropic Reynolds stresses that control the global dynamics of the solar convection zone. This review discusses the state of our understanding of convection in the Sun, with a focus on helioseismic diagnostics. We present our considerations with the interests of fluid dynamicists in mind.

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arXiv2015

The EChO science case

The discovery of almost 2000 exoplanets has revealed an unexpectedly diverse planet population. Observations to date have shown that our Solar System is certainly not representative of the general population of planets in our Milky Way. The key science questions that urgently need addressing are therefore: What are exoplanets made of? Why are planets as they are? What causes the exceptional diversity observed as compared to the Solar System? EChO (Exoplanet Characterisation Observatory) has been designed as a dedicated survey mission for transit and eclipse spectroscopy capable of observing a large and diverse planet sample within its four-year mission lifetime. EChO can target the atmospheres of super-Earths, Neptune-like, and Jupiter-like planets, in the very hot to temperate zones (planet temperatures of 300K-3000K) of F to M-type host stars. Over the next ten years, several new ground- and space-based transit surveys will come on-line (e.g. NGTS, CHEOPS, TESS, PLATO), which will specifically focus on finding bright, nearby systems. The current rapid rate of discovery would allow the target list to be further optimised in the years prior to EChO's launch and enable the atmospheric characterisation of hundreds of planets. Placing the satellite at L2 provides a cold and stable thermal environment, as well as a large field of regard to allow efficient time-critical observation of targets randomly distributed over the sky. A 1m class telescope is sufficiently large to achieve the necessary spectro-photometric precision. The spectral coverage (0.5-11 micron, goal 16 micron) and SNR to be achieved by EChO, thanks to its high stability and dedicated design, would enable a very accurate measurement of the atmospheric composition and structure of hundreds of exoplanets.

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arXiv2015

Time-distance helioseismology: A new averaging scheme for measuring flow vorticity

Time-distance helioseismology provides information about vector flows in the near-surface layers of the Sun by measuring wave travel times between points on the solar surface. Specific spatial averages of travel times have been proposed for distinguishing between flows in the east-west and north-south directions and measuring the horizontal divergence of the flows. No specific measurement technique has, however, been developed to measure flow vorticity. Here we propose a new measurement technique tailored to measuring the vertical component of vorticity. Fluid vorticity is a fundamental property of solar convection zone dynamics and of rotating turbulent convection in particular. The method consists of measuring the travel time of waves along a closed contour on the solar surface in order to approximate the circulation of the flow along this contour. Vertical vorticity is related to the difference between clockwise and counter-clockwise travel times. We applied the method to characterize the vortical motions of solar convection using helioseismic data from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) and from the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). Away from the equator, a clear correlation between vertical vorticity and horizontal divergence is detected. Horizontal outflows are associated with negative vorticity in the northern hemisphere and positive vorticity in the southern hemisphere. The signal is much stronger for HMI than for MDI observations. We characterize the spatial power spectrum of the signal by comparison with a noise model. Vertical vorticity at horizontal wavenumbers below 250/R_Sun can be probed with this helioseismic technique.

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arXiv2014

Image compression in local helioseismology

Context. Several upcoming helioseismology space missions are very limited in telemetry and will have to perform extensive data compression. This requires the development of new methods of data compression. Aims. We give an overview of the influence of lossy data compression on local helioseismology. We investigate the effects of several lossy compression methods (quantization, JPEG compression, and smoothing and subsampling) on power spectra and time-distance measurements of supergranulation flows at disk center. Methods. We applied different compression methods to tracked and remapped Dopplergrams obtained by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory. We determined the signal-to-noise ratio of the travel times computed from the compressed data as a function of the compression efficiency. Results. The basic helioseismic measurements that we consider are very robust to lossy data compression. Even if only the sign of the velocity is used, time-distance helioseismology is still possible. We achieve the best results by applying JPEG compression on spatially subsampled data. However, our conclusions are only valid for supergranulation flows at disk center and may not be valid for all helioseismology applications.

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