arXiv subjects

Laurent Gizon

Publications and source records attributed to Laurent Gizon.

At least 91 records · Page 5Linked to original sources

arXiv2019

An improved multi-ridge fitting method for ring-diagram helioseismic analysis

Context: There is a wide discrepancy in current estimates of the strength of convection flows in the solar interior obtained using different helioseismic methods applied to observations from SDO/HMI. The cause for these disparities is not known. Aims: As one step in the effort to resolve this discrepancy, we aim to characterize the multi-ridge fitting code for ring-diagram helioseismic analysis that is used to obtain flow estimates from local power spectra of solar oscillations. Methods: We updated the multi-ridge fitting code developed by Greer et al.(2014) to solve several problems we identified through our inspection of the code. In particular, we changed the merit function to account for the smoothing of the power spectra, model for the power spectrum, and noise estimates. We used Monte Carlo simulations to generate synthetic data and to characterize the noise and bias of the updated code by fitting these synthetic data. Results: The bias in the output fit parameters, apart from the parameter describing the amplitude of the p-mode resonances in the power spectrum, is below what can be measured from the Monte-Carlo simulations. The amplitude parameters are underestimated; this is a consequence of choosing to fit the logarithm of the averaged power. We defer fixing this problem as it is well understood and not significant for measuring flows in the solar interior. The scatter in the fit parameters from the Monte-Carlo simulations is well-modeled by the formal error estimates from the code. Conclusions: We document and demonstrate a reliable multi-ridge fitting method for ring-diagram analysis. The differences between the updated fitting results and the original results are less than one order of magnitude and therefore we suspect that the changes will not eliminate the aforementioned orders-of-magnitude discrepancy in the amplitude of convective flows in the solar interior.

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arXiv2019

Signature of solar g modes in first-order p-mode frequency shifts

Context. Solar gravity modes (g modes) are buoyancy waves trapped in the solar radiative zone that have been very difficult to detect at the surface. Solar g modes would complement solar pressure modes (p modes) in probing the central regions of the Sun, for example the core rotation rate. Aims. A detection of g modes using changes in the large frequency separation of p modes has recently been reported. However, it is unclear how p and g modes interact. The aim of this study is to evaluate to what extent g modes can perturb the frequencies of p modes. Methods. We computed the first-order perturbation to global p-mode frequencies due to a flow field and perturbations to solar structure caused by a g mode. We focused on long-period g modes and assumed that the g-mode perturbations are constant in time. The surface amplitude of g modes is assumed to be $1$ mm s$^{-1}$, which is close to the observational limit. Results. Gravity modes do perturb p-mode frequencies to first order if the harmonic degree of the g mode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupole p modes, all frequency shifts are smaller than $0.1$ nHz, or $2\times10^{-8}$ in relative numbers. This is because the relative perturbation to solar structure quantities caused by a g mode of realistic amplitude is of the order of $10^{-6}$ to $10^{-5}$. We find that structural changes dominate over advection. Surprisingly, the interaction of g and p modes takes place to a large part near the surface, where p modes spend most of their propagation times and g modes generate the largest relative changes to solar structure. Conclusions. It appears to be impossible to detect g modes solely through their signature in p-mode frequency shifts. Whether g modes leave a detectable signature in p-mode travel times under a given observational setup remains an open question.

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arXiv2019

Average motion of emerging solar active region polarities I: Two phases of emergence

Our goal is to constrain models of active region formation by tracking the average motion of active region polarity pairs as they emerge onto the surface. We measured the motion of the two main opposite polarities in 153 emerging active regions (EARs) using line-of-sight magnetic field observations from the Solar Dynamics Observatory Helioseismic Emerging Active Region (SDO/HEAR) survey (Schunker et al. 2016). We first measured the position of each of the polarities eight hours after emergence and tracked their location forwards and backwards in time. We find that, on average, the polarities emerge with an east-west orientation and the separation speed between the polarities increases. At about 0.1 days after emergence, the average separation speed reaches a peak value of 229 +/- 11 m/s, and then starts to decrease, and about 2.5 days after emergence the polarities stop separating. We also find that the separation and the separation speed in the east-west direction are systematically larger for active regions with higher flux. Our results reveal two phases of the emergence process defined by the rate of change of the separation speed as the polarities move apart. Phase 1 begins when the opposite polarity pairs first appear at the surface, with an east-west alignment and an increasing separation speed. We define Phase 2 to begin when the separation speed starts to decrease, and ends when the polarities have stopped separating. This is consistent with the picture of Chen, Rempel, & Fan (2017): the peak of a flux tube breaks through the surface during Phase 1. During Phase 2 the magnetic field lines are straightened by magnetic tension, so that the polarities continue to move apart, until they eventually lie directly above their anchored subsurface footpoints.

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arXiv2019

Time-distance helioseismology of solar Rossby waves

Context. Solar Rossby waves (r modes) have recently been discovered in the near-surface horizontal flow field using the techniques of granulation-tracking and ring-diagram analysis applied to six years of SDO/HMI data. Aims. Here we apply time-distance helioseismology to the combined SOHO/MDI and SDO/HMI data sets, which cover 21 years of observations from May 1996 to April 2017. The goal of this study is to provide an independent confirmation over two solar cycles and in deeper layers of the Sun. Methods. We have measured south-north helioseismic travel times along the equator, which are sensitive to subsurface north-south flows. To reduce noise, the travel times were averaged over travel distances from 6$^\circ$ to 30$^\circ$; the mean distance corresponds to a p-mode lower turning point of 0.91 $R_\odot$. The 21-year time series of travel-time measurements was split into three seven-year subsets and transformed to obtain power spectra in a corotating frame. Results. The power spectra all show peaks near the frequencies of the classical sectoral Rossby waves for azimuthal wavenumbers in the range $3 \leq m \leq 15$. The mode frequencies and linewidths of the modes with $m \leq 9$ are consistent with a previous study whereas modes with $m \geq 10$ are shifted toward less negative frequencies by 10--20 nHz. While most of these modes have e-folding lifetimes on the order of a few months, the longest lived mode, $m=3$, has an e-folding lifetime of more than one year. For each mode, the rms velocity at the equator is in the range of 1--3 m s$^{-1}$ , with the largest values for $m\sim10$. No evidence for the $m=2$ sectoral mode is found in the power spectrum, implying that the rms velocity of this mode is below $\sim$0.5 m s$^{-1}$.

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arXiv2019

Supervised Neural Networks for Helioseismic Ring-Diagram Inversions

The inversion of ring fit parameters to obtain subsurface flow maps in ring-diagram analysis for 8 years of SDO observations is computationally expensive, requiring ~3200 CPU hours. In this paper we apply machine learning techniques to the inversion in order to speed up calculations. Specifically, we train a predictor for subsurface flows using the mode fit parameters and the previous inversion results, to replace future inversion requirements. We utilize Artificial Neural Networks as a supervised learning method for predicting the flows in 15 degree ring tiles. To demonstrate that the machine learning results still contain the subtle signatures key to local helioseismic studies, we use the machine learning results to study the recently discovered solar equatorial Rossby waves. The Artificial Neural Network is computationally efficient, able to make future flow predictions of an entire Carrington rotation in a matter of seconds, which is much faster than the current ~31 CPU hours. Initial training of the networks requires ~3 CPU hours. The trained Artificial Neural Network can achieve a root mean-square error equal to approximately half that reported for the velocity inversions, demonstrating the accuracy of the machine learning (and perhaps the overestimation of the original errors from the ring-diagram pipeline). We find the signature of equatorial Rossby waves in the machine learning flows covering six years of data, demonstrating that small-amplitude signals are maintained. The recovery of Rossby waves in the machine learning flow maps can be achieved with only one Carrington rotation (27.275 days) of training data. We have shown that machine learning can be applied to, and perform more efficiently than the current ring-diagram inversion. The computation burden of the machine learning includes 3 CPU hours for initial training, then around 0.0001 CPU hours for future predictions.

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arXiv2018

Solar meridional circulation from twenty-one years of SOHO/MDI and SDO/HMI observations: Helioseismic travel times and forward modeling in the ray approximation

The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996-April 2017. Our data analysis corrects for several sources of systematic effects: P-angle error, surface magnetic field effects, and center-to-limb variations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. The travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and 24. Except for cycle 24's northern hemisphere, the measurements favor a single-cell meridional circulation model where the poleward flows persist down to $\sim$0.8 $R_\odot$, accompanied by local inflows toward the activity belts in the near-surface layers. Cycle 24's northern hemisphere is anomalous: travel-time differences are significantly smaller when travel distances are greater than 20$^\circ$. This asymmetry between northern and southern hemispheres during cycle 24 was not present in previous measurements (e.g., Rajaguru & Antia 2015), which assumed a different P-angle error correction where south-north travel-time differences are shifted to zero at the equator for all travel distances. In our measurements, the travel-time differences at the equator are zero for travel distances less than $\sim$30$^\circ$, but they do not vanish for larger travel distances. This equatorial offset for large travel distances need not be interpreted as a deep cross-equator flow; it could be due to the presence of asymmetrical local flows at the surface near the end points of the acoustic ray paths.

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arXiv2018

Signal and noise in helioseismic holography

Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holograms contain noise due to the stochastic nature of solar oscillations. We provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculate holograms in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. To illustrate the theory, we compute the hologram intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the hologram intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-to-noise ratio is approximately constant with depth. Averaging the hologram intensity over a number $N$ of frequencies above 3 mHz increases the signal-to-noise ratio by a factor nearly equal to the square root of $N$. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the individual contributions of the long-lived modes of oscillation.

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arXiv2018

Revisiting the exomoon candidate signal around Kepler-1625b

Transit photometry of the exoplanet candidate Kepler-1625b has recently been interpreted to show hints of a moon. We aim to clarify whether the exomoon-like signal is really caused by a large object in orbit around Kepler-1625b. We explore several detrending procedures, i.e. polynomials and the Cosine Filtering with Autocorrelation Minimization (CoFiAM). We then supply a light curve simulator with the co-planar orbital dynamics of the system and fit the resulting planet-moon transit light curves to the Kepler data. We employ the Bayesian Information Criterion (BIC) to assess whether a single planet or a planet-moon system is a more likely interpretation of the light curve variations. We carry out a blind hare-and-hounds exercise using many noise realizations by injecting simulated transits into different out-of-transit parts of the original Kepler-1625 data: 100 sequences with 3 synthetic transits of a Kepler-1625b-like planet and 100 sequences with 3 synthetic transits of this planet with a Neptune-sized moon. The statistical significance and characteristics of the exomoon-like signal strongly depend on the detrending method, and the data chosen for detrending, and on the treatment of gaps in the light curve. Our injection-retrieval experiment shows evidence for moons in about 10% of those light curves that do not contain an injected moon. Strikingly, many of these false-positive moons resemble the exomoon candidate. We recover up to about half of the injected moons, depending on the detrending method, with radii and orbital distances broadly corresponding to the injected values. A $Δ$BIC of -4.9 for the CoFiAM-based detrending indicates an exomoon around Kepler-1625b. This solution, however, is only one out of many and we find very different solutions depending on the details of the detrending method. It is worrying that the detrending is key to the interpretation of the data.

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arXiv2018

Global-scale equatorial Rossby waves as an essential component of solar internal dynamics

The Sun's complex dynamics is controlled by buoyancy and rotation in the convection zone and by magnetic forces in the atmosphere and corona. While small-scale solar convection is well understood, the dynamics of large-scale flows in the solar convection zone is not explained by theory or simulations. Waves of vorticity due to the Coriolis force, known as Rossby waves, are expected to remove energy out of convection at the largest scales. Here we unambiguously detect and characterize retrograde-propagating vorticity waves in the shallow subsurface layers of the Sun at angular wavenumbers below fifteen, with the dispersion relation of textbook sectoral Rossby waves. The waves have lifetimes of several months, well-defined mode frequencies below 200 nHz in a co-rotating frame, and eigenfunctions of vorticity that peak at the equator. Rossby waves have nearly as much vorticity as the convection at the same scales, thus they are an essential component of solar dynamics. We find a transition from turbulence-like to wave-like dynamics around the Rhines scale of angular wavenumber of twenty; this might provide an explanation for the puzzling deficit of kinetic energy at the largest spatial scales.

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arXiv2018

Sensitivity kernels for time-distance helioseismology: efficient computation for spherically-symmetric solar models

The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, but can be computationally expensive. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric. Kernels are typically expressed as products of Green's functions that depend upon depth, latitude and longitude. Here, we compute the spherical harmonic decomposition of the kernels and show that the integrals in latitude and longitude can be performed analytically. In particular, the integrals of the product of three associated Legendre polynomials can be computed thanks to the algorithm of Dong and Lemus (2002). The computations are fast and accurate and only require the knowledge of the Green's function where the source is at the pole. The computation time is reduced by two orders of magnitude compared to other recent computational frameworks. This new method allows for flexible and computationally efficient calculations of a large number of kernels, required in addressing key helioseismic problems. For example, the computation of all the kernels required for meridional flow inversion takes less than two hours on 100 cores.

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arXiv2018

Fragile detection of solar g modes by Fossat et al

The internal gravity modes of the Sun are notoriously difficult to detect, and the claimed detection of gravity modes presented in Fossat et al. 2017 is thus very exciting. Given the importance of these modes for understanding solar structure and dynamics, the results must be robust. While Fossat et al. 2017 described their method and parameter choices in detail, the sensitivity of their results to several parameters were not presented. Therefore, we test the sensitivity to a selection of them. The most concerning result is that the detection vanishes when we adjust the start time of the 16.5 year velocity time series by a few hours. We conclude that this reported detection of gravity modes is extremely fragile and should be treated with utmost caution.

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arXiv2018

Comparison of Travel-Time and Amplitude Measurements for Deep-Focusing Time--Distance Helioseismology

The purpose of deep-focusing time--distance helioseismology is to construct seismic measurements that have a high sensitivity to the physical conditions at a desired target point in the solar interior. With this technique, pairs of points on the solar surface are chosen such that acoustic ray paths intersect at this target (focus) point. Considering acoustic waves in a homogeneous medium, we compare travel-time and amplitude measurements extracted from the deep-focusing cross-covariance functions. Using a single-scattering approximation, we find that the spatial sensitivity of deep-focusing travel times to sound-speed perturbations is zero at the target location and maximum in a surrounding shell. This is unlike the deep-focusing amplitude measurements, which have maximum sensitivity at the target point. We compare the signal-to-noise ratio for travel-time and amplitude measurements for different types of sound-speed perturbations, under the assumption that noise is solely due to the random excitation of the waves. We find that, for highly localized perturbations in sound speed, the signal-to-noise ratio is higher for amplitude measurements than for travel-time measurements. We conclude that amplitude measurements are a useful complement to travel-time measurements in time--distance helioseismology.

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arXiv2017

Atmospheric radiation boundary conditions for high frequency waves in time-distance helioseismology

The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ($\sim$5.3~mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider the radiative boundary conditions recently developed by Barucq et al. (2017) for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the `infinite atmosphere' solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a VAL atmospheric model.

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arXiv2017

Iterative inversion of synthetic travel times successful at recovering sub-surface profiles of supergranular flows

We develop a helioseismic inversion algorithm that can be used to recover sub-surface vertical profiles of 2-dimensional supergranular flows from surface measurements of synthetic wave travel times. We carry out seismic wave-propagation simulations through a 2-dimensional section of a flow profile that resembles an averaged supergranule, and a starting model that has flows only at the surface. We assume that the wave measurements are entirely without realization noise for the purpose of our test. We expand the vertical profile of the supergranule stream function on a basis of B-splines. We iteratively update the B-spline coefficients of the supergranule model to reduce the travel-times differences observed between the two simulations. We carry out the exercise for four different vertical profiles peaking at different depths below the solar surface. We are able to accurately recover depth profiles of four supergranule models at depths up to $8-10\,\text{Mm}$ below the solar surface using $f-p_4$ modes, under the assumption that there is no realization noise. We are able to obtain the peak depth and the depth of the return flow for each model. A basis-resolved inversion performs significantly better than one where the flow field is inverted for at each point in the radial grid. This is an encouraging result and might act as a guide in developing more realistic inversion strategies that can be applied to supergranular flows in the Sun.

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arXiv2017

Problems in computational helioseismology

We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the non-linear inverse problem of time-distance helioseismology (finite amplitude pertubations to the medium). Numerical experiments were conducted to determine the number of frequencies required to reconstruct density and sound speed in the solar interior.

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arXiv2017

SOLARIS: Solar Sail Investigation of the Sun

In this paper, we detail the scientific objectives and outline a strawman payload of the SOLAR sail Investigation of the Sun (SOLARIS). The science objectives are to study the 3D structure of the solar magnetic and velocity field, the variation of total solar irradiance with latitude, and the structure of the corona. We show how we can meet these science objective using solar-sail technologies currently under development. We provide a tentative mission profile considering several trade-off approaches. We also provide a tentative mass budget breakdown and a perspective for a programmatic implementation.

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arXiv2017

Sensitivity of Helioseismic Measurements of Normal-mode Coupling to Flows and Sound-speed Perturbations

In this article, we derive and compute the sensitivity of measurements of coupling between normal modes of oscillation in the Sun to underlying flows. The theory is based on first-Born perturbation theory, and the analysis is carried out using the formalism described by \citet{lavely92}. Albeit tedious, we detail the derivation and compute the sensitivity of specific pairs of coupled normal modes to anomalies in the interior. Indeed, these kernels are critical for the accurate inference of convective flow amplitudes and large-scale circulations in the solar interior. We resolve some inconsistencies in the derivation of \citet{lavely92} and reformulate the fluid-continuity condition. We also derive and compute sound-speed kernels, paving the way for inverting for thermal anomalies alongside flows.

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arXiv2017

Evidence for photometric activity cycles in 3203 Kepler stars

In recent years it has been claimed that the length of stellar activity cycles is determined by the stellar rotation rate. It is observed that the cycle period increases with rotation period along the so-called active and inactive sequences. In this picture the Sun occupies a solitary position in between the two sequences. Our goal is to measure cyclic variations of the stellar light curve amplitude and the rotation period using four years of Kepler data. Periodic changes of the light curve amplitude or the stellar rotation period are associated with an underlying activity cycle. Using the McQuillan et al. 2014 sample we compute the rotation period and the variability amplitude for each Kepler quarter and search for periodic variations of both time series. To test for periodicity in each stellar time series we consider Lomb-Scargle periodograms and use a selection based on a False Alarm Probability (FAP). We detect amplitude periodicities in 3203 stars between 0.5-6 years covering rotation periods between 1-40 days. Given our sample size of 23,601 stars and our selection criteria that the FAP is less than 5%, this number is almost three times higher than that expected from pure noise. We do not detect periodicities in the rotation period beyond those expected from noise. Our measurements reveal that the cycle period shows a weak dependence on rotation rate, slightly increasing for longer rotation period. We further show that the shape of the variability deviates from a pure sine curve, consistent with observations of the solar cycle. Our measurements do not support the existence of distinct sequences in the P_rot-P_cyc plane, although there is some evidence for the inactive sequence for rotation periods between 5-25 days. Unfortunately, the total observing time is too short to draw sound conclusions on activity cycles with similar length as the solar cycle.

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