arXiv subjects
Publications and source records attributed to L. Gizon.
A data and computation center for helioseismology has been set up at the Max Planck Institute for Solar System Research in Germany to prepare for the SDO mission. Here we present the system infrastructure and the scientific aims of this project, which is funded through grants from the German Aerospace Center and the European Research Council.
One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models, which are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun $τ_{5000}=1$ level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986) and the penumbral model of Ding and Fang (1989). The OPAL equation of state tables are used to derive the sound speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45$^\circ$ at the umbral-penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p$_1$, and p$_2$ wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations.
Time-distance helioseismology and related techniques show great promise for probing the structure and dynamics of the subphotospheric layers of the Sun. Indeed time-distance helioseismology has already been applied to make inferences about structures and flows under sunspots and active regions, to map long-lived convective flow patterns, and so on. Yet certainly there are still many inadequacies in the current approaches and, as the data get better and the questions we seek to address get more subtle, methods that were previously regarded as adequate are no longer acceptable. Here we give a short and partial description of outstanding problems in local helioseismology, using time-distance helioseismology as a guiding example.
Time-distance helioseismology is a technique for measuring the time for waves to travel from one point on the solar surface to another. These wave travel times are affected by advection by subsurface flows. Inferences of plasma flows based on observed travel times depend critically on the ability to accurately model the effects of subsurface flows on time-distance measurements. We present a Born approximation based computation of the sensitivity of time distance travel times to weak, steady, inhomogeneous subsurface flows. Three sensitivity functions are obtained, one for each component of the 3D vector flow. We show that the depth sensitivity of travel times to horizontally uniform flows is given approximately by the kinetic energy density of the oscillation modes which contribute to the travel times. For flows with strong depth dependence, the Born approximation can give substantially different results than the ray approximation.
In this paper we describe the semi-spectral linear MHD (SLiM) code which we have written to follow the interaction of linear waves through an inhomogeneous three-dimensional solar atmosphere. The background model allows almost arbitrary perturbations of density, temperature, sound speed as well as magnetic and velocity fields. We give details of several of the tests we have used to check the code. The code will be useful in understanding the helioseismic signatures of various solar features, including sunspots.
Solar Orbiter is intended to become ESA's next solar mission in heritage of the successful SOHO project. The scientific objectives of the mission, its design, and its scientific payload are reviewed. Specific emphasis is given to the perspectives of Solar Orbiter with respect to helioseismology.
Various methods of helioseismology are used to study the subsurface properties of the sunspot in NOAA Active Region 9787. This sunspot was chosen because it is axisymmetric, shows little evolution during 20-28 January 2002, and was observed continuously by the MDI/SOHO instrument. (...) Wave travel times and mode frequencies are affected by the sunspot. In most cases, wave packets that propagate through the sunspot have reduced travel times. At short travel distances, however, the sign of the travel-time shifts appears to depend sensitively on how the data are processed and, in particular, on filtering in frequency-wavenumber space. We carry out two linear inversions for wave speed: one using travel-times and phase-speed filters and the other one using mode frequencies from ring analysis. These two inversions give subsurface wave-speed profiles with opposite signs and different amplitudes. (...) From this study of AR9787, we conclude that we are currently unable to provide a unified description of the subsurface structure and dynamics of the sunspot.
In local helioseismology numerical simulations of wave propagation are useful to model the interaction of solar waves with perturbations to a background solar model. However, the solution to the equations of motions include convective modes that can swamp the waves we are interested in. For this reason, we choose to first stabilise the background solar model against convection by altering the vertical pressure gradient. Here we compare the eigenmodes of our convectively stabilised model with a standard solar model (Model S) and find a good agreement.
The Sun supports a rich spectrum of internal waves that are continuously excited by turbulent convection. The GONG network and the MDI/SOHO space instrument provide an exceptional data base of spatially-resolved observations of solar oscillations, covering an entire sunspot cycle (11 years). Local helioseismology is a set of tools for probing the solar interior in three dimensions using measurements of wave travel times and local mode frequencies. Local helioseismology has discovered (i) near-surface vector flows associated with convection (ii) 250 m/s subsurface horizontal outflows around sunspots (iii) ~50 m/s extended horizontal flows around active regions (converging near the surface and diverging below), (iv) the effect of the Coriolis force on convective flows and active region flows (v) the subsurface signature of the 15 m/s poleward meridional flow, (vi) a +/-5 m/s time-varying depth-dependent component of the meridional circulation around the mean latitude of activity, and (vii) magnetic activity on the far side of the Sun.
The POLAR Investigation of the Sun (POLARIS) mission uses a combination of a gravity assist and solar sail propulsion to place a spacecraft in a 0.48 AU circular orbit around the Sun with an inclination of 75 degrees with respect to solar equator. This challenging orbit is made possible by the challenging development of solar sail propulsion. This first extended view of the high-latitude regions of the Sun will enable crucial observations not possible from the ecliptic viewpoint or from Solar Orbiter. While Solar Orbiter would give the first glimpse of the high latitude magnetic field and flows to probe the solar dynamo, it does not have sufficient viewing of the polar regions to achieve POLARIS' primary objective : determining the relation between the magnetism and dynamics of the Sun's polar regions and the solar cycle.
Solar oscillations consist of a rich spectrum of internal acoustic waves and surface gravity waves, stochastically excited by turbulent convection. They have been monitored almost continuously over the last ten years with high-precision Doppler images of the solar surface. The purpose of helioseismology is to retrieve information about the structure and the dynamics of the solar interior from the frequencies, phases, and amplitudes of solar waves. Methods of analysis are being developed to make three-dimensional images of subsurface motions and temperature inhomogeneities in order to study convective structures and regions of magnetic activity, like sunspots.
With the aim of studying magnetic effects in time-distance helioseismology, we use the first-order Born approximation to compute the scattering of acoustic plane waves by a magnetic cylinder embedded in a uniform medium. We show, by comparison with the exact solution, that the travel-time shifts computed in the Born approximation are everywhere valid to first order in the ratio of the magnetic to the gas pressures. We also show that, for arbitrary magnetic field strength, the Born approximation is not valid in the limit where the radius of the magnetic cylinder tends to zero.
We present independent observations of the solar-cycle variation of flows near the solar surface and at a depth of about 60 Mm, in the latitude range $\pm45^\circ$. We show that the time-varying components of the meridional flow at these two depths have opposite sign, while the time-varying components of the zonal flow are in phase. This is in agreement with previous results. We then investigate whether the observations are consistent with a theoretical model of solar-cycle dependent meridional circulation based on a flux-transport dynamo combined with a geostrophic flow caused by increased radiative loss in the active region belt (the only existing quantitative model). We find that the model and the data are in qualitative agreement, although the amplitude of the solar-cycle variation of the meridional flow at 60 Mm is underestimated by the model.
We calculate the scattering effects associated with the interaction of a surface gravity or {\it f} mode with a thin magnetic flux tube embedded in a realistically stratified medium. We find that the dominant scattered wave is an $f$ mode with amplitude and phase of 1.17% and around $49^\circ$ relative to the incident wave, compared to the values of 0.13% and $40^\circ$ estimated from observations. The extent of scattering into high-order acoustic $p$ modes is too weak to be accurately characterized. We recover the result that the degree of scattering is enhanced as (a) the frequency of the incident wave increases and (b) the flux tube becomes magnetically dominated.
To recover the flow information encoded in travel-time data of time-distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a 2+1 dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise covariance properties of the travel times which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Due to ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector solar flows in the quiet Sun at spatial resolutions of 7-10 Mm using generally 24 h of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone.
The propagation of solar waves through the sunspot of AR 9787 is observed using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magneto-hydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere, less so for lower field strengths. Constraining the sunspot model with helioseismology is only possible because the direct effect of the magnetic field on the waves has been fully taken into account. Our work shows that the full-waveform modeling of sunspots is feasible.
We present an up-to-date estimate for the prospect of using the Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) for an unambiguous detection of solar g modes (f < 400 micro Hertz) through their gravitational signature. There are currently two major efforts to detect low-frequency gravitational effects, ASTROD and the Laser Interferometer Space Antenna (LISA). Using the most recent g mode surface amplitude estimates, both observational and theoretical, it is unclear whether LISA will be capable of successfully detecting these modes. The ASTROD project may be better suited for detection as its sensitivity curve is shifted towards lower frequencies with the best sensitivity occurring in the range 100-300 micro Hertz.
Time-distance helioseismology has shown that f-mode travel times contain information about horizontal flows in the Sun. The purpose of this study is to provide a simple interpretation of these travel times. We study the interaction of surface-gravity waves with horizontal flows in an incompressible, plane-parallel solar atmosphere. We show that for uniform flows less than roughly 250 m s$^{-1}$, the travel-time shifts are linear in the flow amplitude. For stronger flows, perturbation theory up to third order is needed to model waveforms. The case of small-amplitude spatially-varying flows is treated using the first-order Born approximation. We derive two-dimensional Fréchet kernels that give the sensitivity of travel-time shifts to local flows. We show that the effect of flows on travel times depends on wave damping and on the direction from which the observations are made. The main physical effect is the advection of the waves by the flow rather than the advection of wave sources or the effect of flows on wave damping. We compare the two-dimensional sensitivity kernels with simplified three-dimensional kernels that only account for wave advection and assume a vertical line of sight. We find that the three-dimensional f-mode kernels approximately separate in the horizontal and vertical coordinates, with the horizontal variations given by the simplified two-dimensional kernels. This consistency between quite different models gives us confidence in the usefulness of these kernels for interpreting quiet-Sun observations.