Time-distance helioseismology: Sensitivity of f-mode travel times to flows

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 Fr\'{e}chet 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.Comment: 34 pages, accepted to Astrophysical Journa

F-mode sensitivity kernels for flows

We compute f-mode sensitivity kernels for flows. Using a two-dimensional model, the scattered wavefield is calculated in the first Born approximation. We test the correctness of the kernels by comparing an exact solution (constant flow), a solution linearized in the flow, and the total integral of the kernel. In practice, the linear approximation is acceptable for flows as large as about 400 m/s.Comment: 4 pages, 3 figures. Proceedings of SOHO18/GONG 2006/HELAS I. Beyond the Spherical Sun: A new era of helio- and asteroseismology. Sheffield, England. August, 200

Spatially resolved vertical vorticity in solar supergranulation using helioseismology and local correlation tracking

Flow vorticity is a fundamental property of turbulent convection in rotating systems. Solar supergranules exhibit a preferred sense of rotation, which depends on the hemisphere. This is due to the Coriolis force acting on the diverging horizontal flows. We aim to spatially resolve the vertical flow vorticity of the average supergranule at different latitudes, both for outflow and inflow regions. To measure the vertical vorticity, we use two independent techniques: time-distance helioseismology (TD) and local correlation tracking of granules in intensity images (LCT) using data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Both maps are corrected for center-to-limb systematic errors. We find that 8-h TD and LCT maps of vertical vorticity are highly correlated at large spatial scales. Associated with the average supergranule outflow, we find tangential (vortical) flows that reach about 10 m/s in the clockwise direction at 40{\deg} latitude. In average inflow regions, the tangential flow reaches the same magnitude, but in the anti-clockwise direction. These tangential velocities are much smaller than the radial (diverging) flow component (300 m/s for the average outflow and 200 m/s for the average inflow). The results for TD and LCT as measured from HMI are in excellent agreement for latitudes between $-$60{\deg} and 60{\deg}. From HMI LCT, we measure the vorticity peak of the average supergranule to have a full width at half maximum of about 13 Mm for outflows and 8 Mm for inflows. This is larger than the spatial resolution of the LCT measurements (about 3 Mm). On the other hand, the vorticity peak in outflows is about half the value measured at inflows (e.g. 4/(10^6 s) clockwise compared to 8/(10^6 s) anti-clockwise at 40{\deg} latitude). Results from MDI/SOHO obtained in 2010 are biased compared to the HMI/SDO results for the same period.Comment: 12 pages, 13 figures (plus appendix), accepted for publication in A&

Rotational splitting as a function of mode frequency for six Sun-like stars

Asteroseismology offers the prospect of constraining differential rotation in Sun-like stars. Here we have identified six high signal-to-noise main-sequence Sun-like stars in the Kepler field, which all have visible signs of rotational splitting of their p-mode frequencies. For each star, we extract the rotational frequency splitting and inclination angle from separate mode sets (adjacent modes with l=2, 0, and 1) spanning the p-mode envelope. We use a Markov chain Monte Carlo method to obtain the best fit and errors associated with each parameter. We are able to make independent measurements of rotational splittings of ~8 radial orders for each star. For all six stars, the measured splittings are consistent with uniform rotation, allowing us to exclude large radial differential rotation. This work opens the possibility of constraining internal rotation of Sun-like stars.Comment: Published in Astronomy and Astrophysics. 4 pages, 3 figure

Interaction of solar inertial modes with turbulent convection. A 2D model for the excitation of linearly stable modes

Inertial modes have been observed on the Sun at low longitudinal wavenumbers. These modes probe the dynamics and structure of the solar convection zone down to the tachocline. While linear analysis allows the complex eigenfrequencies and eigenfunctions of these modes to be computed, it gives no information about their excitation nor about their amplitudes. We tested the hypothesis that solar inertial modes are stochastically excited by the turbulent motions entailed by convection. We have developed a theoretical formalism where the turbulent velocity fluctuations provide the mechanical work necessary to excite the modes. The modes are described by means of a 2D linear wave equation, relevant for the quasi-toroidal modes observed on the Sun, with a source term, under the beta plane approximation. Latitudinal differential rotation is included in the form of a parabolic profile that approximates the solar differential rotation at low and mid latitudes. We obtain synthetic power spectra for the wave's latitudinal velocity, longitudinal velocity, and radial vorticity, with azimuthal orders between 1 and 20. The synthetic power spectra contain the classical equatorial Rossby modes, as well as a rich spectrum of additional modes. The mode amplitudes are found to be of the same order of magnitude as observed on the Sun (~ 1 m/s). There is a qualitative transition between low and high azimuthal orders: the power spectra for m < 5 show modes that are clearly resolved in frequency space, while the power spectra for m > 5 display regions of excess power that consist of many overlapping modes. The general agreement between the predicted and observed inertial mode amplitudes supports the assumption of stochastic excitation by turbulent convection. Our work shows that the power spectra are not easily separable into individual modes, thus complicated the interpretation of the observations.Comment: 19 pages, accepted for publication in Astronomy & Astrophysic

STUDY OF A SINGLE-CHARGED IONS ECR SOURCE MATCHING OF THE EXTRACTED BEAM TO AN ISOTOPE SEPARATOR

A new ECR ion-source has been designed and studied for single-charged ion beams. A very stable regime has been obtained with an ion-source made of two identical stages in cascade. The RF power supplies consist of two 2.45 GHz magnetrons. The discharge chamber is made of two coaxial Pyrex tubes. The external one ensures vacuum and HT insulation. The tubes are aligned inside the two multimode cavities axially limited by three magnetic coils. The ion beam is extracted at 20 kV and focused with electric lenses. For argon and xenon, 1 mA single-charged ion currents have been extracted. The influence of various parameters has been progressively achieved with a set-up including a 60° analyzing magnet and with the 120° on-line isotope separator at SARA. From emittances and images observed it appears difficult to compensate charge space effects. Suggestions and future developments are proposed to improve qualities of the isotopic separation

Constructing and Characterising Solar Structure Models for Computational Helioseismology

In this paper, we construct background solar models that are stable against convection, by modifying the vertical pressure gradient of Model S (Christensen-Dalsgaard et al., 1996, Science, 272, 1286) relinquishing hydrostatic equilibrium. However, the stabilisation affects the eigenmodes that we wish to remain as close to Model S as possible. In a bid to recover the Model S eigenmodes, we choose to make additional corrections to the sound speed of Model S before stabilisation. No stabilised model can be perfectly solar-like, so we present three stabilised models with slightly different eigenmodes. The models are appropriate to study the f and p1 to p4 modes with spherical harmonic degrees in the range from 400 to 900. Background model CSM has a modified pressure gradient for stabilisation and has eigenfrequencies within 2% of Model S. Model CSM_A has an additional 10% increase in sound speed in the top 1 Mm resulting in eigenfrequencies within 2% of Model S and eigenfunctions that are, in comparison with CSM, closest to those of Model S. Model CSM_B has a 3% decrease in sound speed in the top 5 Mm resulting in eigenfrequencies within 1% of Model S and eigenfunctions that are only marginally adversely affected. These models are useful to study the interaction of solar waves with embedded three-dimensional heterogeneities, such as convective flows and model sunspots. We have also calculated the response of the stabilised models to excitation by random near-surface sources, using simulations of the propagation of linear waves. We find that the simulated power spectra of wave motion are in good agreement with an observed SOHO/MDI power spectrum. Overall, our convectively stabilised background models provide a good basis for quantitative numerical local helioseismology. The models are available for download from http://www.mps.mpg.de/projects/seismo/NA4/.Comment: 35 pages, 23 figures Changed title Updated Figure 1

Sensitivity of solar f-mode travel times to internal flows

We compute f-mode travel-time sensitivity kernels for flows. Using a two-dimensional model, we show that it is important to account for several systematic effects, such as the foreshortening and the projection of the velocity vector onto the line of sight. Correcting for these effects is necessary before any data inversion is attempted away from the center of the solar disk.Comment: Conference proceedings of SOHO 17, 7-11 May, 2006, Giardini Naxos, Italy. 4 page