Linear Sensitivity of Helioseismic Travel Times to Local Flows

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.Comment: 6 pages, 6 figure

Surface-effect corrections for oscillation frequencies of evolved stars

Accurate modelling of solar-like oscillators requires that modelled mode frequencies are corrected for the systematic shift caused by improper modelling of the near-surface layers, known as the surface effect. ... We investigate how much additional uncertainty is introduced to stellar model parameters by our uncertainty about the functional form of the surface effect. At the same time, we test whether any of the parametrizations is significantly better or worse at modelling observed subgiants and low-luminosity red giants. We model six stars observed by Kepler that show clear mixed modes. We fix the input physics of the stellar models and vary the choice of surface correction ... Models using a solar-calibrated power law correction consistently fit the observations more poorly than the other four corrections. Models with the remaining four corrections generally fit ... about equally well, with the combined surface correction by Ball & Gizon perhaps being marginally superior. The fits broadly agree on the model parameters within about the $2\sigma$ uncertainties, with discrepancies between the modified Lorentzian and free power law corrections occasionally exceeding the $3\sigma$ level. Relative to the best-fitting values, the total uncertainties on the masses, radii and ages of the stars are all less than 2, 1 and 6 per cent, respectively. A solar-calibrated power law ... appears unsuitable for use with more evolved solar-like oscillators. Among the remaining surface corrections, the uncertainty in the model parameters introduced by the surface effects is about twice as large as the uncertainty in the individual fits for these six stars. Though the fits are thus somewhat less certain because of our uncertainty of how to manage the surface effect, these results also demonstrate that it is feasible to model the individual mode frequencies of subgiants and low-luminosity red giants. ...Comment: Accepted for publication in Astronomy & Astrophysics. 13 pages, 6 figures, 5 tables. Abstract slightly abridged to meet arXiv's 1920 character limi

SLiM: a code for the simulation of wave propagation through an inhomogeneous, magnetised solar atmosphere

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.Comment: 6 pages, 7 figure

Validated helioseismic inversions for 3-D vector flows

According to time-distance helioseismology, information about internal fluid motions is encoded in the travel times of solar waves. The inverse problem consists of inferring 3-D vector flows from a set of travel-time measurements. Here we investigate the potential of time-distance helioseismology to infer 3-D convective velocities in the near-surface layers of the Sun. We developed a new Subtractive Optimally Localised Averaging (SOLA) code suitable for pipeline pseudo-automatic processing. Compared to its predecessor, the code was improved by accounting for additional constraints in order to get the right answer within a given noise level. The main aim of this study is to validate results obtained by our inversion code. We simulate travel-time maps using a snapshot from a numerical simulation of solar convective flows, realistic Born travel-time sensitivity kernels, and a realistic model of travel-time noise. These synthetic travel times are inverted for flows and the results compared with the known input flow field. Additional constraints are implemented in the inversion: cross-talk minimization between flow components and spatial localization of inversion coefficients. Using modes f, p1 through p4, we show that horizontal convective flow velocities can be inferred without bias, at a signal-to-noise ratio greater than one in the top 3.5 Mm, provided that observations span at least four days. The vertical component of velocity (v_z), if it were to be weak, is more difficult to infer and is seriously affected by cross-talk from horizontal velocity components. We emphasise that this cross-talk must be explicitly minimised in order to retrieve v_z in the top 1 Mm. We also show that statistical averaging over many different areas of the Sun allows for reliably measuring of average properties of all three flow components in the top 5.5 Mm of the convection zone.Comment: 14 pages main paper, 9 pages electronic supplement, 28 figures. Accepted for publication in Astronomy & Astrophysic

SLiM: a code for the simulation of wave propagation through an inhomogeneous, magnetised solar atmosphere

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.Comment: 6 pages, 7 figure

Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation

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.Comment: 21 pages, Accepted in Solar Physic

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&