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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., Comment: 17 pages, 5 figures, 2 tables, accepted for publication in ApJ. v2: typo in arXiv author list corrected

High-quality astrometric, spectroscopic, interferometric and, importantly, asteroseismic observations are available for $\alpha$ Cen A, which is the closest binary star system to earth. Taking all these constraints into account, we study the internal structure of the star by means of theoretical modelling. Using the Aarhus STellar Evolution Code (ASTEC) and the tools of Computational Bayesian Statistics, in particular a Markov chain Monte Carlo algorithm, we perform statistical inferences for the physical characteristics of the star. We find that $\alpha$ Cen A has a probability of approximately 40% of having a convective core. This probability drops to few percents if one considers reduced rates for the $^{14}$N(p,$\gamma$)$^{15}$O reaction. These convective cores have fractional radii less than 8% when overshoot is neglected. Including overshooting also leads to the possibility of a convective core mostly sustained by the ppII chain energy output. We finally show that roughly 30% of the stellar models describing $\alpha$ Cen A are in the subgiant regime., Comment: 17 pages, 7 figures, accepted for publication in MNRAS

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., Comment: 9 pages, 1 figure, 6 tables

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., Comment: 9 pages, 7 figures. Accepted for publication in Astronomy & Astrophysics

In previous work we identified six Sun-like stars observed by Kepler with exceptionally clear asteroseismic signatures of rotation. Here, we show that five of these stars exhibit surface variability suitable for measuring rotation. In order to further constrain differential rotation, we compare the rotation periods obtained from light-curve variability with those from asteroseismology. The two rotation measurement methods are found to agree within uncertainties, suggesting that radial differential rotation is weak, as is the case for the Sun. Furthermore, we find significant discrepancies between ages from asteroseismology and from three different gyrochronology relations, implying that stellar age estimation is problematic even for Sun-like stars., Comment: Accepted for publication in A&A. 5 pages, 4 figures

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., Comment: 16 pages, 15 figures; Tables 2 & 4 will entirely be available (later...)

We present the first detections by the NASA K2 Mission of oscillations in solar-type stars, using short-cadence data collected during K2 Campaign\,1 (C1). We understand the asteroseismic detection thresholds for C1-like levels of photometric performance, and we can detect oscillations in subgiants having dominant oscillation frequencies around $1000\,\rm \mu Hz$. Changes to the operation of the fine-guidance sensors are expected to give significant improvements in the high-frequency performance from C3 onwards. A reduction in the excess high-frequency noise by a factor of two-and-a-half in amplitude would bring main-sequence stars with dominant oscillation frequencies as high as ${\simeq 2500}\,\rm \mu Hz$ into play as potential asteroseismic targets for K2., Comment: Accepted for publication in PASP; 16 pages, 2 figures

Supergranules in the quiet Sun are outlined by a web-like structure of enhanced magnetic field strength, the so-called magnetic network. We aim to map the magnetic network field around the average supergranule near disk center. We use observations of the line-of-sight component of the magnetic field from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The average supergranule is constructed by coaligning and averaging over 3000 individual supergranules. We determine the positions of the supergranules with an image segmentation algorithm that we apply on maps of the horizontal flow divergence measured using time-distance helioseismology. In the center of the average supergranule the magnetic (intranetwork) field is weaker by about 2.2 Gauss than the background value (3.5 Gauss), whereas it is enhanced in the surrounding ring of horizontal inflows (by about 0.6 Gauss on average). We find that this network field is significantly stronger west (prograde) of the average supergranule than in the east (by about 0.3 Gauss). With time-distance helioseismology, we find a similar anisotropy. The observed anisotropy of the magnetic field adds to the mysterious dynamical properties of solar supergranulation., Comment: 4 pages, 4 figures, accepted for publication in A&A Letters

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&A

We measure rotation periods for 12151 stars in the Kepler field, based on the photometric variability caused by stellar activity. Our analysis returns stable rotation periods over at least six out of eight quarters of Kepler data. This large sample of stars enables us to study the rotation periods as a function of spectral type. We find good agreement with previous studies and vsini measurements for F, G and K stars. Combining rotation periods, B-V color, and gyrochronology relations, we find that the cool stars in our sample are predominantly younger than ~1Gyr., Comment: Published 12/2013 in ASP Conference Series, Vol. 479, Progress in Physics of the Sun and Stars, p. 137. http://aspbooks.org/custom/publications/paper/479-0137.html

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 (Fr\'echet) 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.

A major goal of helioseismology is the three-dimensional reconstruction of the three velocity components of convective flows in the solar interior from sets of wave travel-time measurements. For small amplitude flows, the forward problem is described in good approximation by a large system of convolution equations. The input observations are highly noisy random vectors with a known dense covariance matrix. This leads to a large statistical linear inverse problem. Whereas for deterministic linear inverse problems several computationally efficient minimax optimal regularization methods exist, only one minimax-optimal linear estimator exists for statistical linear inverse problems: the Pinsker estimator. However, it is often computationally inefficient because it requires a singular value decomposition of the forward operator or it is not applicable because of an unknown noise covariance matrix, so it is rarely used for real-world problems. These limitations do not apply in helioseismology. We present a simplified proof of the optimality properties of the Pinsker estimator and show that it yields significantly better reconstructions than traditional inversion methods used in helioseismology, i.e.\ Regularized Least Squares (Tikhonov regularization) and SOLA (approximate inverse) methods. Moreover, we discuss the incorporation of the mass conservation constraint in the Pinsker scheme using staggered grids. With this improvement we can reconstruct not only horizontal, but also vertical velocity components that are much smaller in amplitude.

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., Comment: 29 pages, 12 figures, in review, Annual Reviews of Fluid Mechanics

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., Comment: 7 pages, 5 figures, accepted for publication in A&A on 19 March 2015

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., Comment: 50 pages, 30 figures. Experimental Astronomy

Helioseismology has provided unprecedented information about the internal rotation of the Sun. One of the important achievements was the discovery of two radial shear layers: one near the bottom of the convection zone (the tachocline) and one near the surface. These shear layers may be important ingredients for explaining the magnetic cycle of the Sun. We measure the logarithmic radial gradient of the rotation rate ($\rm d\ln\Omega/\rm d\ln r$) near the surface of the Sun using 15 years of f mode rotational frequency splittings from the Michelson Doppler Imager (MDI) and four years of data from the Helioseismic and Magnetic Imager (HMI). We model the angular velocity of the Sun in the upper $\sim 10$ Mm as changing linearly with depth and use a multiplicative optimally localized averaging inversion to infer the gradient of the rotation rate as a function of latitude. Both the MDI and HMI data show that $\rm d\ln\Omega/\rm d\ln r$ is close to $-1$ from the equator to 60$^{\circ}$ latitude and stays negative up to 75$^{\circ}$ latitude. However, the value of the gradient is different for MDI and HMI for latitudes above $60^{\circ}$. Additionally, there is a significant difference between the value of $d\ln\Omega/d\ln r$ using an older and recently reprocessed MDI data for latitudes above $30^\circ$. We could reliably infer the value of $\rm d\ln\Omega/\rm d\ln r$ up to 60$^{\circ}$, but not above this latitude, which will hopefully constrain theories of the near-surface shear layer and dynamo. Furthermore, the recently reprocessed MDI splitting data are more reliable than the older versions which contained clear systematic errors in the high degree f modes., Comment: 4 pages, 5 figures, accepted for publication in A&A Letters

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., Comment: 6 pages, 6 figures. Published in Astronomy & Astrophysics

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., Comment: 7 pages, 6 figures

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 figures

After emerging to the solar surface, the Sun's magnetic field displays a complex and intricate evolution. The evolution of the surface field is important for several reasons. One is that the surface field, and its dynamics, sets the boundary condition for the coronal and heliospheric magnetic fields. Another is that the surface evolution gives us insight into the dynamo process. In particular, it plays an essential role in the Babcock-Leighton model of the solar dynamo. Describing this evolution is the aim of the surface flux transport model. The model starts from the emergence of magnetic bipoles. Thereafter, the model is based on the induction equation and the fact that after emergence the magnetic field is observed to evolve as if it were purely radial. The induction equation then describes how the surface flows -- differential rotation, meridional circulation, granular, supergranular flows, and active region inflows -- determine the evolution of the field (now taken to be purely radial). In this paper, we review the modeling of the various processes that determine the evolution of the surface field. We restrict our attention to their role in the surface flux transport model. We also discuss the success of the model and some of the results that have been obtained using this model., Comment: 39 pages, 15 figures, accepted for publication in Space Sci. Rev

Space-based observations of solar-like oscillations present an opportunity to constrain stellar models using individual mode frequencies. However, current stellar models are inaccurate near the surface, which introduces a systematic difference that must be corrected. We introduce and evaluate two parametrizations of the surface corrections based on formulae given by Gough (1990). The first we call a cubic term proportional to $\nu^3/\mathcal{I}$ and the second has an additional inverse term proportional to $\nu^{-1}/\mathcal{I}$, where $\nu$ and $\mathcal{I}$ are the frequency and inertia of an oscillation mode. We first show that these formulae accurately correct model frequencies of two different solar models ... We then incorporate the parametrizations into a modelling pipeline that simultaneously fits the surface effects and the underlying stellar model parameters. We apply this pipeline to synthetic observations of a Sun-like stellar model, solar observations degraded to typical asteroseismic uncertainties, and observations of the well-studied CoRoT target HD52265. For comparison, we also run the pipeline with the scaled power-law correction proposed by Kjeldsen et al. (2008). The fits to synthetic and degraded solar data show that the method is unbiased and produces best-fit parameters that are consistent with the input models and known parameters of the Sun. Our results for HD52265 are consistent with previous modelling efforts and the magnitude of the surface correction is similar to that of the Sun. The fit using a scaled power-law correction is significantly worse but yields consistent parameters ... We find that the cubic term alone is suitable for asteroseismic applications and it is easy to implement in an existing pipeline. ... This parametrization is thus a useful new way to correct model frequencies so that observations of individual mode frequencies can be exploited., Comment: Accepted for publication in Astronomy & Astrophysics. 10 pages, 8 figures, 1 full page table

Context: Studying the motions on the solar surface is fundamental for understanding how turbulent convection transports energy and how magnetic fields are distributed across the solar surface. Aims: From horizontal velocity measurements all over the visible disc of the Sun and using data from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI), we investigate the structure and evolution of solar supergranulation. Methods: Horizontal velocity fields were measured by following the proper motions of solar granules using a newly developed version of the coherent structure tracking (CST) code. With this tool, maps of horizontal divergence were computed. We then segmented and identified supergranular cells and followed their histories by using spatio-temporal labelling. With this dataset we derived the fundamental properties of supergranulation, including their motion. Results: We find values of the fundamental parameters of supergranulation similar to previous studies: a mean lifetime of 1.5 days and a mean diameter of 25~Mm. The tracking of individual supergranular cells reveals the solar differential rotation and a poleward circulation trend of the meridional flow. The shape of the derived differential rotation and meridional flow does not depend on the cell size. If there is a background magnetic field, the diverging flows in supergranules are weaker. Conclusions: This study confirms that supergranules are suitable tracers that may be used to investigate the large-scale flows of the solar convection as long as they are detectable enough on the surface., Comment: 8 pages, 14 figures, accepted for publication in Astronomy&Astrophysics

The Solar Orbiter mission, to be launched in July 2017, will carry a suite of remote sensing and in-situ instruments, including the Polarimetric and Helioseismic Imager (PHI). PHI will deliver high-cadence images of the Sun in intensity and Doppler velocity suitable for carrying out novel helioseismic studies. The orbit of the Solar Orbiter spacecraft will reach a solar latitude of up to 21 deg (up to 34 deg by the end of the extended mission) and thus will enable the first local helioseismology studies of the polar regions. Here we consider an array of science objectives to be addressed by helioseismology within the baseline telemetry allocation (51 Gbit per orbit, current baseline) and within the science observing windows (baseline 3 x 10 days per orbit). A particularly important objective is the measurement of large-scale flows at high latitudes (rotation and meridional flow), which are largely unknown but play an important role in flux transport dynamos. The full range of Earth-Sun-spacecraft angles provided by the orbit will enable helioseismology from two vantage points by combining PHI with another instrument: stereoscopic helioseismology will allow the study of the deep solar interior and a better understanding of the physics of solar oscillations in both quiet Sun and sunspots. We have used a model of the PHI instrument to study its performance for helioseismology applications. As input we used a 6 hr time-series of realistic solar magneto-convection simulation (Stagger code) and the SPINOR radiative transfer code to synthesize the observables. The simulated power spectra of solar oscillations show that the instrument is suitable for helioseismology. In particular, the specified point spread function, image jitter, and photon noise are no obstacle to a successful mission., Comment: 35 pages, 12 figures. Accepted for publication in Space Science Reviews

In time-distance helioseismology, information about the solar interior is encoded in measurements of travel times between pairs of points on the solar surface. Travel times are deduced from the cross-covariance of the random wave field. Here we consider travel times and also products of travel times as observables. They contain information about e.g. the statistical properties of convection in the Sun. The basic assumption of the model is that noise is the result of the stochastic excitation of solar waves, a random process which is stationary and Gaussian. We generalize the existing noise model (Gizon and Birch 2004) by dropping the assumption of horizontal spatial homogeneity. Using a recurrence relation, we calculate the noise covariance matrices for the moments of order 4, 6, and 8 of the observed wave field, for the moments of order 2, 3 and 4 of the cross-covariance, and for the moments of order 2, 3 and 4 of the travel times. All noise covariance matrices depend only on the expectation value of the cross-covariance of the observed wave field. For products of travel times, the noise covariance matrix consists of three terms proportional to $1/T$, $1/T^2$, and $1/T^3$, where $T$ is the duration of the observations. For typical observation times of a few hours, the term proportional to $1/T^2$ dominates and $Cov[\tau_1 \tau_2, \tau_3 \tau_4] \approx Cov[\tau_1, \tau_3] Cov[\tau_2, \tau_4] + Cov[\tau_1, \tau_4] Cov[\tau_2, \tau_3]$, where the $\tau_i$ are arbitrary travel times. This result is confirmed for $p_1$ travel times by Monte Carlo simulations and comparisons with SDO/HMI observations. General and accurate formulae have been derived to model the noise covariance matrix of helioseismic travel times and products of travel times. These results could easily be generalized to other methods of local helioseismology, such as helioseismic holography and ring diagram analysis.

The Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) filtergrams, taken at six wavelengths around the Fe I 6173.3 {\AA} line, contain information about the line-of-sight velocity over a range of heights in the solar atmosphere. Multi-height velocity inferences from these observations can be exploited to study wave motions and energy transport in the atmosphere. Using realistic convection simulation datasets provided by the STAGGER and MURaM codes, we generate synthetic filtergrams and explore several methods for estimating Dopplergrams. We investigate at which height each synthetic Dopplergram correlates most strongly with the vertical velocity in the model atmospheres. On the basis of the investigation, we propose two Dopplergrams other than the standard HMI-algorithm Dopplergram produced from HMI filtergrams: a line-center Dopplergram and an average-wing Dopplergram. These two Dopplergrams correlate most strongly with vertical velocities at the heights of 30 - 40 km above (line-center) and 30 - 40 km below (average-wing) the effective height of the HMI-algorithm Dopplergram. Therefore, we can obtain velocity information from two layers separated by about a half of a scale height in the atmosphere, at best. The phase shifts between these multi-height Dopplergrams from observational data as well as those from the simulated data are also consistent with the height-difference estimates in the frequency range above the photospheric acoustic cutoff frequency., Comment: accepted for publication in Solar Physics

Context. The object HD 43587Aa is a G0V star observed during the 145-day LRa03 run of the COnvection, ROtation and planetary Transits space mission (CoRoT), for which complementary High Accuracy Radial velocity Planet Searcher (HARPS) spectra with S/N>300 were also obtained. Its visual magnitude is 5.71, and its effective temperature is close to 5950 K. It has a known companion in a highly eccentric orbit and is also coupled with two more distant companions. Aims. We undertake a preliminary investigation of the internal structure of HD 43587Aa. Methods. We carried out a seismic analysis of the star, using maximum likelihood estimators and Markov Chain Monte Carlo methods. Results. We established the first table of the eigenmode frequencies, widths, and heights for HD 43587Aa. The star appears to have a mass and a radius slightly larger than the Sun, and is slightly older (5.6 Gyr). Two scenarios are suggested for the geometry of the star: either its inclination angle is very low, or the rotation velocity of the star is very low. Conclusions. A more detailed study of the rotation and of the magnetic and chromospheric activity for this star is needed, and will be the subject of a further study. New high resolution spectrometric observations should be performed for at least several months in duration.

We study Doppler velocity measurements at multiple heights in the solar atmosphere using a set of six filtergrams obtained by the Helioseismic magnetic Imager on board the Solar Dynamics Observatory. There are clear and significant phase differences between core and wing Dopplergrams in the frequency range above the photospheric acoustic cutoff frequency, which indicates that these are really "multi-height" datasets., Comment: 4 pages, 3 figures, in the proceedings "Progress in Physics of the Sun and Stars: A New Era in Helio- and Asteroseismology" (ASP Conference Series)

Context : We still do not know which mechanisms are responsible for the transport of angular momentum inside stars. The recent detection of mixed modes that contain the signature of rotation in the spectra of Kepler subgiants and red giants gives us the opportunity to make progress on this issue. Aims: Our aim is to probe the radial dependance of the rotation profiles for a sample of Kepler targets. For this purpose, subgiants and early red giants are particularly interesting targets because their rotational splittings are more sensitive to the rotation outside the deeper core than is the case for their more evolved counterparts. Methods: We first extract the rotational splittings and frequencies of the modes for six young Kepler red giants. We then perform a seismic modeling of these stars using the evolutionary codes CESAM2k and ASTEC. By using the observed splittings and the rotational kernels of the optimal models, we perform inversions of the internal rotation profiles of the six stars. Results: We obtain estimates of the mean rotation rate in the core and in the convective envelope of these stars. We show that the rotation contrast between the core and the envelope increases during the subgiant branch. Our results also suggest that the core of subgiants spins up with time, contrary to the RGB stars whose core has been shown to spin down. For two of the stars, we show that a discontinuous rotation profile with a deep discontinuity reproduces the observed splittings significantly better than a smooth rotation profile. Interestingly, the depths that are found most probable for the discontinuities roughly coincide with the location of the H-burning shell, which separates the layers that contract from those that expand. These results will bring observational constraints to the scenarios of angular momentum transport in stars., Comment: Accepted in A&A, 27 pages, 18 figures

Linear time-domain simulations of acoustic oscillations are unstable in the stellar convection zone. To overcome this problem it is customary to compute the oscillations of a stabilized background stellar model. The stabilization, however, affects the result. Here we propose to use a perturbative approach (running the simulation twice) to approximately recover the acoustic wave field, while preserving seismic reciprocity. To test the method we considered a 1D standard solar model. We found that the mode frequencies of the (unstable) standard solar model are well approximated by the perturbative approach within $1~\mu$Hz for low-degree modes with frequencies near $3~\mu$Hz. We also show that the perturbative approach is appropriate for correcting rotational-frequency kernels. Finally, we comment that the method can be generalized to wave propagation in 3D magnetized stellar interiors because the magnetic fields have stabilizing effects on convection., Comment: 14 pages. Published online in Solar Physics, available at http://link.springer.com/article/10.1007/s11207-013-0457-7

We use asteroseismic data obtained by the NASA Kepler Mission to estimate the fundamental properties of more than 500 main-sequence and sub-giant stars. Data obtained during the first 10 months of Kepler science operations were used for this work, when these solar-type targets were observed for one month each in a survey mode. Stellar properties have been estimated using two global asteroseismic parameters and complementary photometric and spectroscopic data. Homogeneous sets of effective temperatures were available for the entire ensemble from complementary photometry; spectroscopic estimates of T_eff and [Fe/H] were available from a homogeneous analysis of ground-based data on a subset of 87 stars. [Abbreviated version... see paper for full abstract.], Comment: Accepted for publication in ApJS; 90 pages, 22 figures, 6 tables. Units on rho in tables now listed correctly as rho(Sun)

PLATO 2.0 has recently been selected for ESA's M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 sec readout cadence and 2 with 2.5 sec candence) providing a wide field-of-view (2232 deg2) and a large photometric magnitude range (4-16 mag). It focusses on bright (4-11 mag) stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for these bright stars to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2%, 4-10% and 10% for planet radii, masses and ages, respectively. The planned baseline observing strategy includes two long pointings (2-3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50% of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include terrestrial planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0., Comment: 63 pages, 17 figures, submitted to Experimental Astronomy (ExA)

We present the first high-resolution solar images in the Mg II k 2796 \AA{} line. The images, taken through a 4.8 \AA{} broad interference filter, were obtained during the second science flight of SUNRISE in June 2013 by the SuFI instrument. The Mg II k images display structures that look qualitatively very similar to images taken in the core of Ca II H. The Mg II images exhibit reversed granulation (or shock waves) in the internetwork regions of the quiet Sun, at intensity contrasts that are similar to those found in Ca II H. Very prominent in Mg II are bright points, both in the quiet Sun and in plage regions, particularly near disk center. These are much brighter than at other wavelengths sampled at similar resolution. Furthermore, Mg II k images also show fibril structures associated with plage regions. Again, the fibrils are similar to those seen in Ca II H images, but tend to be more pronounced, particularly in weak plage., Comment: Accepted for publication in The Astrophysical Journal Letters

High-quality data from space-based observatories present an opportunity to fit stellar models to observations of individually-identified oscillation frequencies, not just the large and small frequency separations. But such fits require the evaluation of a large number of accurate stellar models, which remains expensive. Here, we show that global-mode oscillation frequencies interpolated in a grid of stellar models are precise and accurate, at least in the neighbourhood of a solar model., Comment: 2 pages, 1 figure. Poster contribution to IAU Symposium 301: Precision Asteroseismology

We comment on the potential for continuing asteroseismology of solar-type and red-giant stars in a 2-wheel Kepler Mission. Our main conclusion is that by targeting stars in the ecliptic it should be possible to perform high-quality asteroseismology, as long as favorable scenarios for 2-wheel pointing performance are met. Targeting the ecliptic would potentially facilitate unique science that was not possible in the nominal Mission, notably from the study of clusters that are significantly brighter than those in the Kepler field. Our conclusions are based on predictions of 2-wheel observations made by a space photometry simulator, with information provided by the Kepler Project used as input to describe the degraded pointing scenarios. We find that elevated levels of frequency-dependent noise, consistent with the above scenarios, would have a significant negative impact on our ability to continue asteroseismic studies of solar-like oscillators in the Kepler field. However, the situation may be much more optimistic for observations in the ecliptic, provided that pointing resets of the spacecraft during regular desaturations of the two functioning reaction wheels are accurate at the < 1 arcsec level. This would make it possible to apply a post-hoc analysis that would recover most of the lost photometric precision. Without this post-hoc correction---and the accurate re-pointing it requires---the performance would probably be as poor as in the Kepler-field case. Critical to our conclusions for both fields is the assumed level of pointing noise (in the short-term jitter and the longer-term drift). We suggest that further tests will be needed to clarify our results once more detail and data on the expected pointing performance becomes available, and we offer our assistance in this work., Comment: NASA Kepler Mission White Paper; 10 pages, 2 figures

Rotation is thought to drive cyclic magnetic activity in the Sun and Sun-like stars. Stellar dynamos, however, are poorly understood owing to the scarcity of observations of rotation and magnetic fields in stars. Here, inferences are drawn on the internal rotation of a distant Sun-like star by studying its global modes of oscillation. We report asteroseismic constraints imposed on the rotation rate and the inclination of the spin axis of the Sun-like star HD 52265, a principal target observed by the CoRoT satellite that is known to host a planetary companion. These seismic inferences are remarkably consistent with an independent spectroscopic observation (rotational line broadening) and with the observed rotation period of star spots. Furthermore, asteroseismology constrains the mass of exoplanet HD 52265b. Under the standard assumption that the stellar spin axis and the axis of the planetary orbit coincide, the minimum spectroscopic mass of the planet can be converted into a true mass of 1.85 (+0.52,-0.42) M_Jupiter, which implies that it is a planet, not a brown dwarf., Comment: Published in Proceedings of the National Academy of Sciences (5 pages, 5 figures, 3 tables). Available at http://www.pnas.org/cgi/doi/10.1073/pnas.1303291110

Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally stationary medium is almost universally invoked. However, the Sun is in a constant state of evolution, on a broad range of spatio-temporal scales. At the zero wavelength limit, i.e., when the wavelength is much shorter than the scale over which the medium varies, the WKBJ (ray) approximation may be applied. Here, we address the other asymptotic end of the spectrum, the infinite wavelength limit, using the technique of homogenization. We apply homogenization to scenarios where waves are propagating through rapidly varying media (spatially and temporally), and derive effective models for the media. One consequence is that a scalar sound speed becomes a tensorial wavespeed in the effective model and anisotropies can be induced depending on the nature of the perturbation. The second term in this asymptotic two-scale expansion, the so-called corrector, contains contributions due to higher-order scattering, leading to the decoherence of the wavefield. This decoherence may be causally linked to the observed wave attenuation in the Sun. Although the examples we consider here consist of periodic arrays of perturbations to the background, homogenization may be extended to ergodic and stationary random media. This method may have broad implications for the manner in which we interpret seismic measurements in the Sun and for modeling the effects of granulation on the scattering of waves and distortion of normal-mode eigenfunctions., Comment: 17 pages, 6 figures, in press, ApJ

Aims: We aim to measure the starspot rotation periods of active stars in the Kepler field as a function of spectral type and to extend reliable rotation measurements from F-, G-, and K-type to M-type stars. Methods: Using the Lomb-Scargle periodogram we searched more than 150 000 stellar light curves for periodic brightness variations. We analyzed periods between 1 and 30 days in eight consecutive Kepler quarters, where 30 days is an estimated maximum for the validity of the PDC_MAP data correction pipeline. We selected stable rotation periods, i.e., periods that do not vary from the median by more than one day in at least six of the eight quarters. We averaged the periods for each stellar spectral class according to B - V color and compared the results to archival vsini data, using stellar radii estimates from the Kepler Input Catalog. Results: We report on the stable starspot rotation periods of 12 151 Kepler stars. We find good agreement between starspot velocities and vsini data for all F-, G- and early K-type stars. The 795 M-type stars in our sample have a median rotation period of 15.4 days. We find an excess of M-type stars with periods less than 7.5 days that are potentially fast-rotating and fully convective. Measuring photometric variability in multiple Kepler quarters appears to be a straightforward and reliable way to determine the rotation periods of a large sample of active stars, including late-type stars., Comment: 5 pages, 3 figures. Online material is available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/557/L10

We compare measurements of horizontal flows on the surface of the Sun using helioseismic time--distance inversions and coherent structure tracking of solar granules. Tracking provides 2D horizontal flows on the solar surface, whereas the time--distance inversions estimate the full 3-D velocity flows in the shallow near-surface layers. Both techniques use HMI observations as an input. We find good correlations between the various measurements resulting from the two techniques. Further, we find a good agreement between these measurements and the time-averaged Doppler line-of-sight velocity, and also perform sanity checks on the vertical flow that resulted from the 3-D time--distance inversion., Comment: 22 pages of the manuscript, 5 figures, 3 tables, accepted for publication in the Astrophysical Journal

In order to assess the ability of helioseismology to probe the subsurface structure and magnetic field of sunspots, we need to determine how helioseismic travel times depend on perturbations to sunspot models. Here we numerically simulate the propagation of f, p1, and p2 wave packets through magnetic sunspot models. Among the models we considered, a ~50 km change in the height of the Wilson depression and a change in the subsurface magnetic field geometry can both be detected above the observational noise level. We also find that the travel-time shifts due to changes in a sunspot model must be modeled by computing the effects of changing the reference sunspot model, and not by computing the effects of changing the subsurface structure in the quiet-Sun model. For p1 modes the latter is wrong by a factor of four. In conclusion, numerical modeling of MHD wave propagation is an essential tool for the interpretation of the effects of sunspots on seismic waveforms., Comment: 5 pages, 3 figures: submitted to A&A

The measurement of the Sun's surface motions with a high spatial and temporal resolution is still a challenge. We wish to validate horizontal velocity measurements all over the visible disk of the Sun from Solar Dynamics Observatory/ Helioseismic and Magnetic Imager (SDO/HMI) data. Horizontal velocity fields are measured by following the proper motions of solar granules using a newly developed version of the Coherent Structure Tracking (CST) code. The comparison of the surface flows measured at high spatial resolution (Hinode, 0.1 arcsec) and low resolution (SDO/HMI, 0.5 arcsec) allows us to determine corrections to be applied to the horizontal velocity measured from HMI white light data. We derive horizontal velocity maps with spatial and temporal resolutions of respectively 2.5 Mm and 30 min. From the two components of the horizontal velocity Vx and Vy measured in the sky plane and the simultaneous line of sight component from SDO/HMI dopplergrams v_D, we derive the spherical velocity components (Vr, Vtheta, Vphi). The azimuthal component Vphi gives the solar differential rotation with a high precision (+-0.037km/s) from a temporal sequence of only three hours. By following the proper motions of the solar granules, we can revisit the dynamics of the solar surface at high spatial and temporal resolutions from hours to months and years with the SDO data., Comment: 8 pages, 13 figures, accepted in Astronomy and Astrophysics

The Square Kilometre Array (SKA) is the most ambitious radio telescope ever planned. With a collecting area of about a square kilometre, the SKA will be far superior in sensitivity and observing speed to all current radio facilities. The scientific capability promised by the SKA and its technological challenges provide an ideal base for interdisciplinary research, technology transfer, and collaboration between universities, research centres and industry. The SKA in the radio regime and the European Extreme Large Telescope (E-ELT) in the optical band are on the roadmap of the European Strategy Forum for Research Infrastructures (ESFRI) and have been recognised as the essential facilities for European research in astronomy. This "White Paper" outlines the German science and R&D interests in the SKA project and will provide the basis for future funding applications to secure German involvement in the Square Kilometre Array., Comment: Editors: H. R. Kl\"ockner, M. Kramer, H. Falcke, D.J. Schwarz, A. Eckart, G. Kauffmann, A. Zensus; 150 pages (low resolution- and colour-scale images), published in July 2012, language English (including a foreword and an executive summary in German), the original file is available via the MPIfR homepage

Convection is the mechanism by which energy is transported through the outermost 30% of the Sun. Solar turbulent convection is notoriously difficult to model across the entire convection zone where the density spans many orders of magnitude. In this issue of PNAS, Hanasoge et al. (2012) employ recent helioseismic observations to derive stringent empirical constraints on the amplitude of large-scale convective velocities in the solar interior. They report an upper limit that is far smaller than predicted by a popular hydrodynamic numerical simulation., Comment: Printed in the Proceedings of the National Academy of Sciences (2 pages, 1 figure). Available at http://www.pnas.org/cgi/doi/10.1073/pnas.1208875109

Sunspots are prominent manifestations of solar magnetoconvection and imaging their subsurface structure is an outstanding problem of wide physical importance. Travel times of seismic waves that propagate through these structures are typically used as inputs to inversions. Despite the presence of strongly anisotropic magnetic waveguides, these measurements have always been interpreted in terms of changes to isotropic wavespeeds and flow-advection related Doppler shifts. Here, we employ PDE-constrained optimization to determine the appropriate parameterization of the structural properties of the magnetic interior. Seven different wavespeeds fully characterize helioseismic wave propagation: the isotropic sound speed, a Doppler-shifting flow-advection velocity and an anisotropic magnetic velocity. The structure of magnetic media is sensed by magnetoacoustic slow and fast modes and Alfv\'{e}n waves, each of which propagates at a different wavespeed. We show that even in the case of weak magnetic fields, significant errors may be incurred if these anisotropies are not accounted for in inversions. Translation invariance is demonstrably lost. These developments render plausible the accurate seismic imaging of magnetoconvection in the Sun., Comment: 4 pages, 4 figures, accepted Physical Review Letters