Context. Active regions (ARs) play an important role in the magnetic dynamics of the Sun. Solar surface flux transport models (SFTMs) are used to describe the evolution of the radial magnetic field at the solar surface. The models are kinematic in the sense that the radial component of the magnetic field behaves as passively advected corks. There is, however, uncertainty about using these models in the early stage of AR evolution, where dynamic effects might be important. Aims. We aim to test the applicability of SFTMs in the first days after the emergence of ARs by comparing them with observations. The models we employ range from passive evolution to models where the inflows around ARs are included. Methods. We simulated the evolution of the surface magnetic field of 17 emerging ARs using a local surface flux transport simulation. The regions were selected such that they did not form fully fledged sunspots that exhibit moat flows. The simulation included diffusion and advection by a velocity field, for which we tested different models. For the flow fields, we used observed flows from local correlation tracking of solar granulation, as well as parametrizations of the inflows around ARs based on the gradient of the magnetic field. To evaluate our simulations, we measured the cross correlation between the observed and the simulated magnetic field, as well as the total unsigned flux of the ARs, over time. We also tested the validity of our simulations by varying the starting time relative to the emergence of flux. Results. We find that the simulations using observed surface flows can reproduce the evolution of the observed magnetic flux. The effect of buffeting the field by supergranulation can be described as a diffusion process. The SFTM is applicable after 90% of the peak total unsigned flux of the AR has emerged. Diffusivities in the range between D = 250- 720 km2 s*1 are consistent with the evolution of the AR flux in the first five days after this time. We find that the converging flows around emerging ARs are not important for the evolution of the total flux of the AR in these first five days; their effect of increasing flux cancellation is balanced by the decrease in flux transport away from the AR.

Context. Solar active regions are associated with Evershed outflows in sunspot penumbrae, moat outflows surrounding sunspots, and extended inflows surrounding active regions. Extended inflows have been identified around established active regions with various methods. The evolution of these inflows and their dependence on active region properties as well as their effect on the global magnetic field are not yet understood. Aims. We aim to understand the evolution of the average inflows around emerging active regions and to derive an empirical model for these inflows. We expect that this can be used to better understand how the inflows act on the diffusion of the magnetic field in active regions. Methods. We analyzed horizontal flows at the surface of the Sun using local correlation tracking of solar granules observed in continuum images of the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. We measured average flows of a sample of 182 isolated active regions up to seven days before and after their emergence onto the solar surface with a cadence of 12 h. About half of the active regions in the sample developed sunspots with moat flows in addition to the surrounding inflows. We investigated the average inflow properties with respect to active region characteristics of total flux and latitude. We fit a model to these observed inflows for a quantitative analysis. Results. We find that converging flows of about 20-30 m s-1 are first visible one day prior to emergence, in agreement with recent results. These converging flows are present regardless of the active region properties of latitude or flux. We confirm a recently found prograde flow of about 40 m s-1 at the leading polarity during emergence. We find that the time after emergence when the latitudinal inflows increase in amplitude depends on the flux of the active region, ranging from one to four days after emergence and increasing with flux. The largest extent of the inflows is up to about 7 ± 1° away from the center of the active region within the first six days after emergence. The inflow velocities have amplitudes of about 50 m s-1.

Magnetic flux generated within the solar interior emerges to the surface, forming active regions (ARs) and sunspots. Flux emergence may trigger explosive events¿such as flares and coronal mass ejections, and therefore understanding emergence is useful for space-weather forecasting. Evidence of any pre-emergence signatures will also shed light on subsurface processes responsible for emergence. In this paper, we present a first analysis of EARs from the Solar Dynamics Observatory/Helioseismic Emerging Active Regions dataset using deep convolutional neural networks (CNN) to characterize pre-emergence surface magnetic field properties. The trained CNN classifies between pre-emergence line-of-sight magnetograms and a control set of nonemergence magnetograms with a true skill statistic (TSS) score of approximately 85% about 3 hr prior to emergence and approximately 40% about 24 hr prior to emergence. Our results are better than a baseline classification TSS obtained using discriminant analysis (DA) of only the unsigned magnetic flux, although a multivariable DA produces TSS values consistent with the CNN. We develop a network-pruning algorithm to interpret the trained CNN and show that the CNN incorporates filters that respond positively as well as negatively to the unsigned magnetic flux of the magnetograms. Using synthetic magnetograms, we demonstrate that the CNN output is sensitive to the length scale of the magnetic regions, with small-scale and intense fields producing maximum CNN output and possibly a characteristic pre-emergence pattern. Given increasing popularity of deep learning, the techniques developed here to interpret the trained CNN¿using network pruning and synthetic data¿are relevant for future applications in solar and astrophysical data analysis.

Context. The solar dynamo consists of a process that converts poloidal magnetic field to toroidal magnetic field followed by a process that creates new poloidal field from the toroidal field. Aims. Our aim is to observe the poloidal and toroidal fields relevant to the global solar dynamo and to see if their evolution is captured by a Babcock-Leighton dynamo. Methods. We used synoptic maps of the surface radial field from the KPNSO/VT and SOLIS observatories, to construct the poloidal field as a function of time and latitude; we also used full disk images from Wilcox Solar Observatory and SOHO/MDI to infer the longitudinally averaged surface azimuthal field. We show that the latter is consistent with an estimate of the longitudinally averaged surface azimuthal field due to flux emergence and therefore is closely related to the subsurface toroidal field. Results. We present maps of the poloidal and toroidal magnetic fields of the global solar dynamo. The longitude-averaged azimuthal field observed at the surface results from flux emergence. At high latitudes this component follows the radial component of the polar fields with a short time lag of between 1-3 years. The lag increases at lower latitudes. The observed evolution of the poloidal and toroidal magnetic fields is described by the (updated) Babcock-Leighton dynamo model.

The internal gravity modes of the Sun are notoriously difficult to detect, and the claimed detection of gravity modes presented by Fossat et¿al. (Astron. Astrophys.604, A40, 2017) is thus very exciting. Given the importance of these modes for understanding solar structure and dynamics, the results must be robust. While Fossat et al. described their method and parameter choices in detail, the sensitivity of their results to several parameters was not presented. Therefore, we test the sensitivity of the results to a selection of the parameters. The most concerning result is that the detection vanishes when we adjust the start time of the 16.5-year velocity time-series by a few hours. We conclude that this reported detection of gravity modes is extremely fragile and should be treated with utmost caution.

Context. Rotational shear in Sun-like stars is thought to be an important ingredient in models of stellar dynamos. Thanks to helioseismology, rotation in the Sun is characterized well, but the interior rotation profiles of other Sun-like stars are not so well constrained. Until recently, measurements of rotation in Sun-like stars have focused on the mean rotation, but little progress has been made on measuring or even placing limits on differential rotation. Aims. Using asteroseismic measurements of rotation we aim to constrain the radial shear in five Sun-like stars observed by the NASA Kepler mission: KIC 004914923, KIC 005184732, KIC 006116048, KIC 006933899, and KIC 010963065. Methods. We used stellar structure models for these five stars from previous works. These models provide the mass density, mode eigenfunctions, and the convection zone depth, which we used to compute the sensitivity kernels for the rotational frequency splitting of the modes. We used these kernels as weights in a parametric model of the stellar rotation profile of each star, where we allowed different rotation rates for the radiative interior and the convective envelope. This parametric model was incorporated into a fit to the oscillation power spectrum of each of the five Kepler stars. This fit included a prior on the rotation of the envelope, estimated from the rotation of surface magnetic activity measured from the photometric variability. Results. The asteroseismic measurements without the application of priors are unable to place meaningful limits on the radial shear. Using a prior on the envelope rotation enables us to constrain the interior rotation rate and thus the radial shear. In the five cases that we studied, the interior rotation rate does not differ from the envelope by more than approximately ± 30%. Uncertainties in the rotational splittings are too large to unambiguously determine the sign of the radial shear.

Aims. We quantify the effect of observational spectroscopic and asteroseismic uncertainties on regularised least squares (RLS) inversions for the radial differential rotation of Sun-like and subgiant stars. Methods. We first solved the forward problem to model rotational splittings plus the observed uncertainties for models of a Sun-like star, HD 52265, and a subgiant star, KIC 7341231. We randomly perturbed the parameters of the stellar models within the uncertainties of the spectroscopic and asteroseismic constraints and used these perturbed stellar models to compute rotational splittings. We experimented with three rotation profiles: solid body rotation, a step function, and a smooth rotation profile decreasing with radius. We then solved the inverse problem to infer the radial differential rotation profile using a RLS inversion and kernels from the best-fit stellar model. We also compared RLS, optimally localised average (OLA) and direct functional fitting inversion techniques. Results. We found that the inversions for Sun-like stars with solar-like radial differential rotation profiles are insensitive to the uncertainties in the stellar models. The uncertainties in the splittings dominate the uncertainties in the inversions and solid body rotation is not excluded. We found that when the rotation rate below the convection zone is increased to six times that of the surface rotation rate the inferred rotation profile excluded solid body rotation. We showed that when we reduced the uncertainties in the splittings by a factor of about 100, the inversion is sensitive to the uncertainties in the stellar model. With the current observational uncertainties, we found that inversions of subgiant stars are sensitive to the uncertainties in the stellar model. Conclusions. Our findings suggest that inversions for the radial differential rotation of subgiant stars would benefit from more tightly constrained stellar models. We conclude that current observational uncertainties make it difficult to infer radially resolved features of the rotation profile in a Sun-like star using inversions with regularisation. In Sun-like stars, the insensitivity of the inversions to stellar model uncertainties suggests that it may be possible to perform ensemble inversions for the average radial differential rotation of many stars with a range of stellar types to better constrain the inversions.

Context. Radial differential rotation is an important parameter for stellar dynamo theory and for understanding angular momentum transport. Aims. 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". Methods. 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 ¿O = -0.35 µHz, 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 ¿O. Results. All the uncertainties on the inferred ¿O for individual stars are of the order 1 µHz. Using 15 stellar models in an ensemble fit, we show that the uncertainty on the average ¿O is reduced to less than the input ¿O, which allows us to constrain the sign of the radial differential rotation. We show that a solar-like ¿O ~ 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 ¿O between F, G, and K-type stars larger than 100 nHz could be detected.

Context. Observations from the Solar Dynamics Observatory (SDO) have the potential for allowing the helioseismic study of the formation of hundreds of active regions, which would enable us to perform statistical analyses. Aims. Our goal is to collate a uniform data set of emerging active regions observed by the SDO/HMI instrument suitable for helioseismic analysis, where each active region is centred on a 60° × 60° area and can be observed up to seven days before emergence. Methods. We restricted the sample to active regions that were visible in the continuum and emerged into quiet Sun largely avoiding pre-existing magnetic regions. As a reference data set we paired a control region (CR), with the same latitude and distance from central meridian, with each emerging active region (EAR). The control regions do not have any strong emerging flux within 10° of the centre of the map. Each region was tracked at the Carrington rotation rate as it crossed the solar disk, within approximately 65° from the central meridian and up to seven days before, and seven days after, emergence. The mapped and tracked data, consisting of line-of-sight velocity, line-of-sight magnetic field, and intensity as observed by SDO/HMI, are stored in datacubes that are 410 min in duration and spaced 320 min apart. We call this data set, which is currently comprised of 105 emerging active regions observed between May 2010 and November 2012, the SDO Helioseismic Emerging Active Region (SDO/HEAR) survey. Results. To demonstrate the utility of a data set of a large number of emerging active regions, we measure the relative east-west velocity of the leading and trailing polarities from the line-of-sight magnetogram maps during the first day after emergence. The latitudinally averaged line-of-sight magnetic field of all the EARs shows that, on average, the leading (trailing) polarity moves in a prograde (retrograde) direction with a speed of 121 ± 22 m s-1 (-70 ± 13 m s-1) relative to the Carrington rotation rate in the first day. However, relative to the differential rotation of the surface plasma, the east-west velocity is symmetric, with a mean of 95 ± 13 m s-1. Conclusions. The SDO/HEAR data set will not only be useful for helioseismic studies, but will also be useful to study other features such as the surface magnetic field evolution of a large sample of EARs. We intend to extend this survey forwards in time to include more EARs observed by SDO/HMI.

Magnetic field emerges at the surface of the Sun as sunspots and active regions. This process generates a poloidal magnetic field from a rising toroidal flux tube; it is a crucial but poorly understood aspect of the solar dynamo. The emergence of magnetic field is also important because it is a key driver of solar activity. We show that measurements of horizontal flows at the solar surface around emerging active regions, in combination with numerical simulations of solar magnetoconvection, can constrain the subsurface rise speed of emerging magnetic flux. The observed flows imply that the rise speed of the magnetic field is no larger than 150 m/s at a depth of 20 Mm, that is, well below the prediction of the (standard) thin flux tube model but in the range expected for convective velocities at this depth. We conclude that convective flows control the dynamics of rising flux tubes in the upper layers of the Sun and cannot be neglected in models of flux emergence.

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. We compare the rotation periods obtained from light-curve variability with those from asteroseismology in order to further constrain differential rotation. 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.

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.

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 s readout cadence and 2 with 2.5 s candence) providing a wide field-of-view (2232 deg 2) 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. The PLATO 2.0 catalogue allows us to e.g.: - complete our knowledge of planet diversity for low-mass objects, - correlate the planet mean density-orbital distance distribution with predictions from planet formation theories,- constrain the influence of planet migration and scattering on the architecture of multiple systems, and - specify how planet and system parameters change with host star characteristics, such as type, metallicity and age. The catalogue will allow us to study planets and planetary systems at different evolutionary phases. It will further provide a census for small, low-mass planets. This will serve to identify objects which retained their primordial hydrogen atmosphere and in general the typical characteristics of planets in such low-mass, low-density range. Planets detected by PLATO 2.0 will orbit bright stars and many of them will be targets for future atmosphere spectroscopy exploring their atmosphere. Furthermore, the mission has the potential to detect exomoons, planetary rings, binary and Trojan planets. The planetary science possible with PLATO 2.0 is complemented by its impact on stellar and galactic science via asteroseismology as well as light curves of all kinds of variable stars, together with observations of stellar clusters of different ages. This will allow us to improve stellar models and study stellar activity. A large number of well-known ages from red giant stars will probe the structure and evolution of our Galaxy. Asteroseismic ages of bright stars for different phases of stellar evolution allow calibrating stellar age-rotation relationships. Together with the results of ESA¿s Gaia mission, the results of PLATO 2.0 will provide a huge legacy to planetary, stellar and galactic science.

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. © 2013 ESO.

We observe and characterize the scattering of acoustic wave packets by a sunspot in a regime where the wavelength is comparable to the size of the sunspot. Spatial maps of wave travel times and amplitudes are measured from the cross-covariance function of the random wave field observed by SOHO/MDI around the sunspot in active region NOAO 9787. We consider separately incoming plane wave packets consisting of f modes and p modes with radial orders up to four. Observations show that the travel-time perturbations diminish with distance far away from the sunspot-a finite-wavelength phenomenon known as wavefront healing in scattering theory. Observations also show a reduction of the amplitude of the waves after their passage through the sunspot. We suggest that a significant fraction of this amplitude reduction is due to the defocusing of wave energy by the fast wave-speed perturbation introduced by the sunspot. This "geometrical attenuation" will contribute to the wave amplitude reduction in addition to the physical absorption of waves by sunspots. We also observe an enhancement of wave amplitude away from the central path: diffracted rays intersect with unperturbed rays (caustics) and wavefronts fold and triplicate. Wave amplitude measurements in time-distance helioseismology provide independent information that can be used in concert with travel-time measurements. © 2013 ESO.

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 interpreting the effects of sunspots on seismic waveforms. © 2013 ESO.

We study properties of waves of frequencies above the photospheric acoustic cut-off of ¿5.3 mHz, around four active regions, through spatial maps of their power estimated using data from the Helioseismic and Magnetic Imager (HMI) and Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). The wavelength channels 1600 Å and 1700 Å from AIA are now known to capture clear oscillation signals due to helioseismic p-modes as well as waves propagating up through to the chromosphere. Here we study in detail, in comparison with HMI Doppler data, properties of the power maps, especially the so-called "acoustic halos" seen around active regions, as a function of wave frequencies, inclination, and strength of magnetic field (derived from the vector-field observations by HMI), and observation height. We infer possible signatures of (magneto)acoustic wave refraction from the observation-height-dependent changes, and hence due to changing magnetic strength and geometry, in the dependences of power maps on the photospheric magnetic quantities. We discuss the implications for theories of p-mode absorption and mode conversions by the magnetic field. © 2012 Springer Science+Business Media Dordrecht.

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 that are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun t5000=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, Astrophys. J. 306, 284) and the penumbral model of Ding and Fang (1989, Astron. Astrophys. 225, 204). 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 1 Mm 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 ver0is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45° 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, p1, and p2 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. © 2010 Springer Science+Business Media B.V.

The cause of enhanced acoustic power surrounding active regions, known as the acoustic halo, is not as yet understood. We explore the properties of the enhanced acoustic power observed near disk center from 21 to 27 January 2002, including AR 9787. We find that i) there exists a strong correlation of the enhanced high-frequency power with magnetic-field inclination, with greater power in more horizontal fields, ii) the frequency of the maximum enhancement increases along with magnetic-field strength, and iii) the oscillations contributing to the halos show modal ridges that are shifted to higher wavenumber at constant frequency in comparison to the ridges of modes in the quiet Sun. © 2010 Springer Science+Business Media B.V.

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 linearised equations of motion include convective modes that can swamp the helioseismic waves that we are interested in. In this article, we construct background solar models that are stable against convection, by modifying the vertical pressure gradient of Model S (Christensen-Dalsgaard et al., 1996, Science272, 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/. © 2011 The Author(s).

The goal of local helioseismology is to elicit three-dimensional information about the sub-surface (or far-side) structure and dynamics of the Sun from observations of the helioseismic wave field at the surface. The physical quantities of interest include flows, sound-speed deviations and magnetic fields. However, strong surface magnetic fields induce large perturbations to the waves making inversions difficult to interpret. The purpose of this paper is to outline the methods of analysis used in local helioseismology, review discoveries associated with the magnetic Sun made using local helioseismology from the past three years, and highlight the efforts towards imaging the interior in the presence of strong magnetic fields © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We used long duration, high quality, unresolved (Sun-as-a star) observations collected by the ground based network BiSON and by the instruments GOLF and VIRGO on board the ESA/NASA SOHO satellite to search for solar-cycle-related changes in mode characteristics in velocity and continuum intensity for the frequency range between 2.5 mHz <\nu<6.8 mHz. Over the ascending phase of solar cycle 23 we found a suppression in the p-mode amplitudes both in the velocity and intensity data between 2.5 mHz lt;\nu< 4.5 mHz with a maximum suppression for frequencies in the range between 2.5 mHz <\nu< 3.5 mHz. The size of the amplitude suppression is 13 ± 2 per cent for the velocity and 9 ± 2 per cent for the intensity observations. Over the range of 4.5 mHz <\nu<5.5 mHz the findings hint within the errors to a null change both in the velocity and intensity amplitudes. At still higher frequencies, in the so called High-frequency Interference Peaks (HIPs) between 5.8 mHz <\nu<6.8 mHz, we found an enhancement in the velocity amplitudes with the maximum 36 ± 7 per cent occurring for 6.3 mHz <\nu< 6.8 mHz. However, in intensity observations we found a rather smaller enhancement of about 5 ± 2 per cent in the same interval. There is evidence that the frequency dependence of solar-cycle velocity amplitude changes is consistent with the theory behind the mode conversion of acoustic waves in a non-vertical magnetic field, but there are some problems with the intensity data, which may be due to the height in the solar atmosphere at which the VIRGO data are taken. © 2010 ESO.

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009a, 2009b). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat. © 2010 Springer Science+Business Media B.V.

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. AR 9787 is visible on helioseismic maps of the farside of the Sun from 15 January, i.e. days before it crossed the East limb. Oscillations have reduced amplitudes in the sunspot at all frequencies, whereas a region of enhanced acoustic power above 5.5 mHz (above the quiet-Sun acoustic cutoff) is seen outside the sunspot and the plage region. This enhanced acoustic power has been suggested to be caused by the conversion of acoustic waves into magneto-acoustic waves that are refracted back into the interior and re-emerge as acoustic waves in the quiet Sun. Observations show that the sunspot absorbs a significant fraction of the incoming p and f modes around 3 mHz. A numerical simulation of MHD wave propagation through a simple mo of AR 9787 confirmed that wave absorption is likely to be due to the partial conversion of incoming waves into magneto-acoustic waves that propagate down the sunspot. 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. The travel-time measurements also imply different subsurface flow patterns in the surface layer depending on the filtering procedure that is used. Current sensitivity kernels are unable to reconcile these measurements, perhaps because they re on imperfect models of the power spectrum of solar oscillations. We present a linear inversion for flows of ridge-filtered travel times. This inversion shows a horizontal outflow in the upper 4 Mm that is consistent with the moat flow deduced from the surface motion of moving magnetic features. From this study of AR 9787, we conclude that we are currently unable to provide a unified description of the subsurface structure and dynamics of the sunspot.

At the surface of the Sun, acoustic waves appear to be affected by the presence of strong magnetic fields in active regions. We explore the possibility that the inclined magnetic field in sunspot penumbrae may convert primarily vertically-propagating acoustic waves into elliptical motion. We use helioseismic holography to measure the modulus and phase of the correlation between incoming acoustic waves and the local surface motion within two sunspots. These correlations are modeled by assuming the surface motion to be elliptical, and we explore the properties of the elliptical motion on the magnetic-field inclination. We also demonstrate that the phase shift of the outward-propagating waves is opposite to the phase shift of the inward-propagating waves in stronger, more vertical fields, but similar to the inward phase shifts in weaker, more-inclined fields. © 2008 The Author(s).

The Local Helioseismology Network Activity is part of the European Helio-and Asteroseismology Network (HELAS). One aspect of the network activity is to collate multipurpose data sets and make them available to the community for local helioseismic analysis. The first stage of the project is underway whereby high quality and useful data sets have been selected and acquired. The HELAS Local Helioseismology Network Activity website at http://www.mps.mpg.de/ projects/seismo/NA4/ provides this data ready to download. Furthermore, the data is supplemented with relevant documentation necessary for further analysis, including details about the data reduction process that has already been applied. The data primarily consists of Doppler velocity observations but also includes observations of the line-of-sight magnetic field, vector magnetic field measurements, intensity and travel time maps. The website will be continuously updated with data thereby providing convenient access to comprehensive data sets appropriate for use in local helioseismology. © 2008 IOP Publishing Ltd.

One of the major, important developments in local helioseismology was the discovery by Duvall et al. (1996) that the travel times of seismic waves into sunspots from the surrounding quiet Sun significantly exceed the same in the reverse direction, a behavior they suggested was the result of rapid downflows directly beneath the sunspot photosphere. This led to the need for rapid near-surface horizontal inflows to replace the mass evacuated from the sunspot subphotosphere by such downflows. The lack of independent evidence for such inflows led to the suggestion that the travel-time asymmetry could be explained by a relative phase delay in the response of the sunspot photosphere to incoming waves with respect to that of the quiet Sun. In the succeeding ten years major progress has been made in our understanding of how magnetic photospheres respond to incoming waves, at the instigation of theoretical work by Spruit, Cally and Bogdan. This has led to the recognition of inclined penumbral magnetic fields as a major avenue for control work on the subject of the travel-time asymmetry and its relation to the absorption of p-modes by magnetic regions. A major recent development has been the discovery by Schunker et al. (2005) that the phase of this response in Doppler observations of penumbral photospheres depends strongly on the vantage of the Doppler measurements projected into the vertical plane of the magnetic field. This discovery heavily reinforces the proposition that the travel-time asymmetry is largely the signature of the same irreversible damping processes that are responsible for the strong absorption of p-modes in magnetic regions. We will elaborate on the implications of the foregoing developments respecting the diagnostics of subphotospheric flows based on seismic observations in which magnetic regions cannot be avoided. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA.

Using helioseismic holography strong evidence is presented that the phase (or equivalent travel-time) of helioseismic signatures in Dopplergrams within sunspots depend upon the line-of-sight angle in the plane containing the magnetic field and vertical directions. This is shown for the velocity signal in the penumbrae of two sunspots at 3, 4 and 5 mHz. Phase-sensitive holography demonstrates that they are significantly affected in a strong, moderately inclined magnetic field. This research indicates that the effects of the surface magnetic field are potentially very significant for local helioseismic analysis of active regions. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA.

Recent observational evidence for magnetic field direction effects on helioseismic signals in sunspot penumbrae is suggestive of magnetohydrodynamic (MHD) mode conversion occurring at lower levels. This possibility is explored using wave mechanical and ray theory in a model of the Sun's surface layers permeated by uniform inclined magnetic field. It is found that fast-to-slow conversion near the equipartition depth at which the sound and Alfvén speeds coincide can indeed greatly enhance the atmospheric acoustic signal at heights observed by Solar and Heliospheric Observatory/Michelson Doppler Imager and other helioseismic instruments, but that this effect depends crucially on the wave attack angle, i.e. the angle between the wavevector and the magnetic field at the conversion/transmission depth. A major consequence of this insight is that the magnetic field acts as a filter, preferentially allowing through acoustic signal from a narrow range of incident directions. This is potentially testable by observation. © 2006 RAS.

We present evidence for the dependence of helioseismic Doppler signatures in active regions on the line-of-sight angle in inclined magnetic fields. Using data from the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory, we performed phase-sensitive holography in the penumbrae of sunspots over the course of several days as the spots traversed the solar disk. Control correlations, which comprise a correlation of the surface wave amplitude with the incoming acoustic wave amplitude from a surrounding region, were mapped. There is a direct dependence of control-correlation phase signatures on the line-of-sight angle in the plane defined by the vertical and magnetic field vectors. The phase shift of waves observed along directions close to the orientation of the magnetic field is smaller than the phase shift observed when the line of sight is at a significant angle with respect to the field orientation. These findings have important implications for local helioseismology. The variation in phase shift (or the equivalent acoustic travel-time perturbations) with line-of-sight direction suggests that a substantial portion of the phase shift occurs in the photospheric magnetic field. Observations of the vector components of the field may be used to develop a proxy to correct these phase perturbations (known as the acoustic showerglass) that introduce uncertainties in the signatures of acoustic perturbations below the surface. © 2005 The American Astronomical Society. All rights reserved.

This paper presents a comparison of local helioseismic observations from within inclined magnetic fields with theoretical mode conversion results. Helioseismic holography is the technique used for the observational analysis of two sunspots in active regions, AR9026 and AR9057. It is found that the surface velocities within the penumbrae of the sunspots are dependent on the magnetic field orientation and the line-of-sight angle. Mode conversion theory also finds that the orientation of the magnetic field is a very important factor. Surface velocity ellipses are created for particular inclinations of the magnetic field both theoretically and observationally, and these compare somewhat favourably. It is concluded that mode conversion is a likely cause of the observed effects on the surface velocities within inclined magnetic fields.

Direct evidence of the dependence of local helioseismic measurements on the orientation of near-surface magnetic fields is presented. MDI Doppler images are used to perform acoustic holography, with the focus placed in various positions within the penumbrae of two sunspots as the spots move across the solar disk. The computed ingression amplitudes are compared to the observed velocities, to determine the phase shifts produced in the penumbral photosphere. Significant phase changes from the acoustic ingression to the observed line-of-sight velocity are found to be sensitive to the line-of-sight direction in the plane of the tilted magnetic field. Modelling of the observational evidence for the influence of active region magnetic fields on acoustic signals will aid in understanding, and potentially ameliorating, the showerglass effect which obscures our view of deeper features.

We present preliminary results from high resolution observations obtained with the Michelson Doppler Imager (MDI) instrument on the SOHO of two large solar flares of 14 July 2000 and 24 November 2000. We show that rapid variations of the line-of-sight magnetic field occured on a time scale of a few minutes during the flare explosions. The reversibility/irreversibility of the magnetic field of both active regions is a very good tool for understanding how the magnetic energy is released in these flares. The observed sharp increase of the magnetic energy density at the time of maximum of the solar flare could involve an unknown component which deposited supplementary energy into the system.