Phase-speed Filter Research Articles

Observations of Running Penumbral Waves Emerging in a Sunspot

Abstract We present results from the investigation of 5 minute umbral oscillations in a single-polarity sunspot of active region NOAA 12132. The spectra of TiO, Hα, and 304 Å are used for corresponding atmospheric heights from the photosphere to lower corona. Power spectrum analysis at the formation height of Hα – 0.6 Å to the Hα center resulted in the detection of 5 minute oscillation signals in intensity interpreted as running waves outside the umbral center, mostly with vertical magnetic field inclination >15°. A phase-speed filter is used to extract the running wave signals with speed v ph > 4 km s−1, from the time series of Hα – 0.4 Å images, and found twenty-four 3 minute umbral oscillatory events in a duration of one hour. Interestingly, the initial emergence of the 3 minute umbral oscillatory events are noticed closer to or at umbral boundaries. These 3 minute umbral oscillatory events are observed for the first time as propagating from a fraction of preceding running penumbral waves (RPWs). These fractional wavefronts rapidly separate from RPWs and move toward the umbral center, wherein they expand radially outwards suggesting the beginning of a new umbral oscillatory event. We found that most of these umbral oscillatory events develop further into RPWs. We speculate that the waveguides of running waves are twisted in spiral structures and hence the wavefronts are first seen at high latitudes of umbral boundaries and later at lower latitudes of the umbral center.

Helioseismic Holography of Simulated Sunspots: dependence of the travel time on magnetic field strength and Wilson depression.

Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-time shifts at frequencies above approximately 3.50 mHz (depending on the phase-speed filter) are insensitive to the magnetic field strength. The travel time of these waves is determined exclusively by the Wilson depression and sound-speed perturbation. The travel time of waves with lower frequencies is affected by the direct effect of the magnetic field, although photospheric field strengths below 1500 G do not leave a significant trace on the travel-time measurements. These results could potentially be used to develop simplified travel-time inversion methods.

VALIDATING TIME-DISTANCE HELIOSEISMOLOGY WITH REALISTIC QUIET-SUN SIMULATIONS

Linear time-distance helioseismic inversions are carried out for vector flow velocities using travel times measured from two $\sim 100^2\,{\rm Mm^2}\times 20\,{\rm Mm}$ realistic magnetohydrodynamic quiet-Sun simulations of about 20 hr. The goal is to test current seismic methods on these state-of-the-art simulations. Using recent three-dimensional inversion schemes, we find that inverted horizontal flow maps correlate well with the simulations in the upper $\sim 3$ Mm of the domains for several filtering schemes, including phase-speed, ridge, and combined phase-speed and ridge measurements. In several cases, however, the velocity amplitudes from the inversions severely underestimate those of the simulations, possibly indicating nonlinearity of the forward problem. We also find that, while near-surface inversions of the vertical velocites are best using phase-speed filters, in almost all other example cases these flows are irretrievable due to noise, suggesting a need for statistical averaging to obtain better inferences.

VERIFICATION OF THE HELIOSEISMOLOGY TRAVEL-TIME MEASUREMENT TECHNIQUE AND THE INVERSION PROCEDURE FOR SOUND SPEED USING ARTIFICIAL DATA

We performed three-dimensional numerical simulations of the solar surface acoustic wave field for the quiet Sun and for three models with different localized sound-speed perturbations in the interior with deep, shallow, and two-layer structures. We used the simulated data generated by two solar acoustics codes that employ the same standard solar model as a background model, but utilize different integration techniques and different models of stochastic wave excitation. Acoustic travel times were measured using a time-distance helioseismology technique, and compared with predictions from ray theory frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the helioseismic theory for sound-speed perturbations, and for the measurement procedure with and without phase-speed filtering of the oscillation signals. This testing verifies the whole measuring-filtering-inversion procedure for static sound-speed anomalies with small amplitude inside the Sun outside regions of strong magnetic field. It is shown that the phase-speed filtering, frequently used to extract specific wave packets and improve the signal-to-noise ratio, does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the perturbation models in all cases. Due to its smoothing nature, the inversion procedure may overestimate sound-speed variations in regions with sharp gradients of the sound-speed profile.

TOMOGRAPHY OF PLASMA FLOWS IN THE UPPER SOLAR CONVECTION ZONE USING TIME-DISTANCE INVERSION COMBINING RIDGE AND PHASE-SPEED FILTERING

The consistency of time--distance inversions for horizontal components of the plasma flow on supergranular scales in the upper solar convection zone is checked by comparing the results derived using two k--\omega filtering procedures -- ridge filtering and phase-speed filtering -- commonly used in time--distance helioseismology. It is shown that both approaches result in similar flow estimates when finite-frequency sensitivity kernels are used. It is further demonstrated that the performance of the inversion improves (in terms of simultaneously better averaging kernel and lower noise level) when the two approaches are combined together in one inversion. Using the combined inversion I invert for horizontal flows in the upper 10 Mm of the solar convection zone. The flows connected with supergranulation seem to be coherent only in the upper ~5 Mm depth, deeper down there is a hint on change of convection scales towards structures larger than supergranules.

Helioseismic Holography of an Artificial Submerged Sound Speed Perturbation and Implications for the Detection of Pre-emergence Signatures of Active Regions

We use a publicly available numerical wave-propagation simulation of Hartlep et al. 2011 to test the ability of helioseismic holography to detect signatures of a compact, fully submerged, 5% sound-speed perturbation placed at a depth of 50 Mm within a solar model. We find that helioseismic holography as employed in a nominal "lateral-vantage" or "deep-focus" geometry employing quadrants of an annular pupil is capable of detecting and characterizing the perturbation. A number of tests of the methodology, including the use of a plane-parallel approximation, the definition of travel-time shifts, the use of different phase-speed filters, and changes to the pupils, are also performed. It is found that travel-time shifts made using Gabor-wavelet fitting are essentially identical to those derived from the phase of the Fourier transform of the cross-covariance functions. The errors in travel-time shifts caused by the plane-parallel approximation can be minimized to less than a second for the depths and fields of view considered here. Based on the measured strength of the mean travel-time signal of the perturbation, no substantial improvement in sensitivity is produced by varying the analysis procedure from the nominal methodology in conformance with expectations. The measured travel-time shifts are essentially unchanged by varying the profile of the phase-speed filter or omitting the filter entirely. The method remains maximally sensitive when applied with pupils that are wide quadrants, as opposed to narrower quadrants or with pupils composed of smaller arcs. We discuss the significance of these results for the recent controversy regarding suspected pre-emergence signatures of active regions.

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time–Distance Helioseismology

As large-distance rays (say, 10 – 24°) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large-separation travel times associated with supergranulation cannot be studied using the standard phase-speed filters of time–distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations, reduce the resultant travel-time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center–annulus travel-time difference [δt oi] in the separation range Δ=10 – 24∘ is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity, 5.1±0.1 seconds, is constant over the distance range. This magnitude of the signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 m s−1 extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 m s−1 at a depth of 2.3 Mm and a peak horizontal flow of 700 m s−1 at a depth of 1.6 Mm.

NOTE ON TRAVEL TIME SHIFTS DUE TO AMPLITUDE MODULATION IN TIME-DISTANCE HELIOSEISMOLOGY MEASUREMENTS

Correct interpretation of acoustic travel times measured by time-distance helioseismology is essential to get an accurate understanding of the solar properties that are inferred from them. It has long been observed that sunspots suppress p-mode amplitude, but its implications on travel times has not been fully investigated so far. It has been found in test measurements using a 'masking' procedure, in which the solar Doppler signal in a localized quiet region of the Sun is artificially suppressed by a spatial function, and using numerical simulations that the amplitude modulations in combination with the phase-speed filtering may cause systematic shifts of acoustic travel times. To understand the properties of this procedure, we derive an analytical expression for the cross-covariance of a signal that has been modulated locally by a spatial function that has azimuthal symmetry, and then filtered by a phase speed filter typically used in time-distance helioseismology. Comparing this expression to the Gabor wavelet fitting formula without this effect, we find that there is a shift in the travel times, that is introduced by the amplitude modulation. The analytical model presented in this paper can be useful also for interpretation of travel time measurements for non-uniform distribution of oscillation amplitude due to observational effects.

HIGH-RESOLUTION HELIOSEISMIC IMAGING OF SUBSURFACE STRUCTURES AND FLOWS OF A SOLAR ACTIVE REGION OBSERVED BYHINODE

We analyze a solar active region observed by the Hinode CaII H line using the time-distance helioseismology technique, and infer wave-speed perturbation structures and flow fields beneath the active region with a high spatial resolution. The general subsurface wave-speed structure is similar to the previous results obtained from SOHO/MDI observations. The general subsurface flow structure is also similar, and the downward flows beneath the sunspot and the mass circulations around the sunspot are clearly resolved. Below the sunspot, some organized divergent flow cells are observed, and these structures may indicate the existence of mesoscale convective motions. Near the light bridge inside the sunspot, hotter plasma is found beneath, and flows divergent from this area are observed. The Hinode data also allow us to investigate potential uncertainties caused by the use of phase-speed filter for short travel distances. Comparing the measurements with and without the phase-speed filtering, we find out that inside the sunspot, mean acoustic travel times are in basic agreement, but the values are underestimated by a factor of 20-40% inside the sunspot umbra for measurements with the filtering. The initial acoustic tomography results from Hinode show a great potential of using high-resolution observations for probing the internal structure and dynamics of sunspots.

Helioseismic Travel-Time Definitions and Sensitivity to Horizontal Flows Obtained from Simulations of Solar Convection

We study the sensitivity of wave travel times to steady and spatially homogeneous horizontal flows added to a realistic simulation of the solar convection performed by Robert F. Stein, Ake Nordlund, Dali Georgobiani, and David Benson. Three commonly used definitions of travel times are compared. We show that the relationship between travel-time difference and flow amplitude exhibits a non-linearity depending on the travel distance, the travel-time definition considered, and the details of the time-distance analysis (in particular, the impact of the phase-speed filter width). For times measured using a Gabor wavelet fit, the travel-time differences become nonlinear in the flow strength for flows of about 300 m/s, and this non-linearity reaches almost 60% at 1200 m/s (relative difference between actual travel time and expected time for a linear behaviour). We show that for travel distances greater than about 17 Mm, the ray approximation predicts the sensitivity of travel-time shifts to uniform flows. For smaller distances, the ray approximation can be inaccurate by more than a factor of three.

Helioseismology of Sunspots: A Case Study of NOAA Region 9787

Various methods of helioseismology are used to study the subsurface properties of the sunspot in NOAA Active Region 9787. This sunspot was chosen because it is axisymmetric, shows little evolution during 20-28 January 2002, and was observed continuously by the MDI/SOHO instrument. (...) Wave travel times and mode frequencies are affected by the sunspot. In most cases, wave packets that propagate through the sunspot have reduced travel times. At short travel distances, however, the sign of the travel-time shifts appears to depend sensitively on how the data are processed and, in particular, on filtering in frequency-wavenumber space. We carry out two linear inversions for wave speed: one using travel-times and phase-speed filters and the other one using mode frequencies from ring analysis. These two inversions give subsurface wave-speed profiles with opposite signs and different amplitudes. (...) From this study of AR9787, we conclude that we are currently unable to provide a unified description of the subsurface structure and dynamics of the sunspot.

NUMERICAL MODELS OF TRAVEL-TIME INHOMOGENEITIES IN SUNSPOTS

We investigate the direct contribution of strong, sunspot-like magnetic fields to helioseismic wave travel-time shifts via two numerical forward models, a 3D ideal MHD solver and MHD ray theory. The simulated data cubes are analyzed using the traditional time-distance center-to-annulus measurement technique. We also isolate and analyze the direct contribution from purely thermal perturbations to the observed travel-time shifts, confirming some existing ideas and bring forth new ones: (i) that the observed travel-time shifts in the vicinity of sunspots are largely governed by MHD physics, (ii) the travel-time shifts are sensitively dependent on frequency and phase-speed filter parameters and the background power below the $p_1$ ridge, and finally, (iii) despite its seeming limitations, ray theory succeeds in capturing the essence of the travel-time variations as derived from the MHD simulations.

Surface-Focused Seismic Holography of Sunspots: I. Observations

We present a comprehensive set of observations of the interaction of p-mode oscillations with sunspots using surface-focused seismic holography. Maps of travel-time shifts, relative to quiet-Sun travel times, are shown for incoming and outgoing p modes as well as their mean and difference. We compare results using phase-speed filters with results obtained with filters that isolate single p-mode ridges, and we further divide the data into multiple temporal frequency bandpasses. The f mode is removed from the data. The variations of the resulting travel-time shifts with magnetic-field strength and with the filter parameters are explored. We find that spatial averages of these shifts within sunspot umbrae, penumbrae, and surrounding plage often show strong frequency variations at fixed phase speed. In addition, we find that positive values of the mean and difference travel-time shifts appear exclusively in waves observed with phase-speed filters that are dominated by power in the low-frequency wing of the p 1 ridge. We assess the ratio of incoming to outgoing p-mode power using the ridge filters and compare surface-focused holography measurements with the results of earlier published p-mode scattering measurements using Fourier – Hankel decomposition.

Analytical Models for Cross‐Correlation Signal in Time‐Distance Helioseismology

In time-distance helioseismology, the time signals (Doppler shifts) at two points on the solar surface, separated by a fixed angular distance are cross-correlated, and this leads to a wave packet signal. Accurately measuring the travel times of these wave packets is crucial for inferring the sub-surface properties in the Sun. The observed signal is quite noisy, and to improve the signal-to-noise ratio and make the cross-correlation more robust, the temporal oscillation signal is phase-speed filtered at the two points in order to select waves that travel a fixed horizontal distance. Hence a new formula to estimate the travel times is derived, in the presence of a phase speed filter, and it includes both the radial and horizontal component of the oscillation displacement signal. It generalizes the previously used Gabor wavelet that was derived without a phase speed filter and included only the radial component of the displacement. This is important since it will be consistent with the observed cross-correlation that is computed using a phase speed filter, and also it accounts for both the components of the displacement. The new formula depends on the location of the two points on the solar surface that are being cross correlated and accounts for the travel time shifts at different locations on the solar surface.

Optimal Gaussian Phase-Speed Filters in Time-Distance Helioseismology

Gaussian phase-speed filters are widely used in time-distance helioseismology to select specific wave packets whose travel times are then measured at the solar surface. This filtering increases the signal-to-noise (S/N) ratio of the temporal cross-covariances that are fitted to derive the travel times. The central phase speeds of these Gaussian filters are prescribed by a solar model; their widths are typically chosen empirically. No systematic study has been published on the effect of this filter width on the S/N ratio of the travel times. Such an analysis requires the ability to generate both noise and signal travel-time perturbations, this is now possible due to the recent introduction of a noise model and Born-approximation sensitivity kernels. These kernels allow for a derivation of travel-time perturbations as functions of a given sound-speed perturbation and are dependent on the phase-speed filters applied to the data, unlike simpler kernels. In this paper, we show that there is indeed an optimum value of the filter width that results in a maximum S/N ratio for the travel-time maps. Narrower filters exclude too much signal to produce useful travel-time perturbation maps, while broader filters are not selective enough.

Sensitivity of Acoustic Wave Travel Times to Sound‐Speed Perturbations in the Solar Interior

For time-distance helioseismology, it is important to establish the relationship between the travel times of acoustic waves propagating between different points on the solar surface through the solar interior and local perturbations to the sound speed in the propagation region. We use the Born approximation to derive a general expression for the linear sensitivity of travel times to local sound-speed perturbations in plane-parallel solar models with stochastic wave sources. The results show that the sensitivity of time-distance measurements to perturbations in sound speed depends on the details of the measurement procedure, such as the phase-speed filter used in typical time-distance data analysis. As a result, the details of the measurement procedure should be taken into account in the inversion of time-distance data. Otherwise, the inferred depths of perturbations may be incorrect.

Wavebreaking and mixing in the northern hemisphere summer stratosphere

The cause of zonal ozone variations observed by the Polar Ozone and Aerosol Measurement II (POAM II) instrument in the Northern Hemisphere summer stratosphere from ∼55° to 65°N and ∼20 to 30 km is investigated using United Kingdom Meteorological Office (UKMO) stratospheric data. Eliassen‐Palm (E‐P) flux vectors calculated from the UKMO data show that wave activity propagates vertically from the troposphere into the stratospheric easterlies during the Northern Hemisphere summer. In the layer between 20 and 30 km the E‐P flux divergence is small but nonzero. Space‐time power spectra show that wave power shifts from eastward propagating waves in the upper troposphere to predominantly westward propagating waves in the middle stratosphere, consistent with phase speed filtering following the Charney‐Drazin theorem. Air parcel trajectories and effective diffusivity calculations show substantial mixing due to breaking of westward propagating waves in the summer easterly wind regime. Changes in mixing properties during the summer season are consistent with changes in the mean state and the wave forcing. We conclude that breaking of large‐scale westward propagating waves in the summer easterlies causes meridional transport and the observed local maximum in ozone variability.