Optimal Masks for Low-Degree Solar Acoustic Modes

We suggest a solution to an important problem of observational helioseismology of the separation of lines of solar acoustic (p) modes of low angular degree in oscillation power spectra by constructing optimal masks for Doppler images of the Sun. Accurate measurements of oscillation frequencies of low-degree modes are essential for the determination of the structure and rotation of the solar core. However, these measurements for a particular mode are often affected by leakage of other p modes arising when the Doppler images are projected on to spherical-harmonics masks. The leakage results in overlaping peaks corresponding to different oscillation modes in the power spectra. In this paper we present a method for calculating optimal masks for a given (target) mode by minimizing the signals of other modes appearing in its vicinity. We apply this method to time series of 2 years obtained from Michelson Doppler Imager (MDI) instrument on board SOHO space mission and demonstrate its ability to reduce efficiently the mode leakage.Comment: to be published in Astrophys.J. Letter

The Cause of Photospheric and Helioseismic Responses to Solar Flares: High-Energy Electrons or Protons?

Analysis of the hydrodynamic and helioseismic effects in the photosphere during the solar flare of July 23, 2002, observed by Michelson Doppler Imager (MDI) on SOHO, and high-energy images from RHESSI shows that these effects are closely associated with sources of the hard X-ray emission, and that there are no such effects in the centroid region of the flare gamma-ray emission. These results demonstrate that contrary to expectations the hydrodynamic and helioseismic responses (''sunquakes") are more likely to be caused by accelerated electrons than by high-energy protons. A series of multiple impulses of high-energy electrons forms a hydrodynamic source moving in the photosphere with a supersonic speed. The moving source plays a critical role in the formation of the anisotropic wave front of sunquakes.Comment: 13 pages, 5 figures, ApJL in pres

Travel Time Shifts due to Amplitude Modulation in Time-Distance Helioseismology

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.Comment: 17 pages, 1 figure, accepted for publication in Ap

Imaging the Solar Tachocline by Time-Distance Helioseismology

The solar tachocline at the bottom of the convection zone is an important region for the dynamics of the Sun and the solar dynamo. In this region, the sound speed inferred by global helioseismology exhibits a bump of approximately 0.4% relative to the standard solar model. Global helioseismology does not provide any information on possible latitudinal variations or asymmetries between the Northern and Southern hemisphere. Here, we develop a time-distance helioseismology technique, including surface- and deep-focusing measurement schemes and a combination of both, for two-dimensional tomographic imaging of the solar tachocline that infers radial and latitudinal variations in the sound speed. We test the technique using artificial solar oscillation data obtained from numerical simulations. The technique successfully recovers major features of the simplified tachocline models. The technique is then applied to SOHO/MDI medium-l data and provides for the first time a full two-dimensional sound-speed perturbation image of the solar tachocline. The one-dimensional radial profile obtained by latitudinal averaging of the image is in good agreement with the previous global helioseismology result. It is found that the amplitude of the sound-speed perturbation at the tachocline varies with latitude, but it is not clear whether this is in part or fully an effect of instrumental distortion. Our initial results demonstrate that time-distance helioseismology can be used to probe the deep interior structure of the Sun, including the solar tachocline.Comment: accepted for publication by Ap

Properties of Flares-Generated Seismic Waves on the Sun

The solar seismic waves excited by solar flares (``sunquakes'') are observed as circular expanding waves on the Sun's surface. The first sunquake was observed for a flare of July 9, 1996, from the Solar and Heliospheric Observatory (SOHO) space mission. However, when the new solar cycle started in 1997, the observations of solar flares from SOHO did not show the seismic waves, similar to the 1996 event, even for large X-class flares during the solar maximum in 2000-2002. The first evidence of the seismic flare signal in this solar cycle was obtained for the 2003 ``Halloween'' events, through acoustic ``egression power'' by Donea and Lindsey. After these several other strong sunquakes have been observed. Here, I present a detailed analysis of the basic properties of the helioseismic waves generated by three solar flares in 2003-2005. For two of these flares, X17 flare of October 28, 2003, and X1.2 flare of January 15, 2005, the helioseismology observations are compared with simultaneous observations of flare X-ray fluxes measured from the RHESSI satellite. These observations show a close association between the flare seismic waves and the hard X-ray source, indicating that high-energy electrons accelerated during the flare impulsive phase produced strong compression waves in the photosphere, causing the sunquake. The results also reveal new physical properties such as strong anisotropy of the seismic waves, the amplitude of which varies significantly with the direction of propagation. The waves travel through surrounding sunspot regions to large distances, up to 120 Mm, without significant decay. These observations open new perspectives for helioseismic diagnostics of flaring active regions on the Sun and for understanding the mechanisms of the energy release and transport in solar flares.Comment: 12 pages, 4 figures, submitted to Ap