linkages between the atmosphere on the Earth and sun Phần 8

Do Active Regions Modify Oscillation Frequencies? 377 few tiles with positive frequency shifts that have no counterparts in the MAI image implying a weaker agreement. To estimate how well we can associate the locations of active regions as locations of frequency shifts, we calculate the Pearson’s corre-lation coefficient (rp) between the shifts and MAI for each of the three ring-days. These are foundto be 0.91,0.93,and 0.88and0.74,0.77,and0.85,forCR 2009and 2058, respectively, and confirms that the correlation between shifts and the surface magnetic activity during the two activity periods are significantly different. This re-sult is consistent with the recent findings inferred from global modes (Jain et al. 2009). Thus the argument that the solar-cycle variations in the global mode frequencies aredueto globalaveragingofthelocaleffectofactiveregions(Hindmanet al.2001) is only partially supported by our analysis. We believe that the weak component of the magnetic field, for example, ubiquitous horizontal field or turbulent field, must be taken into account to fully explain the frequency shifts, particularly during the minimal-activity phase of the solar cycle. Acknowledgment We thank John Leibacher for a critical reading of the manuscript. This research was supported in part by NASA grants NNG 05HL41I and NNG 08EI54I. This work utilizes data obtained by the Global OscillationNetwork Group program, managed bythe National Solar Obser-vatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrof´ısica de Canarias, and Cerro Tololo Interamerican Observatory. This work also utilizes 96-min magnetograms from SOI/MDI on board Solar and Heliospheric Observatory (SOHO). SOHO is a project of international cooperation between ESA and NASA. References Corbard, T.,Toner, C., Hill,F., Hanna, K. D., Haber, D. A., Hindman, B. W.,Bogart, R. S. 2003, In: ESA SP-517, Local and Global Helioseismology: The Present and Future, H. Sawaya-Lacoste (ed.), ESA SP vol. 517, p. 255 Hill, F. 1988, ApJ, 333, 996 Hindman, B., Haber, D., Toomre, J., Bogart, R. 2000, Solar Phys., 192, 363 Hindman, B. W., Haber, D. A., Toomre, J., Bogart, R. S. 2001, In: Helio- and Asteroseismology at the Dawn of the Millennium, A. Wilson (ed.), ESA SP vol. 464, p. 143 Howe, R., Haber, D. A., Hindman, B. W., Komm, R., Hill, F., Gonzalez Hernandez, I. 2008, In: Subsurface and Atmospheric Influences on Solar Activity, R. Howe, R. W. Komm, K. S. Balasubramaniam, G. J. D. Petrie (eds.), ASP Conf. Ser., vol. 383, p. 305 Jain, K., Bhatnagar, A. 2003, Solar Phys., 213, 257 Jain, K., Tripathy, S. C., Hill, F. 2009, ApJ, 695, 1567 Deep-Focus Diagnostics of Sunspot Structure H. Moradi and S.M. Hanasoge Abstract In sequel to Moradi et al. [2009, ApJ, 690, L72], we employ two established numerical forward models (a 3D ideal MHD solver and MHD ray theory) in conjunction with time–distance helioseismology to probe the lateral extent of wave-speed perturbations produced in regions of strong, near-surface magnetic fields. We continue our comparisons of forward modeling approaches by extending our previous surface-focused travel-time measurements with a common midpoint deep-focusing scheme that avoids the use of oscillation signals within the sunspot region. The idea is to also test MHD ray theory for possible application in future inverse methods. 1 Introduction In Moradi et al. (2009), we used two recently developed numerical MHD forward models in conjunction with surface-focused (i.e., center-to-annulus) time–distance measurements to produce numerical models of travel-time inhomogeneities in a simulated sunspot atmosphere. The resulting artificial travel-time perturbation pro-files clearly demonstrated the overwhelming influence that MHD physics, as well as phase-speed and frequency filtering, have on local helioseismic measurements in the vicinity of sunspots. However, there are numerous caveats associated with surface-focused time– distance measurements that use oscillation signals within the sunspot region, as the useofsuchoscillationsignalsis nowknowntobetheprimarysourceofmostsurface H. Moradi () School of Mathematical Sciences, Monash University, Australia and Visiting Scientist: Indian Institute of Astrophysics, Bangalore, India S.M. Hanasoge Max-Planck-Institut fu¨r Sonnensystemforschung, Katlenburg-Lindau, Germany and Visiting Scientist: Indian Institute of Astrophysics, Bangalore, India S.S. Hasan and R.J. Rutten (eds.), Magnetic Coupling between the Interior 378 and Atmosphere of the Sun, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-02859-5 35, Springer-Verlag Berlin Heidelberg 2010 Deep-Focus Diagnostics of Sunspot Structure 379 effects in sunspot seismology. These surface effects can be essentially categorized into two groups. The first revolves around the degree to which observations made within the sunspot region are contaminated by magnetic effects (e.g., Braun 1997; Lindsey and Braun 2005; Schunker et al. 2005; Braun and Birch 2006; Couvidat and Rajaguru 2007; Moradi et al. 2009), while the second concerns the degree to which atmospheric temperature stratification in and around regions may affect the absorption line used to make measurements of the Doppler velocity (e.g., Rajaguru et al. 2006, 2007). There have been attempts in the past to circumvent such problems by adopting a time–distance measurement geometry known as “deep-focusing,” which avoids the use of data from the central area of the sunspot by only cross-correlating the oscillation signal of waves that have a first-skip distance larger than the diameter of the sunspot (e.g., Duvall 1995; Braun 1997; Zhao and Kosovichev 2006; Rajaguru 2008). In this analysis, we follow up on the comparative study presented in Moradi et al. (2009) by using our two established forward models, in conjunction with a deep-focusing scheme known as the “common midpoint” (CMP) method to probe the sub-surface dynamics of our artificial sunspot. 2 The Flux Tube and Forward Models The background stratification of our model atmosphere is given by an adiabati-cally stable, truncated polytrope (Bogdan et al. 1996), smoothly connected to an isothermal atmosphere. The truncated polytrope is described by: index m D 2:15, reference pressure p0 D 1:21 105 gcm1 s2, and reference density 0 D 2:78 107 gcm3. The flux tube (peak field strength of 3kG) is modeled by an axisymmetric magnetic field geometry based on the Schlu¨ter and Temesva´ry (1958) self-similar solution. The derived MHS sunspot model achieves a consis-tent sound-speed decrease (see Fig.1), with a peak reduction of about 45% at the surface (z D 0) and less than 1% at z D 2Mm, while the one-layered wave-speed enhancement is also confined to the near-surface layers, approaching 180% at the surface and around less than 0.5% at z D 2Mm. 0 −0.5 −10 −1 −20 −1.5 −30 −2 −40 −20 0 20 r [Mm] 20 20 0 0 −20 −20 −40 −20 0 20 x [Mm] Fig. 1 Some properties of the model sunspot atmosphere. Lefthand panel: the near-surface thermal/sound-speed perturbation profile shown as a function of sound-speed squared. Righthand panel: a Doppler power map normalized to the quiet Sun 380 H. Moradi and S.M. Hanasoge The two forward models presented in Moradi et al. (2009) are again used for our analysis. The first forward model integrates the linearized ideal MHD wave equations according to the recipe of Hanasoge (2008), where waves are excited via a precomputed deterministic source function that acts on the vertical momentum equation. To simulate the suppression of granulation related wave sources in a sunspot (e.g., Hanasoge et al. 2008),the source activity is muted in a circular region of 10Mm radius. The simulations produce artificial line-of-sight (Doppler) veloc-ity data cubes, extracted at a height of 200km above the photosphere, effectually mimicking Michelson Doppler Imager (MDI) Dopplergrams. The data cubes have dimensions of 200 200Mm2 512min, with a cadence of 1min and a spatial resolution of 0:718Mm. Figure 1 depicts a normalized power map derived from the simulated Doppler velocity measurements. The second forward model employs the MHD ray tracer of Moradi and Cally (2008), where 2D ray propagation is modeled through solving the governing equa-tions of the ray paths derived using the zero-order eikonal approximation and the magneto-acoustic dispersion relation. It should be noted that neither forward model accounts for the presence of sub-surface flows. 3 Common Midpoint Deep-Focusing The CMP method is often utilized in geophysics applications such as multichannel seismic acquisition (Shearer 1999). It measures the travel time at the point on the surface halfway between the source and the receiver (see Fig.2). Cross-correlating numerous source–receiver pairs in this manner results in the method being mostly sensitive to a small regionin the deep interiorsurroundingthe lower turningpoint of the ray. A reworking of this method has been applied to helioseismic observations CMP [r = 0Mm] 0 r1 r2 5 10 15 20 30 20 10 0 10 20 30 r Mm Fig. 2 An illustration of the CMP deep-focus geometry indicating the range of rays used for this study. The CMP method measures the travel time at the point on the surface located at the half-way point between a source (r1) and receiver (r2). For the above rays, the CMP is located on the central axis of the spot (r D 0Mm) Deep-Focus Diagnostics of Sunspot Structure 381 by Duvall (2003), and has the obvious advantage of allowing one to study the wave-speed structure directly beneath sunspots without using the oscillation signals inside the perturbed region. Our method for measuring time–distance deep-focus travel times is somewhat similar to the approach undertaken by Braun (1997) and Duvall (2003). First, the annulus-to-annulus cross-covariances (e.g., between oscillation signals located between two points on the solar surface, a source at r1 and a receiver at r2, as illus-trated in Fig.2) are derivedby dividingeach annulus ( D jr2 r1j) into two semi-annuli and cross-correlating the average signals in these two semi-annuli. Then, to further increase the signal-to-noise ratio (SNR), we average the cross-covariances over three distances, respectively, slightly smaller than, and larger than, . In the end, the five (mean) distances chosen (42.95, 49.15, 55.35, 61.65, and 68Mm, respectively) are large enough to ensure that we sample only waves with a first-skip distance greater than the diameter of the sunspot at the surface (about 40Mm). Because of the oscillation signal at any location being a superposition of a large number of waves of different travel distances, the cross-covariances are very noisy and need to be phase-speed filtered first in the Fourier domain, using a Gaussian filter for each travel distance. The application of appropriatephase-speed filters iso-lates waves that travel desired skip distances, meaning that even though we average over semi-annuli, the primary contribution to the cross covariances is from these waves. In addition to the phase-speed filters, we also apply an f -mode filter that re-movesthef -moderidgecompletely(as it is of nointerest to us inthis analysis),and we also apply Gaussian frequencyfilters centered at ! D 3.5,4.0, and 5.0mHz with ı! D 0:5mHz band-widths to study frequency dependencies of travel times (e.g., Braun and Birch 2008; Moradi et al. 2009). To extract the required travel times, the cross-covariances are fitted by two Gabor wavelets (Kosovichev and Duvall 1997): one for the positive times and one for the negative times. Even after significant filtering and averaging, the extracted CMP travel times are still inundated with noise. This is certainly an ever-present complication in lo-cal helioseismology, as there is a common expectation (with all local helioseismic methods and inversions) of worsening noise and resolution with depth. Realization noise associated with stochastic excitation of acoustic waves can significantly im-pair our ability to analyze the true nature of travel-time shifts on the surface (and by extension, also affect our interpretation of sub-surface structure). But, as we have full control over the wave excitation mechanism and source function, we have the luxury of being able to apply realization noise subtraction to improve the SNR and obtain statistically significant travel-time shifts from the deep-focus measurements. This is accomplished in the same manner as Hanasoge et al. (2007), that is, by performing two separate simulations, one with the perturbation (i.e., the sunspot simulation) and another without (i.e., the quiet simulation). We then subtract the travel times of the quiet data from its perturbed counterpart (see Fig.3), allowing us to achieve an excellent SNR. Finally, to compare theory with simulations, we also estimate deep-focusing time shifts using the MHD ray tracer of Moradi and Cally (2008). The single-skip magneto-acoustic rays are propagated from the inner (lower) turning point of their trajectories at a prescribed frequency (see e.g., Fig.2). These rays do not undergo ... - tailieumienphi.vn