- Email: [email protected]
Taiwan oscillation network: Probing the solar interior
TAIWAN OSCILLATION NETWORK: PROBING THE SOLAR INTERIOR Dean-Yi Chou and the TON Team I
Physics Department, Tsing Hua University, Hsinchu, 300~3, Taiwan, R.O.C.
ABSTRACT In this review paper, we describe the present status of the project of the Taiwan Oscillation Network (TON) and discuss the recent scientific results using the TON data, especially the results from a new method: acoustic imaging. The TON is a ground-based network to measure solar intensity oscillations for the study of the solar interior. Four telescopes have been installed in Tenerife (Spain), Big Bear (USA), Huairou (PRC), and Tashkent (Uzbekistan). The TON telescopes take K-line full-disk solar images of diameter 1000 pixels at a rate of one image per minute. The TON high-spatial-resolution data are specially suitable for the study of local properties of the Sun. Recently we developed a new method, acoustic imaging, to construct the acoustic signals inside the Sun with the acoustic signals measured at the solar surface. From the constructed signals, we can form intensity map and phase-shift map of an active region at various depths. The direct link between the these maps and the subsurface magnetic field suffers from the poor vertical resolution of acoustic imaging. An inversion method is developed to invert the measured phase-shift distribution to estimate the source distribution based on the ray approximation. We also discuss the application of acoustic imaging to image the active regions on the far-side of the Sun that may be used for the solar activity forecast. THE PROJECT
OF TAIWAN OSCILLATION
NETWORK
The Taiwan Oscillation Network (TON) is a ground-based network measuring K-line intensity oscillation for the study of the internal structure of the Sun. The TON project has been funded by the National Research Council of ROC since July of 1991. The plan of the TON project is to install several telescopes at appropriate longitudes around the world to continuously measure the solar oscillations. So far four telescopes have been installed. The first telescope was installed at the Teide Observatory, Canary Islands, Spain in August of 1993. The second and third telescopes were installed at the Huairou Solar Observing Station near Beijing and the Big Bear Solar Observatory, California, USA in 1994. The fourth telescope was installed in Tashkent, Uzbekistan in July of 1996. The TON is designed to obtain informations on high-degree solar p-mode oscillations, along with intermediatedegree modes. A discussion of the TON project and its instrument is given by Chou et al. (1995). Here we give a brief description. The TON telescope system uses a 3.5-inch Maksutov-type telescope. The annual average diameter of the Sun is set 1000 pixels. A K-line filter, centered at 3934~i, of FWHM = 10~ and a prefilter of FWHM = 100~ are placed near the focal plane. The measured amplitude of intensity oscillation is about 2.5%. A 16-bit water-cooled CCD is used to take images. The image size is 1080 by 1080 pixels. The exposure time is set to 800-1500 ms, depending on the solar brightness. The photon noise, about 0.2%, is greater than the thermal noise of the CCD and circuit. The image data are recorded by two 8-mm Exabyte tape drives. 1The TON Team includes: Ming-Tsung Sun (Department of Mechanical Engineering, Chang-Gung University, Kwei-San, Taiwan); Antonio Jimenez (Instituto Astrofisica de Canarias, Observatorio del Teide, Tenerife, Spain); Guoxiang Ai and Honqi Zhang (Huairou Solar Observing Station, Beijing Observatory, Beijing); Philip Goode and William Marquette (Big Bear Solar Observatory, New Jersey Institute of Technology, Newark, NJ 07102, U.S.A.); Shuhrat Ehgamberdiev and Oleg Ladenkov (Ulugh Beg Astronomical Institute, Tashkent, Uzbekistan). -31 -
D.-Y. Chou and the TON Team The TON full-disk images have a spatial sampling window of 1.8 arcseconds per pixel, and they can provide information of modes up to 1 ~ 1000. The TON high-resolution data is specially suitable to study local helioseismology. In this paper, we discuss a new method, acoustic imaging, first developed by the TON group to study the local property of the solar interior, such as active regions. A NEW METHOD:
ACOUSTIC
IMAGING
The conventional analysis in helioseismology is the mode decomposition. A time series of intensity or Doppler images is decomposed into eigenmodes. For example, in the spherical coordinates, the eigenmodes are characterized by radial order n, spherical harmonic degree l, azimuthal order m, and frequency w. Many mode properties can be obtained from the mode decomposition, such as (1) the dispersion relation: the relation between w and (n,l, m), (2) power spectra: the power distribution among modes, and (3) the line profile of each mode. These mode properties can be used to infer the internal structure of the Sun. The mode decomposition can be applied to global modes or local modes. For the global modes, the mode properties provide the global information on the solar interior. For the local modes, it provides the information below the solar surface in a local area, such as an active region. Duvall et al. (1993) first apply time-distance analysis, commonly used in earth seismology, to the solar acoustic waves. Time-distance analysis is performed directly in the spacetime domain to obtain a relation between wave travel time and travel distance, time-distance relation. The time-distance relation is determined by the physical conditions of the region through which the waves pass. Thus time-distance analysis is a useful tool to study the local structure. Recently the TON group developed a new technique, acoustic imaging, based on the time-distance, to construct the acoustic signal at a point on the solar surface or in the solar interior at a target time with the acoustic signals measured at the solar surface. Its development was motivated by the success of imaging underwater objects with ambient acoustic noise in the ocean (Buckingham et al., 1992; Chang et al., 1997). A resonant solar p-mode is trapped and multiply reflected in a cavity between the surface and a layer in the solar interior. The acoustic signal emanating from a point at the surface propagates downward to the bottom of the cavity and back to the surface at a different horizontal distance from the original point. Different p-modes have different paths and arrive at the surface with different travel times and different distances from the original point. The modes with the same angular phase velocity w/1 have approximately the same ray path and form a wave packet, where w is the mode frequency and l is the spherical harmonic degree. The relation between travel time and travel distance of the wave packet can be measured in the time-distance analysis (Duvall et al., 1993). The acoustic signals measured at the surface can be coherently added, based on the time-distance relation, to construct the signal at a target point and a target time (Chou et al., 1998, 1999; Chou 2000) "r2
~out,in(t) ---- Z
W(T, 0 ) . + ( 0 , t •
(1)
T---TI
where ~out(t) and ~in(t) are the constructed signals at the target point at time t, ~(0, t+T) is the azimuthalaveraged signal measured at the angular distance 0 from the target point at time t + T, where T and 0 satisfy the time-distance relation, and W(T, 0) is the weighting function. The positive sign corresponds to ~out which is constructed with the waves propagating outward from the target point. The negative sign corresponds to ~in which is constructed with the waves propagating inward toward the target point. The constructed signals ~out and ~I/in contains different information. The coherent sum defined in equation (1) is called the computational acoustic lens since it plays a role as a lens in optics. The summation variable T in equation (1) is evenly spaced in the interval (Tl,T2). The range of T corresponds to an annular region in space, which is called the aperture of the acoustic lens. Since each point on the time-distance curve corresponds to a wavepacket formed by the modes with the same
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Taiwan Oscillation Network: Probing the Solar Interior w/l, each aperture corresponds to a range of w/l. Using different apertures corresponds to using different ranges of modes to construct signals. Usually data is filtered with a Gaussian in frequency. The central frequency is defined as the frequency of the acoustic lens. For a fixed frequency, each aperture (annulus) is associated with a range of I. Thus an acoustic lens is characterized by w, l range, and focal depth. The time-distance relation used in equation (1) is not limited to the one-bounce time-distance relation. It can be more than one bounces. The property of signals constructed with multiple bounces is discussed in Chou et al. (1998; 1999), Braun et al. (1998), and Chou and Duvall (2000). For a target point on the surface, one can use the measured time-distance relation. For a target point located below the surface, one has to use the time-distance relation computed with a standard solar model and the ray approximation (D'Silva and Duvall, 1995; Chang et al., 1997). The degree of success of the reconstruction can be tested by the correlation between the constructed time series and the observed time series for a point on the surface. With 512-minute TON data, the peak of the correlation function between the observed time series and the constructed time series (~out or ~in) is about 0.47 for an aperture (annulus) of 2 - 1 7 ~ (Chou et al., 1998). If ~out and ~in are combined after phase matching, the peak of the correlation function between the observed time series and the combined constructed time series is about 0.68. The correlation between the observed time series and constructed time series increases with the aperture size (Chou et al., 1998). The constructed signal contains information on intensity and phase. The intensity at the target point can be computed by summing I~out,in(t)l 2 over time. The first acoustic intensity images of the solar interior were constructed with the TON data (Chang et al. 1997). One can also compute the absorption map with (~n- Pout)//:~n, where/~n,out are ingoing and outgoing intensity, respectively. For example, the power map, constructed outgoing map and constructed ingoing map of NOAA 7978 are shown in Figure 1. The acoustic power is the local rms value of the amplitude of acoustic oscillations. The darker area in the acoustic power maps corresponds to the lower acoustic power, which correlates well with magnetic fields or plages. The constructed outgoing intensity consists of the dissipation and emission at the target point and the dissipation along the wave path from the target point to the observing point. The local suppression and enhancement of p-modes are not included in the constructed intensity, while they appear in the local acoustic power (Chou et al. 1999). The ingoing intensity map shows no signature of magnetic region as expected because the ingoing waves in the surrounding area have not been affected by the local properties of the target point before they reach the target point (Chang et al. 1997; Chou et al. 1999). The slightly darker features at the location of the active region are probably caused by the lower observed signals in magnetic regions inside the annular region (aperture), which are used to construct the signal at the target point. The phase of constructed signals can be studied by the cross-correlation function between ~out(t) and ~in(t) (Chen et al. 1998). It is noted that ~out(t) and ~in(t) have to be constructed with the same waves; otherwise, there will be no correlation between ~out(t) and ~in(t). The cross-correlation function in magnetic regions is different from that in the quiet Sun. The phase and envelope peak of the cross-correlation function are defined as Tph and Ten, respectively. Both Tph and Ten are smaller in the sunspot than the quiet Sun, implying a larger sound speed in the sunspot. The changes in Tph and Ten relative to the quiet Sun are defined as the phase shift 5Tph and the envelope shift 5~'en, respectively. It is noted that ~Tph is different from 5Ten in the sunspot. 5Tph and 5Ten have different origins (Chou and Duvall 2000; Chou et al. 2000). ~'ren in magnetic regions is caused by the change in the travel time of the wave packet, which could be due to the change in group velocity along the wave path or the change in wave path. ~'ph is the change in phase change accumulated along the wave path. The cause of 5Tph is more complicated than that of ~'en. Besides the changes in phase velocity and wave path, the phase changes at the boundaries of mode cavity and flux tubes also contribute to ~Tph. The presence of magnetic fields modifies the physical conditions of the plasma that results in a change in the travel time of the wave packet and the phase change accumulated along the wave path. Thus measured (~Tph together with (~Ten in magnetic regions provide information on the structure and physical conditions in the magnetic regions. Two-dimensional phase-shift maps at different focal depths were first given in Chen et al. (1998) using the TON data. Since the error in determining Ten is larger than Tph, it needs a longer time series to determine
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D.-Y. Chou and the TON Team Ten with a reasonable S/N. The envelope-shift maps were first given by Chou et al. from a 2000-minute time series taken with the SOHO/MDI instrument (Chou et al. 2000). Examples of phase-shift map and envelope-shift map of NOAA 7978 are shown in Figure 1. Figure 1 shows that the phase shift measurement is more sensitive to the magnetic fields than the acoustic intensity measurement. The features in the phaseshift maps are surprisingly similar to those in the observed power maps. The phase-shift maps also correlate well with K-line images even for weak plages in the quiet Sun (Chen et al. 1998). The features in the envelope-shift maps also correlate with acoustic power and magnetic fields, but with a larger fluctuation. Both (~Tph and 5Ten in a sunspot increase with frequency. The frequency dependences of (~Tph and r together provides useful information on the structure of the sunspot (Chou et al. 2000). INVERSION
PROBLEMS
IN ACOUSTIC IMAGING
Although the goal of acoustic imaging is to construct the signal at the target point, the constructed signal contains not only the signal at the target point, but also the signals of other points. In other words, the spatial resolution of acoustic lens of acoustic imaging is finite. It is important to know the spatial resolution of acoustic different lenses so that the intensity maps and phase-shift maps of active regions can be correctly interpreted to learn the subsurface structure of active regions. There are two different effects involved in determining the spatial resolution of measured intensity maps and phase-shift maps. One is the wave property. Another is the non-locality effect: the waves passing through the target point also pass through the regions other than the target point. The nonlocal effect exists even in the ray approximation. The constructed signals at the target point, ~out(t) and ~in(t), contain information integrated along the ray paths (Chou et al. 1999). That is the constructed signals contain not only the local effect at the target point, but also the nonlocal effect. The contribution of nonlocal effect depends on the density of the ray distribution in the ray approximation. The phase shift (or change in travel time) at the target point ~', (~T(~'), can be expressed as (Chou and Sun 2000b)
gTph(~ = / K(r', r162
'
(2)
where the source S - 5c/c is the fraction of change in wave speed. The kernel K(~', r is proportional to the density of the ray distribution. The effect of flow on phase shifts can be eliminated by averaging the phase shifts measured with the rays of opposite directions (Chen et al. 1998). ~7ph discussed here is such an average. Each acoustic lens has one kernel. The kernel can be computed with a standard solar model based on the ray theory (Chou and Sun 2000a). Although the kernel K(~', r has a maximum at the target point ~', its value is not negligibly small in the region near the target point. The distribution of the kernel determines the spatial resolution of the constructed phase-shift images. Since the distribution of 5Tph in equation (2) can be measured in acoustic imaging, with the kernels one can do both forward problems and inverse problems. In forward problems, 5Tph is computed from the given model source with equation (2). Forward computations with model sources can provide information on the spatial resolution of various acoustic lenses. In the forward study of an active region, the given source is varied such that the computed 5Tph is close to the measured (~Tph. The forward study of the active region NOAA 7981 has been discussed in Chou and Sun (2000a). One can also invert the measured (~Tphto estimate the source distribution S in equation (2). We have used an inversion method, regularized least-squares fit, to invert equation (2) (Sun and Chou 2000). The inversion method has been applied to study an active region, NOAA 7981 (Chou and Sun 2000a). Figure 2 shows the result of inversion. The phase-shift maps of NOAA 7981 measured with the TON data at various depths are shown in the right column in Figure 2. The 2-d source maps from inversion at the same depths are shown in the left column. The source from inversion has a smaller vertical extent than the measured (~Tph. The dark fuzzy features corresponding to the plages in the measured phase-shift map diminish at depths of 4.4 and 8.8 Mm, and disappear at a depth of 17.6 Mm in Figure 2. In the future study, we will improve the S/N of measured ~Tph and increase the number of (~Tph in the vertical direction to improve the quality of the estimated source.
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Taiwan Oscillation Network: Probing the Solar Interior
Figure 1: Observed power map, absorption map, constructed outgoing map, constructed ingoing map, phase-shift map, and envelope-shift map of NOAA 7978 using a 2000-minute time series taken with the SOHO/MDI instrument (from Chou 2000). The data is filtered with a Gaussian filter of FWHM = 1 mHz centered at 3.5 mHz. The size of aperture used is 2 - 6~ (a two-degree circle is shown in the upper left map). The dimension of each map is 24.0 ~ in longitude and 24.7 ~ in latitude. The largest phase shift and envelope shift in the central sunspot are 1.5 minutes and 5.3 minutes, respectively.
Figure 2: Measured phase-shift maps of NOAA 7981 at various depths (right column) using the TON data and 2-D source maps from inversion (left column) (from Chou and Sun 2000a). The grey scales are chosen such that the maximum values of source map and the phase-shift map at the surface have the same tone. The grey scale of the phase-shift maps is from -2 minutes to 2 minutes. The vertical extent of the estimated (computed) source is smaller than that of the measured phase shifts. The noise in estimated source increases with depth because the value of kernel decreases with depth.
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D.-Y. Chou and the TON Team APPLICATIONS
TO S P A C E W E A T H E R
PREDICTIONS
The acoustic imaging technique can be used to image active regions at the far-side of the Sun. If the perturbation of acoustic waves caused by an active region at the far-side of the Sun can reach the near-side of the Sun and be detected, one can apply the technique of the acoustic imaging to image the active regions at the far-side of the Sun. We have used the TON data to construct the intensity and phase-shift maps of NOAA 7981, a medium-size active region, when it was at the far-side of the Sun; but none shows a detected signal above the noise level (Chou et al. 1998). Lindsey and Braun (2000) applied the technique of acoustic imaging (they call helioseismic holography) with the SOHO/MDI data to construct phase-shift map of the active region NOAA 8194, a very large active region, and saw its phase-shift features. Although the spatial resolution of their phase-shift map for the active region at the far-side of the Sun is rather low because only low-/modes can survive to reach the near-side of the Sun, this exciting result sheds light on the forecast of solar activities at the far-side of the Sun and on the possibility of the earlier space weather prediction. ACKNOWLEDGMENTS DYC and the TON project are supported by NSC of ROC under grants NSC-89-2112-M-007-038. We thank all members of the TON Team for their efforts to keep the TON project working. We are grateful to the GONG Data Team for providing the software package GRASP. REFERENCES Braun, D. C., Lindsey, C., Fan, Y., and Fagan, M., Seismic Holography of Solar Activity, Astrophys. J. 502, 968 (1998). Buckingham, M. J., Berkhout, B. V., and Glegg, S. A., Imaging the Ocean with Ambient Noise, Nature 356, 327 (1992). Chang, H.-K., Chou, D.-Y., LaBonte, B., and the TON Team, Ambient Acoustic Imaging in Helioseismolog, Nature 389, 825 (1997). Chen, H.-R., Chou, D.-Y., Chang, H.-K., Sun, M.-T., Yeh, S.-J, LaBonte, B., and the TON Team, Probing the Subsurface Structure of Active Regions with the Phase Information in Acoustic Imaging, Astrophys. J. 501, L139 (1998). Chou, D.-Y., Sun, M.-T., Huang, T.-Y. et al., Taiwan Oscillation Network, Solar Phys. 160, 237 (1995). Chou, D.-Y., Chang, H.-K., Chen, H.-R., LaBonte, B., Sun, M.-T., Yeh, S.-J., and the TON Team, Results of Acoustic Imaging with the TON data, in Proc. SOHO6/GONG98 Workshop on Structure and Dynamics of the Interior of the Sun and Sun-like Stars, ed. S. Korzennik and A. Wilson (ESA SP-418; Noordwijk:ESA), 597 (1998). Chou, D.-Y., Chang, H.-K., Sun, M.-T., LaBonte, B., Chen, H.-R., Yeh, S.-J., and the TON Team, Acoustic Imaging in Helioseismology, Astrophys. J. 514, 979, (1999). Chou, D.-Y., Acoustic Imaging of Solar Active Regions, Solar Phys. 192, 241 (2000). Chou, D.-Y., Sun, M.-T., and Chang, H.-K., A Study of Sunspots with Phase Time and Travel Time of p-Mode Waves in Acoustic Imaging, Astrophys. J. 532, 622 (2000). Chou, D.-Y. and Duvall, T. L. Jr., Phase Time and Envelope Time in Time-Distance Analysis and Acoustic Imaging, Astrophys. J. 533, 568 (2000). Chou, D.-Y. and Sun, M.-T., Phase Shifts of Acoustic Imaging and the Subsurface Structure of Active Region, in Proc. SOHO10/GONG2000 Workshop on Helio- and Astero-Seismology at the Dawn of the Millennium (ESA SP-464; Noordwijk:ESA), 157 (2000a). Chou, D.-Y. and Sun, M.-T., Kernels of Acoustic Imaging, in Proc. SOHO10/GONG2000 Workshop on Helio- and Astero-Seismology at the Dawn of the Millennium (ESA SP-464; Noordwijk:ESA), 195 (2000b). -36-
Taiwan Oscillation Network: Probing the Solar Interior D'Silva, S. and Duvall, T. L. Jr., Time-Distance Helioseismology in the Vicinity of Sunspots, Astrophys. J. 438, 454 (1995). Duvall, T. L. Jr., Jefferies, S. M., Harvey, J. W., and Pomoerantz, M. A., Time-Distance Helioseismology, Nature 362 430 (1993). Lindsey, C. and Braun, D. C., Seismic Imnages of the Far Side of the Sun, Science, 287, 1799 (200). Sun, M.-T. and Chou, D.-Y., The Inverse Problem in Acoustic Imaging, in Proc. SOHO10/GONG2000 Workshop on Helio- and Astero-Seismology at the Dawn of the Millennium (ESA SP-464; Noordwijk:ESA), 251 (2000).
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Physics Department, Tsing Hua University, Hsinchu, 300~3, Taiwan, R.O.C.
ABSTRACT In this review paper, we describe the present status of the project of the Taiwan Oscillation Network (TON) and discuss the recent scientific results using the TON data, especially the results from a new method: acoustic imaging. The TON is a ground-based network to measure solar intensity oscillations for the study of the solar interior. Four telescopes have been installed in Tenerife (Spain), Big Bear (USA), Huairou (PRC), and Tashkent (Uzbekistan). The TON telescopes take K-line full-disk solar images of diameter 1000 pixels at a rate of one image per minute. The TON high-spatial-resolution data are specially suitable for the study of local properties of the Sun. Recently we developed a new method, acoustic imaging, to construct the acoustic signals inside the Sun with the acoustic signals measured at the solar surface. From the constructed signals, we can form intensity map and phase-shift map of an active region at various depths. The direct link between the these maps and the subsurface magnetic field suffers from the poor vertical resolution of acoustic imaging. An inversion method is developed to invert the measured phase-shift distribution to estimate the source distribution based on the ray approximation. We also discuss the application of acoustic imaging to image the active regions on the far-side of the Sun that may be used for the solar activity forecast. THE PROJECT
OF TAIWAN OSCILLATION
NETWORK
The Taiwan Oscillation Network (TON) is a ground-based network measuring K-line intensity oscillation for the study of the internal structure of the Sun. The TON project has been funded by the National Research Council of ROC since July of 1991. The plan of the TON project is to install several telescopes at appropriate longitudes around the world to continuously measure the solar oscillations. So far four telescopes have been installed. The first telescope was installed at the Teide Observatory, Canary Islands, Spain in August of 1993. The second and third telescopes were installed at the Huairou Solar Observing Station near Beijing and the Big Bear Solar Observatory, California, USA in 1994. The fourth telescope was installed in Tashkent, Uzbekistan in July of 1996. The TON is designed to obtain informations on high-degree solar p-mode oscillations, along with intermediatedegree modes. A discussion of the TON project and its instrument is given by Chou et al. (1995). Here we give a brief description. The TON telescope system uses a 3.5-inch Maksutov-type telescope. The annual average diameter of the Sun is set 1000 pixels. A K-line filter, centered at 3934~i, of FWHM = 10~ and a prefilter of FWHM = 100~ are placed near the focal plane. The measured amplitude of intensity oscillation is about 2.5%. A 16-bit water-cooled CCD is used to take images. The image size is 1080 by 1080 pixels. The exposure time is set to 800-1500 ms, depending on the solar brightness. The photon noise, about 0.2%, is greater than the thermal noise of the CCD and circuit. The image data are recorded by two 8-mm Exabyte tape drives. 1The TON Team includes: Ming-Tsung Sun (Department of Mechanical Engineering, Chang-Gung University, Kwei-San, Taiwan); Antonio Jimenez (Instituto Astrofisica de Canarias, Observatorio del Teide, Tenerife, Spain); Guoxiang Ai and Honqi Zhang (Huairou Solar Observing Station, Beijing Observatory, Beijing); Philip Goode and William Marquette (Big Bear Solar Observatory, New Jersey Institute of Technology, Newark, NJ 07102, U.S.A.); Shuhrat Ehgamberdiev and Oleg Ladenkov (Ulugh Beg Astronomical Institute, Tashkent, Uzbekistan). -31 -
D.-Y. Chou and the TON Team The TON full-disk images have a spatial sampling window of 1.8 arcseconds per pixel, and they can provide information of modes up to 1 ~ 1000. The TON high-resolution data is specially suitable to study local helioseismology. In this paper, we discuss a new method, acoustic imaging, first developed by the TON group to study the local property of the solar interior, such as active regions. A NEW METHOD:
ACOUSTIC
IMAGING
The conventional analysis in helioseismology is the mode decomposition. A time series of intensity or Doppler images is decomposed into eigenmodes. For example, in the spherical coordinates, the eigenmodes are characterized by radial order n, spherical harmonic degree l, azimuthal order m, and frequency w. Many mode properties can be obtained from the mode decomposition, such as (1) the dispersion relation: the relation between w and (n,l, m), (2) power spectra: the power distribution among modes, and (3) the line profile of each mode. These mode properties can be used to infer the internal structure of the Sun. The mode decomposition can be applied to global modes or local modes. For the global modes, the mode properties provide the global information on the solar interior. For the local modes, it provides the information below the solar surface in a local area, such as an active region. Duvall et al. (1993) first apply time-distance analysis, commonly used in earth seismology, to the solar acoustic waves. Time-distance analysis is performed directly in the spacetime domain to obtain a relation between wave travel time and travel distance, time-distance relation. The time-distance relation is determined by the physical conditions of the region through which the waves pass. Thus time-distance analysis is a useful tool to study the local structure. Recently the TON group developed a new technique, acoustic imaging, based on the time-distance, to construct the acoustic signal at a point on the solar surface or in the solar interior at a target time with the acoustic signals measured at the solar surface. Its development was motivated by the success of imaging underwater objects with ambient acoustic noise in the ocean (Buckingham et al., 1992; Chang et al., 1997). A resonant solar p-mode is trapped and multiply reflected in a cavity between the surface and a layer in the solar interior. The acoustic signal emanating from a point at the surface propagates downward to the bottom of the cavity and back to the surface at a different horizontal distance from the original point. Different p-modes have different paths and arrive at the surface with different travel times and different distances from the original point. The modes with the same angular phase velocity w/1 have approximately the same ray path and form a wave packet, where w is the mode frequency and l is the spherical harmonic degree. The relation between travel time and travel distance of the wave packet can be measured in the time-distance analysis (Duvall et al., 1993). The acoustic signals measured at the surface can be coherently added, based on the time-distance relation, to construct the signal at a target point and a target time (Chou et al., 1998, 1999; Chou 2000) "r2
~out,in(t) ---- Z
W(T, 0 ) . + ( 0 , t •
(1)
T---TI
where ~out(t) and ~in(t) are the constructed signals at the target point at time t, ~(0, t+T) is the azimuthalaveraged signal measured at the angular distance 0 from the target point at time t + T, where T and 0 satisfy the time-distance relation, and W(T, 0) is the weighting function. The positive sign corresponds to ~out which is constructed with the waves propagating outward from the target point. The negative sign corresponds to ~in which is constructed with the waves propagating inward toward the target point. The constructed signals ~out and ~I/in contains different information. The coherent sum defined in equation (1) is called the computational acoustic lens since it plays a role as a lens in optics. The summation variable T in equation (1) is evenly spaced in the interval (Tl,T2). The range of T corresponds to an annular region in space, which is called the aperture of the acoustic lens. Since each point on the time-distance curve corresponds to a wavepacket formed by the modes with the same
-32-
Taiwan Oscillation Network: Probing the Solar Interior w/l, each aperture corresponds to a range of w/l. Using different apertures corresponds to using different ranges of modes to construct signals. Usually data is filtered with a Gaussian in frequency. The central frequency is defined as the frequency of the acoustic lens. For a fixed frequency, each aperture (annulus) is associated with a range of I. Thus an acoustic lens is characterized by w, l range, and focal depth. The time-distance relation used in equation (1) is not limited to the one-bounce time-distance relation. It can be more than one bounces. The property of signals constructed with multiple bounces is discussed in Chou et al. (1998; 1999), Braun et al. (1998), and Chou and Duvall (2000). For a target point on the surface, one can use the measured time-distance relation. For a target point located below the surface, one has to use the time-distance relation computed with a standard solar model and the ray approximation (D'Silva and Duvall, 1995; Chang et al., 1997). The degree of success of the reconstruction can be tested by the correlation between the constructed time series and the observed time series for a point on the surface. With 512-minute TON data, the peak of the correlation function between the observed time series and the constructed time series (~out or ~in) is about 0.47 for an aperture (annulus) of 2 - 1 7 ~ (Chou et al., 1998). If ~out and ~in are combined after phase matching, the peak of the correlation function between the observed time series and the combined constructed time series is about 0.68. The correlation between the observed time series and constructed time series increases with the aperture size (Chou et al., 1998). The constructed signal contains information on intensity and phase. The intensity at the target point can be computed by summing I~out,in(t)l 2 over time. The first acoustic intensity images of the solar interior were constructed with the TON data (Chang et al. 1997). One can also compute the absorption map with (~n- Pout)//:~n, where/~n,out are ingoing and outgoing intensity, respectively. For example, the power map, constructed outgoing map and constructed ingoing map of NOAA 7978 are shown in Figure 1. The acoustic power is the local rms value of the amplitude of acoustic oscillations. The darker area in the acoustic power maps corresponds to the lower acoustic power, which correlates well with magnetic fields or plages. The constructed outgoing intensity consists of the dissipation and emission at the target point and the dissipation along the wave path from the target point to the observing point. The local suppression and enhancement of p-modes are not included in the constructed intensity, while they appear in the local acoustic power (Chou et al. 1999). The ingoing intensity map shows no signature of magnetic region as expected because the ingoing waves in the surrounding area have not been affected by the local properties of the target point before they reach the target point (Chang et al. 1997; Chou et al. 1999). The slightly darker features at the location of the active region are probably caused by the lower observed signals in magnetic regions inside the annular region (aperture), which are used to construct the signal at the target point. The phase of constructed signals can be studied by the cross-correlation function between ~out(t) and ~in(t) (Chen et al. 1998). It is noted that ~out(t) and ~in(t) have to be constructed with the same waves; otherwise, there will be no correlation between ~out(t) and ~in(t). The cross-correlation function in magnetic regions is different from that in the quiet Sun. The phase and envelope peak of the cross-correlation function are defined as Tph and Ten, respectively. Both Tph and Ten are smaller in the sunspot than the quiet Sun, implying a larger sound speed in the sunspot. The changes in Tph and Ten relative to the quiet Sun are defined as the phase shift 5Tph and the envelope shift 5~'en, respectively. It is noted that ~Tph is different from 5Ten in the sunspot. 5Tph and 5Ten have different origins (Chou and Duvall 2000; Chou et al. 2000). ~'ren in magnetic regions is caused by the change in the travel time of the wave packet, which could be due to the change in group velocity along the wave path or the change in wave path. ~'ph is the change in phase change accumulated along the wave path. The cause of 5Tph is more complicated than that of ~'en. Besides the changes in phase velocity and wave path, the phase changes at the boundaries of mode cavity and flux tubes also contribute to ~Tph. The presence of magnetic fields modifies the physical conditions of the plasma that results in a change in the travel time of the wave packet and the phase change accumulated along the wave path. Thus measured (~Tph together with (~Ten in magnetic regions provide information on the structure and physical conditions in the magnetic regions. Two-dimensional phase-shift maps at different focal depths were first given in Chen et al. (1998) using the TON data. Since the error in determining Ten is larger than Tph, it needs a longer time series to determine
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D.-Y. Chou and the TON Team Ten with a reasonable S/N. The envelope-shift maps were first given by Chou et al. from a 2000-minute time series taken with the SOHO/MDI instrument (Chou et al. 2000). Examples of phase-shift map and envelope-shift map of NOAA 7978 are shown in Figure 1. Figure 1 shows that the phase shift measurement is more sensitive to the magnetic fields than the acoustic intensity measurement. The features in the phaseshift maps are surprisingly similar to those in the observed power maps. The phase-shift maps also correlate well with K-line images even for weak plages in the quiet Sun (Chen et al. 1998). The features in the envelope-shift maps also correlate with acoustic power and magnetic fields, but with a larger fluctuation. Both (~Tph and 5Ten in a sunspot increase with frequency. The frequency dependences of (~Tph and r together provides useful information on the structure of the sunspot (Chou et al. 2000). INVERSION
PROBLEMS
IN ACOUSTIC IMAGING
Although the goal of acoustic imaging is to construct the signal at the target point, the constructed signal contains not only the signal at the target point, but also the signals of other points. In other words, the spatial resolution of acoustic lens of acoustic imaging is finite. It is important to know the spatial resolution of acoustic different lenses so that the intensity maps and phase-shift maps of active regions can be correctly interpreted to learn the subsurface structure of active regions. There are two different effects involved in determining the spatial resolution of measured intensity maps and phase-shift maps. One is the wave property. Another is the non-locality effect: the waves passing through the target point also pass through the regions other than the target point. The nonlocal effect exists even in the ray approximation. The constructed signals at the target point, ~out(t) and ~in(t), contain information integrated along the ray paths (Chou et al. 1999). That is the constructed signals contain not only the local effect at the target point, but also the nonlocal effect. The contribution of nonlocal effect depends on the density of the ray distribution in the ray approximation. The phase shift (or change in travel time) at the target point ~', (~T(~'), can be expressed as (Chou and Sun 2000b)
gTph(~ = / K(r', r162
'
(2)
where the source S - 5c/c is the fraction of change in wave speed. The kernel K(~', r is proportional to the density of the ray distribution. The effect of flow on phase shifts can be eliminated by averaging the phase shifts measured with the rays of opposite directions (Chen et al. 1998). ~7ph discussed here is such an average. Each acoustic lens has one kernel. The kernel can be computed with a standard solar model based on the ray theory (Chou and Sun 2000a). Although the kernel K(~', r has a maximum at the target point ~', its value is not negligibly small in the region near the target point. The distribution of the kernel determines the spatial resolution of the constructed phase-shift images. Since the distribution of 5Tph in equation (2) can be measured in acoustic imaging, with the kernels one can do both forward problems and inverse problems. In forward problems, 5Tph is computed from the given model source with equation (2). Forward computations with model sources can provide information on the spatial resolution of various acoustic lenses. In the forward study of an active region, the given source is varied such that the computed 5Tph is close to the measured (~Tph. The forward study of the active region NOAA 7981 has been discussed in Chou and Sun (2000a). One can also invert the measured (~Tphto estimate the source distribution S in equation (2). We have used an inversion method, regularized least-squares fit, to invert equation (2) (Sun and Chou 2000). The inversion method has been applied to study an active region, NOAA 7981 (Chou and Sun 2000a). Figure 2 shows the result of inversion. The phase-shift maps of NOAA 7981 measured with the TON data at various depths are shown in the right column in Figure 2. The 2-d source maps from inversion at the same depths are shown in the left column. The source from inversion has a smaller vertical extent than the measured (~Tph. The dark fuzzy features corresponding to the plages in the measured phase-shift map diminish at depths of 4.4 and 8.8 Mm, and disappear at a depth of 17.6 Mm in Figure 2. In the future study, we will improve the S/N of measured ~Tph and increase the number of (~Tph in the vertical direction to improve the quality of the estimated source.
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Taiwan Oscillation Network: Probing the Solar Interior
Figure 1: Observed power map, absorption map, constructed outgoing map, constructed ingoing map, phase-shift map, and envelope-shift map of NOAA 7978 using a 2000-minute time series taken with the SOHO/MDI instrument (from Chou 2000). The data is filtered with a Gaussian filter of FWHM = 1 mHz centered at 3.5 mHz. The size of aperture used is 2 - 6~ (a two-degree circle is shown in the upper left map). The dimension of each map is 24.0 ~ in longitude and 24.7 ~ in latitude. The largest phase shift and envelope shift in the central sunspot are 1.5 minutes and 5.3 minutes, respectively.
Figure 2: Measured phase-shift maps of NOAA 7981 at various depths (right column) using the TON data and 2-D source maps from inversion (left column) (from Chou and Sun 2000a). The grey scales are chosen such that the maximum values of source map and the phase-shift map at the surface have the same tone. The grey scale of the phase-shift maps is from -2 minutes to 2 minutes. The vertical extent of the estimated (computed) source is smaller than that of the measured phase shifts. The noise in estimated source increases with depth because the value of kernel decreases with depth.
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D.-Y. Chou and the TON Team APPLICATIONS
TO S P A C E W E A T H E R
PREDICTIONS
The acoustic imaging technique can be used to image active regions at the far-side of the Sun. If the perturbation of acoustic waves caused by an active region at the far-side of the Sun can reach the near-side of the Sun and be detected, one can apply the technique of the acoustic imaging to image the active regions at the far-side of the Sun. We have used the TON data to construct the intensity and phase-shift maps of NOAA 7981, a medium-size active region, when it was at the far-side of the Sun; but none shows a detected signal above the noise level (Chou et al. 1998). Lindsey and Braun (2000) applied the technique of acoustic imaging (they call helioseismic holography) with the SOHO/MDI data to construct phase-shift map of the active region NOAA 8194, a very large active region, and saw its phase-shift features. Although the spatial resolution of their phase-shift map for the active region at the far-side of the Sun is rather low because only low-/modes can survive to reach the near-side of the Sun, this exciting result sheds light on the forecast of solar activities at the far-side of the Sun and on the possibility of the earlier space weather prediction. ACKNOWLEDGMENTS DYC and the TON project are supported by NSC of ROC under grants NSC-89-2112-M-007-038. We thank all members of the TON Team for their efforts to keep the TON project working. We are grateful to the GONG Data Team for providing the software package GRASP. REFERENCES Braun, D. C., Lindsey, C., Fan, Y., and Fagan, M., Seismic Holography of Solar Activity, Astrophys. J. 502, 968 (1998). Buckingham, M. J., Berkhout, B. V., and Glegg, S. A., Imaging the Ocean with Ambient Noise, Nature 356, 327 (1992). Chang, H.-K., Chou, D.-Y., LaBonte, B., and the TON Team, Ambient Acoustic Imaging in Helioseismolog, Nature 389, 825 (1997). Chen, H.-R., Chou, D.-Y., Chang, H.-K., Sun, M.-T., Yeh, S.-J, LaBonte, B., and the TON Team, Probing the Subsurface Structure of Active Regions with the Phase Information in Acoustic Imaging, Astrophys. J. 501, L139 (1998). Chou, D.-Y., Sun, M.-T., Huang, T.-Y. et al., Taiwan Oscillation Network, Solar Phys. 160, 237 (1995). Chou, D.-Y., Chang, H.-K., Chen, H.-R., LaBonte, B., Sun, M.-T., Yeh, S.-J., and the TON Team, Results of Acoustic Imaging with the TON data, in Proc. SOHO6/GONG98 Workshop on Structure and Dynamics of the Interior of the Sun and Sun-like Stars, ed. S. Korzennik and A. Wilson (ESA SP-418; Noordwijk:ESA), 597 (1998). Chou, D.-Y., Chang, H.-K., Sun, M.-T., LaBonte, B., Chen, H.-R., Yeh, S.-J., and the TON Team, Acoustic Imaging in Helioseismology, Astrophys. J. 514, 979, (1999). Chou, D.-Y., Acoustic Imaging of Solar Active Regions, Solar Phys. 192, 241 (2000). Chou, D.-Y., Sun, M.-T., and Chang, H.-K., A Study of Sunspots with Phase Time and Travel Time of p-Mode Waves in Acoustic Imaging, Astrophys. J. 532, 622 (2000). Chou, D.-Y. and Duvall, T. L. Jr., Phase Time and Envelope Time in Time-Distance Analysis and Acoustic Imaging, Astrophys. J. 533, 568 (2000). Chou, D.-Y. and Sun, M.-T., Phase Shifts of Acoustic Imaging and the Subsurface Structure of Active Region, in Proc. SOHO10/GONG2000 Workshop on Helio- and Astero-Seismology at the Dawn of the Millennium (ESA SP-464; Noordwijk:ESA), 157 (2000a). Chou, D.-Y. and Sun, M.-T., Kernels of Acoustic Imaging, in Proc. SOHO10/GONG2000 Workshop on Helio- and Astero-Seismology at the Dawn of the Millennium (ESA SP-464; Noordwijk:ESA), 195 (2000b). -36-
Taiwan Oscillation Network: Probing the Solar Interior D'Silva, S. and Duvall, T. L. Jr., Time-Distance Helioseismology in the Vicinity of Sunspots, Astrophys. J. 438, 454 (1995). Duvall, T. L. Jr., Jefferies, S. M., Harvey, J. W., and Pomoerantz, M. A., Time-Distance Helioseismology, Nature 362 430 (1993). Lindsey, C. and Braun, D. C., Seismic Imnages of the Far Side of the Sun, Science, 287, 1799 (200). Sun, M.-T. and Chou, D.-Y., The Inverse Problem in Acoustic Imaging, in Proc. SOHO10/GONG2000 Workshop on Helio- and Astero-Seismology at the Dawn of the Millennium (ESA SP-464; Noordwijk:ESA), 251 (2000).
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