Sushant Tripathy1, C. Barban2, K. Jain1, S. Kholikov1 and ...
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Mode Frequencies – Single-observable Fitting vs. Multi-spectral Fitting: Fitting of Intensity-Velocity Cross Spectrum using GONG and HMI Oscillation Data Sushant Tripathy 1 , C. Barban 2 , K. Jain 1 , S. Kholikov 1 and F. Hill 1 1 National Solar Observatory, Tucson, USA, 2 LESIA, Observatoire de Paris, Meudon, France Email: [email protected] Abstract: Simultaneous measurements of various observables at different heights in the solar atmosphere offer the prospect of studying the sensitivity of helioseismic inferences to the choice of observed height. These measurements can also be used to obtain better estimates of oscillation mode parameters if used simultaneously. Using GONG and HMI data, we compare mode parameters obtained from a single-observable fitting and those from a cross-spectral fitting (VIFIT) using four spectra simultaneously viz. velocity (V), intensity (I), the phase difference and the coherence between the intensity and velocity spectra. ℓ - ν diagram: Mode Asymmetry: GONG HMI Data and Analysis: We used two sets of GONG data spanning 216 days (5 May – 6 Dec 2009 and 2 Jan – 4 Aug 2012) corresponding to low- and high-activity periods of solar cycle 24. We also use 108 days of V and I data (2 Jan – 18 Apr 2012) from HMI. The I and V spherical harmonic time series corresponding to ℓ = 15 - 50 are corrected for the frequency shifts due to the solar rotation. Then m-averaged V power, I power, V-I phase difference and V-I coherence spectra are computed as defined in Barban et al (2004). The oscillation mode parameters are derived by simultaneous fitting of all 4 spectra with the model of Severino et al. (2001) which is based on a coherent signal that contains p-modes, modeled as Lorentz profiles, correlated and uncorrelated backgrounds and an incoherent noise. Figure 6: The ℓ-ν diagrams of the fitted modes. Open circles correspond to modes fitted with the multispectral VI procedure (blue) while the diamonds correspond to the modes fitted using only V data with a modified Nigam asymmetric profile (red). Mode Amplitude: Figure 2: The velocity and intensity power spectra, the coherence and I-V phase difference of the p-mode at ℓ = 35 and n = 7 for 2012 GONG data. The solid lines, superimposed on the observed data (dots) are the best value obtained with the model of Severino et al. (2001) and demonstrates that the observed spectra are well reproduced by the model based on (i) coherent component that includes p-modes, (ii) a fraction of the solar background that is correlated (cc) with p-modes, (iii) a fraction that is uncorrelated (cu) with the p-modes, and (iv) an incoherent noise component n. Figure 7: The difference between the oscillation frequencies derived using the V data using symmetric Lorentzian and modified Nigam asymmetric profiles for GONG during low-activity period in 2009 (left) and high-activity period in 2012 (middle), and for HMI during high-activity period in 2012 (right). The HMI V and I data have been re-binned to GONG resolution though JSOC. The resulting images are subsequently processed through the NSO/GONG time series pipeline. Figure 11: Phase difference between I and V for GONG (left panel) and HMI (right panel). The phase difference in HMI is different from GONG due to the different spectral lines. It will be interesting to analyze the phase difference between various background components. Summary: Oscillation mode parameters for ℓ = 15-50 were derived from the high-resolution GONG and HMI velocity and intensity data using the cross-spectral V-I fitting process. The mode frequencies derived from cross-spectral fitting procedure are lower than those derived using an asymmetrical profile. However, the differences are negligible in the 3 mHz band. The phase difference between V and I obtained from GONG high-resolution data is similar to those obtained by Barban et al. for GONG classic (low resolution) data. However, the phase difference for HMI data is different than GONG due to different spectral lines. We also see a turn over in phase at high frequency regime. The mean amplitude of HMI data is found to be lower compared to GONG data. A clear solar cycle dependence is seen in mode frequencies while other mode parameters, e.g., amplitudes and line widths do not show obvious variation with solar activity. This needs to be investigated. We further plan to extend this analysis to other epochs, wavelengths as well as to higher degrees. Figure 8: Difference in frequencies between 2012 and 2009 using different fitting methods depicting solar cycle variation in GONG data. Power Spectrum: Amplitudes of Background and Incoherent Components: Comparison between Observed and Modeled Spectra: Figure 9: Difference in mode frequencies between HMI and GONG spectra derived using the VI fitting for the degree range 15 - 50. Figure 13: Logarithm of the background amplitudes as a function of frequency. It appears that all three of the V background components turnover at high frequencies. The plots also show that power laws may be useful descriptors of some of the parameters e.g., the cu components and the incoherent noise components. Figure 10: Mean V and I amplitudes as a function of frequency for GONG (left panels) and HMI (right panels) showing the usual shape, reaching a maximum value near 3 mHz. The shape of the distribution is asymmetric, agreeing with earlier studies. However, the change in amplitude in two different activity periods in GONG data is not clearly seen. Figure 1: The m-averaged HMI V power spectra for ℓ=50. The SHT coefficients have been corrected for frequency shifts caused by the solar rotation. Figure 3: Same as Figure 2 but for HMI data. Figure 5: Same as Figure 4 but for HMI data. Figure 4: Modeled helioseismic spectra for ℓ = 35 and n = 7 for GONG showing the sensitivity to the background components. The solid line is the best fit, the dashed and dotted line is the same fit parameter but with cu = 0 and cc = 0 in both V and I, respectively. It demonstrates that the opposite asymmetries of the I and V line profiles arise from the interaction of the mode and cc (dashed lines) while the dominant contribution to the phase difference and coherence profiles comes from the cu (dotted line), producing both a phase jump and two symmetric coherence dips. Mode Width: Figure 12: Line width as a function of frequency showing the well known plateau at intermediate frequencies but a clear solar cycle variation is not seen. Abstract ID # 19503 Paper # SH13B-4096 This work utilizes GONG data obtained by the NSO Integrated Synoptic Program (NISP), managed by the National Solar Observatory (NSO), the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation (NSF). The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísica de Canarias, and Cerro Tololo Interamerican Observatory. HMI data courtesy of SDO (NASA) and the HMI consortium. This work is supported in part by NASA grant NNH- 12AT11I to the NSO.
Transcript of Sushant Tripathy1, C. Barban2, K. Jain1, S. Kholikov1 and ...
V – I Phase Difference:
Mode Frequencies – Single-observable Fitting vs. Multi-spectral Fitting:
Fitting of Intensity-Velocity Cross Spectrum using GONG and HMI Oscillation Data
Sushant Tripathy1, C. Barban2, K. Jain1, S. Kholikov1 and F. Hill1 1 National Solar Observatory, Tucson, USA, 2 LESIA, Observatoire de Paris, Meudon, France
Email: [email protected] Abstract: Simultaneous measurements of various observables at different heights in
the solar atmosphere offer the prospect of studying the sensitivity of helioseismic inferences to the choice of observed height. These measurements can also be used to obtain better estimates of oscillation mode parameters if used simultaneously. Using GONG and HMI data, we compare mode parameters obtained from a single-observable fitting and those from a cross-spectral fitting (VIFIT) using four spectra simultaneously viz. velocity (V), intensity (I), the phase difference and the coherence between the intensity and velocity spectra.
ℓ - ν diagram:
Mode Asymmetry:
GONG HMI
Data and Analysis: We used two sets of GONG data spanning 216 days (5 May – 6 Dec 2009 and 2 Jan – 4 Aug 2012) corresponding to low- and high-activity periods of solar cycle 24. We also use 108 days of V and I data (2 Jan – 18 Apr 2012) from HMI. The I and V spherical harmonic time series corresponding to ℓ = 15 - 50 are corrected for the frequency shifts due to the solar rotation. Then m-averaged V power, I power, V-I phase difference and V-I coherence spectra are computed as defined in Barban et al (2004). The oscillation mode parameters are derived by simultaneous fitting of all 4 spectra with the model of Severino et al. (2001) which is based on a coherent signal that contains p-modes, modeled as Lorentz profiles, correlated and uncorrelated backgrounds and an incoherent noise.
Figure 6: The ℓ-ν diagrams of the fitted modes. Open circles correspond to modes fitted with the multispectral VI procedure (blue) while the diamonds correspond to the modes fitted using only V data with a modified Nigam asymmetric profile (red).
Mode Amplitude:
Figure 2: The velocity and intensity power spectra, the coherence and I-V phase difference of the p-mode at ℓ = 35 and n = 7 for 2012 GONG data. The solid lines, superimposed on the observed data (dots) are the best value obtained with the model of Severino et al. (2001) and demonstrates that the observed spectra are well reproduced by the model based on (i) coherent component that includes p-modes, (ii) a fraction of the solar background that is correlated (cc) with p-modes, (iii) a fraction that is uncorrelated (cu) with the p-modes, and (iv) an incoherent noise component n.
Figure 7: The difference between the oscillation frequencies derived using the V data using symmetric Lorentzian and modified Nigam asymmetric profiles for GONG during low-activity period in 2009 (left) and high-activity period in 2012 (middle), and for HMI during high-activity period in 2012 (right). The HMI V and I data have been re-binned to GONG resolution though JSOC. The resulting images are subsequently processed through the NSO/GONG time series pipeline.
Figure 11: Phase difference between I and V for GONG (left panel) and HMI (right panel). The phase difference in HMI is different from GONG due to the different spectral lines. It will be interesting to analyze the phase difference between various background components.
Summary: Oscillation mode parameters for ℓ = 15-50 were derived from the high-resolution GONG and HMI velocity and intensity data using the cross-spectral V-I fitting process.
The mode frequencies derived from cross-spectral fitting procedure are lower than those derived using an asymmetrical profile. However, the differences are negligible in the 3 mHz band.
The phase difference between V and I obtained from GONG high-resolution data is similar to those obtained by Barban et al. for GONG classic (low resolution) data. However, the phase difference for HMI data is different than GONG due to different spectral lines. We also see a turn over in phase at high frequency regime.
The mean amplitude of HMI data is found to be lower compared to GONG data.
A clear solar cycle dependence is seen in mode frequencies while other mode parameters, e.g., amplitudes and line widths do not show obvious variation with solar activity. This needs to be investigated.
We further plan to extend this analysis to other epochs, wavelengths as well as to higher degrees.
Figure 8: Difference in frequencies between 2012 and 2009 using different fitting methods depicting solar cycle variation in GONG data.
Power Spectrum:
Amplitudes of Background and Incoherent Components:
Comparison between Observed and Modeled Spectra:
Figure 9: Difference in mode frequencies between HMI and GONG spectra derived using the VI fitting for the degree range 15 - 50.
Figure 13: Logarithm of the background amplitudes as a function of frequency. It appears that all three of the V background components turnover at high frequencies. The plots also show that power laws may be useful descriptors of some of the parameters e.g., the cu components and the incoherent noise components.
Figure 10: Mean V and I amplitudes as a function of frequency for GONG (left panels) and HMI (right panels) showing the usual shape, reaching a maximum value near 3 mHz. The shape of the distribution is asymmetric, agreeing with earlier studies. However, the change in amplitude in two different activity periods in GONG data is not clearly seen.
Figure 1: The m-averaged HMI V power spectra for ℓ=50. The SHT coefficients have been corrected for frequency shifts caused by the solar rotation. Figure 3: Same as Figure 2 but for HMI data. Figure 5: Same as Figure 4 but for HMI data.
Figure 4: Modeled helioseismic spectra for ℓ = 35 and n = 7 for GONG showing the sensitivity to the background components. The solid line is the best fit, the dashed and dotted line is the same fit parameter but with cu = 0 and cc = 0 in both V and I, respectively. It demonstrates that the opposite asymmetries of the I and V line profiles arise from the interaction of the mode and cc (dashed lines) while the dominant contribution to the phase difference and coherence profiles comes from the cu (dotted line), producing both a phase jump and two symmetric coherence dips.
Mode Width:
Figure 12: Line width as a function of frequency showing the well known plateau at intermediate frequencies but a clear solar cycle variation is not seen.
Abstract ID # 19503 Paper # SH13B-4096
This work utilizes GONG data obtained by the NSO Integrated Synoptic Program (NISP), managed by the National Solar Observatory (NSO), the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation (NSF). The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísica de Canarias, and Cerro Tololo Interamerican Observatory. HMI data courtesy of SDO (NASA) and the HMI consortium. This work is supported in part by NASA grant NNH-12AT11I to the NSO.
