ON THE FLARE INDUCED HIGH-FREQUENCY GLOBAL WAVES IN THE SUN BRAJESH KUMAR 0 Udaipur Solar Observatory, Physical Research Laboratory, Dewali, Badi Road, Udaipur 1 0 2 313 004, India n a J [email protected] 5 2 and ] R S SAVITA MATHUR . h p Indian Institute of Astrophysics, Koramagala, Bangalore 560 034, India - o r t [email protected] s a [ and 1 v 1 R. A. GARC´IA 3 3 4 Laboratoire AIM, CEA/DSM-CNRS, Universit´e Paris 7 Diderot, IRFU/SAp, Centre de . 1 0 Saclay, 91191, Gif-sur-Yvette, France 0 1 : [email protected] v i X r and a P. VENKATAKRISHNAN Udaipur Solar Observatory, Physical Research Laboratory, Dewali, Badi Road, Udaipur 313 004, India [email protected] Received ; accepted – 2 – ABSTRACT Recently, Karoff & Kjeldsen (2008) presented evidence of strong correlation between the energy in the high-frequency part (5.3<ν<8.3 mHz) of the acoustic spectrum of the Sun and the solar X-ray flux. They have used disk-integrated intensity observations of the Sun obtained from the VIRGO (Variability of so- lar IRradiance and Gravity Oscillations) instrument on board SOHO (Solar and Heliospheric Observatory)spacecraft. Similarsignatureofflaresinvelocityobser- vations has not been confirmed till now. The study of low-degree high-frequency wavesintheSunisimportantforourunderstandingofthedynamicsofthedeeper solar layers. In this paper, we present the analysis of the velocity observations of the Sun obtained from the MDI (Michelson and Doppler Imager) and the GOLF (Global Oscillations at Low Frequencies) instruments on board SOHO for some major flare events of the solar cycle 23. Application of wavelet techniques to the time series of disk-integrated velocity signals from the solar surface using the full-disk Dopplergrams obtained from the MDI clearly indicates that there is enhancement of high-frequency global waves in the Sun during the flares. This signature of flares is also visible in the Fourier Power Spectrum of these velocity oscillations. On the other hand, the analysis of disk-integrated velocity observa- tions obtained from the GOLF shows only marginal evidence of effects of flares on high-frequency oscillations. Subject headings: Sun: atmosphere, Sun: flares, Sun: oscillations – 3 – 1. INTRODUCTION In the Sun, the typical distribution of acoustic power of photospheric oscillations peaks at around 5 min (Leighton, Noyes, & Simon 1962) with a general decrease to negligible power at higher frequencies. This behaviour of the acoustic spectrum has been understood in terms of trapped oscillations in a cavity (Ulrich 1970; Leibacher & Stein 1971). The eigen-functions corresponding to the band of oscillations in the region of 5 minutes peak in the convection zone, which seems to be the dominant source of excitation of the solar oscillations (Goldreich, Murray, and Kumar, 1994). Apart from these normal modes of oscillations (p modes), researchers have found the presence of high-frequency oscillations (frequencies higher than the solar-photospheric acoustic cutoff at about 5.3 mHz) in the solar-acoustic spectrum (Libbrecht & Kaufman 1988; Libbrecht 1988; Chaplin et al. 2003; Jim´enez et al. 2005; Karoff & Kjeldsen 2008). Unlike the normal p modes, the driving mechanism of these high-frequency solar oscillations is still not well established. Balmforth & Gough (1990) suggest that the high-frequency waves are partly reflected by the sudden change in temperature at the transition region between the chromosphere and the corona. Kumar & Lu (1991) explain these high-frequency waves as an interference phenomenon between ingoing and outgoing waves from a localized source just beneath the photosphere. Wolff (1972) suggested that large solar flares can stimulate free modes of oscillation of the entire Sun, by causing a thermal expansion that would drive a compression front to move into the solar interior. Several researchers have tried to study the effect of flares on the acoustic-velocity oscillations of the Sun. The progress in this field escalated recently with the advent of continuous data from dedicated instruments such as MDI (Michelson and Doppler Imager) (Scherrer et al. 1995) on board SOHO (Solar and Heliospheric Observatory) spacecraft and GONG (Global Oscillation Network Group) (Harvey et al. – 4 – 1995). Haber et al. (1988) reported an average increase in the power of intermediate-degree modes after a major flare (of class X13/3B) using a few hours of solar-oscillations data obtained by the Dunn telescope at National Solar Observatory/ Sacramento Peak, USA. Braun & Duvall (1990) could not detect acoustic-wave excitation from an X-class flare. Kosovichev & Zharkova (1998) reported the first detection of “solar quakes” inside the Sun, caused by the X2.6 flare of 9 July 1996, using the MDI Dopplergrams. Following this result, Donea et al. (1999) found an acoustic source associated with a flare using seismic images produced with helioseismic-holography technique. Application of ring-diagram analysis showed that the power of the global p modes appears to be larger in several flare-producing active regions as compared with the power in non-flaring regions of similar magnetic field strength (Ambastha et al. 2003). Additionally, Donea & Lindsey (2005) have reported emission of seismic waves from large solar flares using helioseismic holography. Some of the large solar flares have been observed to produce enhanced high-frequency acoustic velocity oscillations in localized parts of active regions (Kumar & Ravindra 2006). Further, Zharkova & Zharkov (2007) reported large downflows associated with seismic sources during the major flare (of class X17.6/4B) of 28 October 2003. Venkatakrishnan et al. (2008) report co-spatial evolution of seismic sources and H-alpha flare kernels during the aforementioned flare event. A search for a correlation between the energy of the low-degree p modes and flares using velocity observations of the Sun remained inconclusive (Gavryusev & Gavryuseva 1999; Chaplin et al. 2004; Ambastha & Antia 2006). The study of low-degree high-frequency (LDHF) waves in the Sun is important as this can bring more constraints on the rotation profile between 0.1 and 0.2 RO (Garc´ıa et al. 2008; Mathur et al. 2008). The effect of flares on such LDHF waves can provide a clue for the origin of these waves. Recently, Karoff & Kjeldsen (2008) have reported that the correlation between – 5 – X-ray flare intensity and the energy in the acoustic spectrum of disk-integrated intensity oscillations (as observed with VIRGO (Variability of Solar IRradiance and Gravity) (Fr¨ohlich et al. 1995) instrument on board SOHO) is stronger for high-frequency waves than for the well known 5-minute oscillations. This correlation was obtained for a long time series of 8 years with time variation of power smoothed with a 24-day filter. This result does not show the immediate consequence of individual flares. For this, we require shorter time series closely associated with the flares. Since, the power spectra are noisier for shorter time series, we need to apply wavelet analysis to the time series. Intensity variations are generally manifestations of pressure variations. However, for a medium stratified by gravity, the waves are not pure acoustic waves, but are acousto-gravity waves. Hence, it will be more profitable to look at the velocity oscillations of the solar atmosphere. Therefore, in this study, we have searched for the effects of flares in the time series of disk-integrated velocity signals from the solar surface using the full-disk Dopplergrams obtained from the MDI instrument. We have also looked for these effects in disk-integrated velocity observations obtained from the GOLF (Global Oscillation at Low Frequency) (Gabriel et al. 1995, 1997) instrument on board SOHO. These studies have been applied to the major solar flares of 28 October 2003 (of class X17.6/4B), 29 October 2003 (of class X10/2B) and 6 April 2001 (of class X5.6/3B) that occurred in the solar cycle 23. Each of the selected events are in decreasing order of flare strength as observed in X-ray (1−8 ˚A) by GOES (Geostationary Operational Environmental Satellite) (Garc´ıa 1994) satellites. Wavelet and Fourier analyses of MDI velocity observations clearly indicate the enhancement in high-frequency global waves in the Sun during the flares. However, this signature of flares is weaker in the case of GOLF as compared to MDI data. – 6 – 2. DATA AND ANALYSIS 2.1. MDI DATA We have used the sequence of MDI full-disk Dopplergrams for three hours spanning the flare obtained on 28 October 2003 (10:00–13:00 UT), 29 October 2003 (19:00–22:00 UT), and 6 April 2001 (18:00–21:00 UT) with a cadence of one minute and spatial sampling rate of 2 arcsec per pixel. We have also used three hours of MDI Dopplergrams for a quiet period (non-flaring condition) as control data. In order to compare the temporal behaviour with the disk-integrated intensity observations by VIRGO, we have summed up the velocity signals over all the pixels of the MDI full-disk Dopplergrams. The images are first examined for pixels having cosmic ray hits and such pixels are replaced by interpolation. A two-point backward difference filter (difference between two consecutive measurements) is applied to these sequences of images to enhance the velocity signals from the p modes and high-frequency waves above the solar background. The sequence of these filtered Doppler images are then collapsed into a single velocity value, excluding the noisy pixels along the solar limb. This process is applied to the time series of Doppler images for all the three aforementioned flare events as well as the quiet period. It is believed that by collapsing the full-disk Doppler images, the acoustic modes with maximum l=0,1,2,3 remain while the modes higher than these are averaged out. Thus, the collapsed velocity value should be the representative of the global acoustic modes. The temporal evolution of these disk-integrated velocity signals for three hours spanning the flare are shown in the upper panel of Figures 1(a), 2(a) and 3(a) and that for the quiet period is shown in Figure 4(a). – 7 – 2.2. GOLF DATA GOLF instrument measures the disk-integrated line-of-sight velocity of the Sun at a cadence of one raw count every 10 s. However, we have rebinned the velocity data from GOLF for every 60 s to match with MDI. We have used the same periods of time for both instruments for the flare events of 28 October 2003, 29 October 2003, and 6 April 2001, as well as for the non-flaring condition. We have worked with the standard velocity time series (Garc´ıa et al. 2005; Ulrich et al. 2000) as well as the original raw-counting rates. We have also checked if there was any anomalous behavior during the analyzed periods of time in the housekeeping data. Indeed, during the flare events of 28-29 October 2003, GOLF raw-counting rates of both photomultipliers suffered an increase in the measurements probably as a consequence of the impact of high-energetic particles. Due to these contaminations, the standard velocity time series have been filtered out during this period and thus, we have been obliged to work with the raw observations obtained by GOLF during the aforementioned flare events. A two-point backward difference filter is applied to the velocity series to remove the effect of the rotation and other slowly varying solar features. The temporal evolution of these filtered velocity signals for three hours spanning the flare are shown in the upper panels of Figures 1(b), 2(b) and 3(b) and that for the quiet period is shown in Figure 4(b). 2.3. WAVELET ANALYSIS OF MDI AND GOLF VELOCITY DATA For the time-frequency analysis of the influence of flares on the high-frequency acoustic modes, we have applied the Wavelet technique (Torrence & Compo 1998) on the velocity time series obtained from MDI and GOLF as described above. We have used the Morlet wavelet, which is the product of a sine wave and a Gaussian function. We have computed the Wavelet Power Spectrum (WPS), which yields the correlation between the wavelet with – 8 – a given frequency and the data along time. For the different events and the two instruments, we notice the presence of power around 3 mHz, corresponding to the region of the normal p modes. Concerning the high-frequency waves above 5 mHz, we can study the evolution of their power with time. We limit our study to the region inside a “cone of influence” corresponding to the periods of less than 25% of the time series length for reliability of the periods. Finally, we have also calculated two confidence levels of detection corresponding to the probability of 90% and 50% that the power is not due to noise. Thus, we have outlined the regions in the WPS where power lies above these confidence levels and these regions are shown in middle panels of the Figures 1-4(a)&(b). A comparison of the WPS for the flare events with that of the quiet period clearly indicates the enhancement of high-frequency waves during these flare events as seen in the data from MDI instrument. However, in the case of GOLF data, some short-lived high-frequency waves are sporadically observed during the flares. The WPS is collapsed along time to obtain the Global-wavelet power spectrum (GWPS). If some power is present during the whole length of our time series, it would be easily seen in the GWPS. This is nearly similar to the commonly used power spectral density. In the Figures 1-4(a)&(b), the GWPS shows a strong peak of the normal p modes which are well known to be existing all the time. However, if the power of high-frequency waves increases only a few times along the three hours of the studied data this would not appear as a strong peak in the GWPS. In case of MDI data, the GWPS for all the three flare events do show a bump corresponding to the high-frequency waves (above 5 mHz). Here again, we have overplotted the significance levels corresponding to probabilities of 90% and 50%. We notice that the normal p-mode peak in the GWPS is above 90% significance level whereas the high-frequency peak is just below 50% significance level, i.e., it has at least 50% probability of being due to noise. However, the GWPS estimated from the MDI velocity data during a quiet period (Figure 4(a)) doesn’t show any peak beyond 5 mHz. – 9 – This supports the idea that the increase of power in the high frequency regime of the GWPS is indeed caused by the flare. In the case of GOLF data, we do not observe this signature in the GWPS estimated for the flare events as the overall high-frequency signal is weak in these observations. To see when the high-frequency waves have an increased power during the flare, we have calculated the scale-average time series in the frequency regime 5-8 mHz. Basically, it is a collapsogram of the WPS along the frequency of the wavelet in the chosen range. For this quantity, we have calculated the confidence level for a 50% probability. These are shown in the lower panels of the Figures 1-4(a)&(b). Here, we observe peaks corresponding to the presence of high-frequency waves in the WPS. In general, the MDI data show more closely spaced high-amplitude peaks as compared to the GOLF data for the flare events, but still mainly around 50% confidence level. A comparison with the same analysis performed for a quiet period (non-flaring condition) neither shows a high-frequency bump beyond 5 mHz in the GWPS (for MDI data) nor high-amplitude peaks in the scale-average time series (for both, MDI and GOLF data). Thus, in spite of the small confidence levels found during this analysis, it indicates a possible relationship between these excess high-frequency power and the flares. 2.4. FOURIER ANALYSIS OF MDI AND GOLF VELOCITY DATA We have also estimated the Fourier Power Spectrum (FPS) from the velocity time series obtained by the MDI and GOLF instruments for the aforementioned flare events and the quiet period. The FPS spectra obtained from the MDI and GOLF data are respectively shown in the left and right panels of Figure 5. In the estimation of FPS spectra, the Power Spectral Density has not been corrected for the transfer function of the two-point backward difference filter (Garc´ıa & Ballot 2008). A correction from the backward difference filter – 10 – will change the slope, thereby affecting the relative amplitudes between the normal p modes and the high-frequency waves. Here, we study the high-frequency waves in an absolute manner for each event and we do not compare them with the normal p modes. Therefore, it does not bias our study. The FPS shown in the Figure 5 depicts dominant power in the 3 mHz band which is due to the normal p modes. These FPS also show significant peaks in the higher frequency band (above 5 mHz) as estimated from MDI data for all the three flare events (strongest for the 6 April 2001 flare event). However, the GOLF data show the strong signature only for the flare event of 29 October 2003. The enhancement of high-frequency power related to the flare of 28 October 2003 has already been seen in the GONG velocity data (Kumar & Venkatakrishnan 2009). Here, we do observe spikes at high-frequency in the FPS from the MDI data and some smaller ones from the GOLF data for these flare events. These spikes are very weak in the case of a quiet period, as seen in both the data sets (c.f., bottom panels of Figure 5). The difference found between the measurements of the two instruments could be a direct consequence of the different heights of the solar atmosphere sampled by each instrument (Ni I v/s Sodium doublet). The GOLF is observing in the high photosphere and the low chromosphere while the MDI or the GONG observes mostly in the deep photosphere close to where VIRGO is observing. Further analysis will be necessary to understand all the particularities of each seismic measurements (c.f. Jim´enez-Reyes et al. (2007)). 3. DISCUSSION AND CONCLUSIONS The existence of high-frequency acoustic waves was first discovered in high-degree observations at the Big Bear Solar Observatory (Libbrecht & Kaufman 1988; Libbrecht 1988) and later in GOLF low-degree disk-integrated observations (Garc´ıa et al. 1998). Recently, they have also been seen in BiSON disk-integrated radial-velocity data