1. Detection of slow magnetoacoustic waves in open field regions on the Sun Dr. Eoghan O’Shea¹ Dr. Dipankar Banerjee², Prof. Gerry Doyle¹ 1. Armagh Observatory, N. Ireland 2. Indian Institute of Astrophysics, Bangalore, India (http://www.arm.ac.uk)

2. 2 The Solar Wind: A constant stream of particles from the Sun into space. One of the effects of the open field lines at the poles and the closed field lines at equatorial regions is a difference in the solar wind speed. At the poles there is the ‘fast’ solar wind At equatorial regions there is the ‘slow’ wind

3. 3 Yohkoh X-Ray coronal image

4. 4 Fast solar wind originates in coronal funnels – speeds of approx. 10 km/s (Tu et al., 2005, Science, 308, 519) But how is it accelerated up to high velocities (  800 km/s)? Answer: Compressional MHD waves(?) (Ofman & Davila, 1997, ApJ, 476, 357)

5. 5 Observational log:  Coronal Diagnostic spectrometer (CDS/SoHO)  Long (~3 hour) temporal series datasets were obtained for the transition region line of O V 629 Å (2.5  10 5 ) and the coronal lines of Mg X 609/624 Å (1  10 6 K), Si XII 520 Å (2.5  10 6 K)  Slit width 4  240 arc sec  Exposure time of 60 sec Two Two sets of observations obtained in November/December 2002: (i) Off-limb regions above the poles (ii) Equatorial and polar coronal holes

6. 6 Location of the CDS observing slit in the Northern Polar Regions s26348r00s26406r00 s26478r00s26542r00 EIT 171 images at 1.3  10 6 K

7. 7 Wavelet measurements in Radiant Flux or ‘Intensity’ in the Northern Polar region (dataset 26363r00, height of 989”) 0.8 mHz=1250s 1 mHz=1000s

8. 8 A statistical approach to measuring time-delay We follow the treatment of Athay & White (1979, ApJ, 229 1147) Phase delays are plotted over the full –180 º to +180 º range and as a function of frequency . (Phases calculated using Fourier techniques from Doyle et al., 1999, A&A, 347, 335 at, at least, the 95% confidence level) The phase difference (or delay) is given by; where T is the time-delay.  will vary linearly with  and will change by 360 º over frequency interval  = 1/T, for a fixed value of T.  Parallel lines in  vs.  plots corresponding to fixed time-delays.  = 2  T

9. 9 Simulated Data For a fixed time delay of 250s (4 mHz) the phases (square symbols) line up along parallel lines with slopes of 2  T, where T=250s. Therefore, measuring the slope will give an estimate of the time delay (if unknown) Similarly, for a fixed time delay of 500s (2 mHz) the phases line up with a spacing of 2 mHz between them.  = 2  T

10. 10 Time delays can be calculated from the slopes, 2  T of the plotted phases, as for the simulated data. Phase delay measurements between different line pairs as labelled, for the off-limb datasets O V-Mg X: 58±7s (17.2 mHz) O V-Si XII: 106±14s (9.43 mHz) Mg X-Si XII: 65±5s (15.4 mHz) Mg X-Si XII: 71±6s (14.1 mHz) Small circles show 95% confidence, large circles 99% confidence

11. 11 Simulated Data For a fixed time delay of 250s (4 mHz) the phases (square symbols) line up along parallel lines with slopes of 2  T, where T=250s. Therefore, measuring the slope will give an estimate of the time delay (if unknown) Similarly, for a fixed time delay of 500s (2 mHz) the phases line up with a spacing of 2 mHz between them.  = 2  T

12. 12 Time delays can be calculated from the slopes, 2  T of the plotted phases, as for the simulated data. Rotate up to horizontal Phase delay measurements between different line pairs as labelled, for the off-limb datasets O V-Mg X: 58±7s (17.2 mHz) O V-Si XII: 106±14s (9.43 mHz) Mg X-Si XII: 65±5s (15.4 mHz) Mg X-Si XII: 71±6s (14.1 mHz)

13. 13 Histograms of phase distribution Significant peaks at 90º and 67.5º intervals.  = 2  (  +n  ) T Confidence levels calculated using a Monte Carlo (randomisation method) with  =  /4 (90º) or 3  /16 (67.5º) and n=0,1,2,3,…n Resonant Cavity?  = 2  T

14. 14 Normalised flux distribution with height (in arcsec) for the 26348r00 and 26482r00 datasets

15. 15 Line Pairs Dataset26348Dataset26482Average O V 629 - Mg X 624 13”12”12.5” (8938 km) O V 629 - Si XII 520 33”32”32.5” (23238 km) Mg X 609 – Si XII 520 23”20”21.5” (15373 km) Mg X 624- Si XII 520 20”20”20” (14300 km) 1” (arcsec)=715 km

16. 16 So, knowing the differences between the formation heights of the lines, and having the measured time delays for the line pairs, we can calculate the propagation speeds: For O V 629 - Mg X 624 this gives a speed of 154±18 km/s For O V 629 - Si XII 520 this gives a speed of 218±28 km/s For Mg X 609 - Si XII 520 this gives a speed of 236±19 km/s For Mg X 624 - Si XII 520 this gives a speed of 201±17 km/s Sound speed at the temperature of Mg X is 171 km/s and at the temperature of Si XII it is 241 km/s. Therefore, we are dealing here with slow magnetoacoustic compressional waves.

17. 17

18. 18 (a) Results for the Equatorial Coronal Hole datasets s26431/s26432 Time delay: 151±54s Prop. Speed: 59±21 km/s  = 2  (  +n  ) T (a):  = 3  /8 (135º) and n=0,1,2,3,…n (b),(c):  =  /4 (90º) and n=0,1,2,3,…n Time delay: 185±33s Prop. Speed: 48±9 km/s Time delay: 127±26s Prop. Speed: 70±14 km/s (b) Results for Northern polar coronal hole dataset s26435 (c) Results for the Southern polar coronal hole datasets s26502/s26503

19. 19 Conclusions:  Detected presence of oscillations and, hence, waves, in open field regions off-limb and in coronal holes.  We confirm the presence of upwardly propagating slow magnetoacoustic type waves (of the type needed to accelerate the fast solar wind)  We find evidence for the phases to have integer frequency intervals (  +n  We find evidence for the phases to have integer frequency intervals (  +n , where n=0,1,2,...etc.) which suggests the presence of resonance (resonant cavity?) high in the solar atmosphere. “Magnetoacoustic wave propagation in off-limb polar regions”, A&A, 2006 (in press) “Magnetoacoustic wave propagation in off-limb polar regions”, A&A, 2006 (in press) “A statistical study of wave propagation in coronal holes”, A&A, 2006 (submitted) “A statistical study of wave propagation in coronal holes”, A&A, 2006 (submitted)