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 (

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 Yohkoh X-Ray coronal image

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

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 A statistical approach to measuring time-delay We follow the treatment of Athay & White (1979, ApJ, ) 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 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 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 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 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 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 Normalised flux distribution with height (in arcsec) for the 26348r00 and 26482r00 datasets

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

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 Mg X 624 this gives a speed of 154±18 km/s For O V Si XII 520 this gives a speed of 218±28 km/s For Mg X Si XII 520 this gives a speed of 236±19 km/s For Mg X 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.

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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 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)