Solar B as a tool for coronal wave studies

1. The 6th Solar B Science Meeting, 8-11/11/2005 Solar B as a tool for coronal wave studies Valery M. Nakariakov University of Warwick United Kingdom

2. Observational evidence for coronal waves is abundant (SOHO, TRACE, RHESSI, NoRH): Periods from 1 s to several min. • (Quasi) Periodicity can be connected with: • Resonance (connected with characteristic spatial scales – e.g. standing modes of coronal structures) • Dispersion (also connected with characteristic spatial scales but indirectly, through wave dispersion – different spectral components propagate at different phase and group speeds) • Nonlinearity / self-organisation (finite amplitude effects and overstabilities – autooscillations, dynamical regimes of reconnection, wave-flow interactions). All these mechanisms provide us with seismological information about physical conditions in the corona 2

3. Kink oscillations of coronal loops (Aschwanden et al. 1999,2002; Nakariakov et al. 1999; Verwichte et al. 2004) • Propagating longitudinal waves in polar plumes and near loop footpoints (Ofman et al. 1997-1999;DeForest & Gurman, 1998; Berghmans & Clette, 1999; Nakariakov et al. 2000; De Moortel et al. 2000-2004) • Standing longitudinal waves in coronal loops (Kliem at al. 2002; Wang & Ofman 2002) • Global sausage mode (Nakariakov et al. 2003) • Propagating fast wave trains. (Williams et al. 2001, 2002; Cooper et al. 2003; Katsiyannis et al. 2003; Nakariakov et al. 2004, Verwichte et al. 2005) Already identified coronal MHD modes: 3

4. Kink oscillations as a tool for coronal seismology: Determination of coronal magnetic field Scheme of the method: Nakariakov, Ofman 2001 4

5. Recent development: transverse oscillations in off-limb arcade observed with TRACE: Verwichte et al. 2004 5

6. First identification of kink second harmonics: P2≈ P1/2, the mode has a node at loop apex. Andries et al. (2004): P2 /P1~H (scale height) P1 P2 A tool for independent estimation of stratification 6

7. Mechanisms responsible for the decay of kink oscillations are still intensively debated. Two most popular theories are • phase mixing with enhanced shear viscosity (or shear viscosity ≈ bulk viscosity), and • resonant absorption (dissipationless). These mechanisms have different scaling of the decay time with oscillation period (Ofman & Aschwanden, 2002): Nakariakov & Verwichte 2005 7

8. Typical parameters of kink oscillations: • Oscillation period P: 2-10 min (<P> = 321 s) • Oscillation duration D: 6-90 min (<D> = 23 min) • Oscillation amplitude A: 0.1-9 Mm (<A> = 2.2 Mm) • V: 1-70 km/s (<V> = 7 km/s) Aschwanden, 2005 Required resolution in EUV: Time Dt < 30 s Spatial Dx < 1 Mm Doppler DV < 1 km/s Kink oscillations with Solar B: Quite consistent with XRT (Dt < 10s, Dx < 1 Mm); Not likely to be detected with EIS (DV = 3 km/s) 8

9. Longitudinal waves as tool for determination of coronal heating function Standard detection method is the time-distance plot for a selected slit on image Distance along slit Observed in coronal fan structures and polar plumes time 9

10. Theory: the evolutionary equation for longitudinal velocity V(z,x): stratification nonlinearity radiative losses - heating thermal conduction Observations vs Theory: • Assume or estimate r(z), T(z), hence H(z),Cs(z) • Obtain m(z) by best fitting, • Estimate radiative losses, • Obtain the heating function. Observed amplitude, V 10

11. Probing sub-resolution structuring by longitudinal waves: amplitude evolution with height. The correlation coefficient of the waves observed in 171Å and 195 Å is found to decrease with distance from source: phase mixing  decrease of the wave amplitude A sum of four waves with different speeds (80, 110, 140 and 170 km/s) within one pixel time Distance along slit 11

12. Simulations: a=171A, 195A Probing sub-resolution structuring by multi-wavelength observations of longitudinal waves:decorrelation of waves measured along the same path in different bandpasses. From King et al. 2003  Decorrelation  Phase mixing Sub-resolution structuring? 12

13. Typical parameters of longitudinal waves: • Oscillation period P: 2.5-9 min (<P> = 282 s) • Oscillation duration D: > 30-60 min • Wavelength l: (15-100)*sin(aLOS) Mm • Oscillation amplitude r: 0.7-14.6% (<r/ro> = 4.1%) • V: 0.1-0.15 Cs (<V> = 4-8 km/s) De Moortel. et al. 2002 Required resolution in EUV: Time Dt < 30 s Spatial Dx < 5 Mm Doppler DV < 1 km/s Duration of observation: >15-60 min (in sit-and-stare mode with sufficiently large FOV) Longitudinal oscillations with Solar B: Quite consistent with XRT (Dt < 10s, Dx < 1 Mm); Not likely to be detected with EIS (DV = 3 km/s) 13

14. How can EIS be useful for coronal wave studies? • Search for torsional modes (not identified in the corona yet): They can be observed as periodic Doppler broadenings of coronal spectral lines; possible amplitude can be of the same order as the amplitude of kink oscillations (e.g. <5%)  V/CA≈ 0.05  V ≈ 20-30 km/s. The period of an N-th standing torsional mode is 2L/CAN , for a typical active regions, the longest periods are a few min – well resolvable with EIS. (See Nakariakov & Verwichte 2005 for more detail, and Williams 2004 for forward modelling). • Standing acoustic modes (well resolved by SUMER): • Observational challenges: • Imaging observation (e.g. 1st or 2nd harmonics?), • Density perturbations? • Cooler lines?, • Identification in flaring light curves Wang et al.. 2003 14

15. http://www.warwick.ac.uk/go/space Conclusions: • Coronal waves provide us with a unique tool for the estimation of coronal magnetic fields, heating function, transport coefficients, independent estimation of stratification, and for probing coronal fine structuring. • XRT will be a primary tool for detection and study of kink oscillations and propagating longitudinal waves. Also, detection of standing longitudinal modes would be very likely. • EIS can be used for the search for torsional modes and for detailed study of standing longitudinal modes. 15

16. References: • Andries, J., Arregui, I, Goossens, M., determination of the coronal density stratification from the observations of harmonic coronal loop oscillations, ApJ 624, L57, 2005 • De Moortel, I.; Ireland, J.; Walsh, R. W.; Hood, A.W., Longitudinal intensity oscillations in coronal loops observed with TRACE - I. Overview of measured parameters, Solar Phys. 209, 61, 2002 • King, D.B., Nakariakov, V.M., Deluca, E.E., Golub, L., McClements, K.G., Propagating EUV disturbances in the Solar corona: Two-wavelength observations, A&A 404, L1, 2003 • Nakariakov, V.M., Ofman, L., Determination of the coronal magnetic field by coronal loop oscillations, A&A 372, L53, 2001 • Nakariakov, V.M., Verwichte, E., Coronal waves and oscillations, Living Rev. Solar Phys., 2, 3, 2005 • Ofman, L.; Aschwanden, M. J., Damping time scaling of coronal loop oscillations deduced from Transition Region and Coronal Explorer observations, ApJ 576, L153, 2002 • Verwichte, E., Nakariakov, V.M., Ofman, L., Deluca, E.E., Characteristics of transverse oscillations in a coronal loop arcade, Solar Phys. 223, 77, 2004 • Wang, T. J et al., Hot coronal loop oscillations observed with SUMER: Examples and statistics, A&A 406, 1105, 2003 • Williams, D.R., Diagnosing MHD wave detections in solar coronal loops: torsional effects, Proc. SOHO-13, ESA SP-547, 2004 16