FIKUT , Budapest A seismological view of the solar atmosphere Istvan Ballai SP 2 RC, University of Sheffield, UK Introduction The terminology, idea and methods of seismology are borrowed from Earths seismology It involves combining high-resolution observations, numerical modeling and analytical models --- obviously every ingredient with its own limitation Seismology starts with the premise that waves are present in the plasma and propagation characteristics (speed, amplitude, attenuation time and length, wavelength, etc) can be determined accurately. The most important factors to determine are the magnetic field (magnitude and structure) and density (also chemical composition, flows, etc. for the interior). Magnetic field is difficult to measure in the upper atmosphere because the Zeeman splitting degenerate. More important is the sub-resolution structure of the magnetic field Density is difficult to measure because of the underlying column of the plasma in each process of measurement. FIKUT , Budapest Introduction Space and solar plasmas are very dynamic, waves and flows are continuously observed by space satellites and ground-based telescopes Dynamical changes in plasmas are driven by restoring (buoyancy) forces, e.g. pressure gradient, gravity force, Coriolis force, MAGNETIC FIELD driven Lorentz force + the convective motion in the interior In general the dynamics, stability and thermal state of the plasma is controlled by the magnetic field Knowledge of the intensity and structure of the magnetic field is essential; luckily some theoretical and observational constraints help us The treatment of dynamics of the solar/stellar plasma must always be studied together with the evolution of the magnetic field FIKUT , Budapest Highly inhomogeneous Concentrations of magnetic field correspond to high temperature regions in the solar corona Observational facts FIKUT , Budapest The role of the magnetic field FIKUT , Budapest Magnetism on the Sun 2D static magnetic model of the transition region by Gabriel (1976) Dowdy et al. (1986) Solar Phys., 105, 35 FIKUT , Budapest Magnetism in the photosphere Courtesy of E. Priest (Physics World, February, 2003) striated penumbra inclined magnetic field continuous out/inflow FIKUT , Budapest Problems with measuring magnetic field intensity in rarefied regions FIKUT , Budapest Dynamics in the photosphere FIKUT , Budapest Dynamics in the photosphere flow velocity and wave-speed perturbation in an active region from time-distance analysis Kosovichev et al Standing sound waves can sample the solar interior. Changes in the properties of oscillations is a major source of information. FIKUT , Budapest Dynamics in the chromosphere Dominated by vertical and horizontal magnetic field (magnetic canopy) Characterized by decrease in density and slight increase in T (reflection of upgoing waves and shocks) Dynamics in the chromosphere FIKUT , Budapest Spicules covering the entire surface (Hinode observations by Okamoto et al. 2009) FIKUT , Budapest The Corona from space Trace FeIX/X 171 A line at 0.95 MKYohkoh SXT (2MK) FIKUT , Budapest Magnetic field in the corona The solar corona consists of myriad of loops Coronal loops are perfect channels for the propagation of waves, flows Anisotropy helps the propagation along loops rather than across Gary, 2001 FIKUT , Budapest MHD waves Waves observed in the MHD domain (2s 150 min) In the absence of other forces (gravity, non-inertial forces) there are three waves possible in plasmas: slow magnetoacoustic, Alfven, fast magnetoacoustic FIKUT , Budapest Linear MHD waves in non-uniform plasma Magnetoacoustic modes Evanescent solutions: modes or trapped or guided (or ducted) waves; Dispersion is determined by the ratio of the longitudinal wavelength to the characteristic spatial scale of inhomogeneity. The modes can have different structures in the transversal direction (inhomogeneity), which allows us to classify them: kink and sausage modes (perturbing or not perturbing the structure axis, respectively) body and surface modes (oscillating or evanescent inside the structure, respectively, and both evanescent outside the structure) FIKUT , Budapest Linear MHD waves in non-uniform plasma Magnetoacoustic modes FIKUT , Budapest Already identified coronal MHD modes: 1.Kink oscillations of coronal loops (Aschwanden et al. 1999,2002; Nakariakov et al. 1999; Verwichte et al. 2004, Ballai et al. 2010) 2.Propagating longitudinal waves in polar plumes and near loop footpoints (Ofman et al ; DeForest & Gurman, 1998; Berghmans & Clette, 1999; Nakariakov et al. 2000; De Moortel et al ) 3.Standing longitudinal waves in coronal loops (Kliem at al. 2002; Wang & Ofman 2002) 4.Global sausage mode (Nakariakov et al. 2003) 5.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) FIKUT , Budapest 19 MHD wave theory development Since the TRACE first observations there has been much work to see how the eigenmodes of coronal loops might be affected by plasma inhomogeneities. These can be separated into two main effects. RADIAL INHOMOGENEITYLONGITUDINAL INHOMOGENEITY AFFECTS DAMPING RATEAFFECTS EIGENFREQUENCIES AND EIGENMODES PLASMA INHOMOGENEITY FIKUT , Budapest Practical use of waves: Coronal seismology Local seismology: using waves propagating in magnetic structures (coronal loops, filaments, solar wind, etc) Global seismology: using waves propagating over very large distances in the quiet Sun, e.g. EIT waves Roberts et al. 1983, Aschwanden et al. 1999, Nakariakov et al many others Uchida 1970, Ballai et al. 2005, Ballai 2007, Long et al. 2008, Vrsnak et al. 2010, etc. Although they may look separate aspects, in reality they are strongly correlated How dynamical is the solar corona? FIKUT , Budapest CoMP measurement Tomczyk et al. (2007) FIKUT , Budapest Case study: kink oscillations as a tool for coronal seismology: Determination of coronal magnetic field Scheme of the method: Local coronal seismology - case study: determination of density structuring Many loop observations show the existence of multiple periods in the same loop, these being the periods of the fundamental mode and 1 st harmonic FIKUT , Budapest (e.g. Ballai et al. 2011) -Two periods observed in TRACE EUV images: 501 and 274 s - Any alteration of period ratio from 2 is a measure of the internal structuring H=73.33 Mm T=1.50.6 MK Local coronal seismology - case study: determination of magnetic field expansion With height loops tend to expand in the radial direction due to pressure depletion FIKUT , Budapest The change in the cross- section of the loop can modify the periods of oscillations, in this case Verth et al. (2007), Ruderman 2008 Other effects (e.g. geometrical) produce second order changes The problem with the P 1 /P 2 seismology The interpretation of two periods in a loop is not unique and the diagnostic results depends on the interpretation Example: Ballai et al. (2011), two periods observed 5015 and 2747 s The problem with the P1/P2 seismology If the two periods belong to the fundamental model and its first harmonic P 1 /P 2 =1.820.02 H=733 Mm, T=1.50.6 MK, B=20.7 G If the two periods belong to the combination of the fundamental mode (visible) and the renmant of the driver (Ballai et al. 2008) P 1 =177.13.5 s, P driver =607.426.8 s, B=5.81.8 G If the two periods belong to oscillations of two unresolved threads (Luna et al. 2008, Robertson and Ruderman 2011) d/R=0.0310.001, B=2.60.4 G Further possible explanations: The two periods belong to the two kink oscillations of a loop with elliptical cross-section (Ruderman 2010) Likely that higher resolution observations could help deciding on the interpretation FIKUT , Budapest Recent development: transverse oscillations in off-limb arcade observed with TRACE: FIKUT , Budapest 28 Radial inhomogeneity Thin tube, thin boundary approximation (Ruderman and Roberts 2002) Damping rate gives information about radial length scales and external and internal density contrast! Damping by resonant absorption (Hollweg 1988, Goossens et al. 1992, Ballai et al. 1999, Ruderman and Roberts 2002 ) very rapid damping of kink oscillations FIKUT , Budapest EIT waves and global seismology Generated by sudden energy releases (flares, CMEs); very well correlated to CMEs, weakly to flares Observed to propagate over large distances, sometimes comparable to the solar radius; the shape is almost circular Able to carry information about the quiet Sun, usually associated with large scale dimmings EIT waves are observed as diffuse emission enhancements immediately followed by expanding dimming regions in running-difference images (Moses et al. 1997; Dere et al. 1997, Thompson et al. 1998). Problems with EIT waves There is no unified concept about EIT waves Most of observations during solar minima Observations hampered by poor resolution (SOHO) or limited FOV (TRACE), but improved by STEREO, HiNODE, SDO, etc. Examples of EIT waves as seen by TRACE, STEREO FIKUT , Budapest TRACE 195 A (1.5 MK) The 13 June 1998 event (Wills-Davey and Thompson 1999, Ballai, Erdlyi and Pintr 2005) 15:25 UT 15:44 UT EIT waves observed by TRACE/EUV Oscillatory motion with periods of about 400 seconds (Ballai, Erdlyi and Pintr 2005) FIKUT , Budapest Application of EIT waves for seismology: Sampling the magnetic field (vertical) Suppose that EIT waves are FMW propagating perpendicular to the ambient magnetic field c=(c S 2 +v A 2 ) 1/2 The propagation height of EIT waves is important since many physical parameters (temperature, density, pressure) have height-dependence Suppose a simple atmosphere such that (Sturrock et al. 1996) F 0 : inward heat flux (1.810 5 erg/cm 2 s) x: normalized height coordinate (=r/R ) T 0 : temperature at the base of the model (=1.3MK) : coefficient of thermal conductivity ( ) FIKUT , Budapest Sampling the magnetic field (vertical) contd... With the sound speed and density calculated at each height, values of the magnetic field (via the Alfvn speed) are obtained to be xTncScS v A (1) B (1) v A (2) B (2) [T]: MK [n]: 10 8 cm -3 [c S ],[v A ]: 10 7 cm/s [B]: G (1): c=250 km/s (2): c=400 km/s FIKUT , Budapest Flare and magnetic field diagnostics EIT waves interact with loops transferring part of their energy to loops loop oscillations Supposing that the entire energy of EIT waves is transferred to loops, the minimum energy of EIT waves is For the event on 13 June 1998, we obtain E=3.810 18 J, for the event on 14 July 1998 (Nakariakov et al. 1999) we obtain E=10 19 J. Since e -1 contains the Alfvn speed, it is possible to derive a formula giving the magnetic field in the oscillating loop provided the energy of the EIT wave can be measured. FIKUT , Budapest Flare and magnetic field diagnostics Time L(Mm) R(Mm) n10 8 (cm -3 ) E(J) x x x x x x x x x x x x x x10 17 Lengths, width and densities taken from Aschwanden et al. (2001) Time given in yymmdd format E: the minimum energy of EIT waves to generate the observed dislocation of loops No particular correlation between the energy and geometrical sizes of loops but a relative good agreement between energy and 1/n FIKUT , Budapest Sampling the magnetic field (tangential) Magnetic map of the quiet Sun Magnetic tomography of the quiet Sun (Ballai 2007) FIKUT , Budapest Conclusions Waves are very good candidates for sampling the corona EIT waves relate flare/CMEs to oscillations in coronal loops, they are very useful tools to diagnose the magnetic field on a larger scale After all, the magnitude of the magnetic field is not the most important factor, instead the of structure (sub-structure) of the magnetic field could be more interesting and important The structure and dynamics of the solar atmosphere is directly related to the presence of magnetic fields Flux tubes in the magnetic network play an important role in heating the upper atmosphere. Their footpoints located in the subphotosphere, are constantly shaken by stochastic convective motions due to which MHD oscillations are excited. Dynamics should be understood in a very global way