Connections from Corona to Geospace Markus Aschwanden et al. Lockheed Martin Solar & Astrophysics Laboratory AIA/HMI Workshop, Monterey Feb 13-17, 2006 Session C7/M5: Connections to Geospace 1. Modeling the Solar Corona Schrijver, Sandman, Aschwanden, & DeRosa (2004)

A full-scale 3D model of the solar corona: (Schrijver et al. 2004) -3D magnetic field model (using Potential source surface model) computed from synoptic (full-Sun) photospheric magnetogram10^5 loop structures -Coronal heating function E_H(x,y,z=0)~B(x,y)^a*L(x,y)^b a~1, b~-1 -Hydrostatic loop solutions E_H(s)-E_rad(s)-E_cond(s)=0

yield density n_e(s) and T_e(s) profiles -Line-of-sight integration yields DEM for every image pixel dEM(T,x,y)/ds = Int[ n_e^2(x,y,z,T[x,y,z])] dz -Free parameters can be varied until synthetic image matches observed ones in each temperature filter -STEREO will provide double constraint with two independent line-of-sights. Heating in Open Corona -Temperature anisotropies of H, OV, (UVCS results)

gyroresonant heating -Line broadening (h)~v_A(h) (Doyle et al., Erdelyi et al.) dissipation of high-frequency Alfven waves at 1-2 R_Sun Heating in Closed Corona -Energy balance E_H-E_rad-E_cond=0 heating required at footpoints E_H(h<20 Mm) -Scaling law of loop width w(T)~T^2 (Aschwanden et al.)

heating in TR (plasma >1) thermal conduction w(T)~T^7/4 Hydrostatic/hydrodynamic modeling of coronal loops requires careful disentangling of neighbored loops, background modeling, multi-component modeling, and multi-filter temperature modeling. Accurate modeling requires the identification of elementary loops. Elementary vs. Composite loops: Each loop strand represents an isolated mini-atmosphere

and has its own hydrodynamic structure T(s), n_e(s), which needs to be extracted by subtracting it from the background coronal structures. SECCHI/EUVI (1.6 pixels) will be able to resolve some individual loops, substantially better than CDS (4 pixels), but somewhat less than TRACE (0.5 pixels). Loops 1 10 30

1 41 234 Widths Loop/Backgr. Instrument Ref. ~12 Mm

? CDS Schmelz et al. (2001) ? 170%150% EIT Schmelz et al. (2003) 7.10.8 Mm 30%20% EIT Aschwanden et al. (1999) ~5.8 Mm 76%34% TRACE/CDS DelZanna & Mason (2003) 3.71.5 Mm ?

TRACE Aschwanden et al. (2000) (no highpass filter) 1.40.2 Mm 8%3% TRACE Aschwanden & Nightingale 2005 (with highpass filter) Elementary Loop Strands The latest TRACE study has shown the existence of elementary loop strands with isothermal cross-sections, at FWHM widths of

<2000 km. TRACE has a pixel size of 0.5 and a point-spread function of 1.25 (900 km) and is able to resolve them, while EUVI (1.6 pixels, PSF~3.2=2300 km) will marginally resolve the largest ones. Triple-filter analysis (171, 195, 284) is a necessity to identify these elementary loop strands. Aschwanden & Nightingale (2005), ApJ 633 (Nov issue) TRACE triple-filter analysis of elementary loop strands (1) The distribution of loop widths N(w), [corrected for point-spread function]

in the CELTIC model is consistent with a semi-Gaussian distribution with a Gaussian width of w_g=0.50 Mm which corresponds to an average FWHM =w_g * 2.35/sqrt(2)=830 km which points to heating process of fluxtubes separated by a granulation size. (Aschwanden & Nightingale 2005) Scaling law of width with temperature

in elementary loop strands Observational result from TRACE Triple-filter data analysis of elementary loop strands (with isothermal cross-sections): w(T ) T 1.97 Loop widths cannot adjust to temperature in corona because plasma- << 1, and thus cross-section w is formed in TR at >1

Thermal conduction across loop widths In TR predicts scaling law: T 7 / 2 T 7 / 2 E H Fc 2 s s L w(T ) T

7/4 T 1.75 2. Modeling the Solar Wind PFSS-models (Potential Field Source Surface) are used to compute full-Sun 3D magnetic field (current-free xB=0)

Open fields occur not only in coronal holes, but also in active regions escape paths of energized particles into interplanetary space Schrijver & DeRosa (2003) Schrijver & DeRosa (2003) find that ~20%-50% (solar min/max) of interplanetary field lines map back to active regions.

SAIC Magnetohydrodymanics Around a Sphere (MAS)-code models magnetic field B(x,y,z) solar wind speeds v(x,y,z) in range of 1-30 solar radii from synoptic magnetogram Model computes stationary solution of resistive MHD Equations n_e, T_e, p, B MAS model simulates coronal streamers (Linker, vanHoven, Schnack1990)

Line-of-sight integration yields white-light images for SECCHI/ COR and HI SAIC/MAS-IP code combines corona (1-30 solar radii) and Inner heliosphere (30 Rs -5 AU) Model reproduces heliospheric current sheet, speeds of fast & slow solar wind, and interplanetary magnetic field NOAA/ENLIL code (Odstrcil et

Al. 2002) is time-dependent 3D MHD code (flux-corrected transport algorithm): inner boundary is sonic point (21.5-30 Rs from WSA code, outer boundary is 1-10 AU. SMEI heliospheric tomography model uses interplanetary scintillation (IPS) data for reconstruction of solar wind (Jackson & Hick 2002)

Exospheric solar wind model computes proton and electron Densities in coronal holes In range of 2-30 Rs (Lamy et al. 2003) Univ.Michigan solar wind code models solar wind with a sum of potential and nonpotential Magnetic field components (Roussev et al. 2003) 3. Modeling of Erupting Filaments

Roussev et al. (2003) Pre-eruption conditions of filaments Envold (2001) Aulanier & Schmieder (2002) -Geometry and multi-threat structure of filaments (helicity, chirality, handedness conservation, fluxropes) -Spatio-temporal evolution and hydrodynamic balance

-Stability conditions for quiescent filaments -Hydrodynamic instability and magnetic instability of erupting filaments leading to flares and CMEs Measuring the twist of magnetic field lines Aschwanden (2004) Measuring the number of turns in twisted loops Testing the kink-instability criterion for stable/erupting loops Monitoring the evolution of magnetic relaxation (untwisting) between preflare and postflare loops

Measuring the twist of magnetic field lines Aschwanden (2004) -Measuring number of turns in (twisted) sigmoids before and after eruption -Test of kink-instability criterion as trigger of flares/CMEs Measuring the twist of erupting fluxropes Gary & Moore (2004)

-Measuring number of turns in erupting fluxropes -Test of kink-instability criterion as trigger of flares/CMEs Triggers for of filaments or Magnetic flux ropes: -draining of prominence material bouancy force (Gibson & Low 1998) (Manchester et al. 2004) -current increase and loss of equilibrium

(Titov & Demoulin 1999) (Roussev, Sokolov, & Forbes) (Roussev et al. 2003) -kink instability unstable if twist > 3.5 (Toeroek & Kliem 2003, Toeroek, KIiem, & Titov 2003) Roussev et al. (2004) MHD simulations of coronal dimming: -evacuation of plasma beneath CME, fast-mode MHD wave

(Wang 2000; Chen et al. 2002; Wu et al. 2001) 5. Modeling of Coronal Mass Ejections (CMEs) pB MAS/ENLIL code streamer, eruption and evolution of CME (Mikic & Linker 1994; Lionello et al. 1998; Mikic et al. 1999) Linker et al. 1999) BATS`RUS-code (ideal MHD code)

Simulates launch of CME by loss of equilibrium of fluxrope (Roussev et al. 2004; Lugaz, Manchester & Gombosi 2005) ENLIL+MAS code: simulates propagation of CME in solar wind, produces accurate shock strenghts, arrival of shocks at 1 AU (Odstrcil et al. 1996, 2002 2004, 2005; Odstrcil & Pizzo 1999) Observation of CME Structure with LASCO/SoHO 6. Modeling of Interplanetary Shocks Odstrcil & Pizzo (1999)

Fast CMEs have speeds of v>2000 km/s formation of fast-mode shock Numerical MHD simulations: - Mikic & Linker (1994) - Odstrcil & Pizzo (1999) - Odstrcil, Pizzo, & Arge (2005) Predicted arrival time at 1 AU depends critically on models of background solar wind which controls shock propagation speed - Odstrcil, Pizzo & Arge (2005)

Odstrcil & Pizzo (1999) CME cannibalism (faster overtakes slower one) compound streams, interactions with CIR (corotating interaction regions) control shock-accelerated particles (SEPs) 7. Modeling of Interplanetary Particle Beams and Radio Emission

Interplanetary radio emission (see also talk by J-L. Bougeret) -electron beams type III -shock waves type II IP space is collisionless -propagation of suprathermal electron and ion beams velocity dispersion bump-in-tail instability Langmuir wave growth at fundamental + harmonic plasma frequency (f_p~n_e^1/2)

Pocquerusse et al. (1996) stochastic growth theory Robinson & Cairns (1998) Type II bursts do not outline entire shock front, but occur only where shock wave intersects preexisting structures Reiner & Kaiser (1999) Interplanetary type II bursts were

All found to be associated with fast CMEs, with shock transit Speeds v>500 km/s Cane, Sheeley, & Howard (1987) Semi-quantitative theory of type II bursts includes magnetic mirror reflection and acceleration of upstream electrons incident on shock (Knock & Cairns 2005) In-situ particle + remote sensing (IMPACT + SWAVES)

(courtesy of Mike Reiner) 8. Modeling of Solar Energetic Particles (SEPs) (see also talks by J.Luhmann and R.Mewaldt) -Two-point in-situ measurements acceleration of flare particles (A) versus acceleration in CME-driven shocks (B) -Efficiency of quasi-parallel vs. quasi-perpendicular shock acc. -Time-of-flight measurements at two spacecraft and Earth localization of acceleration sources (flare, CME, CIR, CME front, preceding shock, CME flank, etc.)

-Quadrature observations shock profile (A) and in-situ (B) Theoretical modeling of SEPs: Diffusive shock acceleration, proton-excited Alfvenic waves upstream of shock, escape of particles upstream of the shock by magnetic focusing (Marti Lee, 2005) (Chee Ng & Don Reames)

SEP propagation over several AU, fast acceleration by coronal shock, co-evolution of Alfven waves in inhomogeneous IP, focusing, convection, adiabatic deceleration, scattering by Alfven waves SEP fluxes and spectra Modeling for STEREO/IMPACT Tylka, Reames, & Ng (1999) 9. Modeling of Geo-effective events

and Space Weather -Arrival time of shocks at Earth will be improved by 3D triangulation of CME propagation with two spacecraft (STEREO 3D v-vector and r-vector reconstruction vs. LASCO CME speed (lower limit) projected in plane of sky -End-to-end models attempted including MHD of lower corona, heliosphere, and magnetosphere + SEP accel. & propagation - CCMC (Community Coordinated Modelin Center, GSFC) - CISM (Center for Integrated Space Weather Modeling, UCB) - CSEM (Center for Space Environment Modeling, UMich) - Solar/Muri (Solar Multidisciplinary Univ. Research Initiative)

CONCLUSIONS -The long-term goal is to create end-to-end models that connect the origin and evolution of phenomena from the corona, through heliosphere, to geospace. Modeling includes background plasma in corona, heliosphere, and solar wind, dynamic phenomena associated with initiation of CMEs in lower corona (filament dynamics, shearing, kinking, loss-of-equilibrium, filament eruption, magnetic reconnection in coronal flare sites), and propagation and evolution of CMEs in interplanetary space (interplanetary shocks, IP particle beams, SEP

acceleration and propagation, geoeffective events, space weather).