# Presentation: 247782

##    Theoretical Modeling

- _for the STEREO Mission_

-        Markus Aschwanden et al.
-  Lockheed Martin Solar & Astrophysics Laboratory

- Solar-B/STEREO Workshop, Turtle Bay Resort, Oahu, Hawaii – Nov 15-18, 2005

- Ref.: Aschwanden et al. (2005), Space Science Rev., (subm.)
-          http://www.lmsal.com/~aschwand/publications/eprints/2005_stereobook.pdf

## et al.:

- GSFC: L.F.Burlaga, M.L.Kaiser, C.K.Ng, D.V.Reames, M.J. Reiner
- Univ.Michigan: T.I.Gombosi, N.Lugaz, W.IV.Ward Manchester, II.Roussev, T..H.Zurbuchen
- Univ.New Hampshire: C.J.Farrugia, A.Galvin, M.A.Lee
- SAIC: J.A.Linker, Z.Mikic, P.Riley
- Rice Univ: D.Alexander, A.W.Sandman
- NRL: J.W.Cook, R.A.Howard
- NOAA/SEC: D.Odstrcil, V.Pizzo
- JPL: P.C.Liewer, E.DeJong
- UCB: J. Luhmann
- MPIS: B.Inhester, R.W.Schwenn, S.Solanki, V.M.Vasyliunas, T.Wiegelmann
- Univ.Bern: L.Blush, P.Bochsler
- Univ.Sydney: I.H.Cairns, P.A.Robinson
- Univ.Goettingen: V.Bothmer
- KFIK RMKI, Budapest, Hungary: K.Kecskemety
- Univ.Arizona: J.Kota
- CNRS: A. Llebaria
- CNRS, LESIA: Maksimovic
- MPES: M.Scholer
- Univ. Kiel: R.Wimmer-Schweingruber

## Phenomena vs. STEREO Detection

- _Phenomena vs. STEREO Detection_

## 1. Modeling the Solar Corona

- _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 magnetogram10^5 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.

- 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.

## Inversion of coronal density with coarse

- _Inversion of coronal density_ with coarse
- Resolution (~15 heliographic deg):
- _White light inversion_ (Thomson scattering)
-           Van de Hulst (1950)
-           Lamy et al. (1997)
-           Llebaria et al. (1999)
- -_Soft X-ray tomography_
-           Hurlburt et al. (1994)
-           Davila (1994)
-           Zidowitz (1997)
- _Numerical MHD simulations (~1” pixels):_
-           Gudiksen & Nordlund (2002, 2005)
-           Mok et al. (2005)

## Stereoscopic reconstruction

- _Stereoscopic reconstruction_
- _of coronal loops, 3D-geometry_:
-     -Loughhead, Wang & Blows (1983)
-     -Berton & Sakurai (1985)
- _Tie-point method:_
-     -Liewer et al. (2000)
-     -Hall et al. (2004)
- _Solar-rotation stereoscopy_:
-     -Koutchmy & Molodensky (1992)
-     -Vedenov et al. (2000)
- _Dynamic stereoscopy:_
-     -Aschwanden et al. (1999, 2000)
- _Magnetic field-aided reconstruction_:
-     -Gary & Alexander (1999)
-     -Wiegelmann & Neukirch (2002)
-     -Wiegelmann & Inhester (2003)
-     -Wiegelmann et al. (2005)

- 3D-reconstruction of coronal loop structures to test
- theoretical models of magnetic field extrapolations.

## Fingerprinting (automated detection) of curvi-linear structures

- Lee, Newman, & Gary (2004), 17th Internat. Conf. On Pattern Recognition, Cambridge UK, 23-26 Aug 2004

- Lee, Newman & Gary
- improve detection of
- coronal loops with
- “Oriented connectivity
- Method” (OCM):
- median filtering
- contrast enhancement
- unsharp mask
- detection threshold
- directional connectivity

##  Elementary vs. Composite 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).

##   1               ~12 Mm                  ?             CDS              Schmelz et al. (2001)

- Loops         Widths                Loop/Backgr.  Instrument                  Ref.

-   1               ~12 Mm                  ?             CDS              Schmelz et al. (2001)
-                 ?                 170%150%   EIT                Schmelz et al. (2003)
-              7.10.8 Mm     30%20%     EIT                Aschwanden et al. (1999)
-   1               ~5.8 Mm           76%34%    TRACE/CDS DelZanna & Mason (2003)
-              3.71.5 Mm           ?             TRACE         Aschwanden et al. (2000)
-                                                                                            (no highpass filter)
-             1.40.2 Mm         8%3%      TRACE          Aschwanden & Nightingale
-                                                                                            2005 (with highpass filter)

## Slide 13

## Model:

- _Model:_

- _Forward-_
- _Fitting_
- to 3 filters
- varying T

## 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)

## The advantage of STEREO is that a loop can be mapped

- from two different directions, which allows for two
- independent background subtractions. This provides an
- important consistency test of the loop identity and
- the accuracy of the background flux subtraction.

- A

- B

- F

- a

- F

- b

- x

- x

- Consistency check: Is F_a = F_b ?

## 2. Modeling the Solar Wind

- _2. Modeling the Solar Wind_

## PFSS-models (Potential Field

- Schrijver & DeRosa (2003)

- 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) 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

- _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

- _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

- _3. Modeling of Erupting Filaments_

- Roussev et al. (2003)

## Pre-eruption conditions of filaments

_**Pre-eruption conditions of filaments**_

- 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

- Envold (2001)

- Aulanier & Schmieder (2002)

## Measuring the twist of magnetic field lines

_**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

_**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

_**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:

- _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)

- _5. Modeling of Coronal Mass Ejections (CMEs)_

- MAS/ENLIL code  streamer, eruption and evolution of CME
- (Mikic & Linker 1994; Lionello et al. 1998; Mikic et al. 1999)
- Linker et al. 1999)

- pB

- 

## BATS`R’US-code (ideal MHD code) 

- _BATS`R’US-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,

- _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 

## 3D Reconstruction from 2 STEREO images

- (either from EUVI or white-light coronagraphs)

- Sun

- CME

- 3D Reconstruction
- Volume

- x

- x

- y

- z

- (0,0,0)

- x-y plane coplanar
- with STEREO
- spacecraft A and B

## Slices with independent 2D reconstructions :

- - Adjacent solutions can be used as additional constraints

## STEREO-A

- STEREO-B

- _2D Slices of reconstruction from 2 views_

## Is 2D reconstruction from two projections unique ?

- x

- y

- u

- v

- Coordinate rotation  (x,y)  (u,v) :

- (STEREO-A)

- (STEREO-B)

- INVERSION

## Slide 39

## 6. Modeling of Interplanetary Shocks

- _6. Modeling of Interplanetary Shocks_

- Odstrcil & Pizzo (1999)

## Fast CMEs have speeds of v>2000 km/s

- Odstrcil & Pizzo (1999)

- 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)
- 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

- _7. Modeling of Interplanetary Particle Beams_
- _    __and Radio Emission_

## Interplanetary radio emission

- Pocquerusse et al. (1996)

- _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)
- 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)

## (courtesy of Mike Reiner)

- In-situ particle + remote sensing (IMPACT + SWAVES)

## 8. Modeling of Solar Energetic Particles (SEPs)

- _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

- -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:

- (Chee Ng & Don Reames)

- _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)
- 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

- _CONCLUSIONS_

- Theory and modeling efforts for the STEREO mission is
-  designed for data data analysis of both remote-sensing
-  (SECCHI, SWAVES) and in-situ instruments (IMPACT,
-  PLASTIC).
- -Modeling includes background plasma in corona,
-  heliosphere, and solar wind, but concentrates on
-  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), attempting end-to-end models from
-  corona, trhough heliosphere, to magnetosphere).