# Presentation: 192706

## Forward-Modeling

- _for 3D Reconstruction_
- _from STEREO Observations_

- Markus J. Aschwanden
-     & LMSAL team

- FIRST STEREO WORKSHOP, Carre de Sciences, March 18-20, 2002, Paris, France

## Observations with TRACE, 171 A: Filaments, Loops, Flares

## Scientific Problems 

- _for Forward-Fitting to STEREO Data :_

- *    3D Geometry  [x(s),y(s),z(s)]
-       of  coronal coronal structures, such as
-       filaments, loops, arcades, flares, CMEs, ...

- *    4D Modeling  EM(x,y,z,t)
-       of temporal evolution of coronal structures

- *   5D Modeling  dEM/dT(x,y,z,t,T)
-      of differential emission measure of coronal structures

## *    3D Geometry  [x(s),y(s),z(s)] 

-       of  coronal coronal structures, such as
-       filaments, loops, arcades, flares, CMEs, ...

- - Geometric definitions :
-   1-dim parametrization along magnetic field lines
-   is in low-beta plasma justified  -->  [x(s),y(s),z(s)]
- - Cross-sectionial variation for loops, --> A(s)
- - Start with tracing in 2D in first STEREO image --> [x(s),y(s)]
- - Model for 3D inflation  z(s),
-   e.g. semi-circular loops with vertical stretching factor
-   z(s)=sqrt[(x(s)^2 + y(s)^2]*q_stretch
- - Forward-fitting to second STEREO image to determine q_stretch

## Flare  2000-Nov-8

*Flare  2000-Nov-8*

*TRACE  171 A*
*2000-Nov-9, 00:05 UT*
*Flare start: Nov 8, 22:42 UT*
*GOES class: M7.4*
*NOAA AR 9213*
*Associated with CME*

## ANIMATION :  2D projections for varying stereo angle

## STEREO - A

- STEREO - B

## Energetics and Flare Plasma Cooling from 30 MK

- down to 1 MK modeled from Yohkoh, GOES, and
- TRACE Observations during the Bastille-Day Event
- 			(14 July 2000)

- Aschwanden M.J. & Alexander,D. 2001, Solar Physics (Dec. issue) Vol.204, p.91-129

- The following 5D model  dEM/dT(x,y,z,t,T) is constrained by data
- analyzed in the publication:

## TRACE, 171 A, 2000-Jul-14, 10:59:32 UT

*TRACE, 171 A, 2000-Jul-14, 10:59:32 UT*

*Highpass-filtered image *

## TRACE, 171 A, 2000-Jul-14, 10:11-10:59 UT, cadence=42 s

*Highpass-filtered movie  *

## The separation of arcade loops is observed 

*Highpass-filtered image, TRACE, 171 A, 2000-Jul-14, 10:59:32 UT *

*Number of postflare loop structures :   N ~ 100*
*Length of arcade :                                 L ~ 180,000 km*
*Average loop separation:                      L/N=1800 km*
*Minimum loop separation (3 pixels) :   ****L=1100 km*

*The separation of arcade loops is observed *
*down to the instrumental resolution !*

## Tracing linear features :

- _--> [x(s),y(s)]_

- High-pass
- filtering

-  Feature tracing,
-  reading coordinates,
-  spline interpolation

## This sequence has time intervals of

- ~10 minutes, which equals about
- the cooling time of each loop
- Thus each frame shows a new set
- of loops, while the old ones cooled
- down and become invisible in next
- frame.

## Temporal evolution

- of EUV-bright flare loops

## In this time sequence, postflare loops

- are illuminated progressively with higher
- altitudes, outlining the full 3D structure

## Tracing ... progressing in time

## Slide 17

## Coordinates or linear structures:  s(x,y,z=0)

## s(x,y)

- _Step 3:_
- _3D Inflation:_  z=0 -> z(x,y)
- - model (e.g. semi-circular loops)
- - magnetic field extrapolation
- - curvature minimization in 3D

- s(x,y,z)

## Slide 20

## Slide 21

## Slide 22

## Slide 23

## Slide 24

## *    3D Fitting:  F[x(s),y(s),z(s)] 

-       Volume rendering of  coronal structures

- - Flux fitting in STEREO image  :

- - Volume filling of flux tube with sub-pixel sampling
- - Render cross-sections by superposition of loop fibers with sub-pixel
-   cross-sections: A=Sum(A_fiber), with w_fiber<pixel
- - Loop length parametrization with sub-pixel steps ds<pixel
- - Flux per pixel sampled from sub-pixel voxels of loop fibers

## Volume rendering of a loop with sub-pixel fibers:

-  sub-pixel element of loop fiber

- Pixel size

## Voluminous structures

- are rendered by
- superposition of
- linear segments
- _Physical principle_:
- optically thin emission
- in EUV and soft X-rays
- is additive

## Forward-Fitting of Arcade Model with 200 Dynamic Loops

- Observations from TRACE 171 A : Bastille-Day flare  2000-July-14

## *    4D Fitting:  F[x(s),y(s),z(s),t] 

-       of  coronal coronal structures

- - Flux fitting in STEREO image #1 at time  t1 :

- - Flux fitting in STEREO image #2 at time t1
- - Sequential fitting of images #1,2 at times  t = t2, t3, .... , tn

## Forward-Fitting of Arcade Model with 200 Dynamic Loops

- Observations from TRACE 171 A : Bastille-Day Flare  2000-July-14

## *    4D Fitting:  F[x(s,t),y(s,t),z(s,t)] 

-       with dynamic model

- Observations that can constrain dynamic models:
-  - loop shear increase
-  - twisting of flux rope
-  - filament eruption
-  - loop expansion
-  - height increase of reconnection X-point
-  - loop relaxation from cusp-shaped loop
-    into dipolar loop after reconnection

## Evolution from high-sheared (blue) to unsheared (yellow) arcade loops 

- Evolution from high-sheared (blue) to unsheared (yellow) arcade loops

## Spatial Mapping of Magnetic Islands to Arcade Loops

*Spatial Mapping of Magnetic Islands to Arcade Loops*

*Each arcade loop is interpreted as a magnetic field line connected with a magnetic island*
*generated in the (intermittent)“bursty regime” of the tearing mode instability. *

- Time

## X-type (Petschek) magnetic reconnection :

- Reconnection X-point

- Acceleration region
-   in cusp

- SXR-bright
- post-flare loop

- N_loop = 100
- E_loop = 5 * 10^29 erg
- R_loop = 17.5 Mm
- n_cusp = 10^9 cm-3
- B_cusp = 30 G
- h_cusp = 17.5 Mm
- V_cusp = 1.5 * 10^26 cm^3
- E_HXR = 25 keV = 4*10^-8 erg

- - Alfvenic outflow speed in cusp  v_A= 2.2 * 10^11  B/sqrt(n) = 2000 km/s
- - Replenishment time of cusp    t_cusp=h_cusp/v_A = 8 s

- Lateral
- inflow

- Reconnection
- outflow v_A

## Eruptive Flare Model

*Eruptive Flare Model*
*(Moore et al. 2000, ApJ)*

*- Initial bipoles with sigmoidally sheared*
*  **and twisted core fields*
*- accomodates confined as well as*
*  **eruptive explosion*
*- Ejective eruption is unleashed by internal*
*  **tether-cutting reconnection*
*- Arcade of postflare loops is formed*
*  **after eruption of the filament and*
*  **magnetic reconnection underneath*

## *    4D Fitting:  F[x(s,t),y(s,t),z(s,t)] 

-       with dynamic model

- Example:
-  - relaxation of cusp-shaped loop after reconnection into dipolar loop
- 	z(s,t) = sqrt[ x(s)^2 + y(s)^2 ] * (h_cusp-r_loop) * exp(-t/t_relax)
-                t_relax = v_A(B,n) / [h_cusp- r_loop]
-  - could constrain cusp height  h_cusp  and magnetic field from v_A(B,n)

## Dynamic Model of Arcade with 200 Reconnecting Loops

- Top
- View

- Side
- View

## Dynamic Model of Arcade with 200 Reconnecting Loops 

- Dynamic Model of Arcade with 200 Reconnecting Loops

- Top
- View

- Side
- View

## *    5D Model:   DEM [x(s),y(s),z(s),T(s),t] 

-       with dynamic physical model

- Ingredients for flare loop model :
- - 3D Geometry  [x(s), y(s), z(s)]
- - Dynamic evolution  [x(s), y(s), z(s), t]
- - Heating function  E_heat(s)
- - Thermal conduction  -F_cond(s)
- - Radiative loss  E_rad(s) = -n_e(s)^2  [T(s)]
- ->  Differential emission measure distribution  dEM(T,t)/dT
- ->  Line-of-sight integration   EM(T)= n_e(z,T,t)^2 dz (STEREO angle)
- ->  Instrumental response function  R(T)
- ->  Observed flux  F(x,y,t)=  EM(T,t) * R(T) dT
- ->  Flux fitting of 5D-model onto 3D flux F(x,y,t)
-       for two stereo angles (4D) and multiple temperature filters (5D)

## Step 4: Use physical hydrostatic

- _Step 4_: Use physical hydrostatic
- models of temperature T(s),
- density n(s), and pressure  p(s),
- to fill geometric structures
- with plasma

## Observed dynamic loops

- The same loops
- how they would look like
- in hydrostatic equilibrium

## GOES light curves in 1-8 A and 0.5-4 A channel 

- GOES light curves in 1-8 A and 0.5-4 A channel

## Double-Ribbon Hard X-Ray Emission 

- Yohkoh SXT: A difference image showing (bright) the extended arcade as seen in soft X-rays. This is a top-down view, so that the basically circular loops that form the cylinder look more or less like straight lines, some tilted (sheared) relative to others. The
- dark S-shaped feature is the pre-flare sigmoid structure that disappeared as the flare developed.

- Yohkoh HXT and SXT overlay: The SXT image is taken on 2000-Jul-14
- at 10:20:41 UT: The HXT image is in the high-energy band, 53-93 keV,
- integrated during 10:19:40-10:20:50 UT. The HXT shows clearly two
- ribbons ar the footpoints of the arcade lined out in soft X-rays. This is the
- first detection of hard X-ray double ribbons (see AGU poster by Masuda).
- [Courtesy of Nariaki Nitta].

- Courtesy of Hugh Hudson,
- Yohkoh Science Nuggets, Sept 15, 2000

## - Hard X-ray emission observed

-   with Yohkoh HXT, 14-93 keV
- - Hard X-ray time profiles consist
-   of thermal emission (dominant
-   in 14-23 keV, Lo channel), which
-   mimics a lower envelope in higher
-   channels
- - Nonthermal HXR emission is
-   dominant at >23 keV energies,
-   manifested by rapidly-varying
-   spiky components
- - High-energy channels (33-93 keV)
-   are delayed by 2-4 s with respect
-   to low-energy channel (23-33 keV)
-   probably due to partial electron
-   trapping

## - Thermal emission is centered at top of arcade on HXT:Lo channel

- - Nonthermal HXR emission is concentrated at footpoints of arcade

## Yohkoh SXT Al12 and Be light curves

- of total emission from flare arcade (within the partial frame FOV)

## TRACE Observations: 2000-July-14, 10:03 UT,   (UV=red, 171 A=blue, 195 A=green)

## TRACE 171 A, 195 A,

- and 284 A light curves
- of total EUV emission
- from flare arcade

## - Composite of HXR, SXR,

-   and EUV light curves
- - HXT 14-23 keV peaks first
- - GOES peaks second
- - SXT peaks third
- - TRACE peaks last
- - Time delays are consistent
-   with flare plasma cooling
-   from high (30 MK) to
-   low (1 MK) temperatures
-   within ~ 10 minutes.

## - The observed peak

-   fluxes in all instruments
-   (TRACE, SXT, GOES,
-   HXT) constrain the
-   differential emission
-   measure distribution
-   dEM(T)/dT of the
-   flare plasma

## - The peak delays constrain a cooling time of  t_cool ~ 400 s (~7 min)

- - Evolution with initial conductive cooling (<1 min) and then radiative cooling (>1 min)
- - The DEM(T) distribution and cooling curve T(t) can be converted
-   into evolution of emission measure  EM(t) and density  n_e(t)

## A) Conductive cooling phase

- B) Radiative cooling phase

## Step 6: Integration along line-of-sight

-             and convolution with instrumental response function

## Dynamic Model of Arcade with 200 Reconnecting Loops

- Top
- View

- Side
- View

## Dynamic Model of Arcade with 200 Reconnecting Loops 

- Dynamic Model of Arcade with 200 Reconnecting Loops

- Top
- View

- Side
- View

## CONCLUSIONS  :

- _Forward modeling for STEREO data at 3 levels of sophistication:_
- 	- 3D geometry [x(s), y(s), z(s)]
- 	- 4D dynamics [x(s), y(s), z(s), t]
- 	- 5D temperature evolution  DEM[x(s),y(s),z(s),T(s),t]

- _What STEREO can provide uniquely :_
-      - 3D geometry of sheared, twisted loops
-      - non-potentiality of magnetic field lines
-      - geometry of current-carrying loops --> currents
-      - 4D reconstruction of loop dynamics
-      - true (unprojected) speeds, acceleration, and deceleration
-      - dynamic forces with 3 vector components
-      - motion of reconnection points, Alfven speed, B-field
-      - 5D models: localization of heating sources
-      - temperature gradients, thermal flows, thermal conduction
-      - unambiguous reconstruction of differential emission distribution
-        along two different line-of-sights

##  http://secchi.lmsal.com/Science/

- - The LMSAL group produces a package of EUVI stereo pair images :
- 	- containing different phenomena (flare, CMEs, filaments)
- 	- in different wavelengths (171, 195, 284, 211 A)
- 	- from different stereo angles (0, 5, 10, 30, 60, 90 deg)
- 	- based on self-consistent hydrostatic/dynamic  models
- 	- FITS format with header info on spacecraft stereo angle
-    to be distributed to STEREO team members.

- _LMSAL STEREO Science website : _

-  http://secchi.lmsal.com/Science/

- * Simulations of STEREO data
- * STEREO software development in IDL/SSW
- * powerpoint and html presentations
- * bibliography on 3D geometry, stereoscopy, tomography