# Presentation: 550634

## test data for future 3D STEREO reconstruction methods.

**observed by SOHO/MDI, as a representation of a real active region, we**
**apply hydrostatic and hydrodynamic coronal loop models to the derived**
**magnetic structures and generate realistic distributions of temperature**
**and density throughout the simulated corona. These distributions are**
**then folded through the EUVI instrument responses and projected onto the plane of the sky to yield simulated EUVI images. The simulated images**
**will also incorporate the EUVI point-spread-function, EUVI pixel size,**
**background emission and noise. These simulations can provide a set of**
**test data for future 3D STEREO reconstruction methods**.

**SIMULATING SECCHI/EUVI OBSERVATIONS OF **
**ACTIVE REGION CORONAE**** **

**David Alexander, James R. Lemen, Jean-Pierre Wuelser, **
**Markus J. Aschwanden and Marc DeRosa **
**Lockheed Martin Solar and Astrophysics Laboratory**

## Introduction

**To simulate the expected observations of the SECCHI/EUVI we have utilized an approach which provides a realistic set of temperature and density distributions throughout an active region.  These simulations are based upon a combination of real data (****magnetograms****), observational results from SOHO/EIT, TRACE and Yohkoh  (****heating rates and heating scale heights****), representations of the coronal field (****potential field extrapolations****),  calculation of temperature and density distributions (****hydrostatic loop models****), expected EUVI characteristics (****pixel size, PSF, temperature response****), and 3D simulation (****volume rendering****).**
**These simulated data provide an appropriate representation of the expected observations and as such provide a useful input to image reconstruction techniques currently being developed for the STEREO mission.**

## Generation of Active Region Field 

**We use a potential field, ********xB=0****, solving Laplace's Equation ********2********=0**** within the coronal volume, where ********=-B****.**

**In spherical polar coordinates,** ******2********=0**** is solved by**

**where the coefficients A****lm**** and B****lm**** are determined by the imposed boundary conditions in radius.  At r=R****sun****, we set **
**            ****the radial component of B  equal to the field **
**            ****observed in an MDI magnetogram M(********,********):**

**We also force the field to become radial at a spherical source surface:********=0**** at r=2.5R****sun****. Once ******** is known, B can then be calculated and the field lines can be traced through the volume using**

## Hydrostatic Solutions 

**The solutions used to determine the distributions of temperature and density along the extrapolated field lines satisfy the usual hydrostatic equations.**
**The heating rate is assumed to be of the form:**

**where E****h0**** is the base heating rate, s is **
**the loop coordinate, and s****h**** is the heating **
**scale height.**
**In what follows we will adopt different **
**forms for E****h0**** but s****h**** will be fixed at s****h**** =10 Mm.**

**Note that for loop lengths >3s****h**** the loop top temperatures are fixed by the base heating rate**

## Random vs. Uniform Heating 

**We apply two different assumptions about the spatial distribution of the heating function throughout the active region.  **
**The first is uniform heating where each field line “sees” the same base heating rate: ****E****h0****=5x10****-4**** ergs cm****-3**** s****-1****. This ensures maximum loop temperatures *****for all loops***** of around 1 MK.**

**To provide for a range of maximum loop temperatures we adopt a random distribution of heating rates with each field line being heated by a differently.  The figure to the left shows the distribution of heating rates.  We constrained the range to ****1x10****-5****<E****h0****<5x10****-2**** ergs cm****-3**** s****-1 **** which yields T****max****~0.5-2.5 MK for these hydrostatic solutions. **

## EUVI Response Function 

**In calculating the expected photon rates in our simulations we have adopted the the EUVI response shown below.  The photon rates here assume an emission measure of 10****44**** cm****-3****.**

## Noise and Background

**In addition to folding the temperature and density distributions through the instrument response, we have also incorporated the instrument pixel size and point spread function (PSF), and added a background signal and random noise.**

**Pixel Size:  ****1.7 arcsec**** ****	****PSF:  ****2D Gaussian with (********x********y********= 0.5 pixels**

**Background: **
**We define a background on macro-pixel scales, where a macro-pixel is 9x9 EUVI pixels (~15”x15”), and choose, for the examples presented here.   ****B(i,j)=b****0****I(i,j)**** where b****0****=10% and I(i,j) is the average emission in the macro-pixel.**

**Noise: ****Poisson noise acting on signal + background**

## 171A

**195A**

**284A**

**0**

**30**

**60**

**90**

**longitude**
**wavelength**

**DATA SET 1: Uniform Heating  - No Noise – No Background**

## 171A

**195A**

**284A**

**0**

**30**

**60**

**90**

**longitude**
**wavelength**

**DATA SET 2: Uniform Heating  - Noise + Background**

**Uniform heating rate optimized for 171A emission**
**resulting in very poor S/N in 284A channel**

## 171A

**171A**

**195A**

**284A**

**0**

**30**

**60**

**90**

**longitude**
**wavelength**

**DATA SET 3: Random Heating  - No Noise – No Background**

## 171A

**195A**

**284A**

**0**

**30**

**60**

**90**

**longitude**
**wavelength**

**DATA SET 4: Random Heating  - Noise + Background**

## Discussion

**The simulated SECCHI/EUVI images presented here provide a series of pre-launch test data suitable as input to the 3D reconstruction algorithms being developed for the STEREO mission.**
**To be effective we have to iterate these simulations with the reconstruction teams and develop a consistent set of test data which best represents the expected observations from the SECCHI EUVI. The data presented here provide a first step towards this.  However, a number of immediate improvements need to be made:**
** ****Simulated data needs to be converted to FITS formats with STEREO **
**   ****or SECCHI adopted headers.**
** ****Simulations in DN/s rather than photons/s.**
** ****More realistic modeling of the background should be performed.  Values **
**  ****consistent with observations should be used and an allowance for  center-  **
**  ****to-limb effects in the projected images should also be included.**
** ****Extension to hydrodynamic models and time variability will also provide **
**  ****more “realism”.**