Solar Coronal Loop Workshop — Palermo 9/3/2004

Emission measure Emission measure distribution in loops distribution in loops

impulsively heated at impulsively heated at the footpointsthe footpoints

Paola Testa, Giovanni Peres, Fabio Paola Testa, Giovanni Peres, Fabio RealeReale

Universita’ di PalermoUniversita’ di PalermoSolar Coronal Loop Workshop — Palermo Solar Coronal Loop Workshop — Palermo

9/3/20049/3/2004

RationaleRationale

Solar Coronal Loop Workshop — Palermo Solar Coronal Loop Workshop — Palermo 9/3/20049/3/2004

GENERAL PROBLEMSGENERAL PROBLEMS

OBSERVATIONAL EVIDENCEOBSERVATIONAL EVIDENCE

CORONAL LOOPS MODELSCORONAL LOOPS MODELS::

standard hydrostatic models vs. standard hydrostatic models vs. observations observations

need for improved need for improved modelsmodels

hydrodynamic model with hydrodynamic model with footpoint footpoint heatingheating

GENERAL PROBLEMSGENERAL PROBLEMS:: spatial and thermal structuring, spatial and thermal structuring,

heating, heating, dynamic properties of dynamic properties of solar and stellar solar and stellar coronae coronae

DIAGNOSTIC TOOLSDIAGNOSTIC TOOLS::


SOLAR CORONASOLAR CORONA:: high spatial and temporal resolution, high spatial and temporal resolution,

spectral informationspectral information

STELLAR CORONAESTELLAR CORONAE:: X-ray spectral coverage with high X-ray spectral coverage with high

spectral spectral resolutionresolution

Coronal LoopsCoronal Loops Loops are basic Loops are basic components of components of the solar corona the solar corona


development of loop modelsdevelopment of loop models::

e.g. e.g. Rosner et al. 1978, Vesecky et al. Rosner et al. 1978, Vesecky et al. 1979, 1979, Serio et al. 1981Serio et al. 1981

TRACE 171TRACE 171ÅÅ

Yohkoh/SXTYohkoh/SXT



apparent disagreement mostly with apparent disagreement mostly with EUV EUV observations (TRACE, SoHO) observations (TRACE, SoHO) ::

e.g. e.g. Aschwanden et al. 2000,2001, Aschwanden et al. 2000,2001, Winebarger Winebarger et al. 2002, Warren et et al. 2002, Warren et al. 2003al. 2003

location of heating? location of heating? ::e.g. e.g. Priest et al. 2000, Aschwanden 2001, Priest et al. 2000, Aschwanden 2001,

Reale 2002Reale 2002



how are active stars how are active stars structured?structured?

can simple loop modelscan simple loop models explainexplain thethe

emission from active stars? emission from active stars? solar analogy for interpreting solar analogy for interpreting stellar coronaestellar coronae??

Coronal Loops in Stellar Coronae?Coronal Loops in Stellar Coronae?


Lack of spatial resolution Lack of spatial resolution we must we must resort to resort to indirect means for comparing indirect means for comparing properties of stellar properties of stellar coronal structures with coronal structures with

solar loopssolar loops

spectral observations spectral observations ::high resolution EUV (high resolution EUV (EUVEEUVE) and X-ray ) and X-ray

spectra spectra ((ChandraChandra, , XMM-NewtonXMM-Newton))

Emission Measure DistributionEmission Measure Distribution

EM(T) = T ne2(T) dV

Coronal Loops in Stellar Coronae?Coronal Loops in Stellar Coronae?


EM(T) expected for hydrostatic loop EM(T) expected for hydrostatic loop models models TT3/23/2 howeverhowever

EM(T) derived from observations are EM(T) derived from observations are steepersteeper and with and with bumpsbumps, i.e. large , i.e. large amounts of almost isothermal plasma amounts of almost isothermal plasma

Scelsi et al. (2004)

31 Com

e.g.e.g.EM(T) of EM(T) of 31Com 31Com from XMM from XMM spectra spectra

New Loop Models?New Loop Models?


can footpoint heating yield loops can footpoint heating yield loops with with characteristics compatible characteristics compatible with with observations?observations?

Problem:Problem: INSTABILITY (INSTABILITY (e.g.e.g. Serio et Serio et

al.1981al.1981))

dynamic loops since static dynamic loops since static solutions do not exist for heating solutions do not exist for heating concentrated at the footpointsconcentrated at the footpoints

how do EM(T) change with how do EM(T) change with characteristics characteristics of heating? of heating?

Loop ModelLoop Model


1-D hydrodynamic loop model symmetric equations solved for half loop uniform cross-section footpoint heated by periodic heat pulses Palermo-Harvard code (Peres et al.,1982; Betta et

al.,1997)

consistently solves the consistently solves the time-time-dependent density, momentum and dependent density, momentum and energy equationsenergy equations for the plasma for the plasma confined by the magnetic fieldconfined by the magnetic field



INITIAL CONDITIONS:INITIAL CONDITIONS:

solutions of hydrostatic loop modelsolutions of hydrostatic loop model (Serio et (Serio et al. 1981)al. 1981)

HEATING FUNCTION:HEATING FUNCTION:satisfy the scaling satisfy the scaling lawslaws p0 ~ (Tmax/1.4·103 )3·1/L

E0 ~ 105 p07/6·L-5/6

EH (s,t) = EH (s)·EH (t) EH (s) = H0·e-(s-s0)2/22

spatial distribution :spatial distribution :

temporal distribution : periodic temporal distribution : periodic pulses with pulses with duty cycle 10%duty cycle 10% intensity of heating scaled from the static intensity of heating scaled from the static modelmodel

= L/3, L/5, = L/3, L/5, L/10L/10

Set of simulationsSet of simulations

[MK] [dyn/cm2] [erg cm-3s-1] [s]

Tmax p0 E0 cool

Initial ConditionsInitial Conditions

0.4513 ~ 2200

303610 ~ 1200


Set of simulationsSet of simulations


Heat PulsesHeat Pulses

cool/4, cool /2E0,4E0L/3,L/5,L/10 10000

5000

H trun [s]

cool/4, cool /2E0,4E0L/3,L/5,L/10

Evolution of footpoint heated Evolution of footpoint heated loopsloopsConstant heatingConstant heating


Evolution of footpoint heated Evolution of footpoint heated loopsloopsImpulsive heatingImpulsive heating


Evolution of footpoint heated Evolution of footpoint heated loopsloops

TemperatureTemperature and and DensityDensity at loop at loop apexapex


Emission measure distributionEmission measure distribution


Emission measure Emission measure distributiondistribution::

models models vs. vs. observations observations


ConclusionsConclusions




adaptive grid initial model atmosphere uses Vernazza, Avrett and

Loeser (1980) to extend the S81 static model to chromospheric temperatures

effective plasma viscosity fractional ionization ne/nH

hydrogen ionization potential

Solar Coronal Loop Workshop — Palermo 9/3/2004

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