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An Impulsive Heating Model

for the Evolution of Coronal Loops

Li Feng & Weiqun Gan

Purple Mountain Observatory

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BackgroundParker : nanoflare heating of the solar corona

Winebarger et al. (2003) : evidences of unsteady heating

Some relative works: Reale et al.(1994);

Betta et al. (1999);

Mendoza-Briceño et al. (2002, 2004, 2005)…

flux braiding

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◆ The hydrodynamic model

◆ Dynamic evolution of the coronal loop

Effects of different heating positions

Effects of different pulse numbers

Effects of different elapsed time

◆ Conclusions and discussion

Outline

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The Hydrodynamic Model

Basic Equations: 0

Vst

gVps

Vt

2

)(10 2||

2/56 TntsEVgTs

TpVUVst

U

，

Heating Function:

2

20

0 2

)(exp)(),(

sF

ssEtgEtsE

2/)2(

/)(

00

00

tttt

tttttg

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Initial and Boundary Conditions

Initial Conditions: T, ne, v=0 Symmetrical Loop Supposed

L=110Mm

Boundary Conditions:

Lower Boundary:

Chromosphere(T=104K)

Upper Boundary:

Temperature gradient is zero

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Some Notes:

Energy Deposition:

Background heating: E0=1.5*10-6 ergs cm-3 s-1 ，

Maximum amplitude of the heating: EF=1.0 ergs cm-3 s-1 ，

Spatial width of the heating: σs = 0.6Mm.

Keep the total heating input (about 1027 ergs) constant in all simulations.

Physical parameters (T, n, v) used to be analyzed :

NRL SOLFTM(Solar Flux Tube Model) to solve the three equations.

All the physical parameters are averaged over the coronal part of the loop.

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Dynamic Evolution 1.Effects of Different Heating Positions

Description of the Evolution

（ 1 ） Initial heating phase（ 2 ） conductive phase（ 3 ） radiative cooling phase（ 4 ） return to a new equilibrium

The conclusion of Winebarger(2003) ：An impulsive heating with different parameters (S0, EF, 2 δ) ;The differences cannot be shown in the radiative cooling phase;TRACE observations of cooling loops do not provide adequate information to discriminate different heating scenarios.

Our similar simulation gets the similar result: heating centered at s0=25Mm and s0=50Mm in the corona.

Single pulse (2δ=500s)

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Left: s0=25Mm(corona),s0=10Mm(chromosphere top);

TRACE observations are not entirely ineffective.

Right: s0=10Mm ： catastrophic cooling：

T: in 2000s,1 0.1MKne： a condensation forms and expands downwardsv： downflows maximum:110kms-1

Spadaro et al. ： maximum: 85kms-1.stronger transient heating, larger downflows.

Effects of Different Heating Positions

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Dynamic Evolution 2.Effects of Different Pulse Numbers

s0=25Mm, one, five, and ten pulses:

Maximum temperatures are almost the same;

Number of temperature peaks varies with the pulse number.

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Left ： so=25Mmno difference during the radiative cooling phase.

Right ： so=10Mm

The effects are shown almost the whole evolution.

Main roles:Weaken and delay the catastrophic cooling.

Effects of Different Pulse Numbers

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Dynamic Evolution 3. Effects of Different Elapsed Time

Left ： s0=25Mm ，

Delay the evolution;Decrease the maximum temperature

Right ： s0=10Mm ，

Catastrophic cooling disappears;A sudden temperature decrease in the initial few hundred seconds.

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According to Mendoza-Briceño et al.(2003, 2005):Increasing the elapsed time can increase the possibility of catastrophic cooling during the initial evolution.

Lowest temperature: 1.65*105K;

In this example, it doesn’t happen due to the background heating

Elapsed Time and Catastrophic Cooling

Five pulses, s0=10Mm ：

0s~200s, two pulses ； 1200s~1500s, three pulses.

Elapsed time： 1000s

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Conclusions and Discussion

► Contrary to the conclusion of Winebarger et al. TRACE can discriminate different heating senarios.

►When the heating is located in the corona, increasing the elapsed time will delay the evolution and decrease the maximum temperature.

►Increasing the pulse number and then the elapsed time, the catastrophic cooling weakens, delays and even disappears. So the more concentratively the heating deposits, the more possibly the catastrophic cooling happens.

►The response of the loop becomes more sensitive when the energy release is located below the transition region than in the corona. It is mainly due to the different conductive efficiency in the two regions.

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SXT and TRACE Loops

As an extended discussion: spatially random heating

33Mm~110Mm 0.8Mm~12Mm

TRACE loops do not always cool from SXT loops.

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The End