Determining the Heating Rate in Reconnection Formed Flare Loops

Wenjuan Liu1, Jiong Qiu1, Dana W. Longcope1, Amir Caspi2,

Courtney Peck2 , Jennifer O'Hara3

1.Department of Physics, Montana State University2.LASP, University of Colorado3.School of Mathematics and Statistics, University of St Andrews

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OutlineMotivation

How much energy is used to heat individual flare loops?

Methods (a few thousand loops) Constructing heating rate from UV light curves at foot points

Modeling plasma evolution in each flare Loop with EBTEL

Results synthetic soft X-ray and EUV emissions from the loops

synthetic UV emissions from the foot points during the decay phase

Discussions and Conclusions

The synthetic light curves and spectra agree well with the obs.

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Motivation-from reconnection to flare emission

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flare foot points and loops (observable)

Magnetic reconnection

energy release/transport (not known in details)

Link: heating rate in individual loops

Methods-constructing the heating rate

For each flare loop, the heating rate (H) is proportional to the impulsive rise of UV 1600 emission at its foot point

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cooling

heating

Methods-calculating plasma evolution

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EBTEL (Klimchuk 2008,

Cargill 2012) model

plasma properties in a few

thousand loops

coronal DEM (>1 MK)

pressure gauge (Fisher 1987)

transition region DEM (0.1~1

MK) during the decay

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Methods-Comparing with observed total radiation

Instrument Temperature (MK)

RHESSI >10

EVE 2~10

AIA (EUV bands) 2~10

AIA (UV bands)TRACE (UV bands)

~0.1

Application-2005 May 13 flare

Overview of the flare

• M8.0 flare, obs. by RHESSI and TRACE

• 5127 loops with cross section area of 1” x 1”

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Length of half-loop (Mm): 33 – 65

Max heating rate in individual loops (ergs/s): 2.4x1024 – 5.7x1025

Duration of heating (s):13 – 131

Total heating energy (erg): 1.22×1031

Results-Comparison with RHESSI

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Obs.Model

light curves in 3-6, 6-12, 12-25 keV

(details see Liu et al. 2013 ApJ, 770,111 )

Application-2011 March 7 flare

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Length of half-loop (Mm): 40-60

Max heating rate in individual loops (ergs/s): 7.4x1023 – 1.3x1025

Duration of heating (s):13 – 131

Total heating energy (erg):4.64x1030

Overview of the flare

• M1.7 flare, obs. by AIA and EUV

• 3057 loops with cross section area of 1” x 1”

Results-Comparison of EUV emissions

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T~10 MK T~6.5 MK

AIA 131 AIA 94

EVE 133Fe XX Fe XX III

EVE 94Fe XVIII

Obs.Model

Results-Comparison of EUV emissions

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T~2.7 MK T~1.9 MK

AIA 335 AIA 211

EVE 335Fe XVI

EVE 211Fe XIV

Obs.Model

• UV 1600 bands is dominated by C IV emission

• C IV line is optically thin transition region line

• The transition region DEM is given from the “pressure gauge” (Fisher 1987) ,when

In the transition region, the conduction is balanced by radiation

the pressure does not vary with height

Results-Comparison with UV light curves at the decay phase

( )DEM T P

12The calculated CIV flux decays at the same rate as observed

Discussions and Conclusions

We use the impulsive rise of UV light curves at the foot points to construct the heating rates in a few thousand loops, and calculate plasma properties of these loops

The synthetic coronal emission and decay-phase C IV emission from the model agree with the obs. very well

The method gives an estimate of total energy (lower limits): 1.22×1031 for the M8.0 flare and 4.64x1030 for the M1.7 flare

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Reference

Fisher, G. H. 1987, ApJ, 317, 502

Fletcher, L., Pollock, J., Potts, H. E., 2004, Solar Physics, 222, 279

Hawley, S. L., & Fisher, G. H. 1992, ApJS, 78, 565

Klimchuk, J. A., Patsourakos S., and Cargill P. J. 2008, ApJ, 682, 1351

Liu, W-J, Qiu, J., Longcope, D. W., Caspi, A. 2013, ApJ, 770, 111

Longcope, D.W., DesJardins, A. C., Carranza-Fulmer, T., Qiu, J., 2010, Solar Physics, 267, 107

Qiu, J., Liu, W.-J., Longcope, D. W. 2012 ApJ, 752, 124

Qiu, J., Liu, W-J., Hill, N., Kazachenko, M. 2010, ApJ, 565, 1335

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Results-Distribution of peak temperature and density for over 5000 flux tubes

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2

2

( )

( ) + = exp (ergs/s/pixel)

2

w/ constraints :

(ergs/s)

= 1 (ergs)

where,

: discrete total

ii i i i i

i

i non thermal RHESSI

i c tr tr GOES

i

t tH Q L C

R

Hdt H dt R R dt R dt

H

energy (heating) flux for the th loop;

: volumetric ad-hoc heating rate for the th loop; : length of the th loop;

: energy flux evaporated to the corona by non-thermal for the ti i

i

i

Q i L i

i h loop;

/ ; , : corona and transition region radiation rates;

: UV peak count rate; : peak time; : rise time (FWHM);

, : scaling factors from best fit, wh

i i i c tr

i i i

tr

H R R

C t

ich are universal for all the loops.

Methods-Construct the heating rate

Temporally and spatially resolvedDetermined by UV and HXR observations

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Methods- loop evolution with EBTEL model

2 20

3 3

2 1 energy conservation

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mass conservation5 5

2 ideal gas law

where,

i ii c tr i

i i

itr ii

i i i i

i B i

dPQ R R

dt L L

dn c cF R

dt c kLT c kLT

P k nT

, , : average pressure, density and temperature of the th loop

: volumetric ad-hoc heating rate for the th loop, construced from UV obs. ;

: length of the th loop;

i i i

i

i

P n T i

Q i

L i

:

2

1

0

: energy flux evaporated to the corona by non-thermal for the th loop;

( ) : corona radiation rate;

: loss rate through transition region; / ;

: conduction fl

i

c

tr tr c

i

R n T

R R R c

F

2 3ux 0.87; 0.5c c 20

Methods- loop evolution with EBTEL model

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AIA response function vs. EVE line contribution function

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