Diagnostics of non-thermal n-distribution

Kulinová, A.

AÚ AVČR, Ondřejov, ČRFMFI UK, Bratislava, SR

Diagnostics of non-thermaln-distribution

Observed flux

Ionization

Level population

Non-thermal n-distribution

Distribution diagnostics using RESIK spectra

Results

Observed flux (optically thin line)

Line flux observed at a distance d from the Sun [ergs.cm-2.s-1]:

G(T,Ne) is a line contribution function [ergs.cm3.s-1]:

N(Xim)/N(X

m) – relative population of an excited state i of an ion X

m – it is a

function of T and Ne

N(Xm)/N(X) – relative population of an ion X

m – it is a function of T

N(X)/N(H) is an abundance of element X

dVNNTGd

dVhAXNd

FV

ee

V

ijijmiij 2

22 4

1

4

1,

ij

e

ij

e

m

m

mi

e hN

A

N

HN

HN

XN

XN

XN

XN

XNNTG ,

Ionization and recombination - I

1. Photoionization vs. Radiative recombination (RR)

Total number of radiative recombinations (RR) per unit volume and time:

Summing over all levels i an j we can obtain total rate coefficient [cm3s

-1]:

EEEh

hXEeXEeXhX

ij

mi

mj

mj

mi

)( vs.)( 11

RRme

RR

RRijm

mj

em

ijRR

RRij

mje

ijRR

XNNdt

dN

dfXN

XNNXN

dt

dN

dfXNNdt

dN

1

01

11

0

1

vvv

vvv

Ionization and recombination - II

2. Collisional ionization (CI) vs. 3-body recombination:

Total number of collisional ionizations per unit volume and time:

Summing over all levels i an j we can obtain total rate coefficient [cm3s

-1]:

)(- :ionizationafter ofenergy

:ionizationfor allow to

vs.

ij

ij

ji

mi

mj

mj

mi

EEEEe

EEE

EEEEE

EeXEeEeXEeEeXEeX

121

1

321

1132211

32211

11

CIme

CI

Eij

CIij

mie

ijCI

XNNdt

dN

mEdfEXNNdt

EdN

21111 v vvv

2

111

1

3. Excitation-autoionization (EA) vs. Dielectronic recombination (DR)

Mechanism populating the energetic levels above the ionization threshold (so called doubly excited states):

a) excitation by inelastic collision with a free electron – excitation of an electron from closed inner shell of an excited ion

b) dielectronic capture – – the free electrons must have

energy E = Ej – Ei – rate coeff. CDIELC is obtained from

The doubly excited state can either autoionize or stabilize through radiative decay, producing a satellite line

mj

mi XEeX 1

Ionization and recombination - III

vs.)(

EEE

hEEEEEEEEEEE

hXXEeXEeEeXEeXEeX

ij

jlljiijl

jlml

mj

mi

mi

mj

ml

221

12

121

aji

mj

DIELCij

mie AXNCXNN 1

Ionization and recombination - IV

The total number of ionizations per unit volume and time resulting from EA

process from Xm to X

m+1

The total number of dielectronic recombinations per unit volume and time is given by:

Time evolution of the populations of each of n ionization stages of elemenent X:

EAme

EA

l jl

Rjl

aj

ajE

ljmle

EA

XNNdt

dN

AA

ACXNN

dt

dN

DRme

DR

i j ll

Rjl

aj

RjlDIELC

ijmie

DR

XNNdt

dN

AA

ACXNN

dt

dN 11

EQULIBRIUM IONIZATION ;

][

0

11

dt

dNXNN

NNNNNdt

dN

mn

m

m

DRRREACIme

DRRRmEACIme

m

Excitation of ions - I

Statistical equilibrium (SE) for levels below the ionization threshold:

These equation involve the most important excitation and de-excitation processes in the solar corona:

Cij D – collisional de-excitation

Cij E – collisional excitation

Aij – excitation and de-excitation due to radiative decay

Generally, calculations of the relative level population is coupled with relative ion population when we need to account for dielectronic recombination and autoionization.

)( ijij

Eije

ij

Dije

ijijij

ij

Ejiej

ij

Djiej

ijACNCNNANCNNCNN

1i

iN

ijE

ijEij dfC vvvv

0

vvvv dfC jiDji

Excitation of ions - II Population of levels above the ionization threshold

The SE for levels of ion Xm

above the ionization threshold must take into account autoionization and excitation through DR. Since higher excited levels are usually less populated than the ground state, and the autoionization rates are large, these levels can be considered to be in coronal model approximation:

CgiDIELC

– diel. capture

Simple way how to treat this calculation is to consider that the two processes on the LHS of the previous equation are completely independent from each

other and they deal with ground levels of different target ions Xgm and Xg

m+1

therefore we can separate the population of the level i of the Xm

in the sum of populations given by the each of the processes and calculate them separately:

usually

11

m

g

mi

DIEL

ijij

aTOT

DIELi

DIELgie

mg XN

XNAANCNXN )(

ijij

aTOT

Ei

Egie

mg AANCNXN )(

ijij

aTOTi

DIELCgie

mg

Egie

mg AANCNXNCNXN )()( 1

Ei

DIELi NN

Non-thermal n-distribution - I This kind of distribution occurs when a beam of accelerated electrons

appears in plasma and is neutralized by the so called return current (Dzifcakova and Karlicky, 2008, SP, 250, 329). Both the electron beam and the return current modify the initial electron distribution function.

The non-thermal n-distribution considered in our study describes the bulk of non-thermal plasma electrons but it does not include the effects of the high-energy tail.

dEkT

E

kT

E

kTBdEEf

nn

exp)(

/ 22

kτ=kT

+n=E

2

3

2

2

Tn

τ3

2

Non-thermal n-distribution - II Changes the ionization and excitation equilibrium - all rates are sensitive to

the electron distribution function - changes in the ratios of spectral line intensities

The line fluxes are also sensitive on functional relation of particular cross sections on energy

To diagnose the shape of the non-thermal distribution it is useful to pick up three (or more) spectral lines in different ionization stages and at least one of them ought to be the satellite line

The ionization equilibrium for Fe using n-distribution has been computed by Dzifcakova (1998, SP 178, 317) and for C, N, O, Ne, Mg, Al, Si, S, Ar, Ca and Ni Dzifcakova (2003-2005).

The set of theoretical spectra has been calculated using a modified version of CHIANTI package and atomic database version 5.2

Bragg Crystal Spectrometer (BCS) and REntgenovsky Spektrometr s Izognutymi Kristalami (RESIK)

These two instruments were bragg crystal spectrometers (bent crystals) which operated on satellite missions dedicated to observe the Sun.

BCS operated on YOHKOH (1991-2001) – viewed the whole Sun in X-rays – 4 bent crystals covered the selected wavelength ranges (1.7636 - 1.8044 Å, 1.8298 - 1.8942 Å, 3.1631 - 3.1912 Å, 5.0160 - 5.1143 Å) to observe resonance line complexes of H-like Fe XXVI and He-like Fe XXV, Ca XIX and S XV; resolving power ~ 3000 - 6000

RESIK operated on CORONAS-F (2001-2003) - viewed the whole Sun in X-rays – 4 bent crystals covered the selected wavelength ranges (3.40 -3.80 Å, 3.83 - 4.27 Å, 4.35 - 4.86 Å, 5.00 - 6.05 Å) to observe the emission lines of H-like, He- and Li-like ions of Ar, K, S, Si; resolving power ~ 1000

We have applied the diagnostics of the n-distribution to RESIK data. We decided to use the lines of Si XIId, Si XIII and Si XIV which dominate the 5.00 - 6.05 Å channel.

Diagnostics• The best diagnostic are the ratios of satellite and allowed lines of ions of one

element in different ionization stages.

• The satellite lines sample the electron distribution function at discrete energies while the intensities of the allowed lines depend on the integral of the product of the collisional cross sections with electron velocity over the distribution function from the excitation energy.

The following lines from RESIK spectra from Channel 4 have been used:

ion wavelength transition

Si XIV 5.217, 5.218 1s 2S1/2 – 2p 2P1/2,3/2

Si XIII 5.681, 5.689 1s2 1S0 – 1s 3p 1,3P1

Si XIId 5.816 1s2 2p 2P1/2,3/2 – 1s 2p 3p 2D3/2,5/2

5.818 1s2 2p 2P3/2 – 1s 2p 3p 2D3/2

Synthetic spectra

• A grid of synthetic spectra (5 - 6 Å) has been calculated using ‘the non-thermal’ modification of CHIANTI package (Dzifčáková, 2006):

• isothermal approximation - log = 6.7 – 7.3 with step 0.02

• constant ne = 1010 cm-3

• column EM = 1022 cm-5, FWHM=20.0 mÅ

• the ionization equilibrium for n-distributions was calculated by Dzifčáková (2005).

CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and George Mason University (USA). The software is distributed as a part of SolarSoft.

RESIK spectra – all chanels Before the analysis of the spectra the linear approximation of continuum has been subtracted.

7 - Jan - 2003, class M4.9 – 'mounds' 21- Jan - 2003, class C8.1 – Level2 data

7 – Jan – 2003: 23:25 – 23:33 – 23:40 UT, M4.9, S14E81 – diagnostics of n

GOES-08 light curve and radio data

Jan 7th, 2003: 23:25 – 23:33 – 23:40 UT,

M4.9, S14E81

Observed type III: 23:31 – 23:32 UTn = 11 and log()=7.296 K 23:31 UT

time int. of observed spectra: 23:20 – 00:35 UT

21 – Jan – 2003: 02:23 – 02:28 – 02:33 UT, C8.1, N14E09 - diagnostics of n

GOES-08 light curve and radio flux

Jan, 21th, 2003: 02:23 – 02:28 – 02:33 UT,

C8.1, N14E09

Observed type III: 02:24 – 02:29 UT

n = 11 and log()=7.267 K 02:26 UT

time int. of observed spectra: 02:24 – 02:34 UT

4 – Oct – 2002: 05:34 – 05:38 – 05:41 UT, M4.0, S19W09 - diagnostics of n

4 – Oct – 2002: 05:34 – 05:38 – 05:41 UT, M4.0, S19W09

GOES 08 RHESSI

Radio Flux

time int. of observed spectra: 05:30 – 05:54 UT

6 – Feb – 2003: 02:07 – 02:12 – 02:14 UT, C3.4, S16E55 - diagnostics of n

6 – Feb – 2003: 02:07 – 02:12 – 02:14 UT, C3.4,

S16E55

time int. of observed spectra: 02:06 – 02:34 UT

Results We have tried to diagnose the shape of non-thermal n-distribution

The diagnostics using allowed and satellite transitions is effective tool but it needs reliable observations

It is possible to probe the non-thermality of the free electron distribution in flaring plasma but the estimated errors of

measurements are about 30%-50%! the non-thermality correlates well with radio emission

Thank you for attention :o)

Ionization and recombination - I For ionization and recombination processes we consider:

1. Photoionization vs. Radiative recombination

2. Collisional ionization vs. 3-body recombination

3. Excitation-autoionization vs. Dielectronic recombination

EEEh

hXEeXEeXhX

ij

mi

mj

mj

mi

)( vs.)( 1

)(- :ioniz.after ofenergy

:ioniz.for allow to

vs.

ij

ij

ji

mi

mj

mj

mi

EEEEe

EEE

EEEEE

EeXEeEeXEeEeXEeX

121

1

321

1132211

32211

11

vs.)(

EEE

hEEEEEEEEEEE

hXXEeXEeEeXEeXEeX

ij

jlljiijl

jlml

mj

mi

mi

mj

ml

221

12

121

RRmRRPHmPH

RRijm

mj

em

ijRRPH

ijm

mim

ijPH

RRij

mje

ijRRPH

ijmi

ijPH

XNdVdt

dNXN

dVdt

dN

dfXN

XNNXN

dVdt

dNd

XN

XN

hcXN

dVdt

dN

dfXNNdVdt

dNdXN

hc

dVdt

dN

1

0

21

11

0

21

4

4

0

0

vvvv

vvvv

Time evolution of parameter ‘n’ and log():

7 – Jan – 2003: 23:25 – 23:33 – 23:40 UT, M4.9,

S14E81 – diagnostics of

The parameter 'n' of the n-distribution reaches value of 11 about 23:31 UT and 23:36 UT and reaches log()=7.296 K and log()=7.264 K, respectively.

21 – Jan – 2003: 02:23 – 02:28 – 02:33 UT, C8.1, N14E09 – diagnostics of

Time evolution of parameter ‘n’ and log():

The parameter 'n' of the n-distribution reaches value of 11 and log()=7.267 K about 02:26 UT .