Diagnostics of non-thermal n-distribution
description
Transcript of Diagnostics of non-thermal n-distribution
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 .