The synthetic emission spectra for the electron non-thermal
distributions by using CHIANTI
Elena Dzifčáková
Department of Astronomy, Physics of the Earth and Meteorology
FMPhI Comenius University, Bratislava
Why to use the CHIANTI database
CHIANTI contains atomic data for the majority of the astronomical interesting ions and has a very good software support.
CHIANTI allows quick computation and analysis of solar spectra and it is an important diagnostic tool of physical parameters of the solar plasma.
The database contains only the collision strengths averaged through the Maxwell distribution. Their approximation function depends on the type of the transition and is performed by 5-point spline functions (Burgess and Tully, 1992).
The often used approximation of the collision strength is a functional form (Abramowitz and Stegun, 1965), where Ck and D are coefficients and u=Ei/Eij:
The collision strength approximation
max
0
lnk
k
kk uDuC
The advantage of this approximation is the simple analytical evaluation of its integral over a distribution function.
The high energy behaviour of
electric dipole transitions
non electric dipole, non exchange transitions
exchange transitions
)ln(uD
.const
2/. Econst
,0C
,/ 22 EC
0D
010 DCC
Econst ln.
The collision strength averaged over the Maxwell distribution
,exp1
ij
iijiijij E
Ed
kT
EE
,max
110
yk
kkk eDEyEyCC
where y=Eij/kT and Ek is an exponential integral of order k. The coefficients Ck and D can be evaluated
from CHIANTI by the least square method.
,exp101716.221
8
i
ijijHY
kT
E
kTI
v
The conditions for the coefficients Ck and D :
Electric dipole transitions
Non electric dipole, non exchange transitions
Exchange transitions
,/4 ijijij EfD
max
0
1k
kk uCy
,0D ,0 0Cy 1max
0
uCyk
kk
,010 DCC ,01
udyy
1max
2
uCyk
kk
How precise is the collision strength determined by this inverse technique?
Electric dipole transitions - no problems with the approximation & good agreement with data (TIPbase)
Fe XV 3s2 1S0-3s3p 1P1 (284.16 Å)
The electric dipole transitions
Fe XV 3s3p 3P1 - 3s3d 3D2 Fe XV 3s3p 3P2 - 3s3d 3D3
Non electric dipole, non exchange transitions
Fe XV 3s2 1S0 - 3p2 1D2 Fe XV 3s3p 3P1 - 3p3d 3F3
Problem - higher high energy limit of from CHIANTI than from data (TIPbase)
Fe XV 3s3p 3P0 -3p3d 3F3 Fe XV 3s3p 3P2 - 3p3d 3P2
Exchange transitions
O VII 1s2 1S - 1s2p 3P
The minimisation of the influence of possible errors
The numerical problems were often with the exchange transitions where the -s can be approximated only by using three or two coefficients. But the fulfilment of the conditions for coefficients guarantees the correct behaviour of for high and threshold energies. The simplest expressions for correspond to expressions which have been often used e.g. by Mewe (1972). It is difficult to compare data for all transitions of every ion. Possible errors in the approximation of cannot be excluded in present time. Their influence on the computation of non-th have been minimised by using:
.approxMaxwell
approxthnonCHIANTI
Maxwellthnon
Non-thermal distributions:kappa distribution
,5.1
12
21123
dEEkT
EkT
mAdEEf
235.15.0
1
A
2/3kTE
NkTp
Non-thermal distributions:power distribution
dEEkTE
kTE
kTm
BEfn
n 21
exp2
2123
,122
21
nBn .12 kTnE
kTn
k22
23
2/3 kE
Pseudo-temperature
Nkp
Computation of the line intensity
Several programs for analytic computation of the electron excitation rate for the non-thermal distributions have been included into CHIANTI software and small modifications of some original routines have been done. New data include: ionization equilibrium: C, N, O, Ne, Mg, Al, Si, S, Ar, Ca and Fe for =2, 3, 5, 7, 10, 25 (-distribution)Si, Ca and Fe for n=1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (power distribution) parameters for approximation of for all the ions above Changes in line intensity depend on the changes in the ionization equilibrium and excitation equilibrium. What can we expect for different distributions?
Changes in the ionization
equilibrium
kappa distribution
full line - Maxwell distribution
dashed line -kappa-distribution, = 2
Changes in the ionization equilibrium
Power distribution
The changes in electron excitation rate
kappa distribution power distribution
Changes in spectrum - kappa distribution
Maxwell distribution
=7 =2
Log T = 6.2
Changes in spectrum - kappa distribution
Maxwell distribution
=7 =3
DEM: quiet sun
Kappa distribution -strong enhancement
of CIV lines
DEM: active regionMaxwell distribution
=5 =2
Changes in spectrum - power distribution
Maxwell distribution
Log = 6.2
n=5 n=15
Changes in spectrum - power distribution
Maxwell distribution
DEM: quiet sun
n=7 n=15
Satellite lines
By using the modification of CHIANTI
we are able to:
model the influence of the shape of the electron distribution function on the spectrum
find the lines whose intensities are sensitive to the shape of the electron distribution function
search for the lines which are suitable for the diagnostics of the non-thermal distributions
To do ...
the computation of the ionization equilibrium for the power distribution for the other elements
the replacement of the parameters for the approximation of from CHIANTI by the parameters derived from TIPbase wherever it is possible
the modification of the other original CHIANTI routines for the kappa and power distributions (the computation of DEM, electron excitation rates…)
Ďakujem za pozornosťThank you very much for
your attention
kappa distribution, iron
Dzifčáková, 2005, to be published
kappa distribution, C and ODzifčáková, Kulinová 2003, SP 218