1. P. Heinzel Astronomical Institute, Czech Academy of Sciences
Partial ionization of hydrogen plasma in the solar atmosphere Non-LTE modeler’s view
P. Heinzel
Astronomical Institute, Czech Academy of Sciences

2. Partial hydrogen ionization in a dynamic chromosphere
Carlsson and Stein 2002, ApJ 572, 626
See also new simulations with Bifrost:
Martínez-Sykora et al. 2015, Phil. Trans. R. Soc. A 373:
Martínez-Sykora et al. 2017, ApJ 847:36

3. Dynamic solar flares Heinzel 1991, Sol. Phys. 135, 65
Kašparová 2009, A&A 499, 923
Allred et al. 2015, ApJ 809, 104
Flarix RHD code
RADYN RHD code

4. Prominence non-LTE models with AD
Fontenla+ 1996

5. NLTE prominence models
Heinzel 2016 and Labrosse (in Solar Prominences, Springer)

6. MALI NLTE transfer code
1D/2D-slab geometry (MALI1D/MALI2D) – Heinzel 2016
isothermal-isobaric slabs, generalization to PCTR
height-velocity dependent radiative boundary conditions (including photoionization by external radiation)
multilevel hydrogen atom with continuum (ionization)
other species like CaII and MgII
coupled radiative transfer + statistical equilibrium
fast numerical solution using the ALI techniques
Non-equilibrium ionization of hydrogen with the MALI code

7. NLTE modeling of partial hydrogen ionization
Input: T, p, D, vnt , H, vflow
Output: ne , nHI , radiative and collisional rates, relaxation times
Prominence or a CME-core is approximated by a 1D/2D slab models
(L-alpha line is optically very thick in prominences, mostly thin in CMEs)
We solve the radiative transfer and statistical-equilibrium equations
for a 5-level + continuum hydrogen atom

8. MALI1D MALI2D Heinzel et al. 2015, A&A 579, A16
Jejčič et al. 2014, Sol. Phys. 289, 2487

9. Grid of models from cool eruptive prominences to hotter CME cores
T-range: – K
p-range: – 1.0 dyn cm-2
D: 5000 and km
vt : 5 km s-1
H: km
zero flow velocity (no Doppler effects in the continua)
Heinzel and Jejčič 2019, in preparation

10. Histogram of the kinetic temperature
(39)
(30)
Heinzel+ 2016, Jejčič+2017, Susino+ 2018

11. Photoionization is negligible for T > K, where hydrogen ionization equilibrium is consistent with CHIANTI or Arnaud & Rothenflug (1985); depends only on T
For T < K, photoionization starts to be important, and namely at low T between
– K where the situation becomes very complex

12. Here we show the partial hydrogen ionization as function of electron density
Variations with T show again that for T > K the ionization degree
doesn‘t depend on the electron density, while for lower T it does. Namely between
and K the effect is important

13. RU and CU are the photoionization and collisional rates from the ground state of hydrogen.
We see how they vary with T and p. At low pressures, the photoionization rates are fixed by the incident continuum radiation (prominence illumination from the solar disk, at given H). At higher pressures, RU rates are higher due to the intrinsic L-continuum radiation

14. Kinetic equilibrium for processes 1 <-> k
𝑑 𝑛 1 𝑑𝑡 = 𝑛 𝑘 𝑅 𝑘1 𝑛 𝑒 ,𝑇 + 𝐶 𝑘1 ( 𝑛 𝑒 ,𝑇) − 𝑛 1 [ 𝑅 1𝑘 𝐽 𝜈 + 𝐶 1𝑘 ( 𝑛 𝑒 ,𝑇)]
(in general we have 5 eqs. for a 5 level H atom)
𝑛 𝐻𝐼 ~ 𝑛 1
𝑛 𝐻𝐼 + 𝑛 𝑘 = 𝑛 𝐻
𝑑 𝑛 1 𝑑𝑡 =0
Special case of ionization equilibrium:
Relaxation time:
t = 1 / ( Pk 1 + P1k )

15. Under cool prominence conditions t_relax can reach 1000 sec
T(K) in units of K
Estimated relaxation times required to achieve the ionization equilibrium from
perturbed plasma states (e.g. T and/or p time variations).
At high temperatures the relaxation is very fast, at typical CME-core pressures t_relax < 10 sec.
Under cool prominence conditions t_relax can reach 1000 sec
(also see Engvold 1980, Sol. Phys. 67, 351)