8 NLTE Line Formation and Models: LINE1

The program LINE1 calculates -- based on a suitable start model (Sect. 3) -- model atmospheres like PRO2, NLTE occupation numbers at fixed temperature and (optional) density stratification (e.g. for new levels in the case of extended model ions), and theoretical line profiles of selected lines under consideration of the most recent line broadening theories.

The input and output options are generally the same like those of PRO2 (Sect. 5.4 and 5.5).

8.1 Input Files

The program LINE1 expects the following input files (only those which are marked with “^*” are necessary):

ABUNDi
It is possible to read occupation numbers for newly implemented levels from 14 additional, already existing models ( --> MODINi). i (from ABUNDi) is a number from 1 to 9 (model 1 is MODIN, with abundance file ABUND, model 2 is MODIN2, with abundance file ABUND2, etc.) and 0, A, B, C, D, E for 10, 11, 12, 13, 14, and 15, respectively. . Abundance ratios are taken from the first model that includes the element, i.e., with ascending priority from 1^st, 2^nd, ..., 15^th model. If the elemental abundances of the input model ( --> MODIN) and of the models MODINi differ, scaling factors can be given in the files ABUNDi which are applied to the occupation numbers of the model MODINi, respectively.
Example:
C |~| 2
N |~| 1.3 It is recommended to add the complete set of occupations numbers to a model that does not include the respective species. Otherwise the lower levels may artificially be underoccupied.

ADJUST
In practice NLTE model atmosphere calculations have shown that is is not possible in all cases to consider all line transitions simultaneously from the beginning. One method to overcome this problem is to reduce the oscillator strengths at the beginning with reduction factors which increase to unity in the course of the iteration.

The input file ADJUST contains the reduction factors and the factors with which the reduction factors are increased every iteration until the original oscillator strengths are reached.
Example:

C4 C4 1.0E-5 1
C422S |~| |~| |~| |~| |~| C422P |~| |~| |~| |~| |~| 0.01 1.05
C452S |~| |~| |~| |~| |~| C452P |~| |~| |~| |~| |~| 1.0E+5 1.0E+00

means:
the oscillator strengths of all C IV line transitions are reduced by a factor of 10^-5. This factor is constant over the whole calculation. Additionally, the C IV 2s-2p line is individually reduced by the factor of 0.01 ( --> total of 10^-7) but this factor (0.01) is increased by 5% every iteration. The C IV 5s-5p line is considered with its correct oscillator strength (10^-5 ^. 10⁺⁵ = 1). In the case that the temperature correction yields negative temperatures, the oscillator strengths are kept at their last value.

ATOMS^*
atomic data file (Sect. 2), like for the start model or extended ...

DATEN
input and output options (Sect. 5.4, 5.5, and 8.3)
this files has to be copied to stdin because LINE1 reads the options from there (e.g. /home/rauch/bimod/line1 < DATEN).

DISTA
The frequency grid for the detailed calculation of line profiles is created by LINE1 itself. The discretization of the frequency points within the line transitions can be split in intervals with different distances from point to point in order to represent the line centers or possible forbidden components (e.g. --> He I 4471Å) with a sufficient number of (narrowly spaced) frequency points. DISTA contains informations how many points at which distance ( in Å) shall symmetrically (to the line center) be inserted in these intervals.

Example:

5 0.1
10 0.3
15 0.5

results in points at ( in Å, only the “red” wing given):
0.0, 0.1, 0.2, 0.3, 0.4, 0.7, 1.0, 1.3, 1.6, 1.9, 2.4, 2.9, 3.4, 3.9, 4.4

In case of many lines and a high resolution, the parameter NRBBMAD (Sect. 1) may become very high. Due to compiler limitations in the size of arrays, no executable may be created then. To avoid this, the use of a respective F_BASE file (Sect. 3) and an adjusted DISTA is recommended.

Example:

F_BASE creates an equidistant frequency grid from 3000 Å to 7000 Å ( = 0.1 Å), then a DISTA

2 0.01
4 0.02
6 0.03
8 0.05
9 100.00
10 0.01

is sufficient (narrow points only until the F_BASE resolution is reached, then just an end point of the line and a CONT/(BLUE/RED) point (Sect. 3). In addition, a dynamical use of DISTA in LINE1_PROF is helpful and is described in Sect. 9.

FGRID^*
frequency grid (Sect. 3), not necessary in the case of line profile calculations (see above)

ION
contains the code for the selected ion (line profile calculations). It differs from theTMAP code (Sect. 2.1): the element is given in CHARACTER*2 format (flushed to the left) and the ionization stage is indicated in the third (and fourth) column.
Examples:
HE2
C |~| 2
CA10

SETF2 creates this file for a given atomic-data file (Sect. 3).

LINIEN this file contains information about the range which has to be considered in the calculation of the line profiles and the selected line to calculate:

BLENDRANGE |~| |~| |~| |~| |~| 40.0*
This card is of special importance and has to be the first record in LINIEN.
• LINE1 searches in the interval [co - cBlendrange,co + cBlendrange] for line frequency points (Sect. 3) of other line transitions. All line transitions with points between CONT RED and CONT BLUE of the selected line (see below), are regarded as a blend and included in the calculation in detail. All other line transitions in the input file ATOMS (see above) are disregarded in the creation of the internal atomic data and frequency grid files by LINE1. This minimizes both, core memory and computational time requirements.
• LINE1 considers in the creation of the internal atomic data and frequency grid files only those radiative bound-free (RBF) transitions with an ionization energy smaller than c/(_o - _Blendrange) because RBF transitions with a higher ionization energy do not contribute to the opacity within the blendrange. This minimizes also the core memory and computational time requirements.

XXXXXXXXXXYYYYYYYYYY
TMAP code (Sect. 2.1) of selected lines for which theoretical line profiles shall be calculated

SETF2 creates this file for a given atomic-data file (Sect. 3).

MODIN*
start model (Sect. 4)

MODINi
see ABUNDi

OP_RBF_XXXX
bound-free cross-sections from the Opacity Project for levels of the ion XXXX

STARK_H1
VCS-like Stark broadening tables for H I
H I line-broadening has changed in since 2008. The reason is that an error (for high members of the spectral series only) in the H I line-broadening tables by Lemke (1997) that were used before. Tremblay & Bergeron (2009) and Tremblay & Bergeron (2015, priv. comm.) provide, parameter-free Stark line-broadening tables for H I considering non-ideal effects. These replaced Lemke’s data for the lowest members of the Lyman (n - n' = 1 - [2 - 21]), Balmer (n - n' = 2 - [3 - 22]), Paschen (n - n' = 3 - [4 - 22]), and Brackett (n - n' = 4 - [5 - 14]) series. These profiles can only consistently used with the Hummer & Mihalas (1988) equation-of-state (cf.,
OCCUPATION |~| PROBABILITY |~| FORMALISM |~| FOR |~| H1
in Sect. 5.4). For higher series members, we use the Holtsmark approximation.

STARK_ALIII
tables for He I (Dimitrijevi & Sahal-Bréchot 1993a)

STARK_HE1
tables of Barnard et al. (1969) and Griem (1974) for He I

STARK_HE2
VCS-like tables for He II (Schöning & Butler 1989a,b)

STARK_C4
tables for C IV (Schöning 1993)

STARK_N5
tables for N V (Schöning 1995)

STARK_HEI
tables for He I (Dimitrijevi & Sahal-Bréchot 1990)

STARK_CIV
tables for C IV (Dimitrijevi et al. 1991b; Dimitrijevi & Sahal-Bréchot 1992c)

STARK_CV
tables for C V (Dimitrijevi & Sahal-Bréchot 1996)

STARK_NV
tables for N V (Dimitrijevi & Sahal-Bréchot 1992b)

STARK_OIV
tables for O IV (Dimitrijevi & Sahal-Bréchot 1995)

STARK_OV
tables for O V (Dimitrijevi & Sahal-Bréchot 1995)

STARK_OVI
tables for O VI (Dimitrijevi & Sahal-Bréchot 1992a)

STARK_SIIV
tables for Si IV (Dimitrijevi et al. 1991a)

STARK_SVI
tables for S VI (Dimitrijevi & Sahal-Bréchot 1993b)

Note: For H I, He I, He II, C IV (STARK_C4), and N V STARK_N5 the tables have only to be loaded. LINE1 uses these data files if they are available. For the other ions an option has to be given (see below) in DATEN to use the broadening tables for all lines of the ion, or for selected line transitions by requesting formula 5 (keyword RBB) in ATOMS (Sect. 2).

8.2 Output Files

The program LINE1 creates (besides STDOUT) the following plot data files (in accordance with the options given). Note that in general wavelengths < 3000 Å are given as vacuum wavelengths and wavelengths > 3000 Å as air wavelengths.

ANGJ_C.DAT
specific intensity (continuum only) for different angles (see PARAMETER NA, Sect. 1)

ANGJ_L.DAT
specific intensity for different angles (see PARAMETER NA, Sect. 1)

PLDEP
departure coefficients for selected levels

PLDIFF
abundance profiles for all elements

PLEFL
emergent flux (complete frequency interval)

PLLP
limit = 1 (complete frequency interval)

PLPRF
line profiles

PLRBF
bound-free cross-sections of selected levels

PLWF
emergent flux (F() - WF denotes wavelength + flux.

PLWFP
emergent flux (F() and relative flux F /F_cont - WFP denotes wavelength + flux + normalized flux (profiles ...).

PLWFP_VACUUM
emergent flux (F() and the relative flux F /F_cont - WFP_VACUUM denotes wavelength + flux + normalized flux (profiles ...). All wavelengths are vacuum wavelengths.

PLWP
emergent flux (F() - WP denotes wavelength + normalized flux (profiles ...).

STRUCTURE
temperature stratification

For the evaluation and visualization of the output and plot data files several auxiliary programs are available (Sect. 11).

8.3 Options

For LINE1 most of the options described in Sect. 5.4 and 5.5 are valid. There are some further options. Their meaning should be clear ...

ACCEPT |~| CHANGED |~| EFFECTIVE |~| TEMPERATURE |~| X
LINE1 generally takes Tefffrom the start model (MODIN). For very large models the change of Teff (in small steps) takes much less times than the complete new calculation with mainly the same (!) parameters. However, still some iterations are needed ...

ACCEPT |~| CHANGED |~| ABUNDANCES
LINE1 generally takes the chemical composition from the start model (MODIN) and ignores ABUNDANCE cards in the input file but for newly implemented elements. For very large models the change of the abundances (in small steps) takes much less times than the complete new calculation with mainly the same (!) parameters. However, also still some iterations are needed ...

CPU-TIME |~| TTTTT

maximum CPU time for the job, TTTTT given in seconds
CPU-TIME |~| 0.0
This card transfers the total cpu time (then: stop) to LINE1. There are load dependent variations of the system cpu time which accounts to the user cpu time. These variations can effect the security time needed by LINE1 in order to complete the iteration, write the model, etc.

DOPPLER |~| PROFILES
This option sets the line broadening of all line transitions in the atomic data file ATOMS generally to Doppler line broadening. This can be used for a quick overview about blends within a selected range.

FORCE USE OF LINE BROADENING TABLES
This option enables the use of line broadening tables instead of approximate formulae during the model atmosphere calculation.

ITERATION |~| IN |~| DEPTHS ii jj kk
The the first kk iterations are carried out only between depth points ii - jj.

LINE |~| TEMPERATURE |~| FROM |~| FORMATION |~| DEPTH
The line temperature T_line is by defaults set to 3
4 ^. Teff (Sect. 3). The different lines form in very different depths, i.e. at different temperatures. This card allows to select the temperature at the formation depth ( = 1) of the line core for every lines as line temperature, respectively.

LINEARIZATION |~| MODE: |~| BLOCK-MATRIX |~| ITERATION, |~| ION
analogously to LINERIZATION |~| MODE ... in Sect. 5.4. This card allows to select one single ion to iterate.

MATRIX |~| INVERSION: |~| MINV
The matrix inversion for the solution of the statistical equations is carried out by the SCILIB routine MINV. Attention: numerically instable for n > 200,..., 220.

MATRIX |~| INVERSION: |~| INV
The matrix inversion is done by an own routine.

MATRIX |~| INVERSION: |~| GIRL
The matrix inversion is done by routine GIRL (single precision). More stable than MINV in some cases!

MATRIX |~| INVERSION: |~| GIRLDP
The matrix inversion is done by routine GIRL (double precision).

MATRIX |~| INVERSION: |~| SGETRF |~| + |~| SGETRI
The matrix inversion is done by the LAPACK routines SGETRF and SGETRI.

MISSING OCCUPATION NUMBERS FROM I MODELS
The occupation numbers of newly considered levels are read from I models (I = max i, see ABUNDi and MODINi, above) in increasing order. A consequence of NLTE modeling is the over-population of low-lying levels. A strong extension of models towards higher levels will not consider their de-population and may underestimate the population of the lowest. In this case, use the REPLACE |~| OCCUPATION |~| NUMBERS card (see below).

MIKROTURBULENCE |~| [KM/SEC] |~| 0.0
analogously to Sect. 5.4. LINE1 considers the microturbulence also in the calculation of the line profiles.

NEWMAXB= 20*
maximum number of linearizations of the Broyden or Kantorovich iterations

REPLACE |~| OCCUPATION |~| NUMBERS |~| FOR |~| AAAA |~| FROM |~| MODEL |~| I
Occupation numbers of model I will be used for all levels of ion AAAA.

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| C |~| IV
With this option, all C IV line transitions in the atomic data file ATOMS are calculated with the stark broadening tables by Dimitrijevi (if found there).

If the Dimitrijevi tables shall be used only for selected lines, in ATOMS formula 5 instead of formula 3 or 4 has to be requested.(Sect. 3).
-- The tables (Sect. 8.1) have to be loaded in any case ... --

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| AL |~| III

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| C |~| V

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| HE |~| I

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| N |~| V

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| O |~| IV

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| O |~| V

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| O |~| VI

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| P |~| V

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| SI |~| IV

USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| S |~| VI
all these cards like USE |~| DIMITRIJEVIC |~| BROADENING |~| TABLES |~| FOR |~| C |~| IV.

PRINT |~| ATOMIC |~| DATA |~| FILE |~| ATOMS_2
print the internally created atomic data file (see above) for the line profile calculations

PRINT |~| EQUIVALENT |~| WIDTH
A small table with the equivalent widths of all selected lines is printed to STDOUT.
Attention: For the calculation of the equivalent widths of the selected lines, the interval [CONT RED,CONT BLUE] (Sect. 3) is used -- with all included blends
In order to study the equivalent widths of selected lines in detail the blendrange has to be set to a small-enough value that includes only the components of the multiplet or the atomic data file ATOMS has to be created with only the requested line transition.

PRINT |~| EQUIVALENT |~| WIDTH |~| (LONG)
like PRINT |~| EQUIVALENT |~| WIDTH but this table includes all frequency points in the interval [CONT RED,CONT BLUE] and gives additionally the accumulated equivalent widths.

PRINT |~| MULTIPLET |~| SPLITTING
LINE1 is able to split the NLTE occupation number of multiplets (see above). With this card all multiplet splittings are reported.

PRINT |~| VCS |~| TABLE

PRINT |~| FORMATION |~| DEPTH |~| OF |~| LINES |~| AND |~| THRESHOLDS

PRINT |~| FREQUENCY |~| GRID |~| FGRID_2
print the internally created frequency grid (see above) for the line profile calculations

PRINT |~| LEVELS |~| WITH |~| LTE |~| START |~| VALUES

PRINT |~| LINES |~| AND |~| BLENDS

PRINT |~| PROFILE |~| TYPES
With this option, information about the used line-broadening theories for all calculated lines is printed to STDOUT. The same information is always included in the plot data file PLPRF as far as the necessary plot option (see below) is active to create it.

PRINT |~| STATISTICS |~| OF |~| FGRID_2

PRINT |~| WARNINGS

PLOT |~| EMERGENT |~| FLUX |~| |~| LOG |~| FNUE |~| / |~| LOG |~| NUE
PLOT |~| EMERGENT |~| FLUX |~| |~| FNUE |~| / |~| NUE
PLOT |~| EMERGENT |~| FLUX |~| |~| LOG |~| FLAM |~| / |~| LOG |~| LAM
PLOT |~| EMERGENT |~| FLUX |~| |~| FLAM |~| / |~| LAM
PLOT |~| EMERGENT |~| FLUX |~| |~| FLAM |~| / |~| LAM |~| |~| INTERVAL: LAMBDAMIN LAMBDAMAX

PLOT |~| LIMIT |~| TAU=1,ITERATION:EACH
With this option, a plot file PLLP is created which contains the geometrical depth (logarithmical) of the limit = 1 for the complete frequency grid. It can be plotted with the program PLXY (Sect. 11).

PLOT |~| LINES
PLOT |~| TEMPERATURE |~| STRATIFICATION,ITERATION:LAST
PLOT |~| TEMPERATURE |~| STRATIFICATION,ITERATION:EACH

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