3 Creation of Frequency Grids

The program SETF2 creates the binary file FGRID which contains the frequency grid used by LTE2, PRO2, and LINE1.

SETF2 processes data from the atomic data file ATOMS. Attention: SETF2 has not the capabilities to detect errors like ATOMS2! For the creation of a frequency grid SETF2 uses only data which belongs to the keywords L, RBF und RBB (Sect. 2.2) and checks these for errors.

Thus, it is indispensable to transform every new or modified, interactively created atomic data file with the program ATOMS2 in order to check for errors and inner consistency.

The program SETF2 is available for all users at Tübingen’s PC cluster in its latest version: /home/rauch/bimod/setf2.Linux_x64.

A frequency grid is unambiguously defined by its input files ATOMS, DATEN, CONTS_MAN, F_BASE, and POS_LIST. All frequency points are clearly named (TYP) in the frequency grid (see below.).

ATOMS

is the atomic data file (Sect. 2).

DATEN

This file contains:

• the effective temperature Teff,

• the output parameter,

• the weight parameter _W ,

• the line parameter,

• the EUV parameters EUVmax und EUVnumber,

• f-value limit.

The effective temperature Teff is necessary for the calculation of the frequency discretization within a line transition (central frequency ₀). The position of the frequency points is depending on the Doppler width Δ_Doppler = . This default value can individually be substituted by the keywords TL in ATOMS.

If the “RBB” record in ATOMS contains the keyword WAVELENGTH: in columns 81-91, SETF2 uses the value directly following this keyword for the central wavelength of the respective line transition. The program FORMEL4 can preset this value which may be replaced or inserted (with the keyword!) manually in order to shift the line to the specified wavelength.

Two edge frequency points are inserted for every bound-free transition in ATOMS (keyword RBF): this is necessary because the ionization into excited levels is considered in detail by PRO2 und LINE1. These frequency points are set at the ionization energy ₀ of the respective level and at ₀ + 10^{-12 .} ₀. These points are used to split up the complete frequency grid in single integration intervals.

For all line transitions in ATOMS a particular number of frequency points is inserted. Their order is controlled by the line parameter. If nothing else is defined in ATOMS (keyword DB), the following arrangements are automatically set:

Table 1: The line parameter and default frequency point arrangements for line transitions line parameter frequency points ( - 0)/ΔDoppler comment 0 5 0, ,,2, universal 1 9 -,-2,-,-,0,,,2, universal -1 5 like 0, in case of line overlaps like 1 universal -3 3 0,, pre-iteration

The choice of line parameter 0 is generally possible for all other line transitions under the premise that the flux gradient is almost constant over the full width of the line. This kind of frequency discretization within a line transition is named “half line”.

An automatical differentiation is made if the line parameter is set to -1. This has the great advantage that fewer frequency points are inserted in the grid, compared to line parameter 1.

The line parameter -3 is equivalent to line parameter -1 but inserts only three points (five in case of overlap) for a line. This saves memory and computational time but is somewhat unrealistic because the line profile is not well represented by this frequency point arrangement. At least a subsequent iteration with a more detailed frequency grid (e.g. created by SETF2 from the same atomic data file ATOMS but with the line parameter -1) is necessary.

The f-value limit can be chosen to represent lines with f-values smaller equal than the f-value limit analogously to line parameter -3, independent from DB values in ATOMS. This reduces slightly the number of frequency points in FGRID.

The frequency grid contains by default the interval 1.0 ^. 10¹² - 2.99792458 ^. 10¹⁷Hz (= 1 Å, Tab.3). The optional parameter EUVmax allows to change the maximum: in the case that EUVmax is larger than 2.99792458 ^. 10¹⁷Hz, EUVnumber indicates the number of frequency points which are inserted by SETF2 in the range 1.0 ^. 10¹⁷ - EUV max Hz; in the case that EUVmax is smaller that 2.99792458 ^. 10¹⁷Hz, EUVnumber is disregarded.

CONTS_MAN

This optional file contains additional frequency points (given in Å or Hz)

In this input file frequency points can be requested to insert which are important for the evaluation of the models, e.g. in the case of the emergent flux and the calculation of specific colors. Doubly requested points are disregarded ...

CONTS_MAN can be created using

/home/rauch/bimod/prep_contsman.Linux_x64 > CONTS_MAN << eos
min max <step / resolving power>
eos

for wavelength or frequency points. In case that the third argument is > 100, prep_contsman assumes it to be the resolving power. prep_contsman accepts more than one input line.

F_BASE

This optional file contains additional frequency points (given in Å or Hz)

If the file F_BASE exists and contains valid input data, all requested points are created as base grid in the interval _min^base - _max^base. The largest base grid can actually contain 200 000 frequency points. Subsequently, SETF2 creates (like described above) the “normal” frequency grid based on ATOMS and DATEN. The line parameter is automatically set to 1.

In contrast to frequency points requested in CONTS_MAN which are definitely present in the created FGRID, all base grid points are eliminated if “normal” frequency points (including points requested in CONTS_MAN) are found in the interval Hz.

F_BASE can be created using prep_contsman, see above.

POS_LIST

This optional file contains additional frequency points (given in Å or Hz)

It should be created by /home/rauch/tools/line_identification_POS.job (edited for the required elements and ionic species) for Kurucz POS lines only.

SETF2 reads the line centers from POS_LIST and creates for each line nine frequency points (Δ/Å  = -0.005,-0.003,-0.002,-0.001, 0.000, 0.001, 0.002, 0.003, 0.005). This is necessary to avoid artificial “fading” of iron-group lines by a later convolution of the synthetic spectrum with a rotational of instrumental profile.

Wavelengths > 2000 Å are given by Kurucz as air wavelengths and are converted into vacuum wavelengths to match the line positions during the model-atmosphere calculations.

After the creation of the frequency grid in accordance with ATOMS, DATEN, CONTS_MAN, F_BASE, POS_LIST the IR, UV, and EUV range and the intervals between the lines and edge are automatically completed.

Every frequency point is unambiguously named in the frequency grid with a CHARACTER*50 string: In detail the fields have the following meaning:

123456

field 1:

• CONT for all continuum points, which were set in accordance to ATOMS, DATEN, CONTS_MAN, and F_BASE
• C/ED for all continuum points, which were automatically created, e.g. in order to separate integration intervals
• EDGE for all continuum points, which were inserted to represent the bound-free transitions in ATOMS (see above)
• LINE for all line transition points

field 2:

• (HALF) for all line transition points, “half lines” (see above)
• (FULL) for all line transition points, “full lines” (see above)
• RED for all continuum points at the end of integration intervals (in general from one bound-free transition to another)
• BLUE — RED (RED and BLUE indicate the location of the point relatively to the threshold / edge: BLUE is set exactly at the threshold frequency, RED is set at longer wavelength, i.e. “redwards” )

field 3:

• ** for threshold frequency points for levels ionizing into excited levels

field 4:

• AUTO_ADD for all automatically inserted continuum frequency points (to fill-up too-large intervals)
• AUTO_IR for all automatically inserted continuum frequency points (to fill-up to the IR limit of 1.0 ^. 10¹²Hz)
• AUTO_UV for all automatically inserted continuum frequency points (to fill-up to the EUV limit of 2.99792458 ^. 10¹⁷Hz)
• BASE for all inserted (and not eliminated — see above) continuum frequency points optionally requested in F_BASE
• MANUELL for all inserted continuum frequency points optionally requested in CONTS_MAN
• HE26 for all edge and line transition frequency points lower level in the TMAP code (Sect. 2.1, here: He II, level with principal quantum number 6.

field 5:

• HE27 for all edge and line transition frequency points upper level in the TMAP code (Sect. 2.1, here: He II, level with principal quantum number 7

field 6:

For all line transition points the position of the point in the line is indicated:

• CONT/RED
• CENTER
• CONT/BLUE

For every frequency point a quadrature weight is calculated corresponding to the weight and the line parameter. The following points are considered:

• integration intervals do not include a complete edge, i.e. EDGE/RED and EDGE/BLUE of the same threshold

• the quadrature weights are calculated following the trapezoidal law for < _W (weight parameter, see above) and following the Simpson law for _W < . The Simpson law is necessary because the flux is exponentially decreasing for > _W and the trapezoid law is not sufficient. In principle, all weights can be calculated following the Simpson law — SETF2 will then insert a few more frequency points.

• “half lines” have corrected weights

• In the case of line overlaps “full lines” have to be considered (automatically: line parameter 1 or — better — -1, or keyword DB in ATOMS)

The output of SETF2 should be controlled in detail. SETF2 comments all operations and gives warnings in case of ambiguity. In the case of fatal errors, SETF2 terminates.

The quadrature weights require special attention: the check sums of all single intervals as well as of the complete frequency grid have to be exactly 1. If this is not the case, it is possible that negative quadrature weights appear (“half lines” in cases were “full lines” are necessary). In order to correct for this, the atomic data file ATOMS has to be modified (keyword DB) or the line parameter has to be set to -1 (this automatically corrects these cases).

Attention: A frequency grid with wrong quadrature weights will cause an abort in programs like PRO2 or LINE1.

The size of the output is controlled by the output parameter:

• PRINT CHECK reduces the output to a minimum, only warnings, fatal errors, and information about the quadrature weights are displayed.

• PRINT gives a complete output, incl. the complete frequency grid.

In both cases the parameter NFMAX, NRBBMAX, NRBBMAD, and NRBFMAW (Sect. 1) are printed, which are valid for ATOMS and FGRID. Under unix a

grep para ¡output filename¿

extracts them from the output file.

• PRINT ASCII FGRID is created formatted.

In case that the input atomic-data file was created by ATOMS2 for line-profile calculations (Sect. 2), SETF2 creates two files, ION_USER and LINIEN_USER, that may be used as input files (ION and LINIEN) for LINE1_PROF (Sect. 9). LINIEN_USER contains a line closest to the center of the RBB interval (ATOMS2, Sect. 2) and a respective BLENDRANGE to cover the complete RBB interval. ION_USER contains the proper ion according to LINIEN_USER.