5.4 Input Options

The program PRO2 can be controlled by a number of input options. Some of them are initialized with a default value (indicated by *) and can be omitted if no other values shall be requested. Indispensable blanks are indicated by |~| . Numerical data can be inserted format free.

. whatever
commented by “.” in the first column, disregarded by PRO2

ABUNDANCE |~| AA x
introduces the abundance of the element AA (flushed to the left). The input x is the number ratio relative to hydrogen. If the start model contains already the element AA, this card is disregarded.

ABUNDANCE |~| AA |~| x |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| |~| MASS |~| FRACTION
introduces the abundance of the element AA (flushed to the left). The input x is the mass fraction. If the start model contains already the element AA, this card is disregarded.

ACCELERATION |~| OF |~| CONVERGENCE |~| FROM |~| ITERATION 999*
the Ng method for acceleration of convergence is used, starting from iteration 999. After every 4th iteration, all photospheric parameters are extrapolated from the previous iterations.

BROYDEN=0*, |~| |~| |~| SWITCH-LIMITS |~| |~| 0-->1, |~| 1-->2, |~| 2-->1 |~| : 1.E-33* 1.E-33* 1.E+33*
This option invokes a quasi-Newton method (“Broyden method”) instead of the Newton-Raphson iteration of the linearized equations.

Newton-Raphson iteration
Broyden method, at the beginning of each Scharmer iteration started by a normal Newton-Raphson iteration step. This is only suitable for diagonal operators ( $/\$ = 3).
Broyden method, at the beginning of each Scharmer iteration started with the updated matrix of the last Scharmer iteration. This is only suitable for diagonal operators ( $/\$ = 3).
like BROYDEN=1, but suitable for tridiagonal operators ( $/\$ = 4).
like BROYDEN=2, but suitable for tridiagonal operators ( $/\$ = 4).

The three switch-limits ₁, ₂, ₃ indicate

switch from BROYDEN=0 1, if the relative corrections of the Scharmer iteration are smaller than ₁. Is (₁ >1.E33) required, the 1st Scharmer iteration immediately starts with the Broyden method.
switch from BROYDEN=1 2, if the relative corrections of the Scharmer iteration are smaller than ₂.
switch back to the next lower BROYDEN stage, if the relative corrections for the temperature or the electron density a higher than ₃. This shall avoid divergent iterations.

While in the case of diagonal operator the switches occur locally following local criteria, the tridiagonal operators require global judgement and used the highest relative correction found in the whole atmosphere. Informations about the switches can be printed to STDOUT (see below).

CHANGE |~| EFFECTIVE TEMPERATURE |~| x
generally, PRO2 takes the information about Teff from the start model (Sect. 4). With this card, the another Teff can be chosen. This works in small steps and takes much less time than the calculation of a new model with almost the same parameters.

CHANGE |~| LOGG |~| x
like CHANGE EFFECTIVE TEMPERATURE, but for a new value of the surface gravity g

CHANGE |~| ABUNDANCE |~| AA |~| x |~| |~| |~| |~| |~| |~| |~| |~| MASS |~| FRACTION
like CHANGE EFFECTIVE TEMPERATURE, see ABUNDANCE for MASS FRACTION.

COMMENT:
With this card any comment can be printed at the beginning of the output.

DEPTH |~| DEPENDENT |~| LINE |~| PROFILES, |~| LINEARIZATION: |~| XXXXX
This option XXXXX = FIRST or EACH |~| is indispensable if depth dependent line profiles shall be calculated. FIRST saves a lot of computational time.

ERRNEW=1.E-10*
limit for the relative corrections to stop the linearizations

ERRSCH=1.E-04*
limit for the relative corrections to stop the Scharmer iteration

FORMAL |~| SOLUTION
PRO2 carries out two formal solutions (with/without line opacities) and saves the line profile in the file LINES.

FREQUENCY |~| GRID |~| FORMATTED
The frequency grid FGRID (input) is formatted.

STEP |~| UP |~| F-VALUES: |~| *****-START: |~| IIII |~| x₁ x₂ x₃
The oscillator strengths of all lines of a selected ion IIII are reduced by a factor of x₁ at the beginning of the iterations and stepped up by a factor of x₂ every x₃ Scharmer iterations.

For ***** the two possibilities INPUT or MODEL can be requested. With INPUT, PRO2 uses the values of x₁, x₂, and x₃ as requested in the card; with MODEL, PRO2 reads these values from the start model (Sect. 4) if a previous PRO2 has not reached unity for all step-up values and thus, written them to the output model.

STEP |~| UP |~| F-VALUES: |~| NO |~| KANTOROVICH |~| RESET |~| AFTER |~| STEP |~| UP
In general, after each increase of f-values, the Broyden/Kantorovich method is reset. This card suppresses this reset.

STEP |~| UP |~| F-VALUES: |~| LIMIT |~| FOR |~| ABS. |~| REL. |~| NG |~| CORRECTION |~| x
In case that the absolute relative total density correction exceeds x (default value: 0.1), the next step up is skipped.

GAMMA=1*
The value defines the optical depth = which separates the region of the line wing for which the core and the wing approximations shall be used.

IGNORE |~| CPU |~| TIME |~| LIMIT
set the security time (necessary to complete the job) equal 0. This can only be used if it is sure that the requested number of iterations can be completed within the jobs run time limit.

INCREASE |~| COLLISIONAL |~| RATES |~| BY |~| FACTOR |~| x
The collisional rates can be increased in order to simulate a LTE model atmosphere. The factor x has to be > 10⁺³⁰, in order to guarantee that collisions dominate the photosphere ...

INNER |~| BOUNDARY: |~| LAMBDA-ITERATION

INPUT-MODEL |~| FORMATTED

ITMAX=1*
maximum number of Scharmer iterations

JACOBI |~| FRESH-UP,INTERVAL 5*
calculation of the Jacobian every 5^th Scharmer iteration. Only valid in case of Broyden or Kantorovich method.

KANTOROVICH=2, |~| |~| |~| SWITCH LIMITS |~| |~| 0-->1, |~| 1-->2, |~| 2-->1 |~| : 1.E33* 0.1* 1.0*
like the BROYDEN card.

Newton-Raphson iteration
Jacobian is calculated at the beginning of every Scharmer iteration but then kept constant.
Jacobian is calculated at the beginning of the 1st Scharmer iteration but then kept constant. A new calculation of the Jacobian is done following the JACOBIFRESH-UP card (see above)

LINEARIZE |~| HYDROSTATIC |~| EQUATION
With this option the hydrostatic equation is solved simultaneously with the statistical equation and not (default) solved subsequently.

NO |~| RENORMALIZATION |~| OF |~| COMPLEX |~| LINE |~| CROSS |~| SECTIONS
undoes a previously made re-normalization of the sample cross-sections for iron group elements

NO |~| TEMPERATURE |~| CORRECTION
the radiative equilibrium is omitted from the linearization

T-CORRECTION |~| ONLY |~| IN |~| LOG |~| M |~| INTERVAL: |~| m_min m_max
the temperature correction is restricted to the selected log m interval.

T-CORRECTION |~| PROFILE: |~| X
the temperature correction is damped by simple functions (ND = total number of depth points)

X

1	depth point / ND
2	(depth point / ND)²
3

LAMBDA=3*
selects the $/\$ operator

$/\$ = 3	diagonal operator by Olson & Kunasz
$/\$ = 4	tridiagonal operator by Olson & Kunasz

Both operators are generally parameter-free. In practice, it is less time consuming to do a $/\$ iteration in the optical thin case. This can be done by requesting a special GAMMA parameter (see above).

In order to accelerate the convergence, both operator switch to core saturation if > 100.

LINEARIZATION |~| MODE: |~| BLOCK-MATRIX-ITERATION, |~| XX YY ZZ
with this option, only the occupation numbers of the given elements (here XX YY ZZ) are iterated. In combination with the card SOLVE STATISTICAL EQUATIONS ONLY, a “classical” line formation iteration is done. In all depth points, XX is Newton-Raphson iterated (inclusive constraint equations) first, then YY, and at least ZZ. Attention: this option alone does not switch off the constraint equations!

LINEARIZATION |~| MODE: |~| BLOCK-MATRIX-ITERATION, |~| ALL
like LINEARIZATION MODE: BLOCK-MATRIX-ITERATION, XX YY ZZ. All elements are iterated in order of their appearance in the atomic data file ATOMS.

MICROTURBULENCE |~| [KM/S] 0.0*
with this option, the microturbulence pressure is considered in the hydrostatic equation but not in the calculation of the line profiles!

NEWMAX=1*
maximum number of linearizations

OCCUPATION |~| PROBABILITY |~| FORMALISM |~| FOR |~| AA
the Hummer-Mihalas formalism is used to calculate the level dissolution for AA = H1 or AA = HE2

OPACITY |~| PROJECT |~| RBF |~| DATA |~| : START |~| AT |~| EDGE
PRO2 can calculate bound-free cross-section using data from the Opacity Project (OP). Here the OP data set is used and the cross-sections start at the threshold energy of the respective level.

OPACITY |~| PROJECT |~| RBF |~| DATA: |~| FULL |~| DATA |~| SET
see above, the complete OP data set is used (which may start at lower energy the the level energy in order to simulate the transition from the line absorption to the continuous absorption at the series limit.

OPACITY |~| PROJECT |~| RBF |~| DATA: |~| ONLY |~| EDGE |~| VALUE
see above, a mean value of the OP data at the threshold energy is calculated, then the absorption cross-sections are calculated using the Seaton formula in hydrogenic approximation.

OPACITY |~| PROJECT |~| RBF |~| DATA: |~| MISSING |~| HYDROGENIC
see above, for those levels which are not found in the OP data set hydrogen-like threshold cross-sections are calculated. Then, the Seaton formula is used.

OPACITY |~| PROJECT |~| RBF |~| DATA: |~| HYDROGENIC
see above, all bound-free transitions, which are found in the atomic data file ATOMS and request explicitly the use of OP data are calculated with hydrogen-like threshold cross-sections and the Seaton formula.

OUTPUT-MODEL |~| FORMATTED

RADIATIVE |~| EQUILIBRIUM: |~| DIFFERENTIAL/INTEGRAL |~| FORM
The radiative equilibrium is calculated using a combination of the differential and the integral method.

READ |~| NEW |~| TEMPERATURE |~| STRUCTURE
A temperature structure is read in from file TEMPERATURE.IN. This temperature may be interpolated from other models in order to speed up the calculation of “in-between” models. TEMPERATURE.IN is an ASCII table with log m and T, however, the log m values are ignored.

REDUCE |~| LOG |~| CVEC |~| x
This options scales the inhomogeneity vector of the linearized equations. This is useful to overcome numerical instabilities and to avoid too-large corrections in the beginning of the iterations. This card has to be inactivated to get a finally converged model.

SAVING |~| MODEL: |~| EACH |~| ITERATION
a temporary model (MODTMP) is saved in the working directory $TMPDIR. An example how to save this temporary model automatically in case of a failed model calculation is given in Sect. D.7.5.

SET |~| TEMPERATURE t log m₁ log m₂ [scaling factor]
within log m₁ < log m < log m₂, the model temperature is set to

t
cubic-spline interpolation of t
linear interpolation of t
t read from model TIN
t is temperature value of next depth point with log m > log m₂.
like t = -3, but an additional third argument (scaling factor) has to be given that is multiplied to the TIN temperature

SHIFT |~| EDGE |~| BBBBBBBBBBFFFFFFFFFF x
The absorption threshold of the level BBBBBBBBBBFFFFFFFFFF given in the TMAP code (Sect. 2.1) is artificially shifted to the frequency point x. Attention: The given frequency x has to fit exactly a point within the frequency grid FGRID! All shifts are printed to STDOUT.

SKIP |~| ATOM |~| AA |~| BELOW x
the element AA (flushed to the left) with occupation numbers less than x are eliminated from the statistical equations

SKIP |~| ION |~| III |~| BELOW x
ion III (flushed to the left) with occupation numbers less than x are eliminated from the statistical equations

SKIP |~| LEVELS |~| BELOW x
levels with occupation numbers less than x are eliminated from the statistical equations

SKIP |~| OCCDRVF |~| AFTER |~| 1ST |~| LINEARIZATION
The derivations of the source functions are only calculated once (in the 1st linearization) and then set equal 0. This saves an enormous amount of computational time but works well only in the case of almost converged models.

SOLVE |~| STATISTICAL |~| EQUATIONS |~| ONLY
switches off the constraint equations for n_e, n_H, n_g, T

SOLVE |~| STATISTICAL |~| EQUATIONS |~| ONLY |~| |~| |~| RE-SOLVE PARTICLE CONSERVATION
switches off the constraint equations for n_e, n_H, n_g, T within the Newton-Raphson iteration. The hydrostatic and particle conservation equations are solved subsequently.

SWITCH |~| OFF |~| LINES
All line transitions are ignored. Attention: sample lines of iron group element can not be switch off with this option.

TIME |~| LIMIT 2000*
cpu time for the job to calculate. Only valid on non-CRAY machines

TRANSITION |~| IN |~| DETAILED |~| RADIATIVE |~| BALANCE |~| XXXXXXXXXXYYYYYYYYYY
With this option, the radiative transition XXXXXXXXXXYYYYYYYYYY given in the TMAP code (Sect. 2.1) is calculated in detailed radiative equilibrium. Thus, this transition is eliminated from the statistical equations but not from the calculation of the opacities and emissivities.

UNSOELD-LUCY |~| TEMPERATURE |~| CORRECTION |~| DAMP= x
With this option, the radiative equilibrium is eliminated from the linearization. The temperature structure is calculated after the linearizations with the Unsöld-Lucy temperature correction method. The damping factor x is used to avoid over-corrections and numerical instabilities.

UPPER |~| AND |~| LOWER |~| LIMITS |~| FOR |~| RELATIVE |~| T-CORRECTION |~| t₁ t₂
The relative temperature corrections (iteration i) are limited to the range T_i ^. t₁ < T_i+1 < T_i ^. t₂ at all depth points.

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