4 Start Models

Start models are necessary for the programs PRO2 and LINE1. They can come from different sources. Within the Tübingen NLTE Model-Atmosphere Package (TMAP)all models can be used as start models. It is distinguished between two types of start models.

4.1 PRO2 and LINE1 Models

A model which is calculated by PRO2 or LINE1 can be used as start model. The convergent models (with the same parameters, same ATOMS and FGRID) from both programs should be identical.

New NLTE-levels, i.e. levels that are not found in the start model, are set to LTE occupation numbers. This is valid especially for completely new elements and can be a problem in the case of higher elemental abundances due to the inconsistency in the conservation of particles ...

For the detailed calculation of line profiles, automatic multiplet splitting is optional in LINE1 for all C IV, N V, O VI levels and a wide variety of C III, N IV, and O V levels. The list of multiplets is permanently updated.

4.2 “LTE” Models

The program LTE2 produces “LTE” models (without any consideration of line blanketing) within a large range of photospheric parameters. The created model has PRO2 format and is a start model for PRO2 or LINE1.

4.3 Calculation of a LTE2 Model

The program LTE2 calculates models in gray approximation. It uses the same atomic data (ATOMS, Sect. 2) and frequency grid files (FGRID, Sect. 3) like PRO2 and LINE1. No line blanketing is considered. LTE2 is controlled via the input file DATEN with a number of options (Sect. 4.3.2).

4.3.1 The Method

The program LTE2 calculates a model atmosphere based on the requested effective temperature Teff, surface gravity g, chemical composition, and the files ATOMS and FGRID.

An equidistant log scale ( is the Rosseland optical depth) with ND depth points (Sect. 1) is created on which start values for the temperature stratification are calculated. This log scale can be manipulated by some options (see below).

With the basic assumption of LTE,

Sn =_ Bn (T ),

the mean intensity of the radiation field is

-p-- 4 J (t) = S(t ) = B [T (t)] = s .T R

i.e. the flux is constant ( dH-
dt = J - S 0). Thus, also the 1st moment of the radiation field dK-
dt = H is constant and yields the exact integral

1 K (t ) = H .t + c = --F .t + c 4

From this, we get K() --> 1
4 F ^. for » 1. K() = 1
3 J() for » 1 is the general solution for the intensity

3 J (t ) = --F [t + q(t)] 4

The temperature at the depth point l is

V~ 3--------------------- Tl = 4--.Teff 4 .[tl + q(t )] 4

q() is called Hopf function.

The hydrostatic equation is solved in inside direction. The first four (outer) depth points are treated following the Runge-Kutta method. Then, the other points are calculated with a predictor-corrector method of Ham. In detail, the electron density at each depth point is calculated for the actual temperature and the given photospheric composition. The iteration method is based on Mihalas, Stellar Atmospheres, Second Edition, 5-2. Subsequently, LTE2 calculates LTE occupation numbers for all levels of all elements using the Saha-Boltzmann equation. From these values, the Rosseland mean opacity _R is determined.

1 p integral oo -1 @Bn ---- =_ ------3- k n .-----dn ¯kR 4sRT 0 @T

LTE2 gives as result the electron density as well as the total particle density for the whole atmosphere. The original log scale is transformed into a log m scale (m is the mass column density, measured from the outer limit of the atmosphere).

In practice, the temperature stratification of the inner atmosphere differs evidently from a “real” LTE or NLTE stratification, even for pure continuum models without consideration of line blanketing. Thus, with these start models, PRO2 or LINE1 need a relatively large number of iterations to calculate the right temperature structure. In order to reduce this number of iterations, an Unsöld-Lucy temperature correction can be carried out until the temperature structure is stable. Some option can be given to control the temperature correction method. (Sect. 4.3.2).

4.3.2 The Options

With some directives in the input file DATEN, LTE2 can be controlled. Especially, the photospheric parameters line effective temperature Teff, surface gravity g, and photospheric abundances (which are necessary in any case) are selected.

The input file DATEN for the program LTE2 has the following structure (Sect. 5.4):

DATEN
T |~| EFF |~| T
LOG |~| G |~| g
ABUNDANCE |~| xx hh

T has to be given in Kelvin; g in cgs; xx element in TMAP code (Sect.2.1), hh abundance fraction by particle numbers.

Please note that sum _i=1^NATOMShh_i = 1! LTE2 will check this. In the case that sum = 1, LTE2 will adopt the given abundances unchanged; if not, LTE2 will re-normalize the given values! Please check STDOUT for respective information!

TAU |~| SCALE |~| MINIMUM |~| -8.0*
This option sets the limit (log ₁) of the outer atmosphere. This limit can be varied under the premise that the atmosphere has to be optically thin over the complete frequency grid at least at the first depth point. (This is one of the basic assumptions of PRO2 and LINE1. Attention: the requested value is only a start value which can be different from that of the finally calculated “LTE” model.

TAU |~| SCALE |~| MAXIMUM |~| 2.6*
This option sets the limit (log _ND) of the inner atmosphere. This limit can be varied under the premise that the atmosphere has to be optically thick over the complete frequency grid at least at the inner depth point. (This is one of the basic assumptions of PRO2 and LINE1. Attention: the requested value is only a start value which can be differ from that of the finally calculated “LTE” model.

TAU |~| SCALE |~| x y z
This option defines the arrangement of the inner depth points.

z = 0.0: depth points are logarithmically equidistant, Δ = (start values)
z > 0.0: like z = 0.0, but the distance (start value) of the innermost depth points (89-90) is z (default is z = 1.0E - 05)
z < 0.0: like z = 0.0, but the distance of the depth points (x y) decreases logarithmically by the factor z

ITMAX=100*
maximum number of iterations of the Unsöld-Lucy temperature correction method
In the case that a negative temperature is detected, LTE2 will stop immediately. The output model contains then the atmospheric structure of the iteration before.

DAMP=0.5*
start value of an artificially introduced damping factor within the Unsöld-Lucy temperature correction method. This factor is partly necessary because the method appears to be unstable in most cases. In the course of the iterations, this value is automatically reduced to increase the stability — this might seem to be convergence ...

EPS=1.0E-6*
“convergence” (see above) limit (to stop the Unsöld-Lucy temperature correction)

LTE2 |~| START |~| MODEL
This option is only valid if the file TIN is available which is the original file TOUT of a former LTE2 run and contains the temperature stratification of the previously calculated “LTE” model.

This option is helpful if a model has not reached the “convergence” limit (see above) in the first run and shall be brought to a better “convergence”. Moreover, the “fake convergence” due to the automatically reduced damping factor can be checked.

OUTPUT |~| MODEL |~| FORMATTED
The output model is saved formatted.

PRO2 |~| START |~| MODEL
This option is only valid if a PRO2 or LINE1 model is supplied as start model MIN. This is helpful to introduce new elements or to vary their abundance ratios. The temperature stratification of a convergent NLTE model is used here to calculate LTE occupation numbers (particle conservation) for all levels of all elements. With this option, ITMAX=0 is set automatically, to preserve the temperature structure. A follow-up line formation calculation (i.e. at fixed temperature) with PRO2 or LINE1 supplies a start model with NLTE occupation numbers and a — hopefully — good approximation of the final temperature stratification.

The following options can be given to control the output of LTE2. Their meaning should be clear ... XXXX can be substituted by EACH or LAST.

PRINT |~| ABUNDANCES
PRINT |~| EMERGENT |~| FLUX
PRINT |~| INTEGRATED |~| EDDINGTON |~| FLUX,ITERATION,XXXX
PRINT |~| OPTIONS
PRINT |~| MODEL |~| ATOMS |~| (OVERVIEW)
PRINT |~| LEVELS
PRINT |~| LTE |~| MODEL
PRINT |~| TEMPERATURE |~| CORRECTIONS,ITERATION,XXXX,ALL |~| DEPTHS
PRINT |~| TEMPERATURE |~| CORRECTIONS,ITERATION,XXXX,MAX.
PRINT |~| WARNINGS

The final model is saved by LTE2 into the file MODELL. The last record in MODELL is:

MODPRG,DATE,TIME

(CHARACTER MODPRG*5,DATE*8,TIME*8 with MODPRG=’LTE2 ’, DATE and TIME with actual creation time) is added in order to identify the model. The temperature structure of the model is saved in the file TOUT (see above).

The program LTE2 is available at Tübingen’s PC/Workstation cluster in its latest version:
/home/rauch/bimod/lte2.Linux_x64.

The actual PARAMETERs are:

• NATOMAX =    3
• NIONMAX =    9
• NLMAX   =  139
• LTEMAX  =  109
• NFMAX   = 1299

Other executables of LTE2 with different PARAMETERs have to be created (Sect. 1).

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