The latest free 32-bit or 64-bit GNAT compiler may be obtained from the AdaCore site
or any of the numerous Linux distributions.

The following files are required for the calculation of a solar or stellar Stokes spectrum
 

• colin_slc_23_06_2022.ada
• lines.inp
• cossam_solar.inp
• cossam_stellar.inp
• cossam_corot.inp
• grev_sau.abund.orig
  
• HD326_lines.list         (or another identically formatted atomic transition list)
• t12000_400_1000G_0d.fil  (atmospheric file provided by Atlas12_ada)

The file  colin_slc_23_06_2022.ada  contains many packages, procedure and functions. GNAT users

have to split (gnatchop) this file, because GNAT requires different compilation units to be in different files.

The following command will split the file:      gnatchop  -w  colin_slc_23_06_2022.ada

Note:  The -w option overwrites existing files.

After splitting (gnat-chopping)  colin_slc_23_06_2022.ada  you have to create the executables  lines 

and  cossam_slc  by issuing the following 2 commands:

     gnatmake  -O3  -gnatfvp  lines
     gnatmake  -O3  -gnatfvp  cossam_slc

Note:  In order to be able to execute lines or cossam_slc, make sure that your system provides

unlimited stacksize. With the tcsh shell for example set "limit stacksize unlimited"

One has now to create the auxiliary files containing the atomic line data; this is done by invoking

    ./lines  lines.inp

lines_run.2062167039	log file
sysom_ess.2062167039	essential model and abundance data
sysom_line.2062167039	data for all the selected lines
sysom_stream.2062167039	binary line data

would be line data and log files created by  lines  on 2022-06-21  18:37

What you have to specify in the input file  lines.inp

1. Number of processors
2. Atmospheric model file
3. Atomic transition list file
4. Zeeman splitting option

   '-'	Lande factors as given in the line file; set to unity if unknown (=99.00)

5. Hydrogen option
   

   'h' or 'H'	Hydrogen line profiles according to the analytical formula of Hubeny
   '-'	No hydrogen lines considered

6. Lower-upper level limit
   

   '0.6667'

   leave unchanged

7. Stark option

   'a', 'A'	Stark broadening according to Gonzalez et al. 1995, A&A, 297, 223
   'v', 'V'	Stark broadening as given in the atomic transition list file; zero if not listed
   'n', 'N'	Stark broadening set zo zero and Unsoeld van der Waals broadening

8. Line strength option

   '-'	Oscillator strengths log gf as given in the line file

9. Partition functions (4-character string)

   'KCIB'

   Cossam uses the Kurucz partition functions from Atlas, leave unchanged

10. Lower limit in lambda (in Angstroms)
11. Upper limit in lambda (in Angstroms)
12. Rel. line opacity contr. limit (typically 0.001 or 0.0005) :
    a line is only considered if the ratio (central line opacity) / (cont. opacity)
    exceeds this limit at any one optical depth
13. Microturbulence (in km/s)
14. Abundance file name
15. The input file has to end with FIN
    
    
    

Step 6a :  The  solar  option of the code is invoked by

    ./cossam_slc  input_file  sysom_ess_extension
 

input_file	sysom_ess_extension
any arbitrary file name is permitted, e.g. cossam_solar.inp	the 10-digit extension of the line data files created with lines

Step 6b :  What you have to specify in the input file cossam_solar.inp

1. Number of processors (cores)
   
2. Sub-Interval size
3. Atmospheric model file
4. Polarised formal solver option

   'Z'	Zeeman Feautrier solver (default)
   'z'	Zeeman Feautrier solver without magneto-optical terms

5. Hydrogen option (must agree with the values given in 'lines.inp')
   Cossam checks for contradictions. You may only exchange 'h' for 'H' and vice versa

   'h' or 'H'	Hydrogen line profiles according to the analytical formula of Hubeny
   '-'	No hydrogen lines considered

6. Lower limit in lambda (in Angstroms)
7. Upper limit in lambda (in Angstroms)
8. Step size in lambda   (in Angstroms)  or  in velocity (in km/s)
   
9. Abundance file name
10. Line selection file name
    

    'file_name'	The spectrum is synthesised only over intervals of +- 1.5 Angstroem centred on each line listed in this file, located between the lower and the upper limit in lambda.
    '-'	no such selection, the spectrum is synthesised for the whole spectral region located between the lower and the upper limit in lambda.

    
    

Finally there is the keyword  SOLEIL (soleil),  followed by the magnetic model data,
 

1. Position  mu = cos(theta)  on the solar disk
2. Field strength   (in Gauss)
3. Field angle (angle between field vector and line-of-sight)  (in degrees)
4. Field azimuth    (in degrees)
    
   
   

Step 7a :  The  stellar  option  (with observer-centred grid)  of the code is invoked by 

    ./cossam_slc  input_file  sysom_ess_extension

 

input_file	sysom_ess_extension
Any arbitrary name is permitted, e.g. cossam_stellar.inp	the 10-digit extension of the line data files created with lines

Step 7b :  What you have to specify in the input file cossam_stellar.inp

1. Number of processors (cores)
   
2. Sub-Interval size
3. Atmospheric model file
4. Polarised formal solver option

   'Z'	Zeeman Feautrier solver (default)
   'z'	Zeeman Feautrier solver without magneto-optical terms

5. Hydrogen option (must agree with the values given in 'lines.inp')
   Cossam checks for contradictions. You may only exchange 'h' for 'H' and vice versa

   'h' or 'H'	Hydrogen line profiles according to the analytical formula of Hubeny
   '-'	No hydrogen lines considered

6. Lower limit in lambda  (in Angstroms)
7. Upper limit in lambda  (in Angstroms)
8. Step size in lambda     (in Angstroms)  or  in velocity  (in km/s)
   
9. Abundance file name
10. Line selection file name
    

    'file_name'	The spectrum is synthesised only over intervals of +- 1.50 Angstroem centred on each line listed in this file, located between the lower and the upper limit in lambda.
    '-'	no such selection, the spectrum is synthesised for the whole spectral region located between the lower and the upper limit in lambda.

    
    

Finally there is the keyword  ETOILE (etoile),  followed by the Oblique Rotator Model data  --  for their

definition see  Stift, MNRAS 172, 133 (1975)  -- and the grid data

1. The inclination i                            (in degrees)
   The 3 Eulerian angles alpha, beta, gamma     (in degrees)
   The decentring parameters y_2 and y_3   [-1 < y_2 < 1,  -1 < y_3 < 1]
2. The dipole moment - half the polar field strength for a centred dipole  (in Gauss)
   The projected rotational velocity  v sin i   (in km/s)
   The rotational phase   [0 <= Phase_rot < 1]
3. The pulsation velocity Vp                    (in km/s)
   The pulsational phase  [0 <= Phase_pul < 1]
   The "quantum numbers" L_puls and M_puls of non-radial pulsation
4. 5 "magic numbers" for the determination of the spatial grid
   
   
   

Step 8a :  The  stellar  option  (with co-rotating grid)   of the code is invoked by 

    ./cossam  input_file  sysom_ess_extension

 

input_file	sysom_ess_extension
Any arbitrary name is permitted, e.g. cossam_corot.inp	the 10-digit extension of the line data files created with lines

Step 8b :  What you have to specify in the input file cossam_corot.inp

1. Number of processors (cores)
   
2. Sub-Interval size
3. Atmospheric model file
4. Polarised formal solver option

   'Z'	Zeeman Feautrier solver (default)
   'z'	Zeeman Feautrier solver without magneto-optical terms

5. Hydrogen option (must agree with the values given in 'lines.inp')
   Cossam checks for contradictions. You may only exchange 'h' for 'H' and vice versa

   'h' or 'H'	Hydrogen line profiles according to the analytical formula of Hubeny
   '-'	No hydrogen lines considered

6. Lower limit in lambda  (in Angstroms)
7. Upper limit in lambda  (in Angstroms)
8. Step size in lambda   (in Angstroms)  or  in velocity  (in km/s)
   
9. Abundance file name
10. Line selection file name
    

    'file_name'	The spectrum is synthesised only over intervals of +- 1.50 Angstroem centred on each line listed in this file, located between the lower and the upper limit in lambda.
    '-'	no such selection, the spectrum is synthesised for the whole spectral region located between the lower and the upper limit in lambda.

    
    

Finally there is the keyword  CO-ROT (co-rot),  followed by the Oblique Rotator Model data  --  for their

definition see  Stift, MNRAS 172, 133 (1975)  --  and the grid data

1. The inclination i                            (in degrees)
   The 3 Eulerian angles alpha, beta, gamma     (in degrees)
   The decentring parameters y_2 and y_3   [-1 < y_2 < 1,  -1 < y_3 < 1]
2. The dipole moment - half the polar field strength for a centred dipole  (in Gauss)
   The projected rotational velocity  v sin i   (in km/s)
   The number of rings (permitted values are : 6,  8,  9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90)

   No. of rings	No. of surface elements
   8	80
   15	284
   24	732
   40	2034
   90	10310

3. The pulsation velocity Vp    (in km/s)
   The pulsational phase   [0 <= Phase_pul < 1]
   The "quantum numbers" L_puls and M_puls of non-radial pulsation
4. The number of rotational phases
5. The rotational phases   [0 <= Phase_rot < 1]
   (there can be only 10 phases per line; 25 phases for example have to be specified on 3 lines)
   

The results of the calculations are written into the file(s)

    cossam_pprof.[10-character-extension]                    in the solar case

    cossam_pprof.[10-digits-extension]                       in the stellar (observer-centred) case

    cosrot_pprof.[phase-number][10-digits-extension]         in the stellar (corotating grid)  case

There are 6 columns:

        wavelength  (in Angstroms)
        Stokes I
        Stokes Q
        Stokes U
        Stokes V
        Continuum

 You get the following log files as a function of these commands

    ./cossam_slc  cossam_solar.inp    sysom_ess_extension    =>  cossam_run.[10-character-extension]
    ./cossam_slc  cossam_stellar.inp  sysom_ess_extension    =>  cossam_run.[10-digits-extension]
    ./cossam_slc  cossam_corot.inp    sysom_ess_extension    =>  cossam_run.[10-digits-extension]

The "magic" 5 numbers
determining a spatial integration grid 

Stift's adaptive grid

The idea for an adaptive spatial integration grid for stellar line profiles subject to rotational and/or pulsational broadening, with or without large-scale magnetic fields, has been first presented by M.J. Stift, MNRAS 217, 55 (1985). A detailed presentation of the underlying philosophy and application to a variety of problems can be found in R.M. Fensl, A&AS 112, 191 (1995).

In short, Stift's scheme ensures that the differences in monochromatic opacity between any 2 adjacent spatial quadrature points on the stellar disk do not exceed some fixed percentage. This makes it possible to employ robust integration algorithms without sacrificing accuracy.

• Doppler shifts due to rotation and/or pulsation
• changes in the direction of the magnetic field vector to the line of sight
• changes in the azimuth of the magnetic field vector
• limb darkening

Del  R_dop  R_cos  R_azi  R_flux :  5.0  2.5  0.5  0.5  2.0

• Del:  an empirical (small) constant which ensures monotonicity of the resolution function
• R_dop: the difference in Doppler shifts between any 2 adjacent points must not exceed 2.5 Doppler widths
• R_cos: the difference in cos(gam)  and in sin^2(gam) - where gam is the field angle - must not exceed the value of 0.5
• R_azi: the difference in sin(2*chi)*sin^2(gam) and in cos(2*chi)*sin^2(gam) - where chi is the azimuth - must not exeed the value of 0.5
• R_flux: the difference in continuous intensity must not exceed a factor of 2

Incl  Alp  Bet  Gam  y_2  y_3   : 50.0   -70.0   40.0   30.0   0.15   -0.10

Dipole moment   Vrot  phi_rot   :  5000.0   17.5   0.000

Landstreet's constant grid

Some (most?) users will prefer to use a grid that is not quite as efficient and sophisticated, but much easier to handle. It is based on a simple recipe given by J. Landstreet and provides equidistant annuli, with the number of quadrature points on each annulus strictly proportional to its radius.

Del  R_dop  R_cos  R_azi  R_flux :  8.0  10.0  0.0  0.0  0.0

• Del:  gives the number of annuli, which in this case number 8
• R_dop: gives the number of quadrature points on the innermost annulus, in this case 10 points; there will be 9- quadrature points on the outermost annulus.
• R_cos, R_azi, R_flux: at least 1 of these parameters has to be set to zero, otherwise COSSAM would try to establish an adaptive grid. The grid does not depend on the values of these 3 parameters.