1. An introduction to the MULTI radiative transfer code Lars Heggland Institute of Theoretical Astrophysics, University of Oslo Kwasan Observatory, Kyoto University

2. Radiative transfer The study of generation and transport of radiation in stellar atmospheres The study of generation and transport of radiation in stellar atmospheres Important physical processes: Important physical processes: Absorption Absorption Emission / reemission Emission / reemission Scattering Scattering  Formation of spectral lines

3. Why is this important? Radiation is one of the few ways to directly collect information about a star Radiation is one of the few ways to directly collect information about a star Spectral line formation is highly dependent on physical parameters such as: Spectral line formation is highly dependent on physical parameters such as: Temperature (ionisation states, intensity) Temperature (ionisation states, intensity) Velocity fields (Doppler shifts) Velocity fields (Doppler shifts)

4. Why is this important? Thus, a wealth of information is contained in spectral lines Thus, a wealth of information is contained in spectral lines By studying specific lines, we can get information about conditions from the photosphere (neutral or singly ionised lines, 5-10000 K) to the corona (highly ionised metal lines, 1 MK ++) By studying specific lines, we can get information about conditions from the photosphere (neutral or singly ionised lines, 5-10000 K) to the corona (highly ionised metal lines, 1 MK ++)

5. Numerical radiative transfer The aim: using theoretical models to explain and reproduce observations The aim: using theoretical models to explain and reproduce observations OR: using models to predict future observations OR: using models to predict future observations The problem is non-trivial due to the complexity of the physical processes and of the atmosphere; simplifications required The problem is non-trivial due to the complexity of the physical processes and of the atmosphere; simplifications required

6. Numerical radiative transfer Real atoms have hundreds of different energy levels Real atoms have hundreds of different energy levels Very computationally intensive Very computationally intensive Many levels have little effect on the studied line Many levels have little effect on the studied line  Make simplified, smaller atomic models Compute one element at a time Compute one element at a time

7. The MULTI code A non-LTE radiative transfer code written by Mats Carlsson A non-LTE radiative transfer code written by Mats Carlsson Written in standard compliant Fortran- 77; designed for portability Written in standard compliant Fortran- 77; designed for portability Freely available for use: http://www.astro.uio.no/~matsc/mul22/index.html Freely available for use: http://www.astro.uio.no/~matsc/mul22/index.html http://www.astro.uio.no/~matsc/mul22/index.html

8. The MULTI code Works in 1D; multi-dimensional analysis can be done by computing several different rays Works in 1D; multi-dimensional analysis can be done by computing several different rays Uses a given background atmosphere; dynamics (waves etc.) can be taken into account by running a simulation for each timestep Uses a given background atmosphere; dynamics (waves etc.) can be taken into account by running a simulation for each timestep

9. The MULTI code Powerful, but complex Powerful, but complex The amount of input data and parameters is high The amount of input data and parameters is high Patience required, experience very useful Patience required, experience very useful Impressive amounts of output data make it worth it Impressive amounts of output data make it worth it

10. Documentation Main: A computer program for solving multi-level non-LTE radiative transfer problems in moving or static atmospheres (available on Carlsson’s website, 46 pages plus appendices) Main: A computer program for solving multi-level non-LTE radiative transfer problems in moving or static atmospheres (available on Carlsson’s website, 46 pages plus appendices) Update: mul22.ps (included in distribution) Update: mul22.ps (included in distribution) multi.help, variables.doc (included) multi.help, variables.doc (included)

11. Input files ATOM: Atomic model (example: 6- level calcium) ATOM: Atomic model (example: 6- level calcium) Complex, but needs only be done once Complex, but needs only be done once CA 2 * ABUND AWGT 6.3304 40.08 *NK NLIN NCNT NFIX 6 5 0 5 * E G ION 0.00000 2.00000 'CA II 3P6 4S 2SE ' 2 13650.248 4.00000 'CA II 3P6 3D 2DE 3/2' 2 13710.900 6.00000 'CA II 3P6 3D 2DE 5/2' 2 25191.535 2.00000 'CA II 3P6 4P 2PO 1/2' 2 25414.465 4.00000 'CA II 3P6 4P 2PO 3/2' 2 95785.470 1.00000 'CA III GROUND TERM ' 3 * F NQ QMAX Q0 IW GA GVW GS 4 1 3.3000E-01 40 300. 3. 0 1.48E08 1.62 3.0E-06 5 1 6.6000E-01 40 300. 3. 0 1.50E08 1.61 3.0E-06 4 2 4.4200E-02 40 75..3 0 1.48E08 2.04 3.0E-06 5 2 8.8300E-03 40 75..3 0 1.50E08 2.01 3.0E-06 5 3 5.3000E-02 40 75..3 0 1.50E08 2.01 3.0E-06 * J I P A0 TRAD ITRAD 6 1 1 2.0363E-19 5915. 2 6 2 1 6.1484E-18 5755. 2 6 3 1 6.1484E-18 5755. 2 6 4 1 2.3823E-18 4925. 2 6 5 1 2.3823E-18 4925. 2 * COLL CA2COL 1.71E-07 1.71E-07 4.27E-07 2.92E-07 1.31E-06 2.08E-07 2.92E-07 2.93E-07 1.29E-06 3.05E-07 1.45E-10 1.88E-10 1.88E-10 2.68E-10 2.68E-10

12. Input files ATMOS: Model atmosphere (example: truncated VAL3C) ATMOS: Model atmosphere (example: truncated VAL3C) Specified on lg column mass, lg optical depth (  500 ) or geometrical depth scale Specified on lg column mass, lg optical depth (  500 ) or geometrical depth scale VAL3C MASS SCALE * LG G 4.44 * NDEP 52 *LG COLUMN MASS TEMPERATURE NE V VTURB -5.279262E+00 4.470000E+05 1.205000E+09 0. 1.128000E+01 -5.270430E+00 1.410000E+05 3.839000E+09 0. 9.870000E+00 -5.269783E+00 8.910000E+04 5.961000E+09 0. 9.820000E+00 -5.268492E+00 5.000000E+04 9.993000E+09 0. 9.760000E+00 -5.267285E+00 3.700000E+04 1.318000E+10 0. 9.730000E+00 * HYDROGEN POPULATIONS * NH(1) NH(2) NH(3) NH(4) NH(5) NP 2.3841E+03 7.9839E-04 2.0919E-04 2.3110E-04 2.9470E-04 1.0030E+09 5.3401E+04 1.8790E-02 7.4560E-03 8.1751E-03 1.0430E-02 3.1990E+09 2.4030E+05 7.5740E-02 2.9400E-02 3.1550E-02 4.0101E-02 5.0310E+09 2.7390E+06 6.7709E-01 1.7230E-01 1.7180E-01 2.1430E-01 9.0170E+09 1.3850E+07 3.2580E+00 4.7581E-01 4.3231E-01 5.2440E-01 1.1970E+10 3.6271E+07 9.2240E+00 8.6389E-01 7.2180E-01 8.5328E-01 1.3710E+10

13. Input files DSCALE: Depth scale to use for calculations DSCALE: Depth scale to use for calculations Does not need to use the same values as the atmosphere model; interpolation is performed Does not need to use the same values as the atmosphere model; interpolation is performed MV45C3 MASS SCALE 45 -6.672232 -5.22498 -5.21206 -5.20977 -5.20795 -5.20536 -5.20078 -5.19238

14. Input files INPUT: Run and output options INPUT: Run and output options Controls starting approximation, number of iterations, convergence limit… Controls starting approximation, number of iterations, convergence limit… Trial and error required for best results Trial and error required for best results DIFF=5.0,ELIM1=0.01,ELIM2=0.001,QNORM=12.85,THIN=0.1, IATOM2=0,ICONV=1,IHSE=0,ILAMBD=0,IOPAC=1,ISTART=2,ISUM=0, ITMAX=300,ITRAN=0,NMU=3, IWABND=0,IWATMS=0,IWATOM=0,IWCHAN=0,IWDAMP=0,IWEMAX=1,IWEQW=0, IWEVEC=0,IWHEAD=0,IWHSE=0,IWLGMX=1,IWLINE=0,IWLTE=0,IWN=0,IWNIIT=0, IWOPAC=0,IWRAD=0,IWRATE=0,IWSTRT=0,IWTAUQ=0,IWTEST=0,IWWMAT=0, IWARN=2,IOPACL=0,ISCAT=0,INCRAD=0,INGACC=1,ICRSW=0, IDL1=1,IDLNY=1,IDLCNT=1

15. Input files ABUND, ABSDAT: used to calculate background opacities ABUND, ABSDAT: used to calculate background opacities Should not need to be changed in a solar photosphere/chromosphere model Should not need to be changed in a solar photosphere/chromosphere model …maybe in the corona and in other stars …maybe in the corona and in other stars

16. Output Lots of data! (See variables.doc) Lots of data! (See variables.doc)variables.doc Intensity, flux, line source functions, population densities, transition rates… Intensity, flux, line source functions, population densities, transition rates… Data written to be readable by IDL; reading and analysis routines are included in the distribution Data written to be readable by IDL; reading and analysis routines are included in the distribution

17. Sample output: C I line in transition zone (pdf file)