How to SYN in Seven Easy Steps

T. A. Nieminen and J. E. R. Ross

Physics Department, The University of Queensland QLD 4072, Australia
+617-3365 3405, +617-3365 1242, timo@physics.uq.edu.au

Introduction

The solar disk centre spectrum can be calculated by (numerically) solving the radiative transfer equation:
m dIl
dtl
= Il - Sl
(1)
where Il is the frequency and depth dependent specific intensity, Sl is the source function, and tl is the optical depth. Given suitable boundary conditions and the source function Sl(tl), the solution is reasonably straightforward. Here we present a recipe in seven easy steps for developing spectral synthesis software such as SYN [1,2].

For an atmosphere in LTE, we can assume that the source function is equal to the Planck radiation function, so Sl(z) = Bl(z). Unfortunately, it is not sufficient to know Sl as a function of physical depth z; we must convert the physical depth scale to an optical depth scale:
tl(z) = ó
õ 		¥

z 
 r(z¢) kl(z¢) dz¢
(2)
This requires calculation of the opacity kl.

Opacity

The core of a spectral synthesis program must be the calculation of opacity. The opacity can be considered to consist of a continuous opacity, and opacity due to atomic line transitions. The main contribution to the continuous opacity is due to bound-free and free-free H- transitions; other major sources (H2+ molecule, photoionisation of metals) also need to be considered. The line opacity can be found from the line strength and line profile for each line in the spectral region of interest.

The recipe

1 Calculate Sl(z) 4 Calculate optical depth scale
2 Calculate continuous opacity 5 Effect of large scale mass motion
3 Calculate line opacities. 6 Numerical integration of radiative
 This requires:  transfer equation (1)
 * line strengths 7 Non-plane parallel corrections
 * damping   
 * thermal and mass motion   

Summary

A recipe for the implementation of spectral synthesis software is presented. The accuracy, efficiency, and ease of implementation of various techniques is considered. Example software will be demonstrated.

References

[1]
J. E. R. Ross SYN spectral synthesis software, http://www.uq.edu.au/~phjross/syn.htm

[2]
T. A. Nieminen MATSYN spectral synthesis toolbox for MATLAB,
http://www.physics.uq.edu.au/people/nieminen/syn.html