C H + h u - ^ C + H 1.35(5) 1.83(4) N H A h v ^ N + H 1.87(4) 1.90(2) OH hu 0 H 1.67(4) 5.70(2) O2 T hp —y 2 0 3.50(4) 5.89(2) O f -h /ii/ ^ 0 + -h 0 4.46(5) 3.16(4) H~ -\-hu H-\-e~ 1.45(7) 9.72(5)
Table 2.2: Comparison of selected photorate coefficients com puted using black body {kbb) and synthetic {ksyn) spectra with a photospheric tem perature of
be seen to differ typically by up to two orders of magnitude in these examples with con siderable implications for the overall chemistry; with much reduced photodissociation and photoionisation, small molecules may form and survive more easily providing the possi bility of precursors to large molecule and dust grains forming earlier in the outflow than has been possible in previous models. This is one of the most im portant reasons for the differences between the results of this work and th a t which has gone before. To com pute photorate coefficients, the four synthetic spectra have been very simply param eterised with ju st a few points (less than 10). Rate coefficients are then calculated for each of these ra diation fields using the process described above. W ith rate coefficients calculated for each of four photospheric tem peratures, a third order polynomial is fitted to for each reaction. It was found most convenient to fit the polynomial to log A; as a function of Teff/10'* (see Appendix C for a complete list of coefficients). This function is used to interpolate a rate coefficient for any photospheric tem perature, the latter being calculated as in equation (2.8). However, these rates are calculated for reactions occurring at the photosphere; at greater distances the radiation field is diluted so we multiply the rate coefficient calculated by the standard dilution factor, W:
W{r) = i
(2.20)where Cgj and Vphot are the ejecta and photospheric radii respectively.
We believe this approach to be a considerable advance on previous m ethods of scal ing interstellar rate coefficients. A ttem pting to go further by, say, solving the radiative transfer equation would firstly not be practical in a model such as this where there ex
60 CHAPTER 2. MODELLING TECHNIQUES 9 10 ,-4 10 ,0 10' ,-4 C 10 2 000 W o v e l e n g t h i n A 4 0 0 0 2 0 0 0
.
W a v e le n g th in A 4000F ig u r e 2.1: S y n th e tic s p e c t r a re p ro d u c e d from Beck e t al. (1995). S p e c tr a c o r r e s p o n d i n g t o four different p h o to s p h e ric t e m p e r a t u r e s as given. E n iian ced C N O a b u n d a n c e s w ere used (fa c to r 10^ ab o v e solar) as a re implied by T N I l m odelling. T h e c o r r e s p o n d i n g black b o d y c o n tin u u m flux is also shown as a d a s h e d line.
ists co n sid e ra b le u n c e r t a i n t y as to b o th th e g e o m etrical d i s t r i b u t i o n o f th e e je c ta a n d t h e physical p ro p e rtie s , b u t w h ere only very few species have o p tic a lly thick t r a n s i t i o n s t h e gain would be negligible.
2.3.1 P h o to r ea c tio n s where no cross-section data are available
W h i l s t for t h e early m odel p re se n te d in c h a p t e r 3 cross-section d a t a w as available for m o s t o f t h e i m p o r t a n t r e a c tio n s used, d a t a was not available for all t h e p h o t o r e a c t i o n s of t h e l a te - tim e m odels p re s e n te d in c h a p t e r 4. T h e only obvious a l t e r n a t i v e is t o r e t u r n to t h e flux r a tio m e t h o d of c a lc u la tin g a r a t e coefficient from coefficients valid in t h e LSAI. Using a black b o d y field is n o t d esirab le however; it has a lre a d y been n o te d t h a t t h e black b o d y flux is often c o n s id e ra b ly g r e a t e r t h a n for realistic r a d ia tio n fields so a b e t t e r s o lu tio n is req u ired . We do, o f course, have s y n th e tic s p e c t r a which m ig h t be used in a sim ilar p rocess however. O n c e a g ain , p a r a m e t e r i s a t i o n s of th e fo u r s p e c t r a p e rm it t h e flux a t a