Spectroscopic analysis of stellar atmosphere chemical compositio

Aller, L. H.

English

NASA Technical Reports Server

, .. f 'The Chemical Composition of Normal S t e l l 7 r  Atmospheres f, d 
One must recognize t h a t  t h e  determination of t h e  chemical 
compositions o f  s t e l l a r  atmospheres i s  bese t  with a number 
o f  d i f f i c u l t i e s ,  which p e r s i s t  even a f t e r  decades o f  progress  
i n  t h e o r e t i c a l  i n t e r p r e t a t i o n  and t e c h n i c a l  improvements i n  
observa t iona l  and experimental c a p a b i l i t i e s .  
i s  t h a t  we cannot gouge out a sanple of a star and analyse 
it by conventional methods; we a r e  r e s t r i c t e d  t o  spectro- 
scopic  data! 
The d i f f i c u l t y  
There a r e  some important d i f f e rences  between t h e  a n d y s i s  
o f  a s t e l l a r  atmosphere and a spectrochemical a n a l y s i s  t h a t  
must be s t r e s s e d  a t  t h e  o u t s e t .  A spectrochemical a n a l y s i s  
involves  t h e  comparison of a sample and a s tandard whose spec- 
t r a  a r e  produced under i d e n t i c a l  condi t ions of e x c i t a t i o n .  
Since one proceeds by a n u l l  method, a determinat ion of t h e  
a c t u a l  q u a n t i t a t i v e  r e l a t i o n s h i p  between t h e  i n t e n s i t y  o f  a 
l i n e  and t h e  number of a t o m s  a c t i n g  t o  produce it i s  not 
requi red .  
The astronomical problem i s  b a s i c a l l y  d i f f e r e n t  i n  t h a t  
one must e x t r a c t  from t h e  observed d a t a ,  not only t h e  requi red  
abundances o f  t h e  elements involved, but a l s o  e s s e n t i a l  para- 
meters of t h e  s t e l l a r  atmosphere - s ince  t h e  appea-mce of any 
s p e c t r a l  l i n e s  depends in t ima te ly  on t h e  temperatu?e and sur- 
f ace  g rav i ty  o f  a s tw  and how t h e  t ; p m p e r n t i i r e  and c?e:nsit;*. 
vary with depth. 
The observat ionnl  da ta  cons i s t  of  measurement.; of t h e  
p o s i t i o n  h (wavelength) of t h e  cen te r  of 3 l i n e ,  t h e  t o t 3 1  
*mount of  energy subt rac ted  by t h e  l i n e  from t h e  continuous 
spectrum (equivalent  width),  and t h e  shape or p r o f i l e  of t h e  
l i n e .  
t h a t  t h e  l i n e s  f r equen t ly  overlap.  
for an abundant metal l i k e  i r o n  which i s  represented i n  solar- 
type  stars by hundreds of l i n e s ,  but becomes a se r ious  prob- 
lem f o r  t h e  very weak l i n e s  of Tare elements. I n  : iddit ion,  
we o f t en  have measurements of t h e  s p e c t r a l  energy d i s t r i b u t i o n  
which g ives  s i g n i f i c a n t  c lues  to t h e  temperature 0 "  t h e  s t a r ,  
p a r t i c u l a r l y  when it can be compared with p red ic t ions  of 
moclern t h e o r i e s  o f  s t e l l a r  atmospheres. In s t a r s  h o t t e r  than  
t h e  sun, one can employ t h e  shapes o f  t h e  hydrogen l i n e s  i n  
order  t o  e s t a b l i s h  s t e l l a r  sur face  g r a v i t i e s ,  provLded t h a t  t h e  
temperature hz~s been reasonably IrJell e s t ab l i shed .  
The problem i s  f u r t h e r  complicated by t h e  circunstance 
This provides  no d i f f i c u l - t y  
The annlys is  o f  a s t e l l a r  .itmosphere m T y  be c a r r i e d  out 
" "7 :2&928 a t  t3.ree l e v e l s  of soph i s t i c? t ion .  2 1.i -&J 
Q 
P (ACCESSION NUMBER) (THRU) -
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3 
L. 
- - -  -+- ---7.+L. - - f i , , p , l , , m a  - the  (1) i:l t h e  conventionai (:iii.ve s l y f l u L l  y - u -  \ , L t L L  - 7 , ,  T /I ) e@-valent w i c 1  L I L  d oi' the i i n z  i ~ c t . ; n l l y  l o g  .VIA, 
i.; I'lotted against  some func t ion  of gfA, where A i s  
t h e  ?bundance, g i s  t h e  s t a t i s t i c x i  w e i t l i t  o f  t h e  
lower l e v e l ,  and f i s  t h e  t r a n s i t i o n  probability. It 
i s  2ssumed t h a t  t h e  atmosphere can be r e p e s e n t e d  by 
a s i n g l e  temperature and pressure.  In t h e  Milne- 
Eddington model, it i s  assumed t h a t  the m t i o  of l i n e  
t o  continuous absorpt ion c o e f f i c i e n t  i s  constant  with 
depth i n  t h e  star.  In  another ,  t h e  SS model, it i s  
zissumed t h s t  t h e  absorpt ion l i n e s  w e  formed obove 
t h e  region t h a t  produces t h e  continuous spectrum. 
I n  t h e  method o f  model atmospheres, one p l o t s  log 
iJ/h agains t  some funct ion o f  gfA, but t a k e s  i n t o  
3ccouat t h e  s t r a t i f i c a t i o n  o f  t h e  atmosphere, i . e .  
t h e  v a r i a t i o n  o f  temperatur-e, p ressure  and absorpt ion 
c o e f f i c i e n t s  with depth i n  t h e  s t e l l a r  atmosghere. 
One chooses a family of' model atmospheres which ? r e  
iJpecified by (usua l ly)  a norm21 E/ne ?nd H,/metal r a t i o ,  
e f f e c t i v e  temperatures , and surf ace g-rzvit i e s  * 2 o r  
e-1ch of  t h e s e  models, one p r e d i c t s  observable para- 
nieters, notcLbly t h e  energy d i s t r i b u t i o n ,  t h e  shapes 
or p r o f i l e s  01 t h e  hydrogm l i n e s ,  m d  t h e  i n t e n c i t y  
r a t i o s  of  c e r t a i n  l i n e s  t h a t  are s e n s i t i v e  t o  exci ta-  
t i o n  condi t ions ,  e .g .  t h ?  r a t i o s  o f  c e r t a i n  Si111 and 
SiIV l i n e s  i n  high temperature s t a r s .  One then  corn- 
pares t h e  p red ic t ions  of t h e  models with t h e  observed 
q u a n t i t i e s  f o r  t h e  stsr i n  quest ion and chooses t h e  
h e s t  f ' i5 t ing model o r  i n t e r n o l a t e s  a model t h a t  bes t  
f i t s  t h e  observat ions.  
( 3 )  I f  observation(a1 m . i t e r i a . 1  of  very high q u i l i t y  i s  
a v a i l a b l e ,  one may employ a ye t  more e labora te  method, 
narnely t h e  c a l c u l a t i o n  o f  ind iv idua l  l i n e  p r o f i l e s .  
The great  advantage o f  t h i s  method i s  t h a t  i t  uses  
a l l  a v a i l a b l e  observat ional  d a t a ,  whereas i f  one izses 
only t h e  equivalent width of a l i n e  he i s  i sno r ing  
a l l  t h e  information contained i n  i t s  shape. A f u r t h e r  
advantage o f  t h i s  method, which w e  r e f e r  t o  as spec- 
t r a l  syn thes i s ,  i s  t h a t  one can handle overlapping 
l i n e s ,  i . e . ,  blends.  I n  f a c t  t h e  method has been 
developed p r e c i s e l y  t o  c a t e r  t o  t h e  s i t u a t i o n  i n  which 
t h e  l i n e  of i n t e r e s t ,  e . g . ,  a l i n e  o f  Ag or Pb i s  
heavi ly  blended w i t h  some o the r  me ta l l i c  l i n e .  
The disadvsntages of t h e  method a r e  f i r s t ,  t h a t  obser- 
va t iona l  mater ia l  o f  very high q u a l i t y  i s  r equ i r ed ,  That i s ,  
one nust  have t h e  t r u e  p r o f i l e  of t h e  l i n e  f r eed  from all 
instrumental  e f f e c t s .  Mater ia l  o f  such h i s h  s p e c t r a l  resolu-  
t i o n  i s  ava i l ab le  a t  t h e  present  t ime only f o r  t h e  sun, although 
3 .  
for ;1 f e ~  -;erg br igh t  : j t s ~ ~ ,  we 2 ~ s  ~ ~ y p r o y ~ h i n r n  recn1ii t : inn 
r C  LL.. . n n n 7 , ;  n 4 - k  n , , - l  i;-T, ?-- 
a A vYv-Y"&.._L- 
,,lit= IGyuA.,Ave cIucAIIvJ. ~ p e c i f i s ? l l y ,  a few sta;. have 
been observed a t  Plount d i l son  with s u f f i c i e n t  r e s o l u t i o n  t o  
Peak can be used on t h e  very b r i g h t e s t  s t a r s  with extremely 
h igh  r e s o l u t i o n  and it will be poss ib le  t o  secure exce l l en t  
data f o r  a number of very i n t e r e s t i n g  ones. 
t ime a r e  needed, and ted ious  p l o t t i n g  of successive approxi- 
mations i s  needed, although it i s  hoped t h a t  a computing 
r o u t i n e  can be developed t o  handle t h i s  s i t u a t i o n .  
\ j u s t i f y  t h e  procedure. The McXatli solar t e l e scope  a t  K i t t  
The second disadvantage i s  t h a t  l a r g e  blocs  of computing 
A t  t h e  o u t s e t ,  one needs a good model atmosphere. For- 
t u n a t e l y , f o r  t h e  sun adequate models a r e  a v a i l a b l e  a t  l e a s t  
f o r  t h e  p a r t s  o€ t h e  s o l a r  atmosphere wherein nost  of t h e  
l i n e  p r o f i l e  i s  developed, Secondly, one must also make some 
assumption about l a r g e  s c a l e  motions o f  t h e  gases i n  t h e  
atmosphere, i . e .  turbulence.  F i n a l l y ,  it i s  necessary t o  
adopt some hypothesis on t h e  c o l l i s i o n a l  l i n e  broadening 
m'echanism. Most l i n e s  are c o l l i s i o n a l  broadened by quadrat ic  
S ta rk  efi'ect o r  van de r  Waals i n t e r a c t i o n s  with hydrogen a toms .  
I f  t h e  p r o f i l e s  o f  t h e  l i n e s  a r e  s u f f i c i e n t l y  accu ra t e ly  
measured? t h e  broadening c o e f f i c i e n t s  can themselves be 
determined empir ica l ly .  The only remaining parameter i s  t h e  
product gfd and s ince  t h e  s t s t i s t i c a l  weight of t h e  lower 
l e v e l  i s  known, t h e  accnracy of t h e  abundance determinat ion 
i s  l imi t ed  by t h e  accuracy of t h e  f-value measurement. 
Some app l i ca t ions  of  t h i s  method, which has been employed 
by J0-m Ross t o  determine t h e  &b-xizdaricce oi diiroixituq in + - v > n  W L i L  
t i o n  of t h e  C r I  h5247.574 l i n e  (Mult iplet  no. 18 i n  t h e  
Iievised Mult iplet  Table).  T h i s  i s  a simple p r o f i l e  f o r  which 
an exce l len t  r ep resen ta t ion  i s  poss ib le .  The computed po in t s  
.2re ind ica ted  by t h e  c i r c l e s .  
SUE i s  sh0,t.n i n  I i g u r e s  1-4. n digvre 1 shows t h e  r aFresPn ta -  
Figure 2 shows t h e  s t eps  i n  t h e  r ep resen ta t ion  of  t h e  
l i n e  p r o f i l e .  From a conventional c w v e  o f  p o w t h  a n a l y s i s  
( i . e .  a previous abundance study) one has a prel iminary e s t i -  
n a t e  o f  log gfA. The l i n e  i s  t o o  s t rong.  The second t r i a l  
g ives  a l i n e  t ha t  i s  t o o  weak and by an i n t e r p o l a t i o n  proce- 
dure one obta ins  a f i n a l  curve which gives  a good representa-  
t i o n  of t h e  l i n e  h4705.019 (mult. no. 186). 
Fig1-i-e 5 shows a chromiiim l-ines 14544.621 of mul t ip l e t  
(33) blended w i t h  an i r o n  l i n e  and a t i t an ium l i n e .  Note t h a t  
i t  i s  necessary here  t o  represent  bo th  t h e  Fe and T i  l i n e s  by 
varying t h e i r  log; gfA's u n t i l  t h e  p r o f i l e s  f i t .  For a l l  of 
t h e s e  l i n e s  it i s  necessary t o  make s l i g h t  ad jus tnen t s  i n  t h e  
b 
4. 
c o l l i s i o n a l  damping p a r a r e t s r s .  - 
Figure 4 shows t h e  synthes iza t ion  o f  t h e  C r I  A5323 
l i n e s .  Here severa l  s t r o n s  con t r ibu to r s  a r e  involved and a 
n m b e r  of successive i t e r a t i o n s  sre r eqc i r ed  t o  reproduce t 3 e  
observed p r o f i l e s .  The C r I  l i n e  i s  flanked by s t rong  blend- 
i n g  lines of o the r  elements. 
It i s  of i n t e r e s t  t h a t  t h e  l i n e  i n t e n s i t i e s  and p r o f i l e s  
can be predicted s o  p r e c i s e l y ,  we have assumed throughout 
t h a t  t h e s e  l i n e s  a r e  formed under condi t ions o f  l o c a l  t he r -  
modynamic equi l ibr ium. Yet t h e  shapes and even t h e  c e n t r a l  
i n t e n s i t i e s  a re  as tonish ingly  accu ra t e ly  reproduced. 
It must be emphasized t h a t  t h e s e  procedures a r e  worth- 
while only f o r  obeervations of high accuracy and l i n e s  of 
p a r t i c u l a r  i n t e r e s t .  Ross considered t h e  chromium l i n e s  
because a grea t  e f f o r t  has been made r e c e n t l y  by seve ra l  
teams o f  workers t o  der ive  f-values f o r  l i n e s  of t h i s  metal. 
!de mention t h e  s t u d i e s  by idilkerson and Chara t i s  (Univ. o f  
Maryland), by G. d .  Wares and h i s  co-workers a t  A i r  Force 
Cambridge, and most  r e c e n t l y  by Paul Byard a t  Ohio S t a t e  
Universi ty .  Unfortunately,  t h e  p rec i s ion  of t h e  chromium 
abundance derived by these  procedures i s  disappoint ing i n  
view of t h e  e f f o r t  involved. That i s  
logN(Gr)/N(H) + 12.00 = 4.73 2 0.26 
where Corliss and Bozman's f -values  have been used,  whereas 
sm3.1ler abundance with a comparable s c a t t e r .  
f-vallj.ps gh-f;ain~?t by ' J a r p s  e t  RI, l e a d  t o  R sompwhat 
A l i n i t i n e ;  f a c t o r  i s  and remains t h e  uncertai -nty i n  
t h e  f-values f o r  t h e  l i n e s  we have t o  use i n  t h e  abundance 
a n a l y s i s .  Different  measurements continue t o  y i e l d  discordant  
r e s u l t s  and u n t i l  t h e i r  problem i s  reso lved ,  our e f f o r t s  t o  
determine abundances w i l l  be f r u s t r a t e d .  
One method which a i m s  t o  evade t h i s  d i f f i c u l t y  i s  t o  
compare t h e  spec t ra  o f  t h e  program s tar  with a s tandard s ta r  
o f  presumrbly known composition. This method of  d i f f e r e n t i a l  
curve of growth a n a l y s i s  has been employed by many workers 
s ince  it was f i r s t  used i n  t h e  l a t e  t h i r t i e s  and e a r l y  f o r t i e s  
by groups a t  Harvard and elsewhere. The advantage of t h e  
method i s  t h a t  t h e  poorly determined f-values  cancel  out 
i fh i le  t h e  e f f e c t s  of blends e t c .  tend t o  be compensated f o r ,  
a t  l e a s t  as  long as one dea l s  with s t a r s  of comparable spec- 
t r a l  and luminosity types .  Much valuable  o o r k  has  been done 
by t h i s  procedure. For exzmple, Wsllers te in  m d  h i s  
co l l abora to r s  have a.naiyzc?d m a n y  s t a r s  by cnrnpring *hem 
with  t h e  sun. The method f a i l s  if t h e  program and-comparison 
stars d i f f e r  by t oo  l a r g e  an i n t e r v a l  i n  sneckral t y p e .  Tor 
example, a comparison of the sun (T  = 5700 K )  and S i r i u s  
(T= 10,500°K) by t h i s  method i s  d i f f i c u l t  because b l ends ,  
t h e  r e l a t i v e  importance of a r c  and enhanced l i n e s ,  et.c. a r e  
so  different i n  t h e  two stars. 
a -  - 
A s  methods o f  ana lys i s  a r e  f u r t h e r  r e f ined  and t h e  
q u a l i t y  of observat ional  ma te r i a l  improves, and p a r t i c u l a r l y  
as good f-value determinations becone a v a i l a b l e ,  we can ex- 
pect  a gradual improvement i n  abundance determinat ions.  Un- 
f o r t u n a t e l y ,  t h e  bot t leneck i s  and w i l l  c e r t a i n l y  remain t h e  
l ack  o f  adequate observat ional  f a c i l i t i e s .  IYany o f  t hose  who 
a r e  capable,  a b l e ,  and w i l l i n g  t o  work on abundance problems 
a r e  unable t o  do s o ,  simply because t h e  necessary t e l e s c o p i c  
equipment does not e x i s t .  
> ,. 
-r .=p 
This  program has been supported i n  p a r t  by NASA grant 
NGR-05-007-046 & o  t h e  Universi ty  of C a l i f o r n i a ,  Los Angeles. .* [ 


The chemical composition of normal stellar atmospheres

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