Excitation of geocoronal hydrogen alpha nightglo

Donahue, T. M.

English

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SPACE RESEARCH ORDINATION NTER 
COMMENTS ON THE EXCITATION OF THE 
GEOCORONAL HOG NIGHTGLOW 
BY 
T. M. DONAHUE 
DEPARTMENT OF PHYSICS 
SRCC REPORT NO. 66 
UNIVERSITY OF PITTSBURGH 
I 
PITTSBURGH, PENNSYLVANIA 
I 4 JANUARY 1968 
ff 653 J ~ l v 6 5  
https://ntrs.nasa.gov/search.jsp?R=19680008782 2020-03-12T09:42:50+00:00Z
Comments on the Excitation of the Geocoronalm Nightglow 
(Planetary and Space Science) 
T. M. Donahue 
The University of Pittsburgh 
Pittsburgh, Pennsylvania 15213 
January 4, 1968 
Reproduction in whole or in part is permissible for any purpose of the 
United States Government. 
Comments on the Excitation of the Geocoronal Nightglow 
T. M. Donahue 
The University of  Pittsburgh 
Pittsburgh, Pennsylvania, U. S. A .  
ABSTRACT 
It i s  pointed out t ha t  t h e  excitation o f  geocoronal hydrogen a t  
night by multiply scattered solar  radiation occurs mainly a t  thousands of 
kilometers above the ear th ' s  surface. The nature of the  hydrogen distri- 
bution below about 400 km i s  of secondary importance i n  the transport  
mechanism and is  weakly excited. 
liyman f3 scat ter ing can be predicted without serious error  even i f  the 
large gradient in  hydrogen density near 100 Inn is  ignored. 
calculation involving plane parallel geometry shows that during so lar  
minimum the expected nightglow Balmer a brightness has approximately the 
For t h i s  reason Balmer (31 exci ta t ion by 
An approximate 
measured value of 2 Rayleighs. 
Tinsley has recently questioned the appl icabi l i ty  of my cal-  
culation Donahue, [ 19641 of the excitation of Balmer 01 by geocoronal hydrogen 
t o  the real atmosphere. H i s  objection was based on my use of  a model devised 
by Thomas [1962] f o r  Lyman a calculations i n  which the density of hydrogen 
varied as r-5. 
above 400 la when the exospheric temperature i s  1250°0 It f'ails, however, 
t o  reproduce the very rapid increase i n  hydrogen density expected a t  lower 
a l t i t udeso  In Thomas' model, for  example, i f  the opt ica l  depth i n  Lyman a 
Such a model f i ts  the expected hydrogen d is t r ibu t ion  w e l l  
i s  unity above I20 km the density at  I20 km is  only 2.3 x 10 4 atoms/cm3 
6 compared t o  be5 x 10 atoms/cm3 in a Kockarts and Nfcolet [ 19631 model with 
the same opt ica l  depth. A t  100 km t h e  discrepancy is  much worse - 2*3  x 10 4 
%tom/cm3 t o  be compared t o  about 1.9 x lo7 atoms/cm 3 . 
I n  the Lyman 01 problem Thomas was concerned with calculating 
brightnesses above I20 km and took i n t o  account the e f fec t  of the  mass of 
hydrogen below I20 km by imposing a boundary a t  120 km which ref lected 
Lyman a with the efficiency dictated by the  albedo of 42 per cent which had 
been observed experimentally. Tinsely argues that i n  t h e  case of Balmer a 
production a t  night by IJrman f3 transport there  may be a s ignif icant  number 
of Lyman f3 scat ter ings a t  low a l t i t u d e  (100 - I20 km) which contribute t o  
the Balmer a observed on the ear th 's  surface. Thus a calculation of the 
Balmer a brightness based on a model which terminates with a perfect ly  
absorbing Layer for  Lyman p a t  I20 km m i g h t  be seriously deficient.  
This is i n  fact  not l i k e l y  to  be the case. The reason is  that ,  
f o r  geometrical reasons, the hydrogen atmosphere below I20 km hardly 
par t ic ipa tes  i n  the radiative transport responsible fo r  the nightglow 
exci ta t ion.  The property of geocoronal hydrogen which is  essent ia l  f o r  
L 
2 
the efficacy of the mechanism of nightglow exci ta t ion by transport  of 
resonance radiation i s  i t s  great scale height. Above the ant i -solar  point, 
l80" from the sun, for  example, t h e  i n i t i a l  excitation of hydrogen by photons 
arr iving there d i r ec t ly  from the sunl i t  atmosphere has a mximum between 
1000 km and 2000 km. A t  200 lun t h e  excitation rate is reduced by a fac tor  
of 3 compared t o  the rate a t  U O O  lune A t  I20 bm it has gone down by another 
factor  of t h e e .  
rate a t  low a l t i t ude  the degree of excitation there  is always small compared 
t o  that above 50s lane There w i l l  Pndeed be an fmgressive maximum i n  the 
volume exc t ta t i sn  r a t e  below 200 km but  the integrated r a t e  i n  the column 
between PO0 and 200 km i s  very smll compared t o  the integrated rate i n  the 
long, allmost uniformly excited column of hydrogen between 200 km and 5000 bm. 
It i s  the  f ac t  t h a t  the i n i t i a l  exeitxation occups predominantly a t  very 
high a l t i t u d e  i n  the outermost th i rd  of the medium's t o t a l  op t i ca l  depth 
whteh i s  ultimately responsible for  t h i s  phenomenon, Far more photons - 
after several  scat9,erings - escape outward than penetrate i n to  the bottom 
ha l f  of the med%.m behw 150 km. 
in the case of m n  p than i n  that of 
Lyman f3 photons survive each scattering. 
of  the hydrogen for Lyman p scattering is constdembly higher than the 
base for  Lyman a. 
Only half of the diffuse Lyman p glow directed downward a t  I20 km penetrates 
below 110 km, 
While multiple scat ter ing does build up the excitation 
This s i tua t ion  is even more aggravated 
a because only 0.88 of the 
Furthemore, the effect ive base 
This is  because of the greater  opacity of O2 f o r  LyImn 
A s  an illustrative exiimple consider e. mdeL fn which the hydrogen 
dfstP-fbution f a  nom1iaed  t o  2.7 x LO7 atoms/cm3 a t  100 km and i n  which 
the  d is t r ibu t ion  is t h a t  appropriate t o  a X500" exospheric temperature i n  
the  daytime and a l000" temperature a t  night. 
depth is 3s above 100 km i n  the day and 6 a t  night. 
For Qman a! the  op t i ca l  
The night time density 
3 
profi le ,  p ( z ) ,  is plotted i n  Fig. 2 .  Above the a n t i  solar  point (solar  
zenith angle of 180") the volume r a t e  of excfta-bion has been calculated as 
a function of z per  uni t  effect ive s o l a r  flux rFoG AvD, where AvD is the  
Doppler l i n e  half width and mFo is the so l a r  flux i n  uni t s  of photons/cn? 
sec i n  uni t  frequency. 
hydrogen, including the region beyond the terminator and solving approxi- 
mately the radiat ive t ransfer  equation f o r  the  volume rate of excitation 
there. 
s o h r  point by photons orfginating i n  the sunlit region and reaching that 
c o L m  wf+,hout scat ter ing i s  then calculated. 
un%t eross section and uni t  effective solar  flux [rFo 6 AvD] is plotted 
a s  nSo in Ffg. 2. 
This has been done by considering first the sunlit 
The rate of excttation along the ve r t i ca l  column above the sub- 
This rate, normalized t o  
It is a lso  plotted per  uni t  op t ica l  depth i n  uni t s  of 
[vF0 AvD] as So i n  Fig. 1 as a function of op t ica l  depth and i n  Fig. 2 
as a function of z .  
of two e f fec t s  - the  Zarge opt ica l  depths along the  paths t o  the highly 
excfted s u n l i t  regions near the terminator and the small sol id  angle sub- 
tended by these regfons, At higher a l t i tudes  the transparency and the 
so l id  angLes increase while tihe hydrogen density s b w l y  decreases. 
e f fec t  of deereastrag density does not. become dominant u n t i l  an a l t i t ude  of 
l2QQ lan is reached. 
( i n  units of optsicah depth) fncreases all the  way t o  7 = 0 (Fig. 1). 
The &mU values of PSo a t  low a l t i t ude  are a r e su l t  
The 
Above that height PSo drops rapidly although SQ 
To compute the steady state excitation rate generated by multiple 
sca t te r ing  of these photons a plane pa??aLLe,l m o d e l  of the atrnoqhere is 
next assumed i n  which the i n i t i a l  Pate of excitation fs So. 
source function is calculated by solving the  in tegra l  equation 
The ultimate 
S(T) = So(T) + S ( T o )  H(T, T ' )  dT' 
4 
discussed, f o r  example, by Donahue and Meier (1967). 
is  the probabili ty that a photon originating somewhere i n  dT1 a t  the l eve l  
at is absorbed i n  a slab of width dT a t  the l eve l  7 .  
i s  plotted i n  Fig. -1, as a function of T. 
(per un i t  op t ica l  depth) and p(z)S(T)/(nFo & AvD) are plotted as functions 
of z. 
H ( 7 ,  7 ,  7 ' )  d7' dT 
S(7)/(nFo 6 AvD) 
In  Fig. 2 both S ( T ) / (  *FoGAv,) 
Multiplying t h i s  l a t t e r  quantity by the l i n e  center cross section 
and by the effect ive l i n e  center SOUP f lux  
gives the  ac tua l  l oca l  volume excitation rate. This product is simply 
gU, the  number of so la r  Tar photons scattered per hydrogen atom before 
at tenw%ion of the so lar  flux. 
The source Functions S ( 7 )  and S o ( 7 )  are volme excitation rates 
divided by 0,~. 
The low degree of excitation below 200 km is evident i n  Fig. 2. 
Hence they indicate the degree of excitation of the  medium. 
In  Fig. 1 there is also plotted the reciprocal of the probabili ty E 
t h a t  a photon w i l l  escape without scattering from a given a l t i tude .  This  
is esseratia3J.y the  mean number of scatterings a photon will suf fer  before 
escape. A good first approximation to  the f inal  source function S is the  
quant i ty  S,/Eo The average number of scat ter ings the or ig ina l  family of 
photons (So) undergoes is 5.1. Most of these occur i n  the upper half of 
the  medium. 
5 
The apparent integrated photon emission rate i n  a column whose 
axis  i s  a t  an angle cos'' p wi th  the v e r t i c a l  is given by 
where the upper l imi t  i s  the appropriate boundary a t  7'  = 0 o r  7' = T~ 
and T ( 7 ,  7') i s  the transmission f'unction, Since 
dT = a pdz 
0 
t h i s  in tegra l  may a l so  be writ ten as 
It can be seen from Fig. 2 tha t  when the transmission function i s  unity the  
column emission r a t e  i n  the zenith a t  T = 6 receives minor contributions 
from the lower half of the medium. The value of the in tegra l  i n  uni t s  of' 
(wFo) 6 AvD is 0.205, O f  this a fraction 0.95 comes from regions higher 
than 110 km and 0.88 from those above I20 km. In fac t  almost ha l f  of the 
photons originate i n  the first opt ica l  depth above 1500 km. An ac tua l  
comparison with the resu l t s  obtained by Thomas with his  power l a w  model 
and those resul t ing from the  present so r t  of calculation confirm the 
expectation that only a small error  r e su l t s  from the use of h i s  approximation 
t o  the  dis t r ibut ion.  
To adapt these resu l t s  t o  Lymsn f3 we note tha t  (lo f o r  Lyman a i s  
Hence i f  there were 6 times a f ac to r  of 6 h r g e r  than that for Lymm f3. 
as much hydrogen i n  the model (To = 36 fo r  Lyman a) the  present calculations 
of S/(nF0) AQ could be taken over fo r  the excitation of the 3p l eve l  
6 
i n  a medium whose opt ica l  depth i s  6 i n  Lyman p. 
times as Urge  but crops, the ac tua l  volume rate of exci ta t ion would remain 
the same, that i s  
O f  course p S  would be 6 
According t o  the NRL observations (Tousey e t  a l ,  1964) the quahtity 
*F 6 AVD 
Since each excftation of the t h i r d  leve l  r e su l t s  i n  Balmer a emission 12 
percent of the t i m e  the predicted W column emission rate observable on 
the surface of the ear th  i s  given by 
was 10 8 photons/cin2 sec i n  un i t  frequency for  I@ i n  1962. 0 
4 n I ( R x )  = 0.2 x 0.12 x lo8 = 2.4 Rayleighs (8 )  
Actually since the ID emission causes a loss of I@ photons a t  each scat ter-  
ing and about 5 scatterings occur before a I@ photon gets en t i re ly  out of 
the medium S ( T )  only builds up t o  about half i t s  analagous IG1 value and 
the  Ha column emissfon rate predicted is only about 1.2 Rayleighs. 
is t o  be compared with the 2 Raylefghs recently reported by Tfnsley (1967) 
and Amstrong (1967) 
This 
Although resu l t s  obtained by t h i s  method of ca l cub t ion  f o r  other 
s o l a r  zenith angles are available and although they a r e  appropriate t o  
so l a r  minimum when the night t i m e  hydrogen abundances may have been as 
large as those discussed nere it is prohbly not vorth vhi le  i;ublfshir;g 
them. 
fo r  hydrogen. 
global hydrogen dis t r ibut ion,  taking account of the  0.88 albedo on 
sca t te r ing  and absorption by 02 are now underway. 
The reason i s  that the plane parallel model is  a poor approximation 
Other calculations using proper geometry, a more r e a l i s t i c  
For a quantitative 
7 
comparison with experiment these a re  cer ta inly preferable. Their resu l t s ,  
however, do not al ter the  fundamental arguments presented here. 
It should be noted here that i n  my previous paper on lW excitation 
I used Thomas' (1962) liu source functions. These a r e  pS/(nF) &Av, rather 
than S ( 7 )  e When multiplied by u0 f o r  Lyman a they 
t ion  ra tes  (per uni t  nF0 & AvD). Thus from h i s  
-2 So(Icll) I PS d z = 3.1 x 10 
gives the integrated emission rate i n  uni t s  of TF0 
give the volume excita- 
Fig. 14 the  in tegra l  
(9 )  
AvD f o r  any hydrogen 
l i n e  f o r  which the medium has an opt ical  depth of unity. I n  the case of 
Qman B t h i s  leads t o  a predicted & h e r  a column emission rate of 0.24R 
a f t e r  allowance fo r  the albedo of 0.88. 
fortunately gives a misleading explanation of the method of calculation 
as Tinsely has pointed out,  
r e su l t s  as published are correct within the  l imitations of the model used. 
Hence, I s t f l l m a i n t a f n  that the  Urge Balmer 01 emissfon rates reported 
fo r  so la r  maximum do not appear t o  be consistent with the 1963 Lyoran f3 
solerr l i n e  prof i le  and the multiple scat ter ing model. 
on so la r  zenith angle is  consistent w i t h  the  model. 
meants, on the other hand, do not seem to present any serious d i f f i c u l t i e s  
of interpretation. 
Amstrong and Tinsley through the next f e w  years and some determinations 
of t h e  solar  w n  p l i n e  center fiux during t'nis period &re cer+&fnly ic 
order 
IQ paper (Donahue, 194) un- 
The method is t he  one set for th  here and the 
Their dependence 
The more recent measure 
Thus a continuation of the observational program of 
One f i n a l  word of comment may be i n  order concerning I@ nightglow 
These are  important as sources f o r  ionization of f luxes i n  the E region. 
O2 a t  night. It i s  not proper t o  in fe r  these by scaling the Balmer a 
8 
arr iving a t  the ground. 
excitation. 
For example, the Lyman 
120 km fo r  the case discussed here is not 6R but only about 3.3R. 
f o r  a so lar  zenith angle of 135" the present type of calculation would 
predict  a zenith emission rate of 5R f o r  Kz and only 1% of I@ a t  I20 km. 
This point has been properly handled i n  the approximste treatment of the 
night time E region by Qgawa and Tohmstsu (1967). 
The reason i s  again the great a l t i t u d e  of the 
Lyman p is seriously attenuated i n  reaching the I20 km region. 
apparent column emission rate i n  the  zenith a t  
Similarly 
Acknowledgements 
The research reported here has been supported i n  pa r t  by the 
National Aeronautics and Space Administration (Contract NASr-179) and the  
National Science Foundation, Atmospheric Sciences Division (Aeronomy), 
under Grant GP-4435. 
9 
References 
E.  B. Amstrong, Planet. Space Sci. - 15, 407-426 (1967). 
T. M. Donahue, Planet. Space Sci. - 12, 149-159 (1964). 
T e M. Donahue and R.  R. Meier, J. Geophys. Res . - 72, 2803 (1967). 
G. Kockarts and M. Nicolet, Ann. Geophys. - 19, 370 (1963). 
G. Thomas, Geophys R e s .  68, 2639 (1963). 
B. A Tinsley, Planet Space Sci - 15, 1757-1776 (1967). 
R.  Tousey, J. D. Purcell,  W. E. Austin, D. L. Garrett  and K. G .  Widing, 
Space Research IV, Ed. P.Muller,North Holland, Amsterdam. 
Figure Captions 
Fig. 1 Source functions ( i n i t i a l  and f ina l )  and most probable number 
of scatterings before escape as functions of op t ica l  depth 
i n  a Kochrts and Nicolet (1963) hydrogen model of op t ica l  
Depth 6, solar  zenith angle 180". 
Fig. 2 Hydrogen Density, I&nan a source functions (Degree of excitation) 
and volume exci ta t ion ra tes  normalized t o  uni t  cross section 
and effect ive so la r  f lux as functions of a l t i t ude ,  180" 
from the sun. 
0 
0 - 
0 
0 
(u 
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- 
0 
0 cu 
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v) 
0 
0 
0 - 
0 
0 
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6J 
0 
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0 m 
0 - 
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- /  I 
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W 
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r h  / '7 \ 
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I I I I 
I o7 
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rr) 
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lo5 
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Altutude in km 
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Figure 2 


Comments on the excitation of the geocoronal H alpha nightglow

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