The physical properties of atoms in superstrong magnetic fields, characteristic of neutron stars, and the possibility of detecting magnetically strongly shifted atomic lines in the spectra of magnetized X-ray pulsars are discussed. It is suggested that it is recommendable to look for magnetically strongly shifted Fe 26 Lyman lines in rotating neutron stars of not too high luminosity using spectrometers working in the energy range 10 - 20 keV, with sensitivities  to minus 4 power photons per sq cm and second, and resolution E/delta E approx. 10-100

Herold, H.

Ruder, H.

Truemper, J.

Wunner, G.

English

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17 
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OBSERVABILITY OF ATOMIC LINE FEATURES I N  
STRONG MAGNET I c FI ELDS 
G ,  WUNNER, H, RUDER, All'? H ,  HEROLD 
Institut f5r Theoretische Physik, Universitat Erlangen-Niirnberg 
West Germany 
J , TROMPER 
Max-Planck-Institut fiir Physik und Astrophysik, 
Institut filr Extraterrestrische Physik, Garching, 
West-Germany 
ABSTRACT 
As an application of our comprehensive investigaticis of the 
physical properties of atoms in superstrong magnetic fields B % 
10l3 - 10 l3 G, characteristic of ne'itron stars, we discuss the 
possibility of detecting magnetically strongly shifted atomic 
lines in the spectra of magnetized X-ray pulsars. Careful esti- 
mates r f  the relevant parameters lead us to the conclusion that it 
would be profitable to look for magnetically strongly shifted 
Fe XXVI Lyman lines in rotating neutron stars of not too high lu- 
minosity using spectrometers working in the energy range 10 - 20 keV, 
with sensitivities 2 
tion E:AE 1, 10-100. 
photons per cm2 and second, and resolu- 
The observation of cyclotron ?eatures in the X-ray spectra of 
accreting neutron stars has confirmed the existence of superstrong 
magnetic fields of the order of B % 10l1 - 10 
1977). The discovery of further lines in the spectra of atomic 
origin for :xample, would provide an independent check on both the 
strengths of the magnetic fields and the assumptions of the physi- 
cal conditions prevailing there. From the source temperatures kT % 
'Research supported in part by the Deutsche Forschungsgemeinschaft (DFG) . 
13 C (cf. TrUmper et a]. 
https://ntrs.nasa.gov/search.jsp?R=19820018203 2020-03-21T07:35:47+00:00Z
472 
10 - 30 keV, derived from the observed spectra, it follows that 
the emitting matter is almost completely ionized, with a small 
fraction of hydrogen-like ions. The cosmic abundance of elements 
then implies that the lines with the largest possible energies 
and the highest intensities are members of the Lyman-series of 
20 
Fig.1. Level scheme for Fe X X V I  and the photon spectrum resulting from the 
drawn transitions for B = 5*10L2G in comparison with B = 0 (dashed lines). The 
states are labelled by the usual field-free quantum numbers N,l,m, and by the 
quantum numbers n,m,U of the adiabatic approximation. The intensities have been 
obtained assuming an average occupation number of one electron in the excited 
state. The onset of the continua is marked by hatching. 
I 
473 j 
FE xxvl 
1 3Po-lSo 0 0 3 ~  
2 2Po-1so 0 0 1 ~  
3 2P-l-lSO O-%OOo 
4 2so --2P-l 002-0-(0 
5 361-2P-l o-n*o-10 
62SO-2PO 002-001 
1s 20 
fiw in keV 
2s 
i t I 
I t 1012 . 
L 
I 
t I 
- 
30 
Fig.2. Energies and intensities of Fe XXVI lines as continuous functions of 
B in the range 1 0 1 1  - 1013 G .  The dasired lines represent the energetic posi- 
tions of the lines, the widths of the corresponding corridors are proportional 
to the logarithms of the intensities in units of lo'* W. 
B in Gauss 
0 10l1 lo1' 5 - 1 0  l 2  5 . 1 0 ~ ~  
Energies of y ' s  
in keV 6.9 7.0 7.9 9.3 15.9 2 1 . 0  39.7 5 2 . 2  
Numbers of y ' s  
in 1015 S - 1  0.28 0 . 3 1  0 . 5 4  0 . 8 2  2 . 5 8  4 . 2 2  1 2 . 5  1 8 . 3  
T a b . 1 .  Energies and numbers of y-quanta of the transition corresponding to 
L in the field-free case for Fe XXVI assuming one excited atom on the time 
average. a 
474 
Using the scaling laws (Surmelian and O'Connell 1974, Wunner 
et al. 1981) of the one-electron energies Em, Em(Z,B) = 
Z2Em(Z=l,B/Z2), (Z nuclear charge, m eigenvalue of the component 
of the angular momentum parallel to the magnetic field), and of 
the oscillator strengths, fTT, (Z,B) = fTT, (Z=l,B/Z2', the energy 
levels, oscillator strengths,transition probabilities, etc. of 
Fe XXVI in magnetic fields of arbitrary strength can immediatc.ly 
be derived from our comprehensive calculations (Wunner and Ruder 
1980, Wunner et al. 1981) of the continuous B-dependence of these 
quantities for the H atom. Fig.1 shows the level schemes of Fe XXVI 
at B = 0 and 5*1012G and the resulting line spectra. The magnetic 
field dependence of both the energies and intensities of these 
lines over the whole regime of interesting field strengths can be 
seen from Fig.2. It is clearly exhibited that from B z 10llG onward 
for 2 = 26 the maqnetic forces begin to outweigh the Coulomb forces, 
to the effect thht the structure of the spectrum changes from the 
field-free form to the magnetic-field-dominated shape. Furthermore 
one recognizes that La (asymptotically 001 + 000) remains the 
strongest transition. In Tab.1 we therefore provide, for this tran- 
sition, the numerical values of the energies, and the numbers of 
y-quanta emitted per second. 
The observability of iron lines in the X-ray spectra of accre- 
ting magnetized neutron stars depends on a number of parameters 
such as plasma temperature and density, abundance of iron, source 
dimensions, magnetic field strength, and, of course, source dis- 
tance. In addition, to be detectable the lines should be suffi- 
cieiltly narrow (AE/E s 0.1). Doppler broadening should be negli- 
gible for iron lines at the typical temperatures of these sources 
(kT % 10 keV), and collision broadening effects can be estimated 
to be less than 1 keV at the prevailing temperatures and densi- 
ties. However, a nontrivial conditian is that the Thomson optical 
depth of the emitting plasma should be T 5 1 ,  in order to avoid 
too large line smearing by Comptonization. 
The appropriate conditions may be found in accreting magnetic 
neutron stars of low luminosity, such as 413900-40. Here one can 
expect that the interaction between the infalling gas and the 
radiation produced via Thomson scattering is small, and the mate- 
rial remains in free fall down to the stellar surface. I f  it is 
stopped there by Coulomb or nuclear collisions (Basko and Sunyaev 
1975, Pavlov and Yakovlev 1976) the heated layer will have a thick- 
ness of 50 g/cm’, viz., T % 20.  However, recent computations by 
Kirk and Galloway (1981) show that plasma effects will considera- 
bly reduce the stopping length to values of the order of a few 
glcm’, which means T % 1 for the heated layer. 
To arrive at a quantitative estimate, let us consider a radia- 
ting hot spot of area lolo cm’ and a thickness 2.5 glcm’ 
sponding to a total number of protons 1.5=10~~), a temperature of 
10 K, and B = 5=1012G. Starting from the Saha equation in a mag- 
netic field (Gnedin et al. 1974), for these conditions the frac- 
tion of Fe XXVI ions in the first excited m = 0 state is calcula- 
ted as 1-10-4, which leads, together with the cosmic Fe abundance 
3=1O-’, to 4.5=10’5 excited Fe ions on the time average. Using 
(corre- 
8 
476 
Tab.1 and assuming a s o u r c e  d i s t a n c e  ->f 1 kpc,  w e  arrive a t  a l i n e  
f l u x  of  i r o n  La-photons o f  1.0-10-3 cm'2s'1, which s h o u l d  be de- 
tectable w i t h  X-ray spectrometers a v a i l a b l e  a t  p r e s e n t .  A c t u a l l y ,  
t h e  i r o n  l i n e  f l u x  from t h e  h o t  p o l a r  s p o t  may be much h i g h e r  t h a n  
t h e  above estimate, i f  t h e  r a d i a t i n g  plasma c o n t a i n s  a s u b s t a n t i a l  
f r a c t i o n  o f  "stirred up" s u r f a c e  material, which s h o u l d  c o n s i s t  of  
pu re  i r o n .  
Of c o u r s e  t h e  d e t a i l e d  shape  and wid th  of  t h e  l i n e  f e a t u r e  are 
s e n s i t i v e l y  a f f e c t e d  by t h e  p h y s i c a l  c o n d i t i o n s  i n  t h e  a c c r e t i o n  
column ( c f .  Yahel 1981) .  For  example it c a n  be imagined t h a t  due  
t o  re sonance  s c a t t e r i n g  l i n e  t r a p p i n g  o c c u r s ,  and a p o s s i b l e  
e m i s s i o n  f e a t u r e  above t h e  continuum background is  changed i n t o  
an  a b s o r p t i o n  f e a t u r e .  A t  any rate, w e  conc lude  t h a t  it would be 
p r o f i t a b l e  i n  f u t u r e  X-ray e x p l o r e r  m i s s i o n s  t o  look f o r  magnet i -  
c a l l y  s h i f t e d  i r o n  l i n e  f e a t u r e s  i n  magnet ic  n e u t r o n  s t a r s ,  u s i n g  
s p e c t r o m e t e r s  working i n  t h e  ene rgy  r ange  10 - 20 keV w i t h  s e n s i -  
t i v i t i e s  o f  10-4cm-2s-1 and energy  r e s o l u t i o n s  EIAE % 10-100. 
REFERENCES 
Basko, M.M., and Sunyaev, R.A. 1975, Astron.Astrophys.42,311 
Gnedin, Yu.N., Pavlov, G.G. , and Tsygan, A.I. 1974, SocPhys. JETP 39,20 
Kirk, J.G., and Galloway, D.J. 1981, Mon.Not.R.astr.Soc. 195,45P 
Pavlov, C.G., and Yakovlev, D.G. 1976, Sov.Phys. JETP 43,389 
Surmelian, G.L. , and O'Connell, R.F. 1974, Ap.J. 190,741 
Trbper, J., Pietsch,W., Reppin, C . ,  Sacco, B., Kendziorra, E., and Staubert,R. 
Wunner, G., ar.d Ruder, H .  198cAp.J. 242,928 
Wunner, G., Ruder, H . ,  and Herold, € I . ,  1981, Ap.J, 247,374 
Yahel, li. 1981, presented at the Sth General Conference of the EPS, Istanbul 
- 
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1977, Ann. N.Y. Acad. S c i .  302,538 
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Observability of atomic line features in strong magnetic fields

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