The cyclotron absorption coefficients in the ordinary and extraordinary modes are calculated for the shock heated region of AM Her. The equations of radiative transfer are solved and the intensity of the emitted UV radiation determined as a function of angle. The average spectrum is shown to have deviations from the previously predicted Rayleigh-Jeans spectrum and the magnetic field of AM Her is deduced to be roughly 5 x 10 to the 7th power gauss

Chanmugam, G.

English

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CYCLOTRON EMISSION FROM AM HERCULIS 1
G. Chanmugam 2
Joint Institute for Laboratory Astrophysics
University of Colorado and National Bureau of Standards
ABSTRACT
The cyclotron absorption coefficients, in the ordinary and extraordi-
nary modes, are calculated for the shock heated region of AM Her. Tbe equa-
tions of radiative transfer are solved and the _ntensity of the emitted UV
radiation determined as a function of angle. The average spectrun is shown
to have deviations from the previously predicted Rayleigh-Jeans spectrum and
the magnetic field of _ Her is deduced to be roughly 5 x 107 gauss.
INTRODUCTION
The _ Herculis binaries are believed to contain a magnetic white dwarf,
accreting matter from a companion star (refs. i-3). The polarized light ob-
served has been interpreted as being due to cyclotron emission, at the funda-
mental cyclotron frequency mc = eB/mc, in a magnetic field B _ 2xlO gauss.
It has been suggested that the matter accreting along the field lines forms a
shock heated region (height h ~ 106 ) cm above the magnetic pole (refs. 4,5).
This region was predicted to be a source of strong optically thick cyclotron
emission peaking in the ultraviolet. However, the observed flux is much
weaker (ref. 6). The theoretical estimates for the self-absorbed cyclotron
emission were made using the angle-averaged cyclotron absorption coefficient
(refs. 4,5,7). Recent estimates (ref. 8), made using the total cyclotron
absorption coefficient and taking angular effects into account, suggest that
the Rayleigh-Jeans spectrum would not be filled and that as a result the UV
flux would be less than was previously predicted (refs. 4,5). In this paper
the absorption coefficients _(_,8) for the ordinary (+) and extraordinary
(-) modes are separately determined and the total intensity of the emitted
radiation deduced as a function of frequency m and the angle 8 between the
direction of the radiation and the magnetic field.
Isupported by NSF Grant AST-76-O6807-A01.
2,TILA Visiting Fellow, on leave from Dept. Physics and Astronomy, Louisiana
State University, Baton Rouge, LA 70803.
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https://ntrs.nasa.gov/search.jsp?R=19810017413 2020-03-21T12:06:54+00:00Z
CYCLOTRON RADIATION
The cyclotron absorption coefficients _(_,8) have been calculated, for
a three-dimensional relativistic ?_xwell distribution (as in ref. 8) for the
electrons, by a modification (ref. 9) of methods previously used (refs. i0,
ii). For the shock heated region of AM Her the Faraday rotation angle _
A(_c/_)2/2_ is >> i, since the dimensionless parameter A _ _p2h/_cC ~ 106
(see eq. (3)), where Up is the plasma frequency and _/_c _ i0. In this
case, the transfer equations for the intensities in the two modes decouple
and (assuming Kirchhoff's law) take the form (ref. i0)
dI±(_,e)
dz + _±(_J,6).l±(_,e) = _±(_,G)IRj , (I)
where IRj = 0_2kT/8_3c2 is the Rayleigh-Jeans intensity per POlarization
mode. For a homogeneous plasma, the solutions are:
I± = IRj[I - exp(-_±L)] (2)
where L is the path length of the radiation through the source. The total
intensity is then given by I = I+ + I_.
RESULTS
The shock heated region is treated as a uniform plasma slab which is
perpendicular to the magnetic field so that the path length of the radiation
is L=h/cos e. The temperature of the slab is taken to be kT = 20 keV, as
may be inferred from the hard X-ray observations (ref. 12), while the dimen-
sionless parameter A is given by (refs. 4,8)
M/M 3/2
o ) 10 8 Bgauss
_ 1.6 x 106 (R/5x108 cm ' (3)
where M is the mass of the white dwarf and R its radius.
The intensity of the emitted radiation is plotted as a function of cos e
for several harmonics in figure i. Consider the radiation at m/_ c = 12, For
cos 0 = 0, the plasma is optically thick for both modes and hence the inten-
sity is that of a black body (flat curve). For increasing values of cos 0
the plasma first becomes optically thin in the ordinary mode (at cos 0 = 0.2)
and then in the extraordinary mode (at cos 0 = 0.4) giving rise to the de-
crease in intensity. For lower harmonics the radiation is optically thick
for a greater range of cos 0 and conversely for higher harmonics. During an
orbital cycle of AM Her, the viewing angle 0 varies.
The total flux F(_) from the plasma slab may be compared to the total
Rayleigh-Jeans flux BRj(_), if emitted as a black body:
516
fl l(cos 0)cos e d(cos 0)
F(_) 0
= (4)
BRj(_) fl 21Rj cos 0 d(cos 0)
0
In figure 2, F(_) is plotted as a function of _/mc' for several values of A.
An important result is that F(m) deviates from the Rayleigh-Jeans flux for
_/mc >_ 6. If the angle-averaged absorption coefficient is used the flux
would follow the Raylelgh-Jeans curve up to a frequency m* and be optically
thin for _ > _*. The value of _* is _12 _c for A -- 1.0 x 106 (ref. 4). For
_ m* also, the angle-averaged results give fluxes higher than F(m): by a
factor _3 for 0_ _ 14 mc and a factor =6 for m/mc _ 30. The values of F(m)
are in good agreement, for _/mc <_ 12, with those obtained using the total
cyclotron absorption coefficient (ref. 8), however for m/mc >_ 12, F(m) is
higher (e.g. by a factor of almost 2 for A = 1.0 x 106' _/_c = 14). This is
because of the neglect of optically thin emission for small angles in ref.
8, an approximation which is good at low frequencies.
Raymond et al. (ref. 6) find that the UV continuum consists of a black
body (kT = 25-30 eV) component, which also produces the soft X-rays (ref.
13), and a flat uneclipsed component produced by the X-ray heated secondary
or by the accreting gas further up the accretion column. They do not however
observe the optically thick cyclotron emission from the hot (kT _ 20 keV)
shock heated region which had been predicted (refs. 4,5). The smallest
value for the predicted cyclotron emission consistent with the soft X-ray
flux is 20 times the observed value at 1500 %. This discrepancy could be
removed if the mass of the white dwarf (M _ 0.6 Me) and the magnetic field
(B = 3 x 107 gauss) are lower than had been previously assumed (ref. 14).
If angular effects are taken into account, as in this paper, a higher field
B = 5 x 107 gauss (with the same mass M = 0.6 _e' so that A = 6.5 x 105 )
would suffice, since %=1500 % would correspond to m/mc _ 14 (figure 2).
Recent UV observations of AM Her by Tanzi et al. (ref. 15) confirm the
low UV flux observed by Raymond et al. (ref. 6). The former however find
that the spectrum from 1150 to 3200 % is well fitted by a power law F(%)
_-2, i.e., F(m) = constant. These observations are in better agreement with
our results than those of ref. 6. The reasons for the differences in the
observations are not entirely clear, but may be due to: (a) the observa-
tions not being carried out at the same time, (b) the neglect of reddening
in ref. 6 and (c) the fit to the UV flllx in ref. 15 being'made without dis-
tinguishing between the eclipsed and uneclipsed flux or subtracting out the
soft X-ray component.
In conclusion it is suggested that the magnetic field in AM Her is
B _ 5 x 107 gauss which is a factor of about 4 below the usually adopted
value. This lower value is consistent with estimates for the field strength
made in understanding the optical polarization observations (ref. 9). The
UV flux from the shock heated region is predicted to deviate from the
Rayleigh-Jeans spectrum.
517.
REFERENCES
i. Tapia, S.: Astrophys. J. (Letters), 212, L125, 1977.
2. Chanmugam, G.; and Wagner, R. L.: Astrophys. J. (Letters), 213, LI3,
1977.
3. Stockman, H. S.; Schmidt, G. D.; Angel, J. R. P.; Liebert, J.; Tapia,
S.; and Beaver, E. A.: Astrophys. J., 217_____815, 1977.
4. Masters, A. R.: The Binary System Containing the Pulsar PSR 1913+16
and Ultraviolet and X-radiation from Accreting Magnetic White _arfs.
Ph.D. Thesis, Univ. of Illinois at Urbana, 1978.
5. Lamb, D. Q.; and Masters, A. R.: Astrophys. J. (Letters), 234___,LII7,
1979.
6. Raymond,. J. C.; Black, J. H.; Davis, R. J.; Dupree, A. K.; Gursky, H.;
Hartmann, L.; and _tilsky, T. A.: Astrophys. J. (Letters), 230____,L95,
1979.
7. Chanmugam, G.; and Wagner, R. L.: Astrophys. J., 232, 895, 1979.
8. Chanmugam, G.: Astrophys. J., 1980, in press.
9. Chanmugam, G.; and Dulk, G. A.: Astrophys. J., to be submitted.
i0. Ramaty, R.: Astrophys. J., 158____,753, 1969.
11. Dulk, G. A.; Melrose, D. B.; and White, S. M.: Astrophys. J., 234,
1137, 1979.
12. Swank, J. H.; Lampton, M.; Boldt, E.; Holt, S.; and Serlemitsos, P. :
Astrophys. J. (Letters), 216, L71, 1977.
13. Tuohy, I. R.; Lamb, F. K.; Garmire, G. P.; and Mason, K. O.:
Astrophys. J. (Letters), 226____,LIT, 1978.
14. Lamb, D. Q.: In Compact Galactic X-ray Sources, Eds. F. K. Lamb and D.
Pines (Univ. of Illinois at Urbana), p. 27.
15. Tanzi, E. G.; Tarenghi, M.; Treves, A.; Howarth, J. D. ; Willis, A. J.;
and Wilson, R.: Astron. Astrophys., in press.
518
16
-i
20
O
-2
I 1 I 1 i I 1
o l 02 o3 o4 o5 o6 07 o8 o9 Jo
cos8
Fig. I. Plot of the log of the intensity I vs. cos 0 for A = 106 ,
h = 106 cm, kT = 20 keV and _/mc = 8, 12, 16 and 2O.
\ 6
A= 2.0 xlO 6
_, ...°.,°,,
_-I_
-- -2 A =0.5 xlO 6/
-3 I I I i I I I I I I2 4 6 8 I0 12 14 16 18 20
oJ/¢_c
Fig. 2. Plot of the log of the flux F(_), in arbitrary units, vs. _/_ for5 c
kT = 20 keV and A = 0.5 x 10b cm, 1.0 x 106 cm and 2.0 x 10 cm.
The curve RJ is the Rayleigh-Jeans flux, dashed curve is due to
Masters (ref. 4) while the dotted curve corresponds to 0.05 times
the Rayleigh-Jeans flux (cf. ref. 6).
519


Cyclotron emission from AM Herculis

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