Magnetic pair production is one of high-energy electromagnetic conversion processes important to the development of pair-photon cascades in pulsars. On the basis of current polar cap models, the properties of magnetic pair production in fast pulsars are discussed. Suppose there is a roughly dipole magnetic field at the stellar surface, the author estimate the effects on non-zero curvature of magnetic field lines upon curvature radiation from primary particles and pair production rate near the surface of pulsars

An, S.

English

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179
OG 8,2-13
ON MAGNETIC PAIR PRODUCTION
ABOVE PAST PULSAR POLAR CAPS
Sh_n An
Physics Department, BeiJing Teachers College
Chin_
ABSTRACT
Ma_aetio pair production is one of high-enersy electro-
m_Enetic conversion processes import&nt to the development
of Pair-photon cascades in pulsars. On the basis of current
l_lar cap models, this p&per is concerned with the proper-
ties of mLgnetic pair production in fast pulsars. Suppose
there is a roughly dil_le magnetic field at the stellar
sarfaoet the author estimate the effects of non-zero cuba-
tare of magnetic field lines upon ourw_ture radiation from
primary particles and pair production rote near the surface
of 1_Llsa_s.
INTRODUCTION
In current pulsar theories 1.2, primary particles accelarated to
extreme relativistic energies .by the electric field component along the
m_tic field near the polar cap emit cureature radiation, the photons
of which, with sufficient energies, will convert into electron-positron
pairs, and the processes will further develop into pair-photon cascade.
The secondary pairs resulting from the _scade (Lorentz factor _,_10 2-
10 3) then produce radio er optical emission via a conherent process,
and the s_lvi_ curvature photons constitute the observ&ble high
• energy x_diatien from pulsars. It is believed that magnetic pair produ-
ction is a very important attenuation mechanism governing the hard 7-
ray emission from pulsars. The main aim of this paper is to estimate
the of feat of non-sero ourvature_..ef ,m_netic field lines in fs_t pul-
sars on the magnetic pair production and the c_rvature radiation from
prima_y particles.
CURVATURE RADIATION AND MAGNETIC PAIR PRODUCTION
In the calonlatlon concerned with palr-photon cascade above polar
https://ntrs.nasa.gov/search.jsp?R=19850026596 2020-03-20T16:48:52+00:00Z
180
0o e.2-1_
cap, it is us_lly thought that primary p_rticles move alon_ curved
magnetic field lines with vanishin_ pitch angle, and that most of the
curvature radiation from primaries Is emitted into a forward cone of
half-a_le _I/T, the power of which, aocordin8 to the current estimate,
Is
where _o denotes the curvature radius of field lines. Theoretically, a
high-energy photon can be absorbed in an external magnetic field to
create e i pair only if the following kinematic condition holds, i.e., _
_stn 9 _ 2mc2, (2)
where _ is the photon energy, and e the a_le at which the photon pro-
pagates to the aBgnetic field. Accordir_ to this view, at the moment
when the photon is Just emitted by a primary particle the thremhold
condition (2) will not be satisfied because 8=0. Thus, the pair can not
be produced until e grows to exceed the threshold condition with the
prop_tin_ of the photon in the curved and rotatin_ dipole magnetic
field.
This point of view, however, would be parti&lly corrected, if the
effects of non-zero curvature of magnetic field lines on motion of
charged particles are taken into account. Within the framework of the
classical theory the associated calculation ( see another conference
paper by the author, OG 6.2-11) shows that the primary particle with a
longitldinal initial velocity parallel to a field line possesses in
fact non-=ere pitch angle _ for which one can approximately write
-' 1.7x1037/BpIlt= c ¢. 1, (3)
where _=v/o,_=eB_mc is the relativistic cyclotron frequency, and Bp
the magnetic field intensity at the pole of pulsar. The citrvature
radius of the particle orbit Roc is then
nee-"R,,c/21sin(%t/2)i, (4)
which differs from the curvature r_dius of the field line Rmc. This
implies that the radiation from primaries is of the synchro-curvatmze
radiation, whose power (averaged over a cyclotron period) can be easily
found with a direct calculationt
____ 2 4 2 2 4_4%2c_2
 i oh-ourv = 0 (e c/oc)dC%t)-"
181
0G 8.2-13
which is Just twice that of the net curvature radiation. Bearing in
mind that the power of synchrotron radiation, arising from the helical
motion of a relativistic particle with the pitch angle _ and Lorentz
factor _ in a constant uniform magnetic field, may be put into the
form 4
which is formally identical with (1), it is immediately evident that in
the case represented by (3) both the synchrotron radiation and the owr-
vature radiation would make roughly the same contributions to the total
power. A direct consequence is that one can establish a quantitative
criterion for estimating the components of synchro-curvature radiation
from a relativistic electron with various possible initial conditions,
that is t the curvature radiation becomes si_lificant only when the
pitch angle of the electron does not increase beyond the value given by
(3), otherwise the synchrotron radiation will be dominant.
On the other hand, it is possible that at the moment when the
photon is Just emitted by the primary the threshold condition (2) with
@=e0=_might be satisfied due to _%O, so the pair could be created. In
pa_-_ticular, in the cases where @0=_1/_/, the curvature photon could
nearly satisfy even a much more severe condition imposed by dynamics of
magnetic pair production, _'5 i.e.,
_ sine_o.2(BcJBp_)mc2, (6)
where
Bor= m2c3/_ "-4.414xI013G.
Under this condition one would anticipate for a considerable pair con-
version rate.
IN APPLICATION TO FAST PULSARS
Fast pulsars possess usually shorter period, and sometimes weaker
magnetic field. Most spectacular and extreme is the millisecond pulsars
such as PSR 1937+214 for which the period P=1.558ms and field intensity
Bp&3xIOSG. 6 Suppose there is a dipole magnetic field at the stellar
surface, and take the stellar radius R&lO6cm, one readily finds the
curvature radius of field lines in the polar cap
" 2.7Xl 06cmR=c = (CRP/2_')I/2 = (7)
and the Lorentz factor of primary particles
182
OG 8.2-13
"Y'-3.1x106(Rmc/106cm)4/7(p/1s)'1/7(Bp/1012G)-1/7&4.4x107 (8)
for PSR 1937+214. Inserting (7) and (8) into (3) we obtain the pitch
angle of primary _rticles
_& 1.7;_1037/BpRmc -" 10-4 >> 1/'Y. (9)
It is easy to see from (4) and (5) that considerable radiations occur
only at about RocfRmc/2 , and so the critical energy of the curvature
photon can be written, approximately,
_r = 31_c 2Roc = c = 1"8xlO12ev" (10)
BY using (9) and (10) we have
_%OOorSin80& _cr_& 570mc 2 >> 2mc2 (11)
Bo-')xl08G. This representation shows clearly that at the momentfor
when the curvature photon is just emitted by the primary the threshold
condition (2) is already exceeded greatly.
Batta 7 has recently placed an upper limit on Bp of 107G for PSR
1937+214 based on rotating neutron star models and realistic equations
of state. If so, one would yield
•%rSneo 6.72104=c2 (12)
which is closer to the value imposed by the dynamic condition (6) th_n
(11).
CONCLUSION
Our results point out that, when the effects of non-zero curvature
of magnetic field lines on the motion of an electron with initial velo-
city exactly parallel to field lines (such as the primary particle in
pulsars) are taken into account, the radiation power would be stronger
than that given by current curvature radiation theories, and the cur_-
ture photonl would convert into pairs more readily. One would expect
that these results would affect to a certain extent the theoretical
estimate for high-energy radiations from the millisecond pulsars.
ACKNOWLEDG_ENT
The author is grateful to Prof. Liaofu Luo for useful discussions.
REFERENCES
1. Ruderman, M. A. et. al., (1975), Astrophys. J. 196, P51.
2. Arorm, J. st. al., (1979), Astrophys. J. 23__!, PS-_.
3. Daugherty, J. K. et. al., (1983), Astrophy$. J. 273, P761.
4. Sutherland, P. G., (1979), Fund. Cos. Phys. 4, Pg"_.
5. Sturrock, P. A., (1971), Astrophys. J. 164, _529.
6. Alpar, M. A. et. al., (1982), Nature 3__Ot_-'P72S.
7- Datta, B., (1984), Nature 30___8,P538.


On magnetic pair production above fast pulsar polar caps

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