An expression for the rate of energy generation by a pulsar an estimate of contribution from all the pulsars in our galaxy to the observed cosmic ray intensity was presented. The theory was then developed to an expanded version, and observational facts supporting the theory were cited

Fan, C. Y.

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160 OG 8.2-3
SCALING FROM JUPITER TO PULSARS AND THE ACCELERATION
OF COSMIC RAY PARTICLES BY PULSARS, III
C. M. Fan
Department of Physics,Universityof Arizona, Tucson, AZ 85721, USA
1. Introduction. In our first paper on this subject (Fan and Wu, 1981), we derived
an expression for the rate of energy generation by a pulsar and estimated the
contribution from all the pulsars in our galaxy to the observed cosmic ray
intensity. The theory was then developed to an expanded version, and
observational facts supporting the theory were cited (Fan et al., 1982; Fan and
Hang, 1983). In this paper we supplement additional evidences.
2. Brief Review. The theory is based on two propositions:
(1) The rate of the energy generation by a spinning pulsar is given by
dT M2_ 2
dt - K Re 2 , (1)
where M, R, and toare respectivelythe magnetic dipole moment, the radius,and
the angular velocity of the pulsar; e is the velocity of light, and K is a
characteristicconstant of the surrounding medium. This expression should be
viewed as Chin's Law in cosmological scale in which the EMF isgenerated by the
spinning magnetized celestialbody and K is a measurement of conductivity of the
medium.
(2) The magnetic dipole moment of the pulsar, M, is related to its angular
momentum L by the following expression:
M = e_L , (2)
where (_isa "form factor,"a characteristicconstant of the interiorof the pulsar.
It is an extrapolation of so-called "Bode's Law" of planetary magnetism. The
relationshipseems to hold approximately true for all celestialbodies whose
magnetic dipie moments and angular momenta have been estimated or measured.
•They are over 15 orders of magnitude with Mercury, Venus, and Mars at the lower
end and 24 Babcock magnetic stars at the upper end of the ladder, including a
neutron star in the middle. The physical reason behind this fundamental relation
is not known.
By combining (1) and (2), we have for the rate of energy generation as
dT K_ 2 L2m 2 Ke 2 I2m"
dt- c 2 R - c 2 R ' (3)
where I isthe monhent of inertiaof the pulsar. Since T = 1/2 l_o2,we have finally
2 dto 2K_ 2 I
- (4)
m s dt c 2 R
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161 OG 8.2-3
The values of K and _ were determined from the observation on Jupiter; they are
2xl0-2/sec and 2x10 -Is gauss cm.s.g -1, respectively. The scaling constant ke¢2 is
then 8x10 -3_ cm.s-l.g -1. Equation (4) allowed us to use measured values of o) and
dm/dt of a pulsar to calculate its I/R, and then, by invoking neutron star models,
we determined the mass m, the moment of inertia I, and the radius IR of the
pulsar and calculated the value of dT/dt.
3. Additional Evidences. An integration of Eq. (4) yields
1 i 2K_ 2 1
o)2- _ =_'t , y= 02 R ' (5)(do
where o)0 is the initial angular velocity of the pulsar. Assume that c00>>_0, then
1
= xt . (6)
Figure 1 is a plot of log(2/o) 3) (-do)/dt) against logo) for 202 pulsars (Fan et al.,
1982). The pulsars at the left lower corner of the figure appear to be on a
straight line given by Eq. (6) with t as a parameter. We interpret the line as the
.... 3b -1 -1
age hmit of all pulsars. Using 8xlO cm.s g for the value of Ko¢2, wel:ind t ~
6x10 is sec (0.5 billion years). Consider the fact that the scaling constant could be
off by a factor of 10, the time limit seems to be reasonable.
The low-energy charged particle (LECP) on Voyager 1 and 2 also detected a
flux of hot plasma escaping from the Saturnian magnetosphere, just like in the
case of Jupiter (Krimigis et al., 1981). Although the dynamics of the Saturnian
magnetoshpere may be complicated by the existence of the rings, the energetic
particles escaping from the system can be used to make an order-of-magnitude
check of the prediction of Eq. (1). Estimating from their published figures, the
escaping flux of 53-85 keV ions from the Saturn appears to be a factor of 100
lower than that from the Jupiter. The prediction of Eq. (1) is 1000.
Refererences
Fan, C. Y. and Wu Jiping, 17th ICIRC, Conf. paper 1, 58 (1981).
Fan, C. Y., et al., Astrophys. 3. 260) 353 (1982).
Fan, C. Y. and H. IR. Hang, 18th ICIRC Conf. paper 2, 287 (1983).
Krimigis, S. M., et al., Science 212, 225 (1981).
182
OG8.2-3
o
34 _
-20
0 I 2 3
Log_d(sec-')
Fig. I. A plot of log(2/m3) (-dm/dt)againstlogm.


Scaling from Jupiter to pulsars and the acceleration of cosmic ray particles by pulsars, 3

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