PULSARS

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Submitted on 1 Jan 1973

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PULSARS

F. Pacini

To cite this version:

F. Pacini. PULSARS. Journal de Physique Colloques, 1973, 34 (C7), pp.C7-35-C7-37.

�10.1051/jphyscol:1973706�. �jpa-00215352�

JOURNAL DE PHYSIQUE

Col/oque C7, supplkment au no 1 1 - 12, Tome 34, Novembre-Dkcembre 1973, page C7-35

PULSARS (*) F. PACINI

National Astronomy and Ionosphere Center Cornell University, Ithaca, New York 14850

and

Laboratorio di Astrofisica Spaziale Frascati, Italy

More than five years have now elapsed since the discovery of the first pulsars, in the winter 1967-68.

About one year later two pulsars were found in known sites of Supernovae explosions, the source PSR 0833 in the Vela Remnant and the source NP 0532 in the Crab Nebula. This led to the general acceptance of the neutron star hypothesis for the basic nature of these objects.

Much work on pulsar electrodynamics was done in the months immediately following these discoveries.

As a result we have probably understood several points of pulsar theory and the consensus about the rotating neutron star hypothesis appears well moti- vated.

Unfortunately, however, the theoretical under- standing of pulsars has come to a standstill in the last couple of years, probably because most of the problems to be solved are of great complexity.

In this talk, I would like to review the basic notions of pulsar electrodynamics with the aim of stressing the remaining ambiguities and unsettled questions.

As is well known, the formation of a neutron star can be accompanied by a very large increase in the strength of the magnetic fields. The electrodynamic behavior of the star is that of a rotating magnetized sphere, as described in classical textbooks.

Consider first the aligned rotator 0 I1 B.

In the laboratory, if we make the experiment, we will see that an external non-rotating circuit connecting the poles and the equator is traversed by a current.

What happens is that inside the sphere the very

Matching the boundary conditions on the star sur- face, one can find the surface charge density and the existence of an external quadrupolar electric field.

If outside the star there is a vacuum, we have E x B

0 and the external field is of order

Q R ,

E

-

^{-- 10"} B , , as-' R , voltslcm .

C

The electric force on a surface charge (proton or electron) greatly exceeds the gravitational attraction

The electric field would in general also exceed the internal microscopic fields in the matter which are of order

x 10" volts/cm.

This implies that protons and electrons can be extracted from the star and form some sort of magne- tosphere which behaves like an extension of the star itself.

Also, if we neglect inertia and assume infinite conductivity along the magnetic lines,

high conductivity would lead to infinite currents unless

the total electric force were equal to zero. The magnetic field lines are equipotentials.

This implies The magnetosphere can corotate as long as the

v x B electromagnetic forces dominate the inertial forces

E - - - -

C u 2

eE(n- - n,) 9 y p 7 .

v = Q x r .

There should be an internal charge redistribution

such that This inequality is bound to fail at

- c/Q or for

v x B very large densities of plasma.

d i v E

div7

47re(n-

n,) It is obvious then that not all the field lines can be associated to corotation. The plasma anchored to

~~~~d upon an Invited paper at the 1973 Meeting of the

those lines which extend beyond the critical distance

French Physical Society (Vittel, May 1973).

cannot corotate when

>

there should be an

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973706

C7-36 F. PACINI

outflow of plasma accompanied by a bending of the field lines. This causes a n energy loss of order

1Q.b ='L

-

⁺ 2)

- ^B:,

(assuming that

E ~ ] ) .

The observed slowing down rates determine B,,, the magnetic field strength a t the critical distance R,.

This is of order lo6 gauss for the Crab pulsar and only a few gauss for pulsars with P -- 1 s. If the field geometry is dipolar, this implies

The usually quoted figure B - 10" gauss for the magnetic field o n neutron stars assumes that the field has a dipolar geometry between the star and the critical distance. However, as we have mentioned before, much stronger multipoles could be present close to the star, and one should not believe too much that the surface fields are of order 10" gauss

all that we really know is that a t r --

certain magnetic torque which we can estimate. The presence of strong multipoles on the surface could drastically affect, for instance, the rate of plasma extraction from the star (in this sense they could influence the pulsar electrodynamics as well).

There are some other points which are relevant to our discussion.

The first concerns the sign of the charges escaping along the open field lines. This is determined by the sign of the electric potential, and one can see that charges of different sign escape along different field lines. There is here, however, a somewhat puzzling situation since, if E x B

0, the sign of the charge density changes along any given field line at a cer- tain point. I t is not clear, or perhaps even highly doubtful, that we can have a stream of charges of one sign surrounded by charges of the opposite sign.

It appears more likely that the condition E x B

0, which entails Ell

0, fails in the open magneto- sphere. In this case the particles could be accelerated along the open field lines by an amount which depends upon the magnitude of the residual electric field. If the field were the vacuum field, the Crab pulsar c o ~ ~ l d accelerate particles electrostatically up to an energy - 1016 eV, giving rise a t the same time to a system of poloidal currents. If the number of escap- ing charges were determined by the Poisson equation, the corresponding poloidal currents would give rise to an extended toroidal field of magnitude

problem in the region

<

by various investigators and, in greater detail, by Mestel. The problem obviously becomes more messy because of the time-dependency. The main novel feature of the obliq~ie rotator consists in the emission of low frequency electron~agnetic waves a t the basic rotation frequency

Again, this leads to an energy loss across the speed of light surface given by the flux of the Poynting vector, i. e.

the same as in the case of an aligned rotator. (It should, however, be noted that before we were dealing with the parallel component, now we are dealing with the perpendicular component of the magnetic field).

Whether these low-frequency electromagnetic waves really exist and propagate away from the pulsar as a pure electromagnetic phenomenon or whether these waves would be of a magnetohydrodynamic type, there is no general consensus. Obviously, the answer depends upon the density of the circum-pulsar plasma.

In any case, there is consensus about the fact that the usual propagation condition

wave frequency > plasma frequency

is irrelevant because one is dealing with a very intense flux of strong waves having an energy density

plasma energy density.

Very little work has yet been done about the exis- tence and the propagation of these waves, but it is clear that these fairly difficult problems have to be investigated.

On the other hand, if they exist, these waves would be exceptionally good carriers of energy. Gunn, Ostriker and others have shown that they would impart very high energies to any charged particle with which they interact. Since the magnetic compo- nent of the wave field also decreased like llr, it has also been suggested that perhaps the whole Crab Nebula is permeated with low frequency waves and that the nebular magnetic field is a wave, rather than a static, field. If so, as shown by Martin Rees, the optical nebular emission would show a few percent of circular polarization which is not observed

Angel and Landstreet have as an observational upper limit - ^{0.03 %.} Of course, this does not rule out the presence of waves in the Nebula

it only implies that their energy density is 5 the energy density of the static field, so that the particles lose energy pre- dominantly in the static field.

We can now summarize as follows the main conse- quences of the unipolar inductor niechanism and of the emission of low frequency electromagnetic waves

at a distance

from the star. Again, for the Crab

energy loss cc

Nebula, B - ^{a t r} - 1 light year. Unipolar inductor \ corotating magnetosphere

Changing the angle between i2 and B from zero poloidal currents, toroidal field

to a finite value does not alter the basic nature of the electrostatic acceleration.

PULSARS C7-37

energy loss

Dipole radiation \ very strong wave field

) extended magnetic wave field acceleration in the wave.

We can also try to compare the predicted conse- quences with the real life, as it manifests itself in the Crab Nebula. This is done in Table I.

TABLE I Theory versus real llfe

Theory Observation

- -

b

IQSZ -- ergs. s-'

-

-'

q(n-

n,) - ^{s-' q}

1 I I ( E ) ~ E =

n(E) monochromatic

B,,, -

BtorIBwave 2

B,,,, -

^B,,, - ^G

Let me make some remarks and mention some of the possible explanations for the discrepancies.

a) The difference between the predicted braking index and the observed value can be due to several causes, including a decreasing moment of inertia for the star and a disalignment of the rotation and magnetic axes.

Personally, I find attractive the idea that this dis- crepancy is simply caused by the outflowing plasma which stretches radially the field lines.

b) The well-known

% or so coincidence bet- ween the pulsar energy loss and the Crab luminosity

should be handled carefully, since we do not really know exactly the stellar moment of inertia.

c)

A serious discrepancy exists between the charge outflow from the pulsar, - sC1, and the number of particles which are continuously accelerated in the Crab Nebula, about 1 0 4 0 s - 1 . It has been suggested that the low energy radio-emitting particles in the nebula are of a fossil nature and have been accelerated very early during (or soon after) the explosion. I t has also been suggested that the low energy particles are accelerated in the filaments. Both these possibilities would reduce but could not eliminate the discre- pancy, and in any case, there are serious arguments against these suggestions. It seems to us more likely that there is very little charge separation in the outflowing plasma.

(1)

The discrepancy between the theoretical mono- chromatic character of the accelerated spectrum and the observed power law spectrum can be removed in various ways. For instance, by using the electro- static acceleration at various distances from the star or, alternatively, by injecting particles at various distances from the star in the wave region.

In real life, one might also have to wonder about acceleration in a wave field where plasma effects cause a ratio E / B

1 or when a static magnetic field is superposed to the waves. Despite these pro- blems, we can be fairly satisfied with the idea that in the first five years since the discovery of pulsars we have probably understood the basic nature and some of the physical properties of these objects.

Acknowledgments. ^-

The National Astronomy

and Ionosphere Center is operated by Cornell Uni-

versity under contract with the National Science

Foundation. This work was also partially supported

by NATO Grant