ASTROPHYSICAL PROBLEMS OF CONDENSED MATTER IN HUGE MAGNETIC FIELDS

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ASTROPHYSICAL PROBLEMS OF CONDENSED MATTER IN HUGE MAGNETIC FIELDS

M. Ruderman

To cite this version:

M. Ruderman. ASTROPHYSICAL PROBLEMS OF CONDENSED MATTER IN HUGE MAGNETIC FIELDS. Journal de Physique Colloques, 1980, 41 (C2), pp.C2-125-C2-131.

�10.1051/jphyscol:1980220�. �jpa-00219812�

ASTROPHYSICAL PROBLEMS OF CONDENSED MATTER IN HUGE MAGNETIC FIELDS M. Ruderman +

Department of Physics, Colombia University

Abstract,- Various aspects of the physics of collapsed stars with huge magnetic fields are surveyed. Special problems include 1) unexplained spectral features in magnetic white dwarfs with magnetic fields well above I O ^ G ; 2) determination of the average dipole field and the local polar cap fields of neutron stars ; 3) the possibility of huge interior toroidal fields ; 4) mechanisms for variations of neu- tron star dipole moments during a pulsar's lifetime ; 5) the structure of condensed matter and its physical properties in neutron star magnetic fields above 1 0 1 2 G ; and 6) the nature of pulsar surfaces and some possible observational consequences.

L. Introduction.- It is fairly certain that the huge magnetic fields of neutron stars and

magnetic white dwarfs are relics from the ti- me of their formation rather than an effect of continuing dynamo action or, for neutron stars, a consequence of a ferromagnetic sta- te of compressed nuclear matter. The simila- rity in numbers of stars in each family

-3 -2

(10 -10 of all stars), of magnetic fluxes 23 24 2

(10 -10 G-cm ) , and of angular momenta may hint at a common ancester. But the ori- gin and structure of the magnetic fields re- main obscure.

Even if the stellar surface fields were accu- rately known there are special physical pro- blems in huge magnetic fields which are exac- cerbated by the absence of experiments in such an environment. Laboratory magnetic fields are insufficient to affect atoms, mo- lecules, and condensed matter in ways that produce very large changes in structure and phenomena. The magnetic part of the Hamilto- nian of a single electron in a uniform field B is

This gives an energy greater than that of Coulomb binding for the K-electron in an a- tom of atomic number Z when

Even for B > 10~ B (Z = 1) perturbation theory is insufficient for descriptions of H atoms, of the outer electrons of other a- toms, and of highly excited states. The surfaces of some magnetic white dwarfs and of most, perhaps all, neutron stars are in this regime. In fields B which approach B

2 3 -1 13 c

= m c ( iie) ~ 4X10 G, fields which may be nearly achieved on some neutron star surfaces, even the properties of the vacuum are significantly altered in ways which af- fect the propagation of radiation through it.<X

In the following sections we shall survey only some aspects of the physics of huge magnetic fields within and on the surface of collapsed stars. Limitations of space preclude consideration of the effects of such fields on accreting plasmas and espe- cially on the emission and transport of po- larized x-ray radiation in such magnetized media. These are fields in which there is now a great deal of interesting work, much of it closely related to x-ray observations.

2. Magnetic White Dwarfs with B > 10 G . - Magnetic white dwarfs with surface fields between 5*10 and 3X10 G constitute about JOURNAL DE PHYSIQUE Colloque C2, supplément au n° 3, Tome 41, mars 1980, page C2-125

Résumé.- On étudie différents aspects de la physique des étoiles effondrées avec de très grands champs magnétiques. Ces problêmes particuliers sont 1) les caracté- ristiques spectrales non expliquées des naines blanches avec champ magnétique très supérieur à ÎO^G ; 2) la détermination du champ de dipôle moyen et des champs lo- caux de calotte polaire des étoiles à neutrons ; 3) la possibilité d'existence de très grands champs magnétiques toroïdaux internes ; 4) les mécanismes de variation du moment dipolaire de l'étoile à neutrons durant la vie d'un pulsar ; 5) la struc- ture de la matière dense et ses propriétés physiques dans le champ magnétique des étoiles à neutrons au-dessus de 10 G ; et 6) la nature de la surface des pulsars et quelques conséquences observationnelles possibles.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980220

c2- 126 JOURNAL DE PHYSIQUE

3% of all white dwarfs. A dozen isolated 0- ve most of the stellar surface, exceeds that nes have been visually observed. Below B

-.

even of a pure dipole(3. The strong absorp- 5x10 7 G Zeeman patterns of H and He are suf- tion features in this hot star may be asso- ficiently identifiable to fix B in the ran- ciated, instead, with a bound-bound atomic ge (5-40)'lO 6 G for five of them. In one ca- absorcjtion line which is approximately sta- se CH and C2 molecular bands fix B in this tionary for B around whatever value exists range. Here the physics and the interpreta- on the surface of GD 229. Some selected tion of spectra seem straightforward. The transitions in certain fields above 2x10 8 presence of fields in excess of 10 8 G is are known for H. (4,5,6

*erred franstronger lcontinuum circular po- Until more transitions, fields, and atoms larization and, in sdme cases, linear pola- have been calculated the interpretation of rization, and also b$ the fact that calcula- these interesting spectral features is li- ted spectra for lower fields are not obser- kely to remain unclear.

ved. Unfortunately non-perturbative spectra

for B considerably in excess of 10 8 G are not 3, Magnetic Fields on Neutron Star Surfaces yet available. Even electron cyclotron reso- Except in the one possible case of Her x -1 nance, which for a free electron occurs at there are not neutron star observations

3 -1 O

X = 12'10 (B8) A, is in the visible region which would give directly the magnetic Here is a regime of atoms in strong magnetic field on the stellar surface. Rather the fields B of order B1 which needs much quan- magnetic field is inferred from the measu- titative work. An interesting case is the red slowing down rate of isolated pulsars, observed spectrum of GD 229 shown in~ig(1) or the spin-up rate of accreting neutron

stars in close binaries, In the former case a variety of models give essentially the same relationship between the magnetic

142 - GO 229 BLACK BODY field at the "light cylinder", a distance

14.4 - 2c/P (P = period) away from the star, and

14.6 - the energy loss rate, If it is assumed that

the field at these large distances can be

r n ~ extrapolated in toward the star with the

distance dependence of a dipole, then the surface dipole component ( B ~ ~ ) is

Bs d

-

^{( P 6 I}

^c2

^{) 1/2 ( 3 )}

4a R~

1.0 12 1.4 1.6 1.8 2.0 2 2 2.4 2 6 2 8 3.0

with $ the measured period spin down rate

1'

x

and I the stellar moment of inertia. For

Fig. 1 Mutichannel spectrophotometry of GD 229 fixed I 5. 1045gcm-2 data give the distri-

(Greenstein and Boksenberg 1978) ( 3 bution of B~~ given in Fig ( 2 ) . where this

A ' (104cm-1).

field is plotted versus P/+, a conventional This spectrum is characterized by a deep re- definition of "age" which may or may not be

a measure of how old the star really is. (7 latively narrow circularly polarized absorp-

"

tion feature at X = 4135 A and a smaller ab-

0

sorption feature at X = 5295 A, If the main absorption is caused by free-electron cyclo- tron resonance absorption, B = 2.6 10 G. 8 But the required uniformity in B to give so narrow an absorption line,

(ah

= 0.05. full

X

width at half maximum) deep enough to invol-

I emission at 58 keV or absorption near 40 kev!1° This would imply a surface polar ma-

I I I \ I I I

I

I

gnetic field of about 5 x1012G. The neutron star of the binary Her x-1 is presumed to have become an x-ray source only since its close companion evolved off its "main se- quence" and filled its own Roche lobe. This

.

should have taken of order 10 years so 9 that the neutron star is very old, Both its

..a

.O age (comparable to that of very "old" pul-

\ ^a; sars) and its spin-up torque suggest a B d

.

^-

_{. .}

an order of magnitude less than B for the S

polar cap implied by the cyclotron resonan-

'\

ce interpretation of its x-ray spectrum. If

\ the polar cap 'B is indeed much larger that

\ B? there must be many miltipoles in the surface field, This non-dipolar structure

I

^{I I I I I} is quite opposed to evidence for very

1 0

' 10' lo6 0' lo8 10'

( geers) smooth fields on magnetic white dwarfs(2 PIP

but is, at best, only hinted at by the data.

Fig 2 : The arrow n = 2.6 gives the observed evolution 4, Interior Fields, Currents, and Evolution of the Crab pulsar with Eq. (3). The dashed

line is a theoretical, model dependent, pul-

.-

AS in the case of other stars, including

sar extinction line. The downward pointing ar- the sun, the surface field of a neutron row is the ultimate evolutionary path when the

dipole decays exponentially. star does not necessarily reflect the inte- rior field. Within a neutron star magnetic The data plotted in Fig (2) are not inconsis-

fields exceeding lol'G could be buried and tent with the scenario that very young pul-

still have x forces balanced by pressu- sars have surface dipole components above a- re-gradients, Tosoidal fields lo2-10 times 3 bout 3 x 1 0 ~ ~ ~ which (at least for the Crab

the average surface 1 G dipole field almost pulsar) seem even to grow somewhat during a-

6 certainly exist beneath the surface of the dolescence. But in old age 12 10 years) the

sun, which would correspond to 1014-1015~

dipole moment diminishes. (7r8 Such an inter- in a neutron star. Possible initial diffe- pretation is, however, hardly compelling and rential rotation during neutron star forma- all pulsars with large P/; are not necessari- tion might have been comparable to average ly even old. angular rotation. It could have built up a Accreting neutron starspin-up torques are al- toroidal field exceeding 1015G in the Crab so only sensitive to the magnetic field far pulsar if equipartion between differential from the star near the "Wlfven-radius" where rotational energy and toroidal field ener- magnetic pressure approximates the rotational gy were achieved, In these contexts an ini-

( 9

energy density of the accreting plasma. tial interior neutron star field as small Extrapolation to the stellar surface general- as several. 1012G would be small.

IY gives BSd in the range lo''

-

^{lo'' and} The electrical conducti;ity of the interior 8-10" G for Her x-1. This is consistent with matter from relativistic (- MeV) dege- typical inferred B~~ of "older" pulsars ; nerate electrons and probably also super- and in the usual scenarios for x-ray binaries conducting protons is sufficient that ohmic the accreting neutron stars are expected to dissipation is ignorable in changifig large

7-

be old. There exists only a single possible scale fields maintained by currents beloG direct measurement of the field at the polar the crust of a neutron star during a pul- cap of a neutron star. This is based upon sar's lifetime. However Easson(ll has pain- the interpretation of the Her x-1 x-ray spec- ted out a novel relaxation mechanism by tral features in terms of electftjn cyclotron which sufficiently strong fields in dynami-

c2- 128 JOURNAL DE PHYSIQUE

cal equilibrium within the star may, never- theless, slowly move. The neutrons of an e- quilibrium neutron star must satisfy

1

^pn

= o where p is the neutron chemical poten- n

tial. For the charged components (assumed, for the moment, to be e and p)

But 8- equilibrium is achieved only when

vn

=

ve + up

which is, therefore, incompatible with j

-

x B

-

= 0. In the presence of j x

-

f? # 0 the charged components are effectively pres- sed upon by an additional force and thus ex- perience an additional pressure even where j = 0. This causes a net chemical potential

-

reduction from e

+

^{p -+ n}

+

^v in some regions and n -+ e

+

^p

+

in others, accompanied by the motion of field lines in reponse to tbe j x B force. With an axisymmetric purely to-

- -

roidal field the inner field lines are com- pressed toward the axis ; the outer ones are pushed out toward the stellar surface. For cold degenerate e, p, and n gases with BCS gaps negleted the time T for a force free state to be achieved is given by (12 T

..

^{10 3}

( ~ ~ ~ 1 - l ~ years. ~ n l e s i p and m BCS gaps are much less than 0.1 ~ e b , this is a very great underestimate for T. But a similarly motiva- ted motion of interior magnetic field lines may be achievable within a gapless pion con- densate. Here the conversion rate between n and eTp by weak interactions is faster. But more important is the rapid strong interac- tion conversion between a-+p and n. But if an interior (toroidal) field is relaxing in this way it can easily force a weaker 1 0 1 2 ~ poloidal field, around which it might be wrapped, to increase as the constant poloi- dal flux is squeezed through a smaller area.

(12 Might this, perhaps, even be observed as an increase in dipole moment for some very young pulsars, reflected in the kind of pos- sible increase with time of the Crab pulsays dipole moment which is one interpretation of its behavior on the plot of Fig (2)? As usu- al much more work remains to be done than has been done.

There are other suggested ways in which wea- ker magnetic fields, of order 1 0 1 2 ~ , may re- lax in neutron stars and thus account for a common interpretation of Fig (2) in terms of

a diminishing dipole moment with pulsar age, after lo6 years.

1) The crust of a neutron star probably so- lidifies well before the motions of the conducting interior of a just formed rapid- ly spinning star allow the magnetic field to achieve an equilibrium state. (7 That part of the field which threads the stellar surface is then frozen until crustal cur- rents die out from ohmic dissipation, which would have an exponential decay time of 10 ⁶ -10 years. A crust is probably strong e- 7 nough to sustain the necessary stresses on- ly for surface fields much less than 1013~.

When relaxation is ultimately allowed to proceed, the expected trend is toward a re- duced dipole moment.

2) It has been suggested that appropriate thermal stabilization may restrain deep in- terior matter motion, but only until the thermal contribution to (pressure) falls below that from ( 4 ~ ) - 1 ~

-

^{x ( V Y} x ~ ( l ~ ' . a This will occur for interior B

..,

¹⁰ 13 ^{G if the} thermal contribution to central pressure is less than about 10'1° of the total, but could occur earlier depending upon the form of B and the cooling mechanisms. For BCS p

-

and m fluids electron thermal pressure is expected to be the dominant contribution near 3x10' K, which is far below the esti- mated superfluid transition temperatures,

l ~ ~ K. -Below this, thermal pressure l ~ ~ ~ gradients can no longer play a significant role in balancing

2

x

5 ,

and interior fluid motion and field relaxation could proceed.

Similar models might use the slow rate for f3

-

decay to give small composition chan- ges after lo6 years which then permit inte- rior movement and thereby field adjustment.

Models that can account for a diminishing dipole moment in older pulsars are consi- derably easier to find then is the compel- ling evidence that the pulsar fields actu- ally behave in this way.

5, Matter in Superstrong Magnetic Fields.- A free non-relativistic electron in a uni-

form magnetic field is confined to move a- bout a field line with quantized kinetic energy

En = &aC

'

^{r d}

^g .

n Blr-lo4 eV. (4) mc

in circles with quantized radii sharp surfaces at which the density became v n = 11q2 p 1 n1 2

&

1/2

..

^2.6 10-lo n*cm.

..

10 gcm-3 over a distance much less than 1 4

a3 B I

12 A, and thus many of the interesting proper-

( 5 ) ties of a star with a condensed matter sur-

for integer n > 0. For B , 5x10 G, lfwc-. 60 12 face. However the simple model which leads.

to Eq (7), or any Fermi-Thomas type approxi- keV' and fi * 10-lOcm. As long as coulOmbr mation, cannot be used to estimate such bin- degeneracy, and thermal energies are all

ding energies, Rather one must a considerably smaller than hwc, equilibrium

much more complex and difficult calculation matter have = l. Because an e- of the condensed matter energy which inclu- lectron spin antiparallel to B given an ad-

-

des ion-electron and electron-electron cor- ditional energy reduction

-

%ac all elec-

relations and it to a similar calcu- trons in this state have spins antiparallel

lation of the binding energy of an atom re-

:

^{and a} kinetic energy that moved from the lattice but still in the hu- from motion along B. A degenerate sea of , .. ge magnetic field. Unfortunately the bin- such electrons has a fermi energy Ef rela-

ding energy of an atom in the condensed mat- ted to electron number density n

e by ter lattice relative to a free atom is the 4 2 4 2 difference of two relatively large energies E , ~ = 2 a A fi n e/m (6) and is not easely calculated, Details of Nuclei of charge -Ze minimize &eirreLa.tive such calculations and the quantum mechani- coulomb energy in a uniform negatively char- cal description of the appropriate wavefunc- ged sea by arranging themselves into a bcc have been discussed (I4 and lattice. The total energy per nucleus for Only a brief be given here* A such a lattice in the uniform degenerate classical electron in a strong magnetic fie- sea of Eg (6) is ^Id attracted to a fixed positive charge

will move as in Fig (3) : motion with the E(R) =

-

^{0.896 + ZIT'Z a 2 p 4}

³²

3 m )'(4.R3 ^(,)

cyclotron frequency wc about a guiding

R center which slowly moves in a circle of

with the radius of a sphere around each radius PI,, about the fixed charge. Bohr- nucleus which contains electrons. Minimi- So-erfeld quantization gives P',I = (2m1 zation of E(R) with respect to R gives a

+

^{1) with m' = 0,1,2,.}

. . ^,

as well as mass density fixing the cyclotron radius at

P.

In the

6/5 wave mechanical description the Schroedin-

p = 9 x 1 0 ~ B X 2 g cm-3 (8) ger wave functions appropriate for minimal

7

cyclotron energies (n = 1 in Eq (4) ) are

2 6 all of the form (Landau orbitals)

For iron nuclei and B12 = 5 this corresponds to a matter density at zero pressure of p-- 2 x 1 0 ~ gcm -3. For He, p

..

7 x 1 0 ~ gcm-3. At these densities for matter at zero external pressure the average electron fermi energy

...

lkev, one two orders of magnitude less than'liwc so the presumption of electrons in lowest Landau orbitals only is reasonable.

This approximation will break down at high pressures and densities where Ef ,-. 6wc This is reached when p 2x10 g6 cm'3 at p

..

3 x 1 0 ~ ~ dynes cm-2, several meters below the

surface of a typical neutron star. "ig.3

.-

If neutron star surfaces have temperatures

qm1

= exp

(- ^$)

^p1

^{I m 1}

e x p (iml+ f ( z )

much less than lattice binding energies, one

could conclude already that such stars had (9)

C2- 130 JOURNAL DE PHYSIQUE

with z =he cordinate along B and f (z) arbi-

'%

tary. Light atoms obtained by putting one e- lectron into each orbital and minimizing the

total energy by varying f(z) give atoms who- 6. Pulsar Surfaces.- Einstein Observatory se dimensions are indicated in Fig (4) where measurements of four typical pulsars (PSR they are compared to a typical atom with B = 0656

+

^{14, 1529}

+

^{28, 1952}

+

29 and 2327

-

o

represented as a sphere of Bohr radius, 20) give average surface temperature limits (I5 in heavier atoms exchange mergy among in tke range (0.6

-

^{1.1) x} lo6 ~ ( l ~ . Thus electrons are important and more than one e- KTmag

-

0.1 keV, far below the binding ener- lectron (with orthogonal f (z) 's) may exist gy ebtimates for .an iron surfaced neutron in the orbitals with small m'. In the conden- star!. Then the neutron star surface is sed matter approximation similar refinements sharp and condensed rather than diffuse and are necessary. For iron the calculated ener- gaseous as on conventional stars, (If T 5 gy, EB, for binding an atom into the conden- lo6 OK it is also solid rather than liquid).

sed matter lattice is indicated below. (14 Such a surface has the following properties a) It is almost a perfect reflector for pho- tons with electric polarization parallel to B for all 45 w

_<

^{-5 uplagma 5 keV. (A cold}

neutron star looks like a shiny silver sphe- re).

b) The Young's modulus parallel to EJ for In most scenarios for the birth of a neutron surface matter 1018 dynes cm-2, about 6 star it is born hot (T >> 10 10 OK) and with times that of steel.

violent internal motions. If it cools to its c) Anelectric field in excess of 1012 volts lowest energy state the surface will be iron is needed to pull positive ions free- as nucleons combine to a- particles, then to ly from the neutron star surface.

c12 and ultimately to Fe. But if the surfacc

is quiet and cooling is too rapid, non-con- This last feature is fundamental to certain vective, and with an x-ray luminosity below models for pulsar radio emission. Spinning the Eddington limit, a thin layer of He may neutron stars do not give polar cap elec- cover the cooled star. (This, may ultimately tric fields in excess of 10' B ~ ~ P - ~ / ~ volts

- -

be removed by pulsar processes for polar sur- /cm. Therefore a significant ion flow can- face ion lift off). For a He surfacg EB is not come from the neutron star polar cap very much less thant that for an Fe surface, unless the cap is heated, at least in cer- but I am unaware of quantitative calculations tain regions, Such heating may be caused

/

by inflowing extreme relativistic electrons

SPHERE OF RADIUS a.

'

Fig.4 : Shapes and sizes of light atoms in a 2 x 1012 G field.

of an electron-position discharge which is expected in 1 0 1 2 ~ fields whenever the po- lar cap electric field reaches about 10 ⁸ volts cm-l.

Pulsar models with ion flow from the polar cap of a spinning magnetized neutron star involve currents of c times B(Pc)-l, the net charge density in the local approxima- tely corotating magnetosphere above the gap. For B

-

^{3 ~ 1and P 0}

..

^{~0.3 s ~this re- ~}

presents a mass flow of 2 x 10 6 g cm'2 yr-l out of the cap. This is a large amount of excavation expected over substantial re- gions of the 10 cm radius cap. Since magne- 4 tized surface matter has a density of 10 4 g ~ r n - ~ the polar cap would be deepened at a

r a t e of 2 m e t e r s p e r y e a r i f it were n o t con- /12/ Ray, A. 1979 Columbia Univ. T h e s i s t i n u a l l y r e f i l l e d from below and p r o b a b l y /13/ chanmugarn, G. 1978 Ap

J. 221,

965 from t h e s i d e s . The composition o f t h e i n i -

/14/ Flowers, E., Lee, J-F., Ruderman, M., t i a l p o l a r c a p s u r f a c e l a y e r i s , t h e r e f o r e , S u t h e r l a n d , P . , H i l l e r b r a n d t , W. and p r o b a b l y i r r e l e v a n t . I f , i n t h e c o u r s e o f ex- filuller, E. 1977 Ap J 215, 291.

c a v a t i o n , d i f f e r e n t s u r f a c e l a y e r composi- /15/ Rudeman, 1974 Physics of Dense t i o n s a r e uncovered t h i s can a f f e c t p u l s a r M a t t e r , IAU Symposium. C. Hansen, ed.

p r o p e r t i e s . Thus a switch Fe

/16/ Helf and, D.

,

Chanan, G . , and Novick, bound i o n s ) t o He ( l o o s e l y bound i o n s ) and R., 1979 p r e p i n t .

back t o t h e He would be e x p e c t e d t o r e s u l t i n a temporary t u r n - o f f o f p u l s a r r a d i o e m i s -

s i o n ( " n u l l i n g " ? ) i n some p u l s a r models a s ' p r e p a r e d a t t h e As9en C e n t e r f o r P h y s i c s w i t h s u p p o r t from t h e N a t i o n a l S c i e n c e l o n g a s t h e H e s u r f a c e l a y e r s u p p l i e s t h e F o u n d a t i o n .

i o n s . More r e f i n e d c a l c u l a t i o n s on t h e b i n - d i n g o f i o n s i n magnetized n e u t r o n s t a r s u r - f a c e s would be needed b e f o r e t h e p o s s i b l e s i g n i f i c a n c e o f s u c h " s t e l l o g i c a l " f e a t u r e s c a n b e e s t i m a t e d . U l t i m a t e l y an u n d e r s t a n - d i n g o f r a d i o - p u l s a r s may depend n o t o n l y on t h e unknown g l o b a l s o l u t i o n f o r t h e magneto- s p h e r e (and beyond) o f a r o t a t i n g n e u t r o n s t a r , b u t a l s o on s e v e r a l o f t h e r e m a r k a b l e p r o p e r t i e s which r e s u l t from t h e i n t e r a c t i o n between condensed m a t t e r and huge magnetic f i e l d s .

/1/ Melrose, D. and S t o n e h ~ m , R . 1976 I 1 Nuovo C i m .32, 43 5 and r e f e r e n c e s t h e r e i n - /2/ Angel, J. Ann. Rev. A s t r o n Astrophys.

1978

16

487, and r e f e r e n c e s t h e r e i n , /3/ G r e e n s t e i n , J. and Boksenberg, A 1978

p r e p r i n t

/4/ Kemic, S., 1974 Ap.

J. 193

213 /5/ Smith, E., Henry, R., Surmelian, G . , )

C o n n e l l , R., and R a j a g o p a l , A 1972 Rev. D

2

3700

/6/ Praddaude, H 1972 Phys Rev A

5

1321 /7/ F l o w e r s , E. and ~ u d e m a n , M. 1977 Ap J.

215, 302 ^I

-

/8/ Kennel, C. e t a 1 1979 t o b e p u b l i s h e d . /9/ Lamb, F. 1977 Ann. NY. Acad S c i

302

482,

( P r o c . E i g t h Texas Symp. on Rel. A s t r o - phys.) Gosh, P. and Lamb, F., 1978 p r e - p i n t

/ l o /

Trumper, J., P i e t s c h , W., Reppin, C.,

Voges, W., S t a u b e r t , R. and K e n d z i o r r a , E. 1978 Ap J.

219

L105

/11/ Easson, I. 1976 N a t u r e ;

263,

486 Easson, I and P e t h i c k , C. t o b e p u b l i s h e d