The recent discovery of cyclotron lines from gamma-ray bursts indicates that the strong magnetic fields of isolated neutron stars might not decay. The possible inverse correlation between the strength of the magnetic field and the mass accreted by the neutron star suggests that mass accretion itself may lead to the decay of the magnetic field. The spin and magnetic field evolution of the neutron star was calculated under the hypothesis of the accretion-induced field decay. It is shown that the calculated results are consistent with the observations of binary and millisecond radio pulsars

Murakami, T.

Nomoto, K.

Shaham, Jacob

Shibazaki, N.

English

NASA Technical Reports Server

N90-22470
Does mass accretion lead to field decay in neutron stars ?
N. Shibazaki*, T. Murakami**, J. Shaharnt and K. Nomoto_
* Department of Physics, Rikkyo University, Tokyo 171, Japan
** Institute of Space and Astronautical Science, Sagamihara, Kanagawa 229, Japan
t l. Department of Physics and Columbia Astrophysics Laboratory, Columbia University,
New York, NY 10027, USA
:_ Department of Astronomy, Faculty of Science, University of Tokyo, Tokyo 113, Japan
The recent discovery 1,2 of cyclotron lines from gamma-ray bursts indicates that
the strong magnetic fields of isolated neutron stars might not decay. The pos-
sible inverse correlation 3 between the strength of the magnetic field and the
mass accreted by the neutron star suggests that mass accretion itself may lead
to the decay of the magnetic field. We calculated the spin and magnetic field
evolution of the neutron star under the hypothesis of the accretion-induced
field decay. We show that the calculated results are consistent with the obser-
vations of binary and millisecond radio pulsars.
Whether neutron stellar magnetic fields decay or not is at present a controversial issue.
Statistical analyses 4,5 of .._ 400 radio pulsars and the study 3 of the origin and evolution
of magnetized neutron stars in binary systems indicate that neutron stars are born with
magnetic fields of 1012G which then decay with a time constant of (5 - 10) x 106yr.
Estimates of age and magnetic field strength of binary millisecond radio pulsars, however,
require 6 that the field decay, if it occurs, should stop or proceed much more slowly on time
scales of > 10°yr, at field strenghts < 101°G. Pulsar models in which magnetic fields do not
decay but align with the rotation axis are shown to also be consistent with the observed
properties of radio pulsars 7,s,9
https://ntrs.nasa.gov/search.jsp?R=19900013154 2020-03-19T23:12:23+00:00Z
Ohmic dissipation of electrical currentsin thecrust hasbeenthought to be the physical
causefor field decayl°. However, recent calculations11of the ohmic decay of dipolar
magnetic fields haveshownthat the field doesnot decayexponentially ashasbeenassumed
in most statistical analysesof radio pulsars and that, if the field occupiesthe entire crust,
it decaysby only less than a factor of 100in a Hubble time.
'I_f the strong magnetic fields of neutron stars do not decay, then the origin of the
weak magnetic fields of less than 101°G,found in binary and millisecond radio pulsars12,
remainsto be explained. Neutron stars in binary and millisecond radio pulsars are thought
to be formed by the iron core collapse of massivestars or by the accretion-induced col-
lapse of massivewhite dwarfs (for reviews seerefs. 13 and 14). In one scenario for the
weak field and rapid rotation of millisecond radio pulsars it is argued that, quite"simply,
white dwarfslS,16J7or iron coresof massivestars 18 with the appropriate field strength and
angular momentum give birth to the observed millisecond radio pulsars after a collapse.
In another scenario, mass accretion in low mass X-ray binaries, which are assumed to be
progenitors of millisecond radio pulsars, is proposed to cause both the field decay 19 and
the spin-up 2°. In fact, Taam and van den Heuvel s found a possible inverse correlation
between the magnetic field strength and the estimated total mass of accreted matter for
binary X-ray sources and for binary and millisecond radio pulsars. This inverse correlation
supports the latter scenario. A study of the evolution of magnetic fields in the crust of a
neutron star 21 showed further that the inward heat flux caused by mass accretion powers
thermomagnetic effects that could remove the strong magnetic field of a neutron star.
In the present paper we examine further the possibility that magnetic fields of neutron
stars indeed decay only when neutron stars undergo mass accretion. We do that by con-
sidering gamma-ray bursts and the periods and field strengths of binary and millisecond
radio pulsars.
The recent discovery 1,2 of cyclotron absorption lines with energies 20 keV and 40
keV from gamma-ray bursts revealed that the central objects of gamma-ray bursters are
2
indeed strongly magnetized neutron stars with magnetic fields of 1012G as has already
been suggested in some theoretical works 22,23. The statistical arguments suggest ,-_ 107yr
(refs. 24 and 25) or >> 10Vyr (ref. 26) for the age of neutron stars in gamma-ray bursters
depending on the assumed distance. When combined with the high field strength, the
latter age estimate contradicts the field decay hypothesis whereas the former does not.
, We note that the absorption lines were seen only in a limited portion of the burst 1.
This observed fact can also be used to test the field decay hypothesis, if the cyclotron
absorption lines appear and disappear due to the rotation of the star, since the presence of
the cyclotron lines depends sensitively on the configuration of the magnetic field relative to
the line of sight 2_. If this is the case, the 5-10s duration of the cyclotron absorption feature
indicates the rotation period of > 10 - 20s. This rotation period and the field strength
put the gamma-ray burst sources into the category of the "turned-off" pulsars 5. If the
spin-down of the neutron star is caused by the magnetic field, which decays exponentially
on a time scale of rB, the variation of the rotation period P with time t is represented by
p2= AB]rB[1--exp(--2t/vB)] + P2o, (1)
where B0 and P0 axe the initial field strength and rotation period, respectively, and the
constant A = 9.8 x 10-4°sG -2 for a stellar moment inertia of 1045 g cm 2 and radius of
106 cm. In order to attain the rotation period of > 10- 20 s from the initial value of maybe
less than 1 s, magnetic braking requires the initial field strength of the neutron star to be
larger than ,,- 2 x 1013G if rB ,-_ 107yr. This value of the initial field is on the high side,
compared to the average values of ,-, 1012G indicated from the statistical analyses of radio
pulsars. In view of that we would like to pursue here the other possibility, namely, that
the magnetic fields of gamma-ray burst sources, which might be isolated neutron stars, do
not decay.
As already mentioned, the weak magnetic fields of less than 101°G are found in binary
and millisecond radio pulsars 12, whose magnetic fields are plotted against rotation periods
in Fig. 1. In the resurrected pulsar scenario2° the progenitors of millisecond radio pulsars
are the low massX-ray binaries and their rapid rotations are the consequenceof the spin-
up due to massaccretion in binary systems. Let us consider the weak magnetic field and
the rapid rotation of these radio pulsars in terms of the hypothesis that mass accretion
leads to both spin-up and field decay. We assumethat the magnetic field decayswith
accretionas
B0 B0
B = 1 + AMImB 1 + MtlmB' (2)
where B is the field strength at time t, AM the accreted mass, rnB the mass constant for
the field decay and M the accretion rate. Equation (2) fits well the inverse correlation
between the magnetic field strength and the estimated mass of the total accreted matter
for binary X-ray sources and binary and millisecond radio pulsars 3. As already noted by
Taam and van den Heuvel 3, this inverse correlation is also consistent with the simple field
decay hypothesis if the larger amount of accreted matter is interpreted simply to reflect the
greater age of the neutron star. Here, however, although we do not advocate any physical
model leading to equation (2), we do assume that a direct relatin between field loss and
accreted mass exists. Note that equation (2) represents a change in the whole field, not
just the component perpendicular to the rotation axis. Using the formula given by Ghosh
and Lamb 2s for the accretion torque, the variation of rotation period is described by
b = -0.11I-1(GM) 3/7(BR )2/7na96/ p2, (3)
where n is the dimensionless accretion torque (for details see ref. 28), R the radius, I
the moment of inertia and G the gravitational constant. The calculated evolutionary
tracks in the magnetic field versus rotation period diagram are illustrated by solid lines in
Fig. 1. Rotation periods and magnetic fields become smaller with increasing time. The
calculations were terminated when the inner edge of the accretion disk reached the surface
of the neutron star. When the mass constant for the field decay is m B > 10-3Mo, the
evolution proceeds along tile equilibrium rotation line 2s (dash-dotted line in Fig. 1), where
the spin-up torque due to accreting matter and the spin-downtorque due to magnetic field
are balanced. This is becausethe time scaleof the field decayis longer than the spin-up
time scale. After mass accretion stops, stars move horizontally rightwaxds in Fig. 1. If
mB > 10-4Mo, the calculated evolutionary tracks are consistent with B and P of binary
and millisecond radio pulsars. These evolutionary tracks are also approximately consistent
with B and P of low mass binary X-ray sources such as suggested from the beat frequency
model 29 for the quasi-periodic X-ray oscillations (see ref. 30 for a review). Note that the
possible inverse correlation s between B and AM is represented well by equation (2) with
me ,-. 10-4Mo. Hence, if we adopt rnB _,_ 10-4M®, the accretion-induced field decay
hypothesis represented by equation (2) is consistent with B, P, and AM as observed or
estimated for binary and millisecond radio pulsars and binary X-ray sources.
The magnetic fields of single radio pulsars are in the range of 1011 - 101SG with a
distribution peak around 1012G. The accreted mass of interstellar matter onto a single
radio pulsar is negligible compared to rnB ,.., 10-4Mo. Hence, the accretion-induced field
decay hypothesis argues that the present field strengths of single radio pulsars should be
equal to their initial values. This assertion, however, conflicts with the results of the
statistical analyses 4,5 of radio pulsars, which suggest that surface fields decay on a time
scale of (5 - 10) x 106yr. Pulsar statistics depends, however, on the assumptions made for
the radio luminosity law, the braking index, the magnetic field evolution, the distribution
of initial field strength and so on. In order to resolve the above conflict, the statistical
analysis under the assumption of no field decay should be conducted, examining especially
the dependence on the assumptions for the above properties.
Mass accretion of neutron stars is likely to give rise to the inward heat flow through
the crust. The thermomagnetic effects in the crust due to this inward heat flux, such
as suggested by Blondin and Freese 21, have been invoked as a possible mechanism of the
accretion- induced field decay. The formula of Blondin and Freese predicts, in its simplest
form, a stronger dependence of the field decay on time compared to equation (2). The field
5
decayformula due to the thermomagnetic effects,however,may dependon the structure of
the crust, the accretionprocess,and the history of the heat flux. More detailed study on the
thermomegnetic effects in the crust is important in order to resolve the controversial issue
of the field decay in neutron stars. Other possible mechanisms for the accretion-induced
field decay should also be explored.
' N.S. and T. M. thank Prof. J. A. van Paraclijs for useful discussions. J. S. thanks
Prof. Y. Tanaka and ISAS for their kind hospitality when this work was conceived. This
research was supported in part by the Grant-in-Aid for Scientific Research of the Ministry
of Education, Science, and Culture (01460011 8, 01540216) and NASA grant NAGW-1618.
This is contribution number 394 of the Columbia Astrophysics Laboratory.
References
1. Murakami, T. et at, Nature, 335, 234-235 (1988).
2. Fenimore, E. E. et al., Astrophys. J. (Letters), 335, L71-L74 (1988).
3. Taam, R. E. & van den Heuvel, E. P. ,1., Astrophys. J., 305, 235-245 (1986).
4. Lyne, A. G., Manchester, R. N. & Taylor, J. H., Mon. Not. R. astr. Soc., 213,
613-639 (1985).
5. Stollman, G. M., Astron. Astrophys., 178, 143-152 (1987).
6. Kulkarni, S. R., Astrophys. J., 306, L85-L89 (1986).
7. Candy, B. N. & Blair, D. G., Astrophys. J., 307, 535-539 (1986).
8. Cheng, A. F., Astrophys. J., 337, 803-813 (1989).
9. Kundt, W., Comments Astrophys., 12, 113-121 (1988).
10. Ostriker, J. P. _ Gunn, J. E., Astrophys. J., 157, 1395-1417 (1969).
11. Sang, Y. _ Chanmugan, G., Astrophys. j. (Letters), 323, L61-L64 (1987).
12. KuIkarni, S. R. in Physics of Neutron Stars and Black HoIes (ed. Tanaka, Y.), 37-53
(Universal Academy Press, 1988).
15.
16.:
17.
18.
19.
13. Van den Heuvel, E. P. J. in The Origin and Evolution Neutron Stars (eds. Helfand,
D. J. & Huang, J. -H.), 393-406 (Reidel, Dordrecht, 1987).
14. Nomoto, K. in The Origin and Evolution Neutron Stars (eds. Helfand, D. J. & Huang,
J.-H.), 282-303 (Reidel, Dordrecht, 1987).
Michel, F. C., Nature, 329, 310-312 (1987).
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Chanmugan, G. & Brecher, K., Nature,
Grindlay, J. E. & Bailyn, C. D., Nature,
Brecher, K. & Chanmugan, G., Nature,
329, 696-698 (1987).
336, 48-50 (1988).
338, 712 (1989).
Van den Heuvel, E. P. $., van Paradijs, 3. A. & Taam, R. E., Nature, 322, 153-155
(1986).
Alpar, M. A., Cheng, A. F., Ruderman, M. A. & Shaham, J., Nature, 300, 728-730
(1982).
Blondin, J. M. & Ft-eese, K.,
Michel, F. C., Astrophys. J.,
Nature, 323, 786-788 (1986).
290, 721-727 (1985).
Liang, E., Comments Astrophys., 12, 35-49 (1987).
Van Paradijs, J. A., Mon. Not. R. astro. Soc., 238, 45-48 (1989).
Hartmann, D., Epstein, R. I. & Woosley, S. E., Astrophys. J. (in press).
Wang, J. C. L. et al., Phys. Rev. Left. (submitted).
Bussard, I:L W. & Lamb, F. K. in Gamma-Ray Transients and Related Astrophysical
Phenomena (eds. Lingenfelter, R. E., Hudson, H. S. & Worrall, D. M.), 189-200
(American Institute of Physics, 1982).
Ghosh, P. & Lamb, F. K., Astrophys. J., 234, 296-316 (1979).
Alpar, M. A. & Shaha_m, J., Nature, 316, 239-241 (1985).
Lewin, W. H. G., van Paradijs, J. & van der Klis, M., Space Sc. Rev., 46, 273-377
(1988).
Figure Captions
Fig. 1. Evolutionary tracks (solid lines)of neutron stars in the magnetic field versusrota-
tion period diagram. Rotation periods and magnetic fields becomesmaller with accreted
massand hencewith increasing time. After massaccretion stops, stars movehorizontally
rightwards. The initial magnetic field is taken as B0 = 1012G, the initial rotation period
is chosen as P0 = 0.5 or 100 s, and the mass accretion rate is fixed at/_ = 1.1 x 1018gm/s.
The mass, radius, and moment of inertia of the neutron star are taken as 1.4Mo, 106 cm,
and 1045gin cm 2, respectively. The dash-dotted and dashed lines denote the equilibrium
rotation 28 and pulsar death lines 5, respectively. The filled circles represent the positions
of binary and millisecond radio pulsars in this diagram.
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Does mass accretion lead to field decay in neutron stars

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