If the recently reported 0.5 ms-period pulsed optical signal from the direction of Supernova 1987A originated in a young neutron star, its interpretation as a rotational period has difficulties. The surface magnetic field would have to be much lower than expected, and the high rotation rate may rule out preferred nuclear equations of state. It is pointed out here that a remnant radial vibration of a neutron star, excited in the supernova event, may survive for several years with about the observed (gravitationally redshifted) period. Heavy ions at the low-density stellar surface, periodically shocked by the vibration, may efficiently produce narrow pulses of optical cyclotron radiation in a surface field of about a trillion gauss

Chen, K.

Hamilton, T. T.

Ruderman, M.

Shaham, Jacob

Wang, Q.

English

NASA Technical Reports Server

N 9 0 - 22 468
Does SN 1987A Contain a Rapidly Vibrating Neutron Star?
Q. Wang, K. Chen, T. T. Hamilton, M. Ruderman and J. Shaham
If the recently reported 0.5 ms period pulsed optical signal from the
direction of SN 1987A 1 originated in a young neutron star, its interpre-
tation as a rotational period has difficulties. First, the upper bound on
the present luminosity of 1987A will limit such a rotating star's surface
magnetic field to < 10 9 G. Unless this field rises to 1012 G in a time
of .._ 103 yrs, because of the emergence of a presently buried field or
from magnetothermal generation 2, such a low field marks this event as
very different from the Crab supernova as well as from those explosions
responsible for the half-dozen other pulsar/supernova remnant associa-
tions. Second, such a high rotation rate without triaxial instability may
place too severe a constraint on the equation of state of nuclear matter
3. Here we point out that a remnant radial oscillation of a neutron star,
excited in the supernova event, may survive for several years and has
the expected (gravitationally red-shifted) period. Heavy ions at the low
density stellar surface, periodically shocked by the vibration, will effi-
ciently produce sharp pulses of optical cyclotron radiation in a surface
field of ,,_ 1012 G. These pulses may be only negligibly modulated by a
(much slower) stellar rotation because of the nearly isotropic emission
mechanism and the strong gravitational bending of light rays 4'5. We
discuss below some details of this model. We do not discuss here a
mechanism for the reported 8 hr modulation 1, which may be the result
of timing noise in much the same way that spurious quasi-sinusoidal
modulations have appeared in period timing analyses of older pulsars G.
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Neutron star vibrations have alreaxiy been discussed at some length in the
literature 7,8. From dimensional considerations the fundamental radial mode pe-
riod is expected to be of order P ,',, (Gp) -1/2 ,'., 10 -s s with p the mean neutron
star density. Typical neutron star models s with M -._ 1M® and R ,-_ 106 cm give
periods close to 4 x 10 -4 s with no sensitivity to the exact central density. This
vibrational period is close to that observed when corrected for the gravitational
red shift (4. x 10-4(1 - 2GM/Rc2) -1/2 ,.- 5 x 10 -4 s). Non-radial and higher
order radial modes would be damped on timescal'es of _< 1 yr 7'8'9 from gravita-
tional, neutrino, and electromagnetic radiation. According to Finzi and Wolf 10,
the major damping source for the fundamental radial mode is the UR.CA neutrino
emission process, which gives a damping time ,-, 102 yrs. However, this timescale
could be reduced dramatically by two effects:
(1) "Exotic" enhancement of the weak interactions, the main source of the
radial vibration damping. These include central _r-condensates, or quark matter
11,12. Confirmation of our modeU may rule out the presence of these in the putative
neutron star produced by SN 1987A, unless the neutrino emission they can give
is suppressed by superfluid energy gaps.
(2) Enhancement of gravitational radiation from coupling to non-radial vibra-
tions. Such coupling will arise when the underlying spherical symmetry is broken,
e.g., if the neutron star is rotating. For a neutron star with a uniform density,
Chau is calculated the rotation-dependent gravitational radiation damping time
to be ,._ 2 x 103 p4 yrs, where P is the rotation period in seconds. Our model
would then require a slowly rotating neutron star, with P _> 10 -1 sec. With such
a period, a 101_ G field does not cause the neutron star spin down power to exceed
the current supernova luminosity.
The optical radiation cannot originate in a region larger than a light-travel
size of 150 kin. Furthermore, because the reported presence of strong first and
4secondharmonics indicates a sharp pulse, the sizeof the emission region should
be much smaller than this, implying emission very close to the stellar surface.
For a pulse luminosity >_5 x 103Sergs-1 (18th magnitude1 at a distance of 55
kpc) any thermal emission must occur at a temperature T > 106 K; upper limits
on the X-ray emission from the supernov_ 14 constrain the emission process to be
nonthermal.
If a radiating particle of charge Z emits energy E per vibration period, the
observed pulse luminosity from an optically thin surface region would require
E/Z _> 8 MeV. (1)
If optically thick only at optical frequencies, it requires E _> 102 MeV. If electron
synchrotron radiation were responsible for the optical emission, the magnetic field
would have to be
105(8/_ eVB sin a < 3.5 x )_e Gauss (2)
to produce optical emission, where e is a typical photon energy in eV and o_ is
a typical electron pitch angle. This extreme constraint on B suggests, instead,
that the radiation arises from cyclotron radiation from stellar surface heavy ions,
Fe +z for example. These will produce optical cyclotron radiation (at much higher
fields) with a typical photon energy of
2Z
e ,,- 3B12"-_-- eV, (3)
where BI_ is the magnetic field value in units of 1012 Gauss and A is the atomic
number of the ion. [WhAle curvature radiation by an electron could fall in the
optical band, this mechanism, generally, has a very low efficiency (,_ e_ h_c-'_m----P-_.""
10 -T) compared to that of synchrotron emission.]
In this ion cyclotron emission model, condition (1) requires the energy of
Fe +26, for example, to be _ .2 Gev per ion; the column density is then _ 2 ×
5in22_-Iv *JGev cm--2" Fully stripped energetic but nonrelativistic Fe ions (or He ++ or
protons) can give strong cyclotron optical emission in a field B ,-* 1012 Gauss. We
propose that these ions can be given the needed velocities as the radial vibration
steepens into a shock when it reaches the small densities and scale heights at the
stellar surface. These strong shocks occur at 0.5 ms intervals, just after the surface
reaches its maximum outward speed, and can accelerate particles to velocities of
order 101° cm/sec 15. Just after the shock the kinetic energy (_ 4 Gev per ion)
carried by ions will dominate that carried by electrons. Because of the short travel
time for the shock passing through the surface of the neutron star and the short
ion cyclotron lifetime (< 10 -5 sec), a sharp pulse is expected within each cycle.
Furthermore, since the emission is concentrated around the ion gyration frequency,
the vibration shocked surface can gives a reasonably eiZficient conversion of internal
vibration energy to optical radiation.
The total luminosity of SN 1987A sets a lower limit to the neutron star ro-
tation period of > 20 B12L_s 1 ms, where Lss is the supernova luminosity in 1038
erg/s. As noted above, our model requires P > 10 -1 sec. As the cyclotron
emission occurs in a magnetic field which varies over the surface of the star, one
expects a modulation at the stellar rotation period. However, the amplitude of
this modulation may be rather small because of the isotropic energy input from
the vibration, the fairly isotropic geometry of cyclotron emission, and the strong
gravitational bending of the emitted light rays 4,5
Future period observations should test our model. The period of the neutron-
star vibration should not increase significantly with time although the luminosity
will decrease as the vibration is damped; the rotation period of the star should
be found to be > 10 -1 s. The optical pulse spectrum should be significantly
different from that of the Crab pulsar, which originates from a very different
mechanism. The frequency corresponding to the peak emission in the SN 1987A
optical pulsar spectrum could be used to estimate the magnetic field at the surface
of the neutron star (see Equation (3)). Observations in other wavelength bands
are highly desirable. The detection of X-rays from the neutron star before the
vibration dies out could provide important input to our understanding of the
origin of the optical light.
We thank D. Helfand, ft. Halpern and J. Applegate for many helpful discus-
sions and R. Muller for an early communication to us of the results in ref 1. This is
Columbia Astrophysics Laboratory contribution No. 371 and has been supported,
in part, by NASA grants NAG8-497 (TTH and QW) and NAGW-567 (JS), and
by National Science Foundation grant AST86-02831 (MR).
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Sasseen, T., Kristian, J. A., Kunkel, W. E., Hamuy, M. A., Imamura, J. N.,
Steiman-Cameron, T. Y., Shelton, I. K., Tuohy, I. R. and Rawlings, S., I.
A. U. Circular No. 4735 (1989).
2. Blandford, R. D., Applegate, J. H., Hernquist, L., Mort. Not. R. a,tr. Soc.,
204, 1025-1048 (1983)
3. Friedman, J. L., Ipser, J. R., and Parker, L., A,trophy,. J., 304, 115-139,
(1986).
4. Pechenick, K. R., Ftaclas, C., and Cohen, J. M., Astrophys. J., 274, 846-857
(1983).
5. Chen, K. and Shaham, J., Astrophys. J., 339, in press (1989).
6. Boynton, P. E., Groth, E: J., Hutchinson, D. P., Nanos, Jr., G. P., Partridge,
R. B., and Wilkinson, D. T., A._trophys. J., 175, 217-241 (1972). This point
has also been made independently by J. Katz, preprint, (1989).
7. Van Horn, H. M., A3trophys. J., 236, 899-903 (1980).
8. Cameron, A. G. W., Ann. Rev. Astron. A_trophy_., 8, 200-208 (1970)
79. McDermott, P. N., Savedoff,M. P., and Van Horn, H. M., Astrophys. J., 281,
746-750 (1984).
10. Finzi, A. and Wolf, R. A., Astrophys. J., 153, 835-848 (1968).
11. Wang, Q., and Lu, T., Phys. I, eit., 148B, 211-214 (1984).
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(1969).
13. Chau, W. Y., Astrophys. J., 147, 664-671 (1967).
14. Sunyaev, R. A., private communication, (1989)
15. Mock, M. S., Ph.D. Thesis (Columbia University) (1968)


Does SN 1987A contain a rapidly vibrating neutron star

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