To overcome difficulties in understanding the origin of the submillisecond optical pulses from SN 1987A a model similar to that of Kundt and Krotscheck for pulsed synchrotron emission from the Crab was applied. The interaction of the expected ultrarelativistic e(sup + or -) pulsar wind with the pulsar dipole electromagnetic wave reflected from the walls of a pulsar cavity within the SN 1987A nubula can generate pulsed optical emission with efficiency at most eta(sub max) is approximately equal to 10(exp -3). The maximum luminosity of the source is reproduced and other observational constraints can be satisfied for an average wind energy flow is approximately equal to 10(exp 38) erg/(s steradian) and for electron Lorentz factor gamma is approximately equal to 10(exp 5). This model applied to the Crab yields pulsations of much lower luminosity and frequency

Kluzniak, W.

Ruderman, M.

Shaham, Jacob

English

NASA Technical Reports Server

N90-22469
ORIGIN OF PULSED EMISSION FROM
THE YOUNG SUPERNOVA REMNANT SN 1987A
CAL 377
M. Ruderman, W. Klu_,niak and J. Shaham
Physics Department and Astrophysics Laboratory, Columbia University
ABSTRACT
To overcome difficulties in understanding the origin of the submillisecond opti-
cal pulses from SN 1987A we apply a model similar to that of Kundt and Krotscheck
for pulsed synchrotron emission from the Crab. The interaction of the expected ul-
trarel_tivistic e :e pulsar wind with the pulsar dipole electromagnetic wave reflected
from the walls of a "pulsar cavity" Within the SN 1987A nebula can generate pulsed
optical emission with efficiency at most Om_x ,_ 10 -3. The maximum luminosity of
the source is reproduced and other observational constraints can be satisfied for an
average wind energy flow _-, lOaeerg/(s;steraclian) and for electron Lorentz factor
"r "-_105. This model applied to the Crab yields pulsations of much lower luminosity
and frequency.
https://ntrs.nasa.gov/search.jsp?R=19900013153 2020-03-19T23:12:15+00:00Z
1. Introduction
The strong luminosity (between 400 and 900 nm) and the short period (P = 0.5 ms)
of the reported optical pulsations from the young supernova remnant (SNR) SN
1987A (Kristian et aI. 1989) raises problems for conventional models of pulsar opti-
cal emission. If relativistic beaming plays no dominant role, a rather small radiating
area._ (cP) 2 is implied, leading to an extraordinarily high optical brightness tem-
perature (kTb >> 1 GeV). It has not been demonstrated how such emission may
arise close to a neutron star. On the other hand, it is widely accepted that pul-
sars may give rise to a wind of relativistic electrons and/or positrons (e ±) (Rees
and Gunn 1974, Kundt and Krotscheck 1977, Kennel and Coroniti 1984, Cheng,
Ho and Ruderman 1986). As suggested by Kundt and Krotscheck for the Crab
nebula, ultra relativistic e _: may give rise to pulsed emission tar from the stellar
surface where the relativistic wind runs into the pulsar dipole electromagnetic wave
reflected from the inner boundary of the surrounding nebula. The main point of
our paper is that such a mechanism can account successfully for the periodicity of
the modulated optical signal reported from SN 1987A and it alleviates the optical
luminosity problem posed by observations.
During the January 18 observation the brightness of the detected pulsed signal
varied from magnitude 17 to 16 reaching at its maximum 1% of the luminosity of
the SN 1987A remnant (Middleditch 1989). Thus, the maximum "optical" pulsed
luminosity of the source was Lopt -- 3 • 1036erg s -1 x Afi/4_r, where Aft is the
solid angle into which the pulsed radiation was beamed. At the same time the
luminosity of the remnant (SNR) was LSNR = 3 • 103Serg/s (Burki and Cramer
1989). Subsequent observations failed to detect the pulses at a limiting magnitude
lower by 2 than the maximum observed (Kristian et al. 1989) and by 8 than that of
the SNR (Ogelman et aI. 1989). By the end of April 1989 the remnant bolometric
luminosity decreased to LSNR = 1 • 103Serg/s. If Lp is the electromagnetic power
of the pulsar and f-_p is the time average (over several months) of this quantity,
then the pulsed luminosity is Lopt = _TLP, where 17 is the efficiency, while the SNR
luminosity is LSNR = f" f,P + Lo(t), where 0 < f _< 1 and the last term (L0 > 0)
represents the luminosity the remnant would have if the pulsar had no power. At
maximum brightness of the optical pulses _ > 3-lO-2f(f,p/Lz)(Af_/4yr). The large
2
value of the numerical coefficient constitutes the "optical luminosity problem."
Below, we find _7_< 10 -3. This implies that emission from the pulsar is beamed
(At'/ << 47r), or the pulsar wind power is only sporadic (Lp << Lp), or most
(Lp -- fLp) of the pulsar spin-down power is either converted into kinetic en-
ergy of the nebula or reradiated at unobserved frequencies, (or all of the above).
At any rate, we conclude that the pulsed-beam synchrotron emission model pre-
seated below can account for all observations if the relatively modest requirement
f(Lp/Lp)(A_l/47r) < 10 -1 is met.
The cavity model is discussed in Section 3, while the constraints implied by
the data on SN 1987A are considered in Sections 4 and 5.
2. Difficulties of magnetospheric models
Optical pulses from the Crab pulsar can originate in that neutron star's (outer)
magnetosphere. But if the neutron star in SN 1987A is a weak-magnetic-fielcl (B. <
109 G) "millisecond" rotator (Kristian e*.aI. 1989, Pacini, Bandiera and Salvati
1989), it is hard to understand how the optical pulses could arise by an analogous
process in its magnetosphere.
Because the Crab pulsar spin rate 2r/Per_b _ 200s -1 _ 60 times less than
that of the 1987A neutron star, the emitting area (at the light cylinder radius) can
be _-, (60) 2 times larger. In additon, the pulsed optical luminosity is an order of
magnitude smaller in the Crab. The needed Crab optical brightness temperature
is then .,. 106 eV, a value generally exceeded for synchrotron radiation of e -v pairs
created by 7-rays in the outer magnetosphere (Cheng, Ho and Ruderman 1986).
Such emission mechanisms do not work for the pulsar in SN 1987A for two reasons.
i) A 10 GeV electron would give peak synchrotron radiation at photon energies above
100 MeV in the pulsar's magne_ospheric field. The fraction of energy emitted into
the optical band would then be very small, _ 10 -5 of the total radiated synchrotron
power.
ii) The detected neutrino burst confirmed that the neutron star in 1987A was formed
hot, as expected (Hirata et aI. 1987, Bionta e_ a/. 1987). The present surface
temperature of the star should be about 5-106K. The whole magnetosphere between
the surface of the star and the "light cylinder" (at r_c - P/21r = 3 • ]06cm) should
then be suffused with keV X-rays. In this (black body) X-ray flux, the mean free
path for inverse Compton scattering by GeV electrons is --, 10acm<< rio. Therefore
effective potential drops along the field lines are limited to AU ,_ 109V by pair
plasma created by the Comptonized photons: e + ,Y --, e + 7 followed by 7 + X -4
e + + e-. On the other hand, magnetospheric currents cannot give magnetic fields
exceeding that of the neutron star. This limits the current flow density along
open field lines to the Goldreich-Julian value an,, = (Goldreich
and Julian 1969), where I_] = 2_r/P. The maximum power of those currents is
Le -- jmaz._3fl-liU. Clearly Lc > Lopt is needed, as the electrons cannot radiate
more energy than they carry. For Lopt = 3 • 1036erg/s, a minimum potential drop
along B of AU _> 1014V is required. This last value is hugely in excess of the
109V value sustainable without electron pair avalanching. The magnetospheric
accelerator would thus have been quenched long before it attains the required power.
It has also been suggested that the neutron star in SN 1987A is ;¢ibrating
with the 0.5 ms period. Wang et al. 1989 proposed cyclotron radiation (in a
B. _ 1012G magnetic field) of ions powered by surface-penetrating shock waves as
the mechanism for optical emission. However, it has not been shown how shocked
ions could gain the necessary velocity perpendicular to B without being fragmented.
Nor has it been shown how stellar vibration of reasonable amplitude could give rise
to rapidly recurring shocks of requisite energy.
We conclude that an origin from within the stellar magnetosphere for the op-
tical pulsations from SN 1987A has not been plausibly demonstrated for either the
vibrational or the rotational model.
3. Pulsar cavities in supernova remnants
Far beyond the light cylinder of a pulsar in a vacuum, the spin-down power is carried
largely in two forms (Rees and Gunn 1974, Kundt and Krotscheck 1977, Kennel and
Coroniti 1984):
a) an ultrarelativistic e+ wind,
b) electromagnetic (EM) fields of the magnetic dipole radiation (from the per-
pendicular component of the pulsar dipole) and a possible toroidal magnetic field
(from the spin-aligned part of the dipole) carried with the wind.
Most of the wind energy is probably due to acceleration of e :_ by the very
strong (time dependent) fields near the pulsar. For a rotating neutron stax with a
non-spin-Migneddipole moment the pulsar spin frequency would be impressedon
the electron wind when the electronsare ejected(in a particular direction) from the
outer magnetosphere and when they are subsequently accelerated. The resulting
e± bunch structure would repeat at any (distant) point at the period P of the
pulsar dipole radiation. If a similar electron injection arid wind creation process
were operative in a strongly pulsating neutron star a modulation at the vibration
frequency of the magnetic dipole would also be expected.
_rhen the pulsar is contained within a young SNR the large pressure from the
pulsar wind and the radiation will create a "cavity" within the remnant. The pulsar
cavity is terminated by a shock at radius d well within the outer nebula radius D.
When pulsar emission is the main source of nebular power (Rees and Gunn 1974)
where a is the ratio of the pulsar outflow magnetic energy to the total energy
density of the wind. For the Crab, Kennel and Coroniti obtain _ _ 3 •10-3 and
dcr_b "_3-I017cm, Kundt and Krotscheck finda ,,_I and dcr_b "_ 101Scm. Adopting
similarvalues of _ for SN 1987A one would then infera cavity radius d ,,,101Scm
in that SNR., smaller than that in the Crab by roughly _he ratio of the SNR ages.
We do not expect thisestimate to be accurate forsuch a young remnant. However,
our model only requires that a cavity with radius d < D exist; for SN 1987A,
D _ 1016cm at the epoch of interest (Papaliolios e_ al. 1989).
The out flowing ultrarelativistic bunches of e=_ do not radiate significantly in
the nearly comoving EM waves. To the extent that EM energy is backscattered
at the cavity wall, they will, however, pass through a magnetic field which may be
taken to be comparable with that of the preshock incident magnetic field
B ,-,., BEM _ (aLplcd 2) 112
1
~ 2. lo (L39 _ drT)"
This value of BEM is similar to the one needed to understand the soft X-ray excess
emission from SN 1987A, if one assumes equlpartition in the nebula (Pacini 1989).
If wB = eB/rnc > 27r/P, the e + wind will lose energy in the cavity mostly by
synchrotron radiation. Had WB < 2r/P the dominant loss mechanism would have
been inverse Compton scattering.
4. Pulsed emission from the SN 1987A
In a B ,-_ 10-2G cavity field, the characteristic synchrotron emission frequency is
--_ 1016_ Hz, giving optical radiation if 76 -----7/106 _ 1/6. The fraction of beam
energy converted to such radiation in a d = 101Scm cavity is 77= 7W2B(e2/rnc4)d -,,
10 -4 for the same values. Because the optical radiation is emitted almost exactly
radially, to a distant observer the radiation would appear to be coming from the
pulsar itself. Thus, cavity and beam parameters of Section 3. could easily give
the kind of optical luminosity observed from SN 1987A if the wind power were
,-_ 1040 x (Af_/47r)--about ten times the spin-down power of the Crab pulsar 1 if
emission is isotropic.
Almost all of the beam power would ultimately be dissipated beyond the cavity
boundary shock in the surrounding nebula where B is expected to be -,_ 102 times
larger than in the cavity. Refer to Section 1. for a discussion of how the current
upper limit on the bolometric luminosity of the nebula can be satisfied.
We must now ask what constraints are imposed on the model parameters by
insisting that the observed optical (or near infrared) synchrotron light is pulsed
with the e + wind frequency 1/P. As shown in the next section, this approach yields
for the various parameters values close to the ones a£1opted directly above. We find
that the size of the nebula places an upper bound r/max,,< 10 -3 on the efficiency of
radiation allowed by the model.
A critical assumption is that the relativistic electrons synchrotron radiate in
an ordered EM field of wavelength eP. This guarantees that the deflection from
the radial direction of the radiating e+ never exceeds an angle (80, eq. [P10]) less
1 The expected pulsed cavity emission from the Crab can be scaled from that
from SN 1987A. For the "optical" frequency wCr_b/w_gs7 = [72B]cr_b/[72B]lgs7 "_
[9  vq -fv/d]crab/[;  Vq --fP/d]lo8,.For comparable7 and oLp, ~    87/500
or A(Crab) ,,- 102#m. With similar approximations and assumptions the ratio of
pulsed cavity emission luminosities from the Crab and SN 1987A is the ratio of
the values of crLpT/d, again correxponding to a reduction of about 500. Thus,
the Crab's pulsed cavity far IR luminosity would be -,_ 103aerg/s. A bump of
about this magnitude appears in the near (A <__3.5pro) IR pulse shape of the Crab
(Middleditch, Pennypacker and Burns 1983).
than the critical one beyond which the pulses would be washed out. If, instead,
the field had been a collection of randomly oriented domains of size cP the average
totM deflection would have been too large, Oo(d/cP) 1/2.
5. Constraints on pulsed beamed synchrotron emission implied by the
SN 1987A data.
By assumption, the optical signal is due to synchrotron radiation of relativistic e ±
(energy 7mc 2) in transverse magnetic field of strength B alternating in direction
with wavelength cP. Before entering an assumed emission zone of radial extent
l, the electrons travel radially outwards a distance d- l from the neutron star.
The electrons radiate into a narrow forward cone of apex angle _ 1/7 about their
instantaneous velocitydirection, which is, itself, at an angle to the initial (radial)
direction of flight. The latter angle is not greater than some maximum deflection
angle 00 (eq. [P10]). Thus, the cross-sectional area of the emission region'seen by
an observer at infinity is _ _rb2, where
b dO, (Pl)
and
0 _ 00 + 1/7 << 1. (P2)
For the purposes of computation we take the optical brightness temperature to
be kTb = 103 GeVx (b2/1012cm 2) -1 and the synchrotron frequency to be
72 eB/rnc = 2 eV/h, (P3)
(i.e. 72B/10SG = 2) to obtain (nearly) optimum efficiency of optical detection.
The maximum extent of the nebula, D m 1016cm places an upper bound on the size
of the emitting region and its radial distance from the star: I < D, d < D.
Notation
7--initial Lorentz factor of the radiating electron
8--maximum angle between line of sight and initial direction of electron motion
_0--maximum deflection angle of electrons
d--radial distance from the neutron star to the emitting region
/--radial extent of the emitting region
7
7rb2--area of emission seen by observer
At--maximum allowed differential time of arrival (t.o.a.)
a, fl, A, da6 _ 1---dimensionless parameters not greater than unity
F, G > 1--dimensionless parameters greater than unity
THE CONSTRAINTS
A class of constraints is introduced by the requirement that the optical pulses
not be washed out. Let the upper bound on the differential spread in time of arrival
of all photons in a pulse be At = aP/5 = a x 10-%, i.e.,
cAt=a x lO6"%m, a_<l, (P4)
Any initial spread in energies (mc2AT) of e + leads to a constraint l,_< 7_(cAt)/AT,
less stringent than the following. We define
a = 5 5_ o0+ v0o. (Ps)
The differential t.o.a, constraint from time of flight delay of the emitting e :1: gives
t= ,_G-_(¢/',_), ,_<_1, (P6)
Differential t.o.a, because of different path lengths due to the transverse extent of
the emitting region gives b = flS-l(cAt), and hence
(PT)
(Strictly speaking A +/_ _< 1, but we are not concerned with factors of 2.) We note
the following limits:
00 << 1/7 _ G = 1,
8o ,-_ 1/7 _ G .-_ 2,
00 >> 1/7=>G= 2 "
The inferredbrightness temperature places a ]ower bound on the e]ectron energy
")' : ]053F/_-2a-282, F > 1. (Ps)
The efficiency of conversion of the electron energy to optical is 17 ".(Synchrotron
pow_)×(7,_) -' × z/_, i.e.,
e)_ lOS.9
r/= C'--_ x , (P9)
where eq. (P3) was used to eliminate B.
Since the magnetic field traversed by the e i alternates in direction, the appro-
priate expression for the deflection angle is 00 ._ PeB/(27cvmc), i.e.
1'30o "_ 1011"4, (P10)
while the size of the nebula limits d and l,
l<d=d16x10a%m, d16 <1. (Pll)
RESTRICTIONS ON 7
Consider the constraints (P6) to (P9) in the following two cases.
i)O0< 7-1
From eq. (P10) this regime holds iff 72 _> 1011"4, i.e. 7 _> 105"7- However, the
constraint (P6) with the subsidiary condition (Pll) then gives a low eiIiciency, since
l = a_ × 10as-%m. Hence, a_ _< 10-2d16 and therefore _ 10-4d16.
ii)00 >> 7 -1
Y_rom point i) above, this can only hold if 7 < 105"7- Now, from eqs. (P5) and
(PIO)
' lOn.4/7s"
Hence, using also eq. (P8), -), = F_'(afl)-_r x 104.0 < l0 t'', i.e.,
104 _ 7 < 105"7- (Pro)
Now, from eqs. (P6), (P7) and (P9), respectively,
1_ (a)0"746x lOS°cm_ (A/fl)r'}(od_)-5/7 x 108"°cm,
d _ (_/_)7_x ]o_._ _ r_(o,/_)-_ x lo__m,
_ (_)7_ × _o-_ _ (_//_)r_/_(o,/;)_× _o-_-,.
(P_3)
(m4)
(ms)
Recall that a is the precision with which fine structure can be observed in the optical
pulses in units of P/5 = 0.1 ins and d16 is the maximum distance of the emitting
region from the pulsar in units of 1016cm. In principle, a is an observable number.
The free parameters A, fl (and F) were introduced to replace upper (lower) bounds
with equalities.
To satisfy l _< d we must have A < fl/2 < 10 -°"3. But (P13) and (Pll) require
(aA)7, 6 < 10S'°d16, giving, upon substitution in eq. (P15), r/ < 10-2"4(aAdl_)l/2.
We conclude that this model allows a maximum efficiency of
3.10-3(d1 ) (P16)
occurring for 7 = lOS'5(d16) 1/6 and the most favorable values possible of the free
parameters (fl = 1, A = 0.5).
We thank Dr. John Middleditch for an informative conversation. This
work was supported in part by NSF grants AST-86-02831 and NAGW-567 and 1618.
REFERENCES
Bionta, R. M. et aI. 1987, Phys. Rev. Left., 58, 1490-1493.
Burki, G., and Cramer, N. 1989, IAU Circular, No. 4729.
Cheng, K., Ho, C., and Ruderman, M. 1986, Ap. J., 300, 522-539.
Goldreich, P., and Julian, W. H. 1969, Ap. J., 157, 869-880.
Hirata, K. e_ aI. 1987, Phys. Rev. Left., 58, 1494-1498.
Kennel, C. F., and Coroniti, F. V. 1984, Ap. J., 283, 694-709.
Kristian, J. eZ aI. 1989, Nature, 338, 234-236.
Kundt, W., and Krotscheck, E. 1977, Astron. Astrophys., 83, 1-21.
Middleditch, J. 1989, private communication.
Middleditch, J., Pennypacker, C., Burns M. S. 1983, Ap. J., 273 261-266.
Ogelman, H. et al. 1989, IAU Circular No. 4743.
Papalios, C., Karovs "tu_,M., Koechlin, L., Nisenson, P., Standley, C., and Heath-
cote, S. 1989, Nature, 338, 565-566.
Rees, M. J., and Gunn, J. E. 1974, M.N.Yi.A.S., 167, 1-
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Origin of pulsed emission from the young supernova remnant SN 1987A

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