Proceedings of International Conference on Physics in ... - KEK

Radiation from Rotation-Powered Pulsars
The Crab pulsar (borne in AD1054), a prototypical
rotation-powered NS, has B ∼ 3 × 10 12 G, and rotates
with an angular frequency <strong>of</strong> ω = 200 Hz. As a result, the
induced Lorentz electric field amounts to
E ∼ RωB ∼ 10 14 Vm −1 , (8)
and the electric potential to ER ∼ 6 × 10 18 V. This ultrahigh
electric field will accelerate electrons (plus probably
positrons), which then emit non-thermal radiation via synchrotron
radiation, inverse Compton scattering, and curvature
radiation [18]. Emergent spectra inevitably span many
orders <strong>of</strong> magnitude in frequency. To observe these objects,
without hampered by background stellar signals, we
may use either radio frequencies, or gamma-ray range as
demonstrated by the Fermi Gamma-ray Space Telescope
launched in 2008 June [1].
ACCRETING X-RAY PULSARS
X-ray Emission
Contrary to rotation-powered NSs, accretion-powered
NSs (those with [g] in Table 1) radiate predominantly in
the X-ray frequency, for the following reason. Consider an
accreting NS with weak MF, radiating spherically at a luminosity
L. Then, the photon momentum flux L/4πr 2 c exerts
an outward force Fout ≡ LσTne/4πr 2 c per unit volume <strong>of</strong>
the accreting matter, with σT being the Thomson cross section.
The maximum luminosity LE, called Eddington limit,
is realized when Fout balances the inward gravitational pull
[right hand side <strong>of</strong> eq.(1)] exerted on the same volume. Assuming
η = 1.2, we then have
LE = 4πGηmpcM/σT = 2.2 × 10 31 (M/1.4M⊙) W.
(9)
Equating this with the blackbody luminosity 4πR 2 σT 4 , the
blackbody temperature is obtained as
T = 2.3 × 10 7 (L/LE) K. (10)
This falls right on the X-ray energy band.
X-ray photons have high penetrating power, as evidenced
by medical diagnostics. However, they cannot penetrate
the atmosphere, which is ∼ 50 times thicker (in Oxygen
column density) than human body. As a result, a number
<strong>of</strong> X-ray astrophysics satellites have been launched. In
Japan, Hakucho (launched in 1979), Tenma (1983), Ginga
(1987), ASCA (1993)[21], and Suzaku (2005)[13] have
been contributing. We are now preparing for the next mission,
ASTRO-H, to be launched in 2014.
Cyclotron Resonances
While eq.(10) applies to spherical accretion onto weak-
FM NSs, the condition somewhat differs when the NS has
a strong MF (X-ray pulsars in Table 1), because the accretion
flow is channeled onto the two magnetic poles, and the
Thomson cross section is magnetically modified [10]. As
a result, the X-ray emission from X-ray pulsars attains a
higher temperature, ∼ 10 8 K, or ∼ 10 keV.
An outstanding property <strong>of</strong> X-ray pulsars is a clear spectral
feature due to electron cyclotron resonance, or Cyclotron
Resonance Scattering Feature (CRSF), which <strong>of</strong>ten
appears in their spectra at an energy <strong>of</strong>
Ea = ¯heB/me = 11.6(B/10 12 G) keV. (11)
So far, CRSFs have been observed, sometimes in multiple
harmonics, all in absorption, from ∼ 15 objects [12], about
half the known X-ray pulsars. Figure 3 gives one <strong>of</strong> the
most prominent examples <strong>of</strong> CRSFs [17].
Equation (11) have been used to directly measure the
surface MF strengths <strong>of</strong> X-ray pulsars. Obviously, this
method gives a much higher accuracy than eq.(7) in measuring
B. The green data points in Fig. 2 refer to these measurements
[12]. The results are concentrated over a rather
narrow range, B = (1−4)×10 12 G, although the region <strong>of</strong>
B > 5 × 10 12 G is yet to be explored with high-sensitivity
hard X-ray instruments, including the Hard X-ray Detector
[20] onboard Suzaku. This result argues against a view,
which was popular in the 1990’s, that the MF <strong>of</strong> strongly
magnetized NSs decay wit time [23].
In Fig. 2, the green data points appear to be rathe distinct
from the more weakly magnetized objects. Then, the
MF strengths may exhibit bimodal behavior. Based on this,
we further speculate that the NS magnetism is a manifestation
<strong>of</strong> ferromagnetism in nuclear matter [12], rather than
the more popular idea <strong>of</strong> permanent current. Those with
B = 10 8−9 G can be interpreted as entirely paramagnetic
objects. The stronger-field objects with B ∼ 10 12 G can be
explained if only ∼ 10 −4 <strong>of</strong> the total NS volume becomes
ferromagnetic. Furthermore, we expect B ∼ 10 16 G if the
entire volume <strong>of</strong> a NS becomes ferromagnetic. Magnetars,
to be described below, may be such objects.
Figure 3: Examples <strong>of</strong> CRSFs, measured from the transient
pulsar X0331+53. The fundamental and 2nd harmonic features
are indicated by arrows. Dashed lines indicate the
underlying thermal spectrum.