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

Abstract
WIDE-BAND X-RAY OBSERVATIONS OF MAGNETARS ∗
K. Makishima, Dept. Physics † and RESCEU, University <strong>of</strong> Tokyo
and the Institute <strong>of</strong> Physical and Chemical Research (RIKEN)
After a brief review <strong>of</strong> physics <strong>of</strong> neutron stars, this article
focuses on so called magnetars, a special subset <strong>of</strong> neutron
stars, which are though to have magnetic fields raching
10 14−15 G. Recent observational results <strong>of</strong> these objects,
made with the Japanese X-ray satellite Suzaku, suggest
that their X-ray to gamma-ray emission results from
photon splitting process in the strong magnetic field.
INTRODUCTION
As a brief introduction to neutron stars, a paragraph may
be spent on stellar evolution. As illustrated in Fig. 1, stars,
first born as protostars, take different evolutionary paths
depending on their initial mass. The lightest ones end up
with planets, where Coulombic repulsion among ions supports
the gravity. Somewhat more massive ones become
brown dwarfs, which employ electron degenerate pressure
instead. Objects with > 0.08 times the solar mass become
normal stars, where classical gas pressure generated by nuclear
fusion balances the gravity. After 10 6−10 years depending
on their initial mass, these stars come to their evolutionary
endpoints. Lightest normal stars leave at their
centers white dwarfs, which are similar to brown dwarfs
except their lack <strong>of</strong> hydrogen. More massive ones experience
gravitational-collapse supernova explosions, and their
cores collapse into neutron stars which are supported by degenerate
neutron pressure. If the initial mass is even higher,
the final gravity is too strong for a neutron star to support,
and the object becomes a black hole.
This article uses the MKSA units, except that magnetic
field B is expressed in Gauss (G); 1 G = 10 −4 T.
DEGENERATE STELLAR OBJECTS
Stellar Equilibrium
The balance between the gravity and pressure p <strong>of</strong> a
spherical star can be expressed at each radius r as
dp/dr = GρMr(r)/r , (1)
where G, ρ and Mr(r) = ∫ r
0 4πr2 ρ(r)dr are the gravitational
constant, mass density, and “mass coordinate”, respectiveky.
Instead <strong>of</strong> exactly solving eq.(1), it is useful to
multiply its both sides by 4πr 3 and integrate from r = 0 to
the stellar surface r = R, to obtain a Viriar relation as
3 < p > V = −Φ ≡
∫ M
0
GMr
r dMr
2 5GM
∼ . (2)
3R
∗ Work supported by T. Enoto, Y.E. Nakagawa, and M. Nakajima
† maxima@phys.s.u-tokyo.ac.jp
Figure 1: A very schematic illustration <strong>of</strong> stellar evolution.
Abscissa at the top indicates initial stellar mass, while that
at the bottom final mass. Time goes from top to bottom.
Here, V is the stellar volume, means volume average,
M ≡ Mr(R) is the stellar mass, Φ is self-gravitational
energy, and the last approximation assumes a constant ρ.
Degenerate Stars
Consider a star which is supported by degenerate pressure
pd <strong>of</strong> some Fermions, <strong>of</strong> which the mass is mf and
density is nf. We may substite p in eq.(2) with the nonrelativistic
degenerate pressure <strong>of</strong> an ideal Fermi gas, i.e.,
pd = A¯hn 5/3
f /mf, where ¯h is the Dirac constant and A is a
numerical constant <strong>of</strong> order unity. Performing elementary
calculations, and using another numerical constant A ′ , we
obtain a mass-radius relation <strong>of</strong> this degenerate star as
R/λf = A ′ α −1
g η −5/3 (M/mn) −1/3 . (3)
Here, mn is the nucleon mass, η is the nucleon-to-Fermion
number ratio, λf ≡ 2π¯h/mfc is the Fermion’s Compton
wavelength, and αg ≡ Gm 2 n/¯hc = 5.9 × 10 −39
is a dimensionless constant representing gravitational interaction.
Thus, the stellar radius is proportional to the
Fermion’s Compton wavelength. If we use the extreme
relativistic expression for pd, an upper limit mass (Chandrasekhar
mass) is derived.
Brown and White Dwarfs
If the Fermions are electrons with λe = 2.4 × 10 −12
m, the star becomes a brown dwarf (η = 1.2) or a white
dwarf (η = 2.0). Normalizing M to the solar mass M⊙ ≡
2.0 × 10 30 kg, and faithfully calculating A ′ , we obtain
R = 1.0 × 10 7 (M/M⊙) −1/3 (2/η) −5/3 m (4)
which implies an object <strong>of</strong> the Earth’s size.