1 Astrophysical Constraints on Dense Matter in Neutron Stars
13
Another possibility, which is described clearly by Freire [82], is that in high
stellar density environments such as globular clusters binary-single interactions
could play a major role. For example, a pulsar could be recycled to millisecond
periods and then an exchange interaction could leave it in an eccentric binary with a
white dwarf or another neutron star. Such a system would have a measurable ˙
ω and
γ , and the neutron star could be high-mass and have excellent timing precision.
We do note that there are two drawbacks to NS-WD systems in globulars
compared to field NS-NS systems. First, although white dwarfs are small they are
not point masses to the degree that neutron stars are. As a result, there is a small
contribution to the precession from the finite structure of the white dwarfs. Second,
even at the high stellar densities of globulars a comparatively large orbit is required
for there to be a significant probability of interaction. To see this, note that the rate
of interactions for a binary of interaction cross section σ is τ −1 = nσ v, where
n is the number density of stars (typically in the core n = 10 5 − 10 6 pc −3 ) and
v ∼ 10 km s −1 is the velocity dispersion. For a system of mass M, the interaction
cross section for a closest approach of a, roughly equal to the semimajor axis of
the binary, is σ ≈ πa(2GM/v 2 + a). If M ≈ 2 M and n = 10 5 pc −3 , this
implies τ = 10 10 yr when a ≈ 0.04 AU. This implies orbital periods greater than
a day, so dynamically formed NS-WD binaries are systematically larger than NSNS binaries formed in situ. Thus longer observation times are required to achieve a
given precision.
1.3.3 Dynamically Estimated Neutron Star Masses and Future
Prospects
For a recent compilation of dynamically estimated neutron star masses and uncertainties, see [115]. From the standpoint of constraints on dense matter, the most
important development over the last few years has been the discovery of neutron
stars with masses M ∼ 2 M , and possibly more. The first such established
mass was for PSR J1614–2230. Demorest et al. [72] determined that its mass is
M = 1.97 ± 0.04 M , which they obtained via a precise measurement of the
Shapiro delay. This measurement was aided by the nearly edge-on orientation of
the system (inclination angle 89.17 ◦ ), which increases the maximum magnitude of
the delay and produces a cuspy timing residual that is easily distinguished from any
effects of an eccentric orbit.
The second large mass that has been robustly established belongs to
PSR J0348+0432. Antoniadis et al. [11] observed gravitationally redshifted optical
lines from the companion white dwarf. The observed Doppler modulation of the
energy of these lines yields a mass ratio when combined with the modulation
of the observed spin frequency of the pulsar. In addition, interpretation of the
Balmer lines from the white dwarf in the context of white dwarf models gives a
precise mass for the white dwarf, and indicates that the neutron star has a mass of
M = 2.01 ± 0.04 M .
13
Another possibility, which is described clearly by Freire [82], is that in high
stellar density environments such as globular clusters binary-single interactions
could play a major role. For example, a pulsar could be recycled to millisecond
periods and then an exchange interaction could leave it in an eccentric binary with a
white dwarf or another neutron star. Such a system would have a measurable ˙
ω and
γ , and the neutron star could be high-mass and have excellent timing precision.
We do note that there are two drawbacks to NS-WD systems in globulars
compared to field NS-NS systems. First, although white dwarfs are small they are
not point masses to the degree that neutron stars are. As a result, there is a small
contribution to the precession from the finite structure of the white dwarfs. Second,
even at the high stellar densities of globulars a comparatively large orbit is required
for there to be a significant probability of interaction. To see this, note that the rate
of interactions for a binary of interaction cross section σ is τ −1 = nσ v, where
n is the number density of stars (typically in the core n = 10 5 − 10 6 pc −3 ) and
v ∼ 10 km s −1 is the velocity dispersion. For a system of mass M, the interaction
cross section for a closest approach of a, roughly equal to the semimajor axis of
the binary, is σ ≈ πa(2GM/v 2 + a). If M ≈ 2 M and n = 10 5 pc −3 , this
implies τ = 10 10 yr when a ≈ 0.04 AU. This implies orbital periods greater than
a day, so dynamically formed NS-WD binaries are systematically larger than NSNS binaries formed in situ. Thus longer observation times are required to achieve a
given precision.
1.3.3 Dynamically Estimated Neutron Star Masses and Future
Prospects
For a recent compilation of dynamically estimated neutron star masses and uncertainties, see [115]. From the standpoint of constraints on dense matter, the most
important development over the last few years has been the discovery of neutron
stars with masses M ∼ 2 M , and possibly more. The first such established
mass was for PSR J1614–2230. Demorest et al. [72] determined that its mass is
M = 1.97 ± 0.04 M , which they obtained via a precise measurement of the
Shapiro delay. This measurement was aided by the nearly edge-on orientation of
the system (inclination angle 89.17 ◦ ), which increases the maximum magnitude of
the delay and produces a cuspy timing residual that is easily distinguished from any
effects of an eccentric orbit.
The second large mass that has been robustly established belongs to
PSR J0348+0432. Antoniadis et al. [11] observed gravitationally redshifted optical
lines from the companion white dwarf. The observed Doppler modulation of the
energy of these lines yields a mass ratio when combined with the modulation
of the observed spin frequency of the pulsar. In addition, interpretation of the
Balmer lines from the white dwarf in the context of white dwarf models gives a
precise mass for the white dwarf, and indicates that the neutron star has a mass of
M = 2.01 ± 0.04 M .