1 Astrophysical Constraints on Dense Matter in Neutron Stars
27
those stars. Nonetheless, the complex phenomenology of kHz QPOs and the lack of
first-principles numerical simulations that display them means that claims that the
ISCO has been detected must be treated with care.
1.4.6 Other Methods to Determine the Radius and Future
Prospects
There are two other noteworthy ways to measure the radius that have been suggested
with particular applications to the double pulsar J0737–3039. The first involves
the binding energy of the lower-mass Pulsar B in that system. Based on an idea
originally proposed by Nomoto [163], Podsiadlowski et al. [179] suggested that
this neutron star formed via an electron-capture supernova (in which electron
captures onto Mg and then Ne in a core cause a loss of pressure support) rather
than the usually considered collapse of an iron core when it goes above the
Chandrasekhar mass. As this electron capture happens at a very specific central
density of 4.5 × 10 9 g cm −3 that corresponds to a well-defined baryonic mass of
M bary = 1.366 − 1.375 M [179], if one could identify this baryonic mass with the
gravitational mass M grav = 1.2489±0.0007 M of Pulsar B then one would have an
extremely precise constraint that would suggest a fairly hard equation of state. The
degree to which this constraint is useful depends on our theoretical certainty that
there is not significant subsequent fallback or expulsion of matter. Current models
do suggest that fallback or expulsion only introduce a spread of ∼0.01 M in the
final baryonic mass (K. Nomoto, personal communication). If this tight range is
confirmed by further work and if Pulsar B is indeed produced by this mechanism,
this could be a useful constraint.
The second method stems from the observation that spin-orbit coupling, which
is dominated in this system by the 23 ms period Pulsar A instead of the 2.8 s period
Pulsar B, leads to precession of the orbital plane and additional pericenter precession
[14, 67, 118, 133, 141]. Orbital plane precession will be difficult to measure, but the
required precision for the extra pericenter precession could be reached in the next
few years [133]. Such a measurement would effectively determine the moment of
inertia I of Pulsar A (potentially to 10%; [133]), and given that I ∼ MR 2 and
M is known well, this would amount to a ∼5% measurement of the radius. It is
unclear whether this will be reachable in practice, because of the confusing effect
of the unknown acceleration of the center of mass of the binary within the Galactic
potential [118].
A final method to mention for completeness (see also the introduction to
Sect. 1.6) is neutron star seismology. Asteroseismology has greatly improved our
understanding of normal stars, and it would do so for neutron stars as well if
particular modes could be identified with confidence. Indeed, fast oscillations that
might be torsional modes have been seen in the tails of giant flares from the soft
gamma-ray repeaters SGR 1900+14 [208] and SGR 1806–20 [209, 231] (see [232]
27
those stars. Nonetheless, the complex phenomenology of kHz QPOs and the lack of
first-principles numerical simulations that display them means that claims that the
ISCO has been detected must be treated with care.
1.4.6 Other Methods to Determine the Radius and Future
Prospects
There are two other noteworthy ways to measure the radius that have been suggested
with particular applications to the double pulsar J0737–3039. The first involves
the binding energy of the lower-mass Pulsar B in that system. Based on an idea
originally proposed by Nomoto [163], Podsiadlowski et al. [179] suggested that
this neutron star formed via an electron-capture supernova (in which electron
captures onto Mg and then Ne in a core cause a loss of pressure support) rather
than the usually considered collapse of an iron core when it goes above the
Chandrasekhar mass. As this electron capture happens at a very specific central
density of 4.5 × 10 9 g cm −3 that corresponds to a well-defined baryonic mass of
M bary = 1.366 − 1.375 M [179], if one could identify this baryonic mass with the
gravitational mass M grav = 1.2489±0.0007 M of Pulsar B then one would have an
extremely precise constraint that would suggest a fairly hard equation of state. The
degree to which this constraint is useful depends on our theoretical certainty that
there is not significant subsequent fallback or expulsion of matter. Current models
do suggest that fallback or expulsion only introduce a spread of ∼0.01 M in the
final baryonic mass (K. Nomoto, personal communication). If this tight range is
confirmed by further work and if Pulsar B is indeed produced by this mechanism,
this could be a useful constraint.
The second method stems from the observation that spin-orbit coupling, which
is dominated in this system by the 23 ms period Pulsar A instead of the 2.8 s period
Pulsar B, leads to precession of the orbital plane and additional pericenter precession
[14, 67, 118, 133, 141]. Orbital plane precession will be difficult to measure, but the
required precision for the extra pericenter precession could be reached in the next
few years [133]. Such a measurement would effectively determine the moment of
inertia I of Pulsar A (potentially to 10%; [133]), and given that I ∼ MR 2 and
M is known well, this would amount to a ∼5% measurement of the radius. It is
unclear whether this will be reachable in practice, because of the confusing effect
of the unknown acceleration of the center of mass of the binary within the Galactic
potential [118].
A final method to mention for completeness (see also the introduction to
Sect. 1.6) is neutron star seismology. Asteroseismology has greatly improved our
understanding of normal stars, and it would do so for neutron stars as well if
particular modes could be identified with confidence. Indeed, fast oscillations that
might be torsional modes have been seen in the tails of giant flares from the soft
gamma-ray repeaters SGR 1900+14 [208] and SGR 1806–20 [209, 231] (see [232]