36
M. C. Miller
greater complexity of the waveforms. No pulsar in a NS-NS binary has a spin
period shorter than 23 ms [205], so the spin parameters of these neutron stars are
j ≡ cJ /GM 2 < ∼ 0.02. In contrast, although inferences of the spins of stellar-mass
black holes are not yet fully vetted, there is growing evidence that many of them
have spin parameters of several tenths, with some possibly approaching j = 1,
the mathematical maximum for black holes [146, 151]. The likely evolutionary
difference is that in the supernova that creates a neutron star or black hole, much
greater amounts of mass fall back to create a black hole than a neutron star, and
this mass will come from significant radii that thus carry considerable angular
momentum. Accretion from a binary subsequent to the production of a black hole
has little effect on either the mass or the angular momentum of the hole (see, e.g.,
[114]). Neutron stars in the high-mass X-ray binaries that could create a double
neutron star pair accrete little mass in the active phase and, empirically, seem to
have relatively strong magnetic fields, so accretion does not spin them up to high
rotation rates.
These statements are not absolute. It could be that there are slowly-spinning
black holes in BH-NS binaries, or rapidly spinning neutron stars in NS-NS
binaries (especially if they are produced dynamically in globular clusters). However,
the expectation at this time is that until tidal effects become important NS-NS
waveforms will be easier to interpret than those from BH-NS coalescences.
This leads us to what those tidal effects might tell us about neutron stars. At
large separations compared to the neutron star radii, nonlinear mode couplings due
to tides will not affect the inspiral phase significantly [225]. Most of the information
that can be obtained from tidal phase deviations from point-mass inspiral exists at
high frequencies [103], and recent comparisons of analytical theory with numerical
simulations suggest that with some calibration the theory does extremely well [25,
69, 79, 108, 124]. An explicit comparison of the expected signals from piecewisepolytropic equations of state suggests that a difference of only 1.3 km in radius could
be distinguished for NS-NS systems out to 300 Mpc with optimal direction and
binary orientation (this corresponds roughly to a direction- and orientation-averaged
distance of 140 Mpc) given a full hybrid post-Newtonian plus numerical relativity
waveform [186]. See Fig. 1.5 for an indication of the different frequencies of tidal
disruptions implied by two candidate equations of state.
Inspirals of neutron stars into black holes have not yet been examined using as
much care with respect to phase deviations. Recent work suggests that although
if the mass ratio is as high as 6:1 a NS-BH coalescence will be indistinguishable
from a BH-BH coalescence with the same masses [80], if the mass ratio is as small
as 2:1 or 3:1, single events at a distance of 100 Mpc could reveal the neutron star
radius to within 10–50% [123, 124], depending on details. This is a case in which
a combination of gravitational wave and electromagnetic observations, along with
simulations, would work very well: the gravitational wave observation identifies
the masses of the black hole and neutron star and the spin of the black hole,
and the electromagnetic observation plus simulations derives information about the
remaining mass of the disk (particularly if the recent promising observations related
to kilonovae hold up; see [24, 214]). Simulations are still very much in their infancy,
M. C. Miller
greater complexity of the waveforms. No pulsar in a NS-NS binary has a spin
period shorter than 23 ms [205], so the spin parameters of these neutron stars are
j ≡ cJ /GM 2 < ∼ 0.02. In contrast, although inferences of the spins of stellar-mass
black holes are not yet fully vetted, there is growing evidence that many of them
have spin parameters of several tenths, with some possibly approaching j = 1,
the mathematical maximum for black holes [146, 151]. The likely evolutionary
difference is that in the supernova that creates a neutron star or black hole, much
greater amounts of mass fall back to create a black hole than a neutron star, and
this mass will come from significant radii that thus carry considerable angular
momentum. Accretion from a binary subsequent to the production of a black hole
has little effect on either the mass or the angular momentum of the hole (see, e.g.,
[114]). Neutron stars in the high-mass X-ray binaries that could create a double
neutron star pair accrete little mass in the active phase and, empirically, seem to
have relatively strong magnetic fields, so accretion does not spin them up to high
rotation rates.
These statements are not absolute. It could be that there are slowly-spinning
black holes in BH-NS binaries, or rapidly spinning neutron stars in NS-NS
binaries (especially if they are produced dynamically in globular clusters). However,
the expectation at this time is that until tidal effects become important NS-NS
waveforms will be easier to interpret than those from BH-NS coalescences.
This leads us to what those tidal effects might tell us about neutron stars. At
large separations compared to the neutron star radii, nonlinear mode couplings due
to tides will not affect the inspiral phase significantly [225]. Most of the information
that can be obtained from tidal phase deviations from point-mass inspiral exists at
high frequencies [103], and recent comparisons of analytical theory with numerical
simulations suggest that with some calibration the theory does extremely well [25,
69, 79, 108, 124]. An explicit comparison of the expected signals from piecewisepolytropic equations of state suggests that a difference of only 1.3 km in radius could
be distinguished for NS-NS systems out to 300 Mpc with optimal direction and
binary orientation (this corresponds roughly to a direction- and orientation-averaged
distance of 140 Mpc) given a full hybrid post-Newtonian plus numerical relativity
waveform [186]. See Fig. 1.5 for an indication of the different frequencies of tidal
disruptions implied by two candidate equations of state.
Inspirals of neutron stars into black holes have not yet been examined using as
much care with respect to phase deviations. Recent work suggests that although
if the mass ratio is as high as 6:1 a NS-BH coalescence will be indistinguishable
from a BH-BH coalescence with the same masses [80], if the mass ratio is as small
as 2:1 or 3:1, single events at a distance of 100 Mpc could reveal the neutron star
radius to within 10–50% [123, 124], depending on details. This is a case in which
a combination of gravitational wave and electromagnetic observations, along with
simulations, would work very well: the gravitational wave observation identifies
the masses of the black hole and neutron star and the spin of the black hole,
and the electromagnetic observation plus simulations derives information about the
remaining mass of the disk (particularly if the recent promising observations related
to kilonovae hold up; see [24, 214]). Simulations are still very much in their infancy,