14
M. C. Miller
In addition to these well-established high masses, there are hints that some black
widow pulsars (those that are currently evaporating their companions) might have
even higher masses. This was first reported for the original black widow pulsar
PSR B1957+20 [223]. For this star the best-fit mass is M = 2.40 ± 0.12 M ,
but at the highest allowed inclination and lowest allowed center of mass motion
the mass could be as low as 1.66 M . More recently, [188] analyzed the gammaray black widow pulsar PSR J1311–3430 and found a mass of M = 2.7 M for
simple heated light curves (but with significant residuals in the light curve), and no
viable solutions with a mass less than 2.1 M . They conclude that better modeling
and more observation is needed to establish a reliable mass, but it is an intriguing
possibility that black widow pulsars have particularly large masses.
From the astrophysical standpoint, it has been proposed that neutron star
birth masses are bimodal, depending on whether the core collapse occurs due to
electron capture or iron core collapse [197]. There is also mounting evidence for
systematically higher masses in systems that are expected to have had substantial
accretion [241]. From the standpoint of nuclear physics, [132] point out that
2.0 M neutron stars place interesting upper limits on the physically realizable
energy density, pressure, and chemical potential. Higher masses would present even
stronger constraints.
To a far greater extent than with the other constraints described in this review,
we can be confident that the mere passage of time will greatly improve the mass
measurements, and indeed all of the timing parameters. Table II of [68] shows
that as a function of the total observation time T (assuming a constant rate of
sampling), the fractional uncertainties in the post-Keplerian parameters scale as
Δ ˙
ω ∝ T −3/2 , Δγ ∝ T −3/2 , Δ ˙
P b ∝ T −5/2 , Δr ∝ T −1/2 , and Δs ∝ T −1/2 ;
for the r and s parameters the improvements are simply due to having more
measurements, whereas the others improve faster with time because the effects
accumulate. Particularly good improvement is expected for the NS-WD systems
because as we describe above they have larger orbits and thus slower precession
than NS-NS systems. There is thus reason to hope that additional high-mass systems
will be discovered.
There are also planned observatories and surveys that will dramatically increase
the number of known pulsars of all types, which will likely include additional NSNS and NS-WD systems. An example of such a planned observatory is the Square
Kilometer Array, which has been projected to increase our known sample of pulsars
by a factor of ∼10. In addition, as [215] pointed out recently, future high-precision
astrometry will be able to deconvolve the parallactic, proper, and orbital motion of
the two components of a high-mass X-ray binary. They estimate that for parameters
appropriate to the Space Interferometry Mission [201] this will yield a neutron star
mass accurate to 2.5% in X Per, to 6.5% in Vela X-1, and to ∼10% in V725 Tau and
GX 301–2.
It is thus probable that in the next ∼10 years we will have far more, and far
better, estimates of the masses of individual neutron stars. We do not, however, have
a guarantee that any of those masses will be close to the maximum allowed. We thus
need additional ways to access the properties of high-density matter. In particular,
M. C. Miller
In addition to these well-established high masses, there are hints that some black
widow pulsars (those that are currently evaporating their companions) might have
even higher masses. This was first reported for the original black widow pulsar
PSR B1957+20 [223]. For this star the best-fit mass is M = 2.40 ± 0.12 M ,
but at the highest allowed inclination and lowest allowed center of mass motion
the mass could be as low as 1.66 M . More recently, [188] analyzed the gammaray black widow pulsar PSR J1311–3430 and found a mass of M = 2.7 M for
simple heated light curves (but with significant residuals in the light curve), and no
viable solutions with a mass less than 2.1 M . They conclude that better modeling
and more observation is needed to establish a reliable mass, but it is an intriguing
possibility that black widow pulsars have particularly large masses.
From the astrophysical standpoint, it has been proposed that neutron star
birth masses are bimodal, depending on whether the core collapse occurs due to
electron capture or iron core collapse [197]. There is also mounting evidence for
systematically higher masses in systems that are expected to have had substantial
accretion [241]. From the standpoint of nuclear physics, [132] point out that
2.0 M neutron stars place interesting upper limits on the physically realizable
energy density, pressure, and chemical potential. Higher masses would present even
stronger constraints.
To a far greater extent than with the other constraints described in this review,
we can be confident that the mere passage of time will greatly improve the mass
measurements, and indeed all of the timing parameters. Table II of [68] shows
that as a function of the total observation time T (assuming a constant rate of
sampling), the fractional uncertainties in the post-Keplerian parameters scale as
Δ ˙
ω ∝ T −3/2 , Δγ ∝ T −3/2 , Δ ˙
P b ∝ T −5/2 , Δr ∝ T −1/2 , and Δs ∝ T −1/2 ;
for the r and s parameters the improvements are simply due to having more
measurements, whereas the others improve faster with time because the effects
accumulate. Particularly good improvement is expected for the NS-WD systems
because as we describe above they have larger orbits and thus slower precession
than NS-NS systems. There is thus reason to hope that additional high-mass systems
will be discovered.
There are also planned observatories and surveys that will dramatically increase
the number of known pulsars of all types, which will likely include additional NSNS and NS-WD systems. An example of such a planned observatory is the Square
Kilometer Array, which has been projected to increase our known sample of pulsars
by a factor of ∼10. In addition, as [215] pointed out recently, future high-precision
astrometry will be able to deconvolve the parallactic, proper, and orbital motion of
the two components of a high-mass X-ray binary. They estimate that for parameters
appropriate to the Space Interferometry Mission [201] this will yield a neutron star
mass accurate to 2.5% in X Per, to 6.5% in Vela X-1, and to ∼10% in V725 Tau and
GX 301–2.
It is thus probable that in the next ∼10 years we will have far more, and far
better, estimates of the masses of individual neutron stars. We do not, however, have
a guarantee that any of those masses will be close to the maximum allowed. We thus
need additional ways to access the properties of high-density matter. In particular,