1 Astrophysical Constraints on Dense Matter in Neutron Stars
25
This is ≈800 Hz for M = 1.4 M and R = 15 km. In comparison, the highest
frequency ever established is 716 Hz, for PSR J1748–2446ad in the globular cluster
Terzan 5 [102]. Weak evidence for an 1122 Hz signal during thermonuclear bursts
from XTE J1739–285 has been claimed [113] but not confirmed. Even if it were
confirmed there would have to be strong evidence that this was the fundamental
frequency instead of the first overtone; the overtone can be dominant, as was shown
for IGR J17511–3057 [8].
Given that neutron stars could spin faster than they do, and that X-ray observations using the Rossi X-ray Timing Explorer are not biased against signals with
ν > 1000 Hz [53], why do the stars not spin faster? A conservative answer
that is in agreement with all data is that magnetic torques during accretion and
spinup limit the frequency. The required dipolar field strengths ∼10 8 G agree with
the fields inferred from the spindown of their descendants (the rotation-powered
millisecond pulsars), and in particular with the adherence of those pulsars to the
spin-up line [144]. Fields of this strength are also consistent with the spin behavior
of stars between transient outbursts [97, 176]. Another possibility is that in many
cases not enough matter has been accreted to reach maximum spin. An exciting
longshot that has received much attention due to the rapid improvements in groundbased gravitational wave detectors is that nonaxisymmetries in neutron stars, e.g.,
Rossby waves [9, 10, 40, 59, 84] (see [98, 142] for recent observational constraints)
or perhaps accretion-induced lumpiness in the stars [31, 218], might counteract
accretion spinup via emission of gravitational radiation. One way to test this
hypothesis is to observe systems that have had multiple transient episodes, because
the spindown between active phases could indicate whether gravitational radiation
(which would depend only on the long-term average accretion rate rather than the
instantaneous rate) emits angular momentum at the required rate. Two such systems
(SAX J1808–3658 and IGR J00291+5934) have been observed with the required
precision. In both cases there is no evidence that gravitational radiation induced
spindown is occurring, but within the observational uncertainties there is room for
contributions at the tens of percent level [96, 175]. Whatever the reason for the spin
ceiling, at this stage there are no known neutron stars with spin frequencies high
enough to rule out any plausible equation of state.
1.4.5 Kilohertz QPOs
Kilohertz quasi-periodic brightness oscillations (kHz QPOs) from accreting neutron
stars have been proposed to constrain the masses and radii of the stars. The basic
phenomenology of kHz QPOs is that there are commonly two relatively narrow
(Q ≡ ν/FWHM ∼ 20−200) QPOs that appear in the power density spectra of more
than 25 neutron star low-mass X-ray binaries. Both frequencies vary by hundreds
of Hertz between and during observations. The higher-frequency of the two often
reaches ν > 1000 Hz, and the lower-frequency peak (which is often the sharper
one, and also commonly has a larger fractional root mean square amplitude) has a
25
This is ≈800 Hz for M = 1.4 M and R = 15 km. In comparison, the highest
frequency ever established is 716 Hz, for PSR J1748–2446ad in the globular cluster
Terzan 5 [102]. Weak evidence for an 1122 Hz signal during thermonuclear bursts
from XTE J1739–285 has been claimed [113] but not confirmed. Even if it were
confirmed there would have to be strong evidence that this was the fundamental
frequency instead of the first overtone; the overtone can be dominant, as was shown
for IGR J17511–3057 [8].
Given that neutron stars could spin faster than they do, and that X-ray observations using the Rossi X-ray Timing Explorer are not biased against signals with
ν > 1000 Hz [53], why do the stars not spin faster? A conservative answer
that is in agreement with all data is that magnetic torques during accretion and
spinup limit the frequency. The required dipolar field strengths ∼10 8 G agree with
the fields inferred from the spindown of their descendants (the rotation-powered
millisecond pulsars), and in particular with the adherence of those pulsars to the
spin-up line [144]. Fields of this strength are also consistent with the spin behavior
of stars between transient outbursts [97, 176]. Another possibility is that in many
cases not enough matter has been accreted to reach maximum spin. An exciting
longshot that has received much attention due to the rapid improvements in groundbased gravitational wave detectors is that nonaxisymmetries in neutron stars, e.g.,
Rossby waves [9, 10, 40, 59, 84] (see [98, 142] for recent observational constraints)
or perhaps accretion-induced lumpiness in the stars [31, 218], might counteract
accretion spinup via emission of gravitational radiation. One way to test this
hypothesis is to observe systems that have had multiple transient episodes, because
the spindown between active phases could indicate whether gravitational radiation
(which would depend only on the long-term average accretion rate rather than the
instantaneous rate) emits angular momentum at the required rate. Two such systems
(SAX J1808–3658 and IGR J00291+5934) have been observed with the required
precision. In both cases there is no evidence that gravitational radiation induced
spindown is occurring, but within the observational uncertainties there is room for
contributions at the tens of percent level [96, 175]. Whatever the reason for the spin
ceiling, at this stage there are no known neutron stars with spin frequencies high
enough to rule out any plausible equation of state.
1.4.5 Kilohertz QPOs
Kilohertz quasi-periodic brightness oscillations (kHz QPOs) from accreting neutron
stars have been proposed to constrain the masses and radii of the stars. The basic
phenomenology of kHz QPOs is that there are commonly two relatively narrow
(Q ≡ ν/FWHM ∼ 20−200) QPOs that appear in the power density spectra of more
than 25 neutron star low-mass X-ray binaries. Both frequencies vary by hundreds
of Hertz between and during observations. The higher-frequency of the two often
reaches ν > 1000 Hz, and the lower-frequency peak (which is often the sharper
one, and also commonly has a larger fractional root mean square amplitude) has a