320
M. Méndez and T. M. Belloni
with the orbital frequency at the inner disc radius. On the other hand, as shown for
instance in [4, 5, 47], it is possible to have frequencies above the Keplerian frequency
at the inner edge of the accretion disc if there is a transition region between the disc
and the neutron-star surface where matter in the disc has to slow down to match the
rotation speed of the neutron star.
Measurements of QPO frequencies and spectral properties of the source offer
another possibility to constrain the mass and radius of a neutron star. A broad iron
emission line at 6.5–7 keV has been observed in about a dozen accreting neutron
stars [26, 31–33, 43–46, 63, 64, 97, 98, 102, 117, 129, 131, 132, 134, 144, 146, 177,
178]. It has been proposed that, like in accreting black-hole systems [48, 140], the
iron line is due to reflection of corona photons off the accretion disc, and that the line
profile is driven by special and GR effects. If this is the case, the shape of the line
profile would depend upon the inner disc radius. Therefore, detecting kHz QPOs in
the power spectrum and a broad iron line in the energy spectrum of the same object
would provide separate ways to constrain the neutron-star parameters in that object
[25].
There is only one source, 4U 1636−53, in which both a broad iron line
in the energy spectrum and kHz QPOs in the power spectrum were observed
simultaneously in four separate occasions [145]. Because these four observations
sampled different spectral states of the source, and presumably the inner radius of
the disc changed between observations [54], this dataset offered the opportunity to
test whether the inner disc radius deduced independently from the line profile and
from the kHz QPOs changed in a consistent way. The main result of this analysis
[145] was that the inner radius of the accretion disc deduced from the frequency of
the upper kHz QPO was correlated with the spectral state of the source, whereas
the radius deduced from the profile of the iron line was not. Because of this, the
combined results from the kHz QPOs and the iron line do not lead to a consistent
value of the neutron-star mass. Since those were the only observations available for
this test, and no new observations of kHz QPOs are possible with current missions,
we have to wait until the eXTP [180] and Athena [122] missions fly to address this
question again. For the moment the jury is still out.
We refer the reader to the chapter in this book by Cole Miller for a more detailed
discussion on methods of constraining neutron-star masses, radii and the equation
of state of the cold dense matter that constitutes these stars.
6.10 Conclusions and Outlook
The kHz QPOs in neutron stars unlocked a new door to study the dynamics of
matter, and the time-dependent interplay between matter and radiation, on very short
time scales in the violent and turbulent environment that surrounds a neutron star,
and under the most extreme conditions in GR. These QPOs also offer a chance
to constrain the mass, radius and internal constitution of these extremely compact
objects, with the potential to unveil the properties of matter under conditions that are
M. Méndez and T. M. Belloni
with the orbital frequency at the inner disc radius. On the other hand, as shown for
instance in [4, 5, 47], it is possible to have frequencies above the Keplerian frequency
at the inner edge of the accretion disc if there is a transition region between the disc
and the neutron-star surface where matter in the disc has to slow down to match the
rotation speed of the neutron star.
Measurements of QPO frequencies and spectral properties of the source offer
another possibility to constrain the mass and radius of a neutron star. A broad iron
emission line at 6.5–7 keV has been observed in about a dozen accreting neutron
stars [26, 31–33, 43–46, 63, 64, 97, 98, 102, 117, 129, 131, 132, 134, 144, 146, 177,
178]. It has been proposed that, like in accreting black-hole systems [48, 140], the
iron line is due to reflection of corona photons off the accretion disc, and that the line
profile is driven by special and GR effects. If this is the case, the shape of the line
profile would depend upon the inner disc radius. Therefore, detecting kHz QPOs in
the power spectrum and a broad iron line in the energy spectrum of the same object
would provide separate ways to constrain the neutron-star parameters in that object
[25].
There is only one source, 4U 1636−53, in which both a broad iron line
in the energy spectrum and kHz QPOs in the power spectrum were observed
simultaneously in four separate occasions [145]. Because these four observations
sampled different spectral states of the source, and presumably the inner radius of
the disc changed between observations [54], this dataset offered the opportunity to
test whether the inner disc radius deduced independently from the line profile and
from the kHz QPOs changed in a consistent way. The main result of this analysis
[145] was that the inner radius of the accretion disc deduced from the frequency of
the upper kHz QPO was correlated with the spectral state of the source, whereas
the radius deduced from the profile of the iron line was not. Because of this, the
combined results from the kHz QPOs and the iron line do not lead to a consistent
value of the neutron-star mass. Since those were the only observations available for
this test, and no new observations of kHz QPOs are possible with current missions,
we have to wait until the eXTP [180] and Athena [122] missions fly to address this
question again. For the moment the jury is still out.
We refer the reader to the chapter in this book by Cole Miller for a more detailed
discussion on methods of constraining neutron-star masses, radii and the equation
of state of the cold dense matter that constitutes these stars.
6.10 Conclusions and Outlook
The kHz QPOs in neutron stars unlocked a new door to study the dynamics of
matter, and the time-dependent interplay between matter and radiation, on very short
time scales in the violent and turbulent environment that surrounds a neutron star,
and under the most extreme conditions in GR. These QPOs also offer a chance
to constrain the mass, radius and internal constitution of these extremely compact
objects, with the potential to unveil the properties of matter under conditions that are