228
D. K. Galloway and L. Keek
predict f c as a function of the Eddington ratio and the neutron star mass and radius.
Fitting these f c curves to the observed data allows for the neutron star parameters
to be measured. This method does not depend on prior knowledge of the source
distance or the atmosphere composition, as the required information is encoded in
the f c curves.
The radii obtained with the cooling-tail method are systematically larger than
with the touchdown method. Each method has a set of assumptions that may
be the source of this systematic uncertainty [63–65, 152, 167]. For example, the
inclusion of stellar rotation in the atmosphere models may reduce the derived radius
[152]. Furthermore, each method appears to work best for a different set of burst
observations. Bursts in the low (hard) flux state conform to the predictions of the
model atmospheres, whereas in the high (soft) flux state the bursts do not exhibit the
expected f c − F relation [91]. In the high flux state the accretion disk is expected to
extend to the neutron star surface, and a spreading layer may cover a substantial part
of the star [156], which reprocesses the burst spectrum. Conversely, studies using
the touchdown method have preferred bursts that show only small deviations from
a blackbody, rather than those that follow the expected f c − F relation [64]. The
source 4U 1608−522 exhibits bursts in both flux states, and an analysis with both
methods illustrates the differences in the obtained results [152]. Further details on
the measurement of mass and radius are presented in [135].
5.3.2 Discrete Spectral Features
Before the thermalized burst spectrum leaves the neutron star, the photons scatter
off electrons in the photosphere. If the photosphere is incompletely ionized, discrete
absorption features may appear in the spectrum. The photon’s energy may take
the electron from one bound state to another (bound-bound transition), which
produces an absorption line at that energy. Alternatively, the photon energy may
exceed the ionization energy required to unbind the electron (bound-free transition).
This creates an absorption edge that starts at the ionization energy and continues
towards higher energies. In the photosphere of an accreting neutron star, hydrogen
and helium are fully ionized. Metals, however, may be only partially ionized and
can produce lines and edges, particularly in the extended photosphere driven by a
strong radius-expansion burst (see Sect. 5.4). A range of metals may produce these
features, depending on the composition of the photosphere [196]. Iron is typically
one of the most abundant heavy metals, and has relatively many transitions to create
discrete absorption features.
Detection of surface features has been a high observational priority for decades,
due to the prospects of constraining the neutron star compactness via the gravitational redshift, measurable from comparing the observed and rest-frame energies
of such features. Although there have been several notable claims for detections of
features (see below), many have been unverified in subsequent observations and/or
been shown to be unlikely to arise from the NS surface. There are a number of
D. K. Galloway and L. Keek
predict f c as a function of the Eddington ratio and the neutron star mass and radius.
Fitting these f c curves to the observed data allows for the neutron star parameters
to be measured. This method does not depend on prior knowledge of the source
distance or the atmosphere composition, as the required information is encoded in
the f c curves.
The radii obtained with the cooling-tail method are systematically larger than
with the touchdown method. Each method has a set of assumptions that may
be the source of this systematic uncertainty [63–65, 152, 167]. For example, the
inclusion of stellar rotation in the atmosphere models may reduce the derived radius
[152]. Furthermore, each method appears to work best for a different set of burst
observations. Bursts in the low (hard) flux state conform to the predictions of the
model atmospheres, whereas in the high (soft) flux state the bursts do not exhibit the
expected f c − F relation [91]. In the high flux state the accretion disk is expected to
extend to the neutron star surface, and a spreading layer may cover a substantial part
of the star [156], which reprocesses the burst spectrum. Conversely, studies using
the touchdown method have preferred bursts that show only small deviations from
a blackbody, rather than those that follow the expected f c − F relation [64]. The
source 4U 1608−522 exhibits bursts in both flux states, and an analysis with both
methods illustrates the differences in the obtained results [152]. Further details on
the measurement of mass and radius are presented in [135].
5.3.2 Discrete Spectral Features
Before the thermalized burst spectrum leaves the neutron star, the photons scatter
off electrons in the photosphere. If the photosphere is incompletely ionized, discrete
absorption features may appear in the spectrum. The photon’s energy may take
the electron from one bound state to another (bound-bound transition), which
produces an absorption line at that energy. Alternatively, the photon energy may
exceed the ionization energy required to unbind the electron (bound-free transition).
This creates an absorption edge that starts at the ionization energy and continues
towards higher energies. In the photosphere of an accreting neutron star, hydrogen
and helium are fully ionized. Metals, however, may be only partially ionized and
can produce lines and edges, particularly in the extended photosphere driven by a
strong radius-expansion burst (see Sect. 5.4). A range of metals may produce these
features, depending on the composition of the photosphere [196]. Iron is typically
one of the most abundant heavy metals, and has relatively many transitions to create
discrete absorption features.
Detection of surface features has been a high observational priority for decades,
due to the prospects of constraining the neutron star compactness via the gravitational redshift, measurable from comparing the observed and rest-frame energies
of such features. Although there have been several notable claims for detections of
features (see below), many have been unverified in subsequent observations and/or
been shown to be unlikely to arise from the NS surface. There are a number of