5 Thermonuclear X-ray Bursts
227
dependent stochastic (Monte Carlo) models are being developed, which in time may
overcome these limitations [131].
When observed in a restricted instrumental energy band, a neutron star atmosphere spectrum is still well-approximated by a Planck function (Fig. 5.6). The
inferred temperature of the blackbody T bb is expected to differ from the atmosphere’s effective temperature T eff by the colour-correction factor, f c ≡ T bb /T eff ,
which is expected to vary as a function of the burst luminosity. f c has been calculated for assumed model atmospheres for application to RXTE/PCA observations
[178], and can similarly be obtained for other instruments using the model-predicted
spectra.
Aside from the temperature, the blackbody flux depends on the size of the
emitting area: the neutron star surface. It is typically assumed that the whole surface
radiates uniformly. 6 At the onset of the brightest bursts, the flux may exceed the
Eddington limit, causing photospheric radius expansion and possibly also driving a
wind from the neutron star surface [41, 141, 153, 196]. During PRE the photospheric
radius increases typically by up to a factor ∼10, but even larger expansions have
been observed (“superexpansion”; Sect. 5.7.1). Once the flux is reduced below the
Eddington limit, the photosphere settles back at its original radius (the “touchdown”
point). After touchdown, one expects the photospheric radius to remain constant,
but substantial evolution in the blackbody normalisation, K bb , can be observed
[64, 207]. We discussed how deviations from a pure blackbody spectrum introduce
a colour correction factor for T bb . To preserve the total blackbody flux F ∝ K bb T 4
bb ,
this produces an equivalent correction to K bb : the proportionality between the
measured blackbody normalisation and the colour correction is K
−1/4
bb
∝ f c (see
Fig. 5.4).
The properties of the continuum burst spectrum have been employed to measure
the neutron star mass and radius (e.g. [133, 134, 185, 186]; see also Miller, this
volume). Two approaches have been used: the “touchdown” and the “coolingtail” methods. The former method uses the flux at touchdown as a measure of the
Eddington limit, which depends on the neutron star mass, in combination with measurements of the blackbody radius and (usually) the source distance [61, 62]. The
radius is measured through the blackbody normalisation, K bb ∝ 4πR 2 , assuming
that f c is constant. It is possible that the photosphere has not completely settled onto
the neutron star at touchdown [167]. Additionally, an accurate measure of f c and the
Eddington limit requires knowledge of the composition of the photosphere as well
as the source distance, which are generally known only approximately.
The cooling-tail method uses the flux-dependent colour corrections from model
atmosphere spectra [177, 178]. Because these models are only valid at fluxes below
the Eddington limit, only the tail of a burst is considered. By measuring K
−1/4
bb ,
one observes how f c changes as the burst flux decreases. The atmosphere models
6 Emission from only part of the surface has been inferred for the 1999 superburst from
4U 1820−30 [17]. This study ignored, however, disk reflection [9], which complicates the
interpretation of superburst spectra [101, 102, 104].
227
dependent stochastic (Monte Carlo) models are being developed, which in time may
overcome these limitations [131].
When observed in a restricted instrumental energy band, a neutron star atmosphere spectrum is still well-approximated by a Planck function (Fig. 5.6). The
inferred temperature of the blackbody T bb is expected to differ from the atmosphere’s effective temperature T eff by the colour-correction factor, f c ≡ T bb /T eff ,
which is expected to vary as a function of the burst luminosity. f c has been calculated for assumed model atmospheres for application to RXTE/PCA observations
[178], and can similarly be obtained for other instruments using the model-predicted
spectra.
Aside from the temperature, the blackbody flux depends on the size of the
emitting area: the neutron star surface. It is typically assumed that the whole surface
radiates uniformly. 6 At the onset of the brightest bursts, the flux may exceed the
Eddington limit, causing photospheric radius expansion and possibly also driving a
wind from the neutron star surface [41, 141, 153, 196]. During PRE the photospheric
radius increases typically by up to a factor ∼10, but even larger expansions have
been observed (“superexpansion”; Sect. 5.7.1). Once the flux is reduced below the
Eddington limit, the photosphere settles back at its original radius (the “touchdown”
point). After touchdown, one expects the photospheric radius to remain constant,
but substantial evolution in the blackbody normalisation, K bb , can be observed
[64, 207]. We discussed how deviations from a pure blackbody spectrum introduce
a colour correction factor for T bb . To preserve the total blackbody flux F ∝ K bb T 4
bb ,
this produces an equivalent correction to K bb : the proportionality between the
measured blackbody normalisation and the colour correction is K
−1/4
bb
∝ f c (see
Fig. 5.4).
The properties of the continuum burst spectrum have been employed to measure
the neutron star mass and radius (e.g. [133, 134, 185, 186]; see also Miller, this
volume). Two approaches have been used: the “touchdown” and the “coolingtail” methods. The former method uses the flux at touchdown as a measure of the
Eddington limit, which depends on the neutron star mass, in combination with measurements of the blackbody radius and (usually) the source distance [61, 62]. The
radius is measured through the blackbody normalisation, K bb ∝ 4πR 2 , assuming
that f c is constant. It is possible that the photosphere has not completely settled onto
the neutron star at touchdown [167]. Additionally, an accurate measure of f c and the
Eddington limit requires knowledge of the composition of the photosphere as well
as the source distance, which are generally known only approximately.
The cooling-tail method uses the flux-dependent colour corrections from model
atmosphere spectra [177, 178]. Because these models are only valid at fluxes below
the Eddington limit, only the tail of a burst is considered. By measuring K
−1/4
bb ,
one observes how f c changes as the burst flux decreases. The atmosphere models
6 Emission from only part of the surface has been inferred for the 1999 superburst from
4U 1820−30 [17]. This study ignored, however, disk reflection [9], which complicates the
interpretation of superburst spectra [101, 102, 104].