224
D. K. Galloway and L. Keek
[200]. 5 Recently, multi-zone simulations that include a full nuclear network show
that the turbulence is convection that is driven by an anti-correlation between the
temperature and the opacity in the ashes layer. As the ashes cool after a burst, the
opacity increases until convection switches on. Convective mixing brings fresh fuel
into the ashes layer, and the recurrence time of the resulting burst is the cooling time
of the order of minutes. Because of the stochastic nature of convection, sufficient
fuel for a follow-up burst is mixed down only ≈30% of the time. Furthermore, after
one follow-up burst, the mixing continues and has the potential to produce another
follow-up burst. This model reproduces many of the observed features of such bursts
(Fig. 5.5): the follow-up bursts have a lower peak luminosity and shorter duration
than the first burst, their recurrence time ranges from a few minutes to a few tens
of minutes, and several follow-up bursts can occur in so-called double, triple, and
quadruple events [16, 58, 99, 138].
5.2.3 Ignition Latitude
Up to now, we have only considered the radial dimension when locating the ignition
point. The latitude is also of importance: most bursting neutron stars spin rapidly
(Sect. 5.5), and consequently the effective surface gravity is reduced near the equator
compared to the polar regions (by a few percent for a typical burster [166]). The
surface of a spinning star follows an isobar (surface of constant pressure), and using
the relation y = −P /g from Sect. 5.1.1.1, we see that a smaller g eff at the equator
yields a larger y than at the poles. Furthermore, this implies that the local mass
accretion rate is higher at the equator. Because y ign depends only weakly on g eff
(e.g., Equation 32 in [14]), burst ignition preferentially occurs at the equator.
The spreading of the flame on the surface of the star was modelled by Spitkovsky
et al. [166]. The difference in speed between the spreading in the latitudinal and
longitudinal directions (with the latter significantly faster at low latitudes) is thought
to give rise to distinct, observable differences in the shape of the burst rises, which
is referred to as the “convexity” of the rise [128]. However, a study of a large sample
of bursts observed by RXTE suggests that bursts occurring when the source is in the
low (hard) spectral state typically ignite on the equator, while bursts observed in the
high (soft) spectral state ignite at higher latitudes [128, 208]. The obvious question
is, why do the latter bursts not also ignite on the equator?
An attractive explanation is that in the high (soft) state, both H and He fuel burns
steadily on the equator, while unsteady burning (likely triggered by He) continues
in regions at higher and lower latitudes. This explanation would also account for
the infrequent, weak bursts that are typically observed in the high (soft) state (cf.
5 Irregular bursting behaviour in early multi-zone models may have been an artefact of their reduced
nuclear reaction networks [181, 200], as this behaviour is absent in later work with large networks
[201].
D. K. Galloway and L. Keek
[200]. 5 Recently, multi-zone simulations that include a full nuclear network show
that the turbulence is convection that is driven by an anti-correlation between the
temperature and the opacity in the ashes layer. As the ashes cool after a burst, the
opacity increases until convection switches on. Convective mixing brings fresh fuel
into the ashes layer, and the recurrence time of the resulting burst is the cooling time
of the order of minutes. Because of the stochastic nature of convection, sufficient
fuel for a follow-up burst is mixed down only ≈30% of the time. Furthermore, after
one follow-up burst, the mixing continues and has the potential to produce another
follow-up burst. This model reproduces many of the observed features of such bursts
(Fig. 5.5): the follow-up bursts have a lower peak luminosity and shorter duration
than the first burst, their recurrence time ranges from a few minutes to a few tens
of minutes, and several follow-up bursts can occur in so-called double, triple, and
quadruple events [16, 58, 99, 138].
5.2.3 Ignition Latitude
Up to now, we have only considered the radial dimension when locating the ignition
point. The latitude is also of importance: most bursting neutron stars spin rapidly
(Sect. 5.5), and consequently the effective surface gravity is reduced near the equator
compared to the polar regions (by a few percent for a typical burster [166]). The
surface of a spinning star follows an isobar (surface of constant pressure), and using
the relation y = −P /g from Sect. 5.1.1.1, we see that a smaller g eff at the equator
yields a larger y than at the poles. Furthermore, this implies that the local mass
accretion rate is higher at the equator. Because y ign depends only weakly on g eff
(e.g., Equation 32 in [14]), burst ignition preferentially occurs at the equator.
The spreading of the flame on the surface of the star was modelled by Spitkovsky
et al. [166]. The difference in speed between the spreading in the latitudinal and
longitudinal directions (with the latter significantly faster at low latitudes) is thought
to give rise to distinct, observable differences in the shape of the burst rises, which
is referred to as the “convexity” of the rise [128]. However, a study of a large sample
of bursts observed by RXTE suggests that bursts occurring when the source is in the
low (hard) spectral state typically ignite on the equator, while bursts observed in the
high (soft) spectral state ignite at higher latitudes [128, 208]. The obvious question
is, why do the latter bursts not also ignite on the equator?
An attractive explanation is that in the high (soft) state, both H and He fuel burns
steadily on the equator, while unsteady burning (likely triggered by He) continues
in regions at higher and lower latitudes. This explanation would also account for
the infrequent, weak bursts that are typically observed in the high (soft) state (cf.
5 Irregular bursting behaviour in early multi-zone models may have been an artefact of their reduced
nuclear reaction networks [181, 200], as this behaviour is absent in later work with large networks
[201].