4.4 Thermal structure of accreted crusts and X-ray bursts
A thermonuclear flash is triggered by an instability in the thermonuclear burning. The relevant
quantities are the local heating rate due to thermonuclear fusion, , and cooling rate, , resulting
from heat diffusion, volume expansion, and neutrino emission. A steady state of an accreting neutron star
corresponds to . It depends on the accretion rate, composition of accreted plasma, structure
and physical properties (thermal conductivity, neutrino emissivity, etc. of the stellar interior.
Examples of the steady thermal structure of accreting neutron stars are shown in Figures 25
||Temperature (local, in the reference frame of the star) vs. density within the crust
of an accreting neutron star (soft EoS of the core, ) in a steady thermal state,
with standard cooling of the core (no fast cooling of the direct Urca type). Upper solid curve
– . Lower solid curve – . H and He burning shells are
indicated by asterisks. Deep crustal heating is included. Dashed line – temperature profile without
deep crustal heating. Based on Figure 3b of Miralda-Escudé el al. .
||Same as in Figure 25, but for fast neutrino cooling due to pion condensation in the inner
core. Based on Figure 3c of Miralda-Escudé et al. .
A stable steady state of an accreting neutron star satisfies
The inequality guarantees that any thermal perturbation will be damped by a self-regulated cooling. Under
the increasing weight of accreted matter, an element of the crust in the He burning shell moves in the
plane, in the direction of increasing . At some moment, after crossing the “ignition line”
burning becomes unstable, and a self-accelerating thermonuclear flash is ignited because
In the standard picture, it is the instability in the helium burning via , which triggers an X-ray
burst (see, e.g., ). The total energy release in a burst can then be easily estimated (neglecting the
general relativistic correction) via
where is the mean energy per nucleon released in the thermonuclear flash (2 – 8 MeV, depending
on composition of burnt material), is the mass of the envelope burnt in
the flash (determined by the ignition density ), and is the atomic mass unit. The
value of can be read from Figure 39. A good model of X-ray bursts should yield
with a recurrence time of hours. This can be satisfied with ignition of helium flashes at
107 g cm–3.