Anisotropy of X-Ray Bursts From Neutron Stars With Concave Accretion Disks

Abstract

Emission from neutron stars and accretion disks in low-mass X-ray binaries is anisotropic. The non-spherical shape of the disk as well as blocking of the neutron star by the disk make the observed flux dependent on the inclination angle of the disk with respect to the line of sight. This is of importance for the interpretation of thermonuclear X-ray bursts from neutron stars. Because part of the X-ray burst is reflected off the disk, the observed burst flux depends on the anisotropies for both direct emission from the neutron star and reflection off the disk. This influences measurements of source distance, mass accretion rate, and constraints on the neutron star's equation of state. Previous predictions of the anisotropy factors assumed a geometrically flat disk. Detailed observations of two so-called superbursts allowed for the direct and the reflected burst fluxes to each be measured separately. The reflection fraction was much higher than what the anisotropies of a flat disk can account for. We create numerical models to calculate the anisotropy factors for different disk shapes, including concave disks. We present the anisotropy factors of the direct and reflected burst fluxes separately, as well as the anisotropy of the persistent flux. Reflection fractions substantially larger than unity are produced in the case where the inner accretion disk increases steeply in height, such that part of the star is blocked from view. Such a geometry could possibly be induced by the X-ray burst if X-ray heating causes the inner disk to puff up.

NICER Observes the Effects of an X-Ray Burst on the Accretion Environment in Aql X-1

“…The disk has, however, been observed to truncate at R in ;15 R g (Sakurai et al 2012;King et al 2016). From Figure 5 in He & Keek (2016) we estimate that for a 1.4 M e and 10 km radius neutron star this gap reduces the reflection fraction to f refl ;0.15. We find triple this value, f refl =0.45±0.08, for the burst.…”

“…At this angle, f refl =0.10 is expected when the disk extends to the stellar surface (He & Keek 2016), and f refl =0.03 for R in ;15 R g . Under these assumptions, reflection contributes only a small part of the soft excess detected by NICER.…”

“…For a highly ionized disk, the fluorescent FeKα line from reflection is challenging to detect during a burst with NICER, whereas the soft excess is highly significant . For an inclination angle of 20° ( King et al 2016) the expected reflection fraction is f refl =0.52 for a thin disk that extends to the neutron star (He & Keek 2016). The disk has, however, been observed to truncate at R in ;15 R g (Sakurai et al 2012;King et al 2016).…”

Thermonuclear Burst Observations for Model Comparisons: A Reference Sample

“…preferential beaming in our direction. As pointed out by He & Keek (2016), the values of ξ b and ξp depend upon the system inclination and the structure of the accretion disk, neither of which are well constrained. For 4U 1636−536, we estimated the distance based on measurements of the burst emission from photospheric radius-expansion (PRE) bursts in MINBAR, assuming that they reach the Eddington limit.…”

“…• (Casares et al 2006), which implies 0.7 ξ −1 b 1.3 for a thin disk (larger values for smaller angles; He & Keek 2016). The observation of a broad fluorescent iron line favors a large inclination angle (Pandel et al 2008), but this depends strongly on the interpretation of the reflection spectrum.…”