For the detail behind the content of this post see “Neutron Star Radius-to-Mass Ratio from Partial Accretion Disc Occultation as Measured through Fe Kα Line Profiles” as submitted to ApJ by Riccardo La Placa et al, March 2020.
The pressure/density relationships (aka equations of state or EoSs) of neutron stars (NSs) are still a hot topic for research. Radius-Mass Ratios of NSs are important keys to finding NS EoSs but are not easy to derive. Masses are much more readily measured than radii. The paper lists seven methods for measuring NS radii, none of which is sufficiently accurate to allow EoS determination, before going on to describe a novel method which may possibly work well in the case of NSs in Low Mass X-Ray Binaries (LMXBs) that are highly-inclined to our line of sight.
The prospective method takes advantage of the near ubiquity of 6.4keV Fe Kα lines that originate from the innermost disc regions of LMXBs (i.e. from relatively close to the NS surface). This proximity means that the line emitting region will sometimes be occulted by the star itself, as shown in Fig. 2 of the paper (see below, noting the relativistic / strong G effects). Point B is within the shaded region that is occulted by the star, and photons from such points, unlike those from points like A, do not reach us.
Figure 3 of the paper (not reproduced here) shows the occultation effect for different inclinations (i = 55, 65, 75o) and NS radii (6, 7 & 8 rg). Figure 4 (ditto) shows the expected loss of total flux for those same nine cases.
Up to this point, the paper is all theoretical, and then they analyse NuSTAR data for 4U 1636-53, a quasi-persistent LMXB with an inclination of 65-75o which exhibits neither eclipses nor dips. The signal to noise ratio (SNR) in the NuSTAR data turns out to not quite be high enough for the desired result.
Finally, they model the same data against the anticipated performance of the Large Area Detector (LAD) of China’s upcoming eXTP mission, due to launch in the mid-20s. Here they are clearly able to show that the region producing the Fe Kα line is occulted, thus proving the utility of the method.
eXTP’s LAD, at 3.4m2, is an order of magnitude larger than past/current instruments. If all goes according to plan, we should soon see a major step forward in NS EoS determination.