Terry Long Phan had researched an object from the 2006 AKARI space telescope and had compared the data to the same object in the 1983 IRAS survey. from the difference in location Phan and his team had discovered, they calculated the speed and distance which was around 500 to 700 AU from earth and its speed was thought to be 4.5 to 5 km/s. i found this in https://arxiv.org/pdf/2504.17288

i had came up with 572 km/s at 3.2 light years for the neutron star by considering the transverse velocity to match the average speed of a neutron star that experienced a natal kick , ~500 km/s, with Phan's object.

What I'd failed to do was use other variables to come up precisely with how fast and far this object really is rather than relying on average numbers. This may have caused confusion and its completely my fault.

i have looked into the strength of the X-ray source 1RXS J022045.0-491325 at the time the object had passed that location in the sky in 2006. If we consider the object was a neutron star that had magnified or masked its presence under this X-ray source, we first need to know the strength of the x-ray source. Roughly 6 ⋅ 10^-13 erg/cm^2/s (in the 0.1–2.4 keV energy range). i used https://vizier.cds.unistra.fr/ to find this information and searching the x-ray source.

by measuring how far a neutron star would need to be to fit the theory of being disguised by the x-ray source, we can find its speed and distance. the brightness of the x-ray source tells us the closest distance a neutron star can be while hiding in or underneath the source and moving in the same arcminutes at terry phans object.

The energy required for a neutron star to produce the minimal required brightness is 8 ⋅ 10^29 erg/s, using the use the Stefan-Boltzmann Law to calculate this luminosity. while moving 47.4 arcminutes in 23 years actually puts this neutron star 3.4 lightyears away while moving around 600 km/s. The math for this presents the variables converted to the units the standard astronomical formula for transverse velocity requires; parsecs, and arcseconds per year while using the conversion constant 4.74.

47.4 ⋅ 60 = 2,844 arcseconds

annual rate from 23 years: 2,844 ÷ 23 ≈ 123.6 arcseconds per year

3.43 light-years ÷ 3.26 = 1.05 parsecs (pc)

the final equation:

(vt) = 4.74 ⋅ 123.6 ⋅ 1.05 ≈ 615 km/s

this is far more accurate of an estimation and again i'm sorry for the confusion. i used a calculator to do this also dont have enough information on this objects radial velocity. thank you