tokens: for the BH in each system and could be supernova (SN), direct collapse (DC), or unsure (U). We have stated that just for the central predicted systemic radial velocity. Refer to Sections 7.1 and 7.4 for the explanation of the suggested birth pathway. a This work. b della Valle et al. ( 1994 ). c Cadolle Bel et al. ( 2007 ). d Gaia Collaboration ( 2018 ). e Kirsten et al. ( 2014 ). 5.2 Systemic radial velocity estimates We have four systems with poorly constrained systemic radial velocities ( Swift J1753.5−0127, MAXI J1820+070, VLA J2130+12, and GRS 1716−249). Using the best distance estimates for these systems, we project them on to the Galactic plane. We estimate the expected systemic radial velocity () of the system at this projected distance on to the Galactic plane and assuming that the system is undergoing pure Galactic rotation about the Galactic Centre. We note that this estimated value of systemic radial velocity is not a true indicator of the systemic radial velocity of the system as it might have received kicks, and thus is probably not following a pure Galactic rotation about the Galactic Centre. Thus for each system, we estimate five probable systemic radial velocity Gaussian distributions with medians of , 50 , and 100 (see Table 5 ). We limit our assumed distributions of the systemic radial velocities based on the fact that out of the systems for which systemic radial velocity is measured, the values lie between −142 ± 1.5 for GRO J1655−40 (Shahbaz et al. 1999 ) and 107 ± 2.9 for SAX J1819.3−2525 (Orosz et al. 2001 ). 6 ANALYSIS – POTENTIAL KICK VELOCITY As explained in Section 1.3 , peculiar velocity of a system when it crosses the Galactic plane is a better probe to understand the kick a BHXB received when the BH was born. Since all the parameters, namely proper motion, systemic radial velocity, and parallax (or distance), have error bars associated with them, it is crucial to propagate these errors appropriately to estimate the Galactocentric orbits of the systems. The age of most BHXBs is not known, which makes integrating the Galactocentric orbits back to the time of birth of the BH uncertain. We thus developed an MC methodology that accounts for the errors on the measured quantities and determines the peculiar velocity every time the system crosses the Galactic plane. The code integrates the Galactocentric orbit of every system in our sample back for 10 Gyr and records the velocity of the system at every plane crossing. Instead of a delta function for the measurement, it involves using Gaussian distributions of the measured parameters with reported uncertainties as standard deviation. Random values are picked from these Gaussian distributions as inputs to galpy (Bovy 2014 ) to create instances of Galactocentric orbits for ∼5000 random draws to make sure we have sampled the input distribution properly. We assume a Galactic potential given by the galpy model MWPotential2014 (see Bovy 2014 ). The Galactocentric orbits are
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