Understanding Compact Object Formation and Natal Kicks. I. Calculation Methods and the Case of GRO J1655−40

In recent years proper motion measurements have been added to the set ofobservational constraints on the current properties of Galactic X-ray binaries.We develop an analysis that allows us to consider all this availableinformation and reconstruct the full evolutionary history of X-ray binariesback to the time of compact object formation. This analysis accounts for masstransfer through the ongoing X-ray phase, tidal circularization before theonset of Roche-lobe overflow, motion through the Galactic potential after theformation of the compact object, and binary orbital dynamics and hydrodynamicmodeling of the core collapse. We apply the analysis to the soft X-raytransient GRO J1655-40 and, for the first time, use its full 3D peculiarvelocity constraints right after core collapse instead of lower limits on thecurrent space velocity given by the present-day radial velocity. We find thatthe system has remained within 200pc from the Galactic plane throughout itsentire life time and that the mass loss and a kick possibly associated with theblack hole (BH) formation imparted a kick velocity of 45-115 km/s to thebinary's center of mass. Right after BH formation, the system consists of a3.5-6.3 Msun BH and a 2.3-4 Msun main-sequence star. At the onset of the X-rayphase the donor is still on the main sequence. We find that a symmetric BHformation event cannot be formally excluded, but that the associated systemparameters are only marginally consistent with the currently observed binaryproperties. BH formation mechanisms involving an asymmetric supernova explosionwith associated BH kick velocities of a few tens of km/s, on the other hand,satisfy the constraints much more comfortably. We also derive an upper limit onthe BH kick magnitude of 210 km/s. (abridged)Comment: Minor revisions. Accepted for publication in Ap