+ Statement of need
+ The majority of stars are born in binaries and multiple star
+ systems (e.g.,
+ Duchêne
+ & Kraus, 2013;
+ Moe
+ & Di Stefano, 2017;
+ Offner
+ et al., 2023), a large subset of which will exchange mass at
+ some point in their lives (e.g.,
+ de
+ Mink et al., 2014;
+ Podsiadlowski
+ et al., 1992;
+ Sana
+ et al., 2012). These massive stars play a critical role in the
+ formation and evolution of galaxies as a result of their feedback
+ (e.g.,
+ Dekel
+ & Silk, 1986;
+ Hopkins
+ et al., 2012;
+ Naab
+ & Ostriker, 2017;
+ Nomoto
+ et al., 2013;
+ Somerville
+ & Davé, 2015). However, binary evolution remains uncertain,
+ with many parameters such as common-envelope efficiency, mass transfer
+ efficiency, angular momentum loss due to mass transfer and the mean
+ magnitude of supernova natal kicks unconstrained over several orders
+ of magnitude
+ (Ivanova
+ et al., 2013; e.g.,
+ Ivanova
+ et al., 2020;
+ Janka,
+ 2012;
+ Katsuda
+ et al., 2018;
+ Marchant
+ & Bodensteiner, 2024;
+ Röpke
+ & De Marco, 2023).
+ Single massive stars are not expected to migrate far from their
+ birth location before reaching core-collapse due to their short
+ lifetimes (
+
+ ≲50,Myr,
+ e.g.,
+ Zapartas
+ et al., 2017). However, binary stars may be disrupted after an
+ initial supernova event, ejecting the secondary star from the system
+ at its orbital velocity (e.g.,
+ Blaauw,
+ 1961;
+ Eldridge
+ et al., 2011;
+ Renzo
+ et al., 2019). Thus, close massive binaries that are disrupted
+ can lead to the displacement of secondary stars significantly farther
+ from star-forming regions. The present-day positions and kinematics of
+ massive stars and binary products are therefore strongly impacted by
+ changes in binary physics that alter the pre-supernova separation.
+ This means that comparing simulations of positions and kinematics of
+ stars and compact objects to observations will enable constraints on
+ binary stellar evolution parameters.
+ The use of positions and kinematics as tracers of binary evolution
+ has been considered in the past. Recent work has shown the importance
+ of accounting for the galactic potential, which can change the
+ velocity of kicked objects (e.g.
+ Disberg
+ et al., 2024a). It is also important to consider the
+ inclination or timing of a supernova kick relative to the galactic
+ orbit, since, for example, a kick out of the galactic plane at an
+ object’s highest galactic vertical position will have a strong effect
+ on its final position. Failing to consider impacts from both a
+ galactic potential and kicks (i.e. velocity impulses) will lead to
+ misleading conclusions regarding the final spatial distributions of
+ the population. Some studies have considered using the galactic
+ potential at the present-day positions of objects to place a lower
+ limit on the peculiar velocity at birth and constrain supernova kicks
+ (Atri
+ et al., 2019;
+ Repetto
+ et al., 2012,
+ 2017;
+ Repetto
+ & Nelemans, 2015), but the accuracy of this method is
+ debated
+ (Mandel,
+ 2016). Other works have considered the impact of the galactic
+ potential for individual special cases, rather than at a population
+ level. For example, Evans et al.
+ (2020)
+ considered the orbits of hyper-runaway candidates evolving through the
+ Milky Way potential, while Neuhäuser et al.
+ (2020)
+ developed software for tracing the motion of stars to investigate the
+ recent nearby supernovae that ejected
+
+ ζ
+ Ophiuchi. Andrews & Kalogera
+ (2022)
+ considered galactic orbits of synthetic populations to place
+ constraints on black hole natal kicks based on observations of a
+ microlensed black hole.
+ Additionally, there are several works that consider a full
+ population of objects integrated through a galactic potential. Sweeney
+ et al.
+ (2022)
+ and Sweeney et al.
+ (2024)
+ used a combination of Galaxia and
+ galpy to predict the spatial distribution of
+ black holes and neutron stars in the Milky Way. Similarly, several
+ works have combined population synthesis with galactic orbit
+ integration (e.g. using COMPAS,
+ Riley
+ et al., 2022; and NIGO,
+ Rossi,
+ 2015) to investigate binary neutron stars and pulsars
+ (Chattopadhyay
+ et al., 2020,
+ 2021;
+ Disberg
+ et al., 2024b;
+ Gaspari,
+ Levan, et al., 2024;
+ Song
+ et al., 2024), as well as binary neutron star mergers and short
+ gamma-ray bursts
+ (Gaspari,
+ Stevance, et al., 2024;
+ Mandhai
+ et al., 2022;
+ Zevin
+ et al., 2020).
+ There is a clear need for a unified open-source tool that provides
+ the theoretical infrastructure for making predictions for the
+ positions and kinematics of massive stars and compact objects, placing
+ these systems in the context of their host galaxy and its
+ gravitational potential. cogsworth fulfils this
+ need, providing a framework for self-consistent population synthesis
+ and galactic dynamics simulations. The code is applicable to a wide
+ range of binary products, both common and rare, from walkaway and
+ runaway stars to X-ray binaries, as well as gravitational-wave and
+ gamma-ray burst progenitors.
+
+