Modeling V1309 Sco with Octo-tiger Dominic C. Marcello, Kundan K. Kadam, Georey C. Clayton, Juhan Frank, Hartmut Kaisar, Patrick M. Motl Abstract Initial Model Evolution and Merger The luminous red , V1309 Scorpii, is known The initial model approximates the V1309 Sco con- to have formed from the merger of a contact bi- tact binary at the onset of the Darwin instability nary. We have developed a grid-based, adaptive (Stepien, 2011). The primary has a total mass of mesh renement code, Octo-tiger, to study merg- 1.55M and a Helium core of 0.17M . The sec- ers of binary star systems. Using Octo-tiger, we ondary has a total mass of 0.17M and a Helium have produced an initial model of V1309 Sco and core of 0.16M . The cores are approximated us- evolved it through merger. The initial model uses ing a polytropic equation of state with polytropic a multi-polytropic structural equation of state and index n = 5. Around the primary's core is a radia- was constructed with the self-consistent eld tech- tive shell of solar composition, approximated using nique. Both stars are initially synchronously rotat- n = 3. Enveloping the primary's radiative shell and ing, in contact, and the system is on the edge of the the core of the secondary is a convective envelope Darwin instability. Once we begin evolving the sys- common to both stars, approximated using 3 n = 2 tem, the components rapidly lose synchronization. and solar composition. The mass of the radiative

After approximately 13 orbits, the smaller compan- shell of the primary is 1.28M . The spin to orbital ion is tidally disrupted and the system merges. angular momentum ratio is 1 , placing the system 3 on the edge of the Darwin instability. We used the HPX bi-polytropic self-consistent eld technique (BSCF) (Kadam, et. al., 2016), modied to allow for a third Octo-tiger is parallelized using the High Perfor- species around the primary. mance ParallaX (HPX) library. HPX is a C++ runtime library for distributed systems. It is de- Darwin Instability signed to overcome the scaling limitations of the The plot below shows the ratio of the primary's Message Passing Interface (MPI). HPX enables ne rotational frequency to the orbital frequency, grained parallelism through lightweight threads and J1 (black), and the ratio of the spin momenta provides an active global address space (AGAS). I1Ωorb to the orbital momentum, J1+J2 (red), versus The programmer can call functions remotely and ac- Jorb time. Because the orbital momentum is below the cess member functions of remote objects. HPX ex- minimum possible value for a synchronized orbit, ecutes user threads concurrently with network com- the components cannot maintain synchronization. munications, hiding latencies. HPX is developed by the Stekar Group at LSU (stellar.cct.lsu.edu).

Octo-tiger Octo-tiger is a code for simulating fully three- dimensional self-gravitating astrophysical uids. It is particularly suited for interacting binaries. The The images above depict equatorial slices of density at various points in the evolution. We show the uid is modeled on a Cartesian adaptive mesh initial model in the top left panel. The density is depicted relative to the initial central density of the renement (AMR) grid using the nite volume secondary. The logarithmic color scale spans ten orders of . The black double headed arrow method. The gravitational eld is computed using is xed at the initial orbital separation, indicating the spatial scale for each plot. Almost immediately the fast multi-pole method (FMM). Octo-tiger pre- after evolution begins, mass ows from the secondary to the primary through the L1 Lagrange point and serves mass, linear momentum, angular momentum, from the secondary to a developing structure through the L2 Lagrange point (upper and energy to machine precision (Marcello 2017, right). Because of the Darwin instability, the stars are not able to maintain tidal synchronization. Orbital Marcello, et. al. 2017). momentum is continuously converted into spin momentum in a futile attempt to maintain synchronization. After approximately 13 orbits, the secondary is tidally disrupted (lower left). The model continues to evolve References for several orbital periods past merger (lower right). Kadam, K., Motl, P.M., Frank, J., Clayton, G.C., Marcello, D.C., 2016, MNRAS, 462, 2237 Marcello, D.C., 2017, under review by ApJ Acknowledgements: We wish to acknowledge the support from the National Science Foundation through Marcello, D.C., Kadam, K., Clayton, G.C., Frank, J., Kaisar, H., Motl, P.M., 2017, under review by the INSPIRE grant AST- 1240655. Portions of this research were conducted with high performance computing Proceedings of Science resources provided by LSU and the Louisiana Optical Network Initiative. Stepien, K., 2011, A&A, 531, A18 Code Repositories: github.com/STEllAR-GROUP/octotiger and github.com/STEllAR-GROUP/hpx