News

New paper "The Equilibrium Tide: An Updated Prescription for Population Synthesis Codes"
July 6 2022
In Preece et al. (2022; link) we present an updated prescription for the equilibrium tides suitable for population synthesis codes. A grid of 1D evolutionary models was created and the viscous timescale was calculated for each detailed model. A metallicity-dependent power-law relation was fitted to both the convective cores and convective envelopes of the models. The prescription was implemented into the population synthesis code Binary Star Evolution and predicts a 16.5% reduction in the overall number of merges, with those involving main-sequence stars most affected. The new prescription also reduces the overall supernova rate by 3.6% with individual channels being differently affected. The single degenerate Ia supernova occurrence is reduced by 12.8%. The merging of two carbon oxygen white dwarfs to cause a Ia supernova occurs 16% less frequently. The number of subsynchronously rotating stars in close binaries is substantially increased with our prescription, as is the number of noncircularized systems at the start of common-envelope evolution.
Public release of MSE
April 21 2022

The Multiple Stellar Evolution (MSE) code developed in our group is now publicly available on GitHub (link). MSE is designed to rapidly model the stellar, binary, and dynamical evolution of multiple-star systems. It includes a number of new features not present in previous population synthesis codes: 1) an arbitrary number of stars, as long as the initial system is hierarchical, 2) dynamic switching between secular and direct N-body integration for efficient computation of the gravitational dynamics, 3) treatment of mass transfer in eccentric orbits, which occurs commonly in multiple-star systems, 4) a simple treatment of tidal, common-envelope, and mass transfer evolution in which the accretor is a binary instead of a single star, 5) taking into account planets within the stellar system, and 6) including gravitational perturbations from passing field stars. The code is written primarily in the C++ language and has few prerequisites; a convenient Python interface is provided. A detailed description of MSE is given in Hamers et al., (2021; url).  

New paper "A Statistical View of the Stable and Unstable Roche Lobe Overflow of a Tertiary Star onto the Inner Binary in Triple Systems"
March 14 2022
In compact stellar triple systems, an evolved tertiary star can overflow its Roche lobe around the inner binary. Subsequently, the tertiary star can transfer mass to the inner binary in a stable manner, or Roche lobe overflow (RLOF) can be unstable and lead to common-envelope (CE) evolution. In the latter case, the inner binary enters the extended envelope of the tertiary star and spirals in toward the donor's core, potentially leading to mergers or ejections. Although studied in detail for individual systems, a comprehensive statistical view on the various outcomes of triple RLOF is lacking. In this ApJS paper, we carry out 1e5 population synthesis simulations of tight triples, self-consistently taking into account stellar evolution, binary interactions, and gravitational dynamics. Also included are prescriptions for the long-term evolution of stable triple mass transfer, and triple CE evolution. Although simple and ignoring hydrodynamic effects, these prescriptions allow for a qualitative statistical study. We find that triple RLOF occurs in ~0.06% of all triple systems. Of these 0.06%, ~64% of cases lead to stable mass transfer, and ~36% to triple CE evolution. Triple CE is most often (~76%) followed by one or multiple mergers in short succession, most likely an inner binary merger of two main-sequence stars. Other outcomes of triple CE are a binary+single system (~23%, most of which do not involve exchange interactions), and a stable triple (~1%). We also estimate the rate of type Ia supernovae involving white dwarf mergers following triple RLOF, but find only a negligible contribution.
New paper "How Important Is Secular Evolution for Black Hole and Neutron Star Mergers in 2+2 and 3+1 Quadruple-star Systems?"
March 1 2022
Mergers of black holes (BHs) and neutron stars (NSs) result in the emission of gravitational waves that can be detected by LIGO. In this paper (Vynatheya & Hamers 2022), we look at 2+2 and 3+1 quadruple-star systems, which are common among massive stars, the progenitors of BHs and NSs. We carry out a detailed population synthesis of quadruple systems using the Multiple Stellar Evolution code, which seamlessly takes into consideration stellar evolution, binary and tertiary interactions, N-body dynamics, and secular evolution. We find that, although secular evolution plays a role in compact object (BH and NS) mergers, (70-85)% (depending on the model assumptions) of the mergers are solely due to common envelope evolution. Significant eccentricities in the LIGO band (higher than 0.01) are only obtained with zero supernova (SN) kicks and are directly linked to the role of secular evolution. A similar outlier effect is seen in the χ eff distribution, with negative values obtained only with zero SN kicks. When kicks are taken into account, there are no systems that evolve into a quadruple consisting of four compact objects. For our fiducial model, we estimate the merger rates (in units of Gpc-3 yr-1) in 2+2 quadruples (3+1 quadruples) to be 10.8 ± 0.9 (2.9 ± 0.5), 5.7 ± 0.6 (1.4 ± 0.4), and 0.6 ± 0.2 (0.7 ± 0.3) for BH-BH, BH-NS, and NS-NS mergers, respectively. The BH-BH merger rates represent a significant fraction of the current LIGO rates, whereas the other merger rates fall short of LIGO estimates.
New paper "Return of the TEDI: Revisiting the Triple Evolution Dynamical Instability Channel in Triple Stars"
February 9 2022
Triple-star systems exhibit a phenomenon known as triple evolution dynamical instability (TEDI), in which mass loss in evolving triples triggers short-term dynamical instabilities, potentially leading to collisions of stars, exchanges, and ejections. Previous work has shown that the TEDI is an important pathway to head-on stellar collisions in the Galaxy, significantly exceeding the rate of collisions due to random encounters in globular clusters. In this ApJ paper, we revisit the TEDI evolutionary pathway using state-of-the-art population synthesis methods that self-consistently take into account stellar evolution and binary interactions as well as gravitational dynamics and perturbations from passing stars in the field. We find Galactic TEDI-induced collision rates on the order of 1e-4/yr, consistent with previous studies which were based on more simplified methods. The majority of TEDI-induced collisions involve main-sequence stars, potentially producing blue straggler stars. Collisions involving more evolved stars are also possible, potentially producing eccentric post-common-envelope systems, and white dwarfs collisions leading to Type Ia supernovae (although the latter with a negligible contribution to the Galactic rate). In our simulations, the TEDI is not only triggered by adiabatic wind mass loss, but also by Roche lobe overflow in the inner binary: when the donor star becomes less massive than the accretor, the inner binary orbit widens, triggering triple dynamical instability. We find that collision rates are increased by ~17% when flybys in the field are taken into account. In addition to collisions, we find that the TEDI produces ~1e-4/yr of unbound stars, although none with escape speeds in excess of 1e3 km/s.
New Research Note on the peak GW frequency emitted by an eccentric binary
December 2 2021
This Research Note of the AAS (link) presents a numerical fit to the peak harmonic gravitational wave (GW) frequency emitted by an eccentric binary system in the post-Newtonian approximation. This fit significantly improves upon a previous commonly-used fit, in particular for eccentricities ~< 0.8, with potentially important implications for some previous predictions of eccentric GW sources in both the LIGO and LISA detector bands. The new fit should be useful for future studies of eccentric sources which are motivated by the anticipation of the detection of eccentric sources in future GW observations.
Visitors from NBIA and mini-workshop
November 11 2021
The Multiple-Star Evolution Group at MPA was happy to receive a group of visitors from the Niels Bohr International Academy (NBIA) consisting of Johan Samsing, Dan D'Orazio, Bin Liu, and Alejandro Vigna-Gómez during the week of November 8. On the occasion of their visit and in collaboration with MPA Director Selma de Mink, a successful mini-workshop on Gravitational Wave Astrophysics was held at MPA on November 9. See here for a few photographs.
New paper on first and second generation BH and NS mergers from 2+2 quadruples
July 26 2021
In Hamers et al. (2021; url), we study black hole (BH) and neutron star (NS) mergers from stellar quadruple system in the 2+2 configuration (two binaries orbiting each other's centre of mass). In such systems, secular evolution can accelerate the merger of one of the inner binaries; subsequently, the merger remnant may interact with the companion binary, yielding a second-generation merger. We model the initial stellar and binary evolution of the inner binaries as isolated systems. In the case of successful compact object formation, we subsequently follow the secular dynamical evolution of the quadruple system. When a merger occurs, we take into account merger recoil, and model subsequent evolution using direct N-body integration. With different assumptions on the initial properties, we find that the majority of first-generation mergers are not much affected by secular evolution, with their observational properties mostly consistent with isolated binaries. A small subset shows imprints of secular evolution through residual eccentricity in the LIGO band, and retrograde spin-orbit orientations. Second-generation mergers are ~1e7 times less common than first-generation mergers, and can be strongly affected by scattering (i.e., three-body interactions) induced by the first-generation merger. In particular, scattering can account for mergers within the low-end mass gap, although not the high-end mass gap. Also, in a few cases, scattering could explain highly eccentric LIGO sources and negative effective spin parameters. In this work, gravitational dynamics and stellar/binary evolution were treated as decoupled effects, and this assumption can break down depending on the system parameters. This will be addressed in future work.
New group member
July 1 2021
The group welcomes a new PhD student, Abinaya Swaruba Rajamuthukumar, who previously completed her Masters in physics at Christ University Bangalore, India. She will be working on white dwarf interactions in multiple-star systems.
Multiple Stellar Evolution (MSE): code paper and semi-public release
January 29 2021

The group announces the semi-public release of the Multiple Stellar Evolution (MSE) code. MSE is designed to rapidly model the stellar, binary, and dynamical evolution of multiple-star systems. It includes a number of new features not present in previous population synthesis codes: 1) an arbitrary number of stars, as long as the initial system is hierarchical, 2) dynamic switching between secular and direct N-body integration for efficient computation of the gravitational dynamics, 3) treatment of mass transfer in eccentric orbits, which occurs commonly in multiple-star systems, 4) a simple treatment of tidal, common-envelope, and mass transfer evolution in which the accretor is a binary instead of a single star, 5) taking into account planets within the stellar system, and 6) including gravitational perturbations from passing field stars. The code is written primarily in the C++ language and has few prerequisites; a convenient Python interface is provided. A detailed description of MSE is given in Hamers et al., (2021; url). For access to the GitHub repository (currently private), please contact A. Hamers. The code will be made publicly available in the future. 

New paper on von Zeipel-Lidov-Kozai oscillations in triple systems
November 9 2020

In Hamers (2020; url), we consider von Zeipel-Lidov-Kozai oscillations in triple systems, and focus on the case when the angular momentum in the inner orbit is not negligible compared to that of the outer orbit (as opposed to the "test particle" approximation). This case applies for example to systems with comparable masses such as stellar triples. We characterise the nature of the oscillations as a function of γ, a ratio of inner-to-outer orbital angular momenta variables. In particular, eccentricity oscillations are more effective at retrograde orientations for non-zero γ; assuming zero initial inner eccentricity, the maximum eccentricity peaks at cos(irel,0) = −γ, where irel,0 is the initial relative inclination. We provide a Python script which can be used to quickly compute these properties. 

Educational book Moving Planets Around released
September 1 2020

The educational book Moving Planets Around by J. Roa, A.S. Hamers, M.X. Cai, and N.W.C. Leigh (link at The MIT Press), offers both an introduction to the laws of celestial mechanics and a step-by-step guide to developing software for direct use in astrophysics research. The text is written engagingly in dialogue form. It not only educates students on the laws of Newtonian gravity, it also provides all that they need to start writing their own software, from scratch, for simulating the dynamical evolution of planets and exoplanets, stars, or other heavenly bodies. The first half of the book develops a fully functional N-body integrator, using state-of-the art integration techniques. The second half of the book focuses on using an advanced integration scheme to conduct real research, leading students in an investigation of the long-term dynamical stability of extrasolar circumbinary planets. At the end of the journey, students will be ready to design, conduct, and publish peer-review quality research. In addition to the physical copy, the book is available online as Open Access (link).  

New group member
September 1 2020

The group welcomes PhD student Pavan Vynatheya, who recently obtained his MSc degree at the Indian Institute of Science Education and Research in Kolkata, India. Pavan will be working on making predictions for gravitational wave sources in multiple-star systems such as triple and quadruple systems, using population synthesis methods. 

New group member
July 8 2020

The group welcomes Holly Preece, who recently obtained her PhD at the University of Cambridge and Armagh Observatory and Planetarium under supervision of Christopher Tout and Simon Jeffery. Holly is an expert on tidal interactions in binary systems.  

New paper on a quadruple origin of GW190412
June 18 2020

In Hamers & Safarzadeh (2020; url), we investigate whether the gravitational wave source GW190412, consisting of two black holes with unusually unequal masses (mass ratio 0.28), could have formed from a "double merger" event in a hierarchical 3+1 quadruple system. In this scenario, the innermost binary merges first due to secular chaotic evolution. In the resulting triple, secular Lidov-Kozai evolution could subsequently lead to a second merger. We show that this scenario produces characteristics that are consistent with GW190412, although its likelihood is highly uncertain due to influences from stellar and binary evolution that were ignored here. 

New paper on MS interactions in systems of the Multiple Star Catalogue
April 22 2020

In Hamers (2020; url), we study the long-term dynamical main-sequence (MS) evolution of hierarchical systems with 3 to 6 stars based on Andrei Tokovinin's Multiple Star Catalogue. We estimate statistical probabilities for strong interactions during the MS such as tidal evolution and mass transfer, and the onset of dynamical instability. Our results indicate that a significant fraction of high-multiplicity systems interact or become dynamically unstable already during the MS, with an increasing importance as the number of stars increases. 

New paper on suborbital effects in multiple systems
April 20 2020

In Hamers (2020; url), we present an update to the SecularMultiple code, which integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested binaries. In the update, we incorporate hybrid integration techniques, allowing orbits to be either directly integrated (N-body method), or averaged over (secular method). We also implement orbit-averaging correction terms. The updated code is freely available on GitHub 

New paper on binary-binary scattering
March 9 2020

In Hamers & Samsing (2020; url), we study the gravitational effects of scattering of two binaries in the "weak" limit, i.e., in which the two binaries approach each other at a relatively large distance. We find that, to good approximation, one can use previous analytic results for binary-single scattering in the weak limit, and replace the mass of the single interloping body with the total mass of the interloping binary. In other words, the point mass approximation works well for weak binary-binary scattering. 

New group member
March 1 2020

The group welcomes Patrick Neunteufel, previously a postdoc a the University of Leicester, and who completed his PhD with Norbert Langer at the Argelander Institute in Bonn in 2017. Patrick is an expert on binary star evolution. 

New web site launched
October 23 2019

A new web site has been launched for the group. Please note that it is still under construction.