Evolution of binary stars on the HR diagram

We studied the evolution of different classes of binary objects that can be observed in a typical stellar cluster, using a grid of detailed massive binary evolution models (Wang et al. 2020) with an initial metallicity of that of the Small Magellanic Cloud (SMC). To compute the models, we use the 1D stellar evolution code MESA (Modules for Experiments in Stellar Astrophysics, Paxton et al. 2011, 2013, 2015, 2018, version 8845).

Our grid consists of 2078 binary models with initial primary masses greater than 5 MSun. This translates to a total cluster mass of ∼10^5 MSun in stars between 0.1 to 100 MSun (assuming a binary fraction of 1. The grid covers an initial mass ratio (mass of secondary over the mass of primary, hence always less than 1) range of 0.3-0.95 and orbital periods of 1 day to 8.6 yrs. In this range of masses, mass ratios, and orbital periods, a Monte Carlo method was used to sample initial binary model parameters assuming a Saltpeter initial mass function (IMF) (Salpeter 1955), a flat distribution of mass ratios and logarithm of initial orbital periods.

Translucent grey circles indicate pre-interaction binaries - binaries that have not yet undergone a mass transfer phase via Roche Lobe overflow. Hence, the grey line traced on the HRD by the collection of pre-interaction binaries together essentially denotes the Single Star Isochrone (SSI). Grey squares indicate the merger product when we expect a binary to merge during the Case A mass transfer phase. We note that we only model and follow the evolution of Main Sequence mergers and not the mergers coming from the Case B channel. As such, the number of mergers in each frame is likely to be the lower limit to the number of merger products. Single star tracks at SMC metallicity are also plotted in the background from 5-100 MSun. When any component of a binary system completes core carbon burning at a certain cluster age (or helium-burning for the most massive stars), we mark the occurrence of a supernova by putting an ‘*’ symbol in the HRD, that fades over three time steps in the animation.

Mass donors and accretors are shown with triangles and diamonds respectively. The binaries that are interacting or have interacted during their Main Sequence lifetime (i.e. the Case A models) are shown in colour, with the colour coding describing the rotation of the component stars (v rot /v crit ) of the binary. All donors and accretors of binaries that have interacted via Case B/C are shown in greyscale. A black frame around the triangles for the mass donor indicates that the surface Hydrogen mass fraction is less than 0.1. Similarly, a black frame around the diamonds for the mass accretors indicates that the surface Helium mass fraction is greater than 0.3. The current age of the cluster is displayed in the center bottom with a time bar that fills up as the animation moves forward in time.

In the table above the legend, (from top) we indicate the number of Algol systems i.e. in the nuclear timescale slow Case A mass transfer phase, the number of Main Sequence merger products that are still burning hydrogen at the core, and the number of cool red supergiants (log T e f f < 3.7) at the respective time frames. Moreover, in the next two rows, we denote the number of OB stars that has a neutron star or black hole companion, arising from Case A and Case B evolution channels, at that cluster age. In the next row, we indicate the number of supernovae that have already happened until the current cluster age of the animation. We report the numbers of supernovae occurring from Case A and Case B donors separately from the other progenitors as we expect that the donor stars that have interacted via the Case A or Case B channels will be highly stripped of their envelopes and will likely be progenitors to stripped-envelope supernova (of type Ib and IIb) while the remaining will be progenitors to type IIp/n. The last line gives the number of pre-interacting binaries having luminosity lesser than the brightest non-interacted binary component by up to 1.5 dex.

The individual components of the binaries that are in the semi-detached configuration and are interacting via the nuclear timescale slow Case A phase are joined together with solid black lines with an arrow indicating the direction of mass transfer (donor to the accretor). On the other hand, the individual components that have interacted in the past via Case A or B mass transfer are connected to each other with grey dotted lines. These are usually the systems where the donor star is a post-Main Sequence helium star and the accretor is a rejuvenated star still burning hydrogen at the core. The black and white dots over the Case A and B accretors denote that the donors of those binaries have imploded/exploded to form a black hole or neutron star respectively.