3. Results and conclusions
We first recall that a detailed comparison of the O-type and WR sample within 3 kpc from the sun reveals a most probable population model (Paper I). This model assumes an overall MCB fraction (binaries with periods up to 10 years) 0.8, a non-conservative case Br evolution where on the average 50% of the mass lost by a primary should leave the binary, taking with it a significant fraction of the angular momentum of the system () and a flat (q) or a (q) which peaks moderately towards 1. For single stars, the alternative evolutionary scenario of Vanbeveren (1991, 1995, 1996) gives the best correspondence with observations.
3.1. The number of O-type runaways formed through binary evolution
MCBs are a fact, SN explosions in MCBs are a fact and thus runaways formed through the binary scenario are a fact. Table 1 gives the theoretically expected number of post-SN O-type stars for different values of the parameters in our population synthesis model as well as the expected number of O-type runaways (runaway velocity 30 ). We always give the numbers relative to the total number of O-type stars (= the number of single O-type stars + the number of unevolved pre-RLOF O-type primaries of MCBs + the number of O type stars with a post-RLOF CHeB companion + the number of post-SN O-type stars, singles and with a CC).
Table 1. The fraction, relative to all O-type stars, of O+CC binaries, O+CC runaways, O-type stars resulting from binary evolution which are single because the binary was disrupted during the previous SN explosion (Osb) and Osb runaways. Different values are considered for the parameters entering the population model (see text).
Only 16-23% of the MCBs remain bound after the SN explosion of the primary.
Between 5% and 25% of the O-type stars are post-SN binary components. The majority is single, however remember that they have had a binary history.
Only 3% (and even less) of all O-type stars are expected to have a CC.
About 5-8% of the O-type stars are runaways with a runaway velocity 30 . Less than of them have a CC.
Accounting for the observed number of O-type runaways and their observed binary frequency, we conclude that the SN explosion in MCBs is responsible for at least 50% of the observed fraction of O-type runaways.
3.2. The number of WR stars with a compact companion
In order to have an idea of the morphology of post-SN WR stars (i.e. WR + CC binaries or 'weird' WR single stars), we start from the observed WR + OB binaries, listed by Smith and Maeder (1989), and continue their evolution with the MCB model discussed in section 2. We first assume that the WR star is at the beginning of its WR phase (i.e. at the beginning of the WNL phase, resp. the WNE phase, resp. the WC phase, when the WR component is a WNL, resp. WNE, resp. WC). Then we assume that the WR star is at the end of its corresponding phase. For each binary we compute the SN survival probability, accounting for the kick velocity distribution discussed earlier. When an OB+CC binary is formed, its further evolution is continued through the spiral-in phase for two values of the efficiency parameter (i.e. = 1 and = 0.5). When the binary does not merge due to spiral-in, a CHeB+CC binary is formed. When the mass of the CHeB component is larger than 5 , the star is considered as a WR star and thus a WR+CC binary is formed. The results are given in table 2. For each system we give the survival probability after the SN explosion of the WR star, the probability that a WR+CC binary is formed and the probability that a 'weird' WR star is formed. For each WR+OB system the minimum and maximum period, and , of the possible CHeB+CC binary after spiral-in and the minimum and maximum runaway velocity, and , of the post-SN system are given. The latter values always correspond to values holding for the bound case. A disrupted OB-type star (thus a disrupted CHeB star) has a runaway velocity in between the minimum and maximum values given in the table.
Table 2. The further evolution of observed WR+OB binaries for an efficiency factor = 1/ = 0.5 during spiral-in.
The majority ( 75 %) of the observed WR + OB binaries will be disrupted as a consequence of the SN explosion of the WR star. The majority of the OB stars of these disrupted binaries will evolve into WR stars, i.e. single WR stars but with a binary history where accretion could have played a major role.
Less than 2% ( = 0.5) and 5% ( = 1) of the observed WR+OB systems will form WR+CC binaries. The periods of these WR+CC binaries range between 0.05-1.3 days ( = 0.5) and 0.05-3.6 days ( = 1).
About 20-30% of the observed WR+OB binaries will produce 'weird' WR stars.
We now start from a sample of unevolved MCBs and single stars satisfying the distributions discussed in section 2. Table 3 gives the number population synthesis results for the WR stars for various values of the parameters in our population model. The following conclusions are based on the numerical results holding for a non-conservative case Br evolutionary model, as suggested at the beginning of this section.
Table 3. Similar as table 1 but for WR stars. We assume that OB+CC mergers loose all their hydrogen rich layers during the merging process and thus a WR star is formed immediately after merging. For a few cases we also made computations with the alternative model i.e the mergers further evolve as single stars.
The expected frequency (relative to all WR stars) of WR+CC binaries is 2.5% ( = 1) and 1% ( = 0.5), with most of them having periods of the order of hours.
About 10%-18% of all WR stars could be 'weird' WR stars, descendants from Thorne- ytkow objects.
About 10-15% of all WR stars are single but with a binary history.
Within 3 kpc from the sun there are 100 WR stars. Accounting for the foregoing conclusions, we predict more than 10 'weird' WR stars, 10-15 single WR stars but with a binary history. We also expect at most 1-3 WR stars with a compact companion orbiting with a period of a few hours.
3.3. The formation of binary pulsars
Similarly as in the previous section we start with a population model and we determine all CHeB+CC binaries. When the mass of the CHeB component is large enough, a second SN explosion occurs. The effect on the binary parameters is again studied using the kick velocity distribution given by Eq. 1. In table 4 we give the formation rate of binary pulsars (neutron star/black hole + neutron star/black hole) for different values of the population model. We conclude (again we only consider the non-conservative case Br models):
Table 4. The number of binary pulsars formed per year assuming a massive star formation rate of 1/year. Different values are considered for the parameters entering the population model.
The formation rate of binary pulsars is about 0.003-0.01 times the formation rate of massive stars.
There are about 5000 massive stars within 3 kpc from the Sun (Humphreys and McElroy, 1984). If we assume that this number is representative for our whole galactic disk and that the galactic disk radius is approximately 13 kpc, we expect about 100000 massive stars in the Galaxy. The average lifetime of a massive star is 24 million years and this gives us a galactic massive star formation rate of 4.2 10-3 /year. We thus obtain a galactic binary pulsar formation rate ranging from 1.3 10-5 to 4.2 10-5 /year. Accounting for the crudeness of this estimate we consider this as a very good agreement with the value which is of the order of 10-5 /year (see section 1) and which is derived from the observed number of binary pulsars in the Galaxy and their expected lifetime.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998