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Astron. Astrophys. 328, 130-142 (1997)

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6. Conclusions

The models discussed in this paper are very crude in their treatment of the encounter processes, of the result of a collision between two stars, and of the evolution of the merger products. Apart from these approximations and the fact that we use a stellar evolution model for population I instead of pop. II stars, the adopted mass function is also highly uncertain. Nonetheless, some interesting results can be delineated.

Comparison with the calculations of Davies & Benz (1995) shows the effect of allowing the merger products to evolve. An immediate consequence of this is the lower prediction for the number of blue and yellow stragglers present in the cluster (as is clear from Fig. 6). The formation rates of blue and yellow stragglers give a poor indication for the actual number of stragglers present in the cluster at a particular instant.

Due to the low density of model S the collision frequency is small. The steep Salpeter mass function also suppresses the encounter rate and the production of stellar curiosities; the majority of the collisions involve two rather low mass main-sequence stars which results in a merger that evolves too slow to produce a blue straggler within the time span of the simulation.

The Hertzsprung-Russell diagram of our model cluster (model C) shows that blue stragglers close to the turn-off point lie on the main sequence, whereas blue stragglers above the turnoff point are mostly found at some distance from the main sequence. The reason for this is that collisions only become important in the cluster when an initial period of low density is followed by the contraction of the cluster core. The more massive blue stragglers are formed in collisions between stars close to the terminal-age main sequence, and evolve relatively quickly. Blue stragglers close to the turn-off are formed in collisions between relatively low-mass stars which did not evolve very far away from the zero-age main sequence, and therefore also the merger products are close to the zero-age main sequence, and evolve slowly. Thus, the point where blue stragglers have left the main sequence gives an indication of the time when collisions in the cluster became frequent (see also Portegies Zwart 1996).

Our model C predicts a depletion of giants, in the core only, up to [FORMULA] shortly after [FORMULA] relative to a collision-less stellar system, in globular clusters with a collapsed core where the fraction of horizontal-branch stars is enhanced. Consequently the depletion of giants relative to the number of horizontal branch stars is strongly present in the high-density stellar system. Collisions between single stars cannot explain the observation that giants can be depleted well outside the core or completely absent in it, as observed in the core of M 15 (Djorgovski et al. 1991).

In our simulated cluster cores the total number of white dwarfs that exceed the Chandrasekhar limit due to accretion from a circum-stellar disc is small, even in the cluster simulation with the highest density. In model C 8% of the white dwarfs experience an accretion-induced collapse, which (after correction for the ratio [FORMULA] between the number of stars in the model and in an actual core - see Table 2) corresponds to 190 supernovae of type Ia during the 6 Gyr of our calculation. If all of these collapses would lead to the formation of a neutron star, and if all of these would remain in the core, this would be a substantial addition to the total number of neutron stars in the core, which is about 460 (after correction for [FORMULA]) at the start of our calculation. This result, however, strongly depends on the adopted mass function for the white dwarfs. The formation-rate of neutron stars with an accretion disc and the subsequent formation of a recycled pulsar or black hole is (to first order) linearly dependent on the number of neutron stars, which depends not only on the initial mass function but also on the subsequent mass segregation in the cluster.


Table 2. Parameters of the different model computations, and corresponding characteristics. Subsequent columns give the name of the model, indication whether a Salpeter mass function or a mass function that is affected by mass segregation is used, core radius, 3-dimensional velocity dispersion [FORMULA] time at which encounters are started, the age of the population at the start of the dynamical interactions, the central stellar number-density in the core, the ratio of the number of stars in the computation to the actual number of stars in the core, the number of encounters during the calculation per star, and the average time between two encounters, anywhere in the core.

The encounter rates between neutron stars and main-sequence stars are similar in our calculations to the rates found in the calculations by Verbunt & Meylan (1988), by Di Stefano & Rappaport (1992) and by Davies & Benz (1995). After a collision between a neutron star and another cluster member the merged object becomes visible as an X-ray source (for at most 1 Gyr) after which it becomes a recycled pulsar or, if its mass exceeds 2  [FORMULA], a black hole. The total number of such X-ray sources, recycled pulsars or black holes scales linearly, in first order, with the number of neutron stars in the cluster core, which is rather uncertain.

Our computations reveal that collisions between single stars result in a small number of recycled pulsars: about 70 are formed in a core (after correction for [FORMULA]) according to model C. Whether this is enough to explain the observed numbers is not clear. The intrinsic luminosity distribution of millisecond pulsars, and hence the fraction of them that is detectable in a typical cluster, is not known; and some clusters with high encounter rates show remarkably few recycled pulsars, the globular cluster NGC 6342 is an example (see Lyne 1993).

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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998