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

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4. A dynamically evolving salpeter mass function

A total of two models are computed, one with a Salpeter type mass function which we call model S (from Salpeter), and one model which we call model C (from Collapsed) with a mass function that is affected strongly by mass segregation.

In the volume of the stellar system in model S, we sprinkle stars according to a Salpeter mass distribution between 0.1 [FORMULA] and 100 [FORMULA]. The total number of stars is irrelevant, since we are considering these stars to be contained in a laboratory-type enclosure, with a thermal distribution of stellar velocities. Our choice for the `temperature' of this distribution is fixed by requiring that stars with a mass [FORMULA] will have a one-dimensional velocity dispersion of 10.0 km/s, in conformity with the same choice made in Sect. 5. The radius of the core was chosen to be [FORMULA]  pc and the computation is started at [FORMULA] and terminated at an age of 16 Gyr. For the computation of the encounter rate a total of 30 bins in mass, equally spaced in the logarithm of the mass between 0.1 and 100 [FORMULA], and 30 bins in radius, equally spaced in the logarithm of radius between 0.1 and 2000 [FORMULA] are used. An additional bin with zero radius is used for the compact stars, i.e. the white dwarfs, neutron stars and black holes.

Fig. 1 shows for model computation S, the relative probabilities of encounters with various types of stars for a [FORMULA] star, at an age of the cluster of 12 Gyr. Due to the small encounter frequency hardly any collision products are present in the stellar system. Only a small number of blue stragglers (stars with a mass larger than the turnoff and with similar radii) have finite probability to be involved in an encounter. The most probable partners for an encounter with a [FORMULA] star are the stars at the low end of the main sequence.

[FIGURE] Fig. 1. Relative encounter probabilities in model calculation S, at time [FORMULA] Gyr, when the turnoff mass is [FORMULA], for a single star with [FORMULA] and [FORMULA] as a function of mass and radius of the other star involved in the encounter. Darker shades indicate higher probabilities. The compact stars (nominally with zero radius) are shown as a bar below 0.1 [FORMULA]: neutron stars between 1.34 and 2 [FORMULA] and white dwarfs at lower masses. All other stars with radius in excess of the radius at the turnoff are the evolved stars. The masses of these stars is similar to the turnoff mass. A small fraction of blue stragglers is visible as an extension of the main-sequence (to the right of the turnoff). The vertical bar in the upper left corner presents a scaling to the gray shades. The lowest square corresponds to an encounter rate of once every 12.7 Tyr decreasing with a factor of two for each subsequent square. The integrated encounter frequency of the [FORMULA] star is 1 encounter every 1.68 Tyr. Almost 13% of the encounters occur with a main-sequence star with a mass of about [FORMULA] (black squares below and to the left).

In Fig. 2 we show the relative frequencies of encounters of different types, and of the resulting collision products for model S. Because the steep mass function the collisions rate is dominated by main-sequence stars; the fraction of collisions involving giants is only small. The most frequent type of encounter is one involving two main-sequence stars, leading to a main-sequence merger remnant with a mass smaller than the turnoff mass or a blue straggler when the mass of the merger exceeds the turnoff mass. If the mass of the merger is less than the turnoff mass, the product is a main-sequence star which is younger than primordial main-sequence stars with the same mass. Such a star will be left behind as a blue straggler once the primordial main-sequence stars leave the main-sequence. Yellow stragglers, i.e. giants not on the main (sub)giant branch of the cluster (which approximately coincides with the evolutionary track of a star with the turn off mass), can be formed directly from encounters between a main-sequence star and a giant, between a main-sequence star and a white dwarf and between a giant and a white dwarf, in decreasing order of importance; encounters between two giants are extremely rare. Our prescriptions put every merger product on the evolutionary track of an ordinary star; the presence of yellow stragglers in our calculations is therefore only due to the formation of giants with a mass larger than about the turnoff mass.

[FIGURE] Fig. 2. Relative frequencies of various types of encounters (upper panel, the curly brackets indicate the collision) and their outcomes (lower panel), for model computation S, integrated over the duration of the calculation. Abbreviations: ms main-sequence star, gs giant, wd white dwarf, ns neutron star, Bss blue straggler, Yss yellow straggler.
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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998