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Astron. Astrophys. 327, 930-946 (1997)

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3. Evolution of the simulations

We show in Fig. 1 the time evolution of run V. A central galaxy is quickly formed beginning with the galaxies initially near the center of the group. Later this galaxy grows from the rest of the members of the cluster, often literally swallowing up an entire companion, as suggested in the galactic cannibalism picture (Ostriker & Hausman 1977). Galaxies also lose material due to tidal forces. This mass is accreted to the center of the potential well which is occupied by the central giant galaxy. The evolution of the other simulations is similar to that of run V in the sense that a central galaxy is quickly formed, growing, however, at different rates in the different simulations. The sole exception is run Vh, where no central object is formed.

[FIGURE] Fig. 1. Time evolution of Run V. Note the rapid formation of the central dominant galaxy from the initial seed of galaxies and the creation of a uniformly distributed background from the material stripped from the satellite galaxies by the tidal forces of the cluster.

In Fig. 2 we plot the mean distance of the galaxies from the center of the cluster, [FORMULA], as a function of time for all our simulations. The central galaxy is not taken into account in this average, and we also do not introduce a weighting by mass. The size of the group diminishes steadily in all the collapsing systems but at different rates. Runs C1 and C2, which are two different realisations of the same initial global conditions, evolve at similar rates until the time of maximum collapse is reached at [FORMULA] Gyr.

[FIGURE] Fig. 2. Time evolution of the mean radius of the group of surviving galaxies for each of our simulations. In the top panel we show the evolution of this parameter for the collapsing clusters and in the lower panel the evolution for the initially virialised clusters. Symbols for collapsing groups: run C1 filled triangles, run C2 filled squares, run Cp diamonds, run Co stars. Virialised groups: run Vh filled stars, run V triangles, run Vc1 circles, run Vc2 swiss crosses.

After this time both systems suffer the same small expansion. The similarity between the results of runs C1 and C2 indicate that the statistical fluctuations in the initial conditions have a small influence on the later evolution of the group. This same conclusion can also be reached by comparing runs Vc1 and Vc2, for which the differences are even smaller. The system of run Co is maximally collapsed at a slightly earlier time. Because its extension along the X axis is smaller than that of the spherical symmetric systems by a factor of 2, it starts out smaller and denser, and hence it collapses faster. In the case of run Cp on the other hand, the extension along the X axis is greater than that of the spherically symmetric systems by a factor of 2, so the system is less dense and the collapse rate is slower. For all virialised groups, except for run Vh, the mean radius of the group increases steadily. As there are no single galaxies left in the central parts the mean radius of the distribution gets bigger. Moreover, a few galaxies acquire enough speed to reach large distances from the system. These factors increase the mean radius of the system. This is not the case for run Vh, where no central dominant galaxy is formed, and for which the mean radius of the cluster stays roughly constant.

Fig. 3 shows that the total number of galaxies diminishes steadily as a function of time, but at different rates for each simulation. Again runs C1 and C2, as well as runs Vc1 and Vc2, behave in a very similar way. For run Cp, initially a bigger prolate system, galaxies need longer times to reach the center and so the number of mergings is lower. On the other hand the number of mergings for run Co is similar to the number of mergings in the spherically collapsing systems, i.e. those of runs C1 and C2. This result is unexpected and we have no clear explanation to offer. For the virialised groups the two extreme cases correspond to run Vh, where only seven galaxies disappear, and runs Vc1 and Vc2, where this number decreases very rapidly at the start and levels off towards the end of the simulation. The difference between run V on the one hand and runs Vc1 and Vc2 on the other is due to the fact that the galaxies in runs Vc1 and Vc2 are closer together, an effect which seems to be stronger than the relatively larger relative velocities between galaxies. Note also the strong difference between run V and run Vh, which are simulations with similar global properties, except for the fact that the latter simulation has no galaxies in its central regions. This shows that the presence of an initial central seed of galaxies initiates the merging instabilities and the formation of the central object via mergings. A central giant galaxy is formed in only three of our four cases with similar virialised initial conditions. For the case of Run Vh the seven galaxies that have disappeared by the end of the simulation are not in a central object. A background is formed by diffuse material that has been stripped from the galaxies, while some galaxies merge in the external parts. On the contrary in run V, where all the evolution of the system is driven by the central object, no mergings between satellite galaxies occur.

[FIGURE] Fig. 3. Time evolution of the number of surviving galaxies in the group for each of our simulations. Panels are as in Fig. 2. Note the rapid decrease of this number for runs Vc1 and Vc2. Symbols as in Fig. 2.

In Fig. 4 we show the time evolution of the mass of the central object. This mass grows steadily in all simulations. For the collapsing systems the central object grows rapidly, at a rate which is in most cases roughly constant with time. Furthermore, the mean rate is higher than that of the virialised groups of the same initial size (runs V and Vh). For the virialised systems Vc1 and Vc2 the rate of the evolution is very rapid at the start of the simulations, due to their small initial radius. Galaxies last longer in the virialised groups of run Vh and run V. Actually in run Vh there is no central object and the mass quoted in this figure corresponds to a distributed background. In run V secondary galaxies also lose material via tidal stripping, but there is a central object growing by accretion of this material and by merging of some satellite galaxies. Differences in the realisations of the initial conditions affect somewhat the result for the collapsing simulations C1 and C2, but hardly so for the virialised ones Vc1 and Vc2.

[FIGURE] Fig. 4. Time evolution of the mass of the central object. This mass always increases steadily with time, except for Run Vh, where no central galaxy is formed and the mass quoted corresponds to the mass of the distributed background. Symbols as in Fig. 2.

In order to differentiate between growth of the central galaxy by mergings and growth by accretion of material from other galaxies and to measure the amount of stripping in each simulation, we plot in Fig. 5 the time evolution of the parameter [FORMULA] defined as:

[FIGURE] Fig. 5. Time evolution of the parameter [FORMULA], defined in the text, which measures the degree of evolution in the surviving galaxies. Positive values of this parameter indicate that the galaxies are suffering stripping of their outer parts, while negative values indicate that some merging between the secondary galaxies is taking place. Symbols as in Fig. 2.

[EQUATION]

where [FORMULA] is the mass in galaxies excluding the central object, [FORMULA] is the mass that this same number of galaxies should have if there were no stripping or merging between them (i.e. the mass of the same number of galaxies in the beginning of the simulation) and [FORMULA] is the mass of the central object. If there are some mergings between the secondary galaxies then [FORMULA] will be greater than [FORMULA] and this parameter will take on negative values. If the dominant effect is the stripping by the tidal potential of the group and merging only takes place between the secondary galaxies and the central object, [FORMULA] will take positive values. The greater the value of this parameter, the greater the amount of mass loss by stripping in the secondary galaxies. Fig. 5 shows that the evolution of [FORMULA] depends strongly on the initial conditions of the system and, for the case of the collapsing simulations, even on the realisation of the initial conditions. In some collapsing groups some mergings between secondary galaxies take place, and these dominate the evolution of the group until there is a big central object formed in the center. Thereafter we only find mergings with this giant galaxy and stripping of the secondary galaxies. In the virialised systems there is no merging between the secondary galaxies. These spiral to the center, losing some material, and finally merge with the central object. We may also note that the effect of stripping is more pronounced in run V, which is the extended virialised system. The core radius of the galaxies, defined as the radius containing [FORMULA] of the most bound particles, remains nearly constant during the simulation, with variations of less than [FORMULA]. The velocity dispersion of this set of particles, which can be taken as a measure of the central velocity dispersion of the galaxy, suffers a small decrease ([FORMULA]).

In Fig. 6 we plot the time evolution of the total mass of the central galaxy and the mass increase due to stripping from the secondary galaxies. The difference between the two gives the contribution from merging of the secondary galaxies with the central object. In order to obtain smoother curves, which are necessary particularly for the derivatives discussed in the next paragraph, we have used 5-point sliding means of the data. As can be seen, merging is the dominant process for most collapsing cases, while for the extended virialised system (run V) the contribution from stripping is dominant. It is interesting to note the difference between the evolutions of the central object in runs C1 and C2, which are different realisations of the same global initial conditions. Their evolution as a group is quite similar, but the evolution of the central object differs considerably. While in run C1 there are nearly no mergings in the first timesteps, in run C2 the central object grows from the start of the simulation. This is simply due to the presence or absence of a couple of galaxies in the central parts. Furthermore, the contribution of merging and stripping to the mass of the central galaxy is very different in the two cases. In run C1 the contribution of stripped material is very small, while it is comparable to that of mergings in run C2. The central galaxy formed in run Co, which is the denser system, also grows quickly, while the galaxy in run Cp, the less dense group, grows slower. For the virialised simulations the galaxy formed in run Vc1, the most tightly bound case, grows very quickly at the start, but after some time, when nearly half of the galaxies have disappeared, the rate levels off. This is not true for the galaxy formed in run V, since the system is less dense, the tidal forces are not as strong and the secondary galaxies in the central parts do not lose their identity as easily. The results for run Vc2 are very similar to those for run Vc1, and thus have not been plotted.

[FIGURE] Fig. 6. The total mass in the central object as a function of time (solid line) and the contribution to this mass from stripped material (dotted line). The contribution of stripped material is quite important in all the cases especially in the initially virialised groups.

Fig. 7 shows the rate at which this mass increase proceeds. The values plotted are the values obtained from those in Fig. 6 using a centered three point approximation for the derivatives. The peaks in the solid lines correspond to recent mergings and the peaks in the dotted lines are associated with massive accretion of stripped material. In collapsing systems the contribution from merging dominates over the contribution from stripping in a fair fraction of the time. On the other hand stripping is more important in the case of initially virialised systems. In the case of run Vc1 the stripping is very important in the initial stages of the simulation. Later on, when the central object is bigger, it is the merging that dominates. The most interesting case is run V, where stripping dominates during nearly all the simulation.

[FIGURE] Fig. 7. Comparison of the rate of increase of mass of the central object due to merging (solid line) and stripping (dotted line). In collapsing systems the contribution from merging dominates over the contribution from stripping in a fair fraction of the time. On the other hand for the central object formed in run V (extended virialised system) the mass increase is mainly dominated by stripped material.
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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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