The sun is a star like any other among the hundred billion or so stars in our galaxy. It is unremarkable in its properties. Its mass is in the mid range of what is normal for stars: there are others more than ten times more massive, and there are also stars more then ten times less massive, but the vast majority of stars have a mass within a factor of ten of that of the sun. Our home star is also unremarkable in its location, at a distance of some thirty thousand light years from the center of the galaxy. Again, the number of stars closer to the center and further away from the center are comparable. Our closest neighbor, Proxima Centauri, lies at a distance of a bit more than four light years.

This distance is typical for separations between stars in our neck of the woods. A light year is ten million times larger than the diameter of the sun (a million km, or three light seconds). In a scale model, if we would represent each star as a cherry, an inch across, the separation between the stars would be many hundreds of miles. It is clear from these numbers that collisions between stars in the solar neighborhood must be very rare. Although the stars follow random orbits without any traffic control, they present such tiny targets that we have to wait very long indeed in order to witness two of them crashing into each other. A quick estimate tells us that the sun has a chance of hitting another star of less than per year. In other words, we would have to wait at least years to have an appreciable chance to witness such a collision. Given that the sun is less than five billion years old, it is no surprise that it does not show any signs of a past collision: the chance that that would have happened was less than one in a hundred million. Life in our galactic suburbs is really quite safe for a star.

There are other places in our galaxy that are far more crowded, and consequently are a lot more dangerous to venture into. We will have a brief look at four types of crowded neighborhoods.

A snapshot of the globular cluster M15, taken with the Hubble Space Telescope.

In the photo above we see a picture of the globular cluster M15, taken with the Hubble Space Telescope. This cluster contains roughly a million stars. In the central region typical distances between neighboring stars are only a few hundredth of a light year, more than a hundred times smaller than those in the solar neighborhood. This implies a stellar density that is more than a million times larger than that near the sun. Since the typical relative velocities of stars in M15 are comparable to that of the sun and its neighbors, a few tens of km/sec, collision times scale with the density, leading to a central time between collisions of less than years. With globular clusters having an age of more than years, a typical star near the center already has a chance of more than a percent to have undergone a collision in the past.

In fact, the chances are much higher than this rough estimate indicates. One reason is the stars spend some part of their life time in a much more extended state. A star like the sun increases its diameter by more than a factor of one hundred toward the end of its life, when they become a red giant. By presenting a much larger target to other stars, they increase their chance for a collision during this stage (even though this increase is partly offset by the fact that the red giant stage lasts shorter than the so-called main-sequence life time of a star, during which they have a normal appearance and diameter). The other reason is that many stars are part of a double star system, a type of dynamic spider web that can catch a third star, or another double star, into a temporary three- or four-body dance. Once engaged in such a dance, the local stellar crowding is enormously enhanced, and the chance for collisions is greatly increased.

A detailed analysis of all these factors predicts that a significant fraction of stars in the core of a dense globular cluster such as M15 has already undergone at least one collision in its life time. This analysis, however, is quiet complex. To study all of the important channels through which collisions may occur, we have to analyze encounters between a great variety of single and double stars, and occasional bound triples and larger bound multiples of stars. Since each star in a bound subsystem can be a normal main-sequence star, a red giant, a white dwarf, a neutron star or even a black hole, as well as an exotic collision product itself, the combinatorial richness of flavors of double stars and triples is enormous. If we want to pick a particular double star, we not only have to choose a star type for each of its members, but in addition we have to specify the mass of each star, and the parameters of its orbit, such as the semi-major axis (a measure for the typical separation of the two stars) as well as the orbital eccentricity.

The goal of our book series is to develop the software tools to make it possible to simulate an entire star cluster like M15, and to analyze the resulting behavior both locally and globally.

In photo below we see an image of the very center of our galaxy. This picture is taken with the Northern branch of the two Gemini telescopes, which is located in Hawaii on top of the mountain Mauna Kea.

An image of the central region of our galaxy, taken with the Gemini North telescope. The center is located on the right just above the bottom edge of the image.

In the very center of our galaxy, a black hole resides with a mass a few million times larger than the mass of our sun. Although the black hole itself is invisible, we can infer its presence by its strong gravitational field, which in turn is reflected in the speed with which stars pass near the black hole. In normal visible light it is impossible to get a glimpse of the galactic center, because of the obscuring gas clouds that are positioned between us and the center. Infrared light, however, can penetrate deeper in dusty regions. It is a false-color image, reconstructed from observations in different infrared wavelength bands.

In the central few light years near the black hole, the total mass of stars is comparable to the mass of the hole. This region is also called the galactic nucleus. Here the stellar density is at least as large as that in the center of the densest globular clusters. However, due to the strong attraction of the black hole, the stars zip around at much higher velocities. Whereas a typical star in the core of M15 has a speed of a few tens of km/sec, stars near the black hole in the center of our galaxy move with speeds exceeding a 1000 km/sec. As a consequence, the frequency of stellar collisions is strongly enhanced.

Modeling the detailed behavior of stars in this region remains a great challenge, partly because of the complicated environmental features. A globular cluster forms a theorist's dream of a laboratory, with its absence of gas and dust and star forming regions. All we find there are stars that can be modeled well as point particles unless they come close and collide, after which we can apply the point particle approximation once again. In contrast, there are giant molecular clouds containing enormous amounts of gas and dust right close up to the galactic center. In these clouds, new stars are formed, some of which will soon afterwards end their life in brilliant supernova explosions, while spewing much of their debris back into the interstellar medium. Such complications are not present in globular clusters, where supernovae no longer occur since the member stars are too old and small to become supernovae.

Most other galaxies also harbor a massive black hole in their nuclei. Some of those have a mass of hundreds of millions of solar masses, or in extreme cases even more than a billion times the mass of the sun. The holy grail of the study of dense stellar systems is to perform and analyze accurate simulations of the complex ecology of stars and gas in the environment of such enormous holes in space. Much of the research on globular clusters can be seen as providing the initial steps toward a detailed modeling of galactic nuclei.

There are many other places in the galactic disk where the density of stars is high enough to make collisions likely, at least temporarily. These are the sites where stars are born. The above photo taken by the Japanese Subaru telescope in Hawaii shows the Orion Nebula, also known as M42, at a distance of 1500 light years from the sun. This picture, too, is taken in infrared light in order to penetrate the dusty regions surrounding the young stars. The four brightest stars in the center, collectively known as the Trapezium, form the most massive stars of a larger conglomeration of stars, all recently formed from the gas and dust that still surrounds them.

In order to study collisions in these star forming regions, we can no longer treat the stars as point masses. Many of the collisions take place while the stars are still in the process of forming. While a protostar is still in the process of contracting from the gas cloud in which it was born, it presents a larger target for collisions with other stars. In addition, a single contracting gas cloud may fission, giving rise to more than one star at the same time. In this way, the correlated appearance of protostars is even more likely to lead to subsequent collisions.

The proper way to model these processes is to combine gas dynamics and stellar dynamics. Much progress has been made recently in this area. One way to use stellar dynamics in an approximate fashion is to begin with the output of the gas dynamics codes, which present the positions and velocities of a group of newly formed stars, and then to follow and analyze the motions of those stars, including their collisions.

Although stars are formed in groups, these groups typically do not stay together for very long. Perturbations from other stars and gas clouds in their vicinity are often enough to break up the fragile gravitational hold they initially have over each other. Some of the more massive groups of newly formed stars, however, are sufficiently tightly bound to survive their environmental harassment. They form the so-called open clusters, where their name indicates that they have central densities that are typically less than what we see in globular clusters.

The open star cluster M67, in a picture taken by the Anglo-Australian Observatory.

The above photo shows one of the richest and densest open clusters, M67, as observed by the Anglo-Australian Observatory. Since this cluster is old enough to have lost its gas and dust, all stars are visible at normal optical wavelengths, at which this image is taken. In the central regions of this cluster, there are indications that some of the stars have undergone close encounters or even collisions. Consequently, this star cluster qualifies as a dense stellar system.

Open clusters typically have fewer members than globular clusters. Also, they are younger. Both facts makes it easier to simulate open clusters than globular clusters, in terms of computer time needed, when we model the stars on a one-to-one basis in a direct N-body simulation.

On the other hand, the densest globular clusters show a higher frequency and a far richer variety of stellar collisions, making them a more interesting laboratory. In that sense, a dynamical simulation of an open cluster can be seen as providing preparatory steps toward the modeling of globular clusters, just as a study of the latter forms a stepping stone toward the investigation of galactic nuclei.

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