Erik Holmberg was interested in the clustering tendencies of galaxies;
galaxies arise in a variety of locations. A few percent can be found in
clusters of hundreds; a still greater fraction can be found in groups
of tens. Our own Galaxy and M31 are both part of a group of galaxies
called the Local Group. In particular, Holmberg wanted to explain the
origins of these groups and clusters, and the mechanism he had in mind
was the mutual tidal capture of galaxies during initial hyperbolic
passages. Initially the galaxies approach each other with sufficient
energy to escape to infinity but lose energy during the encounter and
thus become bound. By assuming a uniform distribution of galaxies,
each with a peculiar velocity of a few hundred kilometers per second,
Holmberg envisaged the gradual accumulation of galaxies into groups
and clusters.
Unfortunately for Holmberg, there is a fundamental problem with
this hypothesis; when the probability for an encounter is estimated,
we find that only one galaxy in ten thousand will have had sufficient
time to be tidally captured during the lifetime of the Universe, quite
at odds with observations.
Despite this, it is interesting to follow Holmberg's experiments
of tidal capture of galaxies during close encounters. These were numerical experiments in which each
galaxy was modeled as 37 mass points arranged in concentric circles
traveling around a common centre. What perhaps was most ingenious
about this arrangement was that the mass points were represented by
light bulbs! By using the inverse square behaviour of light, Holmberg
had uncovered a method to mimic gravitational forces - this was the
most computationally intensive part of the problem. Photocells were
used to detect the magnitude and direction of the "gravitational
force", i.e. the light, and so it was possible to map the trajectories
of the mass points by graphical integration.
Holmberg simulated planar encounters between disk galaxies using
this technique; he was able to estimate the efficiency of tidal
capture for a variety of approach velocities, rotations and minimum
separations. Whatsmore he correctly noted that the maximum tidal
distortion occurs after the passage of the interloper through
pericenter. However, he did not report any problems with bar
instabilities, something which should have plagued such a cold disk,
and he also noted that tidal capture was most efficient during
retrograde passages when the disks counter-rotated in an opposite
sense to their orbital motion. As noted in Barnes (1996), this is "curious".
In addition to the hyperbolic passages, Holmberg did investigate
parabolic encounters and used them to illustrate tidal deformations,
but because of the number of mass points involved and the
approximations made, felt that this was not sufficient for a detailed
study of tidal response. Hence an opportunity was missed to uncover
the tidal origins of bridges and tails.