Ever since Kahn and Woltjer (1959) developed a method for calculating the
mass of the Local Group based on gravitational interaction between Milky Way
and Andromeda galaxy attempts have been made to better understand the dynamics
of the Local Group. Later Zheng et al. (1991) showed that if Maffei 1 is close
enough to the Local Group it may have had a considerable effect on the Local
Group dynamics. Valtonen et al. (1993) and Byrd et al. (1994) confirmed the
necessity of including the Maffei group and possibly even the Local Group
dwarf galaxies in any dynamical models of the Local Group.
This research continues directly the work of Zheng, Valtonen, and Byrd by
using the same computer simulation program and adopting some parameters from
their work. The original N-body code by Aarseth (1971) has been modified to
meet the demands of the Local Group simulations. Modifications made during
this research include adding the third dimension and adding more dwarf
galaxies. Also all known parameters have been updated when necessary. Due to
uncertainties in the distance estimations to the nearby Sculptor group two
different programs have been run: one with and another without the Sculptor
group.
The programs simulate the trajectories of included galaxies backwards through
time starting from the present situation and ending to the Big Bang. As main
results the programs give the age of the Universe, transverse velocities of
the galaxies, and their departure velocities from the Big Bang or the Little
Bang (Valtonen et al. 1995). Although the trajectories of the galaxies differ
considerably between the two programs there are some similarities as well,
such as the age of the Universe which ranges between 17 and 18 billion years.
The results are consistent with the previous works as well as with some
observational data available.
Everything began nearly forty years ago when Kahn and Woltjer (1959)
formulated a method for Local Group timing. They used the local giant
galaxies, our own Milky Way and Andromeda galaxy, as a gravitational binary
system. Kahn and Woltjer believed that as these two galaxies contribute nearly
90 % of the total observable mass of the Local Group no other galaxies needed
to be included in this model unless, as they pointed out, there are other
galaxies hidden by absorption in the galactic plane.
Some of these hidden galaxies began to be revealed almost ten years later when
Paolo Maffei (1968) found two large galaxies just behind the zone of
avoidance. Later named as Maffei 1 and Maffei 2 these galaxies are actually
part of a small group of galaxies dominated by Maffei 1 and IC 342. I shall
call this group Maffei group.
Maffei group entered the Local Group studies as Zheng et al. (1991) proposed
that Maffei 1 could have had dynamical interaction with the Local Group some
6.5 billion years ago. They proposed that Maffei 1 could have escaped from
another nearby group, the Sculptor group, which has passed through the Local
Group. They also dismissed the previous idea of massive halos around the
galaxies. However, their results were highly dependent on the distance of
Maffei 1, which is very unreliable. Moreover, the number of galaxies in Maffei
group raises questions how such system could survive intact the needed close
encounter with the Local Group galaxies.
The work continued as Valtonen et al. (1993) returned to the Maffei group and
calculated a total mass for the system and an age for the universe. Later Byrd
et al. (1994) included some smaller Local Group galaxies in the model. Their
conclusion was that the history of the Local Group is very complex and it is
important to include accurate masses and distances of as many members of the
Local Group as possible.
The Zheng, Valtonen, and Byrd researches used a version of Nbody Fortran
program by Aarseth (1971) to simulate the trajectories of the galaxies in the
extended Local Group. The simulation program includes initial positions and
radial velocities of the galaxies. For simplification the Maffei and Sculptor
groups are treated as point masses. Some initial values including masses of
galaxies and their transverse velocities both in xy-plane and along z-axis are
given to the program in an input file.
After the initial conditions are clear to the program it starts to calculate
the places and velocities of the galaxies at certain intervals which have been
defined to be 80 million years. Maximum time is given in the input file but
there is a routine in the program that checks the distance between Andromeda
galaxy and Milky Way and stops the simulation if this distance becomes too
small (indicating the Big Bang).
The Big Bang is actually the ultimate goal. The parameters given in the input
file determine trajectories of the galaxies. Changing these parameters one is
able to change the trajectories and eventually such parameters are found that
the galaxies come together in the Big Bang. An alternative destination is the
Little Bang that has been proposed taking place in the Local Group history
some 4-10 billion years ago (Valtonen et al. 1995).
In the end the program creates two output files. One of them includes the
initial values of position and speed for each galaxy, the time and
participants of galaxy mergers, the total integration time, and the positions
and speeds of those galaxies that have not merged. As the time is reversed
the mentioned mergings actually mean occasions when a galaxy separates from
another. The other output file consists of series of numbers indicating first
the time and then the corresponding positions of galaxies as values of X, Y,
and Z. This file can then be run in a movie program that shows the actual
trajectories of the galaxies on screen.
The link here shows the trajectories of the
galaxies in the model with Maffei group but without Sculptor
group. The view is of supergalactic XY-plane from above. The large
image contains trajectories for the last 14 billion years while the
first 3.5 billion years are depicted in the small image. Different
galaxies are represented by different colours. The symbols on the
trajectories show the galaxy positions with 3.5 billion years in
between. The colours and symbols match those in the explanations
underneath. Each trajectory ends up in a round symbol that shows the
current positions of the Local Group galaxies. In this simulation it takes
17.5 billion years for the galaxies to reach the Big Bang. It is clearly
visible that the dwarfs Leo A and IC 1613 never merge with any other object.
Therefore there is either something wrong with this model or these dwarfs
originate from elsewhere. Origin outside the Local Group could be true for
Leo A but it would seem curious for IC 1613 which is in the close vicinity of
Andromeda galaxy. Other galaxies behave more or less ordinarily in this model.
There is a close encounter of Andromeda galaxy and Maffei group about four to
five billion years ago.
The numerical result sheet shows the number of the
galaxy (or galaxy group), the name of the galaxy, the mass of the galaxy
(Valtonen 1996), the galaxy's distance from the Milky Way at the present time
(various sources), the measured present day radial velocity (de Vaucouleurs
1991), the present day total transverse velocity from simulations, the time
the galaxy departed from some other object (the time increases into the past),
and the number of this object (BB = the galaxy has existed ever since the Big
Bang).
The other model included also the Sculptor group (no graph, the
numerical results). This simulation was
finished in 17 billion years with just the Leo A dwarf unmerged. In
this simulation there is a clear Little Bang occurring some seven
billion years ago among Andromeda galaxy, Maffei and Sculptor groups,
and some dwarfs. What actually triggers this Little Bang and what
kinds of processes are involved is not possible to extract from these
simulations. This model is less reliable than the one without
Sculptor group, which is why there is no graph.
Very similar age for the Universe (17-17.5 Gyr) was obtained with both of
these considerably different simulations. This is clearly an effect created
by the somewhat anomalous movement of the Milky Way. The main difference
between including the Sculptor group and leaving it out is therefore on its
gravitational interaction with the Local Group dwarf galaxies.
The influence of dwarf galaxies to the merging times of larger galaxies and
consequently the dwarf galaxies should not be overlooked. Their initially
infinitesimal effect on a large galaxy's trajectory is multiplied by the
chaotic effects of eighteen galaxies interacting with each other. In extreme
cases the chaotic behaviour can substantially change the outcome of a
simulation even when the change of an initial parameter is very small. Due to
the chaotic effects and complexity of this 18-body system the initial
parameters should be as accurate as possible and definitively more accurate
than at the moment. The Local Group galaxies and their physical parameters
are curiously poorly known - after all they are the closest extragalactic
objects to us.
The galaxies' positions vary much within the local volume including all the
three dimensions and some galaxies possess consequently even a higher
velocity component along Z-axis than in XY-plane. This gives a reason to
believe that three-dimensional models are required for accurate Local Group
modelling. However, as errors of initial parameters are very high the
approximation with two-dimensional model seems to give adequate results for
present-day analysis of Local Group history. All in all there is still a lot
of both theoretical and observational research to be done in our galactic
neighbourhood.
Aarseth, S. J., 1971, Astrophysics and Space Science, 14, 20:
Numerical experiments of the N-body problem
Byrd, G., Valtonen, M., McCall, M., Innanen, K., 1994, The Astronomical
Journal, 107, 2055: Orbits of the Magellanic Clouds and Leo I in
Local Group history
de Vaucouleurs, G., de Vaucouleurs, A., Corwin, Jr., H. G., Buta, R. J.,
Paturel, G., Fouque, P., 1991, Third Reference Catalogue of Bright
Galaxies, New York: Springer-Verlag
Kahn, F. D., Woltjer, L., 1959, The Astrophysical Journal, 130,
705: Intergalactic matter and the Galaxy
Maffei, P., 1968, Publications of the Astronomical Society of the
Pacific, 80, 618: Infrared object in the region of IC 1805
Valtonen, M. J., Byrd, G. G., McCall, M. L., Innanen, K. A., 1993, The
Astronomical Journal, 105, 886: A revised history of the Local
Group and a generalized method of timing
Valtonen, M. J., McCall, M. L., Innanen, K. A., Zheng, J.-Q., Byrd, G. G.,
1995, in Dark matter (AIP Conference Proceedings 336), eds. Holt, S.
S., Bennett, C. L., New York: American Institute of Physics, 450: The Little
Bang: Peculiarities in the Local Group and some dynamical explanations
Valtonen, M. J., 1996, in preparation
Zheng, J.-Q., Valtonen, M. J., Byrd, G. G., 1991, Astronomy and
Astrophysics, 247, 20: Maffei 1 as an interloper of the Local
Group of galaxies and the mass of the Local Group