Simulations of the Local Group Dynamics


Rami Rekola
Tuorla Observatory
FIN-21500 PIIKKIÖ
Finland


Abstract


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.



Introduction


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.



Simulations


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.



Results


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.



Conclusions


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.




References


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



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