Moving Supermassive Black Holes in the Centers of Galaxies Nico

1
Inertial Effects from Companion Galaxies Driving
Warps in Disk Galaxies N. F. Comins1, N.
Palestini1, E. F. Borra2, R. Hohlfeld3,4,5, L.
Wholly1 1Department of Physics and Astronomy,
University of Maine 2Département de Physique,
Université Laval 3Center for Computational
Science, Boston University 4Wavelet Technologies,
Inc. 5PhaseCapital LP
Abstract Most disk galaxies, including the Milky
Way, are observed to be warped1 (Figure 1). The
mechanisms for this warping are not well
understood. We explore warping caused by the
passage of a distant galaxy (the intruder).
For this presentation, we have carried out N-Body
simulations with plausible interaction parameters
that give significant warps having amplitudes
comparable to those observed in some disk
galaxies. We propose that the distortion on the
disk due to the intruder is caused in part by the
effects of pseudoforces that occur while the two
galaxies interact. These pseudoforces are highly
non-linear dynamics whose theoretical equations
we are now studying. Further observations of
galaxies with these signature integral-shaped
warps, located in the vicinity of massive,
relatively distant neighbors, would support the
existence of this mechanism.
Figure 1. Warped spiral galaxy ESO510-13.
(Hubble)
The Simulations We set up each simulation using
GENICS2, which generates the initial positions
and velocities for 20,000 particles in our test
galaxy. We insert the intruder as a single
particle. This data set is then uploaded to
Boston Universitys computer Twister3 and evolved
using GADGET-24. We have created simulations
covering all classes5 of warps, but are focusing
on the canonical integral-shaped ones. In each
simulation the mass of the disk is 1 in natural
units, thus each particle has a mass of 1/20,000.
For the intruder, we set an initial position,
velocity and its total mass. Figure 2 shows the
coordinate system we use for our calculations and
the initial relative orientation of the galaxy
and intruder.
The Theory We propose that the overall shapes of
the warps in the disk galaxies we are studying
are driven, in part, by pseudoforces. These
forces come into play as the stars and other
matter in the galaxy are pulled out of the
initial plane of its orbit by the intruders
gravitational attraction. This disturbance
causes all or part of the disk to tilt slightly
towards the intruder. However, this deflection
does not immediately generate the integral
shape distribution. Rather, it gives rise to the
three pseudoforces of classical mechanics (see
below), which have components perpendicular to
the plane of the tilted disk. (Prior to the
tilt, all these pseudoforces are in the plane of
the disk.) The pseudoforces on the tilted disk,
we believe, cause the deflections of particles
into the integral sign distribution. For
reference, the pseudoforces are given by The
coordinates are as shown in Figure 2. From the
equations above we will estimate the magnitude
and direction of the deflection on each side of
the disk due to each of the pseudoforces. We
plan to compare the analytical magnitudes of the
deflections with warp amplitudes obtained from
the simulations.
Results In the figures below, the natural
coordinate system of GENICS and GADGET has the
origin fixed at the initial position of the
center of the disk. (The coordinate system of
Figure 2 is set up by the authors to clarify the
equations of motion of the three bodies of
interest.) Figure 3 shows a side view of the
density contours of an unwarped galaxy simulation
(no intruder). The red line in (b) through the
contour maxima indicates that the disk is flat
over its entire extent. Figure 4 shows the same
view for a perturbed galaxy whose intruder has
passed perpendicularly to the initial plane of
the disk. At the time of the snapshot, the
intruder is up and to the left. With the same
red reference line drawn, secondary red lines
follow the warped contours in the simulations
outer regions. In a second distant encounter run
(Figure 5), we show alternate views of the same
data. As a further comparison with our distant
encounter results, we present in Figure 6 the
results of a close encounter started at the same
initial angle as the run in Figure 5.
Discussion The simulations show that
gravitational interactions between galaxies lead
to warping of galactic disks. Presently we are
investigating the persistence and stability of
warps. Kahn and Woltjer5, Binney et al.6, Tubbs
and Sanders7, and Shen and Sellwood8, have
detailed arguments regarding the persistence of
warps. If pseudoforces drive the warps, then the
effect should persist for more than a few
rotations. Our latest simulations are able to
explore this issue. So far, we see that in long
runs in which the intruder passes once and then
recedes, the disk maintains its warp for at least
three rotations. In many cases, observations
suggest that the intruder galaxies are often
bound to the warped galaxy. We are presently
setting up and running simulations of bound
systems.
References 1K. Kuijken I. García-Ruiz Galactic
Disk Warps. In ASP Conf. Ser. 230, Galaxy Disks
and Disk Galaxies, ed. by J. G. Funes E. M.
Corsini (Sheridan Books, Ann Arbor 2001) pp
401408 2Schwarzmeier J., On the Simulations of
Galaxy Dynamics and Their Application to Physics
Education. Ph.d. diss., U. West Bohemia,
2007. 3IBM pSeries 655 shared memory cluster
consisting of 72 processors on the Boston
University Campus (http//scv.bu.edu/). 4Springel
V., Mon. Not. R. Astron. Soc. 364, 1105
(2005). 5Kahn, F. D., and Woltjer, L., ApJ. 130,
705 (1959). 6Binney, J., Jiang, I., Dutta, S.,
MNRAS, 297, 1237 (1998.) 7Tubbs, A. D. Sanders,
R. H. Astrophys. J. 230, 736 (1979). 8Shen, J.,
Sellwood, J. A., MNRAS, 370, 2 (2006).
Acknowledgements Funding for this project has
been provided by the Maine Space Grant
Consortium. A special thanks to the Center for
Computational Science at Boston University on
whose supercomputer cluster, Twister, the
simulations were run.