Received 20th March 1998
Abstract.
NGC 4449 is an active star-forming dwarf galaxy of Magellanic type.
From radio observations van Woerden et al. (1975) found an extended
H I-Halo around NGC 4449 which is at least a factor
of 10 larger than the optical diameter D25≅5.6 kpc.
More recently, Bajaja et al. (1994) and Hunter et al. (1998) discerned
details in the H I-halo:
a disk-like feature around the center of NGC 4449 and a lopsided arm
structure.
In a series of simulations we demonstrated that the main features can be
obtained by a gravitational interaction between NGC 4449 and another dwarf
galaxy, DDO 125.
According to these calculations the closest approach between both galaxies
happened ∼3·108 yr ago at a minimum distance of
30-35 kpc on a nearly parabolic orbit.
In that case, the dynamical mass of DDO 125 should not be smaller than
10% of NGC 4449.
Before the encounter the observed H I was organized in
a disk with a radius of 25-30 kpc around the center of NGC 4449
which had an inclination angle of 55° to 70°.
The origin of this disk is still not clear, but it might have been a previous
additional interaction.
1. Introduction
Comparing the optical images of NGC 4449 and the Large Magellanic Cloud,
there are many similarities like the size or the assumed mass, though
NGC 4449 has a more active star formation.
Therefore, NGC 4449 has widely been used as a reference galaxy for
Magellanic type irregulars.
On the other hand, radio observations performed by van Woerden et al. (1975)
exhibited a large H I-structure exceeding the Holmberg
diameter of 11 kpc (we will assume a distance of 3.9 Mpc in this
paper).
Recent observations by Bajaja et al. (1994) with the Effelsberg telescope and,
more detailed results by Hunter et al. (1998) with the VLA revealed a complex
structure of several components
(Fig. 1):
An elongated ellipse of H I gas centered on NGC 4449
has a total mass of 1.1·109 Msun.
This gas shows a rigid rotation inside 11 kpc reaching a level of
97 km s-1 in the deprojected speed.
Outside 11 kpc the rotation curve is flat.
Bajaja et al. (1994) derived a dynamical mass of
7.0·1010 Msun inside 32 kpc,
and a H I gas mass fraction of 3.3%.
Furthermore, the H I gas inside the optical part of
NGC 4449 is counterrotating with respect to the outer regions.
South of the galactic center a streamlike structure of 25 kpc emanates
which abruptly splits into two parts:
A small spur (5 kpc) which points towards DDO 125, another close
irregular galaxy, and a long extended stream.
The latter first points 24 kpc to the north, then 49 kpc north-east
and, finally, 27 kpc to the south-east, by this covering 180° around
NGC 4449.
Remarkable are the long straight sections and the abrupt changes of direction.
The total mass of the streamers measured by the VLA observations is about
1·109 Msun.
Hunter et al. (1998) pointed out that by comparison with Effelsberg data there
is an additional diffuse H I mass not detected in the VLA
observations which amounts to two-thirds of the H I in
the extended structures.
In order to explain the outer distribution of H I there
are two classes of explanations:
The first one assumes that the H I around NGC 4449
is still in an ongoing galaxy formation stage and the detected
H I might fall into the galaxy.
However, it seems to be unlikely that such large-scale, lopsided and regular
structure can be maintained over such a long period, as e.g. an orbital period
of more than 1 Gyr for the outer streamer.
Already, the high internal velocity dispersion of 10 km s-1
would destroy the streamers on a timescale of 2·108 yr
(Hunter et al. 1998).
The alternative model is an interaction between NGC 4449 and DDO 125
explaining the streamer as a tidal feature.
However, it is not obvious how the abrupt angles can be produced or why there
is no bridge between both galaxies.
Additionally, the optical images of both galaxies show no sign of any
interaction like tidal tails.
In this paper we investigate the latter scenario addressing the question
whether the observed structures can be formed by tidal interaction at all and
what are the constraints on the mass distribution or orbits for both galaxies.
[Click here to see Fig. 1!]
2. Numerical models
2.1. Methods
Since the gravitational force in an encounter of two galaxies is assumed to
be the dominant force, we apply an N-body approach for the dynamics of
the H I.
Though the effects of neglecting gasdynamics are not clear, such an ansatz
has been used successfully for e.g. M81 and NGC 3077
(Thomasson & Donner 1993).
For our models we use two different N-body schemes:
a self-consistent N-body integration using the GRAPE3Af special purpose
computer (Sugimoto et al. 1990) and a restricted N-body simulation
(Pfleiderer & Siedentopf 1961; Toomre & Toomre 1972).
The basic idea of the latter method is to reduce the N-body problem into
N 1-body problems by assuming that the gravitational potential is formed
by a simple relation.
Here we assume that the gravitational forces on each particle are given
by the superposition of the forces exerted by two point-like objects
(the galaxies) moving on Keplerian orbits.
Hence one needs only (test) particles at the interesting halo locations instead
of a large number of particles which have to create a stable and
self-consistent galactic configuration.
Additionally, the computation of the forces is much faster than for a
consistent model.
In total, the speedup of the numerical calculation is a factor of 1000 or more.
On the other hand, the simplified treatment of the galactic potential prohibits
any effect of the tidal interaction on the orbits of both galaxies, e.g. no
transfer of orbital angular momentum into galactic spin is possible (i.e. no
merging).
In order to overcome this problem, we used the restricted N-body method
only for scanning the parameter range and checked representative models by
detailed self-consistent simulations.
However, no significant differences have been found in the parameter range of
interest.
2.2. Initial conditions
The initial conditions for the simulations characterize both,
the galactic orbits and the distribution of the H I gas.
Since the difference in heliocentric velocity between NGC 4449 and
DDO 125 is only 10 km s-1, we are looking almost
face-on the orbital plane (except for the unlikely case that both galaxies
are now in closest approach).
Hence, the actual distance between both galaxies is 42 kpc.
The mass of NGC 4449 is fixed to the observed value within 32 kpc,
i.e. MNGC 4449 = 7·1010 Msun.
Thus, the unknown orbital parameters are the eccentricity e of the orbit,
the mass ratio q ≡ MDDO 125 / MNGC 4449
and the minimum distance dmin at closest approach.
The original configuration of the H I-distribution is
much poorly constrained.
Assuming that the central ellipsoidal H I feature is
the tidally unaffected remnant of an originally rotationally supported
H I disk around NGC 4449 and presuming a prograde
encounter, we can determine the rotational sense of the disk (NE-part is
pointing towards us) and roughly its orientation, i.e. position angle.
However, the inclination i is less clear.
Moreover, the initial size Rmax of the disk or the regularity
of the H I distribution is completely unknown.
3. Results
In a series of simulations we varied the orbital parameter (minimum distance
dmin, the eccentricity ε, the mass ratio q)
as well as the disk parameter (size Rmax of the disk,
its position angle α and an inclination i).
Qualitatively, the main features found by Hunter et al. (1998) can be
reproduced by a nearly parabolic orbit, a mass ratio q = 0.15 and a
minimum distance dmin = 30 kpc (upper left panel of
Fig. 2).
The parameters for the disk orientation are chosen in agreement with Hunter et
al.'s suggestion of i = 60°, α = 230°, whereas the disk
radius was set to Rmax = 27 kpc ≤ dmin.
Though the numerical model is not a fit of the data, the characteristic sizes
and locations of the streamers as well as the unaffected disk can be found.
The material seen between the streamer and the disk which is not found in
Hunter's data probably corresponds to the extended H I-mass
seen in the single dish observations by van Woerden et al. (1975).
In order to check the significance of the model parameters the remaining three
plots in Fig. 2 show the influence
of changing the inclination (i = 80°), the size of the
H I-disk (Rmax = 20 kpc) or
the mass ratio (q = 0.05).
We find that the relative size of the streamers or their orientation with
respect to DDO 125 strongly depend on these parameters.
[Click here to see Fig. 2!]
4. Discussion
The numerical models are basically able to reproduce the morphology of the
streamers, at least if one identifies the outer edges of the particle
distribution with the location of the streamers.
A more detailed investigation of the surface densities in the N-body
simulations exhibits clearly the large stream pointing to the North-West,
and also the stream emanating from the centre, however, the stream starting
at the tip of the central stream pointing to the North is less clear,
if existing at all.
Another feature seen in the numerical models is a strong mass concentration
at the southwestern edge of the disk which seems not to be in the observational
data.
Finally, the smaller mass concentration detected in the South-West cannot
be explained by the interaction at all.
On the other hand, the sensitivity of the models to variations of the initial
parameters, especially to the variation of the observed disk orientation makes
it unlikely that the successfully reproduced structures are formed by chance
and no interaction takes place at all.
Moreover, we think that the initial H I-distribution is
more complex and the model of a completely rotationally supported disk-like
H I distribution which is very smoothly distributed might
be too simple.
Another important constraint is the total mass of DDO 125.
Tully et al. (1978) derived from single dish observations a total mass of
5·108 Msun (corrected for a distance
of 3.9 Mpc).
Such a low mass would rule out the interaction scenario, because it can not
produce sufficient tidal features.
However, Ebneter et al. (1987) reported VLA-observations which show
a linear increase of the rotation curve out to the largest radii where
H I has been detected, i.e. out to twice the optical
radius.
This already allows for a lower mass limit of DDO 125 which is a factor 8
larger than the value of Tully et al., i.e. 5.7% of NGC 4449.
Additionally, no flattening of the rotation curve nor any decline has been
observed.
Thus, the dynamical mass of DDO 125 is probably at least 10% or more
of the mass of NGC 4449 which is in agreement with the mass ratio derived
from the numerical model.
Acknowledgments.
The simulations were partly performed with the GRAPE3af special purpose
computer in Kiel (DFG Sp345/5).
References
- Bajaja E., Huchtmeier W.K., Klein U., 1994, A&A 285, 388
- Hunter D., Wilcots E.M., van Woerden H., Gallagher J.S.,
Kohle S., 1998, ApJ 495, L47
- Ebneter K., Davis M., Jeske N., Stevens M., 1987, BAAS 19, 681
- Pfleiderer J., Siedentopf H., 1961, Zs. f. Ap. 51, 201
- Sugimoto D., Chikada Y., Makino J., Ito T., Ebisuzaki T.,
Umemura M., 1990, Nat 345, 33
- Thomasson M., Donner K.J., 1993, A&A 272, 153
- Toomre A., Toomre J., 1972, ApJ 178, 623
- Tully R.B., Bottinelli L., Fisher J.R., Gouguenheim L., Sancisi R.,
van Woerden H., 1978, A&A 63, 37
- van Woerden H., Bosma A., Mebold U., 1975, in 'La Dynamique des
Galaxies Spirales', Weliachew L. (ed.), p. 483
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| First version: | 12th | August, | 1998
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| Last update: | 14th | November, | 1998
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Jochen M. Braun &
Tom Richtler
(E-Mail: jbraun|richtler@astro.uni-bonn.de)