A&A 484, 299-302 (2008)
DOI: 10.1051/0004-6361:20078318
S. Pedrosa1,2 - P. B. Tissera1,2 - I. Fuentes-Carrera3 - C. Mendes de Oliveira4
1 - Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, Argentina
2 - Instituto de Astronomía y Física del Espacio, Casilla de Correos 67, Suc. 28, 1428 Buenos Aires, Argentina
3 - GEPI, Observatoire de Paris, CNRS, Université Paris Diderot, Place Jules Janssen, 92190 Meudon, France
4 - Universidade de São Paulo, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Astronomia, Rua do Matão 1226, Cidade Universitária 05508-900 São Paulo SP, Brazil
Received 19 July 2007 / Accepted 31 March 2008
Abstract
Context. Rotation curves of interacting galaxies often show that velocities are either rising or falling in the direction of the companion galaxy.
Aims. We seek to reproduce and analyse these features in the rotation curves of simulated equal-mass galaxies suffering a one-to-one encounter as possible indicators of close encounters.
Methods. Using simulations of major mergers in 3D, we study the time evolution of these asymmetries in a pair of galaxies during the first passage.
Results. Our main results are: (a) the rotation curve asymmetries appear right at pericentre of the first passage, (b) the significant disturbed rotation velocities occur within a small time interval, of
,
and, therefore, the presence of bifurcation in the velocity curve could be used as an indicator of the pericentre occurrence. These results are in qualitative agreement with previous findings for minor mergers and flybys.
Key words: galaxies: interactions - galaxy: kinematics and dynamics - galaxies: spiral
Rotation curves of interacting and merging galaxies are often highly disturbed. First observations of Rubin et al. (1991) showed several cases of sinusoidal rotation curves and asymmetries for a large fraction of compact group galaxies obtained from long-slit spectroscopy. Although Mendes de Oliveira et al. (2003) have shown that many of these peculiarities are smoothed over when rotation curves (hereafter RC) are derived from 2D velocity maps, some disturbances still remain, indicating their true nature as a global feature of the galaxy. For interacting galaxies, features on the RCs are related not only to the structure of the disk itself, but also to the external perturbations due to the companion (e.g. Rubin & Ford 1983; Elmegreen & Elmegreen 1990; Chengalur et al. 1994; Salo & Laurikainen 2000; Marquez et al. 2002; Hernandez Toledo et al. 2003; Fuentes Carrera et al. 2004; Garrido et al. 2005). One noticeable perturbation in a rotation curve occurs when the velocity on one side decreases considerably, while the other side remains fairly constant. Commonly these features, so-called bifurcations, happen when there is a close companion galaxy. An example of this behaviour can be seen in Fig. 1, obtained by Fuentes Carrera et al. (2004), where the RC of a galaxy, in a pair of galaxies of similar sizes and masses, is displayed.
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Figure 1: Rotation curve of the spiral galaxy NGC 5953 in the interacting galaxy pair KPG 468 (Hernandez Toledo et al. 2003) within the inner 15'', derived from a full 2D velocity map. A velocity bifurcation between the approaching side (full circles) and receding one (empty circles) can be seen at 9''. The companion NGC 5954 is a galaxy of similar size and morphological type. |
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The natural question to ask here is how these velocity disturbances
relate to the passage of the companion galaxy and if they can be
used as a timer of the stage of evolution of an interaction.
Recently, Kronberger et al. (2006, hereafter Kron 06) have investigated
disturbed RCs in simulated interacting galaxies. Using simulations,
those authors reproduced the observations of intermediate redshift
galaxies (
)
by putting a virtual slit along the major axis
of each investigated system (see also, Barton et al. 1999).
They also found that the features associated with the perturbations in
the RCs strongly depend on the viewing angles, particularly for the
derived asymmetry parameters (Dale et al. 2001), which presented quite a
large dispersion for minor mergers and flybys. For major mergers, no
similar detailed study of the temporal behaviour of these
asymmetries has been made. This motivated us to revisit Kronberger's
study focussing on the analysis of the time evolution of the
asymmetries for major mergers. Furthermore, we chose to peform
our analysis in 3D to uncover the real level of disturbance of the
systems. For this purpose, we used N-body/hydrodynamic simulations
with cooling, star formation, and supernova feedback.
We ran pre-prepared initial conditions of major mergers involving
Milky Way-type galaxies. We used the procedure developed by Springel et al. (2005) to construct near-equilibrium galaxies, each one
consisting of a dark matter halo, a disk of gas and stars, and a
bulge with a virial velocity of 160 km s-1. The
gaseous and stellar disks have exponential surface densities with a
scale-length, ,
of 2.5 kpc h-1 and a
scale-height of
.
The bulge component follows a Hernquist profile (Hernquist 1990) with a scale-length of
.
The dark matter halo is consistent with a Hernquist profile scaled to match the inner density distribution of dark matter haloes found in cosmological simulations (Navarro et al. 1996) with a
concentration parameter c=9. We use 20 000, 10 000, 50 000, and
30 000 particles to represent the stellar disk, the stellar bulge,
the gas, and the dark matter components, respectively, of a given
galaxy. Baryonic masses range from
for particles on the disk to
in the bulge component, while the dark matter particles have
.
We assume a
fraction of baryons initially in the form of gas. We also ran a higher resolution simulation with 600 000 total particles to
discard resolution effects.
The two identical galaxies were given an initial relative velocity of 200 km s-1. The minimum separation, ,
achieved after 1.3 Gyr h-1, during the first passage is 30 kpc h-1. Galaxies are set on parabolic orbits and will merge due to
dynamical friction. We investigated four possible configurations for
the encounter. We ordered the experiments using the orbital
parameters of Toomre & Toomre (1972) as i1=0 and i2=0 for A;
i1=0 and i2=180 for B ; i1=45, i2=-45 and
for C; i1=-45, i2=45 and
for D. We chose these initial configurations to study the
kinematical behaviour of the galaxies between the extreme cases of a
parallel encounter versus a perpendicular one. For experiment A, we
also ran two simulations changing the minimum separation at
pericentre: A1 and A2 with
=15 kpc h-1 and
=50 kpc h-1, respectively.
The simulations were run by using the Tree-SPH Gadget-2 code (Springel 2005). The cold gas can form new stars following the Kennicutt law, according to a stochastic algorithm (Scannapieco et al. 2005). However, since the initial gas component is a small fraction of the total mass, the impact of new stars is not important for this analysis.The systems experienced a number of close encounters until they finally merged. We focus only on the perturbation arising during the first close passage.
In a disk structure supported by rotation and in equilibrium within
its potential well, the only velocity component should be a
tangential velocity ()
on the plane perpendicular to the
angular momentum of the system. In practice, this is not necessarily
the case. Motions of stars and gas in the disk can be modified by
the presence of structures in the disk or by external perturbations.
In this case, particular features on the RCs, such as bifurcations,
may appear.
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Figure 2: Circular (continuous line) and tangential velocities (triangles and squares) in experiment A show clear bifurcation. Triangles and squares denote opposite orientations along a given direction used to measure the curves. The side that shows a declining tangential velocity is the one closest to the companion galaxy. Error bars correspond to the standard deviations of the mean values computed within each bin. |
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Figure 3:
Velocity residuals as a function of time estimated for baryons within ![]() ![]() |
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At a given time during the interaction, the simulated RCs are constructed by calculating
on the rotation plane (defined as the plane perpendicular to the total angular momentum of the system) as a function of the distance to the mass centre of the galaxy (r). For the purposes of analysing possible asymmetries in the RCs, we considered
within four cones of a solid angle of 60 degrees along two orthonormal directions on the disk plane:
-
,
-
.
We note that results are insensitive to variations of these angles.
In fact, we have varied these angles between 10 and 60 degrees,
finding no significant changes in the trends. By analysing the
velocities and angular momentum of the mass within these angles, we
can study the effects of interactions in different regions of the
disks and look for loss of symmetry in the velocity patterns.
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Figure 4:
Asymmetry parameter as a function of time for our four
experiments (A, B, C, D) along the ![]() ![]() |
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We calculated the mean tangential velocity,
,
estimated in equally-spaced radial bins of size 1.5 kpc h-1. We
also estimated the velocity that particles on circular orbits within
a potential well dominated by dark matter should statistically have
as
,
where
is the total mass (baryons plus dark matter)
within r. For systems in rotational equilibrium within such a
potential well, we should find that
.
Important departures from this relation will be assumed to be
indicative of a loss or a gain of angular momentum by the action of
an external force. Before the galaxies start interacting, the disks
are in rotational equilibrium within their potential wells,
regardless of the angular sector chosen to measure
.
In order to assess the effects of the interaction on the rotation
curves, we analysed the departures of
from
,
within each adopted angle as a function of time, for the four
experiments performed. Figure 2 shows an example of a
disturbed RC in the
-
direction for experiment A. A
very asymmetric response of the disk can be seen. For this RC, the
velocity on the left side of the galaxy (
direction)
decreases considerably, while the velocity on the right side of the
galaxy (
direction) remains fairly constant, producing a
bifurcation similar to those reported by observations (Fig. 1).
In order to study the presence of these bifurcations in the RCs
along the interaction event, we defined the residual velocities
between the RC and the circular velocity as:
.
By estimating R as a function of radius, we can quantify the difference - and its amplitude - between the measured tangential velocity on one side of the galaxy and the tangential velocity on the opposite side.
Since we are interested in the evolution of these differences with
time, we defined a mean residual velocity
at each given time,
averaging out the corresponding residuals (the central regions of
the galaxies are excluded to avoid an artificial weakening of the
signal originated by the disk structure). Figure 3
shows the mean residuals calculated for experiment A, as a function
of time, in the
-
direction. From this figure, we can
observe that, in general, significant residuals are present,
starting at
1.25 Gyr h-1, which corresponds
to the time of peripassage. We note that the largest bifurcations
appear when the RC is measured within the angular sector closer to
the companion galaxy. This can be seen in Fig. 3
where the
direction, which is the one closest to the
companion, shows the largest mean residuals. A detailed analysis of
the angular momentum content of the simulated galaxies shows that
these residuals can be directly linked to the variation of angular
momentum on orthogonal directions.
In order to quantify if bifurcations in the RCs can be used as a timer of the stage in the interaction, we analyse the evolution with time of the global RC asymmetry as defined by Dale et al. (2001). This asymmetry parameter (hereafter AP) is calculated as the area between the approaching and receding halves of the RC, normalised by the average area under the curve. Figure 4 shows that when the simulated galaxies have galaxy-galaxy distances of approximately r = 30 kpc h-1, significant signal of asymmetry appears. Similar levels of AP are detected in our four experiments, although the details of the features vary from one to the other.
Hence, according to the trends shown in Figs. 3 and 4, two galaxies need to be very close to start experiencing
a significant, internal re-distribution of angular momentum and
mass, but when this has occurred, the RCs remain perturbed for an
extended period until they reach equilibrium again, after almost
of the pericentre, when the centres of masses
are separated by more than 200 kpc h-1, in agreement
with previous findings for minor mergers and flybys (e.g., Kron 06).
A detailed analysis of the evolution of the AP displayed in
Fig. 4 shows that before the peripassage, the AP for the
four experiments remains approximately at a value of .
From the
peripassage, a noticeable increase is detected with values up
20% and greater than 10%, and with a mean AP that, at
least, doubles the level registered up to peripassage. After 0.5 Gyr h-1 from peripassage, it starts decreasing. A similar analysis for A1 and A2 shows that AP anticorrelates with
.
We find no AP greater than
for
larger than
50 kpc h-1 in this merger configuration.
We calculated the AP for the RCs of 3 galaxies in isolated pairs
of galaxies of similar masses, studied by Fuentes-Carrera
(2004) and 2 galaxies in Hickson Compact Groups observed by
Mendes de Oliveira et al. (2003), which show bifurcations. We
derived all RCs from full 2D velocity field maps by averaging large
velocity cones around the major axes of the galaxies. Therefore,
they are good representations of their kinematics as a whole. They
have been corrected by inclination so that the comparison with
simulations is as precise as possible. In the case of the pairs
studied by Fuentes Carrera, the asymmetry values obtained are:
for NGC 5426,
NGC 5427, and
for NGC 5953. A
similar behaviour is obtained for the galaxies in groups:
for
HCG7c and
for HCG 96a. We have also calculated AP for
non-bifurcated-RC galaxies (HCG 10d, HCG 88a, HCG 88c, HCG 88d, HCG 89a, HCG 91c1, HCG 96d) in compact groups. The obtained mean value
was
,
which is very similar, qualitatively, to the one found in
the simulations, during the unperturbed phase (
). It is
interesting to note that the galaxies with bifurcated RC in
compact groups are spiral galaxies with only one companion of
similar mass (HCG 07a and HCG 96c, respectively), and several other
considerably less massive companions (1/3 of the mass of the first
ranked galaxy, at most). Hence, from the analysis of these high
quality observed RCs we get similar results to those found in
simulations for the asymmetry value of the bifurcated RCs.
We studied the RCs of two simulated Milky Way-type galaxies during their first encounter. We performed four simulations with different orientations of the angular momentum direction of the systems. The simulated RCs displayed bifurcations consistently with observational findings. The evolution of the features with time were investigated.
Our main conclusions are that the asymmetry parameter (defined by
Dale et al. 2001) shows a clear increase at the peripassage, reaching
values larger by a factor of two than the levels detected for RCs in
equilibrium. After 0.5 Gyr h-1, the
asymmetry parameter begins to decrease again to lower values. We
found that observed RCs corrected by inclination yield a similar
behaviour. The most significant asymmetries are detected at
peripassage when the systems are separated
30 kpc h-1. In our experiments, we found that the perturbations in the
RCs can be detected even after almost 1 Gyr h-1 of
the peripassage, in agreement with previous works for minor mergers
and flybys (Kron 06). Therefore, the asymmetry parameter could be
used to roughly estimate if the pericentre has occurred in the last
0.5 Gyr h-1. The question of whether these
features can always be seen in RCs of interacting galaxies might
depend on the viewing angle (Kron 06). However, the good agreement of the
observational and numerical results we obtained encourages us to carry out a more comprehensive comparison with observations in a future paper.
Acknowledgements
I.F.C. acknowledges the financial support of FAPESP grant No. 03/01625-2 and the Sixth Framework Program of the EU for a Marie Curie Postdoctoral Fellowship. C.M.d.O. acknowledges support from the Brazilian agencies FAPESP (projeto temático 01/07342-7), C.N.P.q., and CAPES. P.B.T. thanks Conicet and Foncyt for their support. This work was partially supported by the European Union's ALFA-II programme (LENAC) Numerical simulations were run on HOPE, Beowulf Cluster at IAFE.