4 Discussion

The long, curved tail of G2 seen in Fig. 3, along with the fact that G1 and G2 have nearly the same redshift, may be taken as an indication for the gravitational interaction of G1 and G2. Such tails of escaping debris from the far side of a victim disk are well-known indicators of the encounter of nearly equal-mass spiral galaxies (e.g. Toomre & Toomre 1972; Schombert et al. 1990). On the other hand, if the ULIRG activity was triggered by this interaction, the large projected distance between these two galaxies is surprising. Murphy et al. (1996) suggested that ULIRGs with large (>10 kpc) nuclear separation may represent a triple merger with a third, undetected nucleus from a previous encounter or, alternatively, that the ULIRG phenomenon can occur in an early phase of the interaction. Below, we briefly discuss IRAS03158+5228 in the light of these two scenarios.

Arguments in favour of the multiple merger scenario were derived from the properties of elliptical galaxies (e.g., Barnes 1984; Mamon 1987; Schweizer 1989; Weil & Hernquist 1996), from the dynamical diversity of ULIRGs (Borne et al. 2000; Cui et al. 2001), and from detailed studies of individual galaxies (Taniguchi & Shioya 1998; Lipari et al. 2000). Multiple encounters and mergers are suggested to occur naturally in compact groups of galaxies (Barnes 1989; Hickson 1997; Borne et al. 2000; Bekki 2001). It seems likely that a fraction of ULIRGs is triggered by such a process. Borne et al. (2000) and Cui et al. (2001) considered the appearance of double or multiple nuclei as a keytest for the multiple merger origin and derived percentages of 20% and 17%, respectively, of multi-nuclei ULIRGs. The fraction of ULIRGs triggered by multiple mergers is certainly larger than the fraction of multi-nuclei systems, since a multiple nucleus is expected to evolve on a short timescale to a double nucleus and finally to a single nucleus. Unfortunately, this method is faced with serious difficulties which can lead to an overestimation of multi-nuclei systems: the morphology of the central regions of ULIRGs has the tendency to be strongly affected by dust obscuration effects and by the appearance of regions of intense star formation on a scale of kpc or sub-kpc. Further, the studies mentioned above did not identify real interacting members with spectroscopic observations. Following Bekki (2001), it seems fair to say that the fraction of ULIRGs formed by multiple merging is still highly uncertain.

Dinh-V-Trung et al. (2001) have studied the six systems with nuclear separations larger than 20 kpc among the ULIRGs from the complete 1 Jy sample (Kim & Sanders 1998). The optical and K'-band imaging observations and optical spectra suggest the multiple merger scenario for only one of those ULIRGs, IRAS14394+5332. It cannot be excluded that IRAS03158+4227 is a multiple merger like IRAS14394+5332. Indeed, the morphologies of these two systems show some similarities. Although we do not find evidence for a close double nucleus, IRAS03158+4227 might be in a more advanced stage, where two nuclei of G1 have coalesced and the inner region is already well relaxed, as seems to be indicated by the radial luminosity profile (Fig. 4).

Figure 4: Intensity profiles of G1 (top) and G2 (bottom) derived from the R-band image by means of the MIDAS procedure fit/ell3. I0 is the central intensity. The angular interval where the image of G1 is affected by the star S1 was excluded from the profile analysis.

Figure 5: High-resolution images of IRAS03158+4228 in the J, H, and K'bands. The scale and the size are the same as in Fig. 3.

Figure 6: Optical low-dispersion spectrum (not flux-calibrated, observer frame) of the ULIRG IRAS 03158+4227 (G1, top) and of the galaxy G2 (bottom).

How can the nuclear activity of G2 be matched by such a scenario? Nuclear activity is not unusual in ULIRG-systems, though the active nuclei are mostly located in the hosts of the ULIRG itself. However, there is one system (IRAS17028+5817) among the widely separated pairs studied by Dinh-V-Trung et al. where the spectrum of the ULIRG's host is of H II-type whereas the companion has a LINER-type spectrum. We cannot exclude that G2 is also a late merger. However, its disk-like structure admits a variant of a multiple merger where the ULIRG activity was triggered by a past merger and the AGN in G2 by the present interaction between G1 and G2.

The simulations by Bekki (2001) have demonstrated that a multiple merger can trigger repetitive starbursts with a star formation rate comparable to ULIRGs. However, the discussion by Bekki suggests that very intense starbursts with an amplitude of 10² $M_{\odot }$/yr are not likely in such an environment. As was stressed already in the Introduction, IRAS03158+4227 is one of the most luminous ULIRGs from the 2 Jy sample. According to the relation derived by Clements et al. (1996), the 60 $\mu$m flux transforms into a high star formation rate of about $2 \times 10^3$ $M_{\odot }$/yr, i.e. much higher than what seems possible in compact groups.

As an alternative to the multiple merger scenario, it seems tempting to speculate that the activities in the centres of G1 and G2 were triggered by the same process, namely an interaction of G1 and G2. Liu & Kennicutt (1995, their Fig. 4) discussed the empirical distribution of the equivalent widths of the H$\alpha +[$N II] line for different merger morphological types. The EWs measured for G1 and G2 (Table 2) are in better agreement with Liu & Kennicutt's morphology type 3 (= systems of two disk galaxies) than with type 2 (= advanced merger which appear to be single). Moreover, according to its infrared colour index f₂₅/ f₆₀<0.2, IRAS03158+4228 belongs to the group of "cool'' ULIRGs which are characterized as a major merger with prominent extended tidal structures and resolved double nuclei rather than by small (<2.5 kpc) nuclei separation systems (Surace et al. 2000).

The simulations by Mihos & Hernquist (1996) have demonstrated that disk/bulge/halo systems with dense central bulges experience strongest gaseous infall and star formation activity in the final stages of coalescence when they are within a few kpc of one another. Their disk/halo models without dense bulges, on the other hand, are most active in earlier phases of merging when the galaxies are separated by tens of kpc. At the beginning of the first starburst phase, the snapshots of the disk/halo merger models by Mihos & Hernquist (their Figs. 11 and 12) show a remarkable similarity with the few morphological details seen in IRAS03158+4227: one galaxy (hereafter: g1) is more concentrated, especially the gas and the young stars, with knots and short arms, whereas the most prominent feature of its interaction partner (hereafter: g2) is an extended curved tail at the opposite side. During the next time steps, when the SFR reaches its maximum, the bridge between g1 and g2 becomes weaker and g1 becomes more concentrated.

The long lopsided tail of G2 is the only visible morphologically peculiar feature of the system. It is therefore important for the understanding of the merger stage of IRAS03158+4227 to know whether this structure can be due to the tidal interaction with G1. Since it is not possible to follow the evolution of the extended tidal structures in the snapshots shown by Mihos & Hernquist, we performed a small series of restricted N-body simulations like those in Toomre & Toomre (1972). The main idea of this method is to derive the orbits of both galaxies from the corresponding two-body problem, e.g. by solving a Kepler problem, if the galaxies are treated as point masses. Using these orbits the time-dependent potential at each point is given by a superposition of the two galactic potentials. Stars are treated as test particles, which reduces the classical N-body problem to N single-body problems. (Details of the applied code are described in Theis & Kohle 2001). The main advantages of this method are a fast computation and a high spatial resolution. However, the method is not self-consistent, because effects of self-gravity (like fragmentation or dynamical friction) are neglected. Anyway, comparisons between self-consistent and restricted N-body calculations demonstrated in several cases a good agreement, provided the encounters are not too strong and/or the duration of the simulated stage is not very long. Therefore, and because there are not many constraints from observations, the restricted N-body simulations should be a good starting point. The results from the present simulations are however considered indicative rather than conclusive.

Figure 7 shows the result of a parabolic encounter with an orbit inclination of 60$^\circ$,

Figure 7: Simulation of the gravitational perturbation of the galaxy G2 by the galaxy G1. Both galaxies have the same dynamical mass of 1012 $M_{\odot }$. Left: projected distribution of the mass particles from G2. G1 is marked by the cross at the bottom. The length is measured in kpc and the time unit is 1.49 Myr. No test particles have been used inside the central kpc. Right: blurred intensity plot of the image from the left hand side, overlaid by a contour plot; the lowest intensity contour approximately corresponds to the detection threshold in the optical images of IRAS03158+4227.

a minimum distance of 15 kpc (reached at t=0), a line-of-sight-velocity of 200 kms^-1, and a final projected distance of 50 kpc. The total (dynamical) mass of each galaxy is 10¹² $M_{\odot }$. Since we are mainly interested in the tidal shape of G2, we resolved only G2 in test particles. Motivated by the observed radial intensity profile, we distributed the test particles in an exponential disk with a scale length of 5 kpc and a cut-off radius at 15 kpc. For simplicity we assumed the disk to be coplanar with the plane of sky. The qualitative agreement between the optical image and the simulations is very good: after $7.5 \times 10^7 ~ \mbox{yr}$ a lopsided structure has been formed. This gives rise to an arc-like structure north-west of G2 and a small spur emanating north-east from the main body of G2. In the simulations, these features are the dense parts of a tidal tail which seems also to exist in the observations (e.g. lower-right panel of Fig. 3). The bridge connecting G1 and G2 may be too weak to be clearly detected. Increasing the line-of-sight velocity to 300 kms^-1 yields very similar results.

The assumption that IRAS03158+4227 is triggered by the interaction between G1 and G2 implicates that the ULIRG phenomenon is not restricted to late binary merger stages. Such an interpretation is supported by further indications. Rigopoulou et al. (1999) reported a lack of any correlation between the stage of merger, measured by the separation of nuclei, and the infrared luminosity in an unbiased sample of 62 ULIRGs. Further, there is no trend of increased ULIRG activity in systems with more centrally concentrated H$\alpha$ emission (Mihos & Bothun 1998), and also the total mass of molecular gas in ULIRGs is not related to the linear separation (Gao & Solomon 1999; Rigopoulou et al. 1999). Finally, Dinh-V-Trung et al. (2001) present evidence for IRAS23327+2913 to be hosted by a non-disturbed spiral-like galaxy which may be interpreted as an early stage of merging.