Abstract

An extended H i cloud (VIRGOH i 21) with an H i mass of ∼108 M and no apparent optical counterpart was recently discovered in the Virgo cluster. In order to understand the origin of physical properties of apparently isolated H i clouds like VIRGOH i 21, we numerically investigate physical properties of tidal H i debris that were formed by galaxy—galaxy interactions in clusters of galaxies. Our hydrodynamical simulations demonstrate that tidal debris with total H i masses of 108–109 M can have (1) a wide spread of H i velocities (>200 km s−1), (2) a small mass fraction of stars (∼10 per cent), and (3) a mean B-band surface brightness of the stellar components fainter than 30 mag arcsec−2. These results suggest that VIRGOH i 21, which lies at a projected distance of ∼150 kpc from the one-armed, H i-rich spiral galaxy M99 (NGC 4254), is tidal debris. We propose that the comparison between the simulated and the observed velocity fields of H i clouds allows us to better understand their nature and origin (e.g. whether they are just tidal debris or are ‘dark galaxies’ that have H i gas only and are embedded within dark matter haloes).

Introduction

Detections of H i structures without apparent stellar counterparts are not uncommon in the outskirts of galaxies and within galaxy groups. The Galactic high-velocity clouds (HVCs) and the prominent H i tidal streams tracing the interaction between the Milky Way and the Magellanic Clouds are the closest examples. Another prime example is the nearby, H i-rich group consisting of the galaxies M 81, M 82, and NGC 3077 which are connected by a beautiful network of H i filaments and streams (Yun, Ho & Lo 1994). In most cases, the location, structure and velocity field of the apparently star-less H i clouds, with respect to the nearby galaxies, clearly indicates their tidal or collisional origin. Hibbard et al. (2001) show a large number of examples collected as part of the ‘H i Rogues Gallery’ of galaxies: there are one-sided tidal tails stretching out to ∼100 kpc (e.g. Appelton et al. 1987; Rots et al. 1990; Clemens et al. 1999), H i rings with 100–200 kpc diameter (e.g. Schneider et al. 1989; Malphrus et al. 1997), etc. On the other hand, isolated H i clouds appear to be extremely rare as shown by the H i Parkes All-Sky Survey (HIPASS) (Koribalski et al. 2004). The most isolated H i cloud discovered, HIPASS J0731–69 (Ryder et al. 2001), lies at a projected distance of 180 kpc from the asymmetric spiral galaxy NGC 2442 within the NGC 2434 galaxy group. Bekki et al. (2005) suggested as a possible formation scenario that this massive cloud is likely to be the high column-density peak of a much larger H i structure.

Davies et al. (2004) recently discovered several H i clouds in the Virgo cluster. At least one of these clouds, VIRGOH i 21 (vhel∼ 2000 km s−1), has no apparent optical counterpart and is, on the basis of its relatively wide H i spectrum, interpreted as a dark matter halo by Minchin et al. (2005). While the projected distance of VIRGOH i 21 to the one-armed spiral galaxy M 99 (NGC 4254, vsys≈ 2400 km s−1) may appear large (25 arcmin or ∼150 kpc at a distance of 20 Mpc), it is by no means exceptional as indicated above. Detailed Very Large Array H i observations of M 99, the brightest spiral in the Virgo cluster, by Phookun, Vogel & Mundy (1993) reveal a large amount of gas (∼2.3 × 108 M) at peculiar velocities of ∼135 km s−1 (with respect to vsys), stretching at least 11 arcmin toward the northwest (in the direction of VIRGOH i 21) in the form of a faint clumpy tail. The total H i mass measured in the M 99 system by Phookun et al. (1993) is 7.6 × 109 M, typical for its morphological type (Sc) and luminosity; the H i mass-to-light ratio is ∼0.1. Using HIPASS we measure an H i flux density of 80 ± 2 Jy km s−1 for M 99 (HIPASS J1218+14), in agreement with the value obtained by Phookun et al. (1993). M 99 has a dynamical mass of ∼1.6 × 1011 M estimated from its rotation curve (Phookun et al. 1993) and the virial theorem. M 99 is located in the outskirts of the Virgo cluster, about 3.7 degrees (∼1.3 Mpc projected distance) northwest of the giant elliptical M 87 and just outside the region of strongest X-ray emission. Minchin et al. (2005) discount tidal origins for the cloud, though the position of the cloud on the outskirts of a large cluster, and the proximity of the H i disturbed spiral NGC 4254 (described above) warrant a closer investigation of the origins of the cloud.

The purpose of this paper is thus to investigate whether the tidal debris scenario is a viable explanation for apparently isolated massive H i clouds like VIRGOH i 21. Based on the numerical simulations on the formation of tidal debris in interacting galaxies in a cluster of galaxies, we particularly discuss:

  1. 1

    whether the observed physical properties of apparently isolated H i clouds, such as a wide velocity spread (ΔV∼ 200 km s−1) of the clouds and no visible counterparts, can be reproduced by the tidal debris scenario; and

  2. 2

    what are key observations that can discriminate between the two scenarios (i.e. ‘dark galaxy’ versus ‘tidal debris’).

We thus focus on the tidal stripping scenario, although ram pressure stripping can also be associated with the origin of isolated H i clouds (e.g. Vollmer, Huchtmeier & van Driel 2005). The present numerical results are discussed in a general way without direct comparison of the results with observations of specific targets (e.g. VIRGOH i 21), though the numerical model is more reasonable for galaxy evolution in the Virgo cluster.

The Model

Details of the disc galaxy models and the external gravitational potential of clusters of galaxies adopted in the present study have already been described in Bekki et al. (2005) and Bekki et al. (2003), respectively, so we give only a brief review here. We investigate the dynamical evolution of stellar and gaseous components in an interacting pair of late-type disc galaxies orbiting the centre of the Virgo cluster by using treesph simulations (Bekki et al. 2002). A late-type disc galaxy with a total mass of Mt, a total disc mass of Md, and a stellar disc size of Rs is assumed to be embedded in a massive dark matter halo with a universal ‘NFW’ profile (Navarro, Frenk & White 1996) with a mass of Mdm, and an exponential stellar distribution with a scalelength (R0) of 0.2Rs. The mass ratio of the dark matter halo to the stellar disc is set to be 9 for all models (i.e. Mdm/Mt= 0.9). The galaxy is assumed to have an extended H i gas disc with an initial size (Rg) of 2 ×Rs, which is consistent with observations (e.g. Broeils & van Woerden 1994). An isothermal equation of state is used for the gas with a sound speed of 5.8 km s−1 (corresponding to 2500 K). The adopted R0Md relation for disc models with different masses is described as:  

(1)
formula
which is consistent both with the observed scaling relation for bright disc galaxies (Freeman 1970) and with the Galactic structural parameters (Binney & Tremaine 1987).

The initial position (xi, i= 1, 2) and velocity (vi) of two interacting galaxies with respect to the cluster centre is described as:  

(2)
formula
and  
(3)
formula
respectively, where Xg(Vg) are the position (velocity) of the centre of mass of an interacting pair with respect to the cluster centre and Xi(Vi) is the location (velocity) of each galaxy in the pair with respect to their centre of mass. Xi and Vi are determined by the orbital eccentricity (e), the galaxy—galaxy pericentre distance (rp), and the mass ratio of the two (m2). Only one of the two interacting galaxies is modelled as a fully self-consistent disc described above whereas the other is modelled as a point mass with the total mass of m2×Mt. Accordingly, the total mass of a pair in a model is (1 +m2)Mt, which corresponds to 2.4 × 1011 M for the model M1 (See Table 1). The self-consistent disc model is inclined by θd (degrees) with respect to the orbital plane of the interacting pair.

Table 1

Model parameters and results.

Table 1

Model parameters and results.

To give our model a realistic radial density profile for the dark matter halo of the Virgo cluster and thereby determine Xg and Vg, we base our model on both observational studies of the mass of the Virgo cluster (e.g. Tully & Shaya 1984) and the predictions from the standard cold dark matter cosmology (NFW). The NFW profile is described as:  

(4)
formula
where r, ρ0, and rs are the distance from the centre of the cluster, the central density, and the scalelength of the dark halo, respectively. The adopted NFW model has a total mass of 5.0 × 1014 M (within the virial radius) and rs of 161 kpc. The centre of the cluster is always set to be (x, y, z) = (0, 0, 0) whereas Xg is set to be (x, y, z) = (Rini, 0, 0). Vg is set to be (vx, vy, vz) = (0, fvVc, 0), where fv and Vc are the parameters controlling the orbital eccentricity (i.e. the larger fv is, the more circular the orbit becomes) and the circular velocity of the cluster at R=Rini, respectively. The orbital plane of the pair is assumed to be inclined by 30 degrees with respect to the xy plane for all models. Thus Rini and fv are the two key parameters for the orbital evolution of the pair. We show the results of the models with fv= 0.5 and e= 1.5 (high-speed, hyperbolic encounters appropriate for cluster galaxy interaction) in the present study. The initial velocity of an interacting pair with respect to the cluster centre is 647 km s−1 for M1 and 621 km s−1 for M2, M3, and M4.

Although we investigated a large number of models, we only show the results of four representative models which produce relatively isolated gas clouds (i.e. tidal debris) without many stars. The model parameters and the resulting physical properties of the tidal debris are summarized in Table 1: Mg (column 7), fs (8), μB (9), and rsep (10) describe the total gas mass within a 100 kpc box within which relatively isolated tidal debris can be seen for each model (see Fig. 1), the mass fraction of stars within the debris, the B-band surface brightness of stars averaged over the 100 kpc box, and the distance of two interacting galaxies in each panel of Fig. 1, respectively. The occurrence of single or double tails depends strongly on the orbits and mass ratios. We emphasize the results of M4, because this model suggests that a past interaction between NGC 4254 and a galaxy (that can not be specified in the present study) can be responsible both for the origin of VIRGOH i 21 and for the morphological properties of NGC 4254 (e.g. the strong one-armed spiral structure and the one-sided tidal plume of gas). Additionally, the two galaxies in the M4 simulation experience a retrograde encounter, and as a result the inner stellar and gaseous components are not strongly disturbed, as is the case for NGC 4254 (Phookun et al. 1993).

Figure 1

Distribution of the stars (cyan) and gas (magenta) in an interacting galaxy pair within the Virgo cluster after ∼2 Gyr orbital evolution for our models M1 to M4. The distributions are projected on to the xy plane with the frame centre coincident with the centre of the disc galaxy. The bar in the lower left corner of each panel represents a scale of 50 kpc. The inserted box has a size of 100 kpc and indicates the location of relatively isolated tidal debris for which structural and kinematical properties are described in the text and in Table 1. The companion, which was modelled as a point mass, is outside the box; the separation between the two interacting galaxies after 2 Gyr is given in Table 1, column (10). Note that M1 and M2 models show leading and trailing H i tails, which have different shapes and densities.

Figure 1

Distribution of the stars (cyan) and gas (magenta) in an interacting galaxy pair within the Virgo cluster after ∼2 Gyr orbital evolution for our models M1 to M4. The distributions are projected on to the xy plane with the frame centre coincident with the centre of the disc galaxy. The bar in the lower left corner of each panel represents a scale of 50 kpc. The inserted box has a size of 100 kpc and indicates the location of relatively isolated tidal debris for which structural and kinematical properties are described in the text and in Table 1. The companion, which was modelled as a point mass, is outside the box; the separation between the two interacting galaxies after 2 Gyr is given in Table 1, column (10). Note that M1 and M2 models show leading and trailing H i tails, which have different shapes and densities.

The B-band mass-to-light ratio (Md/LB, where LB is the B-band luminosity of a disc) is assumed to be four for estimating the surface brightness of tidal tails and debris. We mainly investigate column density distributions and velocity fields of tidal debris for different viewing angles (θi), i.e. the angle between the z-axis and the line-of-sight that is always within the yz plane.

The models presented in this paper investigate high-speed hyperbolic encounters between the two galaxies, appropriate for cluster galaxy interactions. Specifically, all models have e= 1.5, with the galaxy—galaxy pericentre distances given Table 1. Under these conditions, the two systems will never merge. Accordingly, tidal interaction (rather than merging) between the two galaxies is one of the more important factors for the formation of isolated H i clouds in the present study.

Results

Fig. 1 summarizes the projected mass distributions of stars and gas after ∼2 Gyr dynamical evolution of interacting galaxies for the four models (M1, M2, M3 and M4). Stars and gas tidally stripped by the galaxy—galaxy interaction (and by the cluster tidal field) cannot return back to the host galaxies owing to the stronger cluster tidal field (e.g. Mihos 2004). As a result of this, they form either tidal debris at the tip of the tidal tails or faint ‘tidal bridges’ connecting the host galaxies. The tidal debris can have large H i masses (108–109 M) and be well detached from their host galaxies. The interaction partners have separated (∼100 kpc) from the tidal tails and debris which are then observed as relatively isolated H i clouds.

Tidal stripping has a much more noticeable effect on the gas than on the stars, because, in our model, the initial gas distributions in the discs are two times more extended than the stellar ones. Therefore, the mass fraction of stars can be small, ranging from 14 per cent (M1) to 57 per cent (M3) within the ‘isolated H i clouds’ (shown within the box of each model in Fig. 1). Stripped stars can be very diffusely distributed and consequently the mean B-band surface brightness (μB) within the 100 kpc box is 33.7 mag arcsec−2 (in model M1). The morphological properties of the gas and stars, the stellar mass fraction, and μB of the stars in the tidal debris (or ‘isolated H i clouds’) are quite diverse and depend on projections. For example, μB is 33.7 mag arcsec−2 for model M2 whereas it is 30.2 mag arcsec−2 for model M3. The derived very faint surface brightness suggests that it is almost impossible to detect any optical counterparts of the tidal debris with current large telescopes and reasonable exposure times.

Fig. 2 shows the column density distribution and velocity field of the tidal debris in model M1. It is clear from this figure that:

Figure 2

Gas column density distribution (left) and velocity field (right) for model M1. The cell size is 2.8 kpc and the viewing angle (θi) is 45°.

Figure 2

Gas column density distribution (left) and velocity field (right) for model M1. The cell size is 2.8 kpc and the viewing angle (θi) is 45°.

  • (i)

    the gaseous distribution is quite irregular and inhomogeneous with local column densities ranging from ∼1017 to ∼1019 cm−2;

  • (ii)

    there is a strong velocity gradient between the upper left and the lower right parts of the debris, but the overall velocity field is appreciably irregular; and

  • (iii)

    there is no clear sign of global rotation.

Result (i) implies that the observed morphology of the tidal debris depends strongly on the column density limit of the observations.

Fig. 3 shows that the simulated spectra (i.e. the integrated Vr distribution) of the gaseous debris can have a wide velocity range (>200 km s−1) for some viewing angles. But unless the gas is shown to be rotating, the velocity spread of the H i spectrum alone does not lead to an estimate of the cloud mass. Streaming motions within the tidal debris are responsible for the wide velocity spread of the gas in the present models. This kind of wide velocity spread in H i gas has been already observed for the relatively isolated massive H i cloud discovered by HIPASS within the NGC 2434 galaxy group (Ryder et al. 2001).

Figure 3

Simulated spectra of the gas in model M1. The normalized flux at each velocity Vr is derived by estimating the total mass of gas particles with radial velocities ∼Vr.

Figure 3

Simulated spectra of the gas in model M1. The normalized flux at each velocity Vr is derived by estimating the total mass of gas particles with radial velocities ∼Vr.

Fig. 4 illustrates how much the simulated velocity fields of the gas in our models differ from that of a regular rotating gas disc. It is a generic result of the present study that the velocity fields of tidal debris do not resemble the typical ‘spider diagrams’ which are characteristic of regular H i kinematics in disc galaxies that are supported by rotation against gravitational fields made by baryonic and dark matter of the galaxies. Velocity fields are the key observational tools to help us determine whether gas clouds are (unbound) tidal debris or are self-gravitating systems embedded within a massive dark matter halo.

Figure 4

Simulated velocity fields for the gas in the initial disc (upper left; inclined for comparison), and the tidal debris resulting from our models: M2 (upper right), M3 (lower left), and M4 (lower right). The colour bar at the bottom of each panel indicates the range of velocities (∼100 to 200 km s−1) in the simulated debris.

Figure 4

Simulated velocity fields for the gas in the initial disc (upper left; inclined for comparison), and the tidal debris resulting from our models: M2 (upper right), M3 (lower left), and M4 (lower right). The colour bar at the bottom of each panel indicates the range of velocities (∼100 to 200 km s−1) in the simulated debris.

Discussion and Conclusions

We have shown that tidal debris formed from interacting galaxies in clusters

  • (i)

    can have a wide velocity spread (>200 km s−1),

  • (ii)

    show μB of stars fainter than 30 mag arcsec−2, and

  • (iii)

    are located far (>100 kpc) from their progenitors.

Our results suggest that the H i cloud VIRGOH i 21, which lies at a distance of ∼150 kpc from the one-armed spiral M 99 (NGC 4254), is likely to be tidal debris rather than a ‘dark galaxy’. We stress that a detailed kinematical study of the H i gas in the extended region around M 99, and of the region between VIRGOH i 21 and M 99 in particular, is necessary to fully understand the origin of the peculiar H i gas.

H i stripped from disc galaxies by ram pressure of hot intracluster gas in clusters of galaxies may well be identified as isolated H i clouds like VIRGOH i 21. If this is the case, which is a more reasonable mechanism for the origin of isolated H i gas clouds like VIRGOH i 21, ram pressure stripping or tidal stripping? Since both models predict that optical counterparts of these H i clouds are hard to detect in currently available telescopes, the only way to answer the above question is to compare the observed H i properties with the simulated ones both for the ram pressure stripping model and for the tidal stripping one. We suggest that the strong velocity gradients along the tidal debris (like streaming motions) seen in the 2D velocity fields of the tidal stripping model (i.e. the present study) can be a key property that is not likely to be easily explained by the ram pressure model. H i structures created by ram pressure stripping would have morphologies and kinematics which varied linearly, whereas tidally generated features would be more structured both morphologically and kinematically. The complex 2D velocity fields shown in Fig. 4 would not be clearly seen in the ram pressure stripping model. We plan to investigate this point for the VIRGOH i 21 and the recently discovered H i cloud close to NGC 4388 (Oosterloo & van Gorkom 2005) in our future papers (Bekki, in preparation).

Recently discovered massive H i clouds with no apparent optical counterparts have provided new clues to several problems of extragalactic astronomy such as the origin of HVCs and intergalactic star-forming regions (e.g. Kilborn et al. 2000; Ryder et al. 2001; Ryan-Weber et al. 2004). Although previous numerical studies have tried to reproduce the observed structural properties of relatively isolated H i clouds (e.g. Bekki et al. 2005), they did not discuss the kinematical properties of the clouds extensively. Simulated velocity fields as well as particle/mass distributions are necessary for comparison with the observed gas kinematics in galaxies and surrounding material to better understand galaxy interactions in various environments.

Owing to the adopted assumption of Rg= 2Rs, both galaxy—galaxy interaction and the cluster tidal field are important for the formation of isolated H i clouds. This can be compared with our previous work (Bekki et al. 2005) in which the group tidal field alone can be responsible for the formation of intragroup H i rings and isolated clouds owing to the adopted assumption of Rg= 5Rs. We suggest that the initial sizes of gas discs (Rg) can determine whether global tidal fields of groups and clusters alone can be responsible for the formation of intragroup and intracluster H i gas clouds. It is not essential that the pair of interacting galaxies pass through the core of the cluster in order for isolated H i clouds to form. If the gas is raised beyond the tidal radius of the galaxy within the cluster, it will evolve away from the host. For those who are interested in more details of the formation processes in isolated H i gas clouds, movies with avi format are available at .

Acknowledgments

We are grateful to the referee John Hibbard for valuable comments. KB acknowledges the financial support of the Australian Research Council throughout the course of this work. The numerical simulations reported here were carried out at Australian Partnership for Advanced Computing (APAC).

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