Abstract

The recent discovery of hidden non-axisymmetric and disc-like structures in bright Virgo dwarf elliptical and lenticular galaxies (dE/dSph/dS0) indicates that they may have late-type progenitors. Using N-body simulations we follow the evolution of disc galaxies within a Λ cold dark matter (ΛCDM) cluster simulated with 107 particles, where the hierarchical growth and galaxy harassment are modelled self-consistently. Most of the galaxies undergo significant morphological transformation, even at the outskirts of the cluster, and move through the Hubble sequence from late-type discs to dwarf spheroidals. None of the discs is completely destroyed, therefore they cannot be the progenitors of ultracompact dwarf (UCD) galaxies. The time evolution of the simulated galaxies is compared with unsharp masked images obtained from Very Large Telescope (VLT) data and the projected kinematics of our models with the latest high-resolution spectroscopic studies from the Keck and Palomar telescopes.

1 Introduction

Early-type dwarfs (dE and dSO) are the most common type of galaxies in the nearby universe, yet their origin is still unknown. These galaxies are found nearly exclusively near bright galaxies and in groups or clusters. Their continuation or separation from the brighter elliptical sequence is currently debated (Graham & Guzmán 2003; Gavazzi et al. 2005). Formation scenarios include mainly two different hypotheses: (i) dEs and dSOs are primordial galaxies, (ii) they are the result of a morphological transformation of spiral and irregular galaxies accreting into the cluster. This latter idea is supported by some observations, i.e. the relative number density of dwarf early-type galaxies increases with the local galaxy density (Ferguson & Sandage 1991), suggesting that the environment drives galaxy evolution. Kormendy & Freeman (2004) investigated the systematic properties of dark matter haloes in late-type and dwarf spheroidal galaxies concluding that they form a single physical sequence as a function of the dark matter core mass. Moore, Lake & Katz (1998) have shown that galaxy harassment in clusters can transform spirals into spheroidals. Harassment can explain the morphological evolution of the small spiral and irregular galaxies observed in clusters at redshift z~0.4 (Dressler et al. 1994) into dwarf ellipticals in the nearby universe (Moore et al. 1996). Moreover, the radial velocities of early-type galaxies in the Virgo cluster seem to indicate that these galaxies are not an old cluster population (Conselice, Gallagher & Wyse 2001), but originate from infalling field galaxies. According to this evolutionary scenario, we expect to find nearby cluster galaxies that are currently undergoing morphological transformation and retain part of their disc nature. Recent observations confirm that early-type galaxies have a broad range of photometric and kinematical characteristics. Jerjen, Kalnajs & Binggeli (2000) and Barazza, Binggeli & Jerjen (2002) discovered hidden spiral structures and bar features in five bright dEs in the Virgo cluster, concluding that a sizeable fraction of all bright early-type dwarfs hosts a disc component. Spirals and discs were also observed within dwarf spheroidal galaxies in the Coma (Graham & Guzmán 2003) and Fornax clusters (De Rijcke et al. 2001). Furthermore, the degree of rotational support is found to vary from 0 to a value close to 1 expected for a galaxy flattened by rotation (De Rijcke et al. 2001; Pedraz et al. 2002; Simien & Prugniel 2002; Geha, Guhathakurta & van der Marel 2003; van Zee, Skillman & Haynes 2004a). The aim of this work is to follow the evolution of disc galaxies orbiting in a cluster environment using high-resolution N-body simulations and to compare the final harassed remnants with the latest photometric and spectroscopic data. Previous studies have suffered from low resolution, and they used idealized cluster models for the initial conditions. We aim to use sufficient resolution that we can follow the detailed morphological evolution, and we evolve the galaxy models within a cluster selected from a cosmological simulation. In addition, the model has cuspy cold dark matter (CDM) haloes and structural parameters as expected in the concordance cosmological model. This study complements that of Gnedin (2003), who studied the evolution of luminous early-type disc galaxies within a cosmological context.

The paper is organized as follows. In Section 2, we present the main characteristics of the galaxy models and the ΛCDM cluster used. The results of the three-dimensional simulations are illustrated in Section 3, while in Sections 4 and 5, we report a projected photometric and kinematical analysis of the simulated remnants and the comparison with observations.

2 Simulations

All the simulations have been carried out using pkdgrav, a parallel multistepping N-body tree code designed for high-force accuracy (Stadel 2001).

The galaxy model is a multicomponent system with a stellar disc embedded in a spherical dark matter halo and was constructed using the technique described by Hernquist (1993). The dark matter distribution initially follows a NFW (Navarro, Frenk & White 1996, 1997) profile, which is adiabatically contracted in response to baryonic infall (Springel & White 1999). The disc has an exponential surface density profile of the form  

(1)
formula
where Md and Rd are, respectively, the disc mass and radial scalelength (in cylindrical coordinates), while the thin vertical structure is characterized by the scaleheight zd, which sets the ‘temperature’ of the disc  
(2)
formula
The structural parameters of the disc and the halo are chosen so that the resulting rotation curve resembles that of a typical bulgeless late-type (Sc/Sd) disc galaxy (Courteau 1997; Persic & Salucci 1997). The model parameters are initialized following the same procedure as Mayer et al. (2002), which was based on the galaxy formation model of Mo, Mao & White (1998). The mass within the virial radius was set equal to 7 × 1010 M and the fraction of mass in the disc is ~6 per cent. The contribution of the different components to the global rotation curve, assuming a disc scalelength Rd= 1.5 kpc and a concentration c= 10 (where c is defined as c=rvir/rs, with rvir and rs, respectively, virial and scale radius of the NFW halo) is plotted in Fig. 1. The halo spin parameter, which sets the disc scalelength in our modelling, is λ= 0.045, where λ relates the angular momentum, J, and the total energy, E, of a system with virial mass Mvir through the relation λ=J|E|1/2G−1M−5/2vir. The model has a central surface brightness μB= 22 mag arcsec−2, assuming an initial V-band mass-to-light ratio (M/L) ≃ 4 (Geha, Guhathakurta & van der Marel 2002) and a B-V colour of 0.77 (van Zee, Barton & Skillman 2004b). The stellar disc satisfies the Toomre (Toomre 1964) stability criterion, which requires, for a rotational supported disc  
(3)
formula
where σR is the radial velocity dispersion, κ is the local epicyclic frequency and Σs the stellar surface density. The efficiency of swing amplification of a disc perturbation with m-fold symmetry is governed by a combination of Q and the parameter Xm2R/(4πm GΣs) (Toomre 1981). The radial profiles of Q and X2 are indicated in Fig. 2.

Figure 1.

The rotation curve of the initial galaxy model. The stellar and dark matter contributions to the total rotation curve are indicated.

Figure 1.

The rotation curve of the initial galaxy model. The stellar and dark matter contributions to the total rotation curve are indicated.

Figure 2.

Q and X2 parameters as function of radius (in units of the disc scalelength, Rd).

Figure 2.

Q and X2 parameters as function of radius (in units of the disc scalelength, Rd).

Each galaxy is modelled with 106 particles, 105 of which are in the disc. The gravitational softening is set to 0.5 kpc for the dark halo and 0.1 kpc for the disc particles. The galaxies were evolved for ~5 Gyr in a ΛCDM cluster with a mass at z= 0 comparable to that of Virgo (Mvir= 3.1 × 1014 M), concentration cNFW= 8.8 and a virial radius Rvir of 1.8 Mpc. The cluster, selected from a 300-Mpc cube simulation (Diemand, Moore & Stadel 2004b) with cosmological parameters ωΛ= 0.732, ωm= 0.268 and σ8= 0.9 (Spergel et al. 2003), was resimulated at high resolution and corresponds to the intermediate resolution cluster D9 of Diemand, Moore & Stadel (2004a). The number of particles within the virial radius is ~6 × 106 and the softening length is 2.4 kpc.

At z= 0.5, we replaced 20 random cluster particles (10 within the virial radius and 10 within 20 per cent of the virial radius) with the high-resolution galaxy model. Only one galaxy model is used, in order to isolate the effects of orbit on the evolution. We assigned to the centre of mass of each galaxy the same orbital position and velocity of the replaced particle. We replace particles rather than haloes so as not to bias the results by omitting ‘overmerged’ haloes. Internal velocities and lengths were rescaled according to the redshift and cosmology. In particular, the comoving velocities at a given redshift z are expressed in terms of the Hubble constant H(z) through the relation  

(4)
formula
where r and x are the physical and comoving coordinates, respectively, and a is the scalefactor 1/(1 +z).

3 Galaxy Evolution

Among the initial sample of 20 galaxies, only 13 are still within the cluster virial radius at z= 0, while the others lie on bound orbits between Rvir and 1.5Rvir. This result is consistent with the fact that about half of the haloes which are presently at the outskirts of the cluster (up to 2Rvir) have a pericentre smaller than Rvir (Moore, Diemand & Stadel 2004).

The evolution of many of the galaxies within the cluster is quite violent, which is due to a sequence of strong gravitational encounters with substructures and the global cluster potential. Most of the central galaxies lose a significant fraction of stars and undergo a complete morphological transformation from discs to spheroidal systems. In order to highlight the presence of hidden structures, we applied to the stellar component of the simulation results the unsharp masking technique (Buta & Crocker 1993; Erwin & Sparke 2002) as described in Barazza et al. 2002. This method consists of the following steps. The intensity of each pixel is replaced with the mean intensity of a given area around the pixel producing a smoothed image. The linear dimension of this area has to be close to the typical scale of the features that we want to uncover. The original image is then divided by the smoothed one. Fig. 3 illustrates the results of the unsharp masking applied to a galaxy of our sample, where the ESO's midas task filter/smooth is used for the image smoothing with a smoothing length of 30–40 pixel, corresponding to ~2 kpc.

Figure 3.

Unsharp masking technique applied to the stellar component of a simulated face-on galaxy (GAL5 of Table 1). The box size is ~20 kpc. Left frame: smoothed stellar surface density produced from the simulation output using beam by J. Stadel. Middle frame: the result of the unsharp masking on the former image, which reveals presence of a bar and a spiral pattern. Right frame: a noise filter is previously applied to the original surface density map, increasing the intensity of the grey channel for randomly selected pixels. As a result in the final unsharp image, the low-density structures disappear and only the bar and a ring feature are still visible.

Figure 3.

Unsharp masking technique applied to the stellar component of a simulated face-on galaxy (GAL5 of Table 1). The box size is ~20 kpc. Left frame: smoothed stellar surface density produced from the simulation output using beam by J. Stadel. Middle frame: the result of the unsharp masking on the former image, which reveals presence of a bar and a spiral pattern. Right frame: a noise filter is previously applied to the original surface density map, increasing the intensity of the grey channel for randomly selected pixels. As a result in the final unsharp image, the low-density structures disappear and only the bar and a ring feature are still visible.

Fig. 4 represents the different phases of the evolution of a galaxy transforming into a dE. The first stage of the evolution is characterized by the formation of a strong bar (Moore et al. 1998) and an open spiral pattern in the disc. The spiral arms are easily stripped, while the remaining material forms a ring structure around the bar. The bar+ring phase is quite stable and is apparent in the final state of several of the remnant galaxies. Often the ring is not directly visible in the simulation output, but is clearly seen after applying the unsharp masking. When gravitational heating due to tidal interactions removes the remaining spiral and ring features, only a naked bar remains. The bar usually undergoes a strong buckling instability and as a result the central part of the galaxy becomes more spherical. The buckled bar is subjected to further tidal heating and loses mass from its edges, becoming rounder the more encounters it suffers and the longer it evolves near to the cluster centre. Fig. 5 illustrates the evolution of bar and buckling instabilities for a representative galaxy which is orbiting close to the centre of the cluster at z= 0. Abar and Abuckling are the bar and buckling amplitudes, defined, respectively, as the Fourier decomposition of the phase of particles in the xy plane and of their vertical positions (Sparke & Sellwood 1987)  

(5)
formula
and  
(6)
formula
Fig. 6 shows a face and edge-on projection of the same galaxy during the buckling phase where the bar appeared at z= 0.3.

Figure 4.

Morphological transformation (face-on projection) of a disc galaxy into a dwarf elliptical (GAL8 of Table 1). From the top left to the bottom right: at t= 0.5 Gyr from the beginning of the simulation, and t= 1.4, 2.4, 4.8 Gyr. The box size is ~20 kpc. The step-like structures visible at the edges of the galaxies are due to features present in the low-density regions of the original smoothed stellar surface density maps, which are amplified by the unsharp masking.

Figure 4.

Morphological transformation (face-on projection) of a disc galaxy into a dwarf elliptical (GAL8 of Table 1). From the top left to the bottom right: at t= 0.5 Gyr from the beginning of the simulation, and t= 1.4, 2.4, 4.8 Gyr. The box size is ~20 kpc. The step-like structures visible at the edges of the galaxies are due to features present in the low-density regions of the original smoothed stellar surface density maps, which are amplified by the unsharp masking.

Figure 5.

Evolution of a representative galaxy (GAL7 of Table 1). Top panel: strength of the bar. Bottom panel: buckling amplitude. The bar forms at t= 1.1 Gyr and strongly buckles at t= 2.4 Gyr.

Figure 5.

Evolution of a representative galaxy (GAL7 of Table 1). Top panel: strength of the bar. Bottom panel: buckling amplitude. The bar forms at t= 1.1 Gyr and strongly buckles at t= 2.4 Gyr.

Figure 6.

Evolution of the stellar surface density of GAL7 from t= 1.4 to 0 Gyr. The colour scale is logarithmic. The top panels represent the face-on projection, while the corresponding edge-on projection is shown on the bottom. The buckling phase, which has a peak at t= 2.4 Gyr, does not destroy the bar, but makes the central vertical structure of the galaxy thicker.

Figure 6.

Evolution of the stellar surface density of GAL7 from t= 1.4 to 0 Gyr. The colour scale is logarithmic. The top panels represent the face-on projection, while the corresponding edge-on projection is shown on the bottom. The buckling phase, which has a peak at t= 2.4 Gyr, does not destroy the bar, but makes the central vertical structure of the galaxy thicker.

Depending on the orbit and on the number of close encounters that the galaxy suffers, the morphological transformation of the stellar component can be complete and produce a pure spheroidal system, or can lead to the formation of a more elongated structure, which still retains disc and bar features (Fig. 7). For a few galaxies orbiting closest to the cluster centre, the tidal effects from the cluster potential become dominant and the evolution is very rapid. Fig. 8 shows the tidal tails generated by a strong impulsive encounter. The stripped mass is a significative fraction of the total stellar mass and the surface density in the tails is comparable with that of the outer disc. We do not expect that these kind of structures will be easily observable in clusters, since their lifetime is quit short (≈0.2 Gyr) due to numerous encounters with other substructures that heat and dissipate the stripped material. Stripped stars tend to create a diffuse distribution around the remnants (see Fig. 9), and in regions close to the centre it is almost impossible to distinguish well-defined stellar streams, even from the debris of a small fraction of the true number of dwarf galaxies in clusters.

Figure 7.

Three different final states of the harassed galaxies (unsharp nosified images). From left to right: bar-like galaxy (GAL7 of Table 1), spherical spheroid (GAL6) and spiral galaxy (GAL3). The addition of noises often hides ring structures surrounding the central bar, which is the case of the first remnant on the left. In order to point out the characteristic structure of the remnants we used two physical scales: the two images on the left have a box side of ~12 kpc, while the box size of the spiral galaxy on the right is ~30 kpc.

Figure 7.

Three different final states of the harassed galaxies (unsharp nosified images). From left to right: bar-like galaxy (GAL7 of Table 1), spherical spheroid (GAL6) and spiral galaxy (GAL3). The addition of noises often hides ring structures surrounding the central bar, which is the case of the first remnant on the left. In order to point out the characteristic structure of the remnants we used two physical scales: the two images on the left have a box side of ~12 kpc, while the box size of the spiral galaxy on the right is ~30 kpc.

Figure 8.

Tidal tails of GAL6 (Table 1) generated during a pericentric passage (unsharp noisified image). These smooth features are visible only for a short time (typically about 0.2–0.3 Gyr) since they are heated and evaporated by continued encounters with cluster substructures.

Figure 8.

Tidal tails of GAL6 (Table 1) generated during a pericentric passage (unsharp noisified image). These smooth features are visible only for a short time (typically about 0.2–0.3 Gyr) since they are heated and evaporated by continued encounters with cluster substructures.

Figure 9.

Intracluster light produced by tidal processes. The colour contrast is chosen in such a way as to point out the low-density regions (light green, corresponding to a surface brightness μ≲ 30 mag arcsec−2) and the traces of stellar streams.

Figure 9.

Intracluster light produced by tidal processes. The colour contrast is chosen in such a way as to point out the low-density regions (light green, corresponding to a surface brightness μ≲ 30 mag arcsec−2) and the traces of stellar streams.

Table 1 summarizes the main properties of the remnant galaxies. The initial model has a virial radius of 85 kpc and the effective radius of the stellar distribution is 2.5 kpc, defined as the radius containing half of the light of the galaxy. While almost all the galaxies lose more than two-thirds of the dark matter halo, galaxies located at outskirts of the cluster do not experience a significative amount of star loss, even if their stellar structure can be perturbed producing open spiral patterns and asymmetric features (last frame on the right of Fig. 7). For these remnants, the reduction of the effective three-dimensional radius, re, is related to the formation of a bar that increases the central stellar density. On the other hand, galaxies orbiting closer to the cluster centre lose up to 90 per cent of their stellar mass, and the decrease of re corresponds to a real decrease in the size of the stellar component. In a few cases, the galaxy loses much more dark matter than stars and becomes baryon dominated in the central region. This is due to the fact that the orbits of the dark matter particles in the halo are more eccentric than those of the star particles, and therefore reach the tidal radius more easily. Table 1 shows that the loss of stellar mass is not a simple function of the mean orbital radius or apocentric/pericentric distance from the cluster centre, confirming the importance of harassment. According to Knebe et al. (2005), tidal interactions with other satellites account for about 30 per cent of the total mass loss experienced by a satellite halo. The last two columns of Table 1 give the mean axial ratios within 2re. There is a clear correlation between the c/a ratio (the flattening of the stellar component) and the final stellar mass. As shown in Fig. 10, massive stellar remnants have smaller c/a values and retain more of their initial disc nature, while galaxies that have lost most of their stars tend to be more spheroidal. The final state is always quite prolate, with the exception of GAL6 and GAL8 (the first two points in the upper left corner of Fig. 10), which are close to spherical. In the case of the less perturbed galaxies, this is due to the fact that the radius 2re defines an area roughly corresponding to the bar region, while most of the other galaxies retain part of the radial anisotropy that originated during the bar phase (Mayer et al. 2001). Fig. 11 illustrates the morphological and kinematic evolution of the stellar component of four representative galaxies of our sample. Each set of three panels represents the galaxy distance from the central cluster (top), the axial ratios (middle) and the ratio between the maximum rotational velocity vmax and the mean velocity dispersion graphic (bottom) as a function of time. All these quantities are measured within 2re. Both shapes and kinematics are not characterized by a smooth evolution, but present peaks and drops not necessarily connected to pericentric passages and indicative of tidal effects associated with close encounters with substructures. The initial steep decrease in the b/a ratio is instead related to the formation of the bar in the inner regions of the disc.

Table 1.

Final state of the remnants. The second column indicates, when available, the apocentric and pericentric distances of the last orbit. For each galaxy, we list three-dimensional (spherically averaged) tidal rt and effective re radius (in kpc), dark matter Mh and stellar Ms mass (in units of 109 M). The tidal radius is calculated using SKID (Stadel 2001), while re is the radius containing half of the light. The last two columns indicate the axial ratios (intermediate and short axis to major axis, respectively) measured within 2re.

Table 1.

Final state of the remnants. The second column indicates, when available, the apocentric and pericentric distances of the last orbit. For each galaxy, we list three-dimensional (spherically averaged) tidal rt and effective re radius (in kpc), dark matter Mh and stellar Ms mass (in units of 109 M). The tidal radius is calculated using SKID (Stadel 2001), while re is the radius containing half of the light. The last two columns indicate the axial ratios (intermediate and short axis to major axis, respectively) measured within 2re.

Figure 10.

Final flattening of the remnants plotted versus the fraction of stellar mass within the tidal radius at z= 0.

Figure 10.

Final flattening of the remnants plotted versus the fraction of stellar mass within the tidal radius at z= 0.

Figure 11.

Each set of three vertical panels represents the morphological and kinematic evolution of a galaxy from Table 1: orbital radius (top panel), axial ratio (centre) and anisotropy parameter (bottom). In the middle panel, the solid line represents the intermediate/major axis ratio b/a, while the dashed line is the short/major axis ratio c/a. The vertical solid lines indicate the pericentric passages. Note that the vertical scale of the top panel in GAL6 differs from the others.

Figure 11.

Each set of three vertical panels represents the morphological and kinematic evolution of a galaxy from Table 1: orbital radius (top panel), axial ratio (centre) and anisotropy parameter (bottom). In the middle panel, the solid line represents the intermediate/major axis ratio b/a, while the dashed line is the short/major axis ratio c/a. The vertical solid lines indicate the pericentric passages. Note that the vertical scale of the top panel in GAL6 differs from the others.

4 Photometric Analysis

In order to compare the results of our simulations with observations, and in particular with Barazza, Binggeli & Jerjen (2003), we selected the remnants within the virial radius at z= 0 (first 13 galaxies of Table 1) and projected them along a random line of sight.

The isodensity contours of the projected discs were fitted with ellipses using the midas task fit/ell3. The ellipses' centres, ellipticity and position angle were considered as free parameters of the fitting procedure. The isophotal contours of a representative galaxy (GAL9) are shown in Fig. 12. Ellipticity and position angle profiles are plotted in Fig. 13, where the independent variable is the equivalent radius graphic, and ap and bp are the major and minor axis of the projected remnant. Even though there is no well-defined trend in the ellipticity profiles, galaxies that preserve a bar component are generally characterized by large ellipticities in the central 2–3 kpc and by a drop in the outer regions. Often, the inner 0.5 kpc exhibits a very low ellipticity corresponding to a small nuclear component produced by buckling instabilities, whereas the external drop is more likely due to disc heating. Rounder systems have a wider range of profiles, with eccentricities that may even increase with radius, as in the case of GAL1

Figure 12.

Elliptical contours of GAL9. A strong isophotal twist is evident in the outer region (see also Fig. 13).

Figure 12.

Elliptical contours of GAL9. A strong isophotal twist is evident in the outer region (see also Fig. 13).

Figure 13

Each set of three vertical panels represents the photometric characteristics of a galaxy from Table 1: B-band surface brightness (top panel), ellipticity (centre) and position angle profile (bottom). The coordinate rp is the equivalent radius graphic, where ap and bp are the major and minor axes of the projected remnant. The Sérsic r1/n model is superimposed on the surface brightness profile (red solid line) and the corresponding best-fitting parameters are given in the top right of the panel. The central surface brightness μ0 is expressed in ‘mag arcsec−2’, r0 is in ‘kpc’ and the shape parameter n is a pure number, which represents the deviation of the profile from an exponential law.

Figure 13

Each set of three vertical panels represents the photometric characteristics of a galaxy from Table 1: B-band surface brightness (top panel), ellipticity (centre) and position angle profile (bottom). The coordinate rp is the equivalent radius graphic, where ap and bp are the major and minor axes of the projected remnant. The Sérsic r1/n model is superimposed on the surface brightness profile (red solid line) and the corresponding best-fitting parameters are given in the top right of the panel. The central surface brightness μ0 is expressed in ‘mag arcsec−2’, r0 is in ‘kpc’ and the shape parameter n is a pure number, which represents the deviation of the profile from an exponential law.

The next step of this analysis consists of calculating the surface brightness profiles of the projected remnants. In order to derive a luminosity, we need to assign an M/L. We expect that the ISM would be rapidly stripped by ram pressure effects such that star formation is truncated shortly after the galaxies enter the cluster environment. In this case, roughly 8 Gyr from the beginning of the simulation, the stellar M/L will have increased by about a factor of 1.5-2 (Mayer et al. 2001). For this reason, we used a B-band M/L~6 for the final remnants. The cumulative light profiles were determined by integrating the light of each galaxy in elliptical apertures with increasing equivalent radius (midas task integrate/ellips) and fixed centre, ellipticity and position angle. For these parameters, we adopted their mean values within a radius corresponding to half of the disc size, in order to avoid uncertainties in the isophote-fitting procedure due to the low-density external regions. In Table 2, we list the effective radius of each projected galaxy defined by rep, which is the radius at which the cumulative light profile reaches half of the value that it has at the isophotal level of 28 mag arcsec−2 (upper B-band magnitude limit in Barazza et al. 2003).

Table 2.

Effective radii (in kpc) of the projected remnants calculated using the integrated light curves. In most of the cases, they do not deviate considerably from the values obtained for the three-dimensional galaxies. A significative exception is GAL13, a disc system viewed almost edge-on.

Table 2.

Effective radii (in kpc) of the projected remnants calculated using the integrated light curves. In most of the cases, they do not deviate considerably from the values obtained for the three-dimensional galaxies. A significative exception is GAL13, a disc system viewed almost edge-on.

The surface brightness profiles, obtained by differentiating the cumulative light curve with respect to the equivalent radius rp (Barazza et al. 2003), are plotted in Fig. 13. The oscillation in the profiles of GAL3 and GAL12 reveals the presence of spiral arms viewed almost face on (Fig. 14), which enhance the local stellar density and produce abrupt changes in the position angle and eccentricity profiles.

Figure 14.

Surface density distribution of the two remnants presenting a nearly face-on spiral pattern. The physical size of both the images is ~12 kpc.

Figure 14.

Surface density distribution of the two remnants presenting a nearly face-on spiral pattern. The physical size of both the images is ~12 kpc.

The intensity profiles between 0.1 kpc (softening length for the stellar component) and the isophotal level of 27 mag arcsec−2 were fitted with a Sérsic profile  

(7)
formula
where I0 (central intensity), r0 (scalelength) and n (shape parameter) are the free parameters of the fit. For n= 1 the Sérsic model corresponds to an exponential law, while a shape parameter n= 4 is indicative of a de Vaucouleurs profile. Converting intensities to surface brightnesses, equation (7) becomes  
(8)
formula
where μ0 is the surface brightness corresponding to I0.

The fitting curves and parameters of those galaxies for which it was possible to fit with a Sérsic model are indicated in Fig. 13. The range of surface brightness parameters agrees quite well with the observations of dwarf galaxies in Virgo. The central surface brightness of our remnants is on average slightly higher than the values observed in B-band by Barazza et al. 2003, who fitted Sérsic profiles over similar radial intervals, the scalelengths obtained from the fitting procedure are comparable with their results. Also note that the quoted central surface brightness values are Sércic fits extrapolated to r= 0. The actual values at our resolution limit are somewhat fainter (Table 3). Galaxies with the smallest values of the shape parameter, n, are not well fitted by a Sérsic profile in the central part. This is the case of GAL4 — apparently a pure spheroidal system with high ellipticity, in reality characterized by a disc component seen edge-on — and of GAL7, which is still an asymmetric bar-like system with a large central nuclear component with small ellipticity values. For GAL7, we also show surface brightness profiles, ellipticity and position angles for the face-on and the end-on projections (Fig. 15). The smallest central ellipticity is associated with the end-on projection, where the bar is viewed down the major axis. Only the less massive remnants GAL6 and GAL8 have surface brightness profiles approaching to exponentials (n~1).

Table 3.

Parameters of the Sérsic fit: central surface brightness (in mag arcsec−2), surface brightness at the softening radius, scalelength (kpc) and shape parameter.

Table 3.

Parameters of the Sérsic fit: central surface brightness (in mag arcsec−2), surface brightness at the softening radius, scalelength (kpc) and shape parameter.

Figure 15.

B-band surface brightness, ellipticity and position angle profiles of the face-on and end-on projections of GAL7.

Figure 15.

B-band surface brightness, ellipticity and position angle profiles of the face-on and end-on projections of GAL7.

5 Kinematics

We attempt to measure the kinematics of the remnants in a similar way as previous authors measuring dwarf galaxies in the Virgo cluster. We measure the kinematics of the 13 projected galaxies analysed in Section 4 using a 0.3 × 12 kpc slit, which corresponds, at the distance of Virgo (15.3 Mpc, Freedman et al. 2001) to 3 × 40 arcsec2. This radial range is comparable with the slit length adopted by van Zee et al. 2004a and allows us to observe in most of the galaxies the turnover of the rotation curve, while the thickness of the slit was set to the softening length of 0.1 kpc. The slit was positioned along the major axis of the projected remnant centred on the galaxy, and star particles within the slit area were binned into a grid. For each grid interval with more than 15 particles — excluding thus the most weakly bound particles at the edges of the system — we calculated the mean particle velocity (relative to the centre of mass of the galaxy) and velocity dispersion along the line of sight. For the two smallest remnants GAL6 and GAL8, we increased the number of bins in order to obtain more precise velocity curves. The resulting kinematic profiles are indicated in Fig. 16, where for each galaxy the line-of-sight velocity (left-hand panels) and velocity dispersion (right-hand panels) are plotted as a function of the radial distance along the major axis. In most of the cases, the remnants lose a large fraction of rotation velocity, but only for one galaxy (GAL6) we do not observe any significative rotation along the major axis. GAL8 shows a well-defined symmetric rotation pattern although its peak velocities is only ~7 km s−1. GAL6 and GAL8 do not show evidences for structures or disc features and are spheroidal systems with a c/a ratio larger (Table 1) than the other remnants and surface brightness profiles well fitted by exponential laws. Moreover, they are quite small (Ms≤ 1.5 × 109 M) baryon-dominated galaxies presently orbiting at ≈100 kpc from the cluster centre.

Figure 16.

Projected kinematic profiles of the remnants within the cluster virial radius at z= 0. The line-of-sight velocity (left-hand panels) and the velocity dispersion (right-hand panels) are plotted as a function of the radial distance along the major axis.

Figure 16.

Projected kinematic profiles of the remnants within the cluster virial radius at z= 0. The line-of-sight velocity (left-hand panels) and the velocity dispersion (right-hand panels) are plotted as a function of the radial distance along the major axis.

Is the lack of rotation observed in GAL6 due to a projection effect, i.e. we are looking at the face-on projection of a rotating system, or is it physically significative?Fig. 17 illustrates the kinematic profiles of GAL6 and GAL8 for different inclinations of the remnant: from the top to the bottom i= 0°, which corresponds to a face-on projection, i= 45° and 90° (edge-on). The last panel on the bottom represents an end-on galaxy, with inclination i= 90° and the three-dimensional major axis aligned with the line of sight. GAL6 shows traces of rotation only for i= 0, with a maximum rotational velocity vmax= 3.7 km s−1, while the other projections have no well-defined rotation curves and values of vmax≲ 2.7 km s−1. In the case of non-rotating galaxies, we estimated an upper limit for vmax by differentiating the average velocities on each side of the major axis and dividing by 2 (Geha et al. 2002). In the calculation of vmax for i= 0° and 90° we excluded points with velocity dispersion larger than 80 km s−1, representing stars close to the tidal radius of the remnant. The projected motion of these stars with respect to the centre of mass is due to stripping processes and not rotation. On the other hand, GAL8 has always a well-defined rotation pattern and there is no preferential direction with zero rotation. Among the other galaxies characterized by low rotation velocities (see Fig. 16), GAL2, GAL9 and GAL10 are more massive systems compared to the two spheroids GAL6 and GAL8, but have still high c/a values, while the low line-of-sight velocity of GAL12 is not related to a morphological transformation, but is simply due to the fact that it is a spiral galaxy viewed face on (Fig. 14).

Figure 17.

Projected kinematic profiles of GAL6 and GAL8 for i= 0° (face-on orientation), i= 45°, i= 90° (edge-on) and i= 90° with the three-dimensional major axis aligned with the line of sight (end-on projection). The line-of-sight velocity (left-hand panels) and the velocity dispersion (right-hand panels) are plotted as a function of the radial distance along the projected major axis.

Figure 17.

Projected kinematic profiles of GAL6 and GAL8 for i= 0° (face-on orientation), i= 45°, i= 90° (edge-on) and i= 90° with the three-dimensional major axis aligned with the line of sight (end-on projection). The line-of-sight velocity (left-hand panels) and the velocity dispersion (right-hand panels) are plotted as a function of the radial distance along the projected major axis.

On the basis of this limited sample we expect non-rotating and slowly rotating dwarfs to have internal and environmental properties substantially different from the rotating ones. In particular, the former seems to be the product of a violent morphological transformation accelerated by the proximity of the cluster centre. This result is apparently in contradiction with Geha et al. (2003), who finds no relationship between the amount of rotation and the morphology or the orbital properties of the galaxies in their sample.

From Fig. 16 it appears evident that although the galaxies lose significant amounts of mass, the velocity dispersion can rise up to 50 km s−1 in the central 1–2 kpc. This is due to the bar formation and the transformation of circular to more radial orbits. The velocity dispersion profiles are typically decreasing at larger radii, but they rise again in those galaxies for which the slit semilength approaches or exceeds the tidal radius.

As the ratio between rotational velocity and velocity dispersion decreases, the galaxy loses rotational support and the flattening becomes dominated by anisotropic pressure. The degree of rotational support can be expressed in terms of the anisotropy parameter (v/σ)* (Binney 1978), defined as  

(9)
formula
where v is the rotational velocity, graphic and are ε the mean projected velocity dispersion and ellipticity, respectively. The theoretical prediction for a rotationally flattened spheroidal is given by (v/σ)*~1 (Binney & Tremaine 1987) and is represented in Fig. 18 by a continuous solid line. Galaxies well below this curve have significant velocity anisotropy.

Figure 18.

The ratio of the maximum rotational velocity, vmax, to the mean velocity dispersion, graphic, plotted versus the mean isophotal ellipticity. Stars represent the simulated sample, while open triangles, open squares, filled triangles and open circles show observational data from van Zee et al. (2004a), Geha et al. (2003), Pedraz et al. (2002) and Bender & Nieto (1990), respectively. For galaxies observed both by Geha et al. (2003) and van Zee et al. (2004a) we assumed the values of vmax and graphic provided by the latter work. Filled circles indicate data relative to dwarf spheroidals in the Fornax cluster from De Rijcke et al. (2003). The solid line represents the theoretical prediction for a galaxy flattened by rotation from Binney & Tremaine (1987).

Figure 18.

The ratio of the maximum rotational velocity, vmax, to the mean velocity dispersion, graphic, plotted versus the mean isophotal ellipticity. Stars represent the simulated sample, while open triangles, open squares, filled triangles and open circles show observational data from van Zee et al. (2004a), Geha et al. (2003), Pedraz et al. (2002) and Bender & Nieto (1990), respectively. For galaxies observed both by Geha et al. (2003) and van Zee et al. (2004a) we assumed the values of vmax and graphic provided by the latter work. Filled circles indicate data relative to dwarf spheroidals in the Fornax cluster from De Rijcke et al. (2003). The solid line represents the theoretical prediction for a galaxy flattened by rotation from Binney & Tremaine (1987).

In order to compare our results with observations, we plotted in Fig. 18 the ratio of the maximum rotational velocity, vmax, to the mean velocity dispersion, graphic, within a radius of 6 kpc versus the mean isophotal ellipticity calculated in the same radial range. In the same plot, we show the observational results for most of the dwarf galaxies in Virgo with published kinematics. We also plot the data for dwarf galaxies in the Fornax cluster by De Rijcke et al. (2003). Some of the galaxies in Fig. 18 (VCC 543, VCC 917, VCC 1036, VCC 1261 and VCC 1308) were observed by both Geha et al. (2003) and van Zee et al. (2004a), using the Keck II and Palomar telescope. The observations of van Zee et al. (2003), which cover a larger radial extent due to the aperture size, gives to significantly higher values of vmax with respect to Geha et al. 2003. This appears to be due to the fact that the smaller slit used by the latter authors only samples the inner rising part of the rotation curve and does not include the maximum value. For example, VCC 917 and VCC 1308, classified as non-rotating galaxies (both with vmax= 0.4 km s−1) by Geha et al. 2003, have vmax > 10 km s−1 according to van Zee et al. 2003, while the rotation curves of the slowly rotating dwarfs VCC 543 and VCC 1036 (vmax= 13 and 14 km s−1 in Geha et al. 2003) peak beyond 15 arcsec with vmax > 40 km s−1. Most of the simulated remnants have a similar range of ellipticities and graphic as the observed dwarfs, even if it is clear that we have some difficulties in reproducing galaxies with a degree of rotational support close to zero. On the other hand, it is possible that the low graphic ratio of some galaxies is due to the small radial range covered by the observations. In order to understand how much the slit length influences the results, in Fig. 19 we plotted the v/σ ratio of the projected remnants as a function of the radial distance along the slit. In most of the cases, v/σ increases with radius (with the remarkable exception of GAL1 whose rotational support drops beyond r= 2.5 kpc). Using a 4-kpc slit, we would find 10 galaxies below graphic, three well below graphic, which is the upper limit assumed by Geha et al. (2003) for non-rotating dwarfs. Increasing the slit length up to 8 kpc, the number of galaxies with a low degree of rotational support is still quite high (seven galaxies with graphic and four with graphic), but only GAL6 has still a graphic, as in the case of the adopted slit length of 12 kpc.

Figure 19.

graphic
v/σ ratio as a function of the radial distance along the major axis for the 13 projected remnants of Fig. 16.

Figure 19.

graphic
v/σ ratio as a function of the radial distance along the major axis for the 13 projected remnants of Fig. 16.

6 Conclusions

We follow the evolution of late-type disc galaxies as they evolve within a hierarchically forming galaxy cluster using N-body simulations. We use a single-galaxy model to explore the effects of cluster-centric position and orbit. Our resolution is such that we can compare with Keck and Palomar kinematics and Very Large Telescope (VLT) imaging data. We find the following.

  1. The cluster environment can be responsible for triggering bar and buckling instabilities.

  2. Tidal shocks with dark matter substructures and the mean cluster potential are both important at driving the evolution from discs to spheroidal structures. However, galaxies within the inner 100 kpc suffer the most complete transformation and mass loss.

  3. None of the discs are completely destroyed and since the surface brightness of our discs within two times the effective radius is well above the resolution limit of the Hubble Space Telescope (HST) photometry (Drinkwater et al. 2003), we do not expect to create ultracompact dwarf (UCD) galaxies by progenitor discs with cuspy dark haloes.

  4. More tidal heating leads to more mass loss, which leads to rounder galaxies.

  5. The kinematics (v/σ) of the stellar remnants is similar to observations of Virgo and Fornax dE/dSph galaxies. Only the most severely disrupted galaxies that lose most of their stellar mass become completely pressure supported. Most of the remnants retain a significant amount of rotational motion.

  6. Unsharp masked images of the galaxies show similar hidden bar and spiral features as some cluster galaxies. These gradually disappear as the galaxies suffer more heating. Our results could be rescaled in time and mass to make statements about possible disc progenitors entering group or even galactic environments. The next step is to self-consistently follow the evolution of galaxies as they form and evolve in different environments.

Acknowledgments

We would like to thank Jürg Diemand for providing the cosmological cluster simulation. We are grateful to Alister Graham, Andrea Macciò, Fabio Barazza, Marla Geha, Frank van den Bosch and Stelios Kazantzidis for useful discussions. The numerical simulations were performed on the Zbox () supercomputer at the University of Zürich. CM and RP are supported by the Swiss National Science Foundation. VPD is supported by a Brooks Fellowship at the University of Washington.

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