THE INTERGALACTIC STELLAR POPULATION FROM MERGERS OF ELLIPTICAL GALAXIES WITH DARK MATTER HALOS

The population of gravitationally unbounded intergalactic (IG) stars has been recently observed in different environments, such as in poor groups (Feldmeier et al. 2004; Castro-Rodríguez et al. 2003), compact tidal groups (White et al. 2003), and nearby galaxy clusters (Ferguson et al. 1998; Durrell et al. 2002; Feldmeier et al. 2004; Gerhard et al. 2005), as well as in higher redshift clusters (Zibetti et al. 2005; Zibetti 2008). The amount of observed IG starlight seems to correlate with the environment, with more IG starlight found in populated clusters, and toward the cluster centers. Zibetti (2008) studied 683 clusters of galaxies, and found that the fraction of diffuse to total starlight decreases with the distances of the unbounded stars from the galactic centers, a result that is also supported by Murante et al.'s (2004) predictions.

Several mechanisms have been proposed to explain the origin of the IG starlight. Muccione & Ciotti (2004) associated the presence of IG stars to the evaporation of galaxies due to tidal interactions with other cluster members, and with the cluster potential well. Conroy et al. (2007) showed that more than 80% of the stars from tidally disrupted sub-halos contribute to the IG starlight.

As an alternative to tidally produced intracluster stars, we (Stanghellini et al. 2006, hereafter Paper I) have shown that dry mergers could produce an IG stellar population compatible with what has been observed to date in the intracluster. Our models in Paper I show that during the merging stage a number of stars from the progenitor systems become unbounded, and the IG to initial starlight obtained was broadly consistent with the observed intracluster star counts.

Murante et al. (2007) analyzed a large number of clusters from a cosmological simulation. They find that most of the stars in the IG stellar population come from the formation of the brightest cluster galaxy, and that most stars of this diffuse component come from merging events and only a minor fraction of the stars derive from tidal interactions.

In this paper, we extend our models of interacting galactic pairs, whose components have dark matter halos. There is now ample evidence that disk galaxies should host a fair amount of dark matter to account for their kinematics (see van Albada et al. 1985, and references therein). A further indication that elliptical galaxies have dark halos comes from cosmological simulations and the hierarchical merging paradigm (see, e.g., Oñorbe et al. 2007). It is thus appropriate to repeat the simulations of colliding pairs of elliptical galaxies as in Paper I, this time assuming that the initial galaxy models have dark halos. We perform our simulations keeping all other assumptions unvaried with respect to those of Paper I, so we can directly compare the results from both sets of simulations.

In Section 2, we introduce our models and all the assumptions made for the galaxies, the dark halos, the stellar populations, and the collisions. Section 3 illustrates the results from the dry-merger simulations, with particular attention to the production of the IG stellar population. The discussion, including comparing the new, dark-haloed models with those of Paper I, is given in Section 4. Section 5 presents the conclusions of our study.

We have performed a series of simulations of dry mergers of pairs of spheroidal galaxies with dark matter halos. We chose the mass ratio between the two colliding galaxies to be M₂/M₁ = 1 and 10.⁴

2.1. Galaxies, Initial Conditions

The initial conditions of the galaxies forming the colliding pairs are similar to those described by González-García & van Albada (2005), who performed a study of the encounters between two spherical systems with dark matter halos. We use the isotropic spherical Jaffe's (1983) approach to model the initial conditions of the luminous matter and the Hernquist (1990) model for the dark matter halos.

The potential for a Jaffe model is

$$\begin{equation} \phi _{\rm L}(r) = \frac{GM_{\rm L}}{r_{\rm J}} \ln \left(\frac{r}{r+r_{\rm J}}\right), \end{equation} \tag{ 1 }$$

where G is Newton's constant and r_J is the half-mass radius of the luminous component.

The potential of the Hernquist model is

$$\begin{equation} \phi _{\rm H}(r) = -\frac{GM_{\rm H}}{r+a}, \end{equation} \tag{ 2 }$$

where a is the scale length used. The half-mass radius of the dark halo component is equal to $(1 + \sqrt{2}) a$. We combined the Jaffe and the Hernquist model to reproduce the haloed galaxy. We obtained a two-parameter family of galaxies that depends on the luminous-to-dark mass ratio, M_L/M_H, and on the half-mass radius ratio,

$$\begin{equation} r_{L_{1/2}}/r_{\rm H_{1/2}} =\frac{r_{\rm J}}{(1+\sqrt{2})a}. \end{equation} \tag{ 3 }$$

The distribution function of the combined system is

$$\begin{equation} f_{\rm T}(E) =f_{\rm L}(E)+f_{\rm H}(E). \end{equation} \tag{ 4 }$$

An algorithm yielding f_L(E) and f_H(E) along the two-parameter family was developed by Smulders & Balcells (1995; see González-García & van Albada 2005 for a detailed description of the algorithm).

In the following, we adopt non-dimensional units with G = 1 for Newton's constant of gravity. The theoretical half-mass radius of the Jaffe model, r_J, and the total luminous mass of the fiducial galaxy in each run are also set to 1. The models may be compared with real galaxies using the following scaling, similar to the one employed in Paper I:

$$\begin{equation} [M] = 4\times 10^{11} \; {M_{\odot }}, \end{equation} \tag{ 5 }$$

$$\begin{equation} [L]= r_{\rm J} = 5 \;{\rm kpc}, \end{equation} \tag{ 6 }$$

$$\begin{equation} [T] = 8.34\times 10^6 \;{\rm yr}. \end{equation} \tag{ 7 }$$

By adopting these units, the velocity unit is

$$\begin{equation} [v] = 587\; {\rm km \; s^{-1}}. \end{equation} \tag{ 8 }$$

The initial systems are spherical and non-rotating, with an isotropic velocity distribution. In this regard they are similar to the set of spherical isotropic systems studied in Paper I.

The observed amount of dark matter in elliptical galaxies is controversial. Elliptical galaxies lack the reliable kinematic tracers that allow the detailed dynamical studies of spiral galaxies. Recently, there have been improvements in recovering the presence of dark matter in elliptical galaxies, such as in the X-ray study by Humphrey et al. (2006), via gravitational lensing (Treu & Koopmans 2004; Mandelbaum et al. 2006), and through stellar dynamics (Thomas et al. 2007). Chakrabarty & Raychaudhury (2008) have applied globular cluster kinematics to estimate a ratio of ∼10 for the dark to luminous mass in the elliptical galaxy NGC 4636. Romanowsky et al. (2003), from observations of the kinematics of planetary nebulae in the outer parts of elliptical galaxies, set a firm upper limit to the amount of their dark matter, although it has been noted that their results may be model dependent (Dekel et al. 2005).

In the present models, we have initially used a range of M_H/M_L values, and calculated the circular velocity curve for those realizations (keeping in mind that we use a composite of the Jaffe and Hernquist models), aiming at a flat-topped curve for a significant radial range. We obtained the best match for M_H/M_L = 2 and 10, and a halo scale length a = 2 which yield component ratios of M_T/M_L = 3 and 11. These ratios are consistent with the observations of Mandelbaum et al. (2006). The models presented here can be viewed as extrapolations of the Paper I models, where no dark matter halo was included (i.e., M_T/M_L = 1). Dark halos have been populated with 5 × 10⁵ particles for all galaxy models, except the smallest galaxy in run 10hP which has 10 times less particles.

The projected surface density of luminous material of such models presents a slope that decreases roughly as R^1/4, which makes it a suitable representation for elliptical galaxies, although the central parts present a cusp.

In Table 1, we summarize the characteristics of the initial models. Column 1 gives the run identification code, where the initial number indicates the mass ratio of the interacting galaxy pair, the small letter denotes the impact parameter (h is for head-on impact), and the capital letter denotes the energy of the orbit, with P for parabolic and Z for zero energy at infinity (or hyperbolic) orbit; Column 2 gives the total-to-luminous mass ratio of the initial galaxies; Column 3 gives the mass ratio of the colliding galaxies (where the masses represent the total masses for each galaxy); Column 4 gives the initial separation r_i, in model units; Column 5 gives the initial relative velocity of the galaxy pair, v_i, also in model units; and Columns 6 and 7 give, respectively, the impact parameter and the orbital energy of the initial setup.

Table 1. Galaxy Input Parameters

Run	MT/ML	M2/M1	ri	vi	b	Eorb
1hP	11	1	40	0.316	0	0
1hZ	11	1	40	1.048	0	0.250
10hP	11	10	19.48	0.336	0	0
1hP3	3	1	40	0.316	0	0

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To appropriately scale the models with mass other than 1, we impose that the luminous mass of initial systems must lie on the fundamental plane (FP) of galaxies which, according to Jørgensen et al. (1996), gives

$$\begin{equation} \log {\rm L} \simeq 0.78 \log {M_T} + {\rm constant}, \end{equation} \tag{ 9 }$$

and we use Fish's (1964) law to scale the radii of the luminous and dark components of the two systems.

Model 1hP is an equal mass encounter (M₁ = M₂) with the interacting galaxies set on a parabolic orbit. The centers of the two galaxies are placed at an initial distance of 4R₁, where R₁ = 10r_J is the galaxy radius. Model 1hZ is an equal mass encounter with the progenitors on a mildly hyperbolic orbit, with all the other parameters as in model 1hP. Model 10hP is an encounter between two galaxies with a mass ratio of 10 on a radial parabolic encounter, initially placed at a distance 3R₁ + R₂, where R₁ and R₂ are, respectively, the radii of the less and the more massive galaxies. Following the definitions above, R₂ = 10r_J and R₁ = 3.16r_J. Finally, model 1hP3 has the same orbital parameters as model 1hP, but with a different total-to-luminous component ratio of the progenitor system, M_T/M_L = 3.

The relative range of the mass of the galaxy pairs chosen for the simulations, M₂/M₁ = 1 or 10, is the extremes of the observed merging galaxy sample by van Dokkum (2005).

2.2. Stellar Components

2.3. Integration Method and Stability

The evolution of the runs and the final states are quite similar to those already described by González-García & van Albada (2005), we refer to the interested reader to that paper for a detailed description of the merger stages. We present a brief description here.

Galaxies in simulation 1hP evolve toward a first passage through pericenter at t = 80 (in model units of time). At this first encounter the systems exchange energy, the halos of the two galaxies already merge, and a fraction of both dark and luminous matter gains enough energy to escape. A similar situation is found in simulation 10hP, although with different timescales. Galaxies in simulation 1hZ, which has the highest initial orbital energy, merge after the first encounter and thus there is only a single release of particles. Simulation 1hP3 shows a different behavior due to the lower relative content of dark matter. The two systems meet at t ∼ 80, but the halos do not merge at this first encounter. A number of particles of the two systems, both dark and luminous, gain enough energy to escape. The two system meet again at t ∼ 150 and finally merge, again exporting some particles (dark and luminous) to the IG population. The simulations are stopped at time t = 200, i.e., t ∼ 1.67 Gyr.

Figure 1 shows the final distribution of the various types of particles in our encounter simulations; in each panel the x-axis represents the distance from the merger center, R, and the y-axis the binding,  E_bind, in dimensionless model units. We plot the results of different particles—from the left to the right panels: dark matter particles, then low-mass, intermediate-mass, and high-mass luminous particles are plotted. The dark and luminous particles show similar qualitative behavior. When the galaxy systems pass through the pericenter, particles gain kinetic energy and may end up having a positive binding energy. Simulation 1hZ presents a larger number of particles with positive binding energy than all other types of encounters. Simulations 1hP and 1hP3 show a moderate number of expelled particles. Finally, simulation 10hP shows very small number of particles with positive binding energy.

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In Figure 2, we plot the logarithm surface density calculated in annuli of increasing radius from the merger's centers versus  R^1/4, where R is the distance from the merger center. The different lines represent the total surface density (solid) and the surface density for each of the luminous populations (see the caption).

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The intermediate regions present a profile close to a de Vaucoleurs profile (see full straight line). The innermost (R^1/4 < 0.7) and outer regions deviate clearly from this profile. The inner parts are affected by the fact that our initial models have a core-like shape after the relaxation run. The outer regions deviate from the de Vaucouleurs profile due to the escaping IG material in a similar fashion as it was explained in Paper I. However, this deviation is less pronounced in the present models given the lower fraction of escaping particles. Deviations from the de Vaucouleurs' slope affected by the IG particles in the outer regions are important outside R^1/4 ∼ 2–2.5. These values are in agreement with those found in Paper I. The surface density excess with respect to a de Vaucouleurs fit (solid thin line) is larger for model 10hP than for model 1hP at large radii. This is due to the deposition of most luminous particles of the small galaxy at these large radii. In all models and at all radii the different populations contribute similarly to the IG population.

In each of the proposed simulations, a fraction of particles escapes the main galactic potential. In Table 3, we give the resulting IG population produced in each run: Column 1 gives the run code; Column 2 gives the mass bin; Column 3 gives the fraction of unbounded luminous mass (with respect to total luminous mass); Column 4 gives the fraction of the luminosity of unbounded particles, L_u, with respect to total luminosity, L_T; and Column 5 gives the fraction of the luminosity of unbounded particles versus the luminosity of the merger remnant, L_m. We also give, for each run and in Column 3, the mass of the total (luminous and dark) unbounded mass as a fraction of the total initial mass.

By examining Table 3, we note that the fraction of gravitationally unbounded mass is higher in the total than in the luminous matter. This is occurring because the dark halos extend further out than the luminous parts of the galaxies, thus the presence of the dark halo potential places the luminous matter deeper into the potential well. The fraction of total unbounded mass is roughly the same in runs 1hP and 10hP, thus it is independent of the initial mass ratio. It is, on the other hand, higher in 1hP3 due to the different internal structures and relative energies while varying the total mass of the dark halo. The situation is different for 1hZ, where the larger available energy results in 12% of the mass being expelled by the merging process.

The luminous mass expelled from the encounters of galaxies with dark halos in Table 3 is less than what was found in the models without dark halos (i.e., Paper I): we find that the modeled stellar-to-total unbounded mass after the parabolic encounters of galaxies with dark halos is about 15 times smaller than in models without dark halos (it goes down to 10 times for the hyperbolic encounters).

González-García & van Albada (2003) and Nipoti et al. (2003) demonstrated that a few merger events between systems on the FP do not destroy such relation (although see Nipoti et al. 2009). The merger remnants in our sample must obey a law like log  L ≃ 0.78log M_T + constant (Jørgensen et al. 1996; Equation (9)). In the present study, we have that M_T = M_L + M_H. Now, if we introduce this in Equation (9), we get

$$\begin{equation} \log \frac{L_1}{L_2}=0.78\log \frac{M_{\rm L1}}{M_{\rm L2}} + 0.78 \log \frac{(M_{\rm T1}/M_{\rm L1})}{(M_{\rm T2}/M_{\rm L2})}. \end{equation} \tag{ 10 }$$

We must translate the mass of our stellar particles into light. Our simulations are gravity-only simulations and we do not have their luminosity. To convert our stellar masses in luminosity we use the relation M_T/M_L ∝ M^0.17_T from Hyde & Bernardi (2009) combined with Equation (9). Both the progenitor and the merged systems are on the FP relation, but the unbounded material is not. So, at a first step we want to compute the following: L_u/L_m = (L₁ + L₂ − L_m)/L_m = (L₁/L_m) + (L₂/L_m) − 1. Using the above mentioned formulas, we get

$$\begin{equation} \frac{L_u}{L_m} = \left(\frac{M_1}{M_m}\right)^{0.94} + \left(\frac{M_2}{M_m}\right)^{0.94} - 1. \end{equation} \tag{ 11 }$$

And we can derive the fractions, which are included in Table 3. Finally, we find that the ratio of luminous unbounded to total material is L_u/L_T = L_u/(L_u + L_m) = 1/[(L_u + L_m)/L_u) = 1/(1 + (L_m/L_u)), also shown in Table 3.

In reviewing all our merging models we find that the total amount of the IG starlight is determined mainly by two factors: the amount of dark matter in the colliding galaxies and the energy of the encounter. The first factor is clearly accounted for when we look at simulations 1hP and 1hP3 from this paper and model 1hP in Paper I : the fractions of IG to total luminosity are ∼4%, ∼6%, and 17% for dark mass amounts of, respectively, 10, 2, and 0 times the amount of the luminous mass. On the other hand, increasing the mass ratio of the colliding galaxies (model 10hP) does not produce a significant increased IG population: the unbounded luminosity produced in this model is small when compared with the other simulations. This is reflecting the fact that most of the IG material originates, in this case, from the low-mass galaxy. This also implies that satellite-like or minor mergers should be at least between 2 and 10 times more frequent to get a similar IG stellar population than that produced by major mergers.

We can compare the present results and those in Paper I with other models and simulations. The semianalytic predictions of Purcell et al. (2007) claim that the intrahalo light should rise from 0.5% to 20% from galaxy halos to poor groups, while it should be between 20%and30% for rich groups and clusters. Such numbers for the IG light in poor groups are in rough agreement with our results for the simulations presented here for models with a dark halo, while their numbers for clusters are in closer agreement with our results from Paper I.

Observations might indicate an increase of the relative IG to total starlight as the mass of the group increases. Loose groups show fractions of the order of less than 2% (Castro-Rodríguez et al. 2003), while clusters like Virgo present fractions around 5%–10% (Arnaboldi et al. 2003) and massive clusters fractions larger than 10% (Feldmeier et al. 2004), although Zibetti et al. (2005) find that the fraction of IG to total starlight is almost independent of the cluster richness.

Aguerri & González-García (2009) show that a galaxy entering a dense environment is stripped away from the outer parts due to tidal stripping with other galaxies (galaxy harassment). The harassed galaxy has, as a consequence, a lower dark-to-luminous mass ratio. This transformation is more severe in dense environments where faster encounters are likely. Thus, denser environments should host systems with lower dark-to-luminous ratios. Conversely, groups should host systems with larger dark-to-luminous ratios.

In summary, in loose groups the potential well of the group is not large enough to strip the galaxy from all its dark matter halo. This scenario is likely to present mergers of galaxies with a fair amount of dark matter involved, like the ones investigated in this paper. The shielding effect of the dark halos should then prevent a large fraction of IG stars in these environments. Dense groups and rich clusters, in contrast, are environments where tidal stripping and tidal harassment with the halo potential should affect primarily the outer parts of the galaxies, stripping away the halo; this might have the effect of lowering the initial relative velocities and the components' dark-to-luminous ratio, and the galaxy pairs might undergo encounters such as those presented for 1hP3 in this paper, or those presented by Paper I. This could explain why these environments present a larger IG light fraction.

The parameter space explored here is naturally limited. In this sense, this paper and Paper I must be viewed as a first attempt. We test the assumption that most of the IG population come from dry mergers, so gaseous mergers involving disk galaxies, star formation, and re-processing are excluded from our modeling. Mergers between gas-free disk (S0-like) galaxies have recently been explored (Wu & Jiang 2009) with results compatible with those presented here.

Other caveats of our approach could be that we do not model the collisions arising from cosmological simulations, and thus we do not have fully cosmological conditions. Our dark matter halo is a Hernquist profile, which is a cored halo profile. However, cosmological simulations tend to produce cuspier density profiles (see, e.g., Navarro et al. 1996). We have run a test simulation with a Navarro–Frenk–White (NFW) dark matter halo profile, constructed with the software described by Widrow & Dubinski (2005), with initial conditions identical to run 1hP. The fractions of unbound light are L_u/L_m = 4.43% and L_u/L_T = 4.24%. These figures are roughly similar to those found in runs with shallower inner profiles. Although the NFW is deeper at the central parts, we must note that the unbound material is extracted from the outer layers of both colliding systems where the potential well is shallower.

Also, in clusters the matter distribution in satellite halos is modified and would be better tested with other profiles like those proposed by Springel et al. (2008). Such problems should be explored in the future using a re-simulation of a cluster or group area from a fully cosmological simulation. Finally, we must note that the IG light could have been pre-processed in groups and later accreted to a cluster, contributing with their share of already unbound stars (see, e.g., Rudick et al. 2006).

We have modeled dry mergers between pairs of elliptical galaxies populated with luminous particles, surrounded by dark matter halos, and predicted the extent of the IG stellar populations produced in these encounters. These simulations modeled different orbital parameters, mass ratios, and varying initial dark-to-luminous mass ratios. These simulations are an extension of those presented in Paper I, which were without dark matter halo.

The merger process injects orbital energy into the final system. Some particles, both luminous and dark, gain enough energy to become unbounded, populating the modeled IG space. The resulting fraction of unbounded to initial dark matter is larger than the corresponding fraction of luminous particles. We also find that the presence of a dark matter halo results in a lower amount of free-floating luminous particles, translating into an expectation of more intracluster or intragroup stars in low dark matter galaxy encounters.

An interesting point would be to know when particles become unbound and which dynamical process (violent relaxation, tidal stripping at pericenter...) is the dominant one. However, this is out of the scope of the present paper and will be investigated in forthcoming papers. Finally, the fraction of IG starlight observed in the different simulations presented in this paper are in rough agreement with those reported in analytical models and in observations of poor galaxy groups. The fractions presented in Paper I are in closer agreement with those observed in the intracluster.

We conclude that dry merging is a viable process to explain the IG unbound stellar population in many specific cases of low group density.

This work was partially supported by the MCyT (Spain) grant AYA2006-15492-C03-01 from the PNAyA, the regional government of Madrid through the ASTROCAM Astrophysics Network (S0505/ESP0237), and by NOAO. We thank the BSC in Barcelona for computing facilities at the MareNostrum supercomputer and at the La Palma node, and the Centro de Computación Científica (UAM, Spain). We thank the anonymous referee for interesting comments which helped to improve the quality of the paper. L.S. thanks the Observatoire de Paris for their hospitality while parts of this work was completed.