CAN DRY MERGING EXPLAIN THE SIZE EVOLUTION OF EARLY-TYPE GALAXIES?

, , , and

Published 2009 November 2 © 2009. The American Astronomical Society. All rights reserved.
, , Citation C. Nipoti et al 2009 ApJ 706 L86 DOI 10.1088/0004-637X/706/1/L86

1538-4357/706/1/L86

ABSTRACT

The characteristic size of early-type galaxies (ETGs) of given stellar mass is observed to increase significantly with cosmic time, from redshift z ≳ 2 to the present. A popular explanation for this size evolution is that ETGs grow through dissipationless ("dry") mergers, thus becoming less compact. Combining N-body simulations with up-to-date scaling relations of local ETGs, we show that such an explanation is problematic, because dry mergers do not decrease the galaxy stellar-mass surface density enough to explain the observed size evolution, and also introduce substantial scatter in the scaling relations. Based on our set of simulations, we estimate that major and minor dry mergers increase half-light radius and projected velocity dispersion with stellar mass as ReM1.09 ± 0.29* and σe2M0.07 ± 0.11*, respectively. This implies that: (1) if the high-z ETGs are indeed as dense as estimated, they cannot evolve into present-day ETGs via dry mergers; (2) present-day ETGs cannot have assembled more than ∼45% of their stellar mass via dry mergers. Alternatively, dry mergers could be reconciled with the observations if there was extreme fine tuning between merger history and galaxy properties, at variance with our assumptions. Full cosmological simulations will be needed to evaluate whether this fine-tuned solution is acceptable.

Export citation and abstract BibTeX RIS

1. INTRODUCTION

In the hierarchical model of structure formation, galaxy mergers are expected to play a central role in the assembly and evolution of galaxies. If present-day early-type galaxies (ETGs) have experienced mergers in relatively recent times (z ≲ 1–2), most of these mergers must have been dissipationless or "dry," because the old stellar populations of ETGs (e.g., Thomas et al. 2005) are inconsistent with substantial recent star formation.

Present-day ETGs satisfy several empirical correlations between half-light radius Re, central stellar velocity dispersion σ0, bulge luminosity L, stellar mass M*, black hole mass MBH, and gravitational lensing mass Mlens, such as the L–σ0 (Faber & Jackson 1976), LRe (Kormendy 1977), MBHL (Magorrian et al. 1998), MBH–σ0 (Ferrarese & Merritt 2000; Gebhardt et al. 2000), MBHM* (Marconi & Hunt 2003), MlensRe, and Mlens–σ0 relations (Nipoti et al. 2009, hereafter NTB09), the fundamental plane (hereafter FP, relating L, Re, and σ0; Dressler et al. 1987; Djorgovsky & Davis 1987) and the lensing mass plane (relating Mlens, σ0, and Re; Bolton et al. 2007, 2008b). The existence of these scaling laws has been used to establish that present-day ETGs did not form by several dry mergers of lower mass progenitors obeying the same scaling laws, because as an effect of dry mergers the galaxy size increases rapidly with mass, while the velocity dispersion remains almost constant, in contrast with the observed correlations (Ciotti & van Albada 2001; Nipoti et al. 2003; Boylan-Kolchin et al. 2006; Ciotti et al. 2007; NTB09).

Photometric and spectroscopic observations of high-redshift (z ≳ 1–2) ETGs suggest that these objects may be remarkably more compact than their local counterparts (e.g., Stiavelli et al. 1999; Daddi et al. 2005; Trujillo et al. 2006; Zirm et al. 2007; Cimatti et al. 2008; van der Wel et al. 2008; van Dokkum et al. 2008, hereafter vD08; Saracco et al. 2009). These findings contributed to renew interest in the proposal that dry merging might be a key process in the growth of ETGs, because it is one of the few known mechanisms able to make galaxies less compact (e.g., Khochfar & Silk 2006; Hopkins et al. 2009c; Naab et al. 2009; van der Wel et al. 2009). However, although dry merging works qualitatively in the right direction, it is not clear whether it works quantitatively.

In this Letter, we address the question of the viability of dry merging as a process driving the structural evolution of ETGs, by testing whether it is able to produce the local scaling laws with their relatively small intrinsic scatters. For this purpose, we use the set of numerical simulations of dissipationless minor and major mergers presented in NTB09 and test them against the stellar-mass scaling relations of the Sloan Lens ACS Survey (SLACS) sample of lens ETGs (M. W. Auger et al. 2009, in preparation). This strategy allows us to construct a direct link between the observed properties of high-redshift (z ≳ 1–2) galaxies—for which estimates of the stellar masses are available—and realistic simulated galaxies, in which the relative distribution of luminous and dark matter has been calibrated on the lensing-mass scaling relations (NTB09).

Throughout the Letter, we adopt Salpeter (1955) initial mass function (IMF), which is consistent with the gravitational lensing constraints for SLACS ETGs (Treu et al. 2009a). Observational data are converted to this calibration when necessary. The main results of this Letter do not depend on this choice, since they involve stellar-mass ratios and the IMF normalization effectively factors out.

2. OBSERVED STELLAR-MASS SCALING RELATIONS

In the present work, we consider the stellar-mass–size, stellar-mass–velocity-dispersion, and stellar-mass FP relations derived by M. W. Auger et al. (2009, in preparation) for the SLACS sample of lens ETGs, assuming Salpeter IMF stellar masses and using the velocity dispersions and rest-frame V-band half-light radii derived from Sloan Digital Sky Survey (SDSS) spectroscopy and Hubble Space Telescope photometry. The correlations are obtained using galaxies with stellar masses generally in the range 11 ≲ log M*/M ≲ 12.

The stellar-mass–size relationship is given by

Equation (1)

with intrinsic scatter in log Re at fixed mass 0.071. The stellar-mass–velocity-dispersion relation is

Equation (2)

where σe2 is the projected velocity dispersion within an aperture radius Re/2. This has an intrinsic scatter in log σe2 at fixed mass of 0.055. Finally, we consider the FP-like correlation

Equation (3)

where c* ≡ σ2e2Re/2GM* is a dimensionless structure parameter. The intrinsic scatter in log c* at fixed M* is 0.077.

We recall that SLACS lenses are indistinguishable from control samples of SDSS galaxies with the same stellar velocity dispersion and size, in terms of luminosity and distribution of environments (Bolton et al. 2006, 2008a; Treu et al. 2006, 2009b). In addition, as discussed in M. W. Auger et al. (2009, in preparation) the above scaling relations are consistent with other scaling relations derived for larger samples of SDSS galaxies with a similar range of masses (e.g., Hyde & Bernardi 2009): in particular the intrinsic scatter of the M*Re relation is consistent with the observed scatter of the widely used correlation found by Shen et al. (2003).

3. EFFECT OF DRY MERGERS ON COMPACT HIGH-z EARLY-TYPE GALAXIES

Here, we combine the scaling laws described above, observations of high-z ETGs, and the results of the N-body simulations presented in NTB09 to address the question of whether dry mergers can be responsible for the observed size evolution of ETGs. The set of simulations (see NTB09 for details) consists of both major and minor dry-merger hierarchies, i.e., sequences of two or three steps in each of which the galaxy mass increases by a factor of ∼2 as a consequence of either a binary equal-mass merger or the accretion of Ns smaller satellites. The seed galaxies and the satellites are spherical, with Navarro et al. (1996) dark-matter distribution, Dehnen (1993) stellar distribution (with central logarithmic slope γ = 1.5), and no gas. Altogether, we consider eight major-merger hierarchies (differing in the orbital energy and angular momentum of the galaxy encounters, and in the stellar mass fraction f* of the seed galaxies) and four minor-merger hierarchies (differing in f*, Ns, and in the phase-space distribution of the satellites' centers of mass). Each galaxy collision is followed up to the virialization of the merger remnant. In the second and third steps of the hierarchies the remnants of the previous steps are used to realize the initial conditions.

The seed galaxies (and consequently all the end products of each merging hierarchy) can be rescaled by fixing arbitrarily the simulation mass and length scales $\tilde{M}_*$ and $\tilde{r}_{*}$ (see NTB09). Though the relative effect of dry mergers on the galaxy structure and kinematics is independent of $\tilde{M}_*$ and $\tilde{r}_{*}$, it is useful to fix these quantities, without loss of generality, to make the comparison with observations straightforward. For our purpose, it is natural to consider seed galaxies with stellar masses and sizes similar to those of high-z ETGs. Here, we take as reference the sample of nine z ∼ 2.3 ETGs studied by vD08, having median stellar mass 〈M*〉 ≃ 2.7 × 1011M (assuming Salpeter IMF; Kriek et al. 2008) and median effective radius 〈Re〉 = 0.9 kpc. These galaxies have a factor of ∼5 smaller size than local ETGs of similar mass, as apparent from the central panel of Figure 1, where their median location in the M*Re plane can be compared with the stellar-mass–size correlation (1) observed locally.

Figure 1.

Figure 1. Structural parameter c* ≡ σ2e2Re/2 GM* (top panel), effective radius (central panel), and projected velocity dispersion (bottom panel) as functions of the stellar mass. The solid and dashed lines represent the local observed correlations (Equations (1)–(3)), with the associated intrinsic scatters. The big hexagon represents the median M* and Re for a sample of nine z ∼ 2.3 ETGs (vD08). The small hexagons with error bars represent the ETG 1255-0 (z = 2.186; vDKF09). The other points and error bars represent the average values and the 1σ scatters (due to projection effects) for the simulated galaxies of the merger hierarchies indicated in the top panel (f* is the stellar mass fraction, L is the orbital angular momentum modulus, and Ns is the number of satellites per step).

Standard image High-resolution image

We then fix $\tilde{M}_*$ and $\tilde{r}_{*}$, such that all our seed galaxy models have total stellar mass M* = 2.7 × 1011M and Re = 0.9 kpc (symbols inside the big hexagon in Figure 1). As a consequence, the velocity unit is given, so our seed galaxy models have projected velocity dispersions σe2 = 532 km s-1 (f* = 0.09) and σe2 = 579 km s-1 (f* = 0.02). In the M*–σe2 plane (bottom panel of Figure 1) these models (represented by the leftmost symbols in the diagram) lie well above the local observed correlation (2). We have little information on the velocity dispersion of high-z ETGs (see Cenarro & Trujillo 2009; Cappellari et al. 2009; van Dokkum et al. 2009, hereafter vDKF09): for 1255-0, an ETG at z = 2.186 with stellar mass M* ≃ 3 × 1011M (after conversion to Salpeter IMF) and half-light radius Re = 0.78 ± 0.17 kpc (Kriek et al. 2009), vDKF09 tentatively measured projected velocity dispersion 510+165−95 km s-1, consistent within the uncertainties with σe2 of our seed galaxy models (see Figure 1, bottom panel). Given the uncertainties on σe2, also the structural parameter c* is poorly constrained for high-z ETGs. Our seed-galaxy models—which were constructed to lie exactly on the lensing mass plane (NTB09)—have c* = 0.11 for f* = 0.09 and c* = 0.13 for f* = 0.02 (leftmost symbols in the top panel of Figure 1), consistent, for M* ∼ 3 × 1011M, with the correlation (3) found for SLACS galaxies, and also with the highly uncertain value of c* estimated for the high-z ETG 1255-0.

In Figure 1, the points with log M*/M > 11.6 show the location of the merger remnants of all steps of the hierarchies in the M*c*, M*Re, and M*–σe2 planes. For the adopted values of the length and mass scales, the timescale to complete one step of the merging hierarchies is in the range 0.5–1.7 Gyr, so all hierarchies can be comfortably completed in the ∼10 Gyr elapsing from z ∼ 2 to the present. The location of the merger remnants with respect to the local scaling laws is quite dependent on the details of their merging history, but it is apparent that all the merger remnants lie significantly below the M*Re relation and above the M*–σe2 relation. On average, minor mergers increase more the galaxy size than major mergers, consistent with the results of Naab et al. (2009), but we also find that different minor-merging events produce remnants with significantly different Re and σe2 for similar M*, even when the initial conditions differ just by the relative phase-space distribution of the centers of mass of the satellites and the central galaxy (see the rightmost pairs of stars in Figure 1).

The behavior of our minor-merger hierarchies in the M*–σe2 plane deserves some discussion. When a galaxy grows by accreting satellites on almost parabolic orbits (as is the case for our minor-merger steps; see NTB09), the virial velocity dispersion of the remnant is lower than that of the progenitor if the mass loss is negligible (Bezanson et al. 2009; Naab et al. 2009). The fact that in some of our minor-merger steps the remnant has slightly higher projected (and virial) velocity dispersion than the progenitor must be ascribed to the significant loss of luminous (see Figure 1) and dark (see NTB09) matter, which is known to have the effect of increasing the velocity dispersion (see Nipoti et al. 2003).

In general, the merger remnants lie close to the FP-like relation M*c*, consistent with previous studies considering the FP (González-García & van Albada 2003; Nipoti et al. 2003; Boylan-Kolchin et al. 2006) or the lensing mass plane (NTB09). An exception is the minor-merging hierarchy with f* = 0.02 seed galaxy (crosses in the diagrams), in which c* increases significantly with stellar mass, reflecting the relatively low M* and high σe2 due to substantial mass loss.

Altogether, considering both major- and minor-merger hierarchies, our results confirm that dry mergers bring compact ETGs closer to the observed correlations. However, quantitatively, the process is not efficient enough to explain the observed size evolution. We note that the final merger remnants (the end products of the last steps of the hierarchies) have exceptionally high stellar masses (M* ≳ 1012M), so one cannot invoke more growth via dry mergers to obtain systems with surface mass density as low as observed in local galaxies. Furthermore, velocity dispersion is approximately conserved along the merger hierarchies, and objects with σe2 ∼ 500 km s-1 are not observed in the local universe.

4. CONSTRAINTS ON THE STELLAR-MASS ASSEMBLY HISTORY OF PRESENT-DAY EARLY-TYPE GALAXIES

Taken at face value, the stellar masses and sizes of the high-z ETGs mean that these systems cannot evolve into present-day ETGs via dry mergers. However, possible observational biases in the high-z measurements (for instance, that the sizes are underestimated; Hopkins et al. 2009b) could make the discrepancy between high- and low-redshift systems smaller. Thus, if one only considers average properties, dry mergers may perhaps be still considered a viable evolutionary mechanism. However, recovering the average size of local ETGs is not sufficient: additional constraints come from the small intrinsic scatter of observed stellar-mass scaling relations, which constrains the dry-merger mass assembly history of present-day ETGs, independently of the actual compactness of their high-z counterparts. A first attempt of constraining the merging history of ETGs using the scatter in the stellar-mass–size relation was performed by Shen et al. (2003), who—on the basis of an analytic parameterization of the size growth due to dry mergers—found that a certain degree of fine tuning in the orbital parameters of the galaxy encounters is required in order to reproduce the local M*Re relation of their SDSS sample of ETGs. We take here a step further, by taking advantage of N-body merger simulations and up-to-date stellar-mass scaling laws, including information on stellar velocity dispersion.

We quantify the growth of galaxies by dry merging by approximating the dependence of the structural parameters on stellar mass with power-law functions (see NTB09 for the lensing-mass analogs): $R_{\rm e}\propto M_*^{\beta _{R}}$, $\sigma _{\rm e2}\propto M_*^{\beta _{\sigma }}$, and $c_*\propto M_*^{\beta _{c}}$. To each step of a hierarchy we associate a value of βR by calculating βR ≡ Δlog Re/Δlog M*, where Δ indicates variation between the remnant and the progenitor. The resulting 30 values of βR are distributed with average 〈βR〉 = 1.09 and standard deviation δβR = 0.29. Doing the same for βσ and βc, we get 〈βσ〉 = 0.07, δβσ = 0.11 and 〈βc〉 = 0.22, δβc = 0.13. Assuming that the galaxy merging history is characterized by slopes β normally distributed with these averages and standard deviations, we can use these quantities to describe how dry mergers move galaxies in the planes M*c*, M*Re, and M*–σe2: the relatively large values of δβ we find mean that dry mergers introduce substantial scatter in these planes.

For the dry-merging scenario to be viable it must not introduce in the scaling relations more scatter than observed. We can use this condition to constrain the properties of the candidate progenitors of local ETGs, assuming as working hypothesis that they formed by dry merging. Let us consider, for example, local ETGs with given stellar mass M'* in the range 1011–1012M probed by the SLACS sample: in Figure 2, the distributions (within 1σ) of c*, Re, and σe2 for these galaxies are represented by the vertical bars, while the loci in the M*c*, M*Re, and M*–σe2 planes of their allowed dry-merging progenitors are shown by the shaded areas. Galaxies lying out of these areas, growing by major or minor dry merging, would populate regions of the parameter space inconsistent with the local observed distributions at the reference mass M'*. It is apparent that the strongest constraint comes from the M*Re plane (central panel), where the allowed region for progenitors spans ∼0.26 dex in M*. This means that a growth in stellar mass by dry merging by more than a factor of ∼1.8 (and in size by more than a factor of ∼1.9) is excluded on the basis of our set of simulations. In other words, present-day massive (M* ∼ 1011–1012M) ETGs cannot have assembled, on average, more than ∼45% of their stellar mass through dry merging. Quantitatively, the constraints on the mass assembly history depend on the specific choice of the orbital parameters and mass ratios of the galaxies: in our set of merging hierarchy simulations there are more major than minor mergers, and we explore a wide range of orbital parameters. One might get different numbers by considering more minor-merging simulations or excluding parts of the orbital parameter space. For instance, if we consider only the eight minor-merger steps, we get 〈βR〉 = 1.30 and δβR = 0.40, giving an upper limit of ∼35% to the fraction of stellar mass assembled via dry mergers by local ETGs. In any case, it is clear that a remarkable degree of fine tuning is required to reproduce the tightness of the local scaling relations with dry mergers.

Figure 2.

Figure 2. Shaded areas represent the distributions in the M*c*, M*Re, and M*–σe2 planes of allowed dry-merging progenitors of local ETGs with stellar mass M'* (vertical bars). The upper and lower boundaries of the shaded areas correspond to 1σ of the distributions, while the solid lines within the shaded areas show their average values. c'*, R'e, and σ'e2 are the average values of c*, Re, and σe2 for local ETGs with mass M'*. The local observed correlations are plotted as in Figure 1.

Standard image High-resolution image

5. CONCLUSIONS

Dry merging makes galaxies less compact. For this reason it has been proposed to be the key to reconcile the compactness of high-z ETGs with the lower stellar-mass surface density of local ETGs.

Our quantitative analysis, based on N-body simulations, shows that it is very hard to reproduce with dry mergers the growth in size of a factor of ∼5 between z ≳ 2 and today reported in the literature for M* ∼ 1011M ETGs, because the average size growth produced by dry merging is not sufficient. The tightness of the local scaling laws of ETGs provides an additional and stringent constraint for the dry-merging scenario. As we have shown, generic dry mergers tend to increase the scatter rather than decrease it because they cannot preserve simultaneously the correlations between stellar mass, velocity dispersion and effective radius. On the basis of our set of major and minor merging simulations, we conclude that—independent of the actual compactness of higher-z ETGs—typical present-day massive ETGs did not assemble more than ∼45% of their stellar mass and grew more than a factor ∼1.9 in size via dry merging. A similar upper limit is also found for the total (dark plus luminous) mass assembly on the basis of the lensing-mass scaling laws (NTB09).

Is this then the end of dry mergers as a major evolutionary mechanism? The only way out could be provided by a high degree of fine tuning of the mix of progenitors and orbits. Although not a natural scenario in our opinion, this fine tuning could perhaps reproduce such tight scaling relations and thus save the day. A systematic exploration of cosmologically motivated merging hierarchies is necessary to find out whether such an extreme fine tuning actually occurs.

The question of what drives the apparent size evolution of ETGs remains open. A possibility is that a combination of different astrophysical processes and observational biases can do the job (e.g., Hopkins et al. 2009a), but it is not excluded that the answer is to be found exploring more exotic scenarios, such as those assuming non-standard dark matter (Lee 2009; Ferrer et al. 2009).

T.T. and M.W.A. acknowledge support from the NSF through CAREER award NSF-0642621, by the Sloan Foundation through a Sloan Research Fellowship, and by the Packard Foundation through a Packard Fellowship, and by NASA through grants from the Space Telescope Science Institute associated with programs 10494, 10798, and 11202. Some numerical simulations were run at CINECA, Bologna, with CPU time assigned under the INAF-CINECA agreement 2008-2010.

Please wait… references are loading.
10.1088/0004-637X/706/1/L86