A&A 614, A66 (2018) Astronomy https://doi.org/10.1051/0004-6361/201832855 & c ESO 2018 Astrophysics Timescales of major mergers from simulations of isolated binary galaxy collisions J. M. Solanes1, J. D. Perea2, and G. Valentí-Rojas1 1 Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, C. Martí i Franquès, 1, 08028 Barcelona, Spain e-mail: [email protected] 2 Instituto de Astrofísica de Andalucía, IAA–CSIC, Glorieta de la Astronomía s/n, 18008 Granada, Spain Received 19 February 2018 / Accepted 27 April 2018 ABSTRACT A six-dimensional parameter space based on high-resolution numerical simulations of isolated binary galaxy collisions has been con- structed to investigate the dynamical friction timescales, τmer, for major mergers. Our experiments follow the gravitational encounters between ∼600 pairs of similarly massive late- and early-type galaxies with orbital parameters that meet the predictions of the Λ-cold dark matter (ΛCDM) cosmology. We analyse the performance of different schemes for tracking the secular evolution of mergers, find- ing that the product of the intergalactic distance and velocity is best suited to identify the time of coalescence. In contrast, a widely used merger-time estimator such as the exhaustion of the orbital spin is shown to systematically underpredict τmer, resulting in relative errors that can reach 60% for nearly radial encounters. We find that the internal spins of the progenitors can lead to total variations in the merger times larger than 30% in highly circular encounters, whereas only the spin of the principal halo is capable of modulating the strength of the interaction prevailing throughout a merger. The comparison of our simulated merger times with predictions from different variants of a well-known fitting formula has revealed an only partially satisfactory agreement, which has led us to recalculate the values of the coefficients of these expressions to obtain relations that fit major mergers perfectly. The observed biases between data and predictions, which do not only apply to the present work, are inconsistent with expectations from differences in the degree of idealisation of the collisions, their metric, spin-related biases, or the simulation set-up. This indicates a certain lack of accuracy of the dynamical friction modelling, arising perhaps from a still incomplete identification of the parameters governing orbital decay. Key words. galaxies: halos – galaxies: interactions – galaxies: kinematics and dynamics – methods: numerical 1. Introduction history of galaxies (e.g. Lidman et al. 2013; Tasca et al. 2014), but also in that of their central supermassive black holes A consequence of the hierarchical nature of structure formation (SMBH) and the subsequent triggering of nuclei activity (e.g. in a cold dark matter (CDM) Universe is that dark haloes are Foreman et al. 2009; Yu et al. 2011; Liu et al. 2011; Koss et al. built through the merging of earlier generations of less massive 2012; Capelo et al. 2017). haloes. To cause gravitationally bound interactions between Virtually all formulas that are currently used to esti- extendedlf-gravitating haloes (and their galaxies) typically mate the merger time, τmer, are based on the idealised requires a dissipative process that reduces the initial orbital Chandraseckhar(1943) description of the deceleration caused energies of the colliding objects. Dynamical friction fulfils this by dynamical friction on a point mass (representing the role by transferring energy and momentum from their relative satellite) travelling through an infinite, uniform, and colli- motion to internal degrees of freedom. As a result, the orbits sionless medium (representing the host). They are mostly of interacting galaxies evolve and may eventually decay and prescriptions inferred from the analytic or semi-analytic mod- culminate in a merger. elling of mergers (e.g. Lacey & Cole 1993; van den Bosch et al. The accurate determination of the merging timescales driven 1999; Taffoni et al. 2003; Gan et al. 2010; Petts et al. 2015; by dynamical friction is therefore a centrepiece of studies of the Silva et al. 2016) or parametric equations tuned by direct evolution of galaxies. For example, in semi-analytic models of comparison with the outcome of numerical simulations of galaxy evolution, the merger times are directly involved in the collisions of live galaxy pairs (e.g. Boylan-Kolchin et al. assessment of many fundamental quantities such as the luminos- 2008; Jiang et al. 2008; Just et al. 2011; McCavana et al. 2012; ity/stellar mass function, the amount of gas available to form new Villalobos et al. 2013), or both (e.g. Colpi et al. 1999). However, stars, the star formation rate, the abundance of first-ranked galax- although several decades of studies of galactic mergers have al- ies, and the distribution of galaxy sizes, metallicities, colours, lowed reaching a general consensus on what probably are the and morphologies (e.g. Kauffmann et al. 1993; Lacey 2001; most relevant parameters in any process of this type, the ex- Ricciardelli & Franceschini 2010; Hirschmann et al. 2012; tent of their impact is still a matter of debate. Factors such as Benson 2012; Muñoz-Arancibia et al. 2015). Of all galaxy- continued mass losses due to tidal interactions, the drag force galaxy interactions, the class of so-called major mergers, exerted by tidal debris, the re-accretion of some of this mate- involving pairs of objects with similar mass, are especially rial onto the colliding galaxies, or the mutual tidal distortion of relevant as they play a central role, not only in the assembly their internal structures are elements that introduce nontrivial Article published by EDP Sciences A66, page 1 of 17 A&A 614, A66 (2018) uncertainties in any attempt to calculate τmer using analytical goal was to establish whether it holds true that when the initial expressions. To these difficulties, which are caused by physical conditions governing mergers are similar, so is their duration, complexity, one must add the lack of a 100% standard method- regardless of the local distribution of matter around the galax- ology regarding the way mergers are tracked. The starting point ies. We have found a relatively important bias between measured of this work is precisely the definition of a new metric for cal- and estimated times, however, that we had not anticipated, whose culating τmer, which is an obligatory first step to compare the magnitude and behaviour surpass what would be expected from outcomes of different experiments under equal conditions and differences in the degree of idealisation of the merger context derive universally valid formulas, in a form that is suitable for (isolated versus cosmological), in the metric, or in the configu- major mergers. With this aim, we have run a suite of nearly 600 ration of the simulations. The present investigation is completed high-resolution N-body simulations of isolated major mergers, by using our simulations to recalculate the coefficients of the with which we further explored the dependence of the merger most popular versions of the merger-time formula with the aim time on a range of orbital parameters and on the mass-ratios, of providing analytical prescriptions that are suitable for major spins, and morphologies of the progenitors that are representa- mergers. tive of such systems. This then is the layout of the paper. In Sect.2 we present Several reasons justify the realisation of this type of re- our suite of simulated binary collisions. After discussing differ- search with controlled experiments. On one hand, they in- ent alternatives for tracking major mergers and measuring their volve a substantial increase in resolution with respect to what length, the new, accurate metric for major mergers is defined would feasible in an entirely cosmological context, at least for in Sect.3, while in Sect.4 we explore the dependence of τmer samples of binary collisions as large as ours, allowing both on a series of parameters that are known to regulate the effec- host and satellites to have more realistic internal structures. tiveness of dynamical friction. Finally, in Sect.5, we first com- On the other hand, we aim to extend former studies that focussed pare the outcome of our simulations with the predictions from a on the duration of mergers from the standpoint of isolated systems well-known set of parametric models for τmer and conclude by by correcting their main weaknesses, for instance, the systematic readjusting the coefficients of these models, so that they offer an adoption of ad hoc initial conditions, such as strongly radial or- improvement in the predicted timescales for major mergers. bits and small pericentric distances. Although there is some phys- After outlining our conclusions in Sect.6, we conclude with two ical basis in this approach, the intention is above all to lead to fast appendices that provide details for the provision of rotation to merging that saves CPU time (e.g. Khochfar & Burkert 2006). our haloes (AppendixA) and the strategy we followed to relate In addition, the initial equilibrium galaxy models of controlled in- the initial conditions of our simulated galaxy pairs to their sub- vestigations of dynamical friction, especially the oldest ones, fre- sequent orbital evolution driven by gravity (AppendixB). quently do not conform to the paradigm that is currently accepted Physical scales are calculated throughout the manuscript for these systems by including haloes with a parameterisation of assuming a standard flat ΛCDM cosmology with present-epoch their internal structure (e.g. isothermal) that is derived from first values of the Hubble parameter, and total mass and dark energy −1 −1 principles, and sometimes, with the just minimum extension re- density parameters equal to H0 = 70 km s Mpc , Ωm;0 = 0.3, quired by the observed flatness of the rotation curves of galactic and ΩΛ;0 = 0.7, respectively.