A study of major mergers using a multi-phase ISM code
aa r X i v : . [ a s t r o - ph . GA ] A ug Astron. Nachr. / AN , No. 88, 789 – 794 (2009) /
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A study of major mergers using a multi-phase ISM code
J. Weniger ,⋆ , Ch. Theis , and S. Harfst Institut f¨ur Astronomie, Universit¨at Wien, T¨urkenschanzstraße 17, 1180 Wien, Austria Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, the NetherlandsThe dates of receipt and acceptance should be inserted later
Key words galaxies: interactions, galaxies: spiral, galaxies: ISM, ISM: clouds, stars: formationGalaxy interactions are a common phenomenon in clusters of galaxies. Especially major mergers are of particular impor-tance, because they can change the morphological type of galaxies. They have an impact on the mass function of galaxiesand they trigger star formation - the main driver of the Galactic Matter Cycle. Therefore, we conducted a study of majormergers by means of a multi-phase ISM code. This code is based on a TREE-SPH-code combined with a sticky particlemethod allowing for star formation controlled by the properties of a multi-phase ISM. This is in contrast to the usuallyimplemented Schmidt law depending mainly on the gas density. Previously, this code was used on isolated galaxies. Sinceour star formation recipe is not restricted to a special type of galaxy, it is interesting to apply it to interacting galaxies, too.Our study on major mergers includes a research of global properties of the interacting system, namely the star formationrate and the star formation efficiency, the evaporation and condensation rates, as well as the mass exchange of distinctcomponents, namely stars, diffuse ISM, and clouds. Investigating these properties provides insight to interrelations be-tween various physical processes. The results indicate that the star formation efficiency as well as the evaporation andcondensation rates are influenced by the interaction. c (cid:13) For some decades it has been known, that galaxy interac-tions play an important role in the evolution of galaxieschanging their morphological type or triggering star forma-tion. Since it is possible to take remarkable pictures of pe-culiar galaxies (see e. g. Arp 1966), the question was raisedif their features are a result of galaxy interactions. Peculiarfeatures are e.g. bridges connecting galaxies or tails protrud-ing from them. The above mentioned assumption seemedlikely, however, it was not clear until numerical simulationscorroborated it. The first simulations only considered gravi-tational forces (e.g. Holmberg 1941; Pleiderer & Siedentopf1961; Toomre & Toomre 1972; Barnes 1988), using differ-ent simplifications on the force calculation owing to thelimited computing power at that time. Nevertheless, thosesimulations already demonstrated, that interactions betweengalaxies change their appearance.Simulations became more sophisticated with increasingcomputer power. Hence, it was feasible to address topicsconcerning the interstellar medium (ISM). Though the ISMonly contributes approximately 10% of the mass of present-day galaxies, it is still an important ingredient: firstly, allstars are formed within the cold phase of the ISM, the mo-lecular clouds. Hence, it is necessary to consider this com-ponent in order to study the star formation rate during ga-laxy interactions. Secondly, the dynamics are strongly in-fluenced by hydrodynamics and especially energy dissipa-tion. Which properties of the ISM are considered depends ⋆ e-mail: [email protected] on the code used (see e.g. the review by Barnes & Hernquist1992). Our code incorporates a 3-phase ISM similar to theproposition by McKee & Ostriker (1977). The code was de-veloped in order to study Milky Way-like galaxies account-ing for several components, namely stars, dark matter, andthe three phases of the ISM (Harfst et al. 2006). The warmand hot phases are treated by smoothed particle hydrody-namics implemented similar to Hernquist & Katz (1989).The molecular clouds are modelled by the sticky particlemethod (for details refer to Theis & Hensler 1993). A sim-ilar code was used by Semelin & Combes (2002), but theyused a different sticky particle method and a different starformation prescription.Major mergers, that are interacting galaxies of aboutequal size, are studied by numerous authors. Often the re-search’s aim is to study the properties of the remnant galaxy(e.g. Barnes 1988; Springel & Hernquist 2005), or to lookfor substructures, such as tidal dwarf galaxies (Duc et al.2004; Bournaud & Duc 2006; Wetzstein et al. 2007). Othergoals are the reproduction of observed major mergers (e.g.Karl et al. 2008), or to study the overall properties of inter-acting galaxies, such as the star formation rate (e.g. Mihos &Hernquist 1996; di Matteo et al. 2008). While studying thestar formation most often the Schmidt-Kennicutt relation(Schmidt 1959; Kennicutt 1998) or some modification of itare used. The Schmidt-Kennicutt relation says that the starformation rate is proportional to the gas density, with theproportionality factor being a constant star formation effi-ciency. This work is distinct in that respect, since it does notuse the Schmidt-Kennicutt relation, but uses a star forma-tion prescription following Elmegreen & Efremov (1997). c (cid:13)
90 J. Weniger, Ch. Theis, & S. Harfst: A study of major mergers using a multi-phase ISM code
Fig. 1
A scheme of all physical processes connecting the differ-ent components of a galaxy. In addition, the gas looses energy byradiative cooling and the molecular clouds by inelastic collisions.
They found that the star formation efficiency is not fixed,but dependent on local properties of the ISM, i.e. the massof the star forming cloud and the pressure in the ambientISM.The main aim of this work is to study the evolutionof the star formation during a major merger. In particularwe are interested in understanding how a locally definedstar formation efficiency affects the star formation rate. Ourstudy also yields the mass exchange rates due to condensa-tion and evaporation.
The interaction participants are described by particles mim-icking distinct components of a galaxy, namely stars, dif-fuse gas, molecular clouds, and dark matter particles. Thosecomponents are connected by various physical processes(see Fig. 1). The processes condensation, evaporation, anda drag force due to ram pressure allow for matter and mo-mentum exchange between the diffuse ISM and the clumpymolecular clouds. Star formation and related feedback ofsupernovae type II and planetary nebulae close the circuitof matter. Energy dissipation is caused by radiative coolingin case of the diffuse ISM and by inelastic collisions in caseof molecular clouds. Since studying the evolution of starformation is the main aim of this work, the next section willdescribe its implementation in more detail. For a thoroughdescription of all other processes we refer to Harfst et al.(2006).
The site of star formation is known to be giant molecularclouds (e.g. Lada & Lada 2003). Since they are representedin our code by sticky particles, those particles have to be
Fig. 2
The star formation scheme according to Harfst et al.(2006). First the molecular cloud is inactive for a period τ ia ( t ).After that time span, a ”star cluster” is formed within the molecu-lar cloud provided that all other star formation criteria are fulfilled( t ). The mass of the embedded star cluster is dependent on thelocal star formation efficiency, ǫ . Finally, the cloud is fragmenteddue to energy input from supernovae type II and the ambient gasis heated ( t ). converted to star particles. The implementation of it worksas follows (Fig. 2): – We assume that it takes τ ia = 200 Myr till gas in amolecular cloud is able to form stars. During this timethe molecular cloud is inactive. In other words, star for-mation is suppressed as long as the age of the molecu-lar cloud, t now − t cld is smaller than τ ia . τ ia is the onlyfree parameter in our star formation prescription and canbe interpreted as a global star formation time scale. Itis gauged by the star formation rate of the Milky Way.Since the mean star formation efficiency, ǫ , in our sim-ulations is approximately 5% (see Fig. 4) and the totalmass in molecular clouds is approximately · M ⊙ (see Table 1), it gives a mean star formation rate of ap-proximately SFR = τ − · ǫ · M cld ≈ ⊙ yr − . – Afterwards stars can be formed. They stay embedded intheir parent molecular cloud. Their mass is determinedby the star formation efficiency, ǫ . A mass criterion anda pressure criterion prevent the formation of too smallstellar particles: the mass of the molecular clouds, m cld ,must exceed . · M ⊙ and the pressure at the posi-tion of the molecular cloud, P gas , must be higher than atenth of the ISM pressure at the position of the Sun inthe Milky Way, i.e. P ⊙ = 3 · K cm − (Elmegreen& Efremov 1997). Note, that the star formation effi-ciency is not constant, but it depends on local proper-ties, namely the gas pressure and the mass of the parentmolecular cloud. – After the most massive stars end their lives as super-novae, the molecular cloud fragments into four piecesof equal mass due to feedback by supernovae.
Following Harfst et al. (2006) the initial galaxies were con-structed by firstly generating a disk/bulge/halo - system us-ing the method of Kuijken & Dubinski (1995). In the nextstep, one fifth of the stellar disk particles were transformedinto molecular clouds and finally the diffuse ISM was addedas an initially slowly rotating homogeneous sphere, which c (cid:13) stron. Nachr. / AN (2009) 791 Table 1
Mass of distinct components of one galaxy andcorresponding number of particles
Component Mass [ M ⊙ ] NR. of particlesBulge-stars 0.17 10000Disk-stars 0.29 75098Clouds 0.04 36347Gas-particles 0.02 9017DM-particles 1.94 100000Total 2.46 230462 will collapse in the first 200 Myr forming a warm disk. Thecollisionless model of Kuijken & Dubinski (1995) realisesan equilibrium configuration. However, the equilibrium isaffected by adding the ISM and the above mentioned pro-cesses. Therefore, we follow the system’s evolution, untila quasi-equilibrium is established. The numerical integra-tion is done by means of a TREE-SPH code combined withthe sticky particle method (Theis & Hensler 1993). Gravita-tional forces are determined by the DEHNEN-Tree (Dehnen2002). See Harfst et al. (2006) for a more thorough descrip-tion.The relaxed galaxy has a mass of . · M ⊙ , thereof79% in dark matter particles. The remaining baryonic mat-ter consists of approximately 12% ISM particles - hence,molecular clouds and diffuse ISM - the rest being disk andbulge stars. The galaxy is realised by a total number of230462 particles. Note, that not only the mass, but also thenumber of clouds, SPH-particles, and disk stars as givenin Table 1 will change throughout the simulations: this iscaused by inelastic collisions, star formation, and feedback.The numbers of dark matter particles ( ) and bulge stars( ), on the other hand, stay constant throughout the sim-ulations. Both galaxies are of equal mass and their rotationis prograde. The galactic planes coincide with the orbitalplane. At t = 0 the galaxies are placed at a separation of100 kpc. Their initial speed is chosen to match a parabolicorbit with a minimum separation of 20 kpc. The run wasstopped at t = 3 Gyr . The code configuration allows to follow the evolution of dif-ferent components and their interrelations. To illustrate thetime evolution, a series of snapshots are plotted in Fig. 3exhibiting the surface density of the cold phase. The distri-bution of the cold phase resembles the distribution of thestars very well. This implies that dissipation does not affectthe cold phase severely. In contrast, the diffuse ISM shows aslightly different distribution (see also Fig. 7). The fist snap-shot of Fig. 3 (top, left) shows the initial configuration. Thefirst passage at t = 400 Myr is pictured in the second panel(top, middle). Afterwards, a series of snapshots features onthe one hand the expansion of the tails and on the other handthe development of a bridge, which vanishes gradually. Thebottom row of Fig. 3 shows a snapshot shortly before the second passage which takes place at t = 1520 Myr , the be-ginning of the merging at t = 1650 Myr , and a quiescentphase after the merging ( t = 2000 Myr ). The beginning ofthe merging is defined by the last local minimum in the po-tential energy of the system, after which the centre of massof the bulge components are no longer separating. In addi-tion, Fig. 4 shows the star formation rate, the star formationefficiency, the number of star formation processes per 10Myr, the evaporation and condensation rate and the evolu-tion of the masses of the different components. The verticaldashed lines in Fig. 4 indicate the first encounter, the secondencounter, and the beginning of the merging.The star formation rate shows fluctuations due to thelimited number of star formation processes during measure-ment intervals of 10 Myr. Still it is obvious that there is amaximum in the star formation rate at 1690 Myr, shortlyafter the merging starts. Another local maximum is givenat 610 Myr, that is 210 Myr after the first passage. How-ever, Fig. 4 suggests an enhanced star formation alreadyprior to the first passage. The period of enhanced star forma-tion located around the first passage is more than 400 Myrlong. In this setup, the reason for enhanced star formation isnot an enhanced number of star formation processes, but anenhanced star formation efficiency: the number of star for-mation processes does not correlate well with the star for-mation rate, but the star formation efficiency does, as onecan easily infer from the left side of Fig. 4. Only the en-hanced star formation prior to the first encounter cannot beexplained by an enhanced star formation efficiency. Here,it seems that the number of star formation processes is cru-cial. Although the mean star formation efficiency is only5%, the maximum star formation efficiency found within atime step can even exceed 50%. In general, Fig. 6 suggests,that the merging facilitates higher star formation efficien-cies. In fact, the maximum star formation efficiency is in themean about 9% higher after t = 1650 Myr . Fig. 5 features amap of the star formation efficiency at t = 550 Myr , hence150 Myr after the first passage. The star formation efficiencyis highest in the centre of the galaxies, but also sites of en-hanced star formation efficiency are recognised in the bridgeand the tails. Though the star formation rate is affected bythe interaction, it is still not extraordinary high. Previous re-search (e.g. Cox et al. 2004) implies that the magnitude ofthe star formation rate depends on the initial conditions, es-pecially on the orbit. Furthermore the fraction of mass inmolecular clouds might be too low to obtain a starburst ofseveral tens up to several hundreds M ⊙ yr − .Other important quantities are the evaporation and con-densation rates. The local maxima in the evaporation rate(at t = 630 Myr and at t = 1710 Myr ) take place approx-imately 20 Myr after the local maxima in the star forma-tion rate. This time interval corresponds to the time delaybetween star formation and feedback due to energy inputof supernovae. Note, however, that the time resolution isonly 10 Myr. The condensation rate has its maximum at ex-actly the same time the merging starts. During this episode c (cid:13)
92 J. Weniger, Ch. Theis, & S. Harfst: A study of major mergers using a multi-phase ISM code
Fig. 3
Snapshots of the interaction. Surface density maps of the clouds are shown (from left to right and top to bottom: t equals 0,400, 550, 750, 1000, 1250, 1500, 1650, 2000 Myr). The first passage takes place at t = 400 Myr, the second at t = 1520 Myr, and themerging starts at t = 1650 Myr.
Fig. 5
The star formation efficiency at t = 550 Myr . condensation outweighs evaporation. In general, however,evaporation exceeds condensation. The mean value for theformer is ⊙ yr − and for the latter . ⊙ yr − . A highcondensation rate coinciding with the beginning of the mer-ging, has also been found in other major mergers performedby us so far. The understanding of this remarkable featureand its implications will be the topic of further study. Fig. 6
Evolution of the maximum star formation efficiency.The three vertical dashed lines indicate the first passage, the sec-ond passage, and the beginning of the merging.
Altogether the mass evolution of distinct componentsshows the following features (see middle and bottom dia-gram of Fig. 4) – In general, the cloud mass is depleted by star formationwhile the stellar mass increases continuously. Further-more, the cloud mass decreases, because evaporation c (cid:13) stron. Nachr. / AN (2009) 793 Fig. 4
Evolution of star formation (left) and mass (right): the star formation rate (left, top), the evolution of the mean star formationefficiency (left, middle), and the number of star formation processes within a sampling period of 10 Myr (left, bottom). On the rightside, the evolution of the evaporation and condensation rates (top), the evolution of mass of stars (middle), and the evolution of massof the ISM (bottom) are plotted. The three vertical dashed lines indicate the first passage, the second passage, and the beginning of themerging. outweighs condensation. As a result only 3% of bary-onic matter are molecular clouds in the end of the sim-ulation. In comparison, the fraction of molecular cloudswas initially 8%. – Due to star formation and related feedback during thefirst passage the stellar mass as well as the mass of thediffuse ISM rises more steeply. – As a consequence of the merging accompanied by en-hanced star formation, the stellar mass increases rapidly.In Fig. 4 one can also distinguish a short period of time,within which the diffuse ISM is diminished by conden-sation, whereas the cloud mass increases.Fig. 7 shows a snapshot of the interaction at t = 550Myr - 150 Myr after the first passage. Different componentsare plotted separately in order to emphasise the multi-phaseproperties of our simulation. In the uppermost panel a sur-face density map of stars is shown. It is easy to pinpoint thetwo galaxies, a bridge connecting them, and tails protrud-ing from each of them. The cold molecular clouds (secondpanel from top) follow the distribution of the stars very well.However, the tail of the warm phase is considerably shorteras one can deduce from the third and forth panel which show a density map of the diffuse ISM and a temperature map, re-spectively. In the temperature map it is easy to identify twophases: a warm phase in the galactic disks, the bridge, andthe tails, and a hot phase primarily located in the halo, butalso in hot supernovae bubbles. The reason behind the short-ened tails is the initial setup of the diffuse gas component.Due to the initial collapse, the warm gaseous disk is initiallymuch smaller than the stellar disk and grows only slowly insize. At the beginning of the interaction the warm gaseousdisk is still smaller than the stellar disk. Since the utmostpart of the tail evolves from the utmost part of the disk, thetail of the warm ISM is not as extended as the stellar tail orthe tail of the cold phase.
We have presented a study of an equal size major merger bymeans of a multi-phase ISM code described in Harfst et al.(2006). We have focused on the evolution of the star for-mation rate as well as on the evaporation and condensationrates. The multi-phase nature of the code allows for an ex-tensive analysis of mass transfer involving galaxy interac- c (cid:13)
94 J. Weniger, Ch. Theis, & S. Harfst: A study of major mergers using a multi-phase ISM code
Fig. 7
This figure shows from top to bottom a surface densitymap of stars, a surface density map of clouds, a density map ofthe diffuse ISM, and a temperature map of the diffuse ISM at time t = 550 Myr (i.e. 150 Myr after the first passage). tions. Furthermore, the star formation prescription accord-ing to Elmegreen & Efremov (1997) allows to follow thestar formation efficiency during the interaction locally. Thestar formation rate as well as the star formation efficiencyincreases due to the first encounter and the merging of thenuclei. In the mean the star formation efficiency is only 5%,but at some locations, usually in the centre of the galaxies,but also in the bridge or the tails, the star formation effi-ciency can be much higher - up to 55%. Yet, a drawback ofour models is an initial gaseous disk which is smaller thanthe stellar disk resulting in a lack of SPH particles at thetip of the tails. Therefore, an improved setup of the SPHcomponent is needed in order to study substructures, suchas tidal dwarf galaxies, within the tip of the tails. Acknowledgements.
JW is a member of the Initiativkolleg (IK)’The Cosmic Matter Circuit’ I033-N of the University of Vienna.The numerical simulations were performed on the Grape cluster ofthe Institute of Astronomy of the University of Vienna. CT is grate-ful for financial support by the project TH511/9-1 within the DFGPriority Programme 1177 ’Galaxy Evolution’. SH is supported bythe NWO Computational Science STARE project 643200503.
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