Ring galaxies from off-centre collisions
aa r X i v : . [ a s t r o - ph . C O ] N ov Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 25 November 2018 (MN L A TEX style file v2.2)
Ring galaxies from off-centre collisions
M. Mapelli & L. Mayer INAF-Osservatorio astronomico di Padova, Vicolo dell’Osservatorio 5, I–35122, Padova, Italy, [email protected] Institute for Theoretical Physics, University of Z¨urich, Winterthurerstrasse 190, CH–8057, Z¨urich, Switzerland
25 November 2018
ABSTRACT
We investigate the formation of RE galaxies (i.e. of collisional ring galaxies with anempty ring), with N-body/SPH simulations. The simulations employ a recipe for starformation (SF) and feedback that has been shown to be crucial to produce realisticgalaxies in a cosmological context. We show that RE galaxies can form via off-centrecollisions (i.e. with a non-zero impact parameter), even for small inclination angles.The ring can be either a complete ring or an arc, depending on the initial conditions(especially on the impact parameter). In our simulations, the nucleus of the targetgalaxy is displaced from the dynamical centre of the galaxy and is buried withinthe ring, as a consequence of the off-centre collision. We find that the nucleus is notvertically displaced from the plane of the ring. We study the kinematics of the ring,finding agreement with the predictions by the analytic theory. The SF history of thesimulated galaxies indicates that the interaction enhances the SF rate. We comparethe results of our simulations with the observations of Arp 147, that is the prototypeof RE galaxies.
Key words: galaxies: interactions – galaxies: peculiar – methods: numerical – galax-ies: individual: Arp 147
Ring galaxies are characterized by a bright ring of gas andstars, whose diameter may be very large ( ≤
100 kpc, Ghosh& Mapelli 2008) and where star formation (SF) is generallyvery intense (Higdon 1995, 1996; Marston & Appleton 1995;Mayya et al. 2005; Romano, Mayya & Vorobyov 2008). Alarge fraction of ring galaxies ( ≈
60 per cent, Few & Madore1986) is thought to form via (almost) head-on collisions withmassive intruder galaxies (at least one tenth of the targetmass). Because of the gravitational perturbation induced bythe bullet galaxy, a density wave propagates through the discof the target galaxy, generating an expanding ring of gas andstars (e.g., Lynds & Toomre 1976; Theys & Spiegel 1976;Toomre 1978; Appleton & James 1990; Appleton & Struck-Marcell 1987a, 1987b; Struck-Marcell & Lotan 1990; Hern-quist & Weil 1993; Mihos & Hernquist 1994; Appleton &Struck-Marcell 1996; Gerber, Lamb & Balsara 1996; Struck1997; Horellou & Combes 2001; Mapelli et al. 2008a, 2008b).Therefore, ring galaxies are unique laboratories where the ef-fects of galaxy interactions can be studied, from a plethoraof different points of view. First, the kinematics of the ringprovides information about the dynamics of the interaction.The simple geometry of ring galaxies, combined with theessential kinematic data, allows us to reconstruct the mainfeatures of the interaction and the time elapsed since it oc- curred. Furthermore, ring galaxies are often characterized byhigh SF rate (SFR, up to ≈
20 M ⊙ yr − ), suggesting thatthe density wave associated with the propagating ring trig-gers the formation of stars. When the density wave reachesthe external region of the target galaxy, SF may involve‘fresh’ gas, almost unpolluted by previous episodes of SF.This likely explains why the only three ring galaxies (theCartwheel, AM1159-530 and Arp 284) for which metallicitymeasurements have been published (Fosbury & Hawarden1977; Weilbacher, Duc & Fritze-v. Alvensleben 2003; Smith,Struck & Nowak 2005) have metallicity Z ≤ . ⊙ (whenrecalibrated on the basis of the electron temperature or ofthe P-method, see, e.g., Pilyugin, V´ılchez & Thuan 2010).One particular subclass of ring galaxies, named RE byTheys & Spiegel (1976), is characterized by the fact that thering is empty at its interior, apparently lacking the nucleus.This class includes objects that are among the closest andthe most studied ring galaxies (e.g., Arp 146, Arp 147, VIIZw 466, I Zw 28, NGC 985, AM 0058-220, AM 2145-543).Arp 147 is generally considered the prototype of this class.Arp 147 has a high SFR ( ∼ −
12 M ⊙ yr − , Romano et al.2008; Rappaport et al. 2010; Fogarty et al. 2011), and a rel-atively young ring: ≈
50 Myr elapsed after the collision, asestimated on the basis of the ring expansion velocity (113 ± − , Fogarty et al. 2011) and diameter ( ∼
15 kpc, deVaucouleurs et al. 1991). Arp 147 has a total stellar mass c (cid:13) Mapelli & Mayer similar to the Milky Way (6 − × M ⊙ , Fogarty et al.2011). A fraction ∼ . − .
34 of the total stellar light is con-tributed by a young (1 −
70 Myr) stellar population (Fogartyet al. 2011). Recently, Rappaport et al. (2010) reported thedetection of 9 ultra-luminous X-ray sources (ULXs, i.e. non-nuclear point-like X-ray sources with luminosity L X > ∼ erg s − ) in the ring of Arp 147.Lynds & Toomre (1976) proposed that an off-centre col-lision can displace the nucleus and make it appear embed-ded in the ring. This idea is supported by observations (e.g.,Thompson & Theys 1978; Schultz et al. 1991), that showthat the suspected remnant nucleus can be distinguishedfrom the other knots of the ring for its lack of SF.Gerber, Lamb & Balsara (1992) confirm, by running N-body/smoothed particle hydrodynamics (SPH) simulations,that RE galaxies form via off-centre collisions. They proposethat the ring of RE galaxies is incomplete and may appear acomplete ring because of the viewing angle. They find thatthe remnant nucleus is not only off-set from the centre, butalso out of the plane of the ring, and appears to be buriedwithin the ring only because of projection effects. On theother hand, Fogarty et al. (2011) find no evidence for theoffset of the nucleus from the plane of the disc, based onkinematics.In this paper, we run N-body/SPH simulations of off-centre galaxy collisions, to study the formation of RE galax-ies. The simulations are described in Section 2. Section 3 re-ports the results and Section 4 summarizes the main conclu-sions. In our simulations, we adopt initial parameters closeto the properties of Arp 147. However, we are not interestedin producing a ‘perfect’ model of Arp 147, but in under-standing the formation of RE galaxies, from a more generalpoint of view. The initial conditions for both the target and the intrudergalaxy are generated by using an upgraded version of thecode described in Widrow, Pym & Dubinski (2008; see alsoKuijken & Dubinski 1995 and Widrow & Dubinski 2005).The code generates self-consistent disc-bulge-halo galaxymodels, derived from explicit distribution functions for eachcomponent, that are very close to equilibrium. In particu-lar, the halo is modelled as a Navarro, Frenk & White (1996,NFW) profile. The disc (when present) is exponential. Thecode also includes the possibility of adding a Hernquist bulge(Hernquist 1993). We generate bulgeless models for the tar-get galaxy and models with bulge for the bullet galaxy.Masses and characteristics lengths of the simulatedgalaxies are listed in Tables 1 and 2. We report the results ofeight runs. Runs A, B, C and D will be considered our fidu-cial models, whereas runs E, F, G and H were performed forcomparison with Gerber et al. (1992). The only differencesamong runs A, B, C and D are the initial mass of gas andstars of the target galaxy. The total initial mass in baryons(gas and stars) is the same (8 . × M ⊙ ) for all the sim-ulations, but the ratio between gas and star mass ( f gas) isdifferent: f gas = 0 .
5, 0 .
2, 0 .
09 and 0 .
05, in run A, B, C andD, respectively. These values of f gas cover the typical rangeobserved for Milky Way-like galaxies (see, e.g., Haynes et al.1999; Geha et al. 2006). Runs E, F, G and H have the same star and gas contentas run D. They differ from run D for the impact parameter(runs E and G) and/or for the target-to-companion massratio (runs F, G and H). Run H differs from the other runsalso for the halo-to-baryon mass ratio ( ∼ . ∼ We initially set the centres of the target and the bul-let galaxy at a distance of three virial radii of the target.For runs A, B, C, D, F and H, the impact parameter is b = 8 kpc. In runs E and G b is = 12 kpc. In all runs,the initial relative velocity between the centres of mass is v rel = 900 km s − (see Mapelli et al. 2008a). The inclina-tion angle (with respect to the symmetry axis of the target)is α = 7 ◦ , with the exception of run H (where α = 0 forcomparison with Gerber et al. 1992). The inclination an-gle and the relative velocity are slightly different from thoseobtained for Arp 147 by the most recent measurements .In the Appendix A, we show a simulation performed with α = 33 ◦ , in agreement with the results by Fogarty et al.(2011). However, the morphology of the ring formed in thissimulation looks very different from that of Arp 147, as toomuch warping is induced by such a large inclination angle.We will investigate the role of inclination angle and warpingin a forthcoming paper. Furthermore, we stress again thatthe aim of this paper is to investigate the formation of REgalaxies, rather than producing a perfect model of Arp 147.The mass resolution of the simulations is 10 M ⊙ forstars and gas, and 5 × M ⊙ for dark matter (DM). Thesoftening length is 0.1 kpc. We simulate the evolution of themodels with the N-body/SPH tree code gasoline (Wadsley,Quinn & Stadel 2004). Radiative cooling, SF and supernova Romano et al. (2008) report a mass ratio M targ /M int =0.57between the ring galaxy and the intruder in the Arp 147 sys-tem. They derive the two masses from the K magnitude andfrom the colours (using the recipes by Bell et al. 2003). Ac-cording to their estimates the stellar mass of the ring galaxyArp 147 is M ∗ = 2 . × M ⊙ . On the other hand, Fogartyet al. (2011) estimate a stellar mass of the ring galaxy Arp 147 M ∗ = 6 . − . × M ⊙ , by combining optical measurementsand galaxy population models. Since Bell et al. (2003) models areknown to be less accurate in the case of late-type galaxies thanin the case of early-type galaxies, it is reasonable to adopt themass estimate by Romano et al. (2008) for the intruder galaxyand that by Fogarty et al. (2011) for the target. Therefore, themass ratio between target and intruder is M targ /M int = 1 . − . M targ /M int = 2 in runsA, B, C, D and E. We also make some check runs (F, G andH), where the mass of the target is the same as the mass of theintruder, for comparison with Gerber et al. (1992). Fogarty et al. (2011) constrain the line-of-sight maximum dis-tance between the two galaxies to be l = 7 . d = 12 . i = 25 ◦ with respect to the plane of thesky. From simple geometrical arguments, this leads to a minimuminclination angle for the interaction of ≈ ◦ , larger than our fidu-cial model (in our model, α = 7 ◦ and v rel = 900 km s − imply l = 30 kpc, d = 15 kpc and i = 20 ◦ ).c (cid:13) , 000–000 ing galaxies from off-centre collisions Table 1.
Initial conditions. Target BulletM ∗ a [10 M ⊙ ] see Table 2 1.91Gas Mass b [10 M ⊙ ] see Table 2 − Halo scale length c [kpc] 6.0 6.0Disc scale length [kpc] 3.7 3.0Disc scale height [kpc] 0.37 0.30Bulge scale length [kpc] − a M ∗ is the total stellar mass of the galaxy. The stars of thetarget are distributed according to an exponential disc. Thestars of the bullet are distributed according to an exponentialdisc (75 per cent of the total stellar mass) and an Hernquistbulge (25 per cent). b The gas of the target is distributedaccording to an exponential disc, with the same parameters(scale length and height) as the stellar disc. c We name haloscale length the NFW scale radius R s ≡ R /c , where R isthe virial radius of the halo (NFW 1996) and c theconcentration (here we assume c = 12 for both galaxies). Figure 1.
Projected mass density of stars and gas in run C.The simulated target galaxy has been rotated by 20 ◦ along the x -axis in the direction of the y -axis and by 20 ◦ counterclockwise,to match the observations of Arp 147. The scale is logarithmic,ranging from 11 .
15 to 7 . × M ⊙ pc − . From top to bottomand from left to right: 10, 30, 50 and 70 Myr after the interaction. (SN) blastwave feedback are enabled, as described in Stinsonet al. (2006, see also Katz 1992). The adopted parametersfor SF and feedback (see Section 3.4) are the same as used inrecent cosmological simulations capable of forming realisticgalaxies in a wide range of masses (e.g., Governato et al.2010; Guedes et al. 2011). We first consider the morphological evolution of the ring inour four fiducial runs (A, B, C and D). Fig. 1 shows thetime evolution of run C. The ring starts developing 20 − −
19 kpc (similar to the observeddiameter of Arp 147). We notice that the target galaxy de-velops a complete ring.Another interesting feature of Fig. 1 is the structure ofthe companion galaxy. We simulate the bullet as an early-type spiral galaxy (with a purely stellar disc and withoutgas). The initial conditions of the bullet were chosen to allowfor the formation of a bar, sufficiently strong to produce aring instability in the disc of the bullet (e.g., Buta & Combes1996; Tiret & Combes 2007). We evolved the companion inisolation till the formation of the resonant ring and we adoptthis configuration as initial condition. This choice was madeto test whether the companion of Arp 147 is a resonant ringgalaxy. The resonant ring of the bullet survives relativelyunperturbed for the first < ∼
50 Myr after the interaction,but it is more and more perturbed in the later stages of theevolution. This result cannot be used to constrain the prop-erties of the companion of Arp 147, since we consider onlyone possible model for the companion. However, this may in-dicate either that the resonant ring of Arp 147 companion ismore stable than our model against the perturbation (e.g.,because of a more massive halo), or that we observe theArp 147 system < ∼
50 Myr after the collision. Both casesare allowed by the data (e.g., Fogarty et al. 2011). A fur-ther possibility is that even the ring of the companion hasa collisional origin (that is, it was formed in the same inter-action as the ring of the target). This hypothesis was pro-posed, e.g., for II Hz 4 (Lynds & Toomre 1976). Although wecannot exclude this scenario for Arp 147, there are varioushints against it. First, the primary is an empty ring, pro-duced by a collision with a large impact parameter, whereasthe secondary is a symmetric ring, with a centred nucleus(although the system is observed with a large inclination),consistent with a nearly axisymmetric collision. These twomorphologies are unlikely to form as a consequence of thesame interaction. Second, the ring of the secondary is verysmooth and regular, as observed in resonant ring galaxies(e.g., NGC 3081, Buta & Purcell 1998).Figs. 2 and 3 show the projected density of gas andstars of the target (seen face-on), respectively, in runs A, B,C and D. The gas has a clumpy structure and is confinedin a thinner ring than the stellar component. Both gas andstars form complete rings. In the simulations with a higherfraction of gas (runs A and B), the distribution of stars isclumpier, because the young stellar population is significant,and tracks the distribution of gas. Instead, in the runs with alower fraction of gas (runs C and D), the old stars dominatethe mass distribution.Fig. 4 shows the surface density profile of gas (top) andstars (bottom) in runs A, B, C and D (which differ only forthe gas to star mass fraction). The four runs behave in a verysimilar way, with a strong density peak in correspondenceof the ring (radius r ∼ −
10 kpc, at t = 50 Myr after thecollision).Fig. 5 shows the projected density of gas (top) and c (cid:13) , 000–000 Mapelli & Mayer
Table 2.
Differences in the initial conditions between runs.Run A Run B Run C Run D Run E Run F Run G Run HTarget DM Mass [10 M ⊙ ] 7.0 7.0 7.0 7.0 7.0 7.0 7.0 2.1M ∗ [10 M ⊙ ] 5.66 7.06 7.77 8.13 8.13 8.13 8.13 8.13Gas Mass [10 M ⊙ ] 2.82 1.42 0.71 0.35 0.35 0.35 0.35 0.35Bullet DM Mass [10 M ⊙ ] 3.7 3.7 3.7 3.7 3.7 7.4 7.4 2.2Impact Parameter b [kpc] 8 8 8 8 12 8 12 8Inclination α [ ◦ ] 7 7 7 7 7 7 7 0In this Table, we show only the parameters that have been changed in different runs. Figure 2.
Mass density of gas of the target galaxy, projected inthe x − y plane, at t = 50 Myr after the collision. From left toright and from top to bottom: run A, B, C and D. The scale islogarithmic, ranging from 2 .
22 to 1 . × M ⊙ pc − . stars (bottom) when the target galaxy is seen edge-on. Onlyruns A and D are shown, but runs B and C are intermediatecases between the plotted ones. We find that, in all the con-sidered runs, the nucleus of the target galaxy is still insidethe disc even in the ring phase: the collision has off-set thenucleus from the dynamical centre and buried it in the ring,but the nucleus is not vertically displaced out of the ring.Actually, the entire ring, including the nucleus, is verticallydisplaced (by < ∼ In our runs A, B, C and D, both the stellar and the gas ringare complete. This is not the case of Gerber et al. (1992)runs: they conclude from their simulations that Arp 147 ringis incomplete and appears complete only because of projec-
Figure 3.
Mass density of stars of the target galaxy, projectedin the x − y plane, at t = 50 Myr after the collision. From left toright and from top to bottom: run A, B, C and D. The scale islogarithmic, ranging from 2 .
22 to 2 . × M ⊙ pc − . tion effects. This discrepancy is likely due to differences inboth the initial conditions and the resolution between oursimulations and that by Gerber et al. (1992). In particular,the main differences between our runs A, B, C and D andthose by Gerber et al. (1992) are the following. (i) Gerberet al. (1992) assume a mass ratio M targ /M int =1 betweentarget and intruder, respectively, while in the runs shownabove we assume M targ /M int =2. (ii) There is no DM haloin the galaxies simulated by Gerber et al. (1992), but just aspherical stellar halo (modelled as a King profile), whereaswe simulate a NFW DM halo. Furthermore, the halo to discmass ratio in Gerber et al. (1992) is only ∼ .
5. (iii) Themass and spatial resolution of Gerber et al. (1992) are a fac-tor of ≥
10 worse than those of our simulations. (iv) In ourruns A, B, C and D, the impact parameter is b = 8 kpc, cor-responding to a distance D = 4 − D = 7 kpc, which means that the c (cid:13) , 000–000 ing galaxies from off-centre collisions Figure 4.
Top panel: surface density profile of gas of the targetgalaxy in run A (dotted line, red on the web), run B (solid line,blue on the web), run C (dashed line, green on the web) andrun D (black dot-dashed line), at t = 50 Myr after the collision.Bottom panel: surface density profile of stars of the target galaxy,at t = 50 Myr after the collision. Lines are the same as in the toppanel. collision is much more off-centre with respect to our simula-tions. (v) The simulations by Gerber et al. (1992) have noinclination angle.To check the importance of these differences, we per-form runs E, F, G and H, exploring various parameters. Inparticular, runs E and G have a larger impact parameter( b = 12 kpc), runs F, G and H have M targ /M int =1. Run Hwas set to reproduce most of the features of Gerber et al.(1992) simulations (i.e., a DM to baryon fraction ∼ . M targ /M int =1, no inclination angle, D = 7 kpc).Fig. 6 shows the density map of gas (face-on) in sim-ulations E, F, G and H, at t = 50 Myr after the interac-tion. The ring is incomplete in these four runs, especially inrun G (with M targ /M int =1 and b = 12 kpc, bottom left-hand panel). In runs E and G (top and bottom left-handpanel) the partial ring is also strongly deformed, as a con-sequence of the large impact parameter, combined with thenon-zero inclination angle (which induces some degree ofwarping).The ring in run H, although incomplete, is much morecircular and less deformed than the other rings: this is dueto the absence of warping in runs with zero inclination an-gle. The fact that the halo-to-disc mass ratio is smaller inrun H than in the other runs has no significant effect on thepropagation of the ring, at least in the initial stages. Thisis a consequence of the fact that the formation of the ringoccurs in the inner regions of the target, that are baryon-dominated (we remind that the baryon mass in run H isthe same as in the other runs). Finally, the ring in run H is Figure 5.
Top panels: mass density of gas of the target galaxy,projected in the y − z plane, at t = 50 Myr after the collision.From left to right: run A and D. Bottom panels: mass density ofstars of the target galaxy, projected in the y − z plane, at t = 50Myr after the collision. From left to right: run A and D. The scaleis logarithmic, ranging from 7 . × − to 7 . × M ⊙ pc − . Figure 6.
Mass density of gas of the target galaxy, projected inthe x − y plane, at t = 50 Myr after the collision. From left toright and from top to bottom: run E, F, G and H. The scale islogarithmic, ranging from 2 .
22 to 1 . × M ⊙ pc − . smaller (by a factor of ∼ .
5) than the ring in run F, at thesame time. This is likely due to the fact that the mass of theintruder is smaller (by a factor of ∼
3) in run H with respectto run F . In fact, we know from the analytic model that theradial velocity perturbation, in the impulse approximation, The total mass of the target is also smaller by a factor of ∼ (cid:13) , 000–000 Mapelli & Mayer
Figure 7.
Mass density of stars of the target galaxy, projectedin the y − z plane, at t = 50 Myr after the collision. From left toright and from top to bottom: run E, F, G and H. The scale islogarithmic, ranging from 7 . × − to 7 . × M ⊙ pc − . scales with the mass of the intruder (see, e.g., equation 2 ofStruck-Marcell & Lotan 1990).In summary, a larger impact parameter is crucial to pro-duce incomplete rather than complete rings, in combinationwith other parameters (e.g., the target-to-intruder mass ra-tio). Therefore, we suggest that RE galaxies form partly ascomplete and partly as incomplete rings, depending on theimpact parameter, on the involved galaxy masses, potentialsand scale-lengths.From the analysis of runs A, B, C and D, we concludedthat the nucleus of the target galaxy is not vertically dis-placed out of the ring (the entire ring, including the nucleus,is vertically displaced by < ∼ ≈ M targ /M int =1 (runs F, G and H). However,we cannot conclude that the nucleus is completely displacedwith respect to the rest of the ring. We cannot make moreaccurate comparisons, as Gerber et al. (1992) do not providemore information about the displacement they find. We ex-pect that the possible differences between our simulationsand those by Gerber et al. (1992) are connected with thedifferent resolution or with the stability of the initial condi-tions.As we discussed in Section 2, we decided to simulatethe target as a bulgeless galaxy. However, we also run acheck case in which the target has a bulge and all the otherproperties are the same as in run D (see Appendix B). Inparticular, we want to check whether the nucleus of the tar-get can be more easily displaced from the plane of the ringafter the collision, if the target has a bulge. The results in-dicate that the presence of a bulge (instead of a nucleus) in inner regions is substantially unchanged, as the baryon mass isunchanged. the target does not change the features of the interaction(e.g., the completeness of the ring, the position of the nu-cleus, the kinematics and SFR, etc.). In particular, there isno displacement of the nucleus from the plane of the ringafter the collision. The simulations also provide information about the kine-matics of the interaction. Fig. 8 shows the most relevantfeatures of the velocity field of the simulated RE galaxy at t = 50 Myr after the collision (run A). The left-hand panelshows the tangential velocity v tan , i.e. the two-dimensionaltangential velocity with respect to the disc of the target.Therefore, v tan represents the rotational component of thetarget disc. The target galaxy rotates almost regularly forradii r > ∼
10 kpc, whereas the rotation is strongly perturbedfor r <
10 kpc, because of the expanding ring.The central panel of Fig. 8 shows the radial velocity v rad with respect to the disc of the target, and measures theexpansion of the ring. v rad has various interesting features.First, the plot of v rad highlights the high-velocity expandingring at r ≈
10 kpc. The ring has a maximum of the expansionvelocity for the negative x − axis (which corresponds to thesouthern part of Arp 147).Second, the matter in the outer parts of the disc ( r > y − axis (which correspondsto the eastern part of Arp 147) has negative values of v rad and is falling toward the centre. This means that the densestpart of the ring (which corresponds to the negative y − axis,see Figs. 2 and 3) is composed of both inner particles thatare directed outwards and outer particles that are directedinwards. This result agrees with the predictions of the ana-lytic caustic theory (see, e.g., Struck-Marcell & Lotan 1990;Appleton & Struck-Marcell 1996; Struck 2010).Third, the matter in the outer parts of the disc ( r > y − axis has v rad ∼
0: itappears still unperturbed by the collision. Actually, this partof the target galaxy is the farthest from the position of theimpact with the intruder. The right-hand panel of Fig. 8shows the ratio between | v rad | and | v tan | and highlights thestrong expansion of the ring, that dominates locally over therotation.Table 3 shows the average values of | v tan | and | v rad | in the inner part of the target galaxy ( r ≤
10 kpc). Thesevalues are very similar for all the runs, as the orbits andthe involved masses are almost the same. In particular, h| v rad |i ∼ ±
80 km s − and h| v tan |i ∼ ±
110 kms − (with the marginal exception of runs G and H). Theradial velocity h| v rad |i is comparable to the value of the ex-pansion velocity derived by Fogarty et al. (2011) for Arp 147( V exp = 113 ± − ), whereas h| v tan |i is quite higher thanthe observed rotational velocity ( V rot = 47 ± − ).However, the value of h| v tan |i obtained from the simulationscannot be directly compared with the observations of V rot ,because these two quantities are defined and derived in sub-stantially different ways. We also stress that the relative ve-locity between the simulated galaxies is quite different fromthe value obtained by Fogarty et al. (2011). Furthermore,the uncertainty associated with h| v tan |i and with h| v rad |i isso large (Table 3) that these are consistent with the obser-vational results by Fogarty et al. (2011) for Arp 147. c (cid:13) , 000–000 ing galaxies from off-centre collisions Figure 8.
Velocity field of gas of the target galaxy in run A, at t = 50 Myr after the collision. Left-hand panel: tangential velocity ofgas (associated with the rotation of the disc) with respect to the disk of the target galaxy, projected in the x − y plane. Central panel:radial velocity of gas (associated with the expansion or infall of the ring) with respect to the disk of the target galaxy, projected in the x − y plane. Right-hand panel: ratio between the modulus of the radial velocity and the modulus of the tangential velocity, projected inthe x − y plane. The scale is linear and color coding is indicated in the panels. Table 3.
Kinematics at t = 50 Myr after the interaction. h| v rad |i [km s − ] h| v tan |i [km s − ]Run A 134 ±
82 186 ± ±
79 187 ± ±
82 207 ± ±
86 218 ± ±
104 216 ± ±
95 156 ± ±
100 217 ± ±
87 193 ± In the simulations, the SF and feedback recipes of Stinsonet al. (2006) are adopted. Three parameters characterize theSF and feedback recipe: (a) the SF threshold n SF , (b) the SFefficiency ǫ SF , and (c) the fraction of SN energy that couplesto the interstellar medium (ISM) ǫ SN . SF occurs when cold( T < × K), virialized gas reaches a threshold density n SF = 5 atoms cm − and is part of a converging flow. Itproceeds at a rated ρ ∗ d t = ǫ SF ρ gas t dyn ∝ ρ . (1)(i.e. locally enforcing a Schmidt law), where ρ ∗ and ρ gas are the stellar and gas densities, and t dyn is the local dy-namical time. We choose ǫ SF = 0 .
1. The relatively high SFdensity threshold that we adopt is the same as that used inrecent cosmological simulations that form realistic galaxies(Guedes et al. 2011) and it has been shown to have a keyrole in determining a realistic inhomogeneous structure ofthe ISM (see, e.g., Mayer 2011). Its value is determined byenforcing that at least one SPH kernel (32 particles) is con-tained within a spherical volume of diameter equal to thelocal Jeans length for gas at density n SF at the lowest tem- peratures allowed by the adopted cooling function (a fewthousand K). In the blastwave feedback model of Stinson etal. (2006), the gas heated by the SN energy is not allowed tocool for a timescale of the order of 10 Myr, the exact valuebeing self-consistently determined by the blastwave solutionof the McKee & Ostriker (1977) model, that assumes a blast-wave produced by the collective effect of many type II SNae.For type I SNae, the energy is instead radiated away on thecooling time (since they explode on longer timescales theywill explode at significantly different time and would hardlyproduce a collective blastwave).To assess the effects of the SFR in our simulations, wewill focus on runs A, B, C and D, that differ only for thegas-to-star fraction. The top panel of Fig. 9 shows the SFRas a function of time in the four considered simulations. Inall the simulations, the SFR has approximately the sametrend: it increases sensibly after the galaxy interaction. Themain difference among the simulations is the normalizationof the SFR, that spans from ≈ ⊙ yr − in run D to ≈ ⊙ yr − in run A. Observations of Arp 147 (Rappaport etal. 2010; Fogarty et al. 2011) indicate a SFR ∼ −
12 M ⊙ yr − , consistent with runs C and D.The central and bottom panels of Fig. 9 show the timeevolution of the total stellar mass of the target (M ∗ ) andof the mass fraction of young stars (M y / M ∗ ; we define asyoung stars those stars that have an age t age ≤
100 Myr at t = 50 Myr after the interaction). The total stellar mass ofthe four simulations, at t = 50 Myr after the interaction,spans from 7 × to 8 × M ⊙ . Therefore, all thesesimulations are consistent with the stellar mass of Arp 147(found to be M ∗ = 6 . − . × M ⊙ by Fogarty et al.2011).However, there are large differences in the role of theyoung stellar population between different runs. In fact,M y / M ∗ ranges from 5 × − (in run D) to 0.17 (in run A)at t = 50 Myr. Since Fogarty et al. (2011) find that the massfraction of young stars in Arp 147 is ≤ c (cid:13) , 000–000 Mapelli & Mayer
Figure 9.
Top panel: SFR as a function of time in run A (opensquares, red on the web), run B (filled circles, blue on the web),run C (filled triangles, green on the web) and run D (blackcrosses). Central panel: total mass in stars (M ∗ ) of the targetgalaxy. Symbols are the same as in top panel. Bottom panel: to-tal mass of young stars (M y ) normalized to the total mass in starsof the target galaxy. Symbols are the same as in top panel. Time t = 0 corresponds to the collision. that only runs C and D are consistent with the observationsof Arp 147.The difference in M y / M ∗ among various runs is con-sistent with the difference expected from the Schmidt law.For example, there is a factor of ∼
34 between run A andD. From the Schmidt law, we expect that the SFR scaleswith ρ . , which means that there should be at least a fac-tor of ≈
23 difference between M y in runs A and D. Sincethe mass of old stars in run D is a factor of ∼ . ∼
32 inM y / M ∗ between run A and D. In this paper, we investigate the formation of RE galaxies(i.e. of collisional ring galaxies with an empty ring) withN-body/SPH simulations. We have shown that RE galaxiescan form via off-centre collisions (i.e. with a non-zero impactparameter), even for small inclination angles ( ∼ − ◦ ).In runs A, B, C and D (where b = 8 kpc and M targ /M int =2), the ring is always complete and it is notproduced by a projection effect. In runs with a larger im-pact parameter ( b = 12 kpc) or with M targ /M int =1, thering looks incomplete, as proposed by Gerber et al. (1992).Therefore, we conclude that RE galaxies can have either complete or incomplete rings, depending on the parametersof the interaction.We find that the nucleus is displaced from the dynam-ical centre of the galaxy, as a consequence of the off-centrecollision. However, the nucleus remains in the (perturbed)plane of the ring. The entire ring (together with the nucleus)is slightly ( < ∼ ∼ −
20 M ⊙ yr − , total starmass M ∗ = 8 × M ⊙ and mass fraction of young starsM y / M ∗ ∼ (0 . − . × − .We stress that we adopt a recent implementation of theSFR and of SNae in our simulations, whose results are ingood agreement with observations (see. e.g., Stinson et al.2006, 2009). However, we do not model the chemical evolu-tion of the gas, which may be very interesting in ring galax-ies, as pointed out by recent papers (e.g., Bournaud et al.2007; Mapelli et al. 2009, 2010; Michel-Dansac et al. 2010).Future N-body models of RE galaxies (and, in general, ofcollisional ring galaxies) should account for multi-phase gas(to describe the evolution of molecular and atomic gas) andinclude metallicity evolution, to shed light on the SF historyof ring galaxies. ACKNOWLEDGMENTS
We thank the referee, C. Horellou, for her comments thatsignificantly improved the paper. We thank the authors ofgasoline (especially J. Wadsley, T. Quinn and J. Stadel). Wealso thank L. Widrow for providing us the code to generatethe initial conditions. The simulations were performed withthe lagrange cluster at the Consorzio Interuniversitario Lom-bardo per L’Elaborazione Automatica (CILEA) and withthe
Yoda linux cluster at the University of Insubria. Wethank S. Rappaport, E. Ripamonti, A. Wolter, D. Fiacconiand A. A. Trani for useful discussions.
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Figure A1.
Projected mass density of stars and gas in the runwith α = 33 ◦ . The simulated target galaxy has been rotatedby 20 ◦ along the x -axis in the direction of the y -axis and by 20 ◦ counterclockwise, to match the observations of Arp 147. The scaleis logarithmic, ranging from 11 .
15 to 7 . × M ⊙ pc − .Toomre A., 1978, In: The large scale structure of the uni-verse; Proceedings of the Symposium, Tallin, Estonian SSR,September 12-16, 1977. Dordrecht, D. Reidel Publishing Co.,p. 109-116Wadsley J. W., Stadel J., Quinn T., 2004, New Astronomy, 9, 137Weilbacher P. M., Duc P.-A., Fritze-v. Alvensleben U., 2003,A&A, 397, 545Widrow L. M., Dubinski J., 2005, ApJ, 631, 838Widrow L. M., Pym B., Dubinski J., 2008, ApJ, 679, 1239 APPENDIX A: LARGE INCLINATION ANGLE
In this appendix, we show a simulation where the inclina-tion angle is α = 33 ◦ (in agreement with the estimates forArp 147 by Fogarty et al. 2011). The velocity componentswere rearranged so that the impact parameter is still 8 kpc.All the other initial conditions of this simulation are thesame as in run D. From Fig. A1, it is evident that the ringof the simulated galaxy is strongly warped, because of thelarge inclination angle. We will investigate in detail the ef-fects of warping in a forthcoming paper. APPENDIX B: TARGET GALAXY WITHBULGE
In this appendix, we discuss the results of a simulation inwhich the target galaxy has a bulge (with a total mass of1 . × M ⊙ ). The other properties of this simulation arethe same as those of run D. Fig. B1 shows the projected c (cid:13) , 000–000 Mapelli & Mayer
Figure B1.
Mass density of gas and stars of the target galaxy inthe check run with bulge, at t = 50 Myr after the collision. Toppanels: mass density of gas (left-hand panel) and of stars (right-hand panel) projected in the x − y plane (i.e., face-on). The scaleis logarithmic, ranging from 2 .
22 to 1 . × M ⊙ pc − and from2.22 to 2 . × M ⊙ pc − in the left-hand and in the right-handpanel, respectively. Bottom panels: the same as the top panels,but the target galaxy is projected in the y − z plane (i.e., edge-on).The scale is logarithmic, ranging from 7 . × − to 7 . × M ⊙ pc − . density of the target galaxy face-on (top) and edge-on (bot-tom) for both the gaseous (left-hand) and the stellar com-ponent (right-hand panel). No significant differences can beobserved with respect to run D in Figs. 2, 3 and 5. In thecase of the target with bulge, the ring is still complete,and the nucleus/bulge is buried within the ring, but it isnot vertically displaced. The SFR (6 M ⊙ yr − at t = 50Myr after the collision) is also very similar to run D (8 M ⊙ yr − ). Furthermore, the kinematics of the ring cannot bedistinguished from run D, as in the simulation with bulge v rad = 149 ±
89 km s − and v tan = 201 ±
111 km s − (weremind that v rad = 149 ±
86 km s − and v tan = 218 ± − in run D, see Table 3). Therefore, the assumptionabout the bulge of the target does not significantly affectour results, in the case of very late-type galaxies, such asArp 147. c (cid:13)000