A minor merger origin for stellar inner discs and rings in spiral galaxies
M. C. Eliche-Moral, A. C. González-García, M. Balcells, J. A. L. Aguerri, J. Gallego, J. Zamorano, M. Prieto
aa r X i v : . [ a s t r o - ph . C O ] M a y Astronomy&Astrophysicsmanuscript no. idisks˙v7 c (cid:13)
ESO 2018July 24, 2018
A minor merger origin for stellar inner discs and rings in spiralgalaxies
M. Carmen Eliche-Moral , A. C. Gonz´alez-Garc´ıa , , , M. Balcells , , , J. A. L. Aguerri , , J. Gallego , J. Zamorano ,& Mercedes Prieto , Departamento de Astrof´ısica, Universidad Complutense de Madrid, E-28040 Madrid, Spain, e-mail: [email protected] Dept. F´ısica Te´orica, Universidad Aut´onoma de Madrid, E-28049, Madrid, Spain Instituto de Astrof´ısica de Canarias, C / V´ıa L´actea, E-38200 La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna, E-38200 La Laguna, Tenerife, Spain Isaac Newton Group of Telescopes, Apartado 321, E-38700 Santa Cruz de La Palma, Canary Islands, SpainReceived 14 January, 2011; accepted 19 May, 2011
ABSTRACT
Context.
Recent observations show that inner discs and rings (IDs and IRs, henceforth) are not preferably found in barred galaxies, afact that points to the relevance of formation mechanisms di ff erent to the traditional bar-origin scenario. In contrast, the role of minormergers in the formation of these inner components (ICs), while often invoked, is still poorly understood. Aims.
We have investigated the capability of minor mergers to trigger the formation of IDs and IRs in spiral galaxies through colli-sionless N-body simulations.
Methods.
We have run a battery of minor mergers in which both primary and secondary are modelled as disc-bulge-halo galaxies withrealistic density ratios. Di ff erent orbits and mass ratios have been considered, as well as two di ff erent models for the primary galaxy(a Sab or Sc). A detailed analysis of the morphology, structure, and kinematics of the ICs resulting from the minor merger has beencarried out. Results.
All the simulated minor mergers develop thin ICs out of satellite material, supported by rotation. A wide morphologicalzoo of ICs has been obtained (including IDs, IRs, pseudo-rings, nested IDs, spiral patterns, and combinations of them), but all withstructural and kinematical properties similar to observations. The sizes of the resulting ICs are comparable to those obtained in realcases with the adequate scaling. The existence of the resulting ICs can be deduced through the features that they imprint in theisophotal profiles and kinemetric maps of the final remnant, as in many real galaxies. Weak transitory oval distortions appear in theremnant center of many cases, but none of them develops a noticeable bar. The realistic density ratios used in the present modelsmake the satellites to experience more e ffi cient orbital circularization and disruption than in previous studies. Combined with the discresonances induced by the encounter, these processes give place to highly aligned co- and counter-rotating ICs in the remnant centre. Conclusions.
Minor mergers are an e ffi cient mechanism to form rotationally-supported stellar ICs in spiral galaxies, neither requiringstrong dissipation nor the development of noticeable bars. The present models indicate that minor mergers can account for the exis-tence of pure-stellar old ICs in unbarred galaxies, and suggest that their role must have been crucial in the formation of ICs and muchmore complex than just bar triggering. Key words. galaxies: bulges — galaxies: evolution — galaxies: formation — galaxies: interactions — galaxies: kinematics anddynamics — galaxies: structure
1. Introduction
Stellar IDs and IRs are found in at least one third of spi-ral galaxies (Erwin & Sparke 2002; Falc´on-Barroso et al. 2006,F06 hereafter). Usually masked by the light coming frombrighter overlapping components, many of them have beendetected through the peculiar features that these ICs im-print in the isophotes or in the kinematic maps of thehost galaxy (van den Bosch et al. 1994; Kormendy et al. 1994;Lauer et al. 1995; Scorza et al. 1998; Scorza & van den Bosch1998; Koprolin & Zeilinger 2000; Rest et al. 2001; Erwin2004; Carollo 2004; Lisker et al. 2006; Comer´on et al. 2008;Morelli et al. 2010; Moiseev et al. 2010; Sil’Chenko 2010).Stellar IDs are found in galaxies of all types, althoughthey tend to reside in Sa-Sb’s. Their radii span fromsome tens of parsecs to ∼ ∼ ∼
10 Gyr (Franx & Illingworth 1988; Bender 1990; van der Marel & Franx 1993;Cinzano & van der Marel 1994; Prieto et al. 2001;Carollo et al. 2002; Erwin & Sparke 2002; Martel et al.2002; Erwin & Sparke 2003; Kormendy & Kennicutt 2004;Morelli et al. 2004; Athanassoula 2005; Cappellari et al. 2007;Emsellem et al. 2007; Peletier et al. 2007). Inner star-formingIRs and pseudo-rings are detected in at least one fifth ofall disc galaxies (Knapen 2005; Moiseev & Bizyaev 2009;de Lapparent et al. 2011). However, accounting for the episodicnature of their star formation histories and their long-livedstable configurations, the total fraction of IRs including purestellar (non star-forming) ones is expected to be much higher(Mazzuca et al. 2006; Sarzi et al. 2007).These stellar ICs could be primordial features in thegalaxy centres, established at an early epoch of rapid,cold accretion flows at high redshift (Bedregal et al. 2006).However, the dramatic decline of the star formation surfacedensity in the discs during the last ∼ tions found between the nuclear and disc global propertiesof spiral galaxies evidence an intertwined star formationhistory for bulges, discs, and ICs that spreads throughtime (Peletier & Balcells 1996; Dom´ınguez-Palmero et al.2008; Dom´ınguez-Palmero & Balcells 2008). Attendingto the high detection fraction of stellar IDs and IRs inbarred galaxies, their origin has been traditionally as-sociated to bar patterns in discs (Combes et al. 1992;Arnaboldi et al. 1995a; van den Bosch & Emsellem 1998;Erwin & Sparke 2002; Regan & Teuben 2003; B¨oker et al.2008; de Lorenzo-C´aceres et al. 2008; Comer´on et al. 2010).This has been corroborated by numerical simulations, thathave shown that the dynamical resonances induced by barsgive place to the rings surrounding them easily. Moreover,the bars induce strong gas inflows to the galaxy centre, whichsettle in circular orbits, inducing star formation that can resultin an ID (Norman et al. 1996; Athanassoula et al. 2009b,a;Comer´on et al. 2010). Other bar-related scenarios propose thatIDs can also be the relics of diluted nested bars or of episodesof starbursts in rings that have shrunk in radius to the galaxycentre over time (Combes et al. 1992; Regan & Teuben 2003;Sil’Chenko & Smirnova 2010).Nevertheless, recent observations indicate that stellar IDsand IRs are not preferably harboured by barred galaxies, beingat least as frequent in non-barred early-type hosts as in barredones (Emsellem et al. 2004; Falc´on-Barroso et al. 2004; Knapen2005; Knapen et al. 2006; Sarzi et al. 2006; Comer´on et al.2010). IRs are easily developed by unstable gas-rich discs in nu-merical simulations (Aumer et al. 2010), but IDs are structuresmore di ffi cult to reproduce spontaneously (Thakar et al. 1997).So, other mechanisms capable of triggering disc resonances be-sides bars are required to explain the existence of stellar IDs andIRs in unbarred galaxies. One of the main alternatives is gasinfall, but simulations indicate that this mechanism is e ffi cientproducing IRs, but not IDs (Thakar & Ryden 1998; Naab et al.2006).Another possible driver is merging, as suggested by theexistence of many ICs exhibiting strong misalignments ordistorted morphologies and / or kinematics with respect to thehost disc (see, e.g., Okumura et al. 1994; Arnaboldi et al.1995b; Buta & Combes 1996; Barnes & Hernquist 1996;Knapen et al. 2004; Reshetnikov et al. 2005; Mazzuca et al.2006; Sil’chenko & Moiseev 2006; Chilingarian et al. 2009;Fa´undez-Abans et al. 2009; Moiseev & Bizyaev 2009;Brosch et al. 2010). This scenario is supported by numeri-cal simulations, which have proven that major mergers candrive the formation of kinematically-decoupled ICs analogousto the ones found in E-S0 galaxies (Hernquist & Barnes 1991;Balcells & Gonz´alez 1998; Bendo & Barnes 2000; Barnes 2001;Jesseit et al. 2007; Di Matteo et al. 2008). Considering that mas-sive E-S0 galaxies have experienced at least one major mergersince z ∼ ff ects of minor mergers on bulge and disc growth and on the satellites have been exten-sively studied (e.g., Hopkins et al. 2010; Henriques & Thomas2010; Tapia et al. 2010a,b; Bartoˇskov´a et al. 2011; Ebrova et al.2011), little attention has been devoted to study specifically theirability to induce the formation of dynamically-cold ICs in galax-ies. One of the earlier studies dealing with this topic wascarried out by Elmegreen et al. (1992), who performed nu-merical simulations of ring-companion interactions to anal-yse the e ff ects of the minor merger onto pre-existing outerrings. Later, Thakar and collaborators tested the formationof counter-rotating discs in spiral galaxies through retrogrademergers of gas-rich dwarfs onto discs (Thakar & Ryden 1996;Thakar et al. 1997; Thakar & Ryden 1998). They found that, al-though counter-rotating thin gaseous discs were formed duringthe minor merger, the obtained sizes were only comparable to thebiggest observational cases. The formed IDs did not have expo-nential profiles either and were highly unstable, quickly derivinginto IRs. This led these authors to conclude that, in order to forma normal counter-rotating disc, ”there must be either little or nopre-existing prograde gas in the primary galaxy, or its dissipativeinfluence must be o ff set by significant star formation activity”.More recently, Aguerri et al. (2001) performed collisionless N-body simulations to test the growth of bulges after the accretionof dense spheroidal satellites. Their undisrupted dense satellitecores sank to the galaxy centre, giving place to kinematically-decoupled components in the remnants, but not supported by ro-tation.Eliche-Moral et al. (2006, EM06 hereafter) studied the ef-fects of the accretion onto disc galaxies using satellites whichthemselves comprised a disc, a bulge, and a dark halo. More im-portantly, the relative densities of primary and secondary weremade to be realistic by imposing that both models lie on theTully-Fisher relation. This was an improvement over previousstudies of mass buildup via accretion, given that the disruption ofthe satellite, the radius of deposition of satellite material, and thedynamical heating of the primary, all depend on the tidal fields,which scale with the relative densities of the two galaxies. EM06reported the formation of dynamically-cold stellar structures inthe centre of remnants, made out of disrupted satellite material.However, that paper was centred on the bulge growth driven bythe minor merger, and hence no analysis or description of theICs was performed. We have therefore extended the simulationsof EM06, sampling di ff erent orbits and initial conditions and us-ing ∼ ff ects and strong bars are not essen-tial to form these dynamically-cold ICs.The paper is structured as follows. We briefly describe themodels in §
2. The formed ICs are analysed geometrically, photo-metrically, and kinematically in §
3. In §
4, we perform a qualita-
Table 1.
Number of particles used in the models
Number of Particles ( / )Experiment type Total D1 B1 H1 D2 B2 H2(1) (2) (3) (4) (5) (6) (7) (8)Big bulge 185 40 10 90 10 5 30Small bulge 415 60 10 300 — — — Columns : (1) Experiment type depending on the used primary galaxymodel (big or small bulge). (2) Total particle number. (3) Numberof primary disc particles. (4) Number of primary bulge particles. (5)Number of primary halo particles. (6) Number of satellite disc parti-cles. (7) Number of satellite bulge particles. (8) Number of satellitehalo particles. tive comparison of the ICs resulting in the models with those de-tected in real spiral galaxies. Model limitations are commentedin §
5. The discussion can be found in §
6. A brief summary ofthe results and some conclusions are finally addressed in § §
2. The models
We have extended the set of collisionless N-body simulationsof minor mergers onto disc galaxies described in EM06, nowusing longer pericenters and di ff erent initial disc galaxies. Theoutcome of the satellite material of a final set of 12 collisionlessmodels has been analysed (six of them come from EM06). Ten ofthese experiments were run using a disc galaxy with a prominentbulge as primary galaxy (equivalent to a Sa-Sb galaxy), whilein another two a primary with a smaller bulge (similar to a Sc)was used to investigate the influence of the primary bulge in theoutcome of the accretion.All the galaxies in the simulations (primary galaxies andsatellites) have an initial bulge-disc-halo structure. The pri-mary galaxy models were built using the GalactICS code(Kuijken & Dubinski 1995), including an exponential disc com-ponent (Shu 1969), a King bulge (King 1966), and a dark halobuilt following an Evans profile (Kuijken & Dubinski 1994).The discs of both primary galaxy models follow an exponen-tial surface density profile both radially and vertically, and wereallowed to relax in isolation for about 10 disc dynamical timesprior to placing them in orbit for the merger simulations. No rel-evant resonant structures appear in the disc. The primary galaxywith a big bulge matches the Milky Way (MW) when the unitsof length, velocity, and mass are R = . v =
220 km s − ,and M = . × M ⊙ , respectively. In this case, the correspond-ing time unit is 20.5 Myr. The primary galaxy with a small bulgematches NGC 253 using the following units of length, velocity,and mass: R = . v =
510 km s − , and M = . × M ⊙ ,implying a time unit of 11.7 Myr. These values, especially whenusing an appropriate M lum / L ratio, yield mass-to-light ratio val-ues close to observations ( M / L ∼ ◦ in direct orbits and to 150 ◦ in ret-rograde orbits, respectively. All satellites have also an azimuthalangle φ = ◦ . For each satellite mass, pericenter distance, andmodel of the primary galaxy considered, a direct and a retro-grade orbit have been computed. Initial orbits were ellipticalwith pericenters equal to one or eight disc scale lengths, de-pending on whether we were running a short or a long pericen-ter orbit. Relative velocities at the first pericenter passage oscil-late between 440–650 km / s, considering the scalings commentedabove.In Table 3, we include the orbital parameters of each merg-ing experiment. As satellite models are scaled down versions ofthe primary model with a big bulge and exhibit di ff erent massratios having the same number of particles, this renders dif-ferent mass particles for the di ff erent components in each ex-periment. The largest mass contrast, and thus the higher two-body errors, are expected in the models with a total mass ratioof 1:18, where a primary halo particle is 10 times more mas-sive than the bulge particles of the satellite. Such extreme ra-tio is well below the limits explored earlier in di ff erent sim-ulations using a similar set of initial models, so the kinemat-ics of the inner regions of the remnant are much better sam-pled in the present models than previously (Balcells & Gonz´alez1998; Gonz´alez-Garc´ıa & Balcells 2005, EM06). The di ff erencein the number of particles for the haloes hosting a big anda small bulge is two folded. On one hand, a bulge-less discmodel stable to bar distortions requires a concentrated halo (see,e.g., Gonz´alez-Garc´ıa & Balcells 2005). On the other hand, themasses of the halo and bulge particles need to be of the sameorder for ensuring low two-body errors. These two constraintsrequired the models with small bulge to have such a high num-ber of halo particles. As we are interested in the physics of theinner regions of the remnants, we intended to balance betweenthe accuracy gained by using a higher number of particles andthe economy of resources in building new stable models for eachsatellite.The evolution of the new models was computed usingGADGET-2 code (Springel et al. 2001; Springel 2005). We useda softening of ε = .
02 in model units and an opening angleof θ = .
6. Considering this tolerance parameter and apply-ing quadrupole-moment corrections, the code computes forceswithin 1% of those given by a direct summation and preservestotal energy better than 0.1%. We evolved all models for ∼ B / D ratios of the main galaxy increase after the merger to B / D ∼ . B / D ∼ . Table 2.
Initial parameters of the primary galaxy models
Experiment type M T , M B , / M D , M Dark , / M L , h D , r B , / h D , h , / h D , z D , / h D , (1) (2) (3) (4) (5) (6) (7) (8)Big primary bulge 6.40 0.51 4.16 1.00 0.20 3.7 0.11Small primary bulge 0.99 0.08 6.98 0.39 0.16 3.8 0.06 Columns : (1) Experiment type depending on the primary galaxy model used (big or small bulge). (2) Total primary mass (simulation units). (3)Bulge-to-disc mass ratio of primary galaxy. (4) Dark-to-luminous mass ratio of primary galaxy. (5) Radial disc scale-length of the primary galaxy.(6) Ratio between the e ff ective radius of primary bulge and primary disc scale-length. (7) Ratio between the radius of the shell containing 95%of luminous material in the primary galaxy and its disc scale-length. (8) Ratio between the vertical and radial disc scale-lengths of the primarygalaxy. bulges. This means that the remnants of the experiments start-ing with a Sb primary galaxy have become S0-Sa’s, while the Scprimary galaxies have been transformed into Sb-Sbc’s after theminor merger (see Graham 2001).We will refer to each model throughout the paper accordingto the following code: M m P[l / s][D / R][b / s], where m indicatesthe bulge-to-satellite mass ratio ( m =
6, 9, or 18 for models withluminous mass ratios equal to 1:6, 1:9, 1:18, respectively), ”Pl”indicates long pericenter and ”Ps” short pericenter, ”D” or ”R”describes the orbit (”D” for direct and ”R” for retrograde), andthe final ”b” or ”s” letter indicates if the primary galaxy had abig or a small bulge (see Table 3).
3. Results
In EM06, we reported the formation of inner dynamically-coldcomponents in minor merger experiments, but we did not anal-yse the resulting ICs neither structurally nor kinematically. In thenext sections, a detailed analysis of the co- and counter-rotatingICs formed in the models described in § In Fig. 1 we show the disruption experienced by the satellite inmodel M18PsDb (model i in Table 3) as an example of the timeevolution of the luminous surface density of the satellite ma-terial during the last moments of the encounter. Although thedi ff erent initial conditions a ff ect to the global shape, size, andeven the number of components in these inner structures, the fi-nal structure in all the experiments resembles a central verticallythin torus or disc (depending on whether the satellite materialreaches the remnant centre or not), embeded into a more ex-tended flat component, similar to a more extended disc. In themodel plotted in the figure, the toroidal structure corresponds tothe central ring visible at R ∼ .
5, while the outer disc corre-sponds to the low density structure that extends up to R ∼ § ff erent epochs during the minor merger. The less bound parti-cles of the satellite (i.e., those from the disc) are disrupted earlierin the interaction. During the first pericenter cross of the orbit, itsouter shells are removed from the satellite by the primary galaxytidal field, giving place to the outer structure of the formed IC(as observed in the first half of snapshots in Fig. 1). The core ofthe satellite takes more time to experience a noticeable disrup-tion. Its material is deposited at inner radii during the last stagesof the encounter. In this section, we describe the geometry and structure of theseICs through their radial and vertical surface brightness profiles,and analyse their misalignment with respect to the galaxy planeof the final remnant and their kinematics.
Figure 2 shows the radial surface density profiles of luminousmaterial initially belonging to the satellite, to its disc, and to itsbulge in the final remnants of all the experiments. In general, theinner structure is basically composed by satellite bulge particles(typically, at R . h D , ( t = / R]s, models e and f), holes (as inM18P[l / s]Db, models i and k), and smooth-length e ff ects. Theresulting fits and their residuals are plotted in the correspondingpanels and sub-panels of Fig. 2.Most of the resulting ICs can be well-approximated byone exponential radial profile or by the addition of two ones.However, notice that the independent ICs identified by each fit-ted exponential radial profile are shaped with material of bothsatellite components: from the bulge and the disc. Only in theexperiments with a small primary bulge, the satellite bulge endsundisrupted in the remnant centre (see the profiles correspondingto the satellite bulge particles in M6PsDs and M6PsRs, frames eand f in the figure). In these models, the outer shells of satellitematerial configure an extended ID structure hosting the undis-rupted satellite core.In order to delimit the radial extent of the ICs characterizedby an unique exponential profile, we have assumed that, in thecase that only one exponential profile is required to explain thewhole radial structure, this IC extends up to the radius at whichthe fitted surface density is equal to 1 /
10 of its central value asextrapolated from the fit. In the case that the structure is bet-ter described by two nested exponential profiles, the innermostone is considered to extend up to the radius where the outer onestarts to dominate the global fit. The outer one will extend fromthis radius up to that at which its surface density drops to 1 / Table 3.
Orbital and scaling parameters of each merger experiment
Model Code Code in EM06 Primary Bulge M L , Sat / M L , Prim R Sat / R Prim R pericenter / h D , θ Prim t fullmerger t total (1) (2) (3) (4) (5) (6) (7) (8) (9)(a) M6 Ps Db M2TF35D Big (b) 1:6 (M6) 0.46 0.73 (Ps) 30 (D) ∼
72 100(b) M6 Ps Rb M2R Big (b) 1:6 (M6) 0.46 0.73 (Ps) 150 (R) ∼
80 100(c) M6 Pl Db — Big (b) 1:6 (M6) 0.46 8.25 (Pl) 30 (D) ∼
93 144(d) M6 Pl Rb — Big (b) 1:6 (M6) 0.46 8.25 (Pl) 150 (R) ∼
110 144(e) M6 Ps Ds — Small (s) 1:6 (M6) 0.25 0.87 (Ps) 30 (D) ∼
40 62(f) M6 Ps Rs — Small (s) 1:6 (M6) 0.25 0.87 (Ps) 150 (R) ∼
44 72(g) M9 Ps Db M3TF35D Big (b) 1:9 (M9) 0.39 0.79 (Ps) 30 (D) ∼
80 100(h) M9 Ps Rb M3R Big (b) 1:9 (M9) 0.39 0.79 (Ps) 150 (R) ∼
87 100(i) M18 Ps Db M6TF35D Big (b) 1:18 (M18) 0.28 0.86 (Ps) 30 (D) ∼
116 122(j) M18 Ps Rb M6R Big (b) 1:18 (M18) 0.28 0.86 (Ps) 150 (R) ∼
142 154(k) M18 Pl Db — Big (b) 1:18 (M18) 0.28 8.19 (Pl) 30 (D) ∼
225 260(l) M18 Pl Rb — Big (b) 1:18 (M18) 0.28 8.19 (Pl) 150 (R) ∼
285 340
Columns : (1) Model code: M m P[l / s][D / R][b / s], where m indicates the bulge-to-satellite mass ratio ( m =
6, 9, or 18 for models with luminous massratios equal to 1:6, 1:9, 1:18, respectively), ”Pl” refers to long pericenter and ”Ps” to short pericenter, ”D” indicates direct orbits and ”R” retrogradeorbit), and the final letter (”b” or ”s”) indicates if the primary galaxy had a big or a small bulge. The letter in parentheses helps to identify eachmodel quickly in the forthcoming figures. (2) Model code in EM06, for those models that were already presented in that paper. (3) Primary galaxymodel used in the experiment (big or small primary bulge, see Table 1). (4) Luminous mass ratio between satellite and primary galaxy. (5) Ratiobetween the luminous half-mass radii of the satellite and the primary galaxy. (6) First pericenter distance of the orbit, in units of the primary discscale-length. (7) Initial angle between the orbital momentum and the primary disc spin. This angle determines if the orbit is prograde (direct) orretrograde. (8) Approximate time of full merger, in simulation units. (9) Total run time of each experiment, in simulation units. of its central value. The radial extent of each radial componentresulting from these criteria are marked in Fig. 2.Summarizing, all the simulated minor mergers give place tocomplex extended ICs in the remnants made out of disruptedsatellite material, with radial surface density profiles that can bewell-described by one or two nested exponential profiles.
An IC with a radial exponential profile can correspond to an IDor to a bulge with S´ersic index n = ff erence between all these components arise in the verticalthickness of the component, as compared to its own radial scale-length and to the one of the host disc. Following Sil’chenko et al.(2011), a ratio of scale-length to scale-height of about 3 is a rea-sonable frontier between spheroids and discs. So, we have esti-mated the ratio between the vertical and the radial scale-lengthsof the formed ICs in each remnant, as well as the ratio of theirscale-heights to the radial scale-length of the remnant discs, inorder to identify them as IDs (thin or thick) or pseudo-bulges.Figure 3 presents the characteristic vertical scale-lengths h z at di ff erent radial positions of the disc, bulge, and all luminousmaterial originally belonging to the satellite in the final rem-nants. The scale-lengths have been derived from exponential fitsto the vertical density profiles at each radius. Only the radial po-sitions with enough particles to ensure a vertical density profileof S / N >
50 have been considered (typically, R . h D , Primary ).The fitting errors are on average .
10% for each estimate. Thefinal scale-length of the disc remnant is marked in each panel asa reference (horizontal dotted lines). We have also indicated theradial extent of each IC, according to the definition adopted in § Λ CDMcosmological simulations, where the disrupted satellites con-tribute to the buildup of the thick disc of the galaxy (Abadi et al.2003). In general, the scale-height of the structure made of dis-rupted satellite material increases with radial position, meaningthat these structures are flared (see asterisks in the figure).The material of the disrupted satellite bulge tends to exhibitlower scale-heights than that of the disrupted satellite disc, butthe di ff erent disruption epochs of both components seems to nota ff ect to their final vertical distributions at a given radial posi-tion, as the scale-heights of both distributions are similar at eachradius (compare red diamonds and blue triangles in the figure).In Fig. 3, we also show the ratio between the vertical andradial scale-lengths of each IC (numbers in black characters ineach frame). Nearly half the innermost ICs formed in the modelswith big primary bulges are thin, as they exhibit ratios typicallybelow ∼ .
4. This means that these innermost components areIDs, according to Sil’chenko et al. (2011) criterion. Other casesexceed the limiting value proposed by these authors (as modelsM6P[s / l]Rb, panels b and d in the figure), meaning that theseICs would be classified as pseudo-bulges in the case that theoriginal primary galaxies lacked of a large central component.As this is not the case (they had a massive central bulge), theICs formed in these models are embeded into the pre-existingbulge or the galaxy thick disc. We also have some question-able cases with vertical-to-radial scale-lengths near the limitingvalue for distinguishing between IDs and pseudobulges, as mod-els M[9 / Fig. 1.
Time evolution of the luminous surface density of the satellite material during the last moments of experiment M18PsDb(experiment ”i” in Table 3). Face-on and edge-on views centred in the initial primary galaxy are plotted (left and right panels,respectively). Snapshots corresponding to times from 101 to 120 are shown from up-to-down and left-to-right of each figure, usinga time step equal to one. If the primary galaxy is scaled to the MW (see § ∼ . ff erent surface density levels in logarithmic scale, with redder colorsindicating higher values. Spatial scales in both axes are provided in simulation units. The disrupted satellite material is finallydeposited in the remnant centre forming an IR (in yellow) embeded into a more extended ID (in green). The IR rotates in the samedirection as the primary disc material.cause the satellite core sinks to the remnant center without expe-riencing disruption. None of these two models develops a pseu-dobulge out of disrupted satellite material, because the undis-rupted satellite core produces a central peak in the radial surfacedensity profile with a S´ersic index n ∼ § Figures 4-5 show the morphology of the ICs formed in each rem-nant. In order to provide a 3D description of the ICs structure,we plot the face-on and edge-on surface density maps of thedisrupted stellar satellite material in all the remnants. The fig-ure shows that the satellite disruption in our experiments hasgiven place to a wide zoo of ICs, all made out of disrupted satel-lite material, and confirms the global morphology derived fromthe radial and vertical surface density profiles of Figs. 2-3 (seeTable 4).Moreover, the maps reveal the existence of substructuresthan make the morphology of the IC even more complex, suchas ring relics (M18PlDb, panel k in Fig. 5), pseudo-rings (i.e., anon-closed ring-like structure like the one developed in exper-iment M18PlRb, panel l in Fig. 5), and spiral arms (M18PsDb,panel i in Fig. 5). The twin clumps observed in some ICs couldbe tracing weak bars or relics of oval distortions (see panels a,c, and d in Fig. 4 and panels h-i in Fig. 5). The global ellipticityand PA profiles of the final remnants seem to support the bar-related origin of some of these structures (see § Our models demonstrate that minor mergers onto disc galax-ies can give place to dynamically-cold thin ICs, with varied mor-phologies ranging from nuclear bars embeded in nested IDs topseudo-rings, covering all di ff erent kinds of inner structures. Numerical simulations have shown that tidal interactions easilyproduce bars and non-axisymmetric distortions (such as ovals)in thin discs through gravitational torques (see Bournaud et al.2005a; Mastropietro et al. 2005; Aguerri & Gonz´alez-Garc´ıa2009). The time evolution of the density maps of the primarydisc material reveals that our simulations are not exceptions:elongated distortions in privileged directions, defined by the or-bit of impact, are induced in the primary disc by the minormerger (see Fig. 6). Some of these transient bar-like distortionsremain until the end of the simulation, but extremely weakened(as in the case of the figure), but most of them dissolve duringthe last stages of the remnant relaxation.The strongest and longest-lived central oval distortions in-duced by the minor merger in the primary disc appear in thecases with a small primary bulge, corroborating many previ-ous studies that have posed that a high mass concentration inthe galaxy centre tends to stabilize the disc, preventing selfgravity and thus bar formation (see, e.g., Pfenniger & Norman1990; Bournaud & Combes 2002; Athanassoula et al. 2005;Eliche-Moral et al. 2006; Cox et al. 2008). All the transitory bar-like or oval patterns formed in the primary discs rotate in thesame direction as the primary disc stars even in the retrogrademergers.The final distribution of primary disc material does not showdistinct ICs, except in experiment M9PsRb (see Fig. 7), wherethe primary disc material develops a pseudo-ring at the locationof the twin clumps observed in the IC made out of satellite mate-rial (see panel h in Fig. 5). Therefore, we are led to conclude thatthe minor mergers do not drive the formation of IDs or IRs madeout of primary material in our experiments, but force the intro-duction of primary disc material to the centre instead, makingthe final galaxy bulge to grow larger (as reported in EM06).The resonances that the minor merger induce in the primarydisc couple with the satellite disruption, triggering the forma-tion of ICs, such as IDs and IRs (see panels d in Fig. 4, and iin Fig. 5). Nevertheless, no clear nuclear bars are developed inthe IC formed out of disrupted satellite material either. So, ourmodels prove that minor mergers can give place to the formationof IRs without requiring the development of noticeable bars.
We have analysed the alignment of the di ff erent inner structuresformed in the merger with respect to the global remnant struc-ture. This analysis is restricted by the fact that our models ex-plore only two orbit inclinations (30 ◦ and 150 ◦ ), hence little canbe said on the e ff ect of di ff erent inclinations in the alignment ofthe resulting ICs. In Fig. 8, we plot the angles between the an-gular momenta of the stars originally belonging to the satellitebulge and disc in the final remnant and its total angular momen-tum (diamonds and triangles, respectively). This figure showsthat there is a nearly co-planarity between the IC formed out ofsatellite bulge material and the final galactic plane of the rem-nant in all the models (notice that their angles are ∼ ◦ in thedirect orbits and ∼ ◦ in the retrograde ones). The alignmentof the structure formed out of satellite disc material is slightly Fig. 3.
Vertical exponential scale-lengths of material in the finalremnants as a function of radius. The plotted physical magni-tudes are provided in simulation units. The letters identifyingeach panel are those used in Table 3 for each model.
Triangles :Material originally from the satellite disc.
Diamonds : From thesatellite bulge.
Asterisks : Stellar material originally in the satel-lite.
Squares : From the original primary disc.
Horizontal dottedline : Scale-length of the final remnant disc, marked as a refer-ence.
Vertical dashed lines : Radial extent of each IC character-ized by an unique exponential profile, according to Fig. 2. Theratio of the vertical to the radial scale-lengths of each IC is in-dicated in black characters (one number per radial exponentialICs). The ratio of the scale-height of each IC to the radial scale-length of the final remnant disc is also indicated in blue charac-ters at the top left of each panel.lower. The near perfect alignment indicates that the plane of theorbit of the satellite has precessed to that of the primary disc
Table 4.
Characteristics of the ICs formed in the remnants
Model Global structure Substructure Rotation Detectable features(1) (2) (3) (4) (5)(a) M6 Ps Db Nested IDs (thin and thick) Clumps Co-rot. —(b) M6 Ps Rb Nested IDs (both thick) Oval distortion Counter-rot. h > ǫ and PA trends of weak oval distortion.(d) M6 Pl Rb IR + ID (thick) Clumps Counter-rot. ǫ and PA trends of weak oval distortion.Ring sections in h and h maps.Dumbbell structure in σ map.(e) M6 Ps Ds Bulge + ID (thick) — Co-rot. —(f) M6 Ps Rs Bulge + ID (thick) — Counter-rot. Central dip in σ map.Dumbbell structure in σ map.(g) M9 Ps Db Nested IDs (thin and thick) Clumps Co-rot. h > + ID (thin) Clumps, spiral arms Co-rot. h > σ map.(k) M18 Pl Db Nested IDs (thin) Ring relics Co-rot. —(l) M18 Pl Rb IR + ID (thin) Pseudo-ring Counter-rot. —
Columns : (1) Model code. (2) Global structure of the formed IC in each remnant, as derived from the radial and vertical surface density profilesshown in Figs. 2-3 ( §§ § § ǫ and PA profiles at the limits of the ICs, as well as rotation in the center, so none of thesetwo features are listed in the Table (see Figs. 12-15 in § by the time the satellite nucleus disrupts, but that precession isincomplete when the satellite loses its disc.The rotation sense of the IC resulting from the disruptedsatellite material can be deduced from this figure: it rotates inthe same direction as the main galaxy disc in direct orbits andcounter-rotates in the retrograde cases. In general, the alignmentbetween the formed ICs and the main body of the galaxy is worsein retrograde experiments (as already known, see references inBournaud 2009). Nevertheless, we can conclude that the ICs re-sulting in these experiments are highly aligned with the finalgalactic plane in all the cases. The ICs formed in our experiments are strongly rotationally-supported, with V max /σ ∼ . ff ects neg-ligibly to the iso-velocity contours of the global maps (noticethat the maps considering all the stars and only those from theprimary galaxy in the remnants are extremely similar in bothmodels). Moreover, the existence of these ICs does not a ff ectappreciably to the velocity dispersion maps either (compare the σ maps of each model including and excluding the satellite ma-terial).Nevertheless, the ICs a ff ect noticeably to the orientation ofthe photometric axes with respect to the kinematic ones. Asshown in the figure, those obtained just considering the primarygalaxy material are noticeably rotated with respect to the ones obtained considering all the stellar content (compare the whiteaxes drawn in the two first velocity maps of the direct model).This is because direct minor mergers drive the formation of largewarps in the primary disc (Roˇskar et al. 2010; Sellwood 2010).The isophotes in the remnant outskirts of the primary disc ma-terial trace these warps, rotating the corresponding photometricaxes with respect to the orientation (see Fig. 10). However, theaddition of a highly-aligned IC in the centre increases the weightof the central regions in the photometry, making the kinematicand photometric axes to be more similar (compare the kinematicand photometric axes in the first velocity map of the direct modelin Fig. 9).On the other hand, a tight alignment between the photomet-ric and kinematic axes is observed in retrograde mergers, inde-pendently on whether we consider the satellite stars in the mapsor not. The reason is that retrograde orbits give place to muchweaker warps than direct ones due to their lower spin-orbit cou-pling (compare the velocity maps of the primary disc material inboth models of the figure).The satellite material in the retrograde models counter-rotates with respect to the material originally from the primarydisc (compare the velocity maps of the retrograde model inFig. 9). However, no counter-rotation is imprinted to the materialcoming from the primary galaxy in any model (but see § §§ § Fig. 6.
Formation of a transitory bar-like distortion in the pri-mary disc material during a minor merger. The time evolu-tion of the surface density map of the primary disc material ofmodel M6PsRs is plotted, using a face-on view of the initial pri-mary galaxy (experiment f in Table 3). Time is shown at the topleft corner of each panel in simulation units. A rainbow colourpalette is used to represent di ff erent surface density levels in log-arithmic scale, with redder colors indicating higher values. Allphysical quantities are given in simulation units. The major axisof the oval distortion formed in the remnant disc by the satelliteimpact is marked with a black line in the last panels. It rotates inthe same direction as the primary disc material (clockwise). Theorbit and rotation of the accreted satellite is counter-clockwise.The life time of this bar-like distortion corresponds to ∼ . § Bender diagrams of our remnants have been obtained using theprocedure introduced by Gonz´alez-Garc´ıa et al. (2006). We ob-tain line-of-sight velocity distributions (LOSVD) for the mergerremnants by choosing a point of view at random for projectingthe particle distribution. We then derive a surface density mapand define iso-density contours to fit ellipses deriving values forthe ellipticity, PA, and the a parameter (the fourth-order Fouriercoe ffi cient measuring the deviation of the iso-density contoursfrom pure ellipses). We place a slit along the major axis of ourellipses up to R =
2. Given the primary disc scale lengths, ourmapping reaches well into the region of the disc. We have binnedthe slit in 10 spatial bins and the velocity interval in 50 bins. Wefind the radial projected velocity and the number of particles ineach bin in velocity for each bin in the slit. In this way we obtaina line-of-sight velocity distribution. Finally, we fit the LOSVD
Fig. 7.
Pseudo-ring structure in the final remnant of modelM9PsRb, made of stars that initially belonged to the primary disc(experiment h in Table 3). It coincides with the location of thetwo twin symmetric clumps observed in the stellar satellite ma-terial in the final remnant. Both substructures are associated toan oval distortion induced by the satellite accretion (see Fig. 5).The pseudo-ring has been marked with a white dashed circle.A rainbow colour palette is used to represent di ff erent surfacedensity levels in logarithmic scale, with redder colors indicat-ing higher values. All physical quantities are given in simulationunits.by a Gaussian and the residuals by a Gauss-Hermite polyno-mial as given by van der Marel & Franx (1993) and Bender et al.(1994). We repeat this process for each remnant for 90 randomlychosen points of view.From the fitting procedure we obtain for each LOSVD avalue for the velocity centroid of the distribution at each spa-tial bin along the slit ( V ), the velocity dispersion ( σ ), and theamplitude of the third Hermite polynomial ( h ), which is a mea-surement of the skewness of the distribution.We show the resulting Bender diagrams for our simulationswith 1:6 mass-ratio in Fig. 11 (the results from the other simu-lations behave similarly). All models present an anti-correlationbetween the V /σ and h parameter. This is something to be ex-pected due to the prominence of short-axis tube orbits in the pro-genitor discs that are kept relatively undisturbed due to the merg-ing event. The large bulge of simulations M6PsDb, M6PsRb,M6PlDb, and M6PlRb (labelled from a to d in Table 3) alsohelps stabilizing these orbits against the e ff ects of the collision-less minor merger. These simulations di ff er in the amplitude ofthe skewness parameter or the V /σ as a consequence of the dif-ferent orbital parameters of the encounters.An interesting di ff erence is to be observed in the two plotscorresponding to simulations with small bulges in the primarydisc: M6PsDs and M6PsRs (models e and f in Table 3). Heremost of the LOSVD present the anti-correlation usual for discs.However for small values of V /σ we find a mild (in the case ofM6PsDs) or stronger (in M6PsRs) correlation of the two param- Fig. 8.
Misalignment between the material initially belonging tothe satellite bulge and disc with respect to the luminous galac-tic plane of the final remnants (diamonds and triangles, respec-tively). The letters identifying each model are those used inTable 3.eters. This is due both to the e ff ect of the small bulge that is notable to stabilize short-axis tube orbits and to the larger contribu-tion of the satellite bulge in the inner parts of these simulations.It is interesting to note that the e ff ect of the counter-rotating orbitof M6PsRs is signalled by the relatively large correlation signa-ture in the central parts of the diagram. The prominence of the primary stars in the final remnant makethe ICs to be completely masked by their mass distribution, insuch a way that no direct detection of any IC can be performedin either the global surface density maps and profiles of the finalremnants. It is encouraging though that indirect detection similarto that attempted and used in observations proves to be success-ful in many cases, as we will show in this section.
Inner structures in real galaxies imprint noticeable features inthe ellipticity ( ǫ ) and PA profiles of the central isophotes ofthe host galaxies (Erwin et al. 2003; Falc´on-Barroso et al. 2004;Chemin & Hernandez 2009). In the right panels of Figs. 12-15,we have plotted the ǫ and PA profiles of the stellar material inall the remnants, assuming an inclined viewing angle ( θ = ◦ , φ = ◦ ). The radial extent of the ICs as defined in § ǫ ≤ .
2, see the cases shown inFig. 12, for example). Nevertheless, the existence of ICs (andeven their radial extensions) can be deduced just attending to theabrupt changes in the trends of the ǫ and PA profiles that appearat the transition region between adjacent ICs (for example, be-tween two nested IDs or between an ID and the outer remnantdisc, see Figs. 12-15). These trend changes are also observed inreal galaxies, associated to isophotes twisting produced by bars and triaxial structures in the bulges (see Jungwiert et al. 1997;Erwin et al. 2003).The existence of weak bar-like or oval distortions in the rem-nant center of some models can be deduced from their globalisophotal profiles. Models M6Pl[D / R]b (panels c in Fig. 12 andd in Fig. 13) exhibit a slight maximum in ǫ and a constant PA atthe radii where the IC presents twin clumps (see the correspond-ing panels in Fig. 4). Nevertheless, as commented above, noneof our remnants develop noticeable nuclear bars, a fact that iscorroborated by the global ellipticity and PA profiles shown inFigs. 12-15.The models with a small primary bulge exhibit central ellip-ticities equal to or greater than that of the outer disc ( ǫ ∼ . + disc galaxies. The ellipticity shows a quick rise in thecore (bulge) region, a slight decrease in the bulge-disc transi-tion region, and a constant value in the disc outer layers, whilethe PA is nearly constant outside the bulge region (see Fig. 13).Some particular features in the ǫ and PA profiles corroboratingthe existence of some of the ICs identified in §§ In many real galaxies, the existence of kinematically-decoupledcomponents that are not detectable through direct imaging is in-ferred from special features in their kinematic maps. In mostcases, the existence of these ICs is later confirmed by unsharpmasking or by direct detection of its gas component in [OIII]or H β emission-line maps (see, e.g., Falc´on-Barroso et al. 2003,F06).Figures 12-15 show the 2D-maps of the kinemetric momentsof the line-of-sight velocity distribution of all the luminous mate-rial in each remnant, using edge-on views. The line-of-sight ve-locity V LOS , the velocity dispersion σ , and the third- and fourth-order coe ffi cients of the Gauss-Hermite expansion h and h areshown for each model. They have been obtained adapting the profit routine (originally designed for profile fitting of spectralemission-lines by GaussHermite series) to N-body data (Ri ff el2010). The rotation velocity maps in these figures di ff er fromthe analogous ones presented in Fig. 9 in the spatial resolution.While those presented in Fig. 9 use an uniform spatial binning,the ones shown in Figs. 12-15 have higher spatial resolution inthe center than in the outskirts to improve the S / N of the esti-mates of the kinemetric moments in low-density regions (analo-gously to what is done in observations, see F06). The central spa-tial resolutions in these figures are similar to those achieved bycurrent observations in the nearby Universe, adopting the scal-ings proposed in § ∼ . S / N havebeen masked in the maps.Figures 12-15 show that the existence of many ICs could bededuced from these maps of kinemetric moments. Many partic-ular features present in these maps that corroborate the existenceof some of the ICs identified in §§ i. Misalignment of kinematic axes .A clear misalignment of the inner and outer kinematic axesof the galaxy is detected in some cases (see model M6PsRb, panel b in Fig. 12), which can be produced by noticeable discwarping (as the case shown in Fig. 10). Rotation reaches thecentral regions in all the remnants. The final rotation fields,although following a typical spider-like diagram, seem quitedistorted in general, as it is characteristic of dissipationlessmodels (Jesseit et al. 2007). In general, experiments with lowermass ratios or larger pericenters imply a smoother destructionof the initial galaxy rotation pattern. ii. Stretching of iso-velocity contours in the centre .The existence of co-rotating IDs and IRs imprints higherrotation in the centre, stretching the iso-velocity contourstowards the major axis at their location. This makes the angle ofthese contours to be more open at the remnant outskirts than inthe centre (see, e.g., models M6PsDs and M6PlDb, panels b andc in Fig. 12). iii. Twisting of central iso-velocity contours in retrogrademodels. As shown in § ∼ ◦ at the coreregion (see model M6PsRb in panel b of Fig. 12, and modelsM18P[s / l]Rb in panels j and l of Fig. 15). iv. S-shaped twists of iso-velocity contours. Almost all the cases exhibit S-shaped or integral-sign-shaped twisting of the central iso-velocity contours at a certainheight in the galactic plane. These features are produced by thesharp decrease of the amount of stars that contributes to thevelocity field at a certain spatial position. Therefore, S-shapedkinematic twists in our models appear at the spatial locationswhere the mass contribution of the ICs becomes negligible(see, e.g., models M6PlRb and M18PsDb, in panels d and i ofFigs. 13 and 14). v. h peaks. The majority of the models with big primary bulges showpositive h values in general, peaking at the location of the ICsformed at the end of the simulation. In particular, the ring geom-etry of the IC resulting in model M6PlRb can be deduced fromthe two well-defined symmetric peaks present in the h maps,which trace its perpendicular sections (panel d in Fig. 13). vi. Correlations between the kinemetric moments. We have found that v LOS and h correlate at the locationof the formed IC in our remnants if it exhibits oval or bar-likedistortions (see models M6Ps[D / R]b and M6PlDb in panels a-c of Fig. 12, and models M9PsRb and M18PsDb in panels h-i of Fig. 14). However, when the ICs show no trace of havinghad them, v LOS - h anti-correlate at the location of the IC, ac-cordingly to the discy structure of the majority of the obtainedICs (see models M18PsRb and M18Pl[D / R]b in Fig. 15). Somemodels also exhibit a mixed behaviour: v LOS - h correlate at theremnant core (at R < .
3) and anti-correlate at the position ofthe h peaks, as occurs in models M6PsDs (panel e in Fig. 13)and M9PsDb (panel g in Fig. 14). This is probably pointing to anorigin related to oval distortions and bar-like distortions in thesecomponents. vii. Dumbbell σ structures. Dumbbell structures in σ maps point to the existence ofcounter-rotating IDs, which rise σ at their location. Althoughall the retrograde models give place to counter-rotating IDs orIRs, dumbbell structures are only observed in models M6PlRband M6PsRs (panels d and f in Fig. 13). viii. Central σ dips. Fig. 10. Final warped disc of model M9PsDb (experiment g inTable 3). An edge-on view of the material originally belongingto the primary disc in the final remnant of this model is shown.A rainbow colour palette is used to represent di ff erent surfacedensity levels in logarithmic scale, with redder colors indicat-ing higher values. All physical quantities are given in simulationunits.In general, the velocity dispersion is very high in the rem-nant centres because the bulge dynamics dominate at those radii.However, it tends to decrease at the bulge-to-disc transitionregion due to the contribution of the co-rotating IC. In ourmodels, σ dips are detected only in the models of small primarybulges (see panels e and f of Fig. 13).Summarizing, the velocity fields of our remnants exhibit fea-tures that reveal the existence of the central ICs formed throughthe satellite accretion, such as the stretching of the iso-velocitycontours in the centre, S-shaped kinematic twists, and dumbbell σ profiles. More inclined views of the remnant smooth out thesefeatures, making the ICs undetectable in the velocity 2D-maps.
4. Qualitative comparison to observations
In this section, we make a qualitative comparison of the prop-erties of the ICs obtained in our minor merger simulations withreal observational cases, to stress the similarities and di ff erencesamong them. Figure 16 compares the morphology of some of the ICs formedin our experiments to observational examples that exhibit similarinner structures from the sample of Erwin & Sparke (2003). Asshown by the figure, the ICs resulting from our minor mergerexperiments are analogous structural and morphologically tothe ICs hosted by many real spiral galaxies. IDs, nested IDs,rings and pseudo-rings, spiral patterns, and even undisruptedclumps with irregular spatial distributions as those observedin our experiments are found in real spiral galaxies (see alsoButa & Combes 1996; Erwin & Sparke 2002; Erwin et al. 2003;Erwin 2004; P´erez-Gallego et al. 2010; Sil’chenko et al. 2011).
Star-forming pseudo-rings are substructures usually associ-ated to gas and starbursts in real galaxies (F06; Shapiro et al.2010; Sil’Chenko 2010). However, although our models donot consider dissipative components, some remnants exhibitstellar ring relics or pseudo-rings in the centre (see modelsM18Pl[D / R]b in panels k and l of Fig. 5).Our remnants have not developed significant nuclear bars(although some of them present signs of weak oval or bar-likedistortions in the center, see § § ∼ . ∼ ∼
360 pcto ∼ . §
2. These valuesare in excellent agreement with those obtained for the IDs de-tected in real galaxies (Erwin & Sparke 2002; Sarzi et al. 2006;Shapiro et al. 2010; Sil’chenko et al. 2011, F06). The IRs andpseudo-rings formed in our simulations are embeded in theseIDs, and thus, exhibit typically lower linear sizes. Adopting thescalings of §
2, our IRs match pretty well the standard 1 kpc-radius IRs that lie between the inner Lindblad resonances ofmany disc galaxies (Erwin & Sparke 2002; Shapiro et al. 2010).Concerning to their vertical distributions, the flared verticalstructure of most the single IDs and nested IDs resulting in ourmodels (see Fig. 3) is extremely similar to the one derived re-cently for the galaxy NCG 7217, composed by two large scalenested stellar discs (Sil’chenko et al. 2011).The existence and extension of many real ICs are usuallyderived from abrupt changes in the trends of the ellipticityand PA profiles of the global galaxy isophotes (Erwin & Sparke2002, 2003; Erwin 2004). As we have shown in § § . ◦ for the ICs harboured by Sa-Sb galaxies, andKrajnovic et al. (2011) find that 90% of the ICs in a sample of260 early-type galaxies can be considered aligned to better than5 deg. Nevertheless, we can not discard the possibility that thismay be facilitated by the moderate inclinations of our simulatedorbits. However, the quick decay of the satellite orbit to the pri-mary disc plane observed in all the models suggests that moreinclined orbital configurations could result into aligned ICs too,and that extreme orbital inclinations would be required to pro-duce noticeably misaligned ICs.Our simulations also demonstrate the feasibility of the sce-nario proposed by F06 to explain the low misalignment of theICs observed in Sa-Sb galaxies as compared to those in E-S0’s(usually above 60 ◦ , see Sarzi et al. 2006). According to these au-thors, if the ICs have resulted from minor mergers, the morphol-ogy of the primary galaxy in the encounter should play a crucialrole in determining its alignment. In our simulations, the evo-lution of the satellite orbit to the primary disc plane prior to its disruption is produced by the low spheroidality of the primarygalaxy potential, which establishes a privileged plane a priori(the primary disc plane). Spheroidal potentials (as those of E-S0 galaxies) do not have any privileged direction, and thus theydo not produce this e ff ect in the orbits of the accreted satellites(Di Matteo et al. 2008). Therefore, our simulations suggest that,if the majority of ICs derive from minor mergers, we should ex-pect to detect more aligned ICs in disc galaxies (as Sa-Sb’s) thanin spheroidal ones (E-S0’s), coherently with observations andwith F06 arguments. Moreover, F06 propose that the existenceof large gas amounts involved in the merger must contribute tothis alignment. Notice that, although the previous sentence mustbe true, our models prove that gas is not strictly necessary toobtain high co-planar ICs in minor mergers. ICs disturb the velocity field of their host galaxies, giving placeto particular kinematical features in the global maps of thegalaxy pointing to their existence. Our remnants exhibit manyof these features, such as disturbed iso-velocity contours in thecenter, noticeable S-shaped kinematic twists at the limiting radiiof the ICs, σ peaks, dumbbell-like σ structures associated tocounter-rotating IDs, and stretching of iso-velocity contours atthe presence of co-rotating ICs (see § § ff ect signif-icantly to the central dynamics of the remnants, which are ba-sically dominated by the host rotating disc instead (see § ff erences as well. In general, ourmodels show h ≥ h peaks at the location of the ICS,in excellent agreement with observations of ICs in early-typegalaxies (F06; Krajnovi´c et al. 2008). However, the V LOS - h cor-relation found in our simulations reproduce the observationaltrends partially. Observations report V LOS - h anti-correlation atthe location of co-rotating ICs in Sa-Sb’s, and correlation ifthe ICs counter-rotate (F06). Nevertheless, our models tend toexhibit V LOS - h anti-correlation, independently on the rotationsense of the IC with respect to the final galaxy (see Figs. 12-15). Although some retrograde models can present correlationfor particular viewing angles (see model M6PsRs, panel f inFig. 11), in general we find anti-correlation (see the rest ofBender diagrams in Fig. 11).Our models do not include the e ff ects of gas dynamics andstar formation, which obviously a ff ect to the kinematical struc-ture of the final remnant (see § V LOS and h to cor- relate (see, e.g., Naab & Burkert 2001). However, the inclusionof gas in the simulation has the opposite e ff ect: it suppressesthem and make V LOS and h to anti-correlate at the remnant cen-tre (Bendo & Barnes 2000; Naab & Burkert 2001; Jesseit et al.2007). Then, our collisionless simulations behave atypically inthis sense, as they tend to exhibit V LOS - h anti-correlation. Thistrend was already obtained by Gonz´alez-Garc´ıa et al. (2006),who showed that such anti-correlations can be kept in a colli-sionless merger simulation whenever a central bulge allows thediscs to retain some of their original angular momentum duringthe merger, making short-axis tube orbits to be still present inthe final remnant.In our models, V LOS - h correlation seems to be more re-lated to the existence of bar-like or oval distortions than tocounter-rotation ( § V LOS - h correlation is related to theexistence of non-axisymmetric distortions in the galaxy disc, theprevious result establishes a correspondence between V LOS - h correlations and counter-rotating ICs, coherently with F06 re-sults. This scenario is supported by the di ff erent V LOS - h trendsexhibited by Sa-Sb and E-S0 galaxies. While ICs hosted bythe later ones are always associated to V LOS - h anti-correlations(Bender et al. 1994), the ICs in early-type discs exhibit corre-lations only if the IC is counter-rotating (F06). This can be ex-plained considering that E-S0’s are more e ffi cient inhibiting barsand ovals than Sa-Sb’s (because they have larger bulges and neg-ligible disc components), a fact that should make the ICs in thesegalaxies to exhibit V LOS - h anti-correlations in general (coher-ently with observations).In conclusion, minor mergers could account for the existenceof many stellar dynamically-cold ICs in spiral galaxies and evenin E-S0’s. The present models prove that they can give placeto ICs with geometrical, structural, and kinematical propertiessimilar to those observed in real galaxies.
5. Model limitations
We have analysed the role of minor mergers in the formationof dynamically-cold thin stellar ICs, without accounting for gasand star formation e ff ects. Obviously, the inclusion of dissipativecomponents in the models would not just provide the formed ICwith an additional recent stellar population or gas component,but it could a ff ect noticeably its final structure and kinematics.The formation of IDs and IRs are associated to the redistri-bution of angular momentum in the remnant disc. In this sense,gas components are expected to contribute noticeably to thisre-distribution, mainly during disc distortions. Nevertheless, re-cent studies have demonstrated that dissipative components (al-though relevant) are not essential or decisive in the formation ofkinematically-decoupled ICs through major mergers. Gas causesthe remnants to appear more round and axisymmetric, wipingout small kinematical misalignments more easily, but the result-ing IC conserves most of its structural properties as compared tocollisionless models (Jesseit et al. 2007).Besides, although star formation triggers the formation ofyoung stars in the IC in simulations of major mergers, the re-sulting IC is still composed by a relevant old stellar component(Di Matteo et al. 2008). If the formation of an ID or IR depended basically on merger-induced gas inflows to the galaxy cen-tre and on the subsequent star formation (Barnes & Hernquist1996; Bournaud et al. 2005b), these substructures should bebluer or, at least, younger than the surrounding bulge compo-nent. However, this is not the case, as IDs exhibit very simi-lar colors to those of their host bulges usually (see Morelli et al.2004; Peletier et al. 2007). Therefore, although gas and star for-mation e ff ects must have been relevant in the formation of IDsand IRs, they may not be essential for it in many cases. Thisis also supported by the significant old underlying stellar com-ponent detected in most IDs and IRs (Buta & Purcell 1998;Buta et al. 1998; van den Bosch et al. 1998; Krajnovi´c & Ja ff e2004; Morelli et al. 2004).The flattened structure of IDs and IRs has been tradition-ally interpreted as a sign of the essential role played by gas intheir formation (Cappellari et al. 2007), but our models provethat central thin rotationally-supported ICs can result from satel-lite disruption without supplying gas to the remnant centre.However, this is a simplified picture of the reality, as the major-ity of the observed IDs and IRs contain recent (or on-going) starformation, dust, and gas, a fact that clearly points to the tight re-lation between dissipative processes and their buildup (see, e.g.,Barnes & Hernquist 1996; van den Bosch & Emsellem 1998;Morelli et al. 2004; Kormendy et al. 2005; Cappellari et al.2007; Peletier et al. 2007, F06). In fact, we could expect that theinclusion of gas and star formation in the models would madethe formed ICs more detectable, accounting for the star forma-tion that minor mergers usually trigger in the centre of galaxydiscs (Kaviraj et al. 2009). So, we intend to re-run these simu-lations including gas and star formation processes in the nearfuture, to determine the e ff ects of dissipative processes in theformation of ICs.
6. Discussion
The present models provide a novel insight into the buildup ofdynamically-cold ICs through minor mergers, because the re-sulting IDs and IRs do not derive from primary disc materialor from a gaseous component as in other studies, but from thedisrupted stellar satellite material. Traditionally, minor merg-ers have been considered as secondary drivers in the forma-tion of IDs or IRs in galaxies, in the sense that the rotationally-supported ICs were thought to come from the bars triggered inthe discs by the encounters, not from the minor merger them-selves. The accreted satellite material did not ended in these ICsexcept if it reached the centre undisrupted (see § §§ ff erence between our models and previous ones fromthe literature lies basically in the satellite characteristics, as wehave found that very di ff erent orbital configurations give place tosimilar ICs (see Table 4). In our models, the discy structure andthe realistic density contrast of the satellites with respect to theprimary galaxies make them to be sensitive to disruption, but re-sistant enough to reach the remnant centre (in contrast with pre-vious models, see Aguerri et al. 2001; Moster et al. 2010). Thisimplies that, if a low-density satellite (as a dS) were accretedby a galaxy, the existence of a prominent bulge in the primary galaxy would induce the complete disruption of the satellite andthe formation of an IC out of it. However, if the accreted satel-lite were dense (such as a dSph or dE) or if the primary galaxyhad a small bulge, the undisrupted satellite core would depositin the centre without disrupting, increasing the spatial density inthe galaxy core.The bar-related origin of numerous bulges and dynamically-cold ICs in galaxies is indisputable (Martinez-Valpuesta et al.2006; Berentzen et al. 2007; Romero-G´omez et al. 2007;Athanassoula et al. 2009a,b, 2010; Bagley et al. 2009;Fisher & Drory 2010), but it is also true that more thanone third of them in Sa-Sb galaxies are apparently unrelated tobars (see references in § / or to the triggered oval distortions) indicates thatit would be very di ffi cult to prove the minor merger origin ofthe resulting ICs by disentangling the stellar population with anexternal origin from the underlying stars. However, the minormerger origin of the ICs in some galaxies is obvious, mainlyif the IC is counter-rotating or it is harboured by a non-relaxedhost (see Haynes et al. 2000; Guti´errez et al. 2002; Shapiro et al.2010; Sil’chenko et al. 2011).The key role of minor mergers in the growth of bulgesof spiral galaxies is evident, as relics of disrupted satellitesand on-going minor mergers are frequently found in nearbygalaxies, indicating that these processes are extremely common(Mart´ınez-Delgado et al. 2007, 2008, 2009, 2010; Knierman2010). Therefore, the present models suggest that the majority ofthe ICs found in spiral galaxies could have had a minor-mergerrelated origin (independently on whether the minor merger trig-gers a noticeable bar or not), and that the role of minor mergersin the formation of ICs may have been much more complex thanjust bar triggering, as traditionally assumed.
7. Summary and conclusions
We have investigated the capability of minor mergers to triggerthe formation of IDs and IRs in spiral galaxies through collision-less N-body simulations. We have extended the simulations ofminor mergers onto disc galaxies presented in EM06, samplinga wider parameter space of initial conditions. Di ff erent orbitsand mass ratios have been considered, as well as two di ff erentmodels for the primary disc galaxy (Sab or Sc galaxy).All the simulated minor mergers have developed thinrotationally-supported ICs out of disrupted stellar satellite ma-terial, with scale lengths analogous to those observed in real IDsand IRs. The resulting ICs are highly aligned to the main galac-tic plane of the remnant, as the original non-spheroidal potentialof the primary galaxy makes the satellite orbit to evolve to itsprivileged plane prior to disruption. This fact provides a possi-ble explanation for the low misalignment observed in the ICsfound in Sa-Sb galaxies as compared to those in E-S0’s. No rel-evant counterparts of these dynamically-cold ICs are obtained inthe remnant material originally belonging to the primary galaxy.The geometrical analysis of these ICs reveals a wide mor-phological zoo of ICs, similar to the observed ones in Sa-Scgalaxies through direct imaging or through unsharp masking, such as IDs, IRs, pseudo-rings, nested IDs, spiral structure, anddi ff erent combinations of them. No noticeable bars have beenformed either in the primary disc or in the IC made out of ac-creted satellite material. The structural and kinematic propertiesof these ICs are analogous to those observed in real galaxies aswell. The existence of these ICs cannot be derived directly fromglobal surface density maps and profiles, but it can be deducedfrom the characteristic features that they imprint to the isophotalprofiles and kinematic maps of the final remnants, analogouslyto many observational cases.Key points to explain the formation of these IDs and IRs inour simulations without requiring significant bars or dissipativecomponents are the structure and density of the satellites, as wellas the existence of a prominent bulge in the primary galaxy. Therealistic satellite-to-primary galaxy density ratios make the satel-lites to be more sensible to orbital circularization and disruptionthan those used in previous simulations.Combined with the disc resonances induced by the en-counter, these three processes (satellite disruption, orbital cir-cularization, and coupling of disruption with merger-triggeredresonances in the disc) give place to highly aligned rotationally-supported ICs in the remnants centre. The existence of big bulgesin the primary galaxies and long-lasting decaying orbits ensurea more e ffi cient satellite disruption, producing thinner ICs. Thisimplies that, if a low-density satellite (such as a dS) were ac-creted by a galaxy with a prominent bulge, it would result inthe complete disruption of the satellite and the formation of arotationally-supported flat IC. However, if the galaxy accretedwere a high-density satellite (such as a dSph or dE) or if the pri-mary galaxy had a small bulge, the undisrupted satellite core isexpected to sink to the galaxy centre without disrupting com-pletely, contributing to the formation of a central bulge. In thissense, minor mergers could account for the existence of old,pure stellar IDs and IRs in many unbarred galaxies (speciallythe counter-rotating ones).Traditionally, minor mergers have been considered just assecondary agents in the formation of dynamically-cold ICs ingalaxies, only responsible for inducing the bars in the galaxydiscs that finally give place to these ICs. Our models suggestthat the majority of the ICs found in spiral galaxies could havehad a minor-merger related origin (independently on whether theminor merger triggers a bar or not), and that the role of minormergers in the formation of ICs may have been much more com-plex than just bar triggering. In conclusion, the present modelsprove that minor mergers are an extremely e ffi cient mechanismto form rotationally-supported stellar ICs in spiral galaxies, nei-ther requiring strong dissipation nor the development of strongbars. Acknowledgements.
We thank our anonymous referee whose sugges-tions helped us to improve the clarity and presentation of the results. Weare also very grateful to P. Erwin, L. S. Sparke, and to the AmericanAstronomical Society for the permission to reproduce some figuresfrom Erwin & Sparke (2003). Supported by the Spanish Ministry ofScience and Innovation (MICINN) under projects AYA2009-10368,AYA2006-12955, and AYA2009-11137, and by the Madrid RegionalGovernment through the AstroMadrid Project (CAM S2009 / ESP-1496,http: // ff .cab.inta-csic.es / projects / astromadrid / main / index.php). Fundedby the Spanish MICINN under the Consolider-Ingenio 2010 Program grantCSD2006-00070: ”First Science with the GTC” (http: // / consolider-ingenio-gtc / ). ACGG is a Ramon y Cajal Fellow of the Spanish MICINN. References
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Radial surface brightness profiles of disrupted satellite material in the final remnants of all the models. The plotted physicalmagnitudes are provided in simulation units. The letters identifying each panel are those used in Table 3.
Circles : Considering allthe stars originally belonging to the satellite.
Red dashed lines : Satellite bulge stars.
Blue dotted lines : Satellite disc stars.
Blacksolid straight lines : Exponential fits to the radial density profiles considering all the satellite stars. The data points plotted in greenhave been excluded from the fits. In the panels corresponding to remnants that are better fitted with two exponential discs, the twoscale-lengths are shown in the frame. When just one exponential disc provides a better fit to the global satellite stellar profile thantwo nested ones, only one scale-length is provided. The root mean square of the global fit is also shown in each remnant.
Orangelight solid curved lines : Total fit to the radial surface density profiles in those cases that are better fitted by two exponential discs.
Vertical dashed lines : Extent of each IC characterized by each fitted exponential radial profile, as defined in the text. The radialextension of the ICs is remarked using a shaded background with di ff erent color for the di ff erent ICs identified in each model (greenfor the innermost ones and orange for the outer ones). Sub-panels : Relative residuals of the fits as a function of the radial position.The models with small primary bulges obey a di ff erent scaling to the rest of models (see § ff er from those in the others, as observed in Figs. 2- 4. Fig. 4.
Morphology of the ICs made out of disrupted satellite stellar material resulting in models with mass ratio 1:6 (models a-f inTable 3). Surface density maps of the stars originally from the satellite in the final remnants are presented, using a face-on and anedge-on view (left and right columns in each model, respectively). A rainbow colour palette is used to represent di ff erent surfacedensity levels in logarithmic scale, with redder colors indicating higher values. The levels of the color scale di ff er from panel topanel, as they have been set automatically to ensure an adequate sampling of the dynamical range of the surface density shown ineach map. Spatial scales in both axes are provided in simulation units. The radial extent of each independent IC (i.e., characterizedby an unique exponential profile, see § Fig. 5.
Morphology of the ICs resulting in models with mass ratio 1:9 and 1:18 out of disrupted satellite stellar material (models g-lin Table 3). See caption of Fig. 4. li c h e - M o r a l e t a l . : A m i no r m e r g e r o r i g i n f o r s t e ll a r i nn e r d i s c s a nd r i ng s i n s p i r a l g a l a x i e s Fig. 9.
Line-of-sight rotation velocity, velocity dispersion, and signal-to-noise ratio ( S / N ) maps of the stellar material coming from di ff erent original components in the finalremnants of models M9PsDb and M9PsRb, using an edge-on view of the remnants (experiments g and h in Table 3). The same levels have been used for the color palette of thevelocity maps of the di ff erent components in each model and in the velocity dispersion maps to remark the high rotational support of the ICs resulting from satellite material(consult the bars on the top of the corresponding columns). Levels are distributed linearly. The maximum level in the bars corresponding to the S / N maps show four di ff erentvalues, corresponding to each one of the frames below, respectively. All physical magnitudes are provided in simulation units. First row : Considering all the stars in the remnant.
Second row : For the stars initially belonging to the primary galaxy.
Third row : For the stars originally in the satellite disc.
Fourth row : For the stars originally in the satellitebulge.
Contours : Surface iso-density contours in the final remnant of the material considered in each map, just as reference.
White straight lines : Photometric axes of the materialconsidered in each panel.
Black straight lines : Kinematical axes of the material considered in each panel. liche-Moral et al.: A minor merger origin for stellar inner discs and rings in spiral galaxies Fig. 11.
Bender diagrams of the remnants resulting from the minor merger experiments run with a mass ratio 1:6. The amplitude ofthe third Hermite polynomial h of the final remnant is plotted against its V /σ for 90 randomly chosen points of view. Fig. 12.
Photometrical and kinematical features imprinted by the formed ICs in the global stellar maps of the final remnants ofmodels M6Ps[D / R]b and M6PlDb (models a to c in Table 3). Left panels: Ellipticity and PA isophotal profiles of all the stars in theremnants, using an inclined view ( θ = ◦ , φ = ◦ ). The extent of the ICs as defined in § V LOS , σ , h , h ). The levels are distributed linearly (simulationunits). The photometric axes defined by the material in the core region of the galaxy are also plotted ( straight lines ). The isophotesof the stellar material in the remnant originally belonging to the satellite are overplotted just as reference ( contours ). Fig. 13.
Photometrical and kinematical features imprinted by the formed ICs in the global stellar maps of the final remnants ofmodels M6PlRb and M6Ps[D / R]s (models d to f in Table 3). See caption of Fig. 12.
Fig. 14.
Photometrical and kinematical features imprinted by the formed ICs in the global stellar maps of the final remnants ofmodels M9Ps[D / R]b and M18PsDb (models g to i in Table 3). See caption of Fig. 12.
Fig. 15.
Photometrical and kinematical features imprinted by the formed ICs in the global stellar maps of the final remnants ofmodels M18PsRb and M18Pl[D / R]b (models j to l in Table 3). See caption of Fig. 12.
Fig. 16.
Comparison of some ICs obtained in our minor merger experiments (first and third columns in the figure) to real ob-servational examples with similar morphologies (second and fourth columns, respectively). The surface density maps of the ICsgenerated in our models are taken from Figs. 4-5 and are in simulation units (consult captions there). The observational examplesare taken from the sample of spiral galaxies with ICs developed by Erwin & Sparke (2003). Coloured maps of real galaxies corre-spond to B − R or V − I color maps of these galaxies, while their grey-scale maps represent unsharp masks in V , R or H bands (seeErwin & Sparke (2003) for a detailed description of each frame). The global inclination of galaxy in the observational cases and thespatial scale of each postage stamp are indicated in each frame. In images of real galaxies, North is up and East is left, except inNGC 4665, which has been rotated 90 ◦ clockwise to emphasize the similarity with the IC resulting in experiment M6PsRb (modelb). For a comparison of the scaled sizes of the ICs resulting in our models with those exhibited by real ICs, consult §
4. Materialfrom Erwin & Sparke (2003) in this figure is reproduced by permission of the American Astronomical Society (AAS) and of theoriginal authors.4. Materialfrom Erwin & Sparke (2003) in this figure is reproduced by permission of the American Astronomical Society (AAS) and of theoriginal authors.