Forming disc galaxies in major mergers: III. The effect of angular momentum on the radial density profiles of disc galaxies
MMNRAS , 1– ?? (2017) Preprint 6 March 2017 Compiled using MNRAS L A TEX style file v3.0
Forming disc galaxies in ma jor mergers: III. The effect ofangular momentum on the radial density profiles of discgalaxies
N. Peschken , (cid:63) , E. Athanassoula , S. A. Rodionov Laboratoire d’Astrophysique de Marseille, 38, rue Fr´ed´eric Joliot-Curie 13388 Marseille cedex 13 FRANCE Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
ABSTRACT
We study the effect of angular momentum on the surface density profiles of disc galax-ies, using high resolution simulations of major mergers whose remnants have down-bending radial density profiles (type II). As described in the previous papers of thisseries, in this scenario, most of the disc mass is acquired after the collision via ac-cretion from a hot gaseous halo. We find that the inner and outer disc scalelengths,as well as the break radius, correlate with the total angular momentum of the initialmerging system, and are larger for high angular momentum systems. We follow theangular momentum redistribution in our simulated galaxies, and find that, like themass, the disc angular momentum is acquired via accretion, i.e. to the detriment ofthe gaseous halo. Furthermore, high angular momentum systems give more angularmomentum to their discs, which affects directly their radial density profile. Addingsimulations of isolated galaxies to our sample, we find that the correlations are validalso for disc galaxies evolved in isolation. We show that the outer part of the discat the end of the simulation is populated mainly by inside-out stellar migration, andthat in galaxies with higher angular momentum, stars travel radially further out. This,however, does not mean that outer disc stars (in type II discs) were mostly born inthe inner disc. Indeed, generally the break radius increases over time, and not takingthis into account leads to overestimating the number of stars born in the inner disc.
Key words: galaxies: spiral – galaxies: structure – galaxies: kinematics and dynamics
The early pioneering work of Freeman (1970) showed clearlythat the radial surface density profile of disc galaxies is wellfitted by an exponential. Later work (Van der Kruit 1979,and later e.g. Pohlen et al. 2002; Erwin, Beckman & Pohlen2005; Guti´errez et al. 2011) revealed the presence of a breakin the profile of most galactic discs, as well as the fact thatboth the inner and the outer parts are well described byexponentials.The break can be of two kinds, depending on the scale-lengths of the two exponentials. If the slope of the outer partof the disc, hereafter called outer disc, is steeper than theslope of the inner part (inner disc), i.e. if the inner disc scale-length is greater than the outer disc one, the profile is calleddownbending, or type II (Pohlen & Trujillo 2006). This is themost common profile for disc galaxies (e.g. Pohlen & Tru-jillo 2006; Azzollini, Trujillo & Beckman 2008; Laine et al. (cid:63)
Contact e-mail: [email protected] c (cid:13) a r X i v : . [ a s t r o - ph . GA ] M a r N. Peschken, E. Athanassoula, S. A. Rodionov redistribute stars from the inner disc to the outer disc, andcan be coupled with a star formation threshold (Roˇskar etal. 2008). On the other hand, type III profiles (upbendingdiscs) remain poorly understood. They are sometimesassociated with a spheroidal component such as a stellarhalo, or with the superposition of a thin and a thick disc,and could be the result of minor mergers, or be linked to astrong bar (Erwin et al. 2005; Younger et al. 2007; Bakos &Trujillo 2012; Comer´on et al. 2012; Herpich et al. 2015b).Although the majority of the present-day spirals is thoughtto have experienced at least one major merger in their his-tory (e.g. Hammer et al. 2009), so far most of the simulatedgalaxies used to investigate the formation of these differentdisc types have been evolved in isolation. Recently, however,we presented in Athanassoula et al. (2016, hereafter A16)three fiducial examples from a large sample of high resolu-tion simulations of a major merger between two disc galaxieswith a hot gaseous halo each, and showed that the remnantsare good models of spirals. In this paper, we aim to studythe role of angular momentum in shaping type II profiles,obtained from our large sample of major merger simulations.The outline is as follows. In section 2, we briefly sum-marise the necessary parts of A16, and describe the fittingprocedure for the radial density profiles. We compute theinitial angular momentum and link it to the scalelengths insection 3. In section 4, we follow the angular momentum re-distribution to explain how the initial angular momentumcan affect the final disc properties. We discuss our results insection 5, and conclude in section 6.
In this section, we will briefly summarise the simulationscharacteristics, which have been obtained and described insome detail in A16. Our simulations start from two spheri-cal protogalaxies consisting only of dark matter (DM) andhot gas, which we set on a given orbit. We use a total of 5.5million particles (2 million for the baryons, 3.5 million forthe DM), with softenings of 25 pc for the gas and 50 pc forthe DM. Each particle’s mass is 5 × M (cid:12) for the gas andstars, and 2 × M (cid:12) for the dark matter. By the time of themerging, a disc has formed in each of the progenitors, whichis destroyed by the merging, its stars ending up mainly ina classical bulge. Gas continues to fall from the halo, andnew discs, both thin and thick, are gradually formed in theremnant. Well-defined spiral arms soon develop in the thindisc, as well as a bar and a boxy/peanut bulge. Each simu-lation ends after 10 Gyr evolution, showing a remnant witha classical bulge-to-total ratio which is consistent with thatof real spiral galaxies.Our simulations are made using the N-body/SPH codeGADGET3, including gas and its physics. The descriptionof this code can be found in Springel & Hernquist (2002) andSpringel (2005). Stars and dark matter are modeled by N-body particles, and gas by SPH particles, with fully adaptivesmoothing lengths. Gravity is computed with a hierarchytree algorithm, and the code uses subgrid physics for thefeedback, star formation and cooling, described in Springel& Hernquist (2003). For a description of the technical aspects of the sim-ulations we refer the reader to Rodionov, Athanassoula &Peschken (2017, hereafter R17). To avoid an excessive cen-tral concentration in our simulated galaxies, which wouldlead to unrealistic circular velocity curves and would delaythe formation of the bar, we added AGN feedback (R17).This is based on a density threshold ρ AGN and a tempera-ture T AGN , while the physics underlying it is described indetail in A16.The simulations have a variety of different orbits for thetwo merging protogalaxies. These orbits are characterisedby their ellipticity, and the initial distance between the twoprogenitors. Each orbit leads to a different merging time,which is difficult to define precisely, but can be approximatedby deriving the time beyond which the distance between thetwo centers of density stays below 1 kpc (see A16).The two protogalactic haloes start with an initial spin,characterised by a spin value f representing the fraction ofparticles rotating with a positive sense of rotation. Thus for f = 1, all the particles rotate in the direct sense, while for f = 0 . f is the same for both protogalax-ies, but in some simulations we introduced a different spin ineach protogalaxy. We ran simulations of mergers with massratios between the two protogalaxies of 1, 1/2, 1/3, 1/4 and1/8. A central AGN is present in the remnant galaxy of themajority of our simulations, as described in A16 and R17,but we include 21 simulations without AGN to cover a largerpart of the available parameter space. Nevertheless, the pres-ence of our AGN affects mainly the central part of the disc(R17), and thus should not have an impact on the analysispresented in this paper.We will first consider a subsample of 132 simulationswhich all have the same total mass, i.e. the same numberof particles (5.5 million), and call it sample A. We also ran67 simulations with various masses, each different from themass of the simulations in sample A. This is done by keepingthe same mass for single particles, but changing the num-ber of particles. We add this group of 67 simulations (calledsample B) to sample A to obtain a new sample of 199 sim-ulations, sample A+B, which we will use in the discussion(section 5.2). To derive the stellar radial density profile, we use axisym-metric concentric cylindrical annuli, and choose z lim =1 kpcas maximum height to keep only the thin disc profile. Asshown in A16, the disc at the end of our three fiducial sim-ulations is composed of an inner and a downbending outerdisc (type II), separated by a break. This is also the case forthe 199 simulations of the sample used in this paper (sampleA+B), therefore we fit the disc part of our profiles with twoexponential functions. We use a “piecewise” fit, which means
MNRAS , 1– ????
MNRAS , 1– ???? (2017) ffect of angular momentum on density profiles Figure 1.
Projected surface stellar density radial profiles for twosimulations, together with the corresponding fits for the disc part.For clarity, the second simulation (in black) has been shifted downby 1 logarithmic unit. Simulation 1 has a higher initial spin pa-rameter λ than simulation 2. that we fit the inner and the outer disc separately with anexponential:Σ in ( R ) = Σ i exp( − Rh i ) , R < R break (1)Σ out ( R ) = Σ o exp( − Rh o ) , R > R break (2)where Σ i , Σ o are normalization factors, h i and h o are theinner and outer disc scalelengths, and R break the break ra-dius. The latter is derived by taking the intersection betweenthe inner and the outer disc fits. The interval to fit for eachpart of the disc is selected manually, and we exclude, aftervisual inspection, every simulation for which the fit is notreliable. Two examples of fits are shown in Fig. 1. Anotherway to make this fit would be to use a double exponentialfunction (or “broken-exponential”) for the whole disc, whichhas been shown to give very similar results (differences inthe scalelengths < Here, we use the dimensionless spin parameter λ (Peebles1969): λ = L | E | / GM / , (3)where L , E and M are respectively the total angular mo-mentum, energy and mass of the system including its darkmatter, gas and stars, computed with respect to the centerof mass of the system, and G is the gravitational constant.The total energy is computed adding the kinetic energy, thegravitational potential energy and the gas internal energy.The total angular momentum L is a conserved quantity, butthe total energy varies with time because of processes such asthe cooling of the gas and the stellar feedback. We thereforehave to specify the time at which we will calculate λ , andmake sure it is calculated consistently for all simulations. Toavoid the technical difficulties inherent in using the mergingtime, we use t=1 Gyr before the merging, which we call theinitial state. How does the disc structure relate to the global spin param-eter λ ? From the definition of angular momentum, we expectthat for two galaxies of the same total mass, the galaxy withthe highest angular momentum will be more extended, as ithas been shown in previous studies (e.g. Dalcanton, Spergel& Summers 1997 and Kim & Lee 2013). We checked thisresult in our simulations by plotting the size of our galacticdiscs at the final state as a function of λ , for the simulationsof sample A. As an estimate of the disc size, we take R
95, thecylindrical radius containing 95 per cent of the total stellarmass. We can see on Fig. 2 that the size of the final galaxyincreases linearly with λ , with a high correlation coefficient.We thus find the disc to be globally larger for high λ galaxies, as expected. However, since the disc is constitutedof an inner and an outer part, which part of the disc isaffected most? We expect at least one of the two discs (inneror outer) to be larger at higher λ . To have a first insight ofthe effect of the spin parameter λ on the parameters of theradial density profiles, we plot in Fig. 1 the profiles at thefinal state (as defined in section 2.2) for two simulationsof sample A with different λ values. We can see that thescalelengths of the simulation with a higher λ (in blue) are MNRAS , 1– ?? (2017) N. Peschken, E. Athanassoula, S. A. Rodionov
Figure 2.
Cylindrical radius containing 95 per cent of the stellarmass at the final state, as a function of the spin parameter λ computed at the initial state, for the simulations of sample A.The corresponding linear fit is plotted in black, with the equationand correlation coefficient given in the top left corner. larger, and its break is located further out. The next stepis to see whether this preliminary result is valid for all thesimulations in sample A, as described below.We examine the discs of the remnants at the final state,and plot the three parameters derived from the fits of the ra-dial density profiles (inner, outer disc scalelength and breakradius) as a function of the initial λ for each simulation insample A (Fig. 3). As described in section 2.2, we excludedall the simulations for which there was some uncertainty inthe fit of the corresponding parameter, which explains whythe number of points is different for each plot. We thus havea total of 97 values for the inner disc scalelength (hereafterinner scalelength), 99 for the outer disc scalelength (outerscalelength) and 84 for the break radius (for which the fitsof both the inner and the outer disc have to be reliable).We see that the inner scalelength, the outer scalelengthand the break radius all increase linearly with λ , so thatlarger angular momentum systems produce discs with largerinner, outer scalelengths and break radii. This confirms theresults of Herpich et al. (2015a) for the inner scalelengthand the break radius for cases with isolated galaxies withno mergers (see discussion in section 5.1), and adds a fur-ther argument showing that the remnant of a major mergerpossesses all the characteristics of a disc galaxy.The correlations of the fits in Fig. 3 are tight, especiallyfor the break radius. The scalelengths show a larger spread,presumably because their values can be more stronglyinfluenced by the presence of morphological componentssuch as bars, spirals or rings than the break radius.It is important to note that all the simulations we have sofar considered (sample A) have identical total masses (gas+ stars + DM) and similar total stellar masses at their finalstate, so that the spread of scalelengths cannot be simply dueto a mass dependence. Thus the spread should be due to thedifferent parameters of the initial conditions in the varioussimulations, such as the halo spin value, and, in particular,to the different orbits of the two progenitors. Figure 3.
From top to bottom we plot respectively the innerscalelengths, the break radii and the outer scalelengths derivedfrom the fits at the final state, each as a function of the spin pa-rameter λ taken at the initial state, for the simulations in sampleA. The corresponding linear fits are plotted in black, with theequation and correlation coefficient given in the top left corner ofeach plot. MNRAS , 1– ????
From top to bottom we plot respectively the innerscalelengths, the break radii and the outer scalelengths derivedfrom the fits at the final state, each as a function of the spin pa-rameter λ taken at the initial state, for the simulations in sampleA. The corresponding linear fits are plotted in black, with theequation and correlation coefficient given in the top left corner ofeach plot. MNRAS , 1– ???? (2017) ffect of angular momentum on density profiles Figure 4.
Correlations of the inner scalelength, the break radius and the outer scalelength, with the total baryonic angular momentumof the final disc, for sample A.
The dimensionless spin parameter λ is computed 1 Gyr be-fore the merging, and is dominated by the halo (hot gas andDM), because the discs of the protogalaxies are of short ex-tent and of low mass, as the merging occurs early in oursample of simulations. Therefore, λ does not seem to be di-rectly related to the final disc of the remnant and to itsproperties such as the scalelengths. To understand how itcan yet influence the final disc, we will first look at the an-gular momentum in the final disc. We define the baryonic disc as the 2 kpc thick pill-box( | z | < R max = 1 . R break , and exclude the inner 3 kpc toremove the bulge part. We then compute the total angularmomentum of the baryonic matter (gaseous + stellar parti-cles) in this volume at the final state, and plot it against thescalelengths and the break radius for all the simulations ofsample A in Fig. 4. We find clear correlations, showing thatthe properties of the disc are directly linked to its angularmomentum.We now need to relate this disc angular momentum tothe initial halo-dominated spin parameter λ . We showed inA16 that the gas from the gaseous halo accretes onto thedisc and thus rebuilds it after the merger, by fuelling starformation in the disc throughout the whole simulation. Wesuggest here that gas accretion from the halo is the mainmechanism gradually transferring angular momentum fromthe gaseous halo to the disc, and investigate this in the fol-lowing subsections. To be able to study the exchanges of angular momentumbetween the disc and the gaseous halo, we first madesure that the angular momentum exchanges between thebaryonic and the dark matter haloes are relatively smalland thus can be neglected in the context of our very simplequalitative explanation. Indeed, we found such exchangesto be of the order of few per cent.To illustrate the angular momentum exchanges in our sim-ulations, we will focus on two fiducial simulations of sampleA, mdf
732 and mdf λ values, mdf
732 having a considerably higher λ than mdf L of these starsto be a thousand times lower than the halo gas, and we thusneglect them.We first plot in Fig. 5 the evolution over time of thetotal mass of the halo gas, the disc gas and the stars in thedisc, separately. As expected (A16), the gaseous halo loosesmass while the stellar disc gains it. In Fig. 6 we further plotthe angular momentum as a function of time for these threecomponents, and we can see that the halo gas is graduallyloosing angular momentum over time, while the angular mo-mentum of the stellar disc is increasing. The gas in the disc isloosing mass and angular momentum due to star formationin the disc. These plot thus show how the gas in the halois accreted onto the disc, where it forms stars (see A16).Therefore, the stellar disc is gaining angular momentum bygas accretion and star formation.Note that this simple angular momentum redistributionpicture implicitly assumes that our system is relativelyisolated. Otherwise, it will be able to exchange matterand/or angular momentum with other galaxies, so that thetotal mass and angular momentum of our system need notbe conserved quantities.Thus, the disc grows from material taken from the gaseoushalo, which directly gives a fraction of its angular momen-tum to the disc. To find how this fraction varies for differentsimulations, we plot (Fig. 7) the final baryonic disc angu-lar momentum (as defined in section 4.1) versus the initialtotal baryonic angular momentum of the system (which inpractice we calculate at the merging time). We find a clearcorrelation, which shows that gaseous haloes with more an-gular momentum create on average discs with more angularmomentum.To conclude, the initial properties of the halo – andin particular its angular momentum – affect the final discstructure via gas accretion, which constitutes a plausiblereason for the disc properties (scalelengths and break radius)to be linked to the initial spin parameter λ . MNRAS , 1– ?? (2017) N. Peschken, E. Athanassoula, S. A. Rodionov
Figure 5.
Total mass of the gaseous halo, the gaseous disc andthe stellar disc as a function of time for two simulations, mdf732(high λ , upper pannel) and mdf780 (low λ , lower pannel). To test the robustness of our results with respect to the timedefined as final state, we fitted the radial density profiles also5.8 Gyr after the merging, instead of 7.8 Gyr. The values ofthe correlation coefficients are reported in Table 1 (2nd row).As expected due to the growth of the disc, the individualvalues of the scalelengths and the break radii are different,but we still find increasing linear trends with λ . Therefore,the time chosen as final state does not seem to be importantfor this study, provided it is consistent for all simulationsand provided it is sufficiently long after the merging for thedisc to have settled. Under these conditions, the increasingtrend with λ should be valid regardless of the disc evolutiontime. We can thus keep 7.8 Gyr after the merging as thefinal state without being concerned about the effect of ourchoice.We also changed the time at which we calculate λ (theinitial state) and used the merging time. We found very littledifference in the results, and the correlation coefficients aresimilar (Table 1, 3rd row). We repeated this analysis, cal-culating λ at various times covering the range between the Figure 6.
Total angular momentum of the gaseous halo, thegaseous disc and the stellar disc as a function of time for twosimulations, mdf732 (high λ , upper pannel) and mdf780 (low λ ,low pannel). Figure 7.
Final baryonic disc angular momentum, as a functionof the total baryonic angular momentum of the system computedat the merging time, for simulations in sample A.MNRAS , 1– ????
Final baryonic disc angular momentum, as a functionof the total baryonic angular momentum of the system computedat the merging time, for simulations in sample A.MNRAS , 1– ???? (2017) ffect of angular momentum on density profiles Figure 8.
Same plots as in Fig. 3, but adding simulations of isolated galaxies (in blue).
Figure 9.
Same plots as in Fig. 3, but showing the effect of spin orientation on our correlations, with the angle between the twoprotogalaxies axes. start of the simulation and the merging, and conclude thatthe time chosen does not change the results significantly. Wecan also use λ at the final state instead of the initial state,to link λ and the disc structure both taken at the sametime. We found again the same increasing trends, with thecorrelation coefficients reported in Table 1 (4th row). Thispoints out the existence of a correlation between the initialand final λ , which we confirmed by plotting one against theother, and argues that for an analysis of this type, one cantake the value of angular momentum at any time, as long asit is consistent for all simulations.We also used λ at t=0 Gyr for all simulations (sampleA), and again find correlations for the scalelengths andthe break radius, although the correlation coefficients areslightly lower (Table 1, last row).To see if the results obtained for our merger simulations arealso valid for isolated galaxies, we included 12 simulationswhich take only one of the protogalaxies used in the mergersimulations, and see how it evolves in isolation. Thisprotogalaxy contains the same number of particles as thesimulations of sample A, to keep the same total mass. To beable to compare the merger to the isolated simulations, wedefine the initial state as the start of the new disc formationfor both, i.e. at the end of the merging for the former, andat t=0 for the latter. We take 7 Gyr after the initial stateas the final state. We find that the isolated galaxies fitwell with the merger simulations (see Fig. 8), which arguesthat the increasing linear trends of the two scalelengthsand the break radius with the angular momentum seemto be the same if the disc is formed in isolation or from amajor merger. Our results should therefore also be valid for isolated galaxies.Herpich et al. (2015a) did a similar analysis to ours, lookingat the dependence of the scalelengths and the break radiiwith the angular momentum, but using a sample of 9simulations of galaxies evolved in isolation. They computedthe spin parameter λ of the halo at the start of thesimulation, and also found that the inner scalelength andthe break radius increase with λ . However, they observed adecreasing trend of the outer scalelength with λ , while wehave an increasing one. We explain this difference by thefact that they included upbending discs in their analysis,whose outer scalelengths are naturally much higher thanfor downbending discs, while we only have downbendingdiscs in our sample. Upbending profiles will be discussedin detail in a future paper (Paper IV). As a consequence,Herpich et al. (2015a) find an increasing trend with λ forthe ratio of the inner scalelength to the outer scalelength,while we do not, our values showing no correlation with λ .We mentioned in section 2.1 that in some simulations, thespin axis of one or both protogalaxies is tilted by a given an-gle; this concerns 34 simulations in sample A. This angle canbe around the X or the Y axis, Z being the axis perpendicu-lar to the orbital plane. We wanted to see if these simulationsbehave differently in our results than the simulations whereboth protogalactic spin axes are parallel, and perpendicularto the orbital plane. In Fig. 9 we plotted again our correla-tions between the scalelengths and λ , but showing the effectof spin orientation. We can see that the simulations wherethe spin axes are not parallel (angle (cid:54) = 0) fit reasonably well MNRAS , 1– ?? (2017) N. Peschken, E. Athanassoula, S. A. Rodionov
Table 1.
Parameters of the linear fits for different plots of λ versus the inner scalelength, break radius and outer scalelength. t i , t f and t merg are respectively the times of the initial state, the final state and the merging, and r c is the correlation coefficient for the linear fitwith equation: f ( λ ) = aλ + b . Inner Scalelength Break Radius Outer Scalelength r c a b r c a b r c a bλ t = t i , t f = t merg + 7 . λ t = t i , t f = t merg + 5 . λ t = t merg , t f = t merg + 7 . λ t = t f , t f = t merg + 7 . λ t = t f , t f = t merg + 5 . λ t =0 , t f = t merg + 7 . Figure 10.
Same plots as in Fig. 3, but adding a sample of 67 simulations (sample B) with total masses different from those of thesimulations in sample A. with the others. We can thus conclude that our results seemto be valid regardless of the spin axis orientation.We also looked at the effect of the presence of a centralAGN on our correlations, and found that the simulationswithout AGN also fit well with the ones having an AGN.This confirms that our AGN only affects the central part ofthe galaxy (R17).The effect of the initial density distribution of gas andDM have also been tested since our sample contains simu-lations with different distribution parameters, such as theinitial characteristic radii of the halo (see A16) or the pres-ence of a central core for DM. Although the correspondingparameter space is very large, our relatively few trials ar-gue that such parameters do not seem to have an effect onthe correlations we found. Various other parameters, suchas the merging orbit, the baryonic to total mass ratio, andthe softening of the gas and DM, were also shown to haveno significant impact on our results.
Here we will analyse the effect of changing the total massin the simulations, using sample B (see section 2.1). Theproblem when analysing simulations of different masses isthat the evolution time-scale is also different. In our analysiswe took a fixed evolution time after the merging (7.8 Gyr) tocompare the properties of the disc, which introduces a small inconsistency when we compare simulations with differenttotal masses.Nevertheless, we expect the time-scales to be similar ifthe total masses are not too different, which is the case ofthe simulations in our subsample of 67 galaxies (sample B)since they have total masses between 0.5 and 2 times thetotal mass of simulations in sample A. We include them inour correlations (Fig. 10) and find again high correlationcoefficients; the sample B fits well with sample A. Further-more, we added simulations of galaxies evolved in isolationas in section 5.1, but with half the number of particles, i.e.with a mass twice lower than the simulations of sample A.We found that these simulations match well in the correla-tions, which again suggests that our results are valid also forgalaxies formed in isolation. Moreover, we included the sim-ulations of sample B in the correlation of the final baryonicdisc angular momentum as a function of the initial baryonicangular momentum (as in Fig. 7), and found again a verygood match.Since the simulations of sample B follow similar trendsas sample A despite their total masses being different, in thefollowing subsections we will include them in our analysis,using the A+B sample.
The formation of outer discs in downbending profile galaxiesis still debated, but one of the main possible scenario relieson the presence of outwards stellar migration to build the
MNRAS , 1– ????
MNRAS , 1– ???? (2017) ffect of angular momentum on density profiles Figure 11.
Radial density profile for a snapshot at t=10 Gyr (inblue), and distribution at time of birth of the stars ending up inthe outer disc (in green). The fit of the profile at t=10 Gyr isplotted in red, and the corresponding break radius is indicatedwith a black vertical line. outer dic (Roˇskar et al. 2008). We thus investigate wherethe stars in the outer disc of our remnant galaxies comefrom, by calculating the radius at which they were born.The stellar discs of the two protogalaxies are separate beforethe collision and thus the birth radius with respect to theremnant galaxy cannot be defined. We therefore use in ouranalysis only the stars born after the merging, as in section2.2. We define at any given time the stars of the outer discas all the stellar particles located beyond the break. We plotin Fig. 11 the distribution of the radii at birth of the starswhich by t=10 Gyr end up in the outer disc, for simula-tion mdf
730 from sample A, which was chosen because ofits smooth profile, allowing us to make our points on migra-tion clearer. Since every star is born at a different time, thisdistribution does not represent a real stellar distribution atany time of the simulation, but it helps visualise the fractionof stars born at a given radius throughout the whole simu-lation. We can see that most stars of the outer disc (78 ± Figure 12.
Mean inside-out migration distance of the stars end-ing up in the outer disc, as a function of the initial spin parameter λ , for sample A+B. in the outer disc between its time of birth and the final state(as defined in section 2.2): D mig = R final − R birth , (4)where R final and R birth are the radii at the final state andat birth for each star. We remove again the stars born be-fore the merging since migration only starts after the colli-sion, or, more precisely, after the disc formation begins (t bd ,A16). Since we are only interested in the outward migrationtowards the outer disc, we also remove the stars migratinginwards, which represent only about 5 per cent of the outerdisc population. We then take the mean over all the remain-ing stars to get a single value for each simulation, whichwe plot versus λ . We repeat this for all the simulations insample A+B and plot the result in Fig. 12. We see a clearincreasing trend of the migration distances with λ , allowingus to conclude that higher initial angular momentum sys-tems lead to discs with higher migration distances towardsthe outer disc. In fact, we find the same result if we considerinside-out migration in the whole disc, and do not restrictourselves to outer disc stars. The stars travel globally furtherout in high angular momentum systems, and this is partic-ularly important in the outer disc, where 94 ( ±
5) per centof the stars have undergone inside-out migration (comparedto 46 ± λ simu-lations having larger scalelengths: if stars travel further out,their final distribution will be more extended, resulting in alarger outer disc. In section 5.3, we showed that most particles ending up inthe outer disc were born inside the break radius, as calcu-
MNRAS , 1– ?? (2017) N. Peschken, E. Athanassoula, S. A. Rodionov lated at t=10 Gyr. However, the stars whose birth distribu-tion has been plotted in Fig. 11 were born at all times afterthe merging. As will be shown for our simulations in PaperIV (see also Perez 2004 and Azzollini et al. 2008 for obser-vations), the break radius generally increases with time, sothat stars which are born inside the 10 Gyr break in Fig. 11could in fact be born beyond the break taken at their time ofbirth. Therefore, we cannot claim that about 80 per cent ofthe outer disc’s stars that were born at a radius which cor-responds to the inner disc at 10 Gyr were actually born inthe inner disc, since their birth radius could be in the outerdisc at their birth time. Although this does not change thefact that most of these stars clearly migrated outwards, itcould question the claim that they travelled from the innerdisc to the outer disc.To solve this, we took the same stars (i.e. the ones in theouter disc at 10 Gyr), and computed the fraction which wasborn in the inner disc defined with respect to the break attheir time of birth. This fraction however depends stronglyon the value taken for the break radius, since the break is of-ten located near the end of structures such as spirals (Laineet al. 2014; Paper IV), which are high star formation areas(A16 for simulations and e.g. Silva-Villa & Larsen 2012 forobservations). Besides, the break radius can be difficult tomeasure precisely at early times (a few Gyr after the merg-ing). We thus defined errorbars for the estimated break po-sition at each time step for every simulation, and excludedall the particles born closer to the break radius than theseerrorbars. To make sure our 10 Gyr outer disc definition isalso reliable, we defined the particles of the outer disc asthe ones located beyond the external errorbar of the breakradius.To exclude the effect of radial displacements due to ra-dial oscillations of stars in their orbit, we chose to use R G – the guiding radius of each star – instead of their regularradius to derive their position with respect to the break. R G is the radius of the circular orbit associated to the angularmomentum of a given star, and can be derived by solvingthe equation: R G = L z v circ ( R G ) , (5)where L z is the vertical component of the angular momen-tum of the star, and v circ is the circular velocity at the guid-ing radius.The fractions of outer disc stars that are born in theinner disc derived with this method cover a wide range ofvalues depending on the simulations, from 10 to 80 per cent.Nevertheless, we find globally lower fractions than the onesfrom section 5.3, as well as the ones from Roˇskar et al. (2008, ∼
85 per cent), which can be explained by the fact that thebreak radius tends to increase with time (see paper IV),so that some stars were born inside the 10 Gyr break butoutside their birth time break, and thus should be consideredas being born in the outer disc. Note that these low fractionscan not be explained by our choice to take the guiding radiusinstead of the regular radius, or to exclude the stars withinthe errorbars of the break radius: we performed the sameanalysis using the radius instead of the guiding radius, andalso keeping the particles inside the errorbars, and foundsimilar results in both cases.
Figure 13.
Fraction of outer disc stars which were born in theinner disc, as a function of the spin parameter λ , for sample A+B.For each star, the inner disc is defined here with respect to thebreak radius derived at its time of birth, as explained in section5.4. To understand the spread of values derived for thefraction of stars born in the inner disc, we tried to plotthese fractions again versus the spin parameter λ (takenfor all the components, 1 Gyr before the merging) in Fig.13. Although having a large scatter (probably because ofthe sensitivity of the values to the break location and itserrorbars, and the difficulty to define them precisely atearly times), this plot shows again an increasing trend ofthe fractions with λ . Therefore, galaxies with high angularmomentum will have an outer disc which is populated bya majority of stars coming from the inner disc, whereasin low angular momentum galaxies, stars in the outer discwill mostly be born in the outer disc. It is important tonote that the trend found in Fig. 13 involves the fraction ofstars, i.e. relative and not absolute numbers. It thus doesnot imply that low angular momentum galaxies form morestars in their outer parts, since the number of stars in theouter disc is different in every simulation.We thus have simulations which have outer discs formedmostly by radial migration, but with a significant amount ofstars in the outer parts which were born in the outer disc.We conclude that not taking into account the fact that thebreak radius changes with time, can lead to overestimat-ing the fraction of stars born in the inner disc in the con-text of radial migration. Therefore, the picture of outer discstars mostly coming from the inner disc has to be used withcaution, since it depends on the angular momentum of thegalaxy. Only galaxies with high spin parameter λ ( λ> λ< MNRAS , 1– ????
Fraction of outer disc stars which were born in theinner disc, as a function of the spin parameter λ , for sample A+B.For each star, the inner disc is defined here with respect to thebreak radius derived at its time of birth, as explained in section5.4. To understand the spread of values derived for thefraction of stars born in the inner disc, we tried to plotthese fractions again versus the spin parameter λ (takenfor all the components, 1 Gyr before the merging) in Fig.13. Although having a large scatter (probably because ofthe sensitivity of the values to the break location and itserrorbars, and the difficulty to define them precisely atearly times), this plot shows again an increasing trend ofthe fractions with λ . Therefore, galaxies with high angularmomentum will have an outer disc which is populated bya majority of stars coming from the inner disc, whereasin low angular momentum galaxies, stars in the outer discwill mostly be born in the outer disc. It is important tonote that the trend found in Fig. 13 involves the fraction ofstars, i.e. relative and not absolute numbers. It thus doesnot imply that low angular momentum galaxies form morestars in their outer parts, since the number of stars in theouter disc is different in every simulation.We thus have simulations which have outer discs formedmostly by radial migration, but with a significant amount ofstars in the outer parts which were born in the outer disc.We conclude that not taking into account the fact that thebreak radius changes with time, can lead to overestimat-ing the fraction of stars born in the inner disc in the con-text of radial migration. Therefore, the picture of outer discstars mostly coming from the inner disc has to be used withcaution, since it depends on the angular momentum of thegalaxy. Only galaxies with high spin parameter λ ( λ> λ< MNRAS , 1– ???? (2017) ffect of angular momentum on density profiles For this series of papers we ran a sample of high resolutionsimulations of which three fiducial cases were describedin A16, where more general information on the runs wasalso given. It was shown there that after a merging, anew disc forms in the remnant from gas accreting fromthe halo. In this paper, we used subsamples derived asdescribed in section 2.1. We derived the stellar radialdensity profiles of the remnants at the end of all thesimulations, and found downbending (type II) profiles.We then derived the corresponding inner and outer discscalelengths, as well as the break radius. We used the spinparameter λ computed 1 Gyr before the merging to havea definition of the angular momentum consistent for allour simulations. Plotting for our sample the values derivedfrom the radial density profiles fits as a function of λ , wefound that the inner, the outer scalelength and the breakradius increase with λ . Therefore, both the inner and theouter discs are larger for higher angular momentum systems.To explain how the initial orbit- and halo-dominated spinparameter λ of the merging system can affect the propertiesof the final remnant disc (mostly composed of stars bornafter the merging), we looked at the angular momentum re-distribution in our simulations. The scalelengths and breakradius correlate with the baryonic angular momentum of thedisc, suggesting a link between the latter and the initial an-gular momentum. To understand how the angular momen-tum of the disc was acquired, we investigated the transfersof the baryonic matter and angular momentum between thehalo and the disc, after making sure that the total baryonicangular momentum is conserved. In the framework of discgalaxy formation from a major merger of two progenitorswith extended gas-rich haloes (A16), it is easy to understandthat the gaseous halo gives angular momentum to the discby accreting its gas onto it. We showed this in two fiducialsimulations with different λ values, with the halo gas grad-ually loosing a fraction of its mass and angular momentumto the stellar disc, by gas accretion and star formation. Wefurther found that haloes with higher initial total angularmomentum (or λ ) will create final discs with higher angularmomentum, and larger scalelengths and break radius.Naturally this scenario is only valid for an isolatedsystem with no interactions with the environment. Thus ourresults, as well as those of other dynamical (and thus nec-essarily idealised) simulations, can not be straightforwadlyextended to a cosmological context, since interactions withenvironment could interfere with the angular momentumexchanges between the gaseous halo and the baryonic disc.The correlations of the scalelengths and the break radiuswith λ are robust and do not change with the time at whichwe fit the radial density profiles, or the time used to com-pute λ . Furthermore, simulations of isolated galaxies followthe same trends, so that our results should be valid for discsformed both in isolation and in major mergers. In some sim-ulations, the spin axes of the protogalaxies are tilted, andwe showed that the spin axis orientations of the two mergingprotogalaxies do not seem to play a role in this analysis.We also included in the correlations a sample of 67merger simulations with total masses lower or higher than the simulations from the main sample. Although the evo-lution time-scale of these simulations is also different, wefound that these simulations (which have total masses rea-sonably close to our main sample) fit well with the others inthe correlations, and thus added them to the sample.We analysed the outer disc origin, and found that thestars ending up in the outer disc were mostly born at smallerradii ( ∼
95 per cent), suggesting inside-out migration as themain formation driver for the outer disc, in good agreementwith previous work on galaxies formed in isolation (Roˇskaret al. 2008). To see the effect of the angular momentum onthis migration, we computed the distance radially travelledby the stars towards the outer disc, and plotted it against thespin parameter λ for the simulations of our sample. We founda clear correlation, galaxies with higher angular momentumhaving larger inside-out migration distances.We also showed that to study the origin of the outerdisc, it is necessary to take into account the fact thatthe break location changes with time, so as to avoidoverestimations of the fraction of stars born in the innerdisc. While ∼
80 per cent of the outer disc stars wereborn inside the break derived at t=10 Gyr, this fractioncan take lower values (under 50 per cent) using the timedependent break, which sets doubt on the picture of theouter disc formed mainly from the inner disc. This fractiondepends on the angular momentum, and is higher in highangular momentum galaxiess. Thus, in some low angularmomentum systems, this fraction can drop to values evenlower than 20 per cent.We can thus conclude that the angular momentum is a keyparameter in the creation of disc structures, as it affectsradial migration, and can explain the large range of valuesobserved for the inner and outer scalelengths in disc galaxiesof a given mass.
ACKNOWLEDGEMENTS
We thank Jean-Charles Lambert for computer assistance,and the referee for useful suggestions. This work was sup-ported in part by the Polish National Science Centre un-der grant 2013/10/A/ST9/00023, and was granted accessto the French HPC resources of [TGCC/CINES/IDRIS] un-der the allocations 2014-[x2014047098], 2015-[x2015047098]and 2016-[x2016047665], made by GENCI, as well as theHPC resources of Aix-Marseille Universit´e financed by theproject Equip@Meso (ANR-10-EQPX-29-01) of the program « Investissements d’Avenir » supervised by the Agence Na-tionale de la Recherche. REFERENCES
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