FORMING DISK GALAXIES IN WET MAJOR MERGERS. I. THREE FIDUCIAL EXAMPLES

Compared to previous simulations on this specific subject, ours presents a numerical and conceptual advantage.

As a numerical advantage, we have a much better resolution than previous simulations tackling the specific question we set out to address: whether or not major mergers of gas-rich disk galaxies can form spirals. Answering this question necessitates a survey of simulations (e.g., Hopkins et al. 2009), which makes the use of high resolution computationally much more expensive than for problems necessitating only few simulations. For this reason, previous attempts were restricted to considerably less than or of the order of half a million particles in total.¹ We increased this number by more than an order of magnitude, adopting for each gas or stellar particle a mass of m_g = 5 × 10⁴M_⊙ and a softening of 25 pc. The dark matter (DM) particles have a mass of m_DM = 2 × 10⁵M_⊙ and a softening of 50 pc. Our simulations contain 2 and 3.5 million particles for the baryons and DM, respectively.

The conceptual improvement concerns the initial conditions of the simulations. In previous works, the progenitors resembled local disk galaxies, except for a higher content of cold gas in the disk, and consisted of a DM halo, a disk, and sometimes a classical bulge with properties compatible to those of local galaxies. It is, however, well established that disk galaxies have cold gas in their disk and hot gas in their halos (e.g., Miller & Bregman 2015). To account for this, we start our simulations with spherical protogalaxies consisting of DM and hot gas. Before the merging, a disk forms in each of the progenitors so we witness the merging of two disc protogalaxies. The two gaseous halos merge into a single halo enveloping the remnant, and thus halo gas accretes onto the remnant disk all through the simulation (Section 3.2). Such gaseous halos also exist in mergings that occur in cosmological simulations (e.g., Governato et al. 2009) or in a few major merger studies (Moster et al. 2011; Kannan et al. 2015) whose remnants have a B/T ratio between 0.7 and 1., thus linking them to ellipticals with a small disk. So, to our knowledge our study is the first to include a hot gaseous component in dynamical simulations of major mergers whose remnants model realistic spiral galaxies.

A full discussion of the code used in these simulations and of their initial conditions is the subject of the next paper in this series (S. Rodionov et al. 2016, in preparation, Paper II). In this and the next two subsections we only summarize the main information necessary here.

We use a version of gadget3, including gas and its physics (Springel & Hernquist 2002; Springel 2005). DM and stars are modeled by N-body particles, and gravity is calculated with a tree code. The code uses an entropy conserving, density-driven formulation of SPH with adaptive smoothing lengths (Springel & Hernquist 2002) and subgrid physics (Springel & Hernquist 2003).

Our feedback, star formation, and cooling follow subgrid physics included in simple recipes given by Springel & Hernquist (2003) and were already used in a number of previous works cited in Section 1. It is beyond the scope of this paper to test other subgrid physics. Nevertheless, note that Cox et al. (2006) showed that the mass profiles of the major merger remnants are robust to substantial changes in subgrid physics parametrizations. Similarly, Hopkins et al. (2009) found that the efficiency with which gas avoids consumption during the merger and can reform a disk does not depend on the subgrid parametrization, unless the feedback is very weak. Most important, Hopkins et al. (2013) introduced detailed, explicit models for stellar feedback in their very high resolution major merger simulations, and found that in all cases the mass profile results of explicit feedback models are nearly identical to those obtained with the subgrid physics we use here, except for some second order differences.

The code described previously has already been used many times to test the relevance of major mergers regarding the formation of disk galaxies (e.g., in Hopkins et al. 2009, and references therein), albeit with initial conditions that do not include gaseous halos. We also used it in a number of our simulations that always include gaseous halos. In those cases, we obtained merger remnants that are disk galaxies with thin and extended disks and realistic spiral arms, but with one serious drawback—the centermost part of the galaxy had a considerable central concentration, leading to an unrealistically high inner maximum of the circular velocity curve (Paper II). Furthermore, this high central mass concentration has the disadvantage of prohibiting bar formation, or at least delaying it beyond the 10 Gyr covered by our simulations. This is in disagreement with observations, because about two-thirds of local disk galaxies are barred (see references in Section 1).

Such excessive concentrations were also obtained in cosmological simulations of disk galaxy formation and were lately addressed by introducing additional feedback in the central regions, mainly in the form of active galactic nucleus (AGN) feedback. Very schematically, in this picture, gas flows inward to the central black hole (BH). Feedback energy is then calculated from the fraction of the luminosity that is radiated by the BH. This energy is distributed to the gas in the central region in the form of thermal energy, thus preventing excessive star formation.

In most studies, the inflow onto the BH is modeled using the Bondi accretion formalism (Hoyle & Lyttleton 1939; Bondi & Hoyle 1944; Bondi 1952), sometimes limiting it by the Eddington accretion rate to prevent excessive accretion. This inflow formalism has two free parameters, the accretion efficiency and the radiative efficiency (Springel et al. 2005). However, the physics of driving BH-generated outflows is not well understood (e.g., Silk & Mamon 2012), and also necessitates resolutions much higher than what we have here. Furthermore it has been criticized by Hopkins & Quataert (2010), who calculated the accretion directly from subparsec "resimulations" of the central region of galaxy-scale simulations.

Our approach is based on the same physics, but because we only want to solve the excessive mass concentration problem and not to model the BH accurately, we adopt a very straightforward, empirical, and parametric method. As gas flows inward, it increases the density in the central regions. As in previous descriptions, we introduce two parameters: a density threshold ρ_AGN and a temperature T_AGN. More specifically, at every time step we give internal energy to gas particles whose local density is larger than the threshold ρ_AGN by increasing their temperature to T_AGN. This density threshold is chosen to ensure that the chosen particles are located in the centermost region. Furthermore, to ensure that the amount of energy we inject is not excessive, at every step we test that the total energy distributed is below that of the Eddington rate (see e.g., Springel et al. 2005). We do this in a probabilistic manner, by setting the probability of a particle receiving internal energy equal to one if the energy to be distributed is less than the Eddington limit, or, if it is higher than that limit, by setting the probability as the ratio of the Eddington limit to the energy we were initially to distribute. A more comprehensive description will be given in Paper II, where we describe the computational and technical aspects in detail.

Although very simple, this description includes the essentials sufficient for our purposes, namely it injects energy in the central regions to prevent excessive star formation. Compared to cases with no AGN feedback, this process leads to mass distributions that are less concentrated in the centermost parts, to more realistic circular velocity curves, and allows bars to grow.

In our scheme no single particle represents the BH, as any spurious off-centering of such a particle or its imperfect correction by analytical drag forces could introduce errors because the BH mass is so much higher than that of the other particles in the simulation. Nevertheless, it is useful to keep track of the evolution of the BH mass (M_BH) with time. We do this by measuring the energy released by our AGN-like feedback as a function of time and then following the simple formalism described in Springel et al. (2005, p. 783).

The following three questions need to be considered here:

• 1.  
  Does the feedback model lead to unphysical results? There are several arguments against this:

  • a  
    The shape of the circular velocity curve, which is unrealistic in simulations without this central feedback, becomes very realistic and compatible with observed rotation curves.
  • b  
    The mass of the BH at the end of the simulation, which is calculated using the energy of the feedback, is 1., 1.4, and 3.3 × 10⁷M_⊙ for our three fiducial simulations. These are reasonable values for disk galaxies. Moreover, we calculated the velocity dispersion of the central parts, σ, directly from our simulation and found that the (M_BH, σ) pair falls near the M_BH–σ relation (Ferrarese & Merritt 2000; Gebhardt et al. 2000) within the observational spread.
  • c  
    Qualitatively, the evolution of M_BH during the merger is similar to that obtained with other AGN feedback prescriptions, namely it increases much more sharply during the merger than after it (e.g., Thacker et al. 2014).
  • d  
    Last, but not least, we ensure that at all times the amount of injected energy does not exceed the Eddington limit, as described previously.
• 2.  
  How is this energy distributed? During the simulations we followed the location of the gas particles to which the energy is deposited. We found that these particles cover a region around the dynamical center of the halo (i.e., around the position of the halo particle with the highest local density). The area they cover may vary from one run to another, but it is always much larger during the merging times. At such times, their characteristic size is of the order of half to one kpc, but becomes considerably smaller after the merger event, when it is of the order of 100 pc. This increase in characteristic size during merging reflects the much larger corresponding feedback, while the extent during the merging time can be compared to the circumnuclear region that is very active during a merger (see e.g., Scoville et al. 1991 for the merging system Arp 220).
• 3.  
  Does this feedback affect the simulation results? Indeed it does, as expected and required. Namely it changes the shape of the circular velocity curve, making it compatible with observations and, as a corollary, it allows the formation of bars, which we know are present in the majority of nearby galaxies (see references in Section 1). Moreover, changes in the values of the two adopted parameters (ρ_AGN and T_AGN) should, and do, affect the simulation results. This is expected because they change the shape of the circular velocity curve and thus the bar properties, which, in turn, influences the dynamics and structure at least in the inner parts of the disk. These changes are most important in the central region hosting the bar, but are much smaller at larger radii (Paper II).

To summarize, our simple parametric description of the central feedback has the desired effect without being unphysical. We thus adopt it for our simulations.

Making a full comparison of the results of our simulations with those obtained with other codes, but with the same initial conditions and the same gas physics and subgrid physics, is beyond the scope of this paper. We, nevertheless, reran one of our fiducial simulation (hereafter, mdf732, see Section 2.6) using the gizmo code (Hopkins 2013, 2014, 2015), after implementing the subgrid physics we use here. This code is a derivative code of GADGET, and uses the same MPI parallelization, domain decomposition, gravity solvers, etc. However, in contrast to that of gadget, the SPH version of gizmo is density independent and includes a more sophisticated treatment of the artificial viscosity term (Cullen & Dehnen 2010), as described in Hopkins (2013, Section 3.1). It can thus handle the phase boundaries better (e.g., between the hot gas in the halo and the much cooler gas in the disk) or the description of cold dense clumps of gas in the otherwise hot halo.

The main difference we found between the results of these two codes is in the hot gaseous halo. This has small gaseous clumps in the simulation run with gadget3, which are either absent or much less prominent in the gizmo run (see also Torrey et al. 2012 and Hayward et al. 2014). On the other hand, we find very good agreement when we compare the properties of the remnants (e.g., their gaseous or stellar projected density radial profile, their cumulative stellar mass, or the mean tangential velocity of the stars or gas and the stellar radial and vertical velocity dispersion profiles).

The good agreement between the properties of these two simulations argues that the clumps present in the halo of the gadget simulation do not greatly influence the behavior of the stellar component. Even the stellar vertical velocity dispersion or the thickness of the stellar disk are in good agreement, which shows that these clumps are not sufficiently massive and/or numerous to noticeably heat up the stellar disk.

We used idealized initial conditions with two identical protogalaxies composed of spherical DM and gaseous halos, of masses M_DM and M_gas, respectively, with M_total/M_gas = 8. The initial density of the DM and the gaseous halo is

$$\begin{eqnarray}&&\rho {(r)=C\mathrm{sech}(r/| {r}_{t}| ){x}^{-{\gamma }_{i}}({x}^{\eta }+1)}^{-({\gamma }_{o}-{\gamma }_{i})/\eta },\end{eqnarray} \tag{ 1 }$$

where r is the spherical radius, x = r/a, and a and r_t are the scale length and tapering radius of the halo, respectively. The constants γ_i, γ_o, and η characterize the shape of the radial density profile. The DM halo has γ_i = 1, γ_o = 3, and η = 1, while the gaseous halo has γ_i = 0, γ_o = 2, and η = 2 (Beta model for β = 2/3, e.g., Miller & Bregman 2015 and references therein). For both we have r_t = 100 kpc and a = 14 kpc. The halo component was built following McMillan & Dehnen (2007; i.e., with a Cuddeford 1991 distribution function). We also add a small amount of spin to the halo. Let f be the fraction of particles with a positive sense of rotation. In cases with no net rotation, f = 0.5; whereas if all particles rotate in the positive (negative) sense, f = 1 (−1). The internal energy of the gas was set by requiring hydrostatic equilibrium (Paper II).

Stars do not exist in the initial conditions, but form during the evolution, so that at the time of the merging, a stellar and a gaseous disk are present in the progenitor galaxies. Thus their density and velocity profiles are set by our initial setup for the hot halo gas distribution and its subsequent evolution, and not directly by the modeller seeking to match, for example, what is measured in nearby galaxies.

In this paper we discuss three simulations: mdf732, mdf778, and mdf780. All three are 1:1 mergers of two identical protogalaxies. We start by adopting the simple case of coplaner mergers, while other orientations will be considered in forthcoming studies. We briefly mention here that preliminary results show, as expected, that the orientation of the spin axes with respect to the orbital plane considerably influences the properties of the remnant, and that this may account for the spread observed in disk sizes, B/T ratios, and gas fractions of nearby galaxies.

The orbits of the centers of density of the two protogalaxies (i.e., the orbits of the location where their DM density is highest) are given in Figure 1(a). Simulations mdf732 and mdf780 have f = 0.6, while mdf778 has 0.55. The adopted AGN parameters are ρ_AGN = 1 M_⊙ pc⁻³ for all three cases; T_AGN = 10⁷ K for mdf732 and mdf778, and 2.5 × 10⁷ K for mdf780. We continued all simulations up to 10 Gyr.

Zoom In Zoom Out Reset image size

In previous works (see papers cited in Section 1), the initial conditions consisted of two fully developed disk galaxies set on a given trajectory. Each consisted of a spherical halo, an exponential stellar disk, and, in some cases, a classical bulge and/or a gaseous disk. Their properties were chosen to represent nearby galaxies; except for the fraction of gas in the disk, which was a free parameter that varied at will. Thus gas fractions were tried in the complete range between 0 and 1, even if this was not necessarily compatible with, for example, the adopted disk scale length (which was usually appropriate for low-redshift Milky Way–like disk galaxies; i.e., 3–5 kpc) or their B/T mass fraction. Although not ideal, these initial conditions allowed previous works to reach interesting conclusions, for example on the crucial role of the initial gas fraction on the nature of the merger remnant. This is presumably due to the fact that violent relaxation occurring during the merging wipes out the details of the initial stellar structures.

We chose to start with very different initial conditions for the progenitors (Section 2). However, before using these initial conditions in our major merger simulations, we made sure that when evolved in isolation, their t = 10 Gyr snapshots gave reasonable approximations of local disk galaxies, and that during their early stages of evolution (i.e., roughly over the first 2 Gyr) they were compatible with the main properties of disk galaxies at such times. The latter entails that the disk be considerably smaller and more perturbed than the disks in local isolated galaxies, and that the fraction of gas in their disk be higher (Bouwens et al. 2004; Ferguson et al. 2004; Elmegreen et al. 2005; Erb et al. 2006; Dahlen et al. 2007; Leroy et al. 2008; Daddi et al. 2010; Tacconi et al. 2010; Rodrigues et al. 2012; Conselice et al. 2013; Genzel et al. 2015, etc.). More information will be given elsewhere (N. Pesehken et al. 2016, in preparation), but we summarize some relevant information in the following.

In our simulations, the protogalaxies at t = 0 consist only of spherical distributions of DM and gas (Section 2.5). From the onset of the simulation, however, the gas in the halo cools radiatively and, getting out of equilibrium, falls inward. Its density increases locally and the first stars form. Thus, the progenitors gradually acquire a disk. This disk, as expected, is much more perturbed and lumpy than the more settled exponential disks to which it evolves later. Figure 2(a) shows the radial surface density profile at five times during the evolution (0.5, 1, 2, 5, and 10 Gyr). It is clear that the disk grows inside-out, relatively fast at early times, and less so later on. The profiles are initially exponential-like, but it is not trivial to adequately measure their scale length, so we measure the cylindrical radius R₇₀, which contains 70% of the stellar mass. It is clear that this quantity increases considerably with time, as expected, particularly at early evolution stages (see Figure 2(b)).

Zoom In Zoom Out Reset image size

Figure 2(c) shows the fraction of gas in the disk component measured within $| {\rm{\Delta }}z| \lt 0.5\;{\rm{kpc}}$. At the relevant times (i.e., the times corresponding to before the merging), the gas fractions are in the ballpark of 60%–30% (i.e., considerably larger than the corresponding gas fractions in nearby disk galaxies), which is in good agreement with observations of both local and intermediate redshift galaxies.

We do not claim that this is a perfect model for galaxies at intermediate redshifts, but it is still a considerable improvement over those used in previous studies. This improvement is a corollary of the existence of a hot gaseous halo in our initial conditions, as this entails a slow formation and evolution of the disk, which becomes gradually more massive and more extended, while the gas fraction in the disk decreases monotonically with time.

The stellar disks of the progenitor galaxies are destroyed by the merging and their stars concentrate in the central regions of the remnant. As shown in the following sections, most form a classical bulge, while the remaining albeit much smaller number of stars, together with stars born during the merger period, contribute to a thick disk and its bar. The gaseous disks of the progenitors are also destroyed, and the gas they included also concentrates in the innermost regions of the remnant, so that the stars that form from it contribute to the classical or disky pseudobulge.

After the end of the merging, gas continues to fall in mainly from the halo, but also, although in much smaller quantities, from the gaseous tails formed during the interaction. Thus a new disk is gradually formed that very early on shows well-defined spiral arms. This gas accretion continues all through the simulation.

Figure 3 gives the morphologies at the end of the simulations:² . mdf732 has the largest disk extent and mdf780 the shortest. Seen face-on, all three galaxies have a clear, extended spiral structure. Let us denote by m the spiral arm multiplicity (i.e., the number of arms at any given radius). mdf778 is mainly bisymmetric (m = 2), while mdf732 and mdf780 are m = 2 in the inner parts and m > 2 at larger radii, reaching m = 5 at the edges of the disk. This increase of m with distance from the center is in good agreement with observations and was explained by Athanassoula et al. (1987; see also Athanassoula 1988, for models including accretion). These authors applied the swing amplification analytical formalism (Toomre 1981; see also reviews by Athanassoula 1984 and Dobbs & Baba 2014) to their rotation curve decompositions result and noted that if the spiral structure was due to swing amplification, the arm multiplicity should increase with distance from the center. Thus the spiral structure in mdf732 and mdf780 is consistent with a swing amplification origin. However, providing tangible proof that these are swing amplification driven spirals is well beyond the scope of this paper.

Zoom In Zoom Out Reset image size

mdf732 has an inner ring with a very asymmetric density distribution along it (i.e., Figure 3, second row, where only the lower half of the ring is clearly visible). Its semimajor axis has the same size as that of the bar and it is elongated in the same direction, both being in good agreement with inner ring observations (e.g., Buta 1995, and references therein). Good examples of such inner rings can be seen in NGC 1433 and NGC 3660. mdf778 and mdf780 have m = 2 spirals emanating from the ends of the bar, roughly perpendicular to it and then trailing behind it, again in good agreement with what happens in observed local galaxies.

The bar size in all three simulations (2.5–4 kpc semimajor axis) is only slightly below the average for the stellar mass in question, and well within the range of observed values for external galaxies (lowest panel of Figure 20 in Díaz-Garca et al. 2015). It should be noted that the three models presented here have a similar stellar mass as the Milky Way, and their barlength closely matches that of the Milky Way bar. To measure the bar strength, we Fourier decomposed the projected surface density of the face-on view, as in Diaz et al., and used the maximum value of the relative m = 2 Fourier component as the bar strength (see, e.g., Diaz et al. for more information on this method). For our three simulations we find values between 0.32 and 0.35, which are in good agreement with observations. However this comparison is less constraining than the one concerning the bar length, because the observed values show a very large spread (second panel of Figure 20 in Díaz-Garca et al. 2015).

We can also make meaningful comparisons concerning the bar morphology. Combining information from three different approaches, namely simulations following bar formation in isolated disk galaxies, orbital structure theory, and observations, Athanassoula (2005; see also Athanassoula 2015 for a review, and references therein) came to the conclusion that bars have a rather complex shape. Namely their outer part is thin both when seen edge-on and face-on, while their inner part is thick when viewed face-on and edge-on. When viewing the bars in our simulations from different angles, we find that they also have this morphology, arguing for a proper dynamical description of bars in our simulations and, most important, arguing that the observed bar shapes are compatible with a scenario of disk formation via major mergers.

The face-on bar morphology also agrees well with observations. In particular, the bar has ansae (Sandage 1961) and a barlens component (Laurikainen et al. 2014; Athanassoula et al. 2015). Seen side-on, the latter is usually referred to as a boxy/peanut/X bulge, but is in fact a part of the bar (i.e., consists of disk material and forms via disk instabilities; Athanassoula 2015, for a review).

The morphology of mdf778 shows a number of embedded structures, namely a bar of radial extent ∼3 kpc, an oval of radial extent ∼14.5 kpc outside the bar, and two m = 2 sets of spirals. The inner set is confined within the oval, while the outer one emanates from the ends of the oval, extends to larger radii (maximum ∼ 16.5 kpc), and falls back to the oval, thus forming an outer pseudoring. Similar embedded structures can be seen e.g. in NGC 1566. The outer pseudoring and the oval have the same low pattern speed (∼18.5 km s⁻¹ kpc⁻¹), while the inner bar has a much higher pattern speed (∼43 km s⁻¹ kpc⁻¹). This morphology is very similar to that of manifold-driven outer spirals and pseudorings (Romero-Gómez et al. 2006; Athanassoula et al. 2009). Furthermore, for manifold theory, the pattern speed of the oval and the outer spirals should be the same, as is the case in mdf778. The ultimate test, however, can be carried out with the help of the orbits of the particles in the spirals (Athanassoula 2012). Indeed in any density wave-based theory, the orbits should traverse the arms, staying longer in the arm than in the interarm. On the contrary, in manifold theory the orbits of the particles start from one of the Lagrangian points nearest the end of the bar (L₁ or L₂) and then follow the arm shape, outlining it until they reach the opposite side of the bar. We followed the orbits of particles in the spirals and found that they stay within the spirals and outline them, which shows that these structures are manifold spirals as in the simulations of Athanassoula 2012). There is thus conclusive evidence for manifold spirals in mdf778.

The gas has, in all three cases, a qualitatively similar morphology to the stars. Note, however, that, contrary to the stars, the gas has a minimum in the central region of the galaxy of an extent comparable to, but somewhat smaller than, the bar size. Further in, at a scale of 1 kpc or less, there is a strong concentration of gas. This morphology is in good agreement both with observations and with results of previous, more idealized simulations (see e.g., Figure 2 in Athanassoula 1992).

The total stellar mass at the end of the simulation is around 5 × 10¹⁰ M_⊙ in all three simulations (i.e., these galaxies are Milky Way–sized). Figure 1(b) shows the azimuthally averaged radial projected surface density profile of mdf732 at t = 10 Gyr. Those of mdf778 and mdf780 are qualitatively the same. The outer parts in all three cases show a downbending truncation (i.e., of Freeman type II; e.g., Freeman 1970; Erwin et al. 2005; Muñoz-Mateos et al. 2013), which is the most common among the truncation types: ∼60% according to Pohlen & Trujillo (2006), or 42% according to Laine et al. (2014).

Figure 1(c) shows the circular velocity curves for mdf732 at t = 10 Gyr, both for the total mass in the galaxy and for its basic components. It is calculated directly from the particle masses and positions in the simulation, without assuming spherical symmetry, contrary to a number of previous works. It is qualitatively the same for the other two cases. The total curve is fairly flat, with two shallow bumps due to the spirals. There is also a somewhat higher bump (15–20 km s⁻¹) in the central region, due to the bulge. The ratio of the velocity due to the baryonic components to the total at 2.2 inner disk scalelengths is about 0.57 (mdf732), 0.62 (mdf778), and 0.69 (mdf780) of the total. Thus, according to the Sackett (1997) criterion, mdf732 and mdf778 are clearly submaximal, while mdf780 is also submaximal but very near the borderline with maximum disks. Compared to the galaxies of the DiskMass survey (Bershady et al. 2011, their Figure 2), our three models have, for their circular velocity, among the highest fraction of disk mass of the survey, or even somewhat higher.

In a totally cold, perfectly axisymmetric disk, all stars will rotate with a velocity equal to the circular velocity. Stars in galactic disks, however, have some radial motion, albeit considerably less than their tangential one. At the other extreme, stars in classical bulges have strongly noncircular motions with considerable radial velocity components, and with either direct or retrograde rotation. In between the two, there are stars in structures such as bars, ovals, or lenses, whose motion is neither as circular as that of disk stars, nor as far from circular as that of classical bulge stars can be.

These different kinematics are reflected in the different values of the normalized angular momentum of a stellar orbit, known as the circularity parameter ε = ${J}_{z}/{J}_{\mathrm{circ}}$, where J_z is the z component of the angular momentum and J_circ is the angular momentum of the circular orbit of the same energy (e.g., Abadi et al. 2003; Aumer & White 2013). Figure 5(a) shows an example (red line) of a histogram of the number of particles as a function of their circularity for a snapshot with only a classical bulge and a disk component. This simulation is in all aspects identical to mdf732, except that no AGN feedback has been included (see Section 2.3 and Paper II). The classical bulge and the disk are clearly distinct, and it is possible to distinguish the disk from the bulge stars simply by introducing a separation limit to their circularity value (ε_lim), which, as can be seen from Figure 5(a) is situated around 0.5. We tested this kinematic way of distinguishing the disk from the classical bulge stars by viewing the spatial distribution of the two thus obtained populations separately and from various viewing angles, and made sure that the disk is adequately distinguished from the classical bulge component. After some trials, we found that ε_lim = 0.5 gave quite satisfactory results and we adopted it. The stars that this method assigns to the disk(bulge) will hereafter be called "kinematic disk(bulge) stars."

A related, very useful quantity is the circularity at birth (ε_birth). As expected, this is very near one for stars born in the disk, but not for stars born in the bulge. Figure 5(b) shows the fraction of stars of a given birth time that are born with ε_birth > ε_lim, as a function of their birth time, for mdf732 and as calculated for ε_lim = 0.5 (red curve). Calculations using ε_lim = 0.6 and 0.7 give quasi-identical results. Note that during the merging, J_circ cannot be adequately defined, so the curve includes only times after 1.55 Gyr. This curve shows considerable structure, which will be discussed in the next subsection.

It is expected that landmark times, such as the merging time, should set clear differences between the stellar populations born before and after them. We want to check whether this is the case in our simulations, and what the corresponding differences are. We assess this by examining the t = 10 Gyr snapshot of mdf732.

An obvious choice for the first landmark time is the merging time. In major mergers, however, there is no clearly and uniquely defined merging time and it is better to define a merging period, or time range. Furthermore, we want to avoid eye estimates of such times because they can be biased and are not reproducible. We thus define the beginning of the merging period as the earliest time after which the distance between the centers of the two merging protogalaxies is always smaller than 1 kpc (t_bm). Although arbitrary, this time has the advantage of being clearly defined and reproducible. We define as the center of each galaxy what is often referred to as the center of density of its halo, calculated from the positions of the halo particles with the highest local density (as defined by the distance to their nearest neighbors; e.g., Casertano & Hut 1985). We measure the distance between the two progenitor centers and find the earliest time after which this distance stays smaller than 1 kpc. For mdf732 it is around 1.4 Gyr.

As a second landmark time, hereafter t_bd, we chose a time associated with the beginning of the disc formation and, more specifically, the time beyond which the vast majority of stars are born with disk kinematics. We estimate this by using ε_birth. Figure 5(b) (red line, calculated for ε_lim = 0.5) shows that the fraction of kinematic disk stars increases strongly with time of birth for up to 2.2 Gyr and that about 95% of stars born after this time have disk kinematics. We thus adopt t_bd = 2.2 Gyr, after verifying that this value holds for other reasonable values of ε_lim. We also introduced a third time at t_by = 9 Gyr, which is somewhat arbitrary and not a landmark time, but is useful because it sets a time such that any stars born after that can be considered young; this allows us to focus on the distribution and kinematics of the youngest stars. For our snapshot, which is at 10 Gyr, the ages of the stars born at t_bm, t_bd, and t_by are 8.6, 7.8, and 1 Gyr, respectively.

We then define five time intervals—[0,t_bm], [t_bm,t_hm], [t_hm,t_bd], [t_bd,t_by], and [t_by, 10] where ${t}_{\mathrm{hm}}\quad =\quad 0.5({t}_{\mathrm{bm}}+{t}_{\mathrm{bd}})$—and separate the stars in five groups according to which time range they were born in (i.e., according to their age). We thus get five separate populations, and their respective number of stellar particles is 99,369, 109,035, 83,960, 71,3081, and 47,376. Their face-on and edge-on views are shown in Figure 4. Corresponding kinematic information for each group is given in Figure 5(c), which shows the distribution of stars as a function of their circularity at 10 Gyr (ε₁₀). Examining this morphological and kinematic information together, we find a number of important results:

• 1.  
  Stars born before the beginning of the merging period (i.e., that are older than 8.6 Gyr; leftmost panels of Figure 4) are concentrated in the innermost couple of kpc and their spatial distribution and radial density profile are that of a triaxial classical bulge. They are the oldest stars in the galaxy and experienced violent relaxation due to the strong evolution of the potential during the merging, thus explaining their very steep radial projected density profiles (Lynden-Bell 1967). Thus, major mergers provide a mechanism for classical bulge formation. Some of these stars rotate prograde and others retrograde with respect to the disk, as expected for a classical bulge (Figure 5(c)). There are, however, considerably more prograde than retrograde stars, i.e., the bulge has internal rotation. This is, at least partly, due to the bar, which can make the bulge more oblate (Athanassoula & Misiriotis 2002) and give it some spin (Athanassoula 2003; Saha et al. 2012).
• 2.  
  Stars born during the first half of the merging period (i.e., with ages between 8.2 and 8.6 Gyr; second column of panels in Figure 4) have a density distribution similar to that of stars born before the merging, although more extended and more flattened. The outermost isodensities of the edge-on view are cusped, as one would expect from a relatively light underlying thick disk. This is corroborated from their angular momentum distribution (green line in Figure 5(c)), which shows a considerable contribution of stars with ε₁₀ near but somewhat less than 1.
• 3.  
  Stars born during the second half of the merging period (third column of panels) have a very different density distribution from that of the two previous groups. In the outer parts they trace a disk extending well beyond the bulge region, and in the inner parts a bar with a vertically thick boxy bulge (Athanassoula 2005). Their circularity distribution (Figure 5(c), red line) also shows the existence of two components: a fast rotating component (i.e., a disk) and a slower component rotating with an average ε₁₀ around 0.25. After examining the spatial distribution of the stars in the latter component, we found that it is the bar (see also Section 3.7). Thus the stars born in this time range contribute partly to the near-axisymmetric disk and partly to the bar.
• 4.  
  The stars within the two last age ranges (younger than 7.8 Gyr) were born during the disk formation era and are thus part of what is commonly referred to as the disk population. This disk is extended and quite thin. Except for the axisymmetric disk, the stars in the fourth age bracket also contribute to the spirals and the bar. For this group of stars, the ansae at the extremities of the bar are clearly visible, and at smaller radii there is an X-like edge-on shape, as in many barred galaxies. Note that both the disk and the bar are vertically thinner than the corresponding structures in the third age bracket.On the other hand, the stars that are younger than 1 Gyr do not participate in the bar structure, but are heavily concentrated in the spiral and ring structures as well as in an innermost very thin structure, which can be called a disky pseudobulge (Kormendy & Kennicutt 2004; Athanassoula 2005). The latter may well exist in the third and fourth age brackets as well, but is less easily discernible in plots as in Figure 4 because of the strong bar contribution to the central parts.The kinematics of these two youngest age ranges (Figure 5(c)) corroborate this. In particular, they show that the stars of the fourth age range contribute partly to the disk and partly to the bar (see also Section 3.7). On the other hand, the stars in the youngest age bracket essentially only contribute to the disk, and more specifically (Figure 4) to its spirals, rings, and the disky pseudobulge.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In the lower panels of Figure 4 we show the projected density radial profiles of each of the five stellar populations, obtained from their face-on views. The oldest population is well fitted by a single Sérsic component with an index between 4.5 and 6 (i.e., corresponding to a classical bulge; Kormendy & Kennicutt 2004; Drory & Fisher 2007). At the other extreme, the youngest population can be fit by three exponential disks: the innermost one corresponding to a disky pseudobulge, and the other two to the inner and outer disks, respectively. Thus, in general, the classical-bulge-to-total stellar mass ratio decreases with the age of the population from 100% to 0%.

In Section 3.5 we discussed a simple way of distinguishing the classical bulge population from that of the disk for snapshots with only these two components. We now extend this to snapshots with bars and/or ovals and apply it to mdf732 at t = 10. The corresponding circularity histogram is given in Figure 5(a) (green line). As expected, the distribution is now much more complex. Namely, there is clearly additional material between the disk and the bulge components, and applying a simple separating criterion to ε would not suffice if an important fraction of stars is in the bar component. Independent of their ε, bar stars should be considered part of the disk component because the bar forms from a disk instability that rearranges the disk material. We therefore conclude that not only all stars with ε > ε_lim belong to the disk, but also a considerable fraction of those with ε < ε_lim. Thus, a more elaborate analysis will be necessary for galaxies with bars.

We therefore divide stars into groups depending on three physical properties: whether their time of birth is before or after t_bd, and whether their kinematics at birth and at 10 Gyr are disk-like or bulge-like. The latter two are ensured by testing whether their circularity at birth and at 10 Gyr (ε₁₀) is bigger or smaller than ε_lim. In this section, as in Section 3.5, we describe results obtained with ε_lim = 0.5. We also tried other values, and some of the corresponding results are reported in Section 3.8.

This division creates eight groups of stars, which are described in Table 1. Groups G1 to G4 include all stars born after t_bd, while groups G5 to G8 include all stars born before t_bd. We viewed each group separately in 3D from different angles to assess its shape and morphology, and we also made projected radial and vertical surface density profiles for different cuts. Whenever a bar is present in the group density distribution, we calculated its position angle (PA); comparing the PA found for all groups, we found that they all agree to within 5° (i.e., to within the accuracy of the estimates). We now consider this information together.

Group G1 consists of stars with disk kinematics, both at birth and at 10 Gyr. Figure 6 (leftmost panels) reveals a thin disk with a strong global spiral structure and a rather weak bar. Its projected density profile (not shown) is exponential with a small central bump due to the bar. It is clearly a disk population and comprises 66% of the stars.

Zoom In Zoom Out Reset image size

Stars in group G2 were born with disk kinematics, and by 10 Gyr evolved to nondisk kinematics. The morphology and photometry of G2 show that 95% of G2 stars form a bar and the remaining 5% form a disk component around it. The bar in G2 has roughly the same orientation and length as that of G1, but is considerably fatter horizontally. Seen edge-on, it has a clear boxy/peanut structure. Most of the stars in G2 were born very soon after t_bd, while those of G1, G3, and G4 are more evenly spread between t_bd and 10 Gyr. Thus the stars in G2 are, on average, older than the stars in these groups. Their circularity argues that they were born in the axisymmetric disk and were trapped by the bar as this grew. G2 comprises 4.56% of the stars.

G3 has disk kinematics at 10 Gyr, but not at birth, while G4 does not have disk kinematics either at 10 Gyr or at birth. The stars in those two groups are concentrated in an inner triaxial object of size roughly 1.4:0.7:0.5, whose PA is, within the errors, the same as that of G1 and G2. Thus, it can be considered to be an inner part of the bar, presumably part of its barlens component (Laurikainen et al. 2014; Athanassoula et al. 2015). Together, G3 and G4 comprise only 1.65% of the stars.

Groups G5 to G8 consist of stars with t_birth < t_bd. For most of these stars, it is not possible to calculate ε_birth because the center of the remnant at such times is not well defined. Instead, we calculate ε at t_bd (ε_bd), because, although this time is early on in the evolution, it is sufficiently late for the center of the remnant to be clearly identified.

At 10 Gyr, the stars of group G5 constitute a thick disk (Figure 6) with no spirals and with a bar of roughly the same length and PA as that of G1, but much fatter in the plane and with no ansae. This thick disk comprises 9.08% of the stars.

Stars in group G6 basically compose a bar, similar in shape and outline to that of G5, while a few of them are in a thick disk that is similar to that of G5. They comprise 3.99% of the stars.

Group G7 has too few stars for us to classify. It comprises 2.37% of the stars.

Most of the stars in group G8 belong to a flattened bulge, as argued by morphology, photometry, and kinematics. G8 isophotes have a bar-like deformation in their central part that is analogous to the "halobar" found in the central parts of halos (Colin et al. 2006; Athanassoula 2007). G8 comprises 12.3% of the stars.

The above procedure distinguishes the disk from the classical bulge component. Groups G1, G2, G5, and G6 are unambiguously linked to the disk, and this also probably is true for G3 and G4. Indeed, they contribute mainly to the bar and, more specifically, to its inner parts. Most of group G8 is linked to the classical bulge. G7 is presumably linked to the bar (i.e., it is a disk population), but not as unambiguously as for the aforementioned disk components. Nevertheless, the uncertainty this entails is very small, 2%–3%.

Note also that the stars in the thick disk are older than those in the thin one, because they were born earlier in the simulation and in a rather restricted time interval, roughly between 1.4 and 2.2 Gyr (i.e., at t = 10 Gyr they have an age between 8.6 and 7.8 Gyr). Thus the oldest stars in this model are in the classical bulge, followed by those in the thick disk, while the youngest are in the thin disk.

In Table 2 we give various estimates of the B/T ratio in our three fiducial simulations at t = 10 Gyr, as well as some close upper limits. Columns 1 and 2 give the run number and t_bd, respectively. Columns 3–8 give results for the method described in Section 3.7, where we extended the simple kinematic decomposition of the stars into a disk and a bulge component, to cases with a bar. There we identified most of group G8 as the classical bulge component and the corresponding B/T values are given in columns 3–5 of Table 2. We were, however, unable to safely identify whether G7 should be considered a disk or a classical bulge component, so we also include an estimate based on the sum of the two components as an upper limit (columns 6–8). We applied this with ε_lim = 0.5 (columns 3 and 6), which is the value we found to be more appropriate (Sections 3.5 and 3.7), but also with ε_lim = 0.6 (columns 4 and 7) and even ε_lim = 0.7 (columns 5 and 8); the last two, and particularly the last one, act more like upper limits. As expected, the smallest values are found when identifying G8 to the classical bulge and using ε_lim = 0.5, while the largest are the upper limits obtained when identifying G7 and G8 as the classical bulge component and using ε_lim = 0.7. It is, however, very reassuring that the differences are small, showing that the upper limits are close to the most probable values.

Hopkins et al. (2009) introduced a different, much simpler and more straightforward method to obtain an estimate of B/T. They assume that the bulge has no global rotation and that it is the only component that includes negative ε values. Under these assumptions the contribution of the bulge is equal to twice the mass of particles that have negative velocities. This was introduced for disk galaxies with no bars, where these assumptions are very reasonable to make. However, as discussed in Section 3.6 and the references therein, bars, although part of the disk population, do not have disk kinematics. Furthermore, they can transmit angular momentum to the classical bulge, so for strongly barred galaxies the estimate from this method can be considered an approximation. We apply this method to our simulations and find values within 10% of our upper limits (Table 2). It is useful to have established this agreement, because the Hopkins et al. method is easy to apply and was used in many previous cases.

To get a third, independent estimate of B/T, we used a decomposition of the radial projected density profile, obtained by averaging the density in cylindrical annuli in the face-on view of the disk. This decomposition is similar to the 1D decompositions used by observers for the radial luminosity profiles; although 1D, it is not straightforward, because the innermost regions may include either both a classical and a disky pseudobulge, or only one of the two. Depending on exactly how the decompositions are done, we find values for mdf732 between 0.09 and 0.15, for mdf778 between 0.10 and 0.18, and for mdf780 between 0.09 and 0.11 (i.e., somewhat lower than, but in good agreement with the kinematic estimates).

The values of the B/T ratio we find here are considerably smaller than those found in previous simulations with no hot gas in the halo. Such simulations are well summarized in Hopkins et al. (2009), where, out of several hundred simulations, only five have B/T ≤ 0.2, and, moreover, these five have 1:8–1:10 progenitor mass ratios. On the contrary, our B/T values are compatible with those of observed spiral galaxies, and do not exclude that such galaxies were formed from major mergers. This is a big improvement over past works and is due to the existence of a hot gaseous halo in the progenitors, which is carried over in the merger remnant. Indeed, as shown in previous subsections, the mass of the classical bulge (B) is roughly set by the number of stars that formed before the merging. On the other hand, the mass of the disk is mainly due to stars that formed after the merging. Due to the gaseous halo, the accretion of gas on the disk continues well after the merging, up to the end of the simulation and presumably well after it. It thus leads to a more extensive and more massive disk than what would be found in the absence of a gaseous halo, and, therefore, smaller B/T values. Comparisons for more simulations and the effect of various progenitor properties and orbital parameters on the B/T values will be given elsewhere.

Observations show that there are spirals, in particular relatively small late types with no or hardly any classical bulge (Kormendy et al. 2010). Our own Galaxy has a classical bulge of low mass (e.g., Shen et al. 2010; Ness et al. 2013a, 2013b), but it is premature to state that it has no classical bulge at all. Our simulations produced considerably lower B/T values than previous ones considering major mergers. So far, however, none of our simulations have given results that are compatible with a total lack of classical bulge. This is a general problem for all disk galaxy formation studies and may be solved by changing the feedback recipes, as attempted in cosmological simulations (e.g., Brook et al. 2012; Brooks & Christensen 2015). Here we simply note that major mergers should be rarer in low density environments, thus if bulgeless disks are found solely, or predominantly, in such environments, their hosts may well not be major merger remnants. Moreover, our aim here is to test whether major mergers may produce disk galaxies, but certainly not to show that they are the only way of making them. Thus it is not necessary for our scenario to be able to form disk galaxies with no classical bulge at all.

When examining the group G5 in mdf732 at 10 Gyr (Section 3.7), we found that its stars form a thick disk (Figure 6). We now discuss its properties further and compare them to those of the observed thick disks. Such a comparison can only be approximate because other groups may also host some thick disk stars. For example, thick disk formation will not stop abruptly at time t_bd, but will continue at subsequent times, albeit at a tapered rate. Moreover, some stars born in the thin disk will be vertically heated (e.g., by the spirals) and thus contribute to the thick disk. Yet it makes sense to use G5 for comparison with observations because it is defined using physical criteria (Section 3.7) and, furthermore, it is a main (presumably the main) contributor to the thick disk. We thus use group G5 as a proxy here, and loosely refer to it as the thick disk component. Note also that even in observations there is more than one way to define the thick disk; Yoachim & Dalcanton (2006), Comeròn et al. (2011a, 2012), and Streich et al. (2016) use different methods and/or different fitting functions, thus introducing considerable differences in the results.

In the disk formation scenario that we consider, the thick disk forms naturally, in agreement with the observational claim of thick disk (near-)ubiquity (Yoachim & Dalcanton 2006; Comeròn et al. 2011b, but see also Streich et al. 2016).

Contrary to the thin disk, the simulated thick disk either has no spirals or they of such low amplitude that they are not discernible by eye. This should be linked to the fact that both density wave (Lin 1967) and swing amplification theories (Toomre 1981) show that hotter and thicker disks harbor lower amplitude spirals. A similar result presumably holds for a manifold origin because it is more difficult to confine a hot stellar population than a cold one (see also Romero-Gómez et al. 2006), but no specific quantitative study has yet been made.

By definition, the stars in group G1 were born after t_bd, while those in group G5 were born before that. Thus the stars in the thick disk are older than the stars in the thin disk, which is in agreement with observations (e.g., Mould 2005; Yoachim & Dalcanton 2008; Comerón et al. 2015).

The bar in the thick disk has the same length and orientation as that of the thin one, but it is much thicker in the disk plane than that of G1, as would be expected from previous works (Athanassoula 1983; see also Athanassoula 2003), where it was shown that the bar is thicker in the disk plane when this disk is hotter. Note also that the bar in the thick disk has no ansae and, when viewed side-on, has a boxy/peanut bulge with a considerably larger vertical extent than that of the thin disk bar. According to this scenario, and since the thin and thick disks coexist, the bar component in the observed galaxies include contributions from both thin and thick disks so that various parts of the bar may have different mean stellar ages.

Observations (Yoachim & Dalcanton 2006; Comeròn et al. 2012) show that the ratio of thick to thin disk mass is a decreasing function of the circular velocity, so more massive galaxies have a relatively less massive thick disk. Yoachim & Dalcanton (2006; see caption of their Figure 22) provide a simple fitting formula for this decrease, which, although poorly constrained for massive galaxies, has the advantage of fitting the whole mass range. Applying it for V_circ = 210 km s⁻¹, we find a ratio of thick to thin disk masses of 0.10, which, given the uncertainties due to the extrapolation, is in good agreement with the value of 0.14 we found in Section 3.7.

We calculated the average tangential velocities of G1 and G5 in an annulus between 5 and 15 kpc from the center. This adopted radial range is not optimum because it includes mainly large radii, where the difference of the two averages will be relatively small, but it was chosen to avoid the bar region, where the kinematics depend mainly on the strength of the bar and only indirectly on the disk thickness. We find 209 and 197 km s⁻¹ for the thin and the thick disk, respectively, values that are as expected in both sense and amplitude. They are also in agreement with the results of Yoachim & Dalcanton (2008), who find that for the higher mass galaxies in their sample, they fail to detect differences between the thin and the thick disk kinematics.

As already discussed in Sections 2 and 3.1, our protogalaxies acquire a baryonic (stellar plus gaseous) disk before the merging. Thus our simulations describe the merging of two disk protogalaxies with a halo composed of DM and gas. Here we examine the role of the halo gas on the formation and evolution on the ensuing disk galaxy by tracking the origin of gaseous and stellar particles, and comparing cases with and without halo gas. We thus use two different approaches.

3.10.1. Tracking the Origin of Gaseous and Stellar Particles in the Disk

In this first approach we use mdf732 to disentangle the gas that would be present in simulations with a gaseous disk but no gas in the halo, from the gas that is present in simulations including a gaseous halo (i.e., all the gas in our simulations). We track each of these two separately and follow how each one evolved up to 10 Gyr (i.e., the end of the run). We also take into account the fact that each gas particle may have stayed in gaseous form or turned into a stellar particle.

To disentangle the gas origin, we use a snapshot at t = 0.85 Gyr, which roughly corresponds to the time of the apocenter following the first pericenter. We also tried other times, between 0.7 and 0.9 Gyr, and found qualitatively the same and quantitatively very similar results. Because the equatorial planes of the two protogalaxies coincide with the orbital plane, we roughly define halo gas as all gas particles with $| {\rm{\Delta }}z| \gt 1\;{\rm{kpc}}$, so the gas that would be present in a simulation with no gaseous halo is only the gas with $| {\rm{\Delta }}z| \lt 1\;{\rm{kpc}}$. The latter includes the gas in the two protogalactic disks before the merging, as well as the gas in the tails formed during the interaction. It is important to include the gas in the tails because it moves initially outward but eventually turns back at larger distances from the center and falls back toward the remnant disk. We can thus roughly assume that by tracking the gas with $| {\rm{\Delta }}z| \lt 1\;{\rm{kpc}}$, we follow the gas that would be present in a simulation with no gas in the halo. Of course the slab $| {\rm{\Delta }}z| \lt 1\;{\rm{kpc}}$ will also contain some halo gas, so the above rough decomposition will give an upper limit of what the gas in cases with no halo gas can do. This upper limit, however, should be quite near the actual value.

Figure 7(a) shows the mass found in the remnant disk still in gaseous form as a function of time, both including (red line) and excluding (blue line) the gas in the halo. The former shows a much weaker decrease with time (less than a factor of 2.5 between 3 and 10 Gyr) than the latter (more than a factor of 10 in the same timeframe). This is due to the gas that accreted from the halo, which leads to much more gas-rich disks throughout the simulation and a slower gas mass decrease.

Zoom In Zoom Out Reset image size

Figure 7(b) gives a similar comparison, but now for the stars. Here we compare the stellar mass formed in cases with no gaseous halo (blue line) to all disk stars (independent of the origin of the gas they were born from; red line). The latter shows a steady increase with time, compared to the former, which is nearly constant. More specifically we witness an increase by a factor of 2.4 for the latter compared to barely a factor of 1.1 for the former.

Figure 7(c) gives the ratio of gaseous to total baryonic mass as a function of time. This decreases from 0.37 at 3 Gyr to 0.092 at 10 Gyr when halo gas accretion is included, while it decreases from 0.1 to 0.01 in the same time range when accretion from the halo is not included.

To summarize, both the stellar and the gaseous disk are more massive when the accretion from the halo gas is taken into account, as expected, while the gas fraction in the disk is more compatible with that of spiral galaxies.

3.10.2. A Test Simulation

To deepen our understanding of the effect of the halo gas component on the disk galaxy formation and evolution, we ran a further simulation. As initial conditions we used a snapshot of simulation mdf780 at t = 1.77 Gyr, in which we replaced the low density gas particles (local density <5 × 10⁻⁴M_⊙ pc⁻³) with collisionless particles. These had the same mass and positions as the gas particles they replaced, and their velocity was taken from the velocity distribution of the halo (as e.g., in Rodionov et al. 2009) to preserve the dynamical equilibrium of the system as much as possible. We also verified that this gas was essentially in the halo and that the gas in the disk and in the tidal tails was not affected by this change. This is run mdf223, which we compare to mdf780 in Figure 8. Even a cursory glance shows that there are important differences between their mass distributions. The disk in mdf780 is much more extended and massive than that of mdf213. These results are in agreement with what we already discussed from the analysis of mdf732 in Section 3.10.1 and the two together show that the gaseous halo plays a crucial role in the formation and evolution of the disk.

Zoom In Zoom Out Reset image size