MERGER SIGNATURES IN THE DYNAMICS OF STAR-FORMING GAS

We use the three-dimensional Monte Carlo radiative transfer code sunrise (Jonsson 2006; Jonsson et al. 2010) to produce mock images of the simulated galaxies described in Section 2. sunrisedetermines the emission from stars and AGNs in the hydrodynamic simulations with spectral energy distribution (SED) templates (Leitherer et al. 1999; Hopkins et al. 2007) and then performs radiative transfer calculations to account for the absorption, scattering, and re-emission by dust. We adopt the same dust model as L14 (the Milky Way-type dust model of Draine & Li 2007). L14 discuss two possible treatments of the sub-resolution ISM structure during radiative transfer (i.e., whether dust mass is derived based on the diffuse gas content in the Springel & Hernquist 2003 model or the total gas content). Here we adopt the conversion that dust mass is based on the diffuse gas content, which can better reproduce the SEDs of the observed interacting galaxies (L14).

We derive optical morphological properties using the mock SDSS $i^{\prime}$-band (${\lambda }_{{\rm{eff}}}=7439$ Å, ${\rm{\Delta }}\lambda =1044$ Å) images produced from sunrise. Rest-frame optical wavelength is an ideal window to trace the disturbed structures induced by galaxy mergers because the emission is dominated by old stellar populations instead of the clumpy star-forming regions (e.g., Abraham et al. 2003; Conselice 2003; Lotz et al. 2004), and it is available for a large sample of star-forming galaxies from z ∼ 0 out to z ∼ 1–3 (e.g., van der Wel et al. 2012; Kartaltepe et al. 2014). The ∼7000–8000 Å regime is not severely affected by dust extinction except for extreme cases like ultraluminous and luminous infrared galaxies ((U)LIRGs; Haan et al. 2011; Hayward et al. 2012). No significant impacts from dust extinction are seen in our morphological analysis based on the $i^{\prime}$-band images throughout the M3M2e and M3M3e simulations. We generate mock $i^{\prime}$-band images at 100 Myr intervals throughout the interaction sequence, and decrease the sampling steps to 20 Myr intervals during the strong interaction phase. For each snapshot, we obtain mock images from seven viewing angles sampled in a regular grid in spherical coordinate.

We then convert the mock images from sunrise to images comparable to real observations. First, we place our simulated galaxies at a distance of 100 Mpc, in which the plate scale of SDSS images (0396) corresponds to a physical size of ∼200 pc. The observed number of counts is determined according to the surface brightness of galaxies at the assumed distance. We then convolve the sunrise images with the typical point-spread function of SDSS $i^{\prime}$ observations (∼13), and add a noise frame extracted from the blank region in real SDSS $i^{\prime}$ images. Examples of processed mock images from the M3M2e and M3M3e simulations are shown in the left panels of Figures 1 and 2, respectively.

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As discussed in Section 1, emission lines from molecular gas and ionized gas are the most common tracers for a large sample of resolved galaxy kinematics at z ∼ 0–3. Therefore, we focus our analysis on the kinematic properties derived from star-forming gas, and we discuss possible impacts using different dynamical tracers in Section 5.4.

We construct the kinematic maps based on the dynamical information from the SPH particles. We select the subset of gas particles that have SFR $\gt \;0$ as a proxy of star-forming gas (where the gas density must be higher than a threshold of n ∼ 0.1 cm⁻³) in the simulated galaxies. In this simple approximation, possible impacts from dust are not included. To convert particle-based information to kinematic maps, we make projected velocity and velocity dispersion maps from seven viewing angles that are consistent with sunriseimages. In each viewing angle, we bin the gas particles into equally-spaced 500 pc × 500 pc bins (500 pc corresponds to ∼1'' at the distance of 100 Mpc). The velocity and velocity dispersion in each pixel are then derived from the median and standard deviation of the gas particles weighted according to their SFR. Finally, we adopt adaptive binning (Cappellari & Copin 2003) for the kinematic maps to ensure that each region (combined from $\geqslant 1$ pixel) contains at least 10 star-forming gas particles. Examples of velocity and velocity dispersion maps from M3M2e and M3M3e simulations are shown in the middle and right panels of Figures 1 and 2, respectively.

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A common kinematic diagnostic of disks and mergers is the complexity of the galaxies' resolved kinematic properties, i.e., whether galaxies show ordered rotational patterns as expected for disk-like galaxies or chaotic patterns as expected for interacting systems. Such identifications have been done via kinematic asymmetries (Shapiro et al. 2008; Bellocchi et al. 2012), visual inspections (e.g., Flores et al. 2006; Epinat et al. 2012), and visual comparisons with galaxy merger simulations (e.g., Hammer et al. 2009).

In this paper, we quantify how the degree of galaxies' kinematic maps deviate from a rotating disk using the kinematic asymmetries defined by Shapiro et al. (2008), which is based on the higher-order moments kinematic coefficients of the velocity and velocity dispersion distributions derived using the kinemetry analysis (Krajnović et al. 2006). The line of sight velocity map or velocity dispersion map $K(a,\psi )$ can be divided into a series of elliptical rings (with semimajor axis a) as velocity or velocity dispersion profiles. These profiles can then be described as an expansion of $N+1$ harmonic terms:

$$\begin{eqnarray}&&K(a,\psi )={A}_{0}(a)+\displaystyle \sum _{n=1}^{N}\;{A}_{n}(a)\mathrm{sin}n\psi +{B}_{n}(a)\mathrm{cos}n\psi ,\end{eqnarray} \tag{ 1 }$$

where ψ is the azimuthal angle. Shapiro et al. (2008) quantify the level of deviation from an ideal disk by defining asymmetric measures of velocity and velocity dispersion fields as:

$$\begin{eqnarray}&&{v}_{\mathrm{asym}}={\langle \displaystyle \frac{{\displaystyle \sum }_{n=2}^{5}{k}_{n,v}/4}{{B}_{1,v}}\rangle }_{r},{\sigma }_{\mathrm{asym}}={\langle \displaystyle \frac{{\displaystyle \sum }_{n=1}^{5}{k}_{n,\sigma }/5}{{B}_{1,v}}\rangle }_{r},\end{eqnarray} \tag{ 2 }$$

where ${k}_{n}={({A}_{n}^{2}+{B}_{n}^{2})}^{1/2}$, the subscripts v and σ refer to the quantifies corresponding to the velocity and velocity dispersion maps, and r refers to the average over all radii. Finally, kinematic asymmetries, K_asym is defined as ${({v}_{\mathrm{asym}}^{2}+{\sigma }_{\mathrm{asym}}^{2})}^{1/2}$.

We measure K_asym of all simulations from the velocity and velocity dispersion maps described in Section 3.2 using the IDL routine Kinemetry ¹⁰ (Krajnović et al. 2006). We adopt the gas density peak position as the center of the kinematic maps, and then use Kinemetry to find the best fit ellipse with position angle and the flattening factor (Q = 1 − e) at each radius step until more than 25% of the data points along an ellipse are not present (the COVER parameter = 0.75). The choice of this COVER parameter typically leads to an outer radius of ∼10 kpc during early interaction stages and ∼5 kpc during strong interaction and post-coalescence phases. The evolution of K_asym along the interaction sequence of M3M2e and M3M3e simulations is shown in the bottom panels of Figures 3 and 4. In general, only one galaxy in the interacting system (the one with higher central density) is included in the calculation when two galaxies are well-separated (≳10 kpc), and the evolution of K_asym does not necessarily follow the same galaxy during the early interaction phases. We also derive K_asym in two additional cases following each galaxy in the interacting system, in which the centers of the kinematic maps are chosen at the positions of the supermassive black holes. We note that Kinemetry can fail to perform the elliptical fitting when the systems traced by the star-forming gas are too compact (e.g., ≲5 pixels across the galaxy), but typically less than 5% of the data do not have K_asym measurements in a given interaction sequence for this reason.

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Various non-parametric statistics have been developed to quantify the irregularity of galaxy structure, and they can be used as indicators for possible disturbance due to galaxy mergers (Bershady et al. 2000; Conselice et al. 2000; Abraham et al. 2003; Conselice 2003; Lotz et al. 2004; Freeman et al. 2013). Extensive work has also been done to quantify the evolution of these parameters along the interaction sequence (e.g., Conselice 2006; Lotz et al. 2008, 2010a, 2010b) and their robustness for nearby and distant galaxies (e.g., Abraham et al. 1996; Overzier et al. 2010; Hung et al. 2014). In this paper, we quantify the morphological properties of the M3M2e and M3M3e simulations only to assist with the kinematic analysis, and refer the reader to the references listed above for detailed discussions of merger observability using morphological properties.

We measure the asymmetry parameter (A; Conselice et al. 2000) of galaxies in the M3M2e and M3M3e simulations from the mock SDSS $i^{\prime}$ images. We follow the definition of A in Conselice et al. (2000), in which it quantifies the deviation from 180^◦ rotational symmetry.

$$\begin{eqnarray}&&A=\displaystyle \sum _{i,j}\displaystyle \frac{| I(i,j)-{I}_{180}(i,j)| }{| I(i,j)| }-\displaystyle \sum _{i,j}\displaystyle \frac{| B(i,j)-{B}_{180}(i,j)| }{| I(i,j)| },\end{eqnarray} \tag{ 3 }$$

where I and I₁₈₀ is the galaxy image and its 180^◦ rotated version, and B and B₁₈₀ represent the background and its 180^◦ rotation. A is often significantly enhanced relative to elliptical or spiral galaxies in the presence of multiple bright components and extremely irregular structure. The merger simulations in Lotz et al. (2008, 2010a, 2010b) have also demonstrated that A is most sensitive to interacting galaxies during the strong interaction phases before the final coalescence and in some cases during the first passage as well.

To derive A, we first use SExtractor (Bertin & Arnouts 1996) to identify galaxies in each mock $i^{\prime}$-band images. The de-blending parameters have been chosen so that the interacting systems are identified as one galaxy when the projected distance between two nuclei is smaller than ∼5–10 kpc. When more than one object is detected in the images, we mask out the detections other than the brightest galaxy and we refill the masked regions with nearby sky. In this case, most of the identified regions along the interaction sequence for deriving A are consistent with the kinematic measurements. We apply a "quasi-Petrosian" method (Abraham et al. 2007) to define the Petrosian radius (r_p) as the effective radius at the isophotal threshold of 0.2 and we define the center of galaxies as where A is minimized (Conselice et al. 2000). Finally, A is derived by summing over all pixels within 1.5 r_p (Equation (1)). The evolution of A along the interaction sequence of M3M2e and M3M3e simulations is shown in the middle panels of Figures 3 and 4.

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Figures 3 and 4 show the evolution of SFR, A, and K_asym along the interaction sequence of the M3M2e and M3M3e simulations. The distribution of A and K_asym from isolated M3 simulations with various viewing angles and time are indicated in gray shaded area. In both M3M2e and M3M3e simulations, A is significantly enhanced only after the second passage of galaxies and before coalescence. During this strong interaction phase, individual galaxies display large scale tidal features and lead to high A even when two galaxies can still be resolved. When the two nuclei are close enough (≲5–10 kpc) to be considered as one system, the multiple bright components can also result in higher values of A. The enhancement of A during the strong interaction phases are consistent with the results of G3G3P and G3G2P simulations in Lotz et al. (2008, 2010b), which use similar progenitor galaxies and orbital parameters but different initial disk orientations. Although a small fraction of the data in Lotz et al. (2010b) have elevated A during the first passage, no significant enhancement is seen in our M3M2e and M3M3e simulations.

The evolution of K_asym approximately tracks A before the coalescence phase in both M3M2e and M3M3e simulations. The low K_asym during the early interacting stages demonstrates that within individual galaxies, only minimal disturbance is seen in the kinematic structures traced by star-forming gas. Although galaxy interactions may begin to affect the SFR and metallicity of individual galaxies during the early phase of interaction (e.g., Scudder et al. 2012; Moreno et al. 2015), this impact may not necessarily reflect on the irregularity in galaxy kinematics. The lack of detectable enhancement in K_asym is the case for each galaxy in the interacting systems. We derive K_asym in two additional cases following two individual galaxies in which the center of the kinematic maps coincide with the positions of supermassive black holes (blue and green solid lines in the bottom panels of Figures 3 and 4). The resulting median K_asym curves show similar trends with the kinematic maps centered at the gas density peak.

From right after the second passage through the coalescence phases, K_asym show significant deviations from the isolated M3 simulations. Most of the snapshots during this strong interaction phase display highly disturbed structure in both velocity and velocity dispersion maps, in which the kinematic structures are dominated by the bulk motion of two nuclei and the merger-induced gas flows. The oscillations of K_asym between second passage and coalescence reflect the projected distance between two nuclei; stronger disturbances are measured when two nuclei approach each other whereas such disturbances decrease as the two nuclei recede from each other. After the two nuclei merge, a gaseous disk survives in the M3M2e simulations and its K_asym decreases to the level of isolated M3 simulations. However, no such structure is formed in the M3M3e simulations, and most of the gas has funneled to the galaxy center and been consumed by the starbursts within ∼100–200 Myr. The K_asym of the M3M3e simulations remain slightly enhanced after the coalescence phase for ∼100 Myr until the star-forming gas is exhausted (SFR ≲ 0.5 M_⊙ yr⁻¹) and kinematics is no longer traced.

In Figure 5, we show the evolution of SFR and K_asym in the b6b5e and b6b6e simulations, which are binary mergers of SMG-type progenitors as described in Section 2. Prior to the coalescence phases, the b6b5e and b6b6e simulations have significantly higher SFR than the M3M2e and M3M3e simulations because the SMG-type progenitor disks are more gas rich and have higher gas densities. Despite these differences, the evolution of K_asym in b6b5e and b6b6e shows a similar trend as M3M2e and M3M3e. For instance, K_asym only begins to elevate significantly after the second passage. A key difference seen between the equal mass mergers M3M3e and b6b6e is that K_asym of b6b6e is elevated for ∼400 Myr after black hole coalescence. This prolonged disturbance in the dynamics of star-forming gas is visible due to a more gradual decline in SFR after coalescence (i.e., it only takes ∼0.25 Gyr for M3M3e to reach a SFR that is 0.01% of its peak SFR after black hole coalescence, whereas it takes ∼1 Gyr for b6b6e to reach 0.01% of its peak SFR).

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We derive the merger observable time (i.e., the time duration that merger signatures are detectable, hereafter MOT) using the median K_asym curves (e.g., the bottom panels of Figures 3 and 4). We define the criterion of a galaxy to be classified as a merger when its K_asym is significantly enhanced, and here we use a threshold of K_asym = 0.15 (a value higher than 95% of galaxies from the isolated M3 simulations). We note that this threshold is comparable to the one defined by Bellocchi et al. (2012) but considerably lower than the criteria used by Shapiro et al. (2008). Since our criteria are defined using simulations of the progenitor disk followed with the same kinematic mapping as the merger simulations, any enhancement in K_asym can be attributed as a result of interactions. The derived MOT with K_asym > 0.15 are 0.22 and 0.36 Gyr for the M3M2e and M3M3e simulations (Table 2). The uncertainties are derived based on the 1σ distributions of the median K_asym curves (the blue shaded area in Figures 3 and 4). Results based on different numerical resolutions typically differ within ±0.1 Gyr.

Since we attribute the main source of uncertainty as the variation due to the viewing angles, it is important to examine whether our choice of seven viewing angles are truly representative to the typical variation in K_asym. We derive K_asym of 70 viewing angles for two snapshots of M3M2e with one in the early interaction stage and the other close to the coalescence. We find that in both snapshots, the 1σ distribution of the data points from 7 viewing angles span a range similar to the distribution derived based on 70 viewing angles. Another concern is whether a time step of 100 Myr is sufficient to trace the variation during the early interaction phases. We have increased the sampling in timestep to 20 Myr before the second passage, and the MOT only increases 20 Myr for the M3M2e simulations and does not change for the M3M3e simulations.

We explore the dependence of MOTs on initial conditions of galaxy merger simulations. Specifically, we focus on whether the choices of gas fractions, orbital parameters, and initial disk orientations may have significant impacts (Table 2). The gas rich runs of M3M2e and M3M3e with doubling the initial gas fraction can lead to molecular gas fraction comparable to local LIRGs or ULIRGs type objects (e.g., Sanders et al. 1991), yet their MOTs remain similar to the original runs. The results from various orbital parameters span a wider range (0.2–0.48 Gyr), in which "orb2 (e = 0.95, ${r}_{p}=27.2)$" have larger MOTs due to its ∼ twice longer duration between second passage and coalescence. We also carry out simulations with four special initial disk orientations, and these variations lead to observable time of 0.20–0.36 Gyr. In all variations based on L14 simulations, merger signatures in K_asym are most visible during the strong interaction phase and only visible for ≲100 Myr after black holes coalescence regardless the availability of star-forming gas. The equal-mass merger simulation with SMG-type progenitors (b6b6e) has doubled MOT compared to M3M3e, in which merger signatures are visible for ∼0.4 Gyr during the post-coalescence phase until its SFR decreases to ∼0.5 M_⊙ yr⁻¹.

The merger/disk classification criteria and the time when the K_asym curves end may introduce additional systematics to MOTs. For example, if we apply a lower classification threshold, e.g., K_asym = 0.11 (a value higher than 68% of galaxies from the isolated M3 simulations), then the MOTs of the M3M2e and M3M3e simulations increase to 0.48 and 0.56 Gyr, respectively. On the other hand, our kinematic analysis stops when SFRs of merger remnants are ≲0.5 M_⊙ yr⁻¹, where no sufficient gas particles are available to make kinematic maps with a even lower SFR. In the case that the disk structure is completely destroyed during the interaction, K_asym remains elevated after black hole coalescence and MOTs may be sensitive to the choice of SFR limits to derive K_asym. However, MOTs of M3M3e and b6b6e do not change significantly when varying SFR limits to several M_⊙ yr⁻¹.

When treating the simulated galaxies at each snapshot and viewing angle as individual systems, we can quantify the observable merger fractions as a function of interaction stages. Figure 6 shows the fraction of simulated galaxies classified as mergers using the criterion ${K}_{\mathrm{asym}}\geqslant 0.15$ for simulations with five different initial disk orientations. Before coalescence, the derived merger fractions of all the M3M2 simulations agree within ∼20%–40% and the M3M3e simulations are typically higher compared to the M3M2e counterparts in all interaction stages. As expected based on the results shown in Section 5.1, the derived merger fractions past the coalescence phases show larger scatters as a result of different remnants in these simulations. These merger fractions are comparable to the results in Hung et al. (2015) when they use the classification scheme in Shapiro et al. (2008) and systematically lower by ∼50% when they use the classification scheme in Bellocchi et al. (2012).

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Spatial resolution is critical for accurately deriving galaxy kinematic properties. For example, Gonçalves et al. (2010) found that the merger fraction of Lyman Break Analogs at z ∼ 0.2 decreases by a factor of two (from ∼70% to ∼38%) when artificially redshifting the sample to ∼2.2, where the spatial resolution is 10 times worse in the redshifted datacubes compared to the original ones. The kinematic measurements in this paper are derived using kinematic maps with a spatial resolution of 0.5 kpc, which can be achieved in seeing-limited observations of local galaxies (e.g., Husemann et al. 2013) and adaptive optics-assisted observations out to z ∼ 0.4 (e.g., Gonçalves et al. 2010). However, typical IFS surveys of z ∼ 1–3 galaxies often have spatial resolution of ≳1 kpc (e.g., Law et al. 2009) except for lensed galaxies (e.g., Yuan et al. 2011; Livermore et al. 2015).

We examine how our kinematic measurements of the M3M2e simulations vary if the spatial resolutions of kinematic maps decreases from 0.5 to 1 kpc. We create the kinematic maps following the description in Section 3.2 but replace the 500 pc × 500 pc grids with the 1 kpc × 1 kpc grids. To ensure a consistent classification as discussed in Section 5.1, we also create low-resolution kinematic maps for the isolated M3 simulations and re-define the merger classification threshold for the low resolution maps as ${K}_{\mathrm{asym}}\geqslant 0.192$ (higher than 95% of the galaxies derived from the isolated M3 simulations). The MOT derived from the median K_asym curve decreases from 0.22 ± 0.04 Gyr with 0.5 kpc resolutions to only 0.14 ± 0.04 Gyr with 1 kpc resolutions. This result demonstrates that with worse spatial resolution, the contrast between disturbed kinematics and comparison disks becomes smaller and thus the merger observable time becomes shorter.

So far, our analyses have focused on galaxy kinematics traced by star-forming gas. However, the flows of stars and gas during galaxy interactions may diverge in the presence of large-scale shocks (e.g., Barnes & Hernquist 1991; Barrera-Ballesteros et al. 2015). It is thus intriguing to quantify how the kinematic merger indicator, K_asym, may depend on which observational tracers are used along the interaction sequence. We create the stellar kinematic maps following the procedures described in Section 3.2 using all of the stellar particles in the simulations. The center of the kinematic maps are chosen as the positions of the supermassive black holes. The velocity and velocity dispersion in each initial bins are determined as the median and standard deviation of all stellar particles weighted according to their masses.

Figure 7 shows the median K_asym curves of the M3M2e and M3M3e simulations derived based on all star particles until the end of our simulations (∼1.5 Gyr after coalescence). Although the star particles in general trace galaxy structure to larger radii than the star-forming gas throughout the interaction, the median K_asym curve traced by stars progresses similarly as the curve traced by star-forming gas in both M3M2e and M3M3e simulations. In both simulations, K_asym does not increase significantly until second passage but the enhancement of K_asym lasts through the entire strong interaction phase. After coalescence, the remnant of the M3M2e simulations exhibits a rotational pattern, and its K_asym reaches a lower, stable value than the K_asym during strong interaction phase. The remnant of the M3M3e simulations still show highly disturbed kinematic structure, and its K_asym remains highly elevated compared to isolated disks and during the interval before second passage.

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One important application of the large IFS surveys is to constrain the merger abundance of star-forming galaxies using kinematically identified close pairs (e.g., López-Sanjuan et al. 2013) or signatures of complex dynamics (e.g., Yang et al. 2008). Our work shows that when defining mergers as galaxies with significantly elevated K_asym, the MOTs are typically 0.2–0.4 Gyr except the equal mass merger with SMG-type progenitors, which has MOT that is approximately twice as long as those of z ∼ 0 mergers due to its more gradual decline in SFR after black hole coalescence. The MOTs can be shorter if the resolution of kinematic maps is worse than ∼0.5 kpc. Since no noise is added in the kinematic maps, the observable times derived here are likely represent the best case scenario at least with currently achievable resolutions. Even during the strong interaction phase (i.e., after second passage and before coalescence), only ∼40%–80% of galaxy mergers show significant enhancement in K_asym (Figure 6). The short merger observable times and the incompleteness of merger fractions reinforce the need of careful corrections when deriving galaxy merger rates and merger fractions using kinematic diagnostics.

The merger observable times based on K_asym are comparable to the morphologically identified merger observable times using Gini coefficient, A, and M₂₀ (Lotz et al. 2008, 2010b), in which both morphology and kinematics-based identifications are most sensitive to galaxy mergers during the strong interaction phases. An advantage of kinematic diagnostics is that the complex kinematics are visible for up to several hundred Myr after black hole coalescence (e.g., M3M3e, M3M2h, b6b6e). Combining morphological and kinematic information can thus provide a more accurate assessment of galaxies' dynamical status. For instance, when defining galaxies as mergers with either elevated A or K_asym, the MOTs of M3M2e and M3M3e simulations increase from 0.22 and 0.36 Gyr to 0.28 and 0.38 Gyr, respectively.

A key result from recent studies of galaxy kinematics is that the velocity dispersion of disk galaxies are systematically higher at higher z (e.g., Law et al. 2009; Epinat et al. 2012; Kassin et al. 2012, although local LIRG-type isolated disks typically have higher velocity dispersion as well; Bellocchi et al. 2013). The increased velocity dispersions are often attributed to the enhanced gas fractions in the high-z disk galaxies, which can lead to highly unstable and turbulent dynamics (e.g., Genzel et al. 2011). However, given the short merger observable times and the <100% merger recovery rates (Figure 6) based on the disturbance in kinematics, some of the disk galaxies identified by IFS surveys may be misidentified or a result of mergers. It is therefore important to quantify the evolution of velocity dispersions during galaxy interactions.

We define a sample of "disk galaxies" from the M3M2e simulations (original and doubled gas fractions) as those galaxies having K_asym consistent with the K_asym of 95% of the isolated M3 simulations. The M3M2e simulations are chosen because the disk structure survives after the coalescence. We measure the intrinsic velocity dispersion¹¹ (${\sigma }_{0}$) of this disk sample, in which we define ${\sigma }_{0}$ as the velocity dispersion at the positions with the largest velocities along the axis of the steepest velocity gradient. Figure 8 shows σ₀ for the disk sample as a function of interaction stage. The star-forming disks surviving after coalescence have a median σ₀ ∼4 times higher than the progenitor disks before the first passage. Even during the strong interaction phases when the dynamics of star-forming gas is dominated by the bulk motion of two nuclei but not coherent rotation, the measured σ₀ can be significantly higher than during earlier interaction stages. This implies that if the disk sample identified by the IFS surveys contains misidentified mergers or merger remnants, this population may also lead to high σ₀.

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Unlike optical imaging surveys, kinematic studies based on IFS observations often require pre-selection of the observed samples (e.g., optical and near-infrared colors) and this may introduce biases when converting the observed merger fractions to the overall galaxy merger rates. To obtain merger recovery rates for arbitrary sample selections, it is important to expand the kinematic analysis conducted in this work to large binary merger simulation library or cosmological simulations that provide a means to test various sample selections that mimic those used in the IFS surveys. However, the paucity of strong merger-induced starbursts in state-of-the-art large-volume cosmological simulations (Sparre et al. 2015) suggests that such simulations may not yet sufficiently resolve the nuclear regions of galaxy mergers. High resolution zoom-in cosmological simulations (e.g., Hopkins et al. 2014) can partially overcome this drawback, but they are computationally expensive, making it challenging to assemble a large sample of interacting galaxy simulations with this technique. Consequently, suites of idealized merger simulations will likely remain the best tool for studies such as the present one for some time.

Although we attempt to address the applicability of our results to z ≳ 2 IFS studies by using the progenitors of gas-rich disks, and the SMG-type progenitors, a possible caveat is that the gas properties assumed in our hydrodynamic simulations may not be comparable to those of high-z star-forming galaxies. For instance, Bournaud et al. (2011) show that interactions between clumpy disks can lead to more chaotic kinematics compared to the progenitors with stabilized ISM. However, it is unclear whether the drastic differences shown by the entire gas content (Figures 3 and 4 in Bournaud et al. 2011) are visible with only dense, star-forming gas. We perform a test run of M3M2e and M3M3e simulations with extreme initial gas fraction (0.8) and soft effective equation of state (${q}_{{\rm{EOS}}}=0.05$), in which these parameters can lead to highly unstable disk within several hundreds Myr after the start of the simulations and large star-forming clumps similar to some z ∼ 1–3 star-forming galaxies (Springel et al. 2005). Yet without a continuous replenishment of gas in these simulations, the gas fractions decrease to only 0.2–0.3 during the strong interaction phase and thus galaxy kinematics at this stage is consistent with other simulation runs with lower initial gas fractions.

Finally, we use gas particles with SFR > 0 (i.e., n ≳ 0.1 cm⁻³) as a proxy of star-forming gas throughout this analysis, yet such simple approximation does not consider possible impacts from dust attenuations or optical depth. Future implementations of radiative transfer codes such as sunrise(Jonsson et al. 2010) to kinematic analysis will allow us to explore the effects of dust extinctions. The mock IFS datacubes will also allow us to intuitively include observational effects such as skylines in the near-infrared observations.