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We measure and compare the pattern speeds of vertical breathing, vertical bending, and spiral density waves in two isolated N-body+SPH simulations, using windowed Fourier transforms over 1 Gyr time intervals. We show that the pattern speeds of the breathing waves match those of the spirals but are different from those of the bending waves. We also observe matching pattern speeds between the bar and breathing waves. Our results not only strengthen the case that, throughout the disc, breathing motions are driven by spirals but indeed that the breathing motions are part and parcel of the spirals., Comment: 5 pages, 4 figures, published in MNRAS Letters

The short-lived buckling instability is responsible for the formation of at least some box/peanut (B/P) shaped bulges, which are observed in most massive, $z=0$, barred galaxies. Nevertheless, it has also been suggested that B/P bulges form via the slow trapping of stars onto vertically extended resonant orbits. The key difference between these two scenarios is that when the bar buckles, symmetry about the mid-plane is broken for a period of time. We use a suite of simulations (with and without gas) to show that when the buckling is sufficiently strong, a residual mid-plane asymmetry persists for several Gyrs after the end of the buckling phase, and is visible in simulation images. On the other hand, images of B/P bulges formed through resonant trapping and/or weak buckling remain symmetric about the mid-plane. We develop two related diagnostics to identify and quantify mid-plane asymmetry in simulation images of galaxies that are within 3{\deg} of edge-on orientation, allowing us to test whether the presence of a B/P-shaped bulge can be explained by a past buckling event. We apply our diagnostics to two nearly edge-on galaxies with B/P bulges from the ${\it Spitzer}$ Survey of Stellar Structure in Galaxies, finding no mid-plane asymmetry, implying these galaxies formed their bulges either by resonant trapping or by buckling more than $\sim 5$ Gyr ago. We conclude that the formation of B/P bulges through strong buckling may be a rare event in the past $\sim 5$ Gyr., Comment: Accepted for pubblication in MNRAS

A detailed study of the morphology of lenticular galaxies is an important way to understand how this type of galaxy formed and evolves over time. Decomposing a galaxy into its components (disc, bulge, bar, ...) allows recovering the colour gradients present in each system, its star formation history, and its assembly history. We use GALFITM to perform a multi-wavelength structural decomposition of the closest lenticular galaxy, NGC 3115, resulting in the description of its stellar light into several main components: a bulge, a thin disc, a thick disc and also evidence of a bar. We report the finding of central bluer stellar populations in the bulge, as compared to the colour of the galaxy outskirts, indicating either the presence of an Active Galactic Nucleus (AGN) and/or recent star formation activity. From the spectral energy distribution results, we show that the galaxy has a low luminosity AGN component, but even excluding the effect of the nuclear activity, the bulge is still bluer than the outer-regions of the galaxy, revealing a recent episode of star formation. Based on all of the derived properties, we propose a scenario for the formation of NGC 3115 consisting of an initial gas-rich merger, followed by accretions and feedback that quench the galaxy, until a recent encounter with the companion KK084 that reignited the star formation in the bulge, provoked a core displacement in NGC 3115 and generated spiral-like features. This result is consistent with the two-phase formation scenario, proposed in previous studies of this galaxy., Comment: Accepted for publication in MNRAS: 22 pages, 15 figures, 7 tables, 1 appendix

The major-axis density profiles of bars are known to be either exponential or 'flat'. We develop an automated non-parametric algorithm to detect flat profiles and apply it to a suite of simulations (with and without gas). We demonstrate that flat profiles are a manifestation of a bar's secular growth, producing a 'shoulder' region (an overdensity above an exponential) in its outskirts. Shoulders are not present when bars form, but develop as the bar grows. If the bar does not grow, shoulders do not form. Shoulders are often accompanied by box/peanut bulges, but develop separately from them and are independent tracers of a bar's growth. They can be observed at a wide range of viewing orientations with only their slope varying significantly with inclination. We present evidence that shoulders are produced by looped x1 orbits. Since the growth rate of the bar moderately correlates with the growth rate of the shoulder strength, these orbits are probably recently trapped. Shoulders therefore are evidence of bar growth. The properties of the shoulders do not, however, establish the age of a bar, because secondary buckling or strong spirals may destroy shoulders, and also because shoulders do not form if the bar does not grow much. In particular, our results show that an exponential profile is not necessarily an indication of a young bar., Comment: 20 pages, 23 figures, 2 tables. Published in MNRAS

The IllustrisTNG simulations reproduce the observed scaling relation between stellar specific angular momentum (sAM) $j_{\rm s}$ and mass $M_{\rm s}$ of central galaxies. We show that the local $j_{\rm s}$-$M_{\rm s}$ relation ${\rm log}\ j_{\rm s} = 0.55 \ {\rm log}\ M_{\rm s} + 2.77$ develops at $z\lesssim 1$ in disk-dominated galaxies. We provide a simple model that describes well such a connection between halos and galaxies. The index 0.55 of the $j_{\rm s}$-$M_{\rm s}$ relation comes from the product of the indices of the $j_{\rm tot}\propto M_{\rm tot}^{0.81}$, $M_{\rm tot}\propto M_{\rm s}^{0.67}$, and $j_{\rm s}\propto j_{\rm tot}$ relations, where $j_{\rm tot}$ and $M_{\rm tot}$ are overall sAM and mass of a halo. A non-negligible deviation from the tidal torque theory, which predicts $j_{\rm tot}\propto M_{\rm tot}^{2/3}$, should be included. This model further suggests that the stellar-to-halo mass ratio of disk galaxies increases monotonically following a nearly power-law function that is consistent with the latest dynamical measurements. Biased collapse, in which galaxies form from the inner and lower sAM portion of their parent halos, has a minor effect at low redshifts. The retention factor of angular momentum reaches $\sim 1$ in disk galaxies with strong rotations, and it correlates inversely with the mass fraction of the spheroidal component, which partially explains the morphological dependence of the $j_{\rm s}$-$M_{\rm s}$ relation., 10 pages, 5 figures, accpeted for publication on ApJL

The Milky Way (MW) stellar halo contains relics of ancient mergers that tell the story of our galaxy's formation. Some of them are identified due to their similarity in energy, actions, and chemistry, referred to as the "chemodynamical space," and are often attributed to distinct merger events. It is also known that our galaxy went through a significant merger event that shaped the local stellar halo during its first billion years. Previous studies using N-body only and cosmological hydrodynamical simulations have shown that such a single massive merger can produce several "signatures" in the chemodynamical space, which can potentially be misinterpreted as distinct merger events. Motivated by these, in this work we use a subset of the GASTRO library, which consists of several smoothed particle hydrodynamics+N-body models of a single accretion event in a MW-like galaxy. Here, we study models with orbital properties similar to the main merger event of our galaxy and explore the implications to known stellar halo substructures. We find that (i) supernova feedback efficiency influences the satellite's structure and orbital evolution, resulting in distinct chemodynamical features for models with the same initial conditions; (ii) very retrograde high-energy stars are the most metal-poor of the accreted dwarf galaxy and could be misinterpreted as a distinct merger; (iii) the most bound stars are more metal-rich in our models, the opposite of what is observed in the MW, suggesting a secondary massive merger; and, finally, (iv) our models can reconcile other known apparently distinct substructures to a unique progenitor., J.A. and C.L. acknowledge funding from the European Research Council (ERC) under the European Unionʼs Horizon 2020 research and innovation program (grant agreement No. 852839). V.P.D. and L.B.S. were supported by STFC Consolidated grant #ST/ R000786/1. L.B.S. acknowledges NASA-ATP grant No. 80NSSC20K0509 and Science Foundation AAG grant No. AST-2009122.

It is now clear that the stars in the Solar neighbourhood display large-scale coherent vertical breathing motions. At the same time, Milky Way-like galaxies experience tidal interactions with satellites/companions during their evolution. While these tidal interactions can excite vertical oscillations, it is still not clear whether vertical breathing motions are excited \textit{directly} by the tidal encounters or are driven by the tidally-induced spirals. We test whether excitation of breathing motions are directly linked to tidal interactions by constructing a set of $N$-body models (with mass ratio 5:1) of unbound, single fly-by interactions with varying orbital configurations. We first reproduce the well-known result that such fly-by interactions can excite strong transient spirals (lasting for $\sim 2.9-4.2$ Gyr) in the outer disc of the host galaxy. The generation and strength of the spirals are shown to vary with the orbital parameters (the angle of interaction, and the orbital spin vector). Furthermore, we demonstrate that our fly-by models exhibit coherent breathing motions whose amplitude increases with height. The amplitudes of breathing motions show characteristic modulation along the azimuthal direction, with compressing breathing motions coinciding with the peaks of the spirals and expanding breathing motions falling in the inter-arm regions -- a signature of a spiral-driven breathing motion. These breathing motions in our models end when the strong tidally-induced spiral arms fade away. Thus, it is the tidally-induced spirals which drive the large-scale breathing motions in our fly-by models, and the dynamical role of the tidal interaction in this context is indirect., Comment: 13 pages, 13 figures, accepted for publication in MNRAS Journal

We use an $N$-body+smoothed particle hydrodynamics simulation of an isolated barred galaxy to study the age dependence of bulge longitudinal proper motion ($��_l$) rotation curves. We show that close to the minor axis ($|l| \sim 0^\circ$) the relatively young stars rotate more rapidly than the old stars, as found by Hubble Space Telescope in the Milky Way's (MW's) bulge. This behaviour would be expected also if the MW were unbarred. At larger $|l|$ a different behaviour emerges. Because younger stars trace a strong bar, their galactocentric radial motions dominate their $��_l$ at $|l| \sim 6^\circ$, leading to a reversal in the sign of $\left< ��_l \right>$. This results in a rotation curve with forbidden velocities (negative $\left< ��_l \right>$ at positive longitudes, and positive $\left< ��_l \right>$ at negative longitudes). The old stars, instead, trace a much weaker bar and thus their kinematics are more axisymmetric, resulting in no forbidden velocities. We develop metrics of the difference in the $\left< ��_l \right>$ rotation curves of young and old stars, and forbidden velocities. We use these to predict the locations where rotation curve reversals can be observed by HST and the Vera Rubin Telescope. Such measurements would represent support for the amplitude of the bar being a continuous function of age, as predicted by kinematic fractionation, in which the bar strength variations are produced purely by differences in the random motions of stellar populations at bar formation., 20 pages, 18 figures, 2 tables, published in MNRAS

The characteristics of the stellar populations in the Galactic Bulge inform and constrain the Milky Way's formation and evolution. The metal-poor population is particularly important in light of cosmological simulations, which predict that some of the oldest stars in the Galaxy now reside in its center. The metal-poor bulge appears to consist of multiple stellar populations that require dynamical analyses to disentangle. In this work, we undertake a detailed chemodynamical study of the metal-poor stars in the inner Galaxy. Using R$\sim$ 20,000 VLT/GIRAFFE spectra of 319 metal-poor (-2.55 dex$\leq$[Fe/H]$\leq$0.83 dex, with $\overline{\rm{[Fe/H]}}$=-0.84 dex) stars, we perform stellar parameter analysis and report 12 elemental abundances (C, Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Mn, Zn, Ba, and Ce) with precisions of $\approx$0.10 dex. Based on kinematic and spatial properties, we categorise the stars into four groups, associated with the following Galactic structures: the inner bulge, the outer bulge, the halo, and the disk. We find evidence that the inner and outer bulge population is more chemically complex (i.e., higher chemical dimensionality and less correlated abundances) than the halo population. This result suggests that the older bulge population was enriched by a larger diversity of nucleosynthetic events. We also find one inner bulge star with a [Ca/Mg] ratio consistent with theoretical pair-instability supernova yields and two stars that have chemistry consistent with globular cluster stars., 26 pages, 15 figures, accepted to MNRAS

The presence of stars on retrograde orbits in disc galaxies is usually attributed to accretion events, both via direct accretion, and through the heating of the disc stars. Recent studies have shown that retrograde orbits can also be produced via scattering by dense clumps, which are often present in the early stages of a galaxy’s evolution. However, so far it has been unclear whether other internally driven mechanisms, such as bars, are also capable of driving retrograde motion. Therefore, in this paper, we investigate the efficiencies with which bars and clumps produce retrograde orbits in disc galaxies. We do this by comparing the retrograde fractions and the spatial distributions of the retrograde populations in four N-body+smooth particle hydrodynamics (SPH) simulations of isolated disc galaxies spanning a range of evolutionary behaviours. We find that both bars and clumps are capable of generating significant retrograde populations of order ${\sim}10{{\ \rm per\ cent}}$ of all stars. We also find that while clump-driven retrograde stars may be found at large galactocentric radii, bar-driven retrograde stars remain in the vicinity of the bar, even if the bar dissolves. Consequently, we find that retrograde stars in the Solar neighbourhood in the clumpy models are exclusively clump-driven, but this is a trace population, constituting $0.01\!-\!0.04{{\ \rm per\ cent}}$ of the total stellar population in this region. Finally, we find that neither bars (including dissolving ones) nor clumps in the models are able to produce rotationally supported counterrotating discs.

We study the physical properties of the ionized gas in local disks using the sample of 38 nearby $\sim10^{8.5-11.2}$M$_\odot$ Star-Forming Main Sequence (SFMS) galaxies observed so far as part of the MUSE Atlas of Disks (MAD). Specifically, we use all strong emission lines in the MUSE wavelength range 4650-9300 \AA\ to investigate the resolved ionized gas properties on $\sim$100 pc scales. This spatial resolution enables us to disentangle HII regions from the Diffuse Ionized Gas (DIG) in the computation of gas metallicities and Star Formation Rates (SFRs) of star forming regions. The gas metallicities generally decrease with radius. The metallicity of the HII regions is on average $\sim$0.1 dex higher than that of the DIG, but the metallicity radial gradient in both components is similar. The mean metallicities within the inner galaxy cores correlate with the total stellar mass of the galaxies. On our, Comment: 21 pages + appendices. Accepted for publication in MNRAS

Vertically thickened bars, observed in the form of boxy/peanut (B/P) bulges, are found in the majority of massive barred disc galaxies in the local Universe, including our own. B/P bulges indicate that their host bars have suffered violent bending instabilities driven by anisotropic velocity distributions. We investigate for the first time how the frequency of B/P bulges in barred galaxies evolves from $z = 1$ to $z\approx 0$, using a large sample of non-edge-on galaxies with masses $M_{\star} > 10^{10}\:M_{\odot}$, selected from the HST COSMOS survey. We find the observed fraction increases from $0^{+3.6}_{-0.0}\%$ at $z = 1$ to $37.8^{+5.4}_{-5.1}\%$ at $z = 0.2$. We account for problems identifying B/P bulges in galaxies with low inclinations and unfavourable bar orientations, and due to redshift-dependent observational biases with the help of a sample from the Sloan Digital Sky Survey, matched in resolution, rest-frame band, signal-to-noise ratio and stellar mass and analysed in the same fashion. From this, we estimate that the true fraction of barred galaxies with B/P bulges increases from $\sim 10\%$ at $z \approx 1$ to $\sim 70\%$ at $z = 0$. In agreement with previous results for nearby galaxies, we find a strong dependence of the presence of a B/P bulge on galaxy stellar mass. This trend is observed in both local and high-redshift galaxies, indicating that it is an important indicator of vertical instabilities across a large fraction of the age of the Universe. We propose that galaxy formation processes regulate the thickness of galaxy discs, which in turn affect which galaxies experience violent bending instabilities of the bar., Published in MNRAS (20 pages, 17 figures), November 2019

To break the degeneracy among galactic stellar components, we extract kinematic structures using the framework described in Du et al. (2019, 2020). For example, the concept of stellar halos is generalized to weakly-rotating structures that are composed of loosely bound stars, which can hence be associated to both disk and elliptical type morphologies. By applying this method to central galaxies with stellar mass $10^{10-11.5}\ M_\odot$ from the TNG50 simulation, we identify three broadly-defined types of galaxies: ones dominated by disk, by bulge, or by stellar halo structures. We then use the simulation to infer the underlying connection between the growth of structures and physical processes over cosmic time. Tracing galaxies back in time, we recognize three fundamental regimes: an early phase of evolution ($z\gtrsim2$), and internal and external (mainly mergers) processes that act at later times. We find that disk- and bulge-dominated galaxies are not significantly affected by mergers since $z\sim2$; the difference in their present-day structures originates from two distinct evolutionary pathways, extended vs. compact, that are likely determined by their parent dark matter halos; i.e., nature. On the other hand, slow rotator elliptical galaxies are typically halo-dominated, forming by external processes (e.g. mergers) in the later phase, i.e., nurture. This picture challenges the general idea that elliptical galaxies are the same objects as classical bulges. In observations, both bulge- and halo-dominated galaxies are likely to be classified as early-type galaxies with compact morphology and quiescent star formation. However, here we find them to have very different evolutionary histories., 31 pages, 28 figures. Accepted for publication in ApJ

In recent years star formation has been discovered in the Milky Way's warp. These stars formed in the warp (warp stars) must eventually settle into the plane of the disc. We use an $N$-body$+$smooth particle hydrodynamics model of a warped galaxy to study how warp stars settle into the disc. By following warp stars in angular momentum space, we show that they first tilt to partially align with the main disc in a time scale of $\sim1$ Gyr. Then, once differential precession halts this process, they phase mix into an axisymmetric distribution on a time scale of $\sim 6$ Gyr. The warp stars end up contaminating the geometric thick disc. Because the warp in our fiducial simulation is growing, the {\it warp stars} settle to a distribution with a negative vertical age gradient as younger stars settle further from the mid-plane. While vertically extended, warp star orbits are still nearly circular and they are therefore subject to radial migration, with a net movement inwards. As a result warp stars can be found throughout the disc. The density distribution of a given population of warp stars evolves from a torus to an increasingly centrally filled-in density distribution. Therefore we argue that, in the Milky Way, warp stars should be found in the Solar Neighbourhood. Moreover, settled warp stars may constitute part of the young flaring population seen in the Milky Way's outskirts., Comment: 21 pages, 25 figures; Published on MNRAS

To understand the formation and evolution of the Milky Way disk, we must connect its current properties to its past. We explore hydrodynamical cosmological simulations to investigate how the chemical abundances of stars might be linked to their origins. Using hierarchical clustering of abundance measurements in two Milky Way-like simulations with distributed and steady star formation histories, we find that abundance clusters of stars comprise different groups in birth place ($R_\text{birth}$) and time (age). Simulating observational abundance errors (0.05 dex), we find that to trace discrete groups of ($R_\text{birth}$, age) requires a large vector of abundances. Using 15-element abundances (Fe, O, Mg, S, Si, C, P, Mn, Ne, Al, N, V, Ba, Cr, Co), up to $\approx$ 10 clusters can be defined with $\approx$ 25% overlap in ($R_\text{birth}$, age). We build a simple model to show that it is possible to infer a star's age and $R_\text{birth}$ from abundances with precisions of $\pm$0.06 Gyr and $\pm$1.17 kpc respectively. We find that abundance clustering is ineffective for a third simulation, where low-$\alpha$ stars form distributed in the disc and early high-$\alpha$ stars form more rapidly in clumps that sink towards the galactic center as their constituent stars evolve to enrich the interstellar medium. However, this formation path leads to large age-dispersions across the [$\alpha$/Fe]-[Fe/H] plane, which is inconsistent with the Milky Way's observed properties. We conclude that abundance clustering is a promising approach toward charting the history of our Galaxy., Comment: Submitted to ApJ

We present detailed morphological, photometric, and stellar-kinematic analyses of the central regions of two massive, early-type barred galaxies with nearly identical large-scale morphologies. Both have large, strong bars with prominent inner photometric excesses that we associate with boxy/peanut-shaped (B/P) bulges; the latter constitute ~ 30% of the galaxy light. Inside its B/P bulge, NGC 4608 has a compact, almost circular structure (half-light radius R_e approx. 310 pc, S��rsic n = 2.2) we identify as a classical bulge, amounting to 12.1% of the total light, along with a nuclear star cluster (R_e ~ 4 pc). NGC 4643, in contrast, has a nuclear disc with an unusual broken-exponential surface-brightness profile (13.2% of the light), and a very small spheroidal component (R_e approx. 35 pc, n = 1.6; 0.5% of the light). IFU stellar kinematics support this picture, with NGC 4608's classical bulge slowly rotating and dominated by high velocity dispersion, while NGC 4643's nuclear disc shows a drop to lower dispersion, rapid rotation, V-h3 anticorrelation, and elevated h4. Both galaxies show at least some evidence for V-h3 correlation in the bar (outside the respective classical bulge and nuclear disc), in agreement with model predictions. Standard 2-component (bulge/disc) decompositions yield B/T ~ 0.5-0.7 (and bulge n > 2) for both galaxies. This overestimates the true "spheroid" components by factors of four (NGC 4608) and over 100 (NGC 4643), illustrating the perils of naive bulge-disc decompositions applied to massive barred galaxies., Revised with final proof corrections; pdflatex, 29 pages, 22 figures; accepted by MNRAS. Data, code, and Jupyter notebooks available at https://github.com/perwin/n4608-n4643

In recent years integral-field spectroscopic surveys have revealed that the presence of kinematically decoupled stellar components is not a rare phenomenon in nearby galaxies. However, complete statistics are still lacking because they depend on the detection limit of these objects. We investigate the kinematic signatures of two large-scale counter-rotating stellar disks in mock integral-field spectroscopic data to address their detection limits as a function of the galaxy properties and instrumental setup. We built a set of mock data of two large-scale counter-rotating stellar disks as if they were observed with the Multi-Unit Spectroscopic Explorer (MUSE). We accounted for different photometric, kinematic, and stellar population properties of the two counter-rotating components as a function of galaxy inclination. We extracted the stellar kinematics in the wavelength region of the calcium triplet absorption lines by adopting a Gauss-Hermite (GH) parameterization of the line-of-sight velocity distribution (LOSVD). We confirm that the strongest signature of the presence of two counter-rotating stellar disks is the symmetric double peak in the velocity dispersion map, already known as the $2\sigma$ feature. The size, shape, and slope of the 2$\sigma$ peak strongly depend on the velocity separation and relative light contribution of the two counter-rotating stellar disks. When the $2\sigma$ peak is difficult to detect due to the low signal-to-noise ratio of the data, the large-scale structure in the $h_3$ map can be used as a diagnostic for strong and weak counter-rotation. The counter-rotating kinematic signatures become fainter at lower viewing angles as an effect of the smaller projected velocity separation between the two counter-rotating components. We confirm that the observed frequency of $2\sigma$ galaxies represents only a lower limit of the stellar counter-rotation phenomenon., Comment: Accepted for publication in Astronomy & Astrophysics. 17 pages, 11 figures, 2 tables

Warps are common features in both stellar and gaseous disks of nearby spiral galaxies with the latter usually easier to detect. Several theories have been proposed in the literature to explain their formation and prevalence, including tidal interactions with external galaxies. Observational correlations also suggest the importance of tides for warp formation. Here, we use the TNG100 run from the magnetohydrodynamical cosmological simulation suite IllustrisTNG to investigate the connection between interactions and the formation of gas warps. We find that in the sample of well-resolved gas-rich spiral galaxies ($10^{10}\lesssim\mathrm{M_{*}/M_{\odot}}\lesssim10^{11}$ at $z=0$) from the simulation TNG100-1, about $16\%$ possess the characteristic S-shaped warp. Around one third of these objects have their vertical morphology induced by interactions with other galaxies. Half of these interactions end with the perturber absorbed by the host. Warps formed in interactions are more asymmetrical than the remaining sample, however after the interaction the asymmetry decreases with time. We find that warps induced by interactions survive on average for $, 13 pages, 11 figures, submitted to MNRAS

Since thin disc stars are younger than thick disc stars on average, the thin disc is predicted by some models to start forming after the thick disc had formed, around 10 Gyr ago. Accordingly, no significant old thin disc population should exist. Using 6-D coordinates from Gaia-DR2 and age estimates from Sanders & Das (2018), we select $\sim 24000$ old stars (${��> 10}$ Gyr, with uncertainties $\lesssim 15\%$) within 2 kpc from the Sun (full sample). A cross-match with APOGEE-DR16 ($\sim 1000$ stars) reveals comparable fractions of old chemically defined thin/thick disc stars. We show that the full sample pericenter radius ($r_\mathrm{per}$) distribution has three peaks, one associated with the stellar halo and the other two having contributions from the thin/thick discs. Using a high-resolution $N$-body+Smooth Particle Hydrodynamics simulation, we demonstrate that one peak, at $r_\mathrm{per}\approx 7.1$ kpc, is produced by stars from both discs which were born in the inner Galaxy and migrated to the Solar Neighbourhood. In the Solar Neighbourhood, $\sim 1/2$ ($\sim 1/3$) of the old thin (thick) disc stars are classified as migrators. Our results suggest that thin/thick discs are affected differently by radial migration inasmuch as they have different eccentricity distributions, regardless of vertical scale heights. We interpret the existence of a significant old thin disc population as evidence for an early co-formation of thin/thick discs, arguing that clump instabilities in the early disc offer a compelling explanation for the observed trends., 12+2 pages, 10 figures, minor changes to match published version

A scenario for the formation of the bi-modality in the chemical space [$\alpha$/Fe] vs [Fe/H] of the Milky Way was recently proposed in which $\alpha$-enhanced stars are produced early and quickly in clumps. Besides accelerating the enrichment of the medium with $\alpha$-elements, these clumps scatter the old stars, converting in-plane to vertical motion, forming a geometric thick disc. In this paper, by means of a detailed analysis of the data from smooth particle hydrodynamical simulations, we investigate the geometric properties (in particular of the chemical thick disc) produced in this scenario. For mono-age populations we show that the surface radial density profiles of high-[$\alpha$/Fe] stars are well described by single exponentials, while that of low-[$\alpha$/Fe] stars require broken exponentials. This break is sharp for young populations and broadens for older ones. The position of the break does not depend significantly on age. The vertical density profiles of mono-age populations are characterized by single exponentials, which flare significantly for low-[$\alpha$/Fe] stars but only weakly (or not at all) for high-[$\alpha$/Fe] stars. For low-[$\alpha$/Fe] stars, the flaring level decreases with age, while for high-[$\alpha$/Fe] stars it weakly increases with age (although with large uncertainties). All these properties are in agreement with observational results recently reported for the Milky Way, making this a plausible scenario for the formation of the Galactic thick disc., Comment: 11 pages, 12 figures; Updated to published (MNRAS) version - inclusion of extra references and minor changes suggested by the referee

We recently developed an automated method, auto-GMM to decompose simulated galaxies. It extracts kinematic structures in an accurate, efficient, and unsupervised way. We use auto-GMM to study the stellar kinematic structures of disk galaxies from the TNG100 run of IllustrisTNG. We identify four to five structures that are commonly present among the diverse galaxy population. Structures having strong to moderate rotation are defined as cold and warm disks, respectively. Spheroidal structures dominated by random motions are classified as bulges or stellar halos, depending on how tightly bound they are. Disky bulges are structures that have moderate rotation but compact morphology. Across all disky galaxies and accounting for the stellar mass within 3 half-mass radii, the kinematic spheroidal structures, obtained by summing up stars of bulges and halos, contribute ~45% of the total stellar mass, while the disky structures constitute 55%. This study also provides important insights about the relationship between kinematically and morphologically derived galactic structures. Comparing the morphology of kinematic structures with that of traditional bulge+disk decomposition, we conclude: (1) the morphologically decomposed bulges are composite structures comprised of a slowly rotating bulge, an inner halo, and a disky bulge; (2) kinematically disky bulges, akin to what are commonly called pseudo bulges in observations, are compact disk-like components that have rotation similar to warm disks; (3) halos contribute almost 30% of the surface density of the outer part of morphological disks when viewed face-on; and (4) both cold and warm disks are often truncated in central regions., 20 pages, 14 figures. Accepted for publication in ApJ. The mass fraction catalogue and images of the kinematically derived galactic structures are publicly available (https://www.tng-project.org/data/docs/specifications/#sec5m)

We investigate the relations between the properties of bars and their host galaxies in a sample of 77 nearby barred galaxies, spanning a wide range of morphological types and luminosities, with 34 SB0-SBa and 43 SBab-SBc galaxies. The sample includes all the galaxies with reliable direct measurement of their bar pattern speed based on long-slit or integral-field stellar spectroscopy using the Tremaine-Weinberg method. We limited our analysis to the galaxies with a relatively small relative error on the bar pattern speed (smaller than 50 per cent) and not hosting an ultrafast bar. For each galaxy, we collected the radius, strength, pattern speed, corotation radius, and rotation rate for the bar and we also collected the Hubble type and absolute SDSS r-band magnitude. We also used literature bulge-to-total luminosity ratio for a subsample of 53 galaxies with an available photometric decomposition. We confirmed earlier observational findings that longer bars rotate with lower bar pattern speeds, shorter bars are weaker, and bars with a small bar rotation rate rotate with higher bar pattern speeds and have smaller corotation radii. In addition, we found that stronger bars rotate with lower bar pattern speeds, as predicted from the interchange of angular momentum during bar evolution, which in turn may depend on different galaxy properties. Moreover, we report that brighter galaxies host longer bars, which rotate with lower bar pattern speeds and have larger corotation radii. This result is in agreement with a scenario of downsizing in bar formation, if more massive galaxies formed earlier and had sufficient time to slow down, grow in length, and push corotation outwards., Comment: revised and accepted for pubblication in Astronomy & Astrophysics

The metal-poor stars in the bulge are important relics of the Milky Way's formation history, as simulations predict that they are some of the oldest stars in the Galaxy. In order to determine if they are truly ancient stars, we must understand the origins of this population. Currently, it is unclear if the metal-poor stars in the bulge ([Fe/H] < -1 dex) are merely halo interlopers, a unique accreted population, part of the boxy/peanut-shaped (B/P) bulge or a classical bulge population. In this work, we use spectra from the VLT/FLAMES spectrograph to obtain metallicity estimates using the Ca-II triplet (CaT) of 473 bulge stars (187 of which have [Fe/H] 50\% probability of being bound to the bulge, and half are halo interlopers. We also see that the occurrence rate of halo interlopers increases steadily with decreasing metallicity across the full range of our sample (-3 < [Fe/H] < 0.5). Our examination of the kinematics of the confined compared to the unbound stars indicates the metal-poor bulge ([Fe/H] < -1 dex) comprises at least two populations; those confined to the boxy/peanut bulge and halo stars passing through the inner galaxy. We conclude that an orbital analysis approach, as we have employed, is important to uncover and understand the composite nature of the metal-poor stars in the inner region., Comment: 18 pages, 12 figures, accepted to MNRAS, comments welcome

The Milky Way's progenitor experienced several merger events which left their imprints on the stellar halo, including the Gaia-Sausage/Enceladus. Recently, it has been proposed that this event perturbed the proto-disk and gave rise to a metal rich ([Fe/H] $>-1$) low angular momentum ($v_�� < 100$ km/s) stellar population. These stars have dynamical and chemical properties different from the accreted stellar halo, but are continuous with the canonical thick disk. In this letter, we use a hydrodynamical simulation of an isolated galaxy which develops clumps that produce a bimodal thin$+$thick disk chemistry to explore whether it forms such a population. We demonstrate clump scattering forms a metal-rich, low angular momentum population, without the need for a major merger. We show that, in the simulation, these stars have chemistry, kinematics and density distribution in good agreement with those in the Milky Way., Accepted for publication in ApJL

Galaxies host a wide array of internal stellar components, which need to be decomposed accurately in order to understand their formation and evolution. While significant progress has been made with recent integral-field spectroscopic surveys of nearby galaxies, much can be learned from analyzing the large sets of realistic galaxies now available through state-of-the-art hydrodynamical cosmological simulations. We present an unsupervised machine learning algorithm, named auto-GMM, based on Gaussian mixture models, to isolate intrinsic structures in simulated galaxies based on their kinematic phase space. For each galaxy, the number of Gaussian components allowed by the data is determined through a modified Bayesian information criterion. We test our method by applying it to prototype galaxies selected from the cosmological simulation IllustrisTNG. Our method can effectively decompose most galactic structures. The intrinsic structures of simulated galaxies can be inferred statistically by non-human supervised identification of galaxy structures. We successfully identify four kinds of intrinsic structures: cold disks, warm disks, bulges, and halos. Our method fails for barred galaxies because of the complex kinematics of particles moving on bar orbits., Accepted for publication in ApJ, 14 pages, 12 figures

The Milky Way bulge shows a box/peanut or X-shaped bulge (hereafter BP/X) when viewed in infrared or microwave bands. We examine orbits in an N-body model of a barred disk galaxy that is scaled to match the kinematics of the Milky Way (MW) bulge. We generate maps of projected stellar surface density, unsharp masked images, 3D excess-mass distributions (showing mass outside ellipsoids), line-of-sight number count distributions, and 2D line-of-sight kinematics for the simulation as well as co-added orbit families, in order to identify the orbits primarily responsible for the BP/X shape. We estimate that between 19-23\% of the mass of the bar is associated with the BP/X shape and that most bar orbits contribute to this shape which is clearly seen in projected surface density maps and 3D excess mass for non-resonant box orbits, "banana" orbits, "fish/pretzel" orbits and "brezel" orbits. {We find that nearly all bar orbit families contribute some mass to the 3D BP/X-shape. All co-added orbit families show a bifurcation in stellar number count distribution with heliocentric distance that resembles the bifurcation observed in red clump stars in the MW. However, only the box orbit family shows an increasing separation of peaks with increasing galactic latitude $|b|$, similar to that observed.} Our analysis shows that no single orbit family fully explains all the observed features associated with the MW's BP/X shaped bulge, but collectively the non-resonant boxes and various resonant boxlet orbits contribute at different distances from the center to produce this feature. We propose that since box orbits have three incommensurable orbital fundamental frequencies, their 3-dimensional shapes are highly flexible and, like Lissajous figures, this family of orbits is most easily able to adapt to evolution in the shape of the underlying potential., 16 pages, 10 figures, Accepted for Publication in MNRAS

From a sample of 84 local barred, moderately inclined disc galaxies, we determine the fraction which host boxy or peanut-shaped (B/P) bulges (the vertically thickened inner parts of bars). We find that the frequency of B/P bulges in barred galaxies is a very strong function of stellar mass: 79% of the bars in galaxies with log (M_{star}/M_{sun}) >~ 10.4 have B/P bulges, while only 12% of those in lower-mass galaxies do. (We find a similar dependence in data published by Yoshino & Yamauchi 2015 for edge-on galaxies.) There are also strong trends with other galaxy parameters -- e.g., Hubble type: 77% of S0-Sbc bars, but only 15% of Sc-Sd bars, have B/P bulges -- but these appear to be side effects of the correlations of these parameters with stellar mass. In particular, despite indications from models that a high gas content can suppress bar buckling, we find no evidence that the (atomic) gas mass ratio M_{atomic}/M_{star} affects the presence of B/P bulges, once the stellar-mass dependence is controlled for. The semi-major axes of B/P bulges range from one-quarter to three-quarters of the full bar size, with a mean of R_{box}/L_{bar} = 0.42 +/- 0.09 and R_{box}/a_{max} = 0.53 +/- 0.12 (where R_{box} is the size of the B/P bulge and a_{max} and L_{bar} are lower and upper limits on the size of the bar)., pdflatex, 17 pages (+ appendices), 15 figures. Revised submission to MNRAS, addressing minor final referee comments

We present surface photometry and stellar kinematics of NGC 4264, a lenticular galaxy in the region of the Virgo Cluster undergoing a tidal interaction with its neighbour, NGC 4261. We measured the bar radius and strength from SDSS imaging and the bar pattern speed from MUSE integral-field spectroscopy. We find that NGC 4264 hosts a strong and large bar, which is rotating fast. The accurate measurement of the bar rotation rate allows us to exclude that the formation of the bar was triggered by the ongoing interaction., 4 pages, 2 figures. Proceedings of IAUS 353, Eds. M. Valluri, and J. A. Sellwood

The direction of the spin vectors of disk galaxies change over time. We present the tilting rate of a sample of galaxies in the NIHAO suite of cosmological hydrodynamical simulations. Galaxies in our sample have been selected to be isolated and to have well determined spins. We compare the tilting rates to the predicted observing limit of Gaia, finding that our entire sample lies above the limit, in agreement with previous work. To test the role of dark matter and of gas we compare the weighted Pearson's correlation coefficients between the tilting rates and various properties. We find no correlation between the dark halo's tilting rate, shape, or misalignment with respect to the disc, and the tilting rate of the stellar disc. Therefore, we argue that, in the presence of gas, the dark halo plays a negligible role in the tilting of the stellar disc. On the other hand, we find a strong correlation between the tilting rate of the stellar disc and the misalignment of the cold gas warp. Adding the stellar mass fraction improves the correlation, while none of the dark matter's properties together with the cold gas misalignment improves the correlation to any significant extent. This implies that the gas cooling onto the disc is the principal driver of disc tilting., 12 pages, 13 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal

Compact ellipticals (cEs) are outliers from the scaling relations of early-type galaxies, particularly the mass-metallicity relation which is an important outcome of feedback. The formation of such low-mass, but metal-rich and compact, objects is a long-standing puzzle. Using a pair of high-resolution N-body+gas simulations, we investigate the evolution of a gas-rich low-mass galaxy on a highly radial orbit around a massive host galaxy. As the infalling low-mass galaxy passes through the host's corona at supersonic speeds, its diffuse gas outskirts are stripped by ram pressure, as expected. However, the compactness increases rapidly because of bursty star formation in the gas tidally driven to the centre. The metal-rich gas produced by supernovae and stellar winds is confined by the ram pressure from the surrounding environment, leading to subsequent generations of stars being more metal-rich. After the gas is depleted, tidal interactions enhance the metallicity further via the stripping of weakly bound, old, and metal-poor stars, while the size of the satellite is changed only modestly. The outcome is a metal-rich cE that is consistent with observations. These results argue that classical cEs are neither the stripped remnants of much more massive galaxies nor the merger remnants of normal dwarfs. We present observable predictions that can be used to test our model., 14 pages, 11 figures; accepted by ApJ. Minor change

The disc structure of the Milky Way is marked by a chemical dichotomy, with high-alpha and low-alpha abundance sequences, traditionally identified with the geometric thick and thin discs. This identification is aided by the old ages of the high-alpha stars, and lower average ages of the low-alpha ones. Recent large scale surveys such as APOGEE have provided a wealth of data on this chemical structure, including showing that an identification of chemical and geometric thick discs is not exact, but the origin of the chemical dichotomy has remained unclear. Here we demonstrate that a dichotomy arises naturally if the early gas-rich disc fragments, leading to some fraction of the star formation occurring in clumps of the type observed in high-redshift galaxies. These clumps have high star formation rate density. They, therefore, enrich rapidly, moving from the low-alpha to the high-alpha sequence, while more distributed star formation produces the low-alpha sequence. We demonstrate that this model produces a chemically-defined thick disc that has many of the properties of the Milky Way's thick disc. Because clump formation is common in high redshift galaxies, we predict that chemical bimodalities are common in massive galaxies., Comment: Accepted to MNRAS

We introduce the study of box/peanut (B/P) bulges in the action space of the initial axisymmetric system. We explore where populations with different actions end up once a bar forms and a B/P bulge develops. We find that the density bimodality due to the B/P bulge (the X-shape) is better traced by populations with low radial, JR,0, or vertical, Jz,0, actions, or high azimuthal action, J{\phi},0. Generally populations separated by JR,0 have a greater variation in bar strength and vertical heating than those separated by Jz,0. While the bar substantially weakens the initial vertical gradient of Jz,0, it also drives a strikingly monotonic vertical profile of JR,0. We then use these results to guide us in assigning metallicity to star particles in a pure N-body model. Because stellar metallicity in unbarred galaxies depends on age as well as radial and vertical positions, the initial actions are particularly well suited for assigning metallicities. We argue that assigning metallicities based on single actions, or on positions, results in metallicity distributions inconsistent with those observed in real galaxies. We therefore use all three actions to assign metallicity to an N-body model by comparing with the actions of a star-forming, unbarred simulation. The resulting metallicity distribution is pinched on the vertical axis, has a realistic vertical gradient and has a stronger X-shape in metal-rich populations, as found in real galaxies., Comment: Submitted to MNRAS. Comments welcome. The appendix of figures for the simulation suite will be available, until journal publication, at http://www.star.uclan.ac.uk/~vpd/appendix.pdf (Caution: 57Mb)

We present surface photometry and stellar kinematics of NGC 4264, a barred lenticular galaxy in the region of the Virgo Cluster undergoing a tidal interaction with one of its neighbours, NGC 4261. We measured the bar radius (a_bar=3.2 +/-0.5 kpc) and strength (S_bar=0.31+/-0.04) of NGC 4264 from Sloan Digital Sky Survey imaging and its bar pattern speed (Omega_bar=71+/-4 km/s/kpc) using the Tremaine-Weinberg method with stellar-absorption integral-field spectroscopy performed with the Multi Unit Spectroscopic Explorer at the Very Large Telescope. We derived the circular velocity (V_circ=189+/-10 km/s) by correcting the stellar streaming velocity for asymmetric drift and calculated the corotation radius (R_cor=2.8+/-0.2 kpc) from the bar pattern speed. Finally, we estimated the bar rotation rate (R_cor/a_bar=0.88+/-0.23). We find that NGC 4264 hosts a strong and large bar extending out to the corotation radius. This means that the bar is rotating as fast as it can like nearly all the other bars measured so far even when the systematic error due to the uncertainty on the disc position angle is taken into account. The accurate measurement of the bar rotation rate allows us to infer that the formation of the bar of NGC 4264 was due to self-generated internal processes and not triggered by the ongoing interaction., 13 pages, 5 figures, MNRAS accepted

We aim at investigating the formation process of weak bars by measuring their properties in a sample of 29 nearby SAB galaxies, spanning a wide range of morphological types and luminosities. The sample galaxies were selected to have an intermediate inclination, a bar at an intermediate angle between the disc minor and major axes, and an undisturbed morphology and kinematics to allow the direct measurement of the bar pattern speed. Combining our analysis with previous studies, we compared the properties of weak and strong bars. We measured the bar radius and strength from the r-band images available in SDSS and bar pattern speed and corotation radius from the stellar kinematics obtained by CALIFA. We derived the bar rotation rate as the ratio between the corotation and bar radii. Thirteen out of 29 galaxies, which were morphologically classified as SABs from a visual inspection, do not actually host a bar component or their central elongated component is not in rigid rotation. We successfully derived the bar pattern speed in 16 objects. Two of them host an ultrafast bar. Using the bar strength to differentiate weak and strong bars, we found that the SABs host shorter bars with smaller corotation radii than their strongly barred counterparts. Weak and strong bars have similar bar pattern speeds and rotation rates, which are all consistent with being fast. We did not observe any difference between the bulge prominence in SAB and SB galaxies, whereas nearly all the weak bars reside in the disc inner parts, contrary to strong bars. We ruled out that the bar weakening is only related to the bulge prominence and that the formation of weak bars is triggered by the tidal interaction with a companion. Our observational results suggest that weak bars may be evolved systems exchanging less angular momentum with other galactic components than strong bars., Comment: 13 pages, 10 figures, accepted for pubblication in A&A

Red clump stars are commonly used to map the reddening and morphology of the inner regions of the Milky Way. We use the new photometric catalogues of the VISTA Variables in the V\'ia L\'actea survey to achieve twice the spatial resolution of previous reddening maps for Galactic longitudes $-10^{\circ}, Comment: Accepted for publication in MNRAS Letters (6 pages, 4 Figures)

Almost two-thirds of disk galaxies in the local universe host bars, which serve as important drivers of secular evolutionary processes. While cosmological simulations are powerful tools to study the formation and evolution of galaxies, they have often struggled to generate reasonable bar populations. We measure the fraction, size, and strength of bars in 3866 disk galaxies from the TNG100 run of the advanced cosmological simulation IllustrisTNG. Consistent with observations, about 55% of disk galaxies with stellar mass $M_* \approx 10^{10.6}\, M_\odot$ are barred, and the relation between bar size and total stellar mass is similar to that found in near-infrared surveys. However, the formation of bars is suppressed in galaxies with $M_* < 10^{10.6}\, M_\odot$, which may result from the difficulty TNG100 has in resolving short bars with radius 10^{10.6}\, M_\odot$ have bars, ~10%-20% higher than observed. TNG100 overproduces relatively short bars (radius ~1.4-3 kpc) with respect to the mass-bar size relation observed in near-infrared surveys. Tracing the progenitors of z=0 massive galaxies we find that the bar fraction increases from 25% to 63% between z=1 and 0. Instead if we select all disk galaxies during z=0-1 with a constant mass cut of $M_* \geqslant 10^{10.6}\, M_\odot$ we find that the bar fraction is a nearly constant 60%., 16 pages, 11 figures. Submitted to ApJ

Short (inner) bars of sub-kiloparsec radius have been hypothesized to be an important mechanism for driving gas inflows to small scales, thus feeding central black holes. Recent numerical simulations have shown that the growth of central black holes in galaxies can destroy short bars, when the black hole reaches a mass of $\sim 0.1\%$ of the total stellar mass of the galaxy. We study $N$-body simulations of galaxies with single and double bars to track the long-term evolution of the central stellar mass distribution. We find that the destruction of the short bar contributes significantly to the growth of the bulge. The final bulge mass is roughly equal to the sum of the masses of the initial pseudo bulge and short bar. The initially boxy/peanut-shaped bulge of S\'ersic index $n\lesssim1$ is transformed into a more massive, compact structure that bears many similarities to a classical bulge, in terms of its morphology ($n \approx 2$), kinematics (dispersion-dominated, isotropic), and location on standard scaling relations (Kormendy relation, mass-size relation, and correlations between black hole mass and bulge stellar mass and velocity dispersion). Our proposed channel for forming classical bulges relies solely on the destruction of short bars without any reliance on mergers. We suggest that some of the less massive, less compact classical bulges were formed in this manner., Comment: 16 pages, 11 figures, accepted for publication in ApJ

We present the late-time evolution of m12m, a cosmological simulation of a Milky Way-like galaxy from the FIRE project. The simulation forms a bar after redshift z = 0.2. We show that the evolution of the model exhibits behaviours typical of kinematic fractionation, with a bar weaker in older populations, an X-shape traced by the younger, metal-rich populations and a prominent X-shape in the edge-on mean metallicity map. Because of the late formation of the bar in m12m, stars forming after 10 Gyr (z = 0.34) significantly contaminate the bulge, at a level higher than is observed at high latitudes in the Milky Way, implying that its bar cannot have formed as late as in m12m. We also study the model's vertex deviation of the velocity ellipsoid as a function of stellar metallicity and age in the equivalent of Baade's Window. The formation of the bar leads to a non-zero vertex deviation. We find that metal-rich stars have a large vertex deviation (~ 40 degrees), which becomes negligible for metal-poor stars, a trend also found in the Milky Way, despite not matching in detail. We demonstrate that the vertex deviation also varies with stellar age and is large for stars as old as 9 Gyr, while 13 Gyr old stars have negligible vertex deviation. When we exclude stars that have been accreted, the vertex deviation is not significantly changed, demonstrating that the observed variation of vertex deviation with metallicity is not necessarily due to an accreted population., Published in MNRAS, 485, 5073. This version includes a few additional figures and discussion requested by the referee. No fundamental changes in the results from the earlier version

We report results from an exploratory study implementing a new probe of Galactic evolution using archival Hubble Space Telescope imaging observations. Precise proper motions are combined with photometric relative metallicity and temperature indices, to produce the proper motion rotation curves of the Galactic bulge separately for metal-poor and metal-rich Main Sequence samples. This provides a "pencil-beam" complement to large-scale wide-field surveys, which to-date have focused on the more traditional bright Giant Branch tracers. We find strong evidence that the Galactic bulge rotation curves drawn from "Metal-rich" and "Metal-poor" samples are indeed discrepant. The "Metal-rich" sample shows greater rotation amplitude and a steeper gradient against line of sight distance, as possibly a stronger central concentration along the line of sight. This may represent a new detection of differing orbital anisotropy between metal-rich and metal-poor bulge objects. We also investigate selection effects that would be implied for the longitudinal proper motion cut often used to isolate a "pure-bulge" sample. Extensive investigation of synthetic stellar populations suggest that instrumental and observational artifacts are unlikely to account for the observed rotation curve differences. Thus, proper motion-based rotation curves can be used to probe chemo-dynamical correlations for Main Sequence tracer stars, which are orders of magnitude more numerous in the Galactic Bulge than the bright Giant Branch tracers. We discuss briefly the prospect of using this new tool to constrain detailed models of Galactic formation and evolution., 67 pages, 41 figures, 23 tables, ApJ accepted

The shape of line-of-sight velocity distributions (LOSVDs) carries important information about the internal dynamics of galaxies. The skewness of LOSVDs represents their asymmetric deviation from a Gaussian profile. Correlations between the skewness parameter (h 3) and the mean velocity ($\overline{V}$) of a Gauss–Hermite series reflect the underlying stellar orbital configurations of different morphological components. Using two self-consistent N-body simulations of disk galaxies with different bar strengths, we investigate ${h}_{3}-\overline{V}$ correlations at different inclination angles. Similar to previous studies, we find anticorrelations in the disk area, and positive correlations in the bar area when viewed edge-on. However, at intermediate inclinations, the outer parts of bars exhibit anticorrelations, while the core areas dominated by the boxy/peanut-shaped (B/PS) bulges still maintain weak positive correlations. When viewed edge-on, particles in the foreground/background disk (the wing region) in the bar area constitute the main velocity peak, whereas the particles in the bar contribute to the high-velocity tail, generating the ${h}_{3}-\overline{V}$ correlation. If we remove the wing particles, the LOSVDs of the particles in the outer part of the bar only exhibit a low-velocity tail, resulting in a negative ${h}_{3}-\overline{V}$ correlation, whereas the core areas in the central region still show weakly positive correlations. We discuss implications for IFU observations on bars, and show that the variation of the ${h}_{3}-\overline{V}$ correlation in the disk galaxy may be used as a kinematic indicator of the bar and the B/PS bulge.