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At least 37 records · Page 2

Final Targeting Strategy for the Sloan Digital Sky Survey IV Apache Point Observatory Galactic Evolution Experiment 2 North Survey

The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is a dual-hemisphere, near-infrared (NIR), spectroscopic survey with the goal of producing a chemodynamical mapping of the Milky Way. The targeting for APOGEE-2 is complex and has evolved with time. In this paper, we present the updates and additions to the initial targeting strategy for APOGEE-2N presented in Zasowski et al. (2017). These modifications come in two implementation modes: (i) “Ancillary Science Programs” competitively awarded to Sloan Digital Sky Survey IV PIs through proposal calls in 2015 and 2017 for the pursuit of new scientific avenues outside the main survey, and (ii) an effective 1.5 yr expansion of the survey, known as the Bright Time Extension (BTX), made possible through accrued efficiency gains over the first years of the APOGEE-2N project. For the 23 distinct ancillary programs, we provide descriptions of the scientific aims, target selection, and how to identify these targets within the APOGEE-2 sample. The BTX permitted changes to the main survey strategy, the inclusion of new programs in response to scientific discoveries or to exploit major new data sets not available at the outset of the survey design, and expansions of existing programs to enhance their scientific success and reach. After describing the motivations, implementation, and assessment of these programs, we also leave a summary of lessons learned from nearly a decade of APOGEE-1 and APOGEE-2 survey operations. Finally, a companion paper, F. Santana et al. (submitted; AAS29036), provides a complementary presentation of targeting modifications relevant to APOGEE-2 operations in the Southern Hemisphere.

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Final Targeting Strategy for the SDSS-IV APOGEE-2S Survey

APOGEE is a high-resolution (R ~ 22,000), near-infrared, multi-epoch, spectroscopic survey of the Milky Way. The second generation of the APOGEE project, APOGEE-2, includes an expansion of the survey to the Southern Hemisphere called APOGEE-2S. This expansion enabled APOGEE to perform a fully panoramic mapping of all of the main regions of the Milky Way; in particular, by operating in the H band, APOGEE is uniquely able to probe the dust-hidden inner regions of the Milky Way that are best accessed from the Southern Hemisphere. In this paper we present the targeting strategy of APOGEE-2S, with special attention to documenting modifications to the original, previously published plan. The motivation for these changes is explained as well as an assessment of their effectiveness in achieving their intended scientific objective. In anticipation of this being the last paper detailing APOGEE targeting, we present an accounting of all such information complete through the end of the APOGEE-2S project; this includes several main survey programs dedicated to exploration of major stellar populations and regions of the Milky Way, as well as a full list of programs contributing to the APOGEE database through allocations of observing time by the Chilean National Time Allocation Committee and the Carnegie Institution for Science. This work was presented along with a companion article, Beaton et al. (2021), presenting the final target selection strategy adopted for APOGEE-2 in the Northern Hemisphere.

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Rotation Curves of Galaxies and Their Dependence on Morphology and Stellar Mass

Here, we study how stellar rotation curves (RCs) of galaxies are correlated on average with morphology and stellar mass (M star ) using the final release of Sloan Digital Sky Survey IV MaNGA data. We use the visually assigned T-types for the morphology indicator, and adopt a functional form for the RC that can model non-flat RCs at large radii. We discover that within the radial coverage of the MaNGA data, the popularly known flat rotation curve at large radii applies only to the particular classes of galaxies, i.e., massive late types (T-type ≥ 1, M star ≳ 10 10.8 M⊙) and S0 types (T-type = –1 or 0, M star ≳ 10 10.0 M⊙). The RC of late-type galaxies at large radii rises more steeply as M star decreases, and its slope increases to about +9 km s –1 kpc –1 at M star ≈ 10 9.7 M⊙. By contrast, elliptical galaxies (T-type ≤ –2) have descending RCs at large radii. Their slope becomes more negative as M star decreases, and reaches as negative as –15 km s –1 kpc –1 at M star ≈ 10 10.2 M⊙. We also find that the inner slope of the RC is highest for elliptical galaxies with M star ≈ 10 10.5 M⊙, and decreases as T-type increases or M star changes away from 10 10.5 M⊙. The velocity at the turnover radius R t is higher for higher M star , and R t is larger for higher M star and later T-types. We show that the inner slope of the RC is coupled with the central surface stellar mass density, which implies that the gravitational potential of central regions of galaxies is dominated by baryonic matter. With the aid of simple models for matter distribution, we discuss what determines the shapes of RCs.

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Landau Modes are Eigenmodes of Stellar Systems in the Limit of Zero Collisions

Abstract We consider the spectrum of eigenmodes in a stellar system dominated by gravitational forces in the limit of zero collisions. We show analytically and numerically using the Lenard–Bernstein collision operator that the Landau modes, which are not true eigenmodes in a strictly collisionless system (except for the Jeans unstable mode), become part of the true eigenmode spectrum in the limit of zero collisions. Under these conditions, the continuous spectrum of true eigenmodes in a collisionless system, also known as the Case–van Kampen modes, is eliminated. Furthermore, because the background distribution function in a weakly collisional system can exhibit significant deviations from a Maxwellian distribution function over long times, we show that the spectrum of Landau modes can change drastically even in the presence of slight deviations from a Maxwellian, primarily through the appearance of weakly damped modes that may be otherwise heavily damped for a Maxwellian distribution. Our results provide important insights for developing statistical theories to describe thermal fluctuations in a stellar system, which are currently a subject of great interest for N -body simulations as well as observations of gravitational systems.

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Estimate of the Mass and Radial Profile of the Orphan–Chenab Stream's Dwarf-galaxy Progenitor Using MilkyWay@home

We fit the mass and radial profile of the Orphan–Chenab Stream's (OCS) dwarf-galaxy progenitor by using turnoff stars in the Sloan Digital Sky Survey and the Dark Energy Camera to constrain N-body simulations of the OCS progenitor falling into the Milky Way on the 1.5 PetaFLOPS MilkyWay@home distributed supercomputer. We infer the internal structure of the OCS's progenitor under the assumption that it was a spherically symmetric dwarf galaxy composed of a stellar system embedded in an extended dark matter halo. We optimize the evolution time, the baryonic and dark matter scale radii, and the baryonic and dark matter masses of the progenitor using a differential evolution algorithm. The likelihood score for each set of parameters is determined by comparing the simulated tidal stream to the angular distribution of OCS stars observed in the sky. We fit the total mass of the OCS's progenitor to (2.0 ± 0.3) × 10 7 M ⊙ with a mass-to-light ratio of γ = 73.5 ± 10.6 and (1.1 ± 0.2) × 10 6 M ⊙ within 300 pc of its center. Within the progenitor's half-light radius, we estimate a total mass of (4.0 ± 1.0) × 10 5 M ⊙ . We also fit the current sky position of the progenitor's remnant to be (α, δ) = ((166.0 ± 0.9)°, (–11.1 ± 2.5)°) and show that it is gravitationally unbound at the present time. The measured progenitor mass is on the low end of previous measurements and, if confirmed, lowers the mass range of ultrafaint dwarf galaxies. Our optimization assumes a fixed Milky Way potential, OCS orbit, and radial profile for the progenitor, ignoring the impact of the Large Magellanic Cloud.

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CLASSY III. The Properties of Starburst-driven Warm Ionized Outflows

We report the results of analyses of galactic outflows in a sample of 45 low-redshift starburst galaxies in the COS Legacy Archive Spectroscopic SurveY (CLASSY), augmented by five additional similar starbursts with Cosmic Origins Spectrograph (COS) data. The outflows are traced by blueshifted absorption lines of metals spanning a wide range of ionization potential. The high quality and broad spectral coverage of CLASSY data enable us to disentangle the absorption due to the static interstellar medium (ISM) from that due to outflows. We further use different line multiplets and doublets to determine the covering fraction, column density, and ionization state as a function of velocity for each outflow. We measure the outflow's mean velocity and velocity width, and find that both correlate in a highly significant way with the star formation rate, galaxy mass, and circular velocity over ranges of four orders of magnitude for the first two properties. We also estimate outflow rates of metals, mass, momentum, and kinetic energy. We find that, at most, only about 20% of silicon created and ejected by supernovae in the starburst is carried out in the warm phase we observe. The outflows' mass-loading factor increases steeply and inversely with both circular and outflow velocity (log–log slope ~–1.6), and reaches ~10 for dwarf galaxies. We find that the outflows typically carry about 10%–100% of the momentum injected by massive stars and about 1%–20% of the kinetic energy. We show that these results place interesting constraints on, and new insights into, models and simulations of galactic winds.

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Hubble Space Telescope Observations within the Sphere of Influence of the Powerful Supermassive Black Hole in PKS 0745-191

We present Space Telescope Imaging Spectrograph observations from the Hubble Space Telescope of the supermassive black hole (SMBH) at the center of PKS 0745-191, a brightest cluster galaxy (BCG) undergoing powerful radio-mode active galactic nucleus (AGN) feedback (P cav ~ 5 × 10 45 erg s -1 ). These high-resolution data offer the first spatially resolved map of gas dynamics within an SMBH's sphere of influence under such powerful feedback. Our results reveal the presence of highly chaotic, nondrotational ionized gas flows on subkiloparsec scales, in contrast to the more coherent flows observed on larger scales. While radio-mode feedback effectively thermalizes hot gas in galaxy clusters on kiloparsec scales, within the core, the hot gas flow may decouple, leading to a reduction in angular momentum and supplying ionized gas through cooling, which could enhance accretion onto the SMBH. This process could, in turn, lead to a self-regulating feedback loop. Compared to other BCGs with weaker radio-mode feedback, where rotation is more stable, intense feedback may lead to more chaotic flows, indicating a stronger coupling between jet activity and gas dynamics. Additionally, we observe a sharp increase in velocity dispersion near the nucleus, consistent with a very massive M BH ~ 1.5 × 10 10 M ⊙ SMBH. The density profile of the ionized gas is also notably flat, paralleling the profiles observed in X-ray gas around galaxies where the Bondi radius is resolved. These results provide valuable insights into the complex mechanisms driving galaxy evolution, highlighting the intricate relationship between SMBH fueling and AGN feedback within the host galaxy.

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Velocity Dispersion σ aper Aperture Corrections as a Function of Galaxy Properties from Integral-field Stellar Kinematics of 10,000 MaNGA Galaxies

Abstract The second moment of the stellar velocity within the effective radius, denoted by σ e 2 , is a crucial quantity in galaxy studies, as it provides insight into galaxy properties and their mass distributions. However, large spectroscopic surveys typically do not measure σ e directly, instead providing σ aper , the second moment of the stellar velocity within a fixed fiber aperture. In this paper, we derive an empirical aperture correction formula, given by σ aper / σ e = ( R aper / R e ) α , using spatially resolved stellar kinematics extracted from approximately 10,000 Sloan Digital Sky Survey–Mapping Nearby Galaxies at Apache Point Observatory integral field unit observations. Our analysis reveals a strong dependence of α on the r -band absolute magnitude M r , g – i color, and Sérsic index n Ser , where α values are lower for brighter, redder galaxies with higher Sérsic indices. Our results demonstrate that the aperture correction derived from previous literature on early-type galaxies cannot be applied to predict the aperture corrections for galaxies with intermediate Sérsic indices. We provide a lookup table of α values for different galaxy types, with parameters in the ranges of −18 > M r > −24, 0.4 < g – i < 1.6, and 0 < n Ser < 8. A Python script is provided to obtain the correction factors from the lookup table.

Astronomy & Astrophysics↗

Stellar kinematics of dwarf galaxies from multi-epoch spectroscopy: application to Triangulum II

ABSTRACT We present new MMT/Hectochelle spectroscopic measurements for 257 stars observed along the line of sight to the ultrafaint dwarf galaxy Triangulum II (Tri II). Combining results from previous Keck/DEIMOS spectroscopy, we obtain a sample that includes 16 likely members of Tri II, with up to 10 independent redshift measurements per star. To this multi-epoch kinematic data set, we apply methodology that we develop in order to infer binary orbital parameters from sparsely sampled radial velocity curves with as few as two epochs. For a previously identified (spatially unresolved) binary system in Tri II, we infer an orbital solution with period $296.0_{-3.3}^{+3.8} \rm ~ d$, semimajor axis $1.12^{+0.41}_{-0.24}\rm ~au$, and systemic velocity $-380.0 \pm 1.7 \rm ~km ~s^{-1}$ that we then use in the analysis of Tri II’s internal kinematics. Despite this improvement in the modelling of binary star systems, the current data remain insufficient to resolve the velocity dispersion of Tri II. We instead find a 95 per cent confidence upper limit of $\sigma _{v} \lesssim 3.4 \rm ~km~s^{-1}$.

Buttry, Rachel (ORCID:0000000155017609)↗

TDCOSMO. XII. Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy

Strong-lensing time delays enable measurement of the Hubble constant ($H_{0}$) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the $H_0$ measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131$-$1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate $H_0$, effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy $D_{\rm d} = 865_{-81}^{+85}$ Mpc and the time-delay distance $D_{\Delta t} = 2180_{-271}^{+472}$ Mpc, giving $H_0 = 77.1_{-7.1}^{+7.3}$ km s$^{-1}$ Mpc$^{-1}$ - for a flat $\Lambda$ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and the line-of-sight effects, and those related to the mass-anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ($H_0 = 78.3^{+3.4}_{-3.3}$ km s$^{-1}$ Mpc$^{-1}$) and for seven lenses ($H_0 = 74.2_{-1.6}^{+1.6}$ km s$^{-1}$ Mpc$^{-1}$), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ($H_0 = 73.3^{+5.8}_{-5.8}$ km s$^{-1}$ Mpc$^{-1}$). This agreement corroborates the methodology of time-delay cosmography.

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AuriDESI: mock catalogues for the DESI Milky Way Survey

The Dark Energy Spectroscopic Instrument Milky Way Survey (DESI MWS) will explore the assembly history of the Milky Way by characterizing remnants of ancient dwarf galaxy accretion events and improving constraints on the distribution of dark matter in the outer halo. We present mock catalogues that reproduce the selection criteria of MWS and the format of the final MWS data set. These catalogues can be used to test methods for quantifying the properties of stellar halo substructure and reconstructing the Milky Way’s accretion history with the MWS data, including the effects of halo-to-halo variance. The mock catalogues are based on a phase-space kernel expansion technique applied to star particles in the Auriga suite of six high-resolution lambda-cold dark matter magnetohydrodynamic zoom-in simulations. They include photometric properties (and associated errors) used in DESI target selection and the outputs of the MWS spectral analysis pipeline (radial velocity, metallicity, surface gravity, and temperature). They also include information from the underlying simulation, such as the total gravitational potential and information on the progenitors of accreted halo stars. We discuss how the subset of halo stars observable by MWS in these simulations corresponds to their true content and properties. These mock Milky Ways have rich accretion histories, resulting in a large number of substructures that span the whole stellar halo out to large distances and have substantial overlap in the space of orbital energy and angular momentum.

dynamics↗

Dissipative dark matter on FIRE – I. Structural and kinematic properties of dwarf galaxies

We present the first set of cosmological baryonic zoom-in simulations of galaxies including dissipative self-interacting dark matter (dSIDM). These simulations utilize the Feedback In Realistic Environments galaxy formation physics, but allow the dark matter to have dissipative self-interactions analogous to standard model forces, parametrized by the self-interaction cross-section per unit mass, (σ/m), and the dimensionless degree of dissipation, 0 < f diss < 1. We survey this parameter space, including constant and velocity-dependent cross-sections, and focus on structural and kinematic properties of dwarf galaxies with $M_{\rm halo} \sim 10^{10-11}{\, \rm M_\odot }$ and $M_{\ast } \sim 10^{5-8}{\, \rm M_\odot }$. Central density profiles (parametrized as ρ ∝ rα) of simulated dwarfs become cuspy when $(\sigma /m)_{\rm eff} \gtrsim 0.1\, {\rm cm^{2}\, g^{-1}}$ (and f diss = 0.5 as fiducial). The power-law slopes asymptote to α ≈ -1.5 in low-mass dwarfs independent of cross-section, which arises from a dark matter ‘cooling flow’. Through comparisons with dark matter only simulations, we find the profile in this regime is insensitive to the inclusion of baryons. However, when $(\sigma /m)_{\rm eff} \ll 0.1\, {\rm cm^{2}\, g^{-1}}$, baryonic effects can produce cored density profiles comparable to non-dissipative cold dark matter (CDM) runs but at smaller radii. Simulated galaxies with $(\sigma /m) \gtrsim 10\, {\rm cm^{2}\, g^{-1}}$ and the fiducial fdiss develop significant coherent rotation of dark matter, accompanied by halo deformation, but this is unlike the well-defined thin ‘dark discs’ often attributed to baryon-like dSIDM. The density profiles in this high cross-section model exhibit lower normalizations given the onset of halo deformation. For our surveyed dSIDM parameters, halo masses and galaxy stellar masses do not show appreciable difference from CDM, but dark matter kinematics and halo concentrations/shapes can differ.

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Dynamics of stellar disc tilting from satellite mergers

The Milky Way’s stellar disc can tilt in response to torques that result from infalling satellite galaxies and their associated tidal debris. In this work, we explore the dynamics of disc tilting by running N-body simulations of mergers in an isolated, isotropic Milky Way-like host galaxy, varying over satellite virial mass, initial position, and orbit. We develop and validate a first-principles understanding of the dynamics that govern how the host galaxy’s stellar disc responds to the satellite’s dark matter (DM) debris. We find that the degree of disc tilting can be large for cosmologically motivated merger histories. In particular, our results suggest that the Galactic disc may still be tilting in response to Gaia-Sausage-Enceladus, one of the most significant recent mergers in the Milky Way’s history. In conclusion, these findings have implications for terrestrial direct detection experiments as disc tilting changes the relative location of the Sun with respect to DM substructure left behind by a merging galaxy.

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Beyond Galaxy Bimodality: The Complex Interplay between Kinematic Morphology and Star Formation in the Local Universe

It is generally assumed that galaxies are a bimodal population in both star formation and structure; star-forming galaxies are disks, while passive galaxies host large bulges or are entirely spheroidal. Here we test this scenario by presenting a full census of the kinematic morphologies of a volume-limited sample of galaxies in the local universe extracted from the MaNGA galaxy survey. We measure the integrated stellar line-of-sight velocity to velocity dispersion ratio (V/σ) for 4574 galaxies in the stellar mass range 9.75 < logM $\star$ [M ⊙ ] < 11.75. We show that at fixed stellar mass, the distribution of V/σ is not bimodal, and that a simple separation between fast and slow rotators is oversimplistic. Fast rotators are a mixture of at least two populations, referred to here as dynamically cold disks and intermediate systems, with disks dominating in both total stellar mass and number. When considering star-forming and passive galaxies separately, the star-forming population is almost entirely made up of disks, while the passive population is mixed, implying an array of quenching mechanisms. Passive disks represent ~30% (both in number and mass) of passive galaxies, nearly a factor of two higher than that of slow rotators, reiterating that these are an important population for understanding galaxy quenching. These results paint a picture of a local universe dominated by disky galaxies, most of which become somewhat less rotation-supported upon or after quenching. While spheroids are present to a degree, they are certainly not the evolutionary end point for the majority of galaxies.

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Existence of tidal tails for the globular cluster NGC 5824

Context: Several dynamically cold streams have been associated with certain globular clusters (GCs) based on orbital energies and angular momenta. Some of these streams are surprisingly far apart from their progenitors and one such pair is Triangulum and NGC 5824. Triangulum can be considered as a piece of the leading tail of NGC 5824 since the cluster’s future orbit matches well with the stream’s track. The existence of the leading tail of NGC 5824 is the motivation behind the search for its trailing tail. Aims: Our goal is to confirm the connection between Triangulum and NGC 5824. We also search for the trailing tail of the cluster. Methods: The selection of member stars of Triangulum is made through various cuts in metallicity, proper motions (PMs), radial velocity and a color–magnitude diagram (CMD). The selected members are compared in phase space to a mock stream that models the disruption of NGC 5824. We then try to detect the trailing tail of the cluster based on a modified matched-filter technique. Stars are assigned weights using their color differences from the cluster’s locus in the CMD. These weights are further scaled, based on the stars’ departures from expected PMs of the model stream. Results: A total of 26 member stars for Triangulum are obtained, 16 of which are newly identified. These members are consistent with the mock stream in the phase space, and their metalicity and position on the CMD are in good agreement with NGC 5824. By applying the matched filter, a tenuous trailing tail of the cluster is detected, spanning ~50° long on sky. The signature matches well with the mock stream’s trajectory. Conclusions: Our results support that the Triangulum stream acts as a part of the leading tail for NGC 5824. On the trailing side, we detected a 50° tail extending from the cluster. The existence of both leading and trailing tails for the GC NGC 5824 is verified.

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Connecting galaxy evolution in clusters with their radial profiles and phase space distribution: results from the IllustrisTNG hydrodynamical simulations

ABSTRACT We study the population of galaxies around galaxy clusters in the hydrodynamic simulation suite IllustrisTNG 300-1 to study the signatures of their evolutionary history on observable properties. We measure the radial number density profile, phase space distribution, and splashback radius for galaxies of different masses and colours over the redshift range z = 0−1. The three primary physical effects which shape the galaxy distribution within clusters are the galaxy quenching, angular momentum distribution, and dynamical friction. We find three distinct populations of galaxies by applying a Gaussian mixture model to their distribution in colour and mass. They have distinct evolutionary histories and leave distinct signatures on their distribution around cluster haloes. We find that low-mass red galaxies show the most concentrated distribution in clusters and the largest splashback radius, while high-mass red galaxies show a less concentrated distribution and a smaller splashback radius. Blue galaxies, which mostly quench into the low-mass red population, have the shallowest distribution within the clusters, with those on radial orbits quenched rapidly before reaching pericentre. Comparison with the distribution of galaxies from the Dark Energy Survey survey around Sunyaev–Zeldovich clusters from the Atacama Cosmology Telescope and South Pole Telescope surveys shows evidence for differences in galaxy evolution between simulations and data.

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A complete catalogue of broad-line AGNs and double-peaked emission lines from MaNGA integral-field spectroscopy of 10K galaxies: stellar population of AGNs, supermassive black holes, and dual AGNs

We analyse the integral field spectroscopy data for the ≈10 000 galaxies in final data release of the MaNGA survey. We identify 188 galaxies for which the emission lines cannot be described by single Gaussian components. These galaxies can be classified into (1) 38 galaxies with broad $\rm H\alpha$ and [O III] $\rm \lambda$5007 lines, (2) 101 galaxies with broad $\rm H\alpha$ lines but no broad [O III] $\rm \lambda$5007 lines, and (3) 49 galaxies with double-peaked narrow emission lines. Most of the broad-line galaxies are classified as active galactic nuclei (AGNs) from their line ratios. The catalogue helps us further understand the AGN-galaxy coevolution through the stellar population of broad-line region host galaxies and the relation between broad lines’ properties and the host galaxies’ dynamical properties. The stellar population properties (including mass, age, and metallicity) of broad-line host galaxies suggest there is no significant difference between narrow-line Seyfert-2 galaxies and Type-1 AGNs with broad $\rm H\alpha$ lines. We use the broad-$\rm H\alpha$ line width and luminosity to estimate masses of black hole in these galaxies, and test the MBH–σe relation in Type-1 AGN host galaxies. Furthermore, we find three dual AGN candidates supported by radio images from the VLA FIRST survey. This sample may be useful for further studies on AGN activities and feedback processes.

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Formation of asymmetric arms in barred galaxies

We establish a dynamical mechanism to explain the origin of the asymmetry between the arms observed in some barred disc galaxies, where one of the two arms emanating from the bar ends is very well defined, while the second one displays a ragged structure, extending between its ridge and the bar. To this purpose, we study the invariant manifolds associated with the Lyapunov periodic orbits around the unstable equilibrium points at the ends of the bar. Matter from the galaxy centre is transported along these manifolds to the periphery, forming this way the spiral arms that emanate from the bar ends. If the mass distribution in the galaxy centre is not homogeneous, because of an asymmetric bar with one side stronger than the other, or because of a non-centred bulge, the dynamics about the two unstable Lagrange points at the ends of the bar will not be symmetric as well. One of their invariant manifolds becomes more extended than the other, enclosing a smaller section and the escaping orbits on it are fewer and dispersed in a wider region. The result is a weaker arm and more ragged than the one at the other end of the bar.

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