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

The second moment of the stellar velocity within the effective radius,denoted by σ^(2)_(e),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 byσ_(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 ofαon the r-band absolute magnitude M_(r),g-i color,and Sérsic index nSer,whereαvalues 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 ofαvalues 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.

Cross-method Analysis of Corotation Radii Data Set for Spiral Galaxies

A corotation radius is a key characteristic of disk galaxies that is essential to determine the angular speed of the spiral structureΩ_p,and therefore understand its nature.In the literature,there are plenty of methods to estimate this value,but do these measurements have any consistency?In this work,we collected a data set of corotation radius measurements for 547 galaxies,300 of which had at least two values.An initial analysis reveals that most objects have rather inconsistent corotation radius positions.Moreover,a significant fraction of galactic disks is distinguished by a large error coverage and almost uniform distribution of measurements.These findings do not have any relation to spiral type,Hubble classification,or presence of a bar.Among other reasons,obtained results could be explained by the transient nature of spirals in a considerable part of galaxies.We have made our collected data sample publicly available,and have demonstrated on one example how it could be useful for future research by investigating a winding time value for a sample of galaxies with possible multiple spiral arm patterns.

Comparing the behavior of orbits in different 3D dynamical models for elliptical galaxies

We study the behavior of orbits in two different galactic dynamical models, describing the motion in the central parts of a triaxial elliptical galaxy with a dense nucleus. Numerical experiments show that both models display regular motion together with extended chaotic regions. A detailed investigation of the properties of motion is made for the 2D and 3D Hamiltonian systems, using a number of different dynamical parameters, such as the Poincare′ surface of a section, the maximal Lyapunov Characteristic Exponent, the S（c） spectrum, the S（w） spectrum and the P （f ） indicator. The numerical calculations suggest that the properties of motion in both potentials are very similar. Our results show that one may use different kinds of gravitational potentials in order to describe the motion in triaxial galaxies while obtaining quantitatively similar results.

Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve （or vice versa）. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the ＂galactic rotation number＂ that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity （such as the ＂flat＂ value in a typical ro- tation curve） and Rg the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.

Model fitting of the kinematics of ten superluminal components in blazar 3C 279

The kinematics of ten superluminal components （C11-C16, C18, C20, C21 and C24） of blazar 3C 279 are studied from VLBI observations. It is shown that their initial trajectory, distance from the core and apparent speed can be well fitted by the precession model proposed by Qian. Combined with the results of the model fit for the six superluminal components （C3, C4, C7a, C8, C9 and C10） already pub-lished, the kinematics of sixteen superluminal components can now be consistently interpreted in the precession scenario with their ejectiontimes spanning more than 25 yr （or more than one precession period）. The results from model fitting show the possible existence of a common precessing trajectory for these knots within a pro- jected core distance of ～0.2-0.4 mas. In the framework of the jet-precession scenario, we can, for the first time, identify three classes of trajectories which are character-ized by their collimation parameters. These different trajectories could be related to the helical structure of magnetic fields in the jet. Through fitting the model, the bulk Lorentz factor, Doppler factor and viewing angle of these knots are derived. It is found that there is no evidence for any correlation between the bulk Lorentz factor of the components and their precession phase （or ejection time）. In a companion paper, the kinematics of another seven components （C5a, C6, C7, C17, C19, C22 and C23） have been derived from model fitting, and a binary black-hole/jet scenario was envisaged. The precession model proposed by Qian would be useful for understanding the kine- matics of superluminal components in blazar 3C 279 derived from VLBI observations, by disentangling different mechanisms and ingredients. More generally, it might also be helpful for studying the mechanism of jet swing （wobbling） in other blazars.

Revisiting the Local Kinematics of the Milky Way using the New Hipparcos Data

With the new Hipparcos data recently released, we reexamine the kinematics in the solar neighborhood. Two different populations of objects, namely the thin-disk O-B5 stars and the thick-disk K-M giants, are selected for tracing the kinematical parameters of the Galaxy. Using a 3-D kinematical model, the components of the solar motion and the Oort constants are derived. The solutions and the kinematics inferred from both types of stars are analyzed. The results obtained with the new data are compared with those from the old Hipparcos data. We conclude that the present solution provides a more reliable estimation of the Oort constants, thanks to the new reduction of the Hipparcos data that provides even more accurate astrometric measurements of stars.

Determining the type of orbits in the central regions of barred galaxies

We use a simple dynamical model which consists of a harmonic oscillator and a spherical com- ponent, in order to investigate the regular or chaotic character of orbits in a barred galaxy with a central spherically symmetric nucleus. Our aim is to explore how the basic parameters of the galactic system in- fluence the nature of orbits, by computing in each case the percentage of chaotic orbits, as well as the percentages of different types of regular orbits. We also give emphasis to the types of regular orbits that support either the formation of nuclear rings or the barred structure of the galaxy. We provide evidence that the traditional xl orbital family does not always dominate in barred galaxy models since we found several other types of resonant orbits which can also support the barred structure. We also found that sparse enough nuclei, fast rotating bars and high energy models can support the galactic bars. On the other hand, weak bars, dense central nuclei, slowly rotating bars and low energy models favor the formation of nuclear rings. We also compare our results with previous related work.

Revisiting the dichotomy of early-type galaxies

We study the relationship between isophotal shapes, central light profiles and kinematic properties of early-type galaxies （ETGs） based on a compiled sample of 184 ETGs. These sample galaxies are included in Data Release 8 of the Sloan Digital Sky Survey and have central light profiles and kinematic properties available from the literature, which were compiled from observations by the Hubble Space Telescope and the ATLAS3D integral-field spectrograph, respectively. We find that there is only a weak correlation between the isophotal shape （a4/a） and the central light profile （within 1 kpc） of ETGs. About two-fifths of ＂core＂ galaxies have disky isophotes, and one-third of ＂power-law＂ galaxies are boxy. Our statistical results also show that there are weak correlations between galaxy luminosity and dynamical mass with a4/a, but such correlations are tighter with a central light profile. Moreover, no clear link has been found between the isophotal shape and the Sersic index. Comparisons show that there are similar correlations between a4/a and ellipticity, and between a4/a and specific angular momentum ARo/2 for ＂power-law＂ ETGs, but there are no such correlations for ＂core＂ ETGs. Therefore, we speculate that the bimodal classifications of ETGs are not as simple as previously thought, though we also find that the disky ETGs with highest a4/a are more elongated and fast rotators.

The bar and spiral arms in the Milky Way: structure and kinematics

The Milky Way is a spiral galaxy with the Schechter characteristic luminosity L*,thus an important anchor point of the Hubble sequence of all spiral galaxies.Yet the true appearance of the Milky Way has remained elusive for centuries.We review the current best understanding of the structure and kinematics of our home galaxy,and present an updated scientifically accurate visualization of the Milky Way structure with almost all components of the spiral arms,along with the COBE image in the solar perspective.The Milky Way contains a strong bar,four major spiral arms,and an additional arm segment(the Local arm)that may be longer than previously thought.The Galactic boxy bulge that we observe is mostly the peanut-shaped central bar viewed nearly end-on with a bar angle of^25°-30°from the SunGalactic center line.The bar transitions smoothly from a central peanut-shaped structure to an extended thin part that ends around R^5 kpc.The Galactic bulge/bar contains^30%-40%of the total stellar mass in the Galaxy.Dynamical modelling of both the stellar and gas kinematics yields a bar pattern rotation speed of^35-40 km s-1 kpc-1,corresponding to a bar rotation period of^160-180 Myr.From a galaxy formation point of view,our Milky Way is probably a pure-disk galaxy with little room for a significant merger-made,"classical"spheroidal bulge,and we give a number of reasons why this is the case.

The density profiles of dark matter halos in spiral galaxies

In spiral galaxies, we explain their non-Keplerian rotation curves (RCs) by means of a non-luminous component embedding their stellar-gaseous disks. Understanding the detailed properties of this component (labelled Dark Matter, DM) is one of the most pressing issues of Cosmology. We investigate the recent relationship (claimed by Walker et al. 2010, hereafter W + 10) between r, the galaxy radial coordinate, and Vh(r), the dark halo contribution to the circular velocity at r, 1) in the framework of the Universal Rotation Curve (URC) paradigm and directly 2) by means of the kinematics of a large sample of DM dominated spirals. We find a general agreement between the W + 10 claim, the distribution of DM emerging from the URC and that inferred in the (low luminosity) objects of our sample. We show that such a phenomenology, linking the spiral’s luminosity, radii and circular velocities, implies an evident inconsistency with (naive) predictions in the Λ Cold Dark Matter (ΛCDM) scenario.

Constraining Mass of M31 Combing Kinematics of Stars,Planetary Nebulae and Globular clusters

We construct a multiple-population discrete axisymmetric Jeans model for the Andromeda(M31)galaxy,considering three populations of kinematic tracers:48 supergiants and 721 planetary nebulae(PNe)in the bulge and disk regions,554 globular clusters extending to~30 kpc,and halo stars extending to~150 kpc of the galaxy.The three populations of tracers are organized in the same gravitational potential,while each population is allowed to have its own spatial distribution,rotation,and internal velocity anisotropy.The gravitational potential is a combination of stellar mass and a generalized NFW dark matter halo.We created two sets of models,one with a cusped dark matter halo and one with a cored dark matter halo.Both the cusped and cored model fit kinematics of all the three populations well,but the cored model is not preferred due to a too high concentration compared to that predicted from cosmological simulations.With a cusped dark matter halo,we obtained total stellar mass of 1.0±0.1×10^(11)M_(☉),dark matter halo virial mass of M_(200)=7.0±0.9×10^(11)M_(☉),virial radius of r_(200)=184±4 kpc,and concentration of c=20±4.The mass of M31 we obtained is at the lower side of the allowed ranges in the literature and consistent with the previous results obtained from the HⅠrotation curve and PNe kinematics.Velocity dispersion profile of the outer stellar halo is important in constraining the total mass while it is still largely uncertain.Further proper motion of bright sources from Gaia or the Chinese Space Station Telescope might help on improving the data and lead to stronger constraints on the total mass of M31.

Stellar dynamical modeling-accuracy of 3D density estimation for edge-on axisymmetric galaxies

From Rybicki’s analysis using the Fourier slice theorem,mathematically it is possible to reproduce uniquely an edge-on axisymmetric galaxy’s 3D light distribution from its 2D surface brightness.Utilizing galaxies from a cosmological simulation,we examine the ability of Syer and Tremaine’s madeto-measure method and Schwarzschild’s method for stellar dynamical modeling to do so for edge-on oblate axisymmetric galaxies.Overall,we find that the methods do not accurately recover the 3D distributions,with the made-to-measure method producing more accurate estimates than Schwarzschild’s method.Our results have implications broader than just luminosity density,and affect other luminosity-weighted distributions within galaxies,for example,age and metallicity.

Empirical formulae to describe some physical properties of small groups of protogalaxies with multiplicity

By means of identical cubic elements,we generate a partition of a volume in which a particle-based cosmological simulation is carried out.In each cubic element,we determine the gas particles with a normalized density greater than an arbitrarily chosen density threshold.By using a proximity parameter,we calculate the neighboring cubic elements and generate a list of neighbors.By imposing dynamic conditions on the gas particles,we identify gas clumps and their neighbors,so that we calculate and fit some properties of the groups so identified,including the mass,size and velocity dispersion,in terms of their multiplicity(here defined simply as the number of member galaxies).Finally,we report the value of the ratio of kinetic energy to gravitational energy of such dense gas clumps,which will be useful as initial conditions in simulations of gravitational collapse of gas clouds and clusters of gas clouds.

To the Theory of Galaxies Rotation and the Hubble Expansion in the Frame of Non-Local Physics

The unified generalized non-local theory is applied for mathematical modeling of cosmic objects. For the case of galaxies the theory leads to the flat rotation curves known from observations. The transformation of Kepler’s regime into the flat rotation curves for different solitons is shown. The Hubble expansion with acceleration is explained as result of mathematical modeling based on the principles of non-local physics. Peculiar features of the rotational speeds of galaxies and effects of the Hubble expansion need not in the introduction of new essence like dark matter and dark energy. The origin of difficulties consists in the total Oversimplification following from the principles of local physics.

The assembly of the Milky Way and its satellite galaxies

In recent years it has become clear that the Milky Way is an important test- ing ground for theories of galaxy formation. Much of this growth has been driven by large surveys, both photometric and spectroscopic, which are producing vast and rich catalogs of data. Through the analysis of these data sets we can gain new and detailed insights into the physical processes which shaped the Milky Way＇s evolution. This review will discuss a number of these developments, first focusing on the disk of the Milky Way, and then looking at its satellite population. The importance of surveys has not gone unnoticed by the Chinese astronomy community and in the final section we discuss a number of Chinese projects that are set to play a key role in the development of this field.

Galactic kinematics and structure defined by open clusters

On the basis of recently published astrophysical parameters of the open clusters, we have selected 301 clusters with measurements of their kinematical parameters to trace the local structure and kinematics of the Galactic disk. The present sample covers a range of over 3.0 kpc from the Sun and gives significant estimates of the disk structure and kinematical parameters of the Galaxy. We derive the disk scale height, vertical displacement of the Sun to the Galactic plane, solar motion with respect to the local standard of rest, circular speed of the Galactic rotation, Galactocentric distance from the Sun, etc. We found that the average scale height of the disk defined by the open clusters is Zh = 58 ± 4pc, with a vertical displacement of the Sun below the Galactic plane of z0 -= - 16±4 pc. Clusters with ages older than 50 Myr are less concentrated in the average plane （Zh=67 ±6pc） than the younger clusters （Zh = 51±5pc）. Using the approximation of axisymmetric circular rotation, we have derived the distance to the Galactic center from the Sun R0 = 8.03 ±0.70 kpc, which is in excellent agreement with the best estimate of the Galactocentric distance. From a kinematical analysis, we found an agedependent rotation of the Galaxy. The older clusters exhibit a lower velocity of vorticity, but have the same shear as the younger clusters. The mean rotation velocity of the Galaxy was obtained as 235 ± 10 km s-1.

Model-fitting of the kinematics of superluminal components in blazar 3C 279

A precessing jet-nozzle model with a precession period of about 25 yr has been proposed by Qian to interpret the change with time of the ejection position an- gle of the superluminal components observed using very long baseline interferometry （VLBI） in the blazar 3C 279. We discuss the kinematic properties of six superluminal knots （C3, C4, C7a, C8, C9 and C10） and show that their trajectory, core-distance and apparent speed, derived from VLBI observations, can be consistently well fitted by the model. Their intrinsic Lorentz factors of bulk superluminal motion are thus derived, and the evidence shows no relation between Lorentz factor and the precession phase. Interestingly, for the C7a and C8 knots, the fitted core-distance ranges from ,,～0.1 mas to ～0.4 mas and for knots C9 and C10 from ～0.2mas to ～1.0-1.5 mas. For knot C4, its trajectory and apparent velocity are well fitted in the core-distance range from H1 mas to ～5 mas, taking into account a curvature of the trajectory at core-distance larger than ,,～3 mas. The consistent fitting of the kinematics of these components clearly demonstrates that the amplitude function and collimation param- eter adopted in the precession model are appropriate and applicable for both the in- ner and outer parts of the jet in 3C 279, but in some cases the jet curvature in the outer parts （or deviation from the model trajectory） needs to be seriously taken into consideration. With the exception of C4, the ejection position angles derived from the precession model are consistent with the values measured by VLBI observations （within about 3° - 6°）. Undoubtedly, the consistent interpretation of the kinematics in terms of the precession model for these superluminal components, with their ejection time spanning -～24 yr, significantly expands its applicability and implies that regular patterns of trajectories （or rotating channels） could exist in some periods.

Kinematics of solar neighborhood stars and its dependence on age and metallicity

We have constructed a catalog containing the best available astrometric, photometric, radial velocity and astrophysical data for mainly F-type and G-type stars （called the Astrometric Catalog associated with Astrophysical Data, ACAD）. This contains 27 553 records and is used for the purpose of analyzing stellar kinematics in the solar neighborhood. Using the Lindblad-Oort model and compiled ACAD, we calculated the solar motion and Oort constants in different age-metallicity bins. The evolution of kinematical parameters with stellar age and metallicity was investigated directly. The results show that the component of the solar motion in the direction of Galactic rotation （denoted S_2） linearly increases with age, which may be a conse- quence of the scattering processes, and its value for a dynamical cold disk was found to be 8.0 ± 1.2 km s^-1. S_2 also linearly increases with metallicity, which indicates that radial migration is correlated to the metallicity gradient. On the other hand, the rotational velocity of the Sun around the Galactic center has no clear correlation with ages or metallicities of stars used in the estimation.

Information from the Kinematics of F and G Stars in the Solar Neighborhood

We have calculated the orbital parameters for 90 stars in Chen et al. and updated the kinematic data for stars in Edvardsson et al. by using the accurate Hipparcos parallaxes and proper motions, and recalculated the α-element abundances in Edvardsson et al. in a way consistent with Chen et al. The two sets of data are combined in a study of stellar populations and characteristics of F & G stars in the solar neighborhood. We confirm the result of Chen et al. that a distinguishable group of stars may belong to the thick disk rather than the thin disk. The ages for the stars are determined using the theoretical isochrones of VandenBerg et al. The age-metallicity relation is investigated for different subgroups according to distance from the sun and galactic orbital parameters. It is found that a mixing of stars with different orbital parameters significantly affect the age-metallicity relation for the disk. Stars with orbits confined to the solar circle all have metallicities [Fe/H] > -0.3 irrespective of their distances from the sun or from the Galactic plane.

Kinematics of the Open Cluster System in the Galaxy

Absolute proper motions and radial velocities of 202 open clusters in the solar neighborhood, which can be used as tracers of the Galactic disk, are used to investigate the kinematics of the Galaxy in the solar vicinity, including the mean heliocentric velocity components （u1, u2, u3） of the open cluster system, the characteristic velocity dispersions （σ1,σ2,σ3）, Oort constants （A, B） and the large-scale radial motion parameters （C, D） of the Galaxy. The results derived from the observational data of proper motions and radial velocities of a subgroup of 117 thin disk young open clusters by means of a maximum likelihood algorithm are： （u1,u2,u3） = （-16.1 ± 1.0,-7.9 ±1.4,-10.4±1.5） km·s^-1, （σ1,σ2,σ3） = （17.0±0.7, 12.2±0.9, 8.0±1.3） km·S^-1, （A, B） = （14.8±1.0, - 13.0±2.7） km·s^-1 kpc^-1, and （C, D） = （1.5 ± 0.7, -1.2 ±1.5） km·s^-1 kpc^-1. A discussion on the results and comparisons with what was obtained by other authors is given.