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.

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.

Chemo-dynamical modelling with Schwarzschild's method

We extend Schwarzschild’s dynamical modelling method to model absorption line strength data as well as the more usual luminosity and kinematic data.Our approach draws on earlier published work by the first author with the Syer & Tremaine made-to-measure(M2M) dynamical modelling method and uses similar ideas to create a chemo-Schwarzschild method.We apply our extended Schwarzschild method to the same four early type galaxies(NGC 1248, NGC 3838, NGC 4452,NGC 4551) as the chemo-M2M work, and are able to recover successfully the 2D absorption line strength for the three lines we model(Hβ, Fe5015, Mg b).We believe that this is the first time Schwarzschild’s method has been used in this way.The techniques developed can be applied to modelling other aspects of galaxies, for example age and metallicity data coming from stellar population modelling, and are not specific to absorption line strength data.

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.

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.

Studying dynamical models of the core galaxy NGC 1399 with merging remnants

An investigation on the possible dynamical models of the core galaxy NGC 1399 is performed.Because early-type galaxies are likely to be formed through merging events, remnant rings are considered in the modeling process.A numerical survey over three parameters is employed to obtain the best-fit models that are completely consistent with observations.It is found that the inner slope of the dark matter profile is cuspy for this core galaxy.The existence of remnant rings in best-fit models indicates a merging history.The remnant ring explains the flattened surface brightness and thus could be the physical counterpart of the core structure of NGC 1399.

An Alternative to Dark Matter? Part 3: An Open Universe (3 Gy to 76 Gy) Galaxies and Structures Rotation

A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as energy of the universe U, cosmological constant EΛ, curvature of space k, energy density ρΛe, age of the universe tΩ (part 1). That energy of the universe, when taken into consideration during the formation of the first galaxies (<1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses (part 2). Indeed, such residual, non-baryonic energy, when considered in Newton’s gravity equation, adds the term FΛ(r), which can partially explain, without recourse to dark matter, the rotations of some galaxies, such as M33, UGC12591, UGC2885, NGC3198, NGC253, DDO161, UDG44, the MW and the Coma cluster. Today, in the MW, that cosmological gravity force is in the order of 1026 times smaller than the conventional gravity force. The model predicts an acceleration of the mass in the universe (q~-0.986);the energy associated with curvature Ek is the driving force behind the expansion of the universe, rather than the energy associated with the cosmological constant EΛ. An equation to determine expansion is obtained using the energy form of the Friedmann equation relative to Planck power PP and cosmic time or Planck force FP acting at the frontier of the universe moving at c. This constant Planck force, from unknown sources, acts everywhere to the expansion of the universe as a stretching effect on the volume. Finally, the model partly explains the value a0 of the MOND theory. Indeed, a0 is not a true constant, but depends on the cosmological constant at the time the great structures were formed (~1 [Gy]), as well as an adjustment of the typical mass and dimension of those great structures, such as galaxies. The constant a0 is a different expression of the cosmological gravity force FΛ as expressed by the cosmological constant, Λ, acting through the energy-mass equivalent during the formation of the structures. It does not put in question the value of G.

An Alternative to the Dark Matter? Part 2: A Close Universe (10^-9s to 3 Gy), Galaxies and Structures Formation

A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as the energy of the universe U, cosmological constant Λ, the curvature of space k, energy density ρΛe (part 1). The age of the universe in cosmic time that is in line with positive energy conservation (in terms of conventional thermodynamics) and the creation of proton, neutron, electron, and neutrino masses, is ~76 [Gy] (observed ~ 70 [km · s-1 · Mpc-1]). In this model, what is usually referred to as dark energy actually corresponds to the energy of the universe that has not been converted to mass, and which acts on the mass created by the energy-mass equivalence principle and the cosmological gravity field, FΛ, associated with the cosmological constant, which is high during the primordial formation of the galaxies (<1 [Gy]). A look at the Casimir effect makes it possible to estimate a minimum Casimir pressure Pc0 and thus determine our possible relative position in the universe at cosmic time 0.1813 (t0/tΩ = 13.8[Gy]/76.1[Gy]). Therefore, from the observed age of 13.8 [Gy], we can derive a possible cosmic age of ~76.1 [Gy]. That energy of the universe, when taken into consideration during the formation of the first galaxies (<1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses.

The Yukawa and Exponential Potentials for a Galaxy’s Spherical Central Bulge*

By adding an extra term to the Newtonian potential, matter outside the orbit of a star adds to the gravitational acceleration acting on that star. In this work, we solve the Poisson equation for non-Newtonian potentials of a spherically symmetric distribution of mass. We derive equations for calculating the centripetal acceleration and velocity of galactic disk stars that are due to the Newtonian and exponential potentials of the galaxy’s central bulge.

LAMOST Experiment for Galactic Understanding and Exploration (LEGUE)——The survey's science plan

We describe the current plans for a spectroscopic survey of millions of stars in the Milky Way galaxy using the Guo Shou Jing Telescope （GSJT, formerly calledthe Large sky Area Multi-Object fiber Spectroscopic Telescope -- LAMOST）. The survey will obtain spectra for 2.5 million stars brighter than r 〈 19 during dark/grey time, and 5 million stars brighter than r 〈 17 or J 〈 16 on nights that are moonlit or have low transparency. The survey will begin in the fall of 2012, and will run for at least four years. The telescope＇s design constrains the optimal declination range for observations to 10~ 〈 di 〈 50~, and site conditions lead to an emphasis on stars in the direction of the Galactic anticenter. The survey is divided into three parts with different target selection strategies： disk, anticenter, and spheroid. The resulting dataset will be used to study the merger history of the Milky Way, the substructure and evolution of the disks, the nature of the first generation of stars through identification of the lowest metallicity stars, and star formation through study of open clusters and OB associations. Detailed design of the LAMOST Experiment for Galactic Understanding and Exploration （LEGUE） survey will be completed in summer 2012, after a review of the results of the pilot survey.

The spiral structure of the Milky Way

The morphology and kinematics of the spiral structure of the Milky Way are long-standing problems in astrophysics.In this review we firstly summarize various methods with different tracers used to solve this puzzle.The astrometry of Galactic sources is gradually alleviating this difficult situation caused mainly by large distance uncertainties, as we can currently obtain accurate parallaxes(a few μas) and proper motions(≈1 km s-1) by using Very Long Baseline Interferometry(VLBI).On the other hand, the Gaia mission is providing the largest, uniform sample of parallaxes for O-type stars in the entire Milky Way.Based upon the VLBI maser and Gaia O-star parallax measurements, nearby spiral structures of the Perseus, Local, Sagittarius and Scutum Arms are determined in unprecedented detail.Meanwhile, we estimate fundamental Galactic parameters of the distance to the Galactic center,R0, to be 8.35 ± 0.18 kpc, and circular rotation speed at the Sun, Θ0, to be 240±10 km s-1.We found kinematic differences between O stars and interstellar masers: the O stars, on average, rotate faster,>8 km s-1than maser-traced high-mass star forming regions.

Halo stream candidates in the LAMOST DR2

We have cross-matched the LAMOST DR2 with the WISE, 2MASS and PPMXL catalogs and obtained a sample of 64 819 FGK metal-poor dwarfs with [Fe/H]〈-0.7, distances within 2 kpc from the Sun and reliable kinematics（space velocities,angular momenta and eccentricities）. With a detection strategy for halo streams provided by Klement et al, nine significant ＂phase-space overdensities＂ with stars on very similar orbits are identified from this sample. Among these overdensities, three were previously known and six are new stream candidates. The kinematics and metallicities of these stream candidates are then analyzed; they have typical halo characteristics.We have extracted the most probable members of each halo stream according to their angles with respect to the North Galactic Pole and investigate the distribution of the angular momenta to further verify their existences. Detailed study of elemental abundances for these members based on high resolution and high signal-to-noise spectra from follow-up observations in the near future is of high interest to understand the origin of these streams.

19 low mass hypervelocity star candidates from the first data release of the LAMOST survey

Hypervelocity stars are believed to be ejected out from the Galactic center through dynamical interactions between（binary） stars and the central supermassive black hole（s）. In this paper, we report 19 low mass F/G/K type hypervelocity star candidates from over one million stars found in the first data release of the LAMOST regular survey. We determine the unbound probability for each candidate using a MonteCarlo simulation by assuming a non-Gaussian proper-motion error distribution, and Gaussian heliocentric distance and radial velocity error distributions. The simulation results show that all the candidates have unbound possibilities over 50% as expected,and one of them may even exceed escape velocity with over 90% probability. In addition, we compare the metallicities of our candidates with the metallicity distribution functions of the Galactic bulge, disk, halo and globular clusters, and conclude that the Galactic bulge or disk is likely the birth place for our candidates.

Peculiar in-plane velocities in the outer disc of the Milky Way

We present the peculiar in-plane velocities derived from LAMOST red clump stars, which are purified and separated by a novel approach into two groups with different ages. The samples are mostly contributed around the Galactic anti-center direction so that we are able to map the radial profiles of the radial and azimuthal velocities in the outer disc. From variations of the in-plane velocities with Galactocentric radius for the younger and older populations, we find that both radial and azimuthal velocities are not axisymmetric at 8 〈 R 〈 14 kpc. The two red clump populations show that the mean radial velocity is negative within R - 9 kpc and positive beyond. This is likely because of the perturbation induced by the rotating bar. The cross-zero radius, R -9 kpc, essentially indicates the rough location of the Outer Lindblad Resonance radius. Given the circular speed of 238 km s^-1, the pattern speed of the bar can be approximated as 45 km s^-1 kpc^-1. The young red clump stars show larger mean radial velocity than the old population by about 3km s^-1 between R-9 and 12kpc. This is possibly because the younger population is more sensitive to the perturbation than the older one. The radial profiles of the mean azimuthal velocity for the two populations show an interesting U-shape, i.e. at R 〈 10.Skpc, the azimuthal velocity declines with R by about 10km s^-1, while at R 〉 10.5 kpc it increases with R to 240 - 245 km s^-1. It is not clear why the mean azimuthal velocity shows this U-shape along the Galactic anti-center direction. Moreover, the azimuthal velocity for the younger population is slightly larger than that for the older one and the difference moderately declines with R. Beyond R0-12 kpc, the azimuthal velocities for the two populations are indistinguishable.

The nature of orbits in a prolate elliptical galaxy model with a bulge and a dense nucleus

We study the transition from regular to chaotic motion in a prolate elliptical galaxy dynamical model with a bulge and a dense nucleus. Our numerical investigation shows that stars with angular momentum Lz less than or equal to a critical value Lzc, moving near the galactic plane, are scattered to higher z, when reaching the central region of the galaxy, thus displaying chaotic motion. An inverse square law relationship was found to exist between the radius of the bulge and the critical value Lzc of the angular momentum. On the other hand, a linear relationship exists between the mass of the nucleus and Lzc. The numerically obtained results are explained using theoretical arguments. Our study shows that there are connections between regular or chaotic motion and the physical parameters of the system, such as the star＇s angular momentum and mass, the scale length of the nucleus and the radius of the bulge. The results are compared with the outcomes of previous work.

Theory of Gravitons in Spiral and Dwarf Galaxy Rotation Curves

We hypothesize that gravitons contribute significantly to the process that flattens galaxy rotation curves. Gravitons travelling against a gravitational field experience an energy loss due to gravitational redshift identical to the effect on light. This energy loss requires an increased rotational velocity to stabilize a galaxy. We will show that this approach successfully explains the rotational properties of spiral and dwarf galaxies.

Stellar Abundance and Galactic Chemical Evolution through LAMOST Spectroscopic Survey

A project of a spectroscopic survey of Galactic structure and evolution with a Large sky Area Multi-Object fiber Spectroscopic Telescope （LAMOST） is presented. The spectroscopic survey consists of two observational modes for various targets in our Galaxy. One is a major survey of the Milky Way aimed at a systematic study of the stellar abundance and Galactic chemical evolution through low resolution （R = 1000 2000） spectroscopy. Another is a follow-up observation with medium resolution （R = 10000） spectrographs aimed at detailed studies of the selected stars with different chemical composition, kinematics and dynamics.

Dark halos acting as chaos controllers in asymmetric triaxial galaxy models

We study the regular or chaotic character of orbits in a 3D dynamical model,describing a triaxial galaxy surrounded by a spherical dark halo component.Our numerical experiments suggest that the percentage of chaotic orbits decreases exponentially as the mass of the dark halo increases.A linear increase of the percentage of the chaotic orbits was observed as the scale length of the halo component increases. In order to distinguish between regular and chaotic motion,we chose to use the total angular momentum Ltot of the 3D orbits as a new indicator.Comparison with other,previously used,dynamical indicators,such as the Lyapunov Characteristic Exponent or the P（f） spectral method,shows that the Ltot indicator gives very fast and reliable results for characterizing the nature of orbits in galactic dynamical models.

Numerical simulation of a possible origin of the positive radial metallicity gradient of the thick disk

We analyze the radial and vertical metallicity and [α/Fe] gradients of the disk stars of a disk galaxy simulated in a fully cosmological setting with the chemo- dynamical galaxy evolution code GCD＋. We study how the radial abundance gradients vary as a function of height above the plane and find that the metallicity （[α/Fe]） gra- dient becomes more positive （negative） with increasing height, changing sign around 1.5 kpc above the plane. At the largest vertical height （2 〈 丨z丨 〈 3 kpc）, our simulated galaxy shows a positive radial metallicity gradient. We find that the positive metallicity gradient is caused by the age-metallicity and age-velocity dispersion relation, where younger stars have higher metallicity and lower velocity dispersion. Due to the age- velocity dispersion relation, a greater fraction of younger stars reaches 丨z丨 〉 2 kpc at the outer region, because of the lower gravitational restoring force of the disk, i.e. flaring. As a result, the fraction of younger stars with higher metallicity due to the age-metallicity relation becomes higher at the outer radii, which makes the median metallicity higher at the outer radii. Combining this result with the recently observed age-metallicity and age-velocity dispersion relation for the Milky Way thick disk stars suggested by Haywood et al., we argue that the observed （small） positive radial metal- licity gradient at large heights of the Milky Way disk stars can be explained by flaring of the younger thick and/or thin disk stars.

Multicolor photometry of the galaxy cluster A98: substructures and star formation properties

An optical photometric observation with the Beijing-Arizona-Taiwan- Connecticut （BATC） multicolor system is carried out for A98 （z =0.104）, a galaxy cluster with two large enhancements in X-ray surface brightness. Spectral energy distributions （SEDs） covering 15 intermediate bands are obtained for all sources detected down to V - 20 mag in a field of 58′× 58′. After star-galaxy separation with colorcolor diagrams, a photometric redshift technique is applied to the galaxy sample for further membership determination. The color-magnitude relation is taken as a further restriction of the early-type cluster galaxies. As a result, a list of 198 faint member galaxies is achieved. Based on the newly generated sample of member galaxies, the dynamical substructures, A98N, A98S, and A98W, are investigated in detail. A separate galaxy group, A98X, is also found to the south of the main concentration of A98, which is gravitationally unbound to A98. For 74 spectroscopically confirmed member galaxies, the environmental effect on the star formation history is investigated. The bright galaxies in the core region are found to have shorter time scales of star formation, longer mean stellar ages, and higher interstellar medium metallicities, which can be interpreted in the context of the hierarchical cosmological scenario.