Gravito-Electrodynamics in Galaxy Rotation Curves. ENG: An Extended Newtonian Gravitation

An extended Newtonian gravitation (ENG) model was developed to explain the rotation curves in galaxies and galaxy clusters. ENG requires the knowledge of a parameter that is a function of the mass of the gravitational source. An approximate eq. for that parameter was obtained (for disk galaxies) that yields asymptotic speeds close to binned measured data. ENG yielded larger circular speeds for galaxy clusters when compared with the MOND results. A classical gravito-electromagnetic model (which neither is based on Einstein GR, nor on gravito-magnetism only) was developed which yielded asymptotic circular speeds very small compared to experimental results. However when ENG was used to develop an extended gravito-electromagnetic model, it yielded results compatible with MOND results for simulated galaxies and larger than MOND results for a simulated galaxy cluster. This model showed measurable increase in the circular speed when compared to ENG alone in the galaxy cluster. The need for modifying the Einstein field equation to address the dark matter problem in the framework of the ENG model was illustrated.

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.

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.

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.

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.

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.

Milky Way globular cluster dynamics:are they preferentially co-rotating?

The motion of baryonic components of the Milky Way is governed by both luminous and dark matter content of the Galaxy.Thus,the dynamics of Milky Way globular clusters(GCs)can be used as tracers to infer the mass model of the Galaxy up to a large radius.In this work,we apply the directly observable line-of-sight velocities to test if the dynamics of the GC population are consistent with an assumed axisymmetric gravitational potential of the Milky Way.For this,we numerically compute the phase space distribution of the GC population where the orbits are either oriented randomly or co-/counter-rotating with respect to the stellar disk.Then we compare the observed position and line-of-sight velocity distribution of^150 GCs with those of the models.We found that,for the adopted mass model,the co-rotating scenario is the favored model based on various statistical tests.We do the analysis with and without the GCs associated with the progenitors of early merger events.This analysis can be extended in the near future to include precise and copious data to better constrain the Galactic potential up to a large radius.

Made-to-measure galaxy modelling utilising absorption line strength data

We enhance the Syer ＆ Tremaine made-to-measure （M2M） particle method of stellar dynamical modelling to model simultaneously both kinematic data and absorption line strength data, thus creating a ＇chemo-M2M＇ modelling scheme. We apply the enhanced method to four galaxies （NGC 1248, NGC 3838, NGC 4452, NGC 4551） observed using the SAURON integral-field spectrograph as part of the ATLAS3D programme. We are able to reproduce successfully the 2D line strength data achieving mean X2 per bin values of ≈ 1 with 〉 95% of particles having converged weights. Because M2M uses a 3D particle system, we are also able to examine the underlying 3D line strength distributions. The extent to which these dis- tributions are plausible representations of real galaxies requires further consideration. Overall, we consider the modelling exercise to be a promising first step in developing a ＇chemo-M2M＇ modelling system and in understanding some of the issues to be addressed. While the made-to-measure techniques developed have been applied to absorption line strength data, they are in fact general and may be of value in modelling other aspects of galaxies.

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.

The relaxation of galaxy clusters at redshift z=0 in IllustrisTNG simulation

We study the dynamical states of the 30 most massive galaxy clusters in the TNG100 simulation at redshift z = 0 using three types of tracers: stars, dark matter particles and satellite galaxies. If the massive galaxy cluster is spherically symmetric and relaxed, we can obtain the underlying total mass distribution accurately from its dynamical tracers using the spherical Jeans equations. Although the three tracers of clusters have very different number densities, velocity dispersions and anisotropies, they still trace the same total mass profile. We obtain the total mass profiles of clusters using these tracers separately and compare them with the true mass distributions. We find that:(1) the kinematics of dark matter trace the total mass of all clusters well and the mass inferred from dark matter are generally consistent with the true mass profiles with relative deviations smaller than ~ 25% at all radii;(2) stars in ~ 60% massive clusters are approaching equilibrium and the total mass of these clusters inferred from stars have relative deviations smaller than ~50% at all radii. Stellar substructures are rich and the mass inferred from stars tend to be over-estimated in the inner region;and(3) satellite galaxies are unrelaxed in the inner region and become more relaxed as the radius increases. The total mass inferred from satellites are under-estimated in all regions.

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.

Stellar kinematics and populations out to 1.5 effective radii in the elliptical galaxy NGC 4636

We present high quality long slit spectra along the major and minor axes out to 1.5 effective radii of the massive galaxy NGC 4636 taken by the Hobby-Eberly Telescope. Using the Fourier Correlation Quotient method, we measured the stellar line-of-sight velocity distribution along the axes. Furthermore, six Lick/IDS indices （Hβ, Mgb, Fe5015, Fe5270, Fe5335, Fe5406） are derived from the clean spectrum. By comparing the measured absorption line strengths with the predictions of Simple Stellar Population （SSP） models, we derived ages, total metallicity and a abundance profiles of the galaxy. This galaxy presents old and [α/Fe] overabundant stellar populations. Indeed, using the SSP model, we obtained the broadband color profiles. The theoretical colors match well with the measured colors and present red sharp peaks at the galaxy center. The sharp peaks of the colors are mainly shaped by the high metallicity in the galaxy＇s center. Interestingly, the galaxy has steep negative metaUicity gradients, but the trend flattens outwards. This result likely suggests that the center and outer regions of the galaxy formed through different formation processes.

Star formation properties of galaxy cluster A1767

Abell 1767 is a dynamically relaxed, c D cluster of galaxies with a redshift of 0.0703. Among 250 spectroscopically confirmed member galaxies within a projected radius of 2.5r200, 243 galaxies（ Digital Sky Survey. Based on this ～97%） are spectroscopically covered by the Sloanhomogeneous spectral sample, the stellar evolutionary synthesis code STARLIGHT is applied to investigate the stellar populations and star formation histories of galaxies in this cluster. The star formation properties of galaxies, such as mean stellar ages, metallicities, stellar masses, and star formation rates, are presented as functions of local galaxy density. A strong environmental effect is found such that massive galaxies in the high-density core region of the cluster tend to have higher metallicities, older mean stellar ages, and lower specific star formation rates（SSFRs）, and their recent star formation activities have been remarkably suppressed. In addition, the correlations of the metallicity and SSFR with stellar mass are confirmed.

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.

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.

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.

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.

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.

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.

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.