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.

An Asymmetric Galactic Stellar Disk Traced by OB-type Stars from LAMOST DR7

Using 9943 OB-type stars from LAMOST DR7 in the solar neighborhood,we fit the vertical stellar density profile with the model including a single exponential distribution at different positions(R,Φ).The distributions of the scale heights and scale length show that the young disk traced by the OB-type stars is not axisymmetric.The scale length decreases versus the azimuthal angleΦ,i.e.,from.■kpc withΦ=-3°to■kpc withΦ=9°.Meanwhile we find signal of non-symmetry in the distribution of the scale height of the north and south of the disk plane.The scale height in the north side shows signal of flaring of the disk,while that of the south disk stays almost constant around h_(s)=130 pc.The distribution of the displaceeent of the disk plane Z_(0)also shows variance versus the azimuthal angleΦ,which displays significant differences with the warp model constrained by the Cepheid stars.We also test different values for the position of the Sun,and the distance between the Sun and the Galactic center affects the scale heights and the displacement of the disk significantly,but that does not change our conclusion that the disk is not axisymmetric.

Comptonization and Reprocessing Processes in Accretion Disks: Applications to the Seyfert 1 Galaxies NGC 5548 and NGC 4051

Simultaneous multi-wavelength observations have revealed complex variability in AGNs. To explain the variability we considered a theoretical model consisting of an inner hot comptonizing corona and an outer thin accretion disk, with interactions between the two components in the form of comptonization and reprocessing. We found that the variability of AGNs is strongly affected by the parameters of the model, namely, the truncated disk radius rmin, the corona radius rs, the temperature KTe and the optical depth TO of the corona. We applied this model to the two best observed Seyfert 1 galaxies, NGC 5548 and NGC 4051. Our model can reproduce satisfactory the observed SEDs. Our fits indicate that NGC 5548 may have experienced dramatic changes in physical parameters between 1989-1990 and 1998, and that NGC 4051 has a much larger truncated disk radius （700 Schwarzschild radii） than NGC 5548 （several tens of Schwarzschild radii）. Since we adopted a more refined treatment of the comptonization process rather than simply assuming a cut-off power law, our results should be more reasonable than the previous ones.

On the metallicity gradients of the Galactic disk as revealed by LSS-GAC red clump stars

Using a sample of over 70 000 red clump（RC） stars with 5%–10% distance accuracy selected from the LAMOST Spectroscopic Survey of the Galactic Anti-center（LSS-GAC）, we study the radial and vertical gradients of the Galactic disk（s） mainly in the anti-center direction, covering a significant volume of the disk in the range of projected Galactocentric radius 7 ≤ RGC ≤ 14 kpc and height from the Galactic midplane 0 ≤ ｜Z ｜ ≤ 3 kpc. Our analysis shows that both the radial and vertical metallicity gradients are negative across much of the volume of the disk that is probed, and they exhibit significant spatial variations. Near the solar circle（7 ≤ RGC ≤ 11.5 kpc）, the radial gradient has a moderately steep, negative slope of-0.08 dex kpc-1near the midplane（｜Z ｜ 〈 0.1 kpc）, and the slope flattens with increasing ｜Z ｜. In the outer disk（11.5 〈 RGC ≤ 14 kpc）, the radial gradients have an essentially constant, much less steep slope of-0.01 dex kpc-1at all heights above the plane, suggesting that the outer disk may have experienced an evolutionary path different from that of the inner disk. The vertical gradients are found to flatten largely with increasing RGC. However, the vertical gradient of the lower disk（0 ≤ ｜Z ｜ ≤ 1 kpc）is found to flatten with RGC quicker than that of the upper disk（1 〈 ｜Z ｜ ≤ 3 kpc）.Our results should provide strong constraints on the theory of disk formation and evolution, as well as the underlying physical processes that shape the disk（e.g. gas flows,radial migration, and internal and external perturbations）.

The evolution of stellar metallicity gradients of the Milky Way disk from LSS-GAC main sequence turn-off stars: a two-phase disk formation history?

Accurate measurements of stellar metallicity gradients in the radial and vertical directions of the disk and their temporal variations provide important constraints on the formation and evolution of the Milky Way disk. We use 297 042 main sequence turn-off stars selected from the LAMOST Spectroscopic Survey of the Galactic Anticenter（LSS-GAC） to determine the radial and vertical gradients of stellar metallicity,△[Fe/H]/△R and △[Fe/H]/△｜Z ｜ of the Milky Way disk in the direction of the anticenter. We determine ages of those turn-off stars by isochrone fitting and measure the temporal variations of metallicity gradients. We have carried out a detailed analysis of the selection effects resulting from the selection, observation and data reduction of LSS-GAC targets and the potential biases of a magnitude limited sample on the determinations of metallicity gradients. Our results show that the gradients, both in the radial and vertical directions, exhibit significant spatial and temporal variations. The radial gradients yielded by stars with the oldest ages（ 11 Gyr） are essentially zero at all heights from the disk midplane, while those given by younger stars are always negative. The vertical gradients deduced from stars with the oldest ages（ 11 Gyr）are negative and only show very weak variations with Galactocentric distance in the disk plane, R, while those yielded by younger stars show strong variations with R.After being essentially flat at the earliest epochs of disk formation, the radial gradients steepen as age decreases, reaching a maximum（steepest） at age 7–8 Gyr, and then they flatten again. Similar temporal trends are also found for the vertical gradients. We infer that the assembly of the Milky Way disk may have experienced at least two distinct phases. The earlier phase is probably related to a slow, pressure-supported collapse of gas, when the gas settles down to the disk mainly in the vertical direction. In the later phase, there are significant radial flows of gas in the disk, and the rate of gas inflow near the solar neighborhood reaches a maximum around a lookback time of 7–8 Gyr.The transition between the two phases occurs around a lookback time between 8 and11 Gyr. The two phases may be responsible for the formation of the Milky Way＇s thick and thin disks, respectively. Also, as a consequence, we recommend that stellar age is a natural, physical criterion to distinguish stars from the thin and thick disks. From an epoch earlier than 11 Gyr to one between 8 and 11 Gyr, there is an abrupt, significant change in magnitude of both the radial and vertical metallicity gradients, suggesting that stellar radial migration is unlikely to play an important role in the formation of the thick disk.

Correlation between excitation index and Eddington ratio in radio galaxies

We use a sample of 111 radio galaxies with redshift z 〈 0.3 to investigate their nuclear properties. The black hole masses of the sources in this sample are estimated with the velocity dispersion/luminosity of the galaxies, or the width of the broad-lines. We find that the excitation index, the relative intensity of low and high excitation lines, is correlated with the Eddington ratio for this sample. The size of the narrow-line region （NLR） was found to vary with ionizing luminosity as RNLR ∝ Lion^0.25 （Liu et al. 2013）. Using this empirical relation, we find that the correlation between the excitation index and the Eddington ratio can be reproduced by photoionization models. We adopt two sets of spectral energy distributions （SEDs）, with or without a big blue bump in ultraviolet as the ionizing continuum, and infer that the modeled correlation between the excitation index and the Eddington ratio is insensitive to the applied SED. This means that the difference between high excitation galaxies and low excitation galaxies is not caused by the different accretion modes in these sources. Instead, it may be caused by the size of the NLR.

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.

Rotation curve of the Galactic outer disk derived from radial velocities and UCAC3 proper motions of carbon stars

The availability of astrometfic data and radial velocities of carbon stars near the Galactic plane enables us to investigate the kinematics of the Milky Way, especially the rotation curve. The recently published Third U. S. Naval Observatory CCD Astrograph Catalog （UCAC3） provides the opportunity to test this problem using three-dimensional velocity in order to obtain more reliable rotation curves. We intend to study the Galactic rotation curve up to 15 kpc using the radial velocities and proper motions of carbon stars. The motivation for using UCAC3 is to provide high precision proper motions which have hardly been used in determining the rotation velocity of tracers. Seventy-four carbon stars and carbon-rich Mira variables toward the anti-center direction （90° 〈 l 〈 270°, ｜b｜ 〈 6°） are picked up from the literature then matched with UCAC3 carbon star candidates to obtain their proper motions. A rigorous geometrical method is employed to compute the rotation velocity of each object. Taking carbon stars as tracers, we find a flat rotation curve of 210 ± 12 kms^-1 assuming R0 = 8.0kpc for the galactocentric distance and V0 = 220kms^-1 for the rotation velocity of the Sun. Due to the uncertainties of distances, the rotation velocities are more dispersed if tangential velocities enter the calculation, compared to those derived from radial velocities only. However, the whole rotation curve shows coherence with previous results. Increasing observation and study of carbon stars would be desirable in order to provide more homogeneous data for the kinematical study of the Galactic disk.

On the metallicity gradient in the Galactic disk

The problem of the chemical composition gradient in the Galactic disk is studied based on a sample of metallicity estimates of open star clusters,using Gaia DR2-improved distance estimates.A clearly non-monotonic variation was observed in the average metallicity of clusters with increasing Galactocentric distance.One can clearly see the metallicity jump of 0.22 in[Fe/H]at a Galactocentric distance of about9.5 kpc,which appears to be linked to the outer boundary of the thinnest and youngest component of the Galactic disk.The absence of a significant metallicity gradient in the internal(R<9 kpc)and external(R>10 kpc)regions of the disk demonstrates the absence of noticeable metal enrichment at times of the order of the ages corresponding to those of the disk regions under consideration.Observational data show that the disk experiences noticeable metal enrichment only during the starburst epochs.No significant dependence was identified between the average metallicity and the age of the clusters.

Disk-Corona Model in Active Galactic Nuclei: an Observational Test

We compiled a sample of 98 radio-quiet active galactic nuclei observed by ASCA, Chandra, XMM-Newton, INTEGRAL and Swift with the aim of testing the formation of hot corona and the magnetic shear stress operating in a disk-corona system. We found a strong correlation between the hard X-ray luminosity, bolometric luminosity LBol and Eddington luminosity LEdd, in the sense that the fraction f of hard X-ray to the bolometric luminosity is inversely proportional to the Eddington ratio. This correlation favors the shear stress tensor being of the form of trФ∝ Pgas, with which the disk-corona structure is stable.

New estimates of scale heights and spiral structures for non-edge-on spiral galaxies

On the basis of Poisson＇s equation for the logarithmic perturbation of matter density, we provide improved estimates of scale heights and spiral structures for non-edge-on spiral galaxies by subtracting the surface brightness distributions from observed images. As examples, the non-edge-on spiral galaxies PGC 24996, which is face-on, and M31, which is inclined, are studied. The scale height, pitch angle and inclination angle of M31, our nearest neighbor, that are presented in this work, agree well with previous research.

Investigating the disk-corona relation in a blue AGN sample

We compile a blue AGN sample from SDSS and investigate how the ratio of hard X-ray to bolometric luminosity depends on the Eddington ratio and black hole mass. Our sample comprises 240 radio-quiet Seyfert 1 galaxies and QSOs. We find that the fraction of hard X-ray luminosity （log（L2-10keV/L bol）） decreases with an increase of the Eddington ratio. We also find that the fraction of hard X-ray luminosity is independent of the black hole mass for radio-quiet AGNs. The relation of log（L2-10 keV/Lbol） decreasing with increasing Eddington ratio indicates that X-ray bolometric correction is not a constant, from a larger sample supporting the results of Vasudevan ＆ Fabian. We interpret our results by the disk corona evaporation/condensation model. In the frame work of this model, Compton cooling becomes efficient in cooling the corona at high accretion rates （in units of Eddington rate）, leading to condensation of coronal gas to the disk. Consequently, the relative strength of the corona to the disk becomes weaker at higher Eddington ratios. Therefore, the fraction of hard X-ray emission to disk emission and hence to the bolometric emission is smaller at higher Eddington ratios. The independence of the fraction of hard X-ray luminosity with respect to the mass of the black hole can also be explained by the disk corona model since the coronal structure and luminosity （in units of Eddington luminosity） are independent of the mass of black holes.

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.

Scale Heights of Non-Edge-on Spiral Galaxies

We present a method of calculating the scale height of non-edge-on spiral galaxies, together with a formula for errors. The method is based on solving Poisson＇s equation for a logarithmic disturbance of matter density in spiral galaxies. We show that the spiral arms can not extend to inside the ＂forbidden radius＂ r0, due to the effect of the finite thickness of the disk. The method is tested by re-calculating the scale heights of 71 northern spiral galaxies previously calculated by Ma, Peng ＆ Gu. Our results differ from theirs by less than 9%. We also present the scale heights of a further 23 non-edge-on spiral galaxies.

Constraints on black hole spins with a general relativistic accretion disk corona model

The peaks in the spectra of the accretion disks surrounding massive black holes in quasars are in the far-UV or soft X-ray band, which are usually not observed. However, in the disk corona model, soft photons from the disk are Comptonized to high energy in the hot corona, and the hard X-ray spectra （lu- minosity and spectral shape） contain information on the incident spectra from the disk. The values of black hole spin parameter a. are inferred from the spectral fitting, which are spread over a large range, ~ -0.94 to 0.998. We find that the inclination angles and mass accretion rates are well determined by the spectral fitting, but the results are sensitive to the accuracy of black hole mass estimates. No tight constraints on the black hole spins are achieved, if the uncertainties in black hole mass measurements are a factor of four, which are typical for the single-epoch reverberation mapping method. Recently, the accuracy of black hole mass measurement has been significantly improved to 0.2 - 0.4 dex with the velocity resolved reverber- ation mapping method. The black hole spin can be well constrained if the mass measurement accuracy is 50%. In the accretion disk corona scenario, a fraction of power dissipated in the disk is transported into the corona, and therefore the accretion disk is thinner than a bare disk for the same mass accretion rate, because the radiation pressure in the disk is reduced. We find that the thin disk approximation, H/R ≤0. 1, is still valid if 0.3 〈 m 〈 0.5, provided half of the dissipated power is radiated in the corona above the disk.

Transport in Astrophysics: III. Diffusion from the Galactic Plane

New solutions, for the stationary and temporary states, are derived for the 1D diffusion of cosmic rays in the presence of losses. The new results are applied to the latitude profile of radiation emitted above the galactic plane. Percolation theory for a spiral galaxy coupled with the evolution of the super-bubbles allows building a model for the radiation of a spiral galaxy as seen face on. The annulus of radiation of our galaxy is also simulated and the excess of radiation observed at the centre of our galaxy is explained by the sine law which arises in the theory of the image.

Systematic comparison of initial velocities for neutron stars in different models

I have studied the initial velocity（Maxwellian and exponential distributions） and the scale height of isolated old（aged≥10^9yr） neutron stars（NSs） at different Galactocentric distances R in three population models. The smooth time-independent 3-D axisymmetric gravitational potentials（MiyamotoNagai and Paczy n′ski models） were also used. The correlation between these quantities significantly affects the shapes of the profiles and distributions of the simulated sample, because the differences in the initial kick can arise from differences in the formation and evolution of NSs with other physical parameters. The scale height of the density distribution increases systematically with R. I have also shown that the distribution of old NSs in these population models agrees with the observed structure of the Galaxy in terms of initial velocities（1-D and 3-D）, as well as the scale height distributions. These distributions tend to have an asymptotic behavior at the point R = 2.75 kpc. This means that the quality of the models can be described in terms of a mean of the fitted Gaussian, and this could also give an overall perspective of the phase space properties of nearby old NSs on a given gravitational potential.

Mapping the Milky Way with LAMOSTⅠ:method and overview

We present a statistical method to derive the stellar density profiles of the Milky Way from spectroscopic survey data, taking into account selection effects. We assume the selection function, which can be altered during observations and data reductions, of the spectroscopic survey is based on photometric colors and magnitude. Then the underlying selection function for a line-of-sight can be recovered well by comparing the distribution of the spectroscopic stars in a color-magnitude plane with that of the photometric dataset. Subsequently, the stellar density profile along a line-of-sight can be derived from the spectroscopically measured stellar density profile multiplied by the selection function. The method is validated using Galaxia mock data with two different selection functions. We demonstrate that the derived stellar density profiles reconstruct the true ones well not only for the full set of targets, but also for sub-populations selected from the full dataset. Finally, the method is applied to map the density pro- files for the Galactic disk and halo, using the LAMOST RGB stars. The Galactic disk extends to about R = 19 kpc, where the disk still contributes about 10% to the total stellar surface density. Beyond this radius, the disk smoothly transitions to the halo without any truncation, bending or breaking. Moreover, no over-density corresponding to the Monoceros ring is found in the Galactic anti-center direction. The disk shows moderate north-south asymmetry at radii larger than 12 kpc. On the other hand, the R-Z tomographic map directly shows that the stellar halo is substantially oblate within a Galactocentric radius of 20 kpc and gradually becomes nearly spherical beyond 30 kpc.

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.