ChJAA, 2006, Vol.6, No.2 -- by Aiying Zhou

On the Calculation of Lyapunov Indicators with Post-stabilization in a Weyl Field

Xin Wu^1,2, Hong Zhang², Xiao-Sheng Wan²

¹ Department of Physics, Nanchang University, Nanchang 330047; xwu@ncu.edu.cn
² Department of Astronomy, Nanjing University, Nanjing 210093; xinwu@nju.edu.cn

Abstract
We present details of a work aiming at the overestimation of Lyapunov exponents defined by the geodesic deviation equations in the previous work. The geodesic deviation vector with post-stabilization is used to compute the fast Lyapunov indicator, considered to be a very sensitive tool for discrimination between ordered or weakly chaotic motions. We make a detailed study of the dynamics in the superposed Weyl field between a black hole and shell of octopoles by using the fast Lyapunov indicator with the Poincaré surface of section. In particular, we examine the effects on the dynamics around the fixed points, of varying one of the three parameters (specific energy E, specific angular momentum L and octopolar moment $\mathcal{O})$ , while keeping the other two fixed, and identify the intervals of the varying parameter where the motion is regular or chaotic.

Key Words: black hole physics -- stars: circumstellar matter -- chaos -- methods: numerical
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Concordance of Kinematics and Lensing of Elliptical Galaxies with WMAP Cosmology

HongSheng Zhao^1,2 and Bo Qin¹

¹ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012;
² SUPA, University of St. Andrews, KY16 9SS, UK; hz4@st-andrews.ac.uk

Abstract
We explore degeneracies in strong lensing model so to make time delay data consistent with the WMAP (Wilkinson Microwave Anisotropy Probe) cosmology. Previous models using a singular isothermal lens often yield a time delay between the observed multiple images too small than the observed value if we ``hardwire'' the now widely quoted post-WMAP ``high'' value of the Hubble constant ( $H_0 \sim 71 \pm 4\kmsmpc$ ). Alternatively, the lens density profile (star plus dark matter) is required to be locally steeper than r^-2 (isothermal) profile near the Einstein radius (of the order 3kpc) to fit the time delays; a naive extrapolation of a very steep profile to large radius would imply a lens halo with a scale length of the order only 3kpc, too compact to be consistent with CDM. We explore more sophisticated, mathematically smooth, positive lens mass density profiles which are consistent with a large halo and the post-WMAP H₀. Thanks to the spherical monopole degeneracy, the ``reshuffling'' of the mass in a lens model does not affect the quality of the fit to the image positions, amplifications, and image time delays. Even better, unlike the better-known mass sheet degeneracy, the stellar mass-to-light and the H₀ value are not affected either. We apply this monopole degeneracy to the quadruple imaged time-delay system PG1115+080. Finally we discuss the implications of the time delay data on the newly proposed relativistic MOND theory.

Key Words: cosmological parameters -- dark matter -- distance scale -- gravitational lensing
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The Feasibility of Constraining Dark Energy Using LAMOST Redshift Survey

Lei Sun, Meng Su, Zu-Hui Fan

Department of Astronomy, Peking University, Beijing 100871; sunl@bac.pku.edu.cn

Abstract
We consider using future redshift surveys with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) to constrain the equation of state of dark energy $\omega$ . We analyze the Alcock & Paczynski (AP) effect imprinted on the two-point correlation function of galaxies in redshift space. The Fisher matrix analysis is applied to estimate the expected error bounds of $\omega_0$ and $\omega_a$ from galaxy redshift surveys, $\omega_0$ and $\omega_a$ being the two parameters in the equation of state parametrization $\omega(z)=\omega_0+\omega_a z/(1+z)$ . Strong degeneracies between $\omega_0$ and $\omega_a$ are found. The direction of the degeneracy in $\omega_0-\omega_a$ plane, however, rotates counter-clockwise as the redshift increases. LAMOST can potentially contribute in the redshift range up to 0.5. In combination with other high redshift surveys, such as the proposed Kilo-Aperture Optical Spectrograph project (KAOS), the joint constraint derived from galaxy surveys at different redshift ranges is likely to efficiently break the degeneracy of $\omega_0$ and $\omega_a$ . We do not anticipate that the nature of dark energy can be well constrained with LAMOST alone, but it may help to reduce the error bounds expected from other observations, such as the Supernova/Acceleration Probe (SNAP).

Key Words: Cosmology: theory -- galaxies: distances and redshifts -- galaxy clustering -- large-scale structure of Universe
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Comptonization and Reprocessing Processes in Accretion Disks: Applications to the Seyfert 1 Galaxies NGC 5548 and NGC 4051

Fan Zhang and Xue-Bing Wu

Department of Astronomy, Peking University, Beijing 100871; wuxb@bac.pku.edu.cn

Abstract
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 $r_{\min}$ , the corona radius r_s, the temperature KT_e and the optical depth $\tau_0$ 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.

Key Words: accretion - accretion disks - galaxies: active - galaxies: individual (NGC 5548, NGC 4051) - galaxies: Seyfert - X-rays: galaxies
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The Inclination, Pitch Angle and Forbidden Radius of Spiral Arms of PGC 35105

Tao Hu¹, Zheng-Yi Shao^2,3 and Qiu-He Peng^1,4,5

¹ Department of Astronomy, Nanjing University, Nanjing 210093; taohu@nju.edu.cn
² Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030
³ Joint Institute for Galaxies and Cosmology, Chinese Academy of Sciences, Shanghai, 200030
⁴ Joint Astrophysics Center of Chinese Academy of Sciences-Peking University, Beijing 100871
⁵ The Open Laboratory of Cosmic Ray and High Energy Astrophysics, Chinese Academy of Sciences, Beijing 100049

Abstract
We have studied some properties including surface brightness in the u, g, r, i, and z bands of the nearly face-on galaxy PGC 35105. By subtracting a model surface brightness distribution from the observed image we obtain the residual image that shows only the spiral arms freed from the contamination by the bulge. From this we measured the inclination, pitch angle, and forbidden radius (identified with the innermost point of the arm) for each of the two arms; and that for each of the five observing bands. We found these three parameters are largely independent of the observing band.

Key Words: galaxies: fundamental parameters -- galaxies: spiral -- galaxies: structure -- galaxies: surface brightness -- galaxies: individual (PGC 35105)
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A Deprojection Analysis of Abell 1650 with XMM-Newton

Shu-Mei Jia^1,2, Yong Chen² and Li Chen¹

¹ Department of Astronomy, Beijing Normal University, Beijing 100875; jiasm@mail.ihep.ac.cn
² Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049

Abstract
We revisit the XMM-Newton observation of the galaxy cluster Abell 1650 with a deprojection technique. We find that the radial deprojected spectra of Abell 1650 can be marginally fitted by a single-temperature model. In order to study the properties of the central gas, we fit the spectra of the central two regions with a two-temperature model. The fits then become significantly better and the cool gas about 1 $\sim$ 2keV can be connected with the gas cooling. Fitting the central spectrum ( $r\le1'$ ) by using a cooling flow model with an isothermal component yields a small mass deposition rate of 10⁺¹¹_-7 $M_{\odot}$ yr^-1, while the standard cooling flow model can not fit this spectrum satisfactorily except that there exists a cut-off temperature having a level of about 3keV. From the isothermal model we derive the deprojected electron density profile n_e(r), and then together with the deprojected temperature profile the total mass and gas mass fraction of cluster are also determined. We compare the properties of Abell 1650 with those of Abell 1835 (a large cooling flow cluster) and some other clusters, to explore the difference in properties between large and small cooling flow cluster, and what causes the difference in the cooling flow of different clusters. It has been shown that Abell 1835 has a steeper potential well and thus a higher electron density and a lower temperature in its center, indicating that the shape of the gravitational potential well in central region determines the cooling flow rates of clusters. We calculate the potential, internal and radiated energies of these two clusters, and find that the gas energies in both clusters are conserved during the collapsing stage.

Key words: galaxies: clusters: individual: Abell 1650 --galaxies: cooling flows -- galaxies: evolution -- galaxies: intergalactic medium -- X-rays: galaxies: clusters
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A Catalog of Luminous Infrared Galaxies in the IRAS Survey and Second Data Release of SDSS

Chen Cao^1,2, Hong Wu¹, Jian-Ling Wang^1,2, Cai-Na Hao^1,2, Zu-Gan Deng^3,1, Xiao-Yang Xia⁴ and Zhen-Long Zou¹

¹ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012; caochen@bao.ac.cn
² Graduate School of Chinese Academy of Sciences, Beijing 100049
³ College of Physical Sciences, Graduate School of Chinese Academy of Sciences, Beijing 100049
⁴ Department of Physics, Tianjin Normal University, Tianjin 300074

Abstract
We selected a sample of luminous infrared galaxies by cross-identification of the Faint Source Catalogue (FSC) and Point Source Catalogue (PSC) of the IRAS Survey with the Second Data Release of the SDSS. The size of our sample is 1267 for FSC and 427 for PSC by using the 2 $\sigma$ significance level cross-section. The ``likelihood ratio" method is used to estimate the individual's reliability and for defining two more reliable subsamples (908 for FSC and 356 for PSC). A catalog of infrared, optical and radio data is compiled and will be used in further work. Some statistical results show that luminous infrared galaxies are quite different from ultra-luminous infrared galaxies. The AGN fractions of galaxies at different infrared luminosities and the radio-infrared correlations are consistent with the previous studies.

Key Words: catalogs -- galaxies: statistics -- infrared: galaxies
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Molecular Gas Distribution around the Supernova Remnant G40.5-0.5

Ji Yang^1,3, Jie-Long Zhang², Zhi-Yong Cai^1,3, Deng-Rong Lu^1,3 and You-Heng Tan²

¹ Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008; jiyang@pmo.ac.cn
² Key Laboratory of Particle Astrophysics, Institute of High-Energy Physics, Chinese Academy of Sciences, Beijing 100049
³ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012

Abstract
The distribution of dense molecular gas around the supernova remnant G40.5-0.5 has been investigated by radio spectroscopic observations in the CO (J=1-0) transition. The molecular gas is found to extend over the entire region of G40.5-0.5. A molecular shell, with a diameter of $\sim26'$ , coincides with the ionized gas as revealed by the cm-radio observations. This coincidence, along with the velocity discontinuity following the shell, provides direct evidence for interaction between the ionized gas and the dense molecular gas. No clear evidence for cosmic-ray acceleration can be identified from this SNR as previously suggested, due to positional uncertainty in relating the SNR shell defined by CO to the EGRET gamma-ray sources, GRO J1904+06, from the gamma-ray observations.

Key Words: ISM: supernova remnant -- ISM: clouds -- radio lines: ISM-- supernovae: individual (G40.5-0.5)
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Current Flows in Pulsar Magnetospheres

Ren-Xin Xu, Xiao-Hong Cui and Guo-Jun Qiao

Department of Astronomy, School of Physics, Peking University, Beijing 100871; r.x.xu@pku.edu.cn

Abstract
The global structure of current flows in pulsar magnetosphere is investigated, with rough calculations of the circuit elements. It is emphasized that the potential of the critical field lines (the field lines that intersect the null surface at the light cylinder radius) should be the same as that of interstellar medium, and that pulsars whose rotation axes and magnetic dipole axes are parallel should be positively charged, in order to close the pulsar's current flows. The statistical relation between the radio luminosity and pulsar's electric charge (or the spindown power) may hint that the millisecond pulsars could be low-mass bare strange stars.

Key Words: pulsars: general -- stars: neutron -- dense matter
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A Non-axisymmetric Spherical $\alpha^2$ -Dynamo

Jie Jiang and Jing-Xiu Wang

National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012; jiangjie@ourstar.bao.ac.cn

Abstract
Using the Chebyshev-tau method, the generation of oscillatory non-axisymmetric stellar magnetic fields by the $\alpha^{2}$ -dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert & Zhang, the spherical $\alpha^{2}$ -dynamo consists of a fully convective spherical shell with inner radius r_i and outer radius $r_{\rm o}$ . A comparison of the critical dynamo numbers of axisymmetric and $\phi$ -dependent modes for different thicknesses of the convective shell and different $\alpha$ -profiles leads to the following qualitative results: (i) when the angular factor of $\alpha$ -profile is $\sin^{n}\theta\cos\theta$ (n=1, 2, 4) the solutions of the $\alpha^{2}$ -dynamo are oscillatory and non-axisymmetric, (ii) the thinner the convective shell, the more easily is the non-axisymmetric mode excited and the higher is the latitudinal wave number, (iii) the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.

Key Words: stars: magnetic fields -- methods: numerical
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Circular Polarization in Pulsar Integrated Profiles: Updates

Xiao-Peng You and Jin-lin Han

National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012; xpyou@bao.ac.cn

Abstract
We update the systematic studies of circular polarization in integrated pulse profiles by Han et al. Data of circular polarization profiles are compiled. Sense reversals can occur in core or cone components, or near the intersection between components. The correlation between the sense of circular polarization and the sense of position angle variation for conal-double pulsars is confirmed with a much large database. Circular polarization of some pulsars has clear changes with frequency. Circular polarization of millisecond pulsars is marginally different from that of normal pulsars.

Key Words: polarization -- pulsars: general
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Transequatorial Filament Eruption and Its Link to a Coronal Mass Ejection

Jing-Xiu Wang^{1, 2},Gui-Ping Zhou¹, Ya-Yuan Wen¹, Yu-Zong Zhang¹, Hua-Ning Wang¹, Yuan-Yong Deng¹, Jun Zhang¹ and Louise K. Harra^{2, 1}

¹ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012; wangjx@ourstar.bao.ac.cn
² Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK

Abstract
We revisit the Bastille Day flare/CME Event of 2000 July 14, and demonstrate that this flare/CME event is not related to only one single active region (AR). Activation and eruption of a huge transequatorial filament are seen to precede the simultaneous filament eruption and flare in the source active region, NOAA AR9077, and the full halo-CME in the high corona. Evidence of reconfiguration of large-scale magnetic structures related to the event is illustrated by SOHO EIT and Yohkoh SXT observations, as well as, the reconstructed 3D magnetic lines of force based on the force-free assumption. We suggest that the AR filament in AR9077 was connected to the transequatorial filament. The large-scale magnetic composition related to the transequatorial filament and its sheared magnetic arcade appears to be an essential part of the CME parent magnetic structure. Estimations show that the filament-arcade system has enough magnetic helicity to account for the helicity carried by the related CMEs. In addition, rather global magnetic connectivity, covering almost all the visible range in longitude and a huge span in latitude on the Sun, is implied by the Nançay Radioheliograph (NRH) observations. The analysis of the Bastille Day event suggests that although the triggering of a global CME might take place in an AR, a much larger scale magnetic composition seems to be the source of the ejected magnetic flux, helicity and plasma. The Bastille Day event is the first described example in the literature, in which a transequatorial filament activity appears to play a key role in a global CME. Many tens of halo-CME are found to be associated with transequatorial filaments and their magnetic environment.

Key Words: Sun: corona - Sun: coronal mass ejections (CMEs) - Sun: activity - Sun: magnetic fields
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The Gyrosynchrotron Radiation Spectrum in a Nonuniform Source

Ai-Hua Zhou

Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008; zhouah@pmo.ac.cn

Abstract
Effects of the energy spectral index $\delta$ , low energy cutoff E₀ and number density N of energetic electrons on gyrosynchrotron spectrum are investigated for a model source with a nonuniform magnetic field. It is found that the flux density $S_{\nu \mp }$ of the x-mode and o-mode systematically increase with increasing E₀, N and with decreasing $\delta$ . The peak frequency of the spectrum, $\nu _p$ , also systematically increases as increasing E₀ and N, but it may not depend on $\delta$ . The gyrosynchrotron radiation in the nonuniform case is polarized predominately in the x-mode at $\nu \geq 3$ GHz. A sense reversal of circular polarization also occurs but at much lower frequencies ( $\nu \leq 3$ GHz). The reversal frequency also increases with increasing E₀ and N, but it perhaps is independent of $\delta$ .

Key Words: Sun: flares -- Sun: radio radiation
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ChJAA, 2006, Vol.6, No.2

Chinese Journal of Astronomy and Astrophysics: Online Edition

http://www.chjaa.org

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