The environmental dependence of u-, g-, r-, i-, and z-band luminosities for galaxies above and below the value of Mr*

Using two volume-limited Main galaxy samples of the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we have explored the difference of the environmental dependence of u-, g-, r-, i-, and z-band luminosities between galaxies above and below the value of M _r^*. It turns out that in the luminous volume-limited sample, all the five band luminosities strongly correlate with local environments. Because the u-band luminosity of galaxies still strongly depends on local environments in the faint volumelimited sample, we conclude that M _r^* is not an important characteristic parameter for the environmental dependence of the u-band luminosity. It is worth noting that for the u-band, the subsample at low density has a higher proportion of luminous galaxies and a lower proportion of faint galaxies than the one at high density, which is opposite to widely accepted conclusion: luminous galaxies exist preferentially in the densest regions of the universe, but faint galaxies are located preferentially in low density regions. Our results show that the environmental dependence of luminosity is not a single trend in different luminosity regions and for different bands.     

Constraining the gravitational redshift of a neutron star from the Σ-meson well depth

The effect of the Σ-meson well depth on the gravitational redshift is examined within the framework of relativistic mean field theory for the baryon octet system. It is found that, for a stable neutron star, the gravitational redshift increases with the central energy density increase or with the mass increase but decreases as the radius increases. Considering a change of U_S^(N)U_{\Sigma}^{(N)} from −30 MeV to 30 MeV, for a stable neutron star the gravitational redshift near to the maximum mass increases. In addition, it is also found that the growth of the U_S^(N)U_{\Sigma}^{(N)} makes the gravitational redshift as a function of M _max/R increase, the higher the U_S^(N)U_{\Sigma}^{(N)} the less the change in the gravitational redshift.     

Potential energy of gravitationally interacting disk galaxies

Methods are developed for analysing the gravitational properties of disks having circularly symmetric distribution of matter. It is shown how this can be conveniently done by assuming that the surface density distribution may be approximated by a polynomial in ascending powers of the distance from the centre of the configuration. A theory has been developed to determine the gravitational potential of a single disk at any point in space in terms of the coefficients of the polynomial defining the surface distribution of matter, and the potential energy of two disks of arbitrary separation and orientation due to their mutual gravitational attraction. The basic functions, required for obtaining the potential in the plane of the disk and the mutual potential energy of two coplanar disks, have been tabulated. Two overlapping coplanar disks attract just like mass-points at a certain separation,r _c , of their centres. The force of attraction of disks is less than the force of attraction of mass-points having masses equal to the masses of the disks, if the separation of the centres is less thanr _c , and greater if the separation is greater thanr _c . For typical galaxies of equal radiiR,r _c ≈R.     

Analysis of the properties of galaxy clusters in the Leo supercluster region

We analyze the properties of galaxy clusters in the region of the Leo supercluster using observational data from the SDSS and 2MASS catalogs. We have selected 14 galaxy clusters with a total dynamical mass of 1.77 × 10¹⁵ M _⊙ in the supercluster region 130 by 60 Mpc in the plane of the sky (z ≃ 0.037). The composite luminosity function of the supercluster is described by a Schechter function with parameters that, within the error limits, correspond to field galaxies and does not differ from the luminosity function of the richer Ursa Major (UMa) supercluster for the same luminosity range (the bright end). The luminosity functions of early-type and late-type galaxies in Leo at the faint end are characterized by a sharp decrease (α = −0.60±0.08) and a steep increase (α = −1.44± 0.10) in the number of galaxies, respectively. In the virialized cluster regions, the fraction of early-type galaxies selected by the u-r color, bulge contribution, and concentration index among the galaxies brighter than M _K ^* + 1 is, on average, 62%. This fraction is smaller than that in the UMa supercluster at a 2–3σ level. The near-infrared luminosities of galaxy clusters down to a fixed absolute magnitude correlate with their masses almost in the same way as for other samples of galaxy clusters (L _200,K ∝ M ₂₀₀^0.63±0.11)).     

Seeable universe and its accelerated expansion: an observational test

From the equivalence principle, one gets the strength of the gravitational effect of a mass M on the metric at position r from it. It is proportional to the dimensionless parameter β ²=2GM/rc ², which normally is ?1. Here G is the gravitational constant, M the mass of the gravitating body, r the position of the metric from the gravitating body and c the speed of light. The seeable universe is the sphere, with center at the observer, having a size such that it shall contain all light emitted within it. For this to occur one can impose that the gravitational effect on the velocity of light at r is zero for the radial component, and non zero for the tangential one. Light is then trapped. The condition is given by the equality R _g =2GM/c ², where R _g represents the radius of the seeable universe. It is the gravitational radius of the mass M. The result has been presented elsewhere as the condition for the universe to be treated as a black hole. According to present observations, for the case of our universe taken as flat (k=0), and the equation of state as p=?ρc ², we prove here from the Einstein’s cosmological equations that the universe is expanding in an accelerated way as t ², a constant acceleration as has been observed. This implies that the gravitational radius of the universe (at the event horizon) expands as t ². Taking c as constant, observing the galaxies deep in space this means deep in time as ct, linear. Then, far away galaxies from the observer that we see today will disappear in time as they get out of the distance ct that is <R _g . The accelerated expanding vacuum will drag them out of sight. This may be a valid test for the present ideas in cosmology. Previous calculations are here halved by our results.     

A semiquantitative general-relativistic model of quasar Markarian 205 interpreted as a massive black hole ejected from NGC 4319

In 1979 I developed a special-relativistic analysis explaining the discrepancy of observed redshifts of spiral NGC 4319 and its companion quasar Markarian 205 by considering besides the Lorentz time dilatation also the gravitational redshift due to the gravitational field of Markarian 205 interpreted in terms of accretion of mass onto a black hole ejected from NGC 4319. In the present paper, a general-relativistic analysis is given. Numerical results of the special and general theories do not differ from each other significantly and admit the conclusion that the radius,r, of the radiating region of Markarian 205 is of the order of the tidal radius of black hole. Several models for various values of the ratio ofr to the Schwarzschild radius,r _s, are constructed. Models with 8.5r/r _s8.7 seem to be most realistic. It becomes clear that the interpretation of quasars in terms of huge black holes accreting stars can explain, in principle, the observed redshifts of quasars ejected from parent galaxies.     

Gravitational potential energy of a disk-sphere pair of galaxies

Algebraic expressions are obtained for the interaction potential energy of a pair of galaxies in which one is disk shaped and the other spherical. The density distribution in the disk galaxy is represented by a polynomial in ascending powers of the distance from the centre of the disk while the density distribution in the spherical galaxy is represented by the superposition of spherical polytropes of integral indices. The basic functions required for obtaining the interaction potential energy of a coplanar disk-sphere pair of galaxies are tabulated. The forces of attraction between a coplanar disk-sphere pair of galaxies are shown graphically for two density models of disk and spherical galaxies. An overlapping coplanar disk-sphere pair of galaxies attract just like two mass-points at a certain separation,r _c, of their centres. The force of attraction is less than that of two mass-points having masses equal to the masses of the two galaxies, if the separation of the centres is less thanr _c, and greater if the separation is greater thanr _c.For a typical coplanar disk-sphere pair of galaxies (the density of the disk is represented by Model II and of the sphere by a polytropic indexn=4) of equal radii, we note the following. At a separation of 0.79R, R being the common radius of the two galaxies, the force of attraction between the pair is the same as if the entire mass of each galaxy is concentrated at its centre. The mass-point model for the two galaxies will overestimate the force of attraction by more than a factor of 10 if the separation is less than 0.36R. For separation greater than the radii of the galaxies the mass-point model will underestimate the force but the departure in this case is less than 33%.     

The Potential Well-Depth ${U_{\Sigma}^{(N)}}$ Constraints on the Surface Gravitational Red-shift of a Proto Neutron Star

The influence of the potential well depth U_S^(N)U_{\Sigma}^{(N)} of Σ in nuclear matter on the surface gravitational red-shift of a proto neutron star is examined within the framework of the relativistic mean field theory for the baryon octet system. It is found that as U_S^(N)U_{\Sigma}^{(N)} increases from −35 MeV to +35 MeV, the surface gravitational red-shift increases and the influence of the negative U_S^(N)U_{\Sigma}^{(N)} on the surface gravitational red-shift is larger than that of the positive ones. Furthermore, the M _max/R and the surface gravitational red-shift corresponding to the maximum mass all increase as the U_S^(N)U_{\Sigma}^{(N)} increases, M _max and R being the maximum mass of the proto neutron star and the corresponding radius respectively.     

Clustering evolution between z=1 and today

We present results of an investigation of clustering evolution of field galaxies between a redshift of z ∼ 1 and the present epoch. The current analysis relies on a sample of ∼ 14000 galaxies in two fields of the COMBO 17 survey. The redshift distribution extends to z ∼ 1. The amplitude of the three-dimensional correlation function can be estimated by means of the projected correlation function w(r _p ). The validity of the deprojection was tested on the Las Campanas Redshift Survey (LCRS). In a flat cosmology with non-zero cosmological constant for bright galaxies (M _B ≤-18) the clustering growth is proportional to (1+z) ^-2. However, the measured clustering evolution clearly depends on Hubble type. While locally the clustering strength of early type galaxies is equal to that of the bright galaxies, at high redshifts they are much stronger clustered, and thus the clustering has to evolve much more slowly. This revised version was published online in August 2006 with corrections to the Cover Date.     

Numerical exploration of the photogravitational restricted five-body problem

We study numerically the restricted five-body problem when some or all the primary bodies are sources of radiation. The allowed regions of motion as determined by the zero-velocity surface and corresponding equipotential curves, as well as the positions of the equilibrium points are given. We found that the number of the collinear equilibrium points of the problem depends on the mass parameter β and the radiation factors q _i , i=0,…,3. The stability of the equilibrium points are also studied. Critical masses associated with the number of the equilibrium points and their stability are given. The network of the families of simple symmetric periodic orbits, vertical critical periodic solutions and the corresponding bifurcation three-dimensional families when the mass parameter β and the radiation factors q _i vary are illustrated. Series, with respect to the mass (and to the radiation) parameter, of critical periodic orbits are calculated.     

Presence of LaO, ScO and VO Molecular Lines in Sunspot Umbral Spectra

High-resolution Fourier Transform Spectrometer sunspot umbral spectra of the National Solar Observatory/National Optical Astronomy Observatory at Kitt Peak were used to detect rotational lines from 19 electronic transition bands of the molecules LaO, ScO and VO, in the wavenumber range of 11 775 to 20 600 cm⁻¹. The presence of lines from the following transitions is confirmed: A ² Π _r1/2 – X ² Σ ⁺(0, 0; 0, 1), A ² Π _r3/2 – X ² Σ ⁺(1, 0), B ² Σ ⁺ – X ² Σ ⁺(0, 0; 0, 1; 1, 0) and C ² Π _r1/2 – A′²Δ _r3/2(0, 0; 1, 1) of LaO; A ² Π _r3/2 – X ² Σ ⁺(0, 0), A ² Π _r1/2 – X ² Σ ⁺(0, 0) and B ² Σ ⁺ – X ² Σ ⁺(0, 0) of ScO; and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 1; 1, 0; 0, 2) and (2, 0) of VO. However, the presence of A ² Π _r3/2 – X ² Σ ⁺(0, 0) and C ² Π _r3/2 – A′²Δ _r5/2(0, 0; 1, 1) of LaO and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 0) of VO are found to be doubtful because the lines are very weak, and detections are difficult owing to heavy blending by strong rotational lines of other molecules. Equivalent widths are measured for well-resolved lines and, thereby, the effective rotational temperatures are estimated for the systems for which the presence is confirmed.     

Mass-to-luminosity ratio in binary galaxies

We have compared the observed distribution of the quantity log(V ₂ ² r_P) for a sample of 233 pairs of galaxies with Monte-Carlo simulations. From such an analysis we have derived an average mass-to-luminosity ratiosM/L _B =18±11. Our result is consistent with a linear increase of the mass with radius at least until distances of about 30 kpc.     

A theory of galactic mass and rotation curves

The goal of this paper is to account for the complete observed rotation curves of disk galaxies without dark matter. To attain that goal, use is made of a conservation law from stability theory of linear waves, leading to a vector-based theory of gravitation. In the theory, galactic centers are sites of strong gravitational fields. The new theory predicts extra matter at the center of disk galaxies, which is well-known to be consistent with intergalactic dynamics. For given disk radiusr ₀ and edge tangential speedv, the greater the deviation of a rotation curve from linear (solid disk rotation), the greater the mass of the galaxy as a multiple of Newtonian massr ₀v²/G, up to a factor of about 1000. In an approximate calculation it turns out that disk density (r) (in kg m^–2) is proportional to 1/r for typical rotation curves. Rotation is characterized by two constants which in turn are determined by the edge speed and mass distribution. Not just any curve shape can be so obtained; in fact, the theoretically possible curves correspond to observed curves.     

A calculation of structural parameters of spherical stellar systems by means of characteristic functions method. I. Theory

To calculate structural parameters of stellar systems such as an effective radius and central space (or surface) density, the method of characteristic functions is suggested. The characteristic function of the system is a Fourier image of their normalized space density profile f₃(r). In the case of spherical symmetry the probability distribution of r (Q₃(r) = (3/a³)r²f₃(r)) and its orthogonal projections have the same characteristic functions. This fact is used to calculate the effective radii of a few star cluster models (King law, Plummer model and Gausian profile). It is shown, that the characteristic function for King law clusters tends to a finite generalised function if the concentration parameter c is large. The expression for the effective radius (at c ≫ 1) is given. The formula of the effective radius in the Plummer model as well as the relation between the one-dimensional central velocity dispersion and the root mean square velocity are obtained. It is shown, that in the Gaussian model and for King law clusters the effective radius (half-mass visual radius) can differ from the effective (harmonic) radius a few times. This fact should be taken into account in estimating the mass-to-light ratio from the virial mass of such systems using the King radius.     

Changes in sizes and shapes of spherical galaxies in head-on collisions

Head-on collisions of two identical spherical galaxies are studied for two initial velocities (1) nearly equal to and (2) greater than the capture velocity. Orbits of about 500 representative stars are computed taking into account the effects of dynamical friction in the motion of the galaxies. From the computer studies the changes in the structure of the galaxies are deduced. The galaxies contract at closest approach and expand as they recede from each other. When the initial velocity is nearly equal to the capture velocity, the mean radius expands to almost double its size and the galaxies have a prolate structure until the closest approach with the longer axis in the direction of motion. The prolate structure is destroyed as the galaxies recede. For larger collision velocity (V ∼ 1.5 V_cap), the mean radius expands by 50 per cent and the galaxies are prolate until the closest approach and distinctly oblate after the collision. The fractional increase in the binding energy is 0.46 in the first case and 0.30 in the second case.     

Photometric Properties of Clusters of Galaxies

We present CCD photometry of 16 Abell clusters and one cluster candidate found in POSS-II field 861. The images were taken at the 0.9 m Telescope at Cerro Tololo, in the g, r and i filters of the Gunn–Thuan system. We tested the idea proposed by Garilli et al. (1996) that there is a population of unusually red galaxies which could be associated with either the field or clusters. Garilli et al. (1996) suggest that these galaxies have anomalously red colours, but we find that these objects are all near the limiting magnitude of the images (20^m<r<22^m) and have colours that are consistent with those expected for stars or field galaxies at z∼0.7. This revised version was published online in July 2006 with corrections to the Cover Date.     

Franck-Condon factors and r-centroids for certain band systems pf astrophysical molecule BeF

The Franck-Condon factors and r-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable numerical integration procedure for the bands of B ² Σ⁺ - X ² Σ⁺, C ²Σ⁺ - X ² Σ⁺ andC ² Σ⁺ - A ² Π_r systems of the astrophysical molecule BeF, using a suitable potential. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimation of potential energy curves, dissociation energies, franck-condon factors and r-centroids of comet interesting molecules

The experimental potential energy curves for the different electronic states of molecules like CN, CO and CS observed in comets are constructed by using the Rydberg-Klein-Rees method as modified by Vanderslice et al. The ground state dissociation energies are determined by curve fitting technique using the five parameter Hulburt-Hirschfelder (H-H)function. The estimated dissociation energies are 7.63 ± 0.187, 10.95 ±0.224 and 7.27 ± 0.152 eV for CN, CO and CS respectively. These values are in good agreement with the literature values. Estimated dissociation energies of CN, CO and CS are used in the relation given by Gaydon and ionization potentials are evaluated for CO and CS molecules. The estimated ionization potentials are 13.92and 12.15 eV for CO and CS molecules respectively. The r-centroids and Franck-Condon factors (FC Factors) for the band system of a ³Π_r – X¹Σ⁺ (a – X) and A¹Π – X ¹Σ⁺ (A -X) of CN, A ²Π_i – X²Σ⁺ (A – X) and B²Σ⁺-X²Σ⁺ (B – X) of CO and a ³Π_r – X¹Σ⁺ (a – X) of CS molecules have been calculated employing an approximate analytical methods of Jarmain and Fraser and Nicholls and Jarmain. The absence of the bands in these systems are explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study of the galaxy DDO 68: New evidence for its youth

DDO 68 (UGC 5340) is the second most metal-poor star-forming galaxy (12 + log(O/H) = 7.14). Its peculiar optical morphology and its HI distribution and kinematics are indicative of a merger origin. We use the u, g, r, and i photometry based on the SDSS images of DDO 68 to estimate its stellar population ages. The Hα images of DDO 68 were used to select several representative regions without nebular emission. The derived colors were analyzed by comparison with the PEGASE2 evolutionary tracks for various star formation (SF) scenarios, including the two extreme cases: (i) an instantaneous starburst and (ii) continuous SF with a constant rate. The (u − g) and (g − r) colors for all of the selected regions are consistent with the scenario of several “instantaneous” SF episodes with ages between ∼0.05 and ∼1 Gyr. The total mass of the visible stars in DDO 68 was estimated by comparing the colors and fluxes of the observed stellar subsystems with PEGASE2 models to be ∼2.4 × 10⁷ M _⊙. This accounts for ∼6% of the total baryonic mass of the galaxy. All of the available data are consistent with the fact that DDO 68 is a very rare candidate for young galaxies. The bulk of its stars were formed during the recent (with the first encounter ∼1 Gyr ago) merger of two very gas-rich disks. DDO 68 is closest in its properties to cosmologically young low-mass galaxies. This article was submitted by the authors in English.