A classification of galactic collisions for galaxies of unequal dimensions

The earlier work on classification of galactic collisions for identical galaxies is extended to the situations where the two colliding galaxies differ in mass and dimension. We consider collisions between galaxies of masses 10⁷, 10⁹, 10¹¹ and 10¹³ M and let their radii be 0.1, 1, 10 and 100 kpc, respectively. The density distribution in both galaxies is represented by that of a polytrope of indexn=4. The type of collision is determined for head-on collisions for initial relative velocities 500, 1000, 2000 and 3000 km s^–1. The corresponding final velocities are also indicated.     

Quasinormal modes of scalar perturbation around a quantum-corrected Schwarzschild black hole

In this paper, we evaluate quasinormal modes (QNMs) of scalar perturbations around a quantum-corrected Schwarzschild black hole by using the third order Wentzel-Kramers-Brillouin (WKB) approximation method. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, the QNMs of the black hole damp more slowly when increasing the quantum correction factor (a), and oscillate more slowly.     

Gravitational potential energy of interpenetrating spherical galaxies in Hernquist’s model

Hernquist’s (1990) mass model for spherical galaxies and bulges described by the deVaucouleur’s profile gives analytical expressions for the density profile and the potential. These have been used to derive a simple and exact analytical expression for the gravitational potential energy of a pair of interpene-trating spherical galaxies represented by this model. The results are compared with those for polytropic and Plummer models of galaxis.     

The dynamics of head-on collisions of spherical stellar systems

Energy changes in a head-on collision between two unequal Plummer model stellar systems (galaxies) are studied analytically under the impulsive approximation. The variation of the disruptive effects within and the mass escape from systems widely differing in mass and scalelength ratios are determined and some physical implications regarding the dynamical stability of the systems undergoing head-on collisions are indicated. It is found that if two systems differ considerably in size, both systems generally survive the collision if (i) the mass of the bigger is greater than about six times the mass of the smaller and (ii) the density of the smaller is more than about twenty-five times the entity of the bigger system, when the velocity at minimum separation is equal to the parabolic velocity of escape.     

N-body simulations of tidal encounters between stellar systems

N-Body simulations have been performed to study the tidal effects of a primary stellar system on a secondary stellar system of density close to the Roche density. Two hyperbolic, one parabolic and one elliptic encounters have been simulated. The changes in energy, angular momentum, mass distribution, and shape of the secondary system have been determined in each case. The inner region containing about 40 per cent of the mass was found to be practically unchanged and the mass exterior to the tidal radius was found to escape. The intermediate region showed tidal distension. The thickness of this region decreased as we went from hyperbolic encounters to the elliptic encounter keeping the distance of closest approach constant. The numerical results for the fractional change in energy have been compared with the predictions of the available analytic formulae and the usefulness and limitations of the formulae have been discussed.     

Exchange of gravitational energy during a collision of galaxies

The problem of the change in internal energy of a colliding galaxy due to tidal effects is considered, assuming that the galaxies may be regarded as spherical stellar systems whose over-all structure remains unchanged during the collision and that the stars move in circular orbits. The numerical estimates thus made for the energy gained by the stars during the collision are compared with those derived on the basis of the assumption that the motions of the stars may be neglected during the encounter (the impulsive approximation) to test the adequacy of the latter approximation. If the two galaxies are of 10¹¹ M , of radii 10 kpc and of mass distribution that of a polytrope of indexn=4; and if the relative distance and velocity at their closest approach are taken as 2 kpc and 1000 km/sec respectively, the mass of escaping stars from a galaxy is estimated to be roughly 4% of the total mass of the galaxy and the total increase in the internal energy of a galaxy during the collision due to the tidal acceleration of all its stars is equal in magnitude to approximately 25% of its initial internal energy, about one-fifth of which is associated with the escaping stars.     

Quasinormal modes and Hawking radiation of a Reissner-Nordström black hole surrounded by quintessence

We investigate quasinormal modes (QNMs) and Hawking radiation of a Reissner-Nordström black hole surrounded by quintessence. The Wentzel-Kramers-Brillouin (WKB) method is used to evaluate the QNMs and the rate of radiation. The results show that due to the interaction of the quintessence with the background metric, the QNMs of the black hole damp more slowly when increasing the density of quintessence and the black hole radiates at slower rate.     

Detailed ground radiometric surveys on Gabal El Sela,Southeastern Desert,Egypt

Gabal El Sela area lies in the extreme southeastern part of the eastern desert in Egypt. It is covered by basement rocks of different compositions. The detailed work in this area covers about 4 km² and it is represented mainly by coarse younger granite as a curved shape extended in NE–SW direction and dissected by many faults in various trends; some of them are invaded by dykes especially the lamprophyre dykes in the ENE–WSW trend. Detailed geological, structural, and radiometric investigations are carried out on the area. The radiometric data are statistically analyzed and the results show that the total count radiometric map reflects six separate anomalies. The field work revealed that four anomalies are related to lamprophyre dykes, the other two anomalies are structurally controlled by NE–SW and E–W faults. These anomalies are followed by some trenches which traced and measured in detail exhibiting the possible extension of these anomalies with depth. These measurements show that lamprophyre dyke has the highest reading of radioactivity, it reaches 270 Ur in the surface and to 6,300 in the trenches. While the granite of the sela area is considered possesses high level of radioactivity, where its radioactivity ranges from 19.9 to 81 Ur with an average of about 32 Ur.     

Rock joint modeling using a visco-plastic multilaminate model at constant normal load condition

Rock joints play an important role in the behavior of rock masses under normal and shear loading conditions. Numerical simulation of the behavior of jointed rock masses is not an easy task due to complexities involved in the problem such as joint roughness, joint shear strength, hardening and softening phenomenon and mesh dependency. In this study for modeling purposes, a visco-plastic multilaminate model considering hardening and softening effects has been employed. For providing the necessary data for numerical simulation, a series of laboratory experiments have been carried out on regular tooth-shape asperities made by gypsum, under constant normal load conditions. Shear stress–shear displacement and normal displacement–shear displacement of artificial joint specimens are simulated using the proposed numerical model at constant normal load condition (CNL). The results indicate the capability of the model for simulating rock joints behavior in both strength and deformation field. Although the numerical model has been developed for simulating the behavior of artificial joints, the concept of the method can also be used for natural rock joints.     

Mean runoff coefficient estimation for ungauged streams in the Kingdom of Saudi Arabia

Runoff coefficient estimation in ungauged watersheds has a priority for rain water harvesting and management of runoff water, for domestic and agriculture activities, in semi-arid and arid regions. To estimate mean runoff coefficient (C _Re) for ungauged streams, Pearson's coefficient of linear correlation (r) was measured. The method of linear regression (y?=?mx?+?c) was applied for 16 gauged catchments representing several regions in the Kingdom of Saudi Arabia, such as Al Qassim, Al Madinah, Riyadh, Asir, Makkah, and Jazan. The studied catchments were equally divided into two groups based on their main streams slopes; group A includes eight gauged streams having main stream slope less than 0.01, where group B includes eight gauged streams having main stream slope equal to or greater than 0.01. The result yields the constant of the linear regression for each group and the mean runoff coefficient of basin by an independent value (basin slope) for group A and an independent value (stream slope) for group B. The results indicate that the measured runoff coefficient (C _Rm) and the estimated runoff coefficient (C _Re) are almost equal to each other.