Dark matter halo profiles in scale-free cosmologies

We explore the dependence of the central logarithmic slope of dark matter halo density profiles α on the spectral index n of the linear matter power spectrum P ( k ) using cosmological N -body simulations of scale-free models [i.e. P ( k ) ∝ k ⁿ ]. These simulations are based on a set of clear, reproducible and physically motivated criteria that fix the appropriate starting and stopping times for runs, and allow one to compare haloes across models with different spectral indices and mass resolutions. For each of our simulations we identify samples of well-resolved haloes in dynamical equilibrium and we analyse their mass profiles. By parametrizing the mass profile using a 'generalized' Navarro, Frenk & White profile in which the central logarithmic slope α is allowed to vary while preserving the r ⁻³ asymptotic form at large radii, we obtain preferred central slopes for haloes in each of our models. There is a strong correlation between α and n , such that α becomes shallower as n becomes steeper. However, if we normalize our mass profiles by r ₋₂, the radius at which the logarithmic slope of the density profile is −2, we find that these differences are no longer present. This is apparent if we plot the maximum slope     as a function of r / r ₋₂– we find that the profiles are similar for haloes forming in different n models. This reflects the importance of concentration, and reveals that the concentrations of haloes forming in steep- n cosmologies tend to be smaller than those of haloes forming in shallow- n cosmologies. We conclude that there is no evidence for convergence to a unique central asymptotic slope, at least on the scales that we can resolve.     

Nonradial oscillations of a neutron star in an inhomogeneous hydrodynamic model

An inhomogeneous model neutron star with a variable density profile of the type ₀(r)=_c[1–(2/3)r²/R²]exp(–r²/R²) is considered, where _c is the central density, R is the star's radius, and is the inhomogeneity parameter in the radial mass distribution. This parameterization adequately reproduces the results of numerical evolutionary calculations of the density profile and enables one to obtain in analytical form the parameters of hydrostatic equilibrium and the eigenmodes of nonradial oscillations of a nonrotating neutron star, modeled by a spherical mass of incompressible, inviscid liquid. It is shown that a characteristic manifestation of the star's inhomogeneity is the presence of a stable dipole f-mode, the lowest one in the spectrum of natural oscillations. The presence of this mode serves as a general and primary criterion that evidently distinguishes all inhomogeneous hydrodynamic models from the homogeneous Kelvin model, in which the quadrupole mode is the lowest stable mode. Estimates obtained for the periods of nonradial pulsations coincide with the periods of micropulses observed in the average pulse profiles of c-pulsars. This suggests that the detected variations in emission intensity in the range of micropulse duration (on the order of 10^–4 sec) are associated with nonradial stellar oscillations.Translated from Astrofizika, Vol. 39, No. 3, pp. 475–488, July–September, 1996.     

Expanding shells in low and high density environments

The gravitational instability of expanding shells evolving in a homogeneous and static medium is discussed. In the low density environment (n = 1 cm^-3), the fragmentation starts in shells with diameters of a few 100 pc and fragment masses are in the range of 5 × 10³ - 10⁶ M _⊙. In the high density environment (n = 10⁵ - 10⁷ cm^-3), shells fragment at diameters of pc producing clumps of stellar masses. The mass spectrum in both environments is approximated by a power law dN/dm ∼ m ^-2.3. This is close to the slope of the stellar IMF. To reproduce the observed mass spectrum of clouds (the spectral index close to ∼ -2.0) we have to assume, that the cloud formation time is independent of the cloud size, similarly to the Jeans unstable medium. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hydrodynamic and turbulent motions in the galactic disk

Statistics in absorption 21-cm data show two main types of clouds at low galactic latitudes: dense small clouds, many of them with molecular cores, with dispersions σ≈1.5 km s⁻¹ and large clouds forming the fine features of the spiral arms (the shingle like features) with a dispersion range α≈3–4 km s⁻¹. Sizes and dispersions of both types of clouds are compatible with the Kolmogorov law of turbulence: σ∞d ^1/3. The large clouds forming the shingle-like features can be considered as the largest clouds of a Kolmogorov spectrum (the initial vortices), or as the hydrodynamic features with minimum sizes in the Galaxy. In order to define hydrodynamic motions in the same sense as given by Ogrodnikov (1965) we use here the tensorial form of the Helmholtz theorem to obtain an approximation for the hydrodynamic motions depending on distances and seen from the local standard of rest:V _r ∞r. The intermediate range of sizes between turbulent motions and hydrodynamic motions is 100<d<300 pc which is also the range of sizes of the large clouds forming the fine features of the spiral arms. A classification on of motions in the Galaxy is postulated: (a) a basic rotation motion given by an smooth unperturbed curveΘ _b (R) associated to the old disk population. (b) Systematic motions of the spiral arms. (c) Systematic motions in the fine structure of the arms. For scale sizes smaller than these fine features one has turbulent motions according to the Kolmogorov law. The densities and sizes of the turbulent clouds behave asn _H ∝d ⁻² in a range of sizes 7 pc<d<300 pc. The obtained gas densities of the clouds are confirmed with the dust densities from photometric studies. The conditions for gravitational binding of the clouds are analyzed. Factors as the geometry and the magnetic field within the clouds increases the critic densities for gravitational binding. When we consider these factors we find that the wide component clouds have densities below such a critical value. The narrow component clouds have densities similar or above the critical value; but the real fraction of collapsing clouds remains unknown as far as the factor of geometry and the inner magnetic field of each cloud are not determinated.     

Star formation in molecular clouds of intermediate mass

Self-consistent multicomponent models of evolution of the interstellar medium have been computed by extending the scheme of Habeet al. (1981) and adding some processes of star formation in molecular clouds, induced by supersonic collisions. A monochromatic spectrum of the molecular clouds has been adopted with a cloud mass of 10⁴ M . The consequences of these simplifying assumptions have been discussed and moreover the influence of several parameters (efficiency of star formation, photoionization rate, cloud radius, and mass) and of the initial conditions has been analyzed. Emphasis has been put on the following points: (1) there is a strong conditioning of the physical state of the intercloud gas on the star formation rate; (2) depending on the total initial mass of the molecular clouds per unit volume , two different regimes of star formation are possible: one, when is larger than a critical value _cr, dominated by collisions between clouds, with a total star formation rate practically constant and a long lifetime for the system, the other, characterized by <_cr, in which the dominant process is due to the expansion ofHii regions: the resulting star formation rate causes the system exhaustion in a relatively short lifetime. Some suggestions are derived concerning the evolution of galaxies.     

The dependence of star formation on initial conditions and molecular cloud structure

We investigate the dependence of stellar properties on the initial kinematic structure of the gas in star-forming molecular clouds. We compare the results from two large-scale hydrodynamical simulations of star cluster formation that resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical, but in the new simulation the power spectrum of the velocity field imposed on the cloud initially and allowed to decay is biased in favour of large-scale motions. Whereas the calculation of Bate et al. began with a power spectrum   P ( k ) ∝ k ⁻⁴  to match the Larson scaling relations for the turbulent motions observed in molecular clouds, the new calculation begins with a power spectrum   P ( k ) ∝ k ⁻⁶  .
Despite this change to the initial motions in the cloud and the resulting density structure of the molecular cloud, the stellar properties resulting from the two calculations are indistinguishable. This demonstrates that the results of such hydrodynamical calculations of star cluster formation are relatively insensitive to the initial conditions. It is also consistent with the fact that the statistical properties of stars and brown dwarfs (e.g. the stellar initial mass function) are observed to be relatively invariant within our Galaxy and do not appear to depend on environment.     

The Role of Giant Molecular Clouds in the Evolution of the Oort Comet Cloud

We estimated the gravitational influence of giant molecular clouds passing near the Solar system on the orbital evolution of Oort cloud comets. We performed a comparative analysis of the accuracies of the following two methods of allowance for the perturbations from giant molecular clouds: the impulse approximation and numerical integration. The impulse approximation yields fairly accurate estimates of the change in the energy of Oort cloud comets and the probability of their ejection under the influence of a molecular cloud if the path of the Solar system does not cross its boundary and if the molecular cloud may be treated as a point perturbing mass. The comet survival probability in the Oort cloud depends significantly on the internal structure of the perturbing molecular cloud and the impact parameter of the encounter. The most massive injection of comets into the planetary region and their ejection from the Oort cloud take place if the Solar system passes through a giant molecular cloud composed of several high-mass condensations. In this case, most of the comets injected into the planetary region were initially comets of the inner Oort cloud (a 10^–4 AU) with high orbital eccentricities.     

Cosmological Evolution of Supergiant Star-Forming Clouds

We present the results of very high resolution CDM simulations of galaxy formation designed to follow the formation and evolution of self-gravitating, supergiant star-forming clouds. We find that the mass spectrum of these clouds is identical to that of globular clusters and GMCs; dN/dM ∝ M ^-1.7 ± 0.1. This revised version was published online in September 2006 with corrections to the Cover Date.     

Giant HVC’s and the Rotation Curves of the Milky Way and M31

We have modelled, for the cases of Milky Way and M31, the effects on the galactic discs, of the arrival at high velocity (≥150 km s⁻¹) of giant HI clouds, with masses of up to 10⁸M⊙. Predictions are compared with the detailed structure of the observed rotation curves for these two galaxies. The model explains the rises and falls observed at large distances from the centre of each galaxy, distributed with a degree of regularity in radius, in terms of a specific type of perturbations driven by the infall of the high velocity clouds (HVC's) arriving from the intracluster medium of the Local Group. The underlying rotation curve is explained conventionally via the distribution of the baryonic and dark matter components of the galaxy in question. This scenario, though tested here on the two major Local Group objects, is in principle applicable to galaxies undergoing minor mergers with subgalactic mass gas clouds.     

NGC 1624 (OCl 403, Cr 53) – A very young open cluster

We present the first CCD photometric UBVRI observations of the not-so-well-studied open cluster NGC 1624 (OCl 403, Cr 53; α₂₀₀₀ = 04 h 40 m 36 s; δ₂₀₀₀ = + 50^˚ 27^′ 42″ Trumpler class = I 2 p N). This cluster was observed on 01 February 2004 with the 2 m Himalayan Chandra Telescope at Hanle using a LN2 cooled 2k × 2k CCD. The cluster presents differential reddening with E(B-V) values ranging from 0.70 to 0.90 mag, which could be attributed to the presence of the HII region wherein the cluster is embedded. It is found to be at a distance of 6.025 ± 0.5 kpc and the age of this cluster is estimated to be ∼3.98 × 10⁶ years. In view of these parameters, it can be considered as a young enough cluster located in the direction of the Perseus constellation with the galactic coordinates of l = 155^˚.35 and b = + 02 ^˚.58. Thus it could also be used as a suitable candidate for tracing the Outer Perseus spiral arm of our Galaxy. The initial mass function slope is derived as 1.65 ± 0.25 by applying the corrections for field star contamination and data incompleteness. This is in good agreement with the Salpeter value within the limits of errors.     

Bifurcation of central configuration in the 2N+1 body problem

The bifurcation of central configuration in the Newtonian N-body problem for any odd number N ≥ 7 is shown. We study a special case where 2n particles of mass m on the vertices of two different coplanar and concentric regular n-gons (rosette configuration) and an additional particle of mass m₀ at the center are governed by the gravitational law he 2n+1 body problem. This system is of two degrees of freedom and permits only one mass parameter μ =m ₀/m. This parameter μ controls the bifurcation. If n≥ 3, namely any odd N ≥ 7, then the number of central configurations is three when μ ≥ μ _c , and one when μ ≥ μ _c . By combining the results of the preceding studies and our main theorem, explicit examples of bifurcating central configuration are obtained for N ≤ 13, for any odd N ∈ [15,943], and for any N ≥ 945.     

Distribution of stars perpendicular to the plane of the galaxy

We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m₀)m^−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v²(m)> ∼ m^−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field K_z, in terms of confluent hypergeometric functions, the limiting trends being K_z∼z for z →0, while K_z → constant for z → infinity. We also study the behaviour of < |z(m)|²>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|²>∼ m^t-θ, for m→ t, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested that observation of < |z(m)|²> can be used as a probe to findx and hence obtain information about the mass spectrum.     

Infrared and Raman spectra of lunar samples from Apollo 11, 12 and 14

We report the room temperature infrared reflectance spectra of several lunar surface rocks in the form of polished slices or butt ends. The spectra were obtained over the frequency range 20-2000 cm^–1 throughout the mid and far infrared (5-500µ) region of the electromagnetic spectrum where the fundamental internal and lattice vibrational modes of all minerals and rocks occur.Some fines samples were examined as pressed pellets and their reflectivities compared with the bulk samples. Several terrestrial minerals and rocks were also investigated. Kramers-Kronig analyses of these reflectance spectra were undertaken and the dispersion of the dielectric response ( and ) and the optical constants (n andk) have been determined over this frequency range. The low frequency and high frequency (infrared) dielectric constants were also calculated from the reflectance data.Raman light scattering measurements were made on all the samples supplied from the first three Apollo missions. Large background scattering proved to be the greatest experimental problem. Successful spectra in nearly all cases were obtained from small crystalline inclusions imbedded in the main ground mass. Some crystalline bulk rocks containing many very fine inclusions gave identifiable spectra and at least three different types were obtained.Supported by NASA Grant NGR 22-011-069 and by a Northeastern University Grant for Basic Research.     

GMRT observations of interstellar clouds in the 21cm line of atomic hydrogen

Nearby interstellar clouds with high (|ν|≥10km s⁻¹) random velocities although easily detected in NaI and CaII lines have hitherto not been detected (in emission or absorption) in the HI 21cm line. We describe here deep Giant Metrewave Radio Telescope (GMRT) HI absorption observations toward radio sources with small angular separation from bright O and B stars whose spectra reveal the presence of intervening high random velocity CaII absorbing clouds. In 5 out of the 14 directions searched we detect HI 21cm absorption features from these clouds. The mean optical depth of these detections is ∼0.09 and FWHM is ∼10km s⁻¹, consistent with absorption arising from CNM clouds.     

Cloud brightness distribution and turbulence in Venus using Galileo violet images

Venus cloud covered atmosphere offers a well-suited framework to study the coupling between the atmospheric dynamics and the structure of the cloud field. Violet images obtained during the Galileo flyby from 12 to 17 February 1990 have been analyzed to retrieve the zonal power spectra of the cloud brightness distribution field between latitudes 70° N and 50° S. The brightness distribution spectra serve as a diagnostic of the eddy kinetic energy spectrum providing indirect information about the distribution of energy along different spatial scales. We composed images covering a full rotation of the atmosphere at the level of the UV contrasted clouds obtaining maps of almost 360° that allowed us to obtain the brightness power spectra from wavenumbers k=1 to 50. A full analysis of the spectrum slope for different latitude bands and ranges of wave numbers is presented. The power spectra follow a classical law k−n with exponent n ranging from −1.7 to −2.9 depending on latitude and the wavenumber range. For the whole planet, the average of this parameter is −2.1 intermediate between those predicted by the classical turbulence theories for three- and two-dimensional motions (n=−5/3 and n=−3). A comparison with previous analysis of Mariner 10 (in 1974) and Pioneer Venus (in 1979) shows significant temporal changes in the cloud global structure and in the turbulence characteristics of the atmosphere.     

Evidence for an Extended Extragalactic Gamma Ray Source

High energy gammay–ray emission from an extended region between the squasars 3C273 and 3C279 in Virgo has been detected by the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory(CGRO). This emission shows a remarkably constant flux over an observation time of years between June 1991 and December 1993. The data analysis shows, that the structure is not the result of an instrumental effect. The object has a perfect power law photon spectrum with index α=-2.06 ± 0.05 which is different from the spectra of the neighboring quasars 3C273 and 3C279. Integration of the spectrum leads to a flux estimation of (7.0± 0.3) × 10^-7 γ cm^-2s^-1 above 100 MeV. No galactic or extragalactic counterpart is found at other wavelengths. Indications point, however, at an extragalactic origin of the gamma radiation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Collapse of primordial clouds and the formation of a central core

The collapse of rotating clouds is investigated using three-dimensional self-gravitating hydrodynamical simulations. We take into account the detailed non-equilibrium chemical reactions for primordial gas that consists of pure hydrogen. The parameters of the collapse and the condition of the fragmentation are compared with those of isothermal clouds. It is shown that the geometrical flatness of the central region of the disc is a good indicator for predicting whether the clouds fragment or not. If the flatness is greater than the critical value, ∼ 4π, a cloud fragments into filaments and blobs. On the other hand, if the flatness is smaller than the critical value, fragmentation is not expected before the central core formation even if the cooling is efficient and the total mass becomes much greater than the local Jeans mass at the centre. The critical mass is found to be 3 × 10⁶ M_⊙ for a typical initial condition. If the initial cloud mass is smaller than this critical value, fragmentation before the central core formation is not expected. For a typically estimated first collapsing cosmological baryonic object, M ≲ 10⁶ M_⊙, central core formation is expected and will have a significant effect on the later evolution of the whole system. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the lifetimes of galactic clusters

From the observed age distribution of galactic clusters within 1 kpc we deduce that the typical total lifetime of a galactic cluster is about 2×10⁸ yr. The individual lifetimes vary between 10⁸ and 10¹⁰ yr. The observed lifetimes are compared with the evaporation times which are found from numerical experiments with star cluster models. These models contain up to 250 stars with a realistic mass spectrum. The effect of the galactic tidal field is taken into account and enhances the rate of escape significantly. Escapers are identified by using the Jacobian integral. We give the evaporation time in years as a function of the median radius for different values of the total mass of a cluster. The agreement between the resulting theoretical lifetimes and the observed values is sufficiently good. We estimate that the tidal field of passing interstellar clouds should be in most cases less efficient in dissolving a galactic cluster than the internal evaporation process combined with the effect of the general galactic field.     

Determination of the area and mass distribution of orbital debris fragments

An important factor in modeling the orbital debris environment is the loss rate of debris due to atmospheric drag and luni/solar perturbations. An accurate knowledge of the area-to-mass ratio of debris fragments is required for the calculation of the effect of atmospheric drag. In general, this factor is unknown and assumed values are used. However, this ratio can be calculated for fragments for which changes in the orbital elements due to atmospheric drag as a function of time are known. This is the inverse of the technique used to determine the atmospheric density from the decay of satellites with accurately known area-to-mass ratios. These kinds of propagation programs are routinely used in predicting the decay of an orbiting vehicle. In this work the area-to-mass ratio of about 2600 fragments arising from the breakup of 24 artificial satellites have been determined. An analysis of the data on about 200 objects (rocket bodies, scientific satellites, etc.) with known mass, size, and shape has also been made. The value of the radar cross-section (RCS), as measured by the Eglin radar operating at 70 cm wavelength, has been correlated to the effective area of these objects. The measurements of the area-to-mass ratio of these objects then provide a calibration of the actual to the calculated mass. It has been shown that the debris mean mass, m, is related to the mean effective area, A, by a power law relation, m = k A ^1.86. However, for a given effective area the mass distribution is very broad. Moreover, the cumulative mass distribution, N(>m), can be expressed as N(>m) = D(m + b), where D, b, and c are constants. The asymptotic slope, c, of low intensity explosions is on the average lower than the slope for high intensity explosions, but there is considerable spread of this slope in each class. Part of the flattening, as indicated by the finite value of the parameter, b, can be understood as arising out of the spread in the RCS values due to the tumbling motion of the fragments and effects related to the detectability of the fragment by the Eglin radar. It has been established that the mass in a given breakup calculated using this technique is in good agreement with the expected mass value. These results can be used in modeling the breakups of other artificial earth satellites and safety analysis.     

A study of the kinematics of the local dark clouds

Lack of reliable estimates of distances to most of the local dark clouds has, so far, prevented a quantitative study of their kinematics. Using a statistical approach, we have been able to extract the average spatial distribution as well as the kinematical behaviour of the local dark clouds from their measured radial velocities. For this purpose, we have obtained radial velocities for 115 southern clouds and used the data from the literature for the northern ones. In this paper we present this new data, analyse the combined data and compare our results with those arrived at by earlier studies. The local clouds are found to be expanding at a speed of ∼ 4 kms^-1 which is in general agreement with the estimates from optical and HI studies. However, it is found that the kinematics of the local clouds is not described by the model proposed for the local HI gas where a ring of gas expanding from a point gets sheared by the galactic rotation. Rather, the observed distribution of their radial velocities is best understood in terms of a model in which the local clouds are participating in circular rotation appropriate to their present positions with a small expansion also superimposed. This possibly implies that cloud-cloud collisions are important. The spatial distribution of clouds derived using such a model is in good agreement with the local dust distribution obtained from measurements of reddening and extinction towards nearby stars. In particular, a region of size ∼ 350 pc in diameter enclosing the Sun is found to be devoid of clouds. Intriguingly, most clouds in the longitude range 100‡ to 145‡ appear to have negative radial velocities implying that they are approaching us. Carried out under the auspices of the Joint Astronomy Program, Department of Physics, Indian Institute of Science, Bangalore in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.