A family of physically realizable perfect fluid spheres representing a quark–stars in general relativity

In the present article, a family of static spherical symmetric well behaved interior solutions is derived by considering the metric potential g ₄₄=B(1−Cr ²)⁻ⁿ for the various values of n, such that (1+n)/(1−n) is positive integer. The solutions so obtained are utilised to construct the heavenly bodies’ like quasi-black holes such as white dwarfs, neutron stars, quarks etc., by taking the surface density 2×10¹⁴ gm/cm³. The red shifts at the centre and on the surface are also computed for the different star models. Moreover the adiabatic index is calculated in each case. In this process the authors come across the quarks star only. Least and maximum mass are fond to be 3.4348M _Θ and 4.410454M _Θ along with the radii 21.0932 km and 23.7245 km respectively.     

On most general exact solution for Vaidya-Tikekar isentropicsuperdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)² < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc ², (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c ², when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq_· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ _⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 10¹⁴ gm cm^-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R ² by −R² in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ² > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres. This revised version was published online in July 2006 with corrections to the Cover Date.     

Third order effect of rotation on stellar oscillations of a <Emphasis Type="Italic">β</Emphasis>-Cephei star

Here the effect of rotation up to third order in the angular velocity of a star on the p, f and g modes is investigated. To do this, the third-order perturbation formalism presented by Soufi et al. (Astron. Astrophys. 334:911, 1998) and revised by Karami (Chin. J. Astron. Astrophys. 8:285, 2008), was used. I quantify by numerical calculations the effect of rotation on the oscillation frequencies of a uniformly rotating β-Cephei star with 12 M _⊙. For an equatorial velocity of 90 km s⁻¹, it is found that the second- and third-order corrections for (l,m)=(5,−4), for instance, are of order of 0.07% of the frequency for radial order n=−3 and reaches up to 0.6% for n=−20.     

Bruns' Theorem: The Proof and Some Generalizations

We give here a proof of Bruns’ Theorem which is both complete and as general as possible: Generalized Bruns’ Theorem.In the Newtonian (n+1)-body problem in ℝ ^p with n≥2 and 1≤p≤n+1, every first integral which is algebraic with respect to positions, linear momenta and time, is an algebraic function of the classical first integrals: the energy, the p(p−1)/2 components of angular momentum and the 2p integrals that come from the uniform linear motion of the center of mass. Bruns’ Theorem only dealt with the Newtonian three-body problem in ℝ³; we have generalized the proof to n+1 bodies in ℝ^p with p≤n+1. The whole proof is much more rigorous than the previous versions (Bruns, Painlevé, Forsyth, Whittaker and Hagiara). Poincaré had picked out a mistake in the proof; we have understood and developed Poincaré’s instructions in order to correct this point (see Subsection 3.1). We have added a new paragraph on time dependence which fills in an up to now unnoticed mistake (see Section 6). We also wrote a complete proof of a relation which was wrongly considered as obvious (see Section 3.3). Lastly, the generalization, obvious in some parts, sometimes needed significant modifications, especially for the case p=1 (see Section 4). This revised version was published online in July 2006 with corrections to the Cover Date.     

Absolute dimensions of the close binary systems V453 Monocerotis and V523 Cassiopeiae

We present multi-colour CCD observations of the low-temperature contact binaries, V453 Mon and V523 Cas. Their light curves are modelled to determine a new set of stellar and orbital parameters. Analysis of mid-eclipse times yields a new linear ephemeris for both systems. A period decrease (dP/dt=2.3×10⁻⁷ days/yr) in V453 Mon is discovered. V523 Cas, however, is detected to show a period increase (dP/dt=9.8×10⁻⁸ days/yr) because of the mass transfer of a rate of 1.1×10⁻⁷ M_⊙ yr⁻¹, from a less massive donor. Using these findings we can determine the physical parameters of the components of V523 Cas to be M ₁=0.76 (3)M _⊙, M ₂=0.39 (2)M _⊙, R ₁=0.74 (2)R _⊙, R ₂=0.55 (2)R _⊙, L ₁=0.19 (3)L _⊙, L ₂=0.14 (3)L _⊙, and the distance of system as 46(9) pc.     

Differential Rotation of Strong Magnetic Flux During Solar Cycles 21 – 23

In the present investigation we measure the differential rotation of strong magnetic flux during solar cycles 21 – 23 with the method of wavelet transforms. We find that the cycle-averaged synodic rotation rate of strong magnetic flux can be written as ω=13.47−2.58sin ² θ or ω=13.45−2.06sin ² θ−1.37sin ⁴ θ, where θ is the latitude. They agree well with the results derived from sunspots. A north–south asymmetry of the rotation rate is found at high latitudes (28°<θ<40°). The strong flux in the southern hemisphere rotates faster than that in the northern hemisphere by 0.2 deg day⁻¹. The asymmetry continued for cycles 21 – 23 and may be a secular property.     

Allan Sandage and the cosmic expansion

This is an account of Allan Sandage’s work on (1) The character of the expansion field. For many years he has been the strongest defender of an expanding Universe. He later explained the CMB dipole by a local velocity of 220±50 km s⁻¹ toward the Virgo cluster and by a bulk motion of the Local supercluster (extending out to ∼3500 km s⁻¹) of 450–500 km s⁻¹ toward an apex at l=275, b=12. Allowing for these streaming velocities he found linear expansion to hold down to local scales (∼300 km s⁻¹). (2) The calibration of the Hubble constant. Probing different methods he finally adopted—from Cepheid-calibrated SNe Ia and from independent RR Lyr-calibrated TRGBs—H ₀=62.3±1.3±5.0 km s⁻¹ Mpc⁻¹.     

Energy-Dependent Timing of Thermal Emission in Solar Flares

We report solar flare plasma to be multi-thermal in nature based on the theoretical model and study of the energy-dependent timing of thermal emission in ten M-class flares. We employ high-resolution X-ray spectra observed by the Si detector of the “Solar X-ray Spectrometer” (SOXS). The SOXS onboard the Indian GSAT-2 spacecraft was launched by the GSLV-D2 rocket on 8 May 2003. Firstly we model the spectral evolution of the X-ray line and continuum emission flux F(ε) from the flare by integrating a series of isothermal plasma flux. We find that the multi-temperature integrated flux F(ε) is a power-law function of ε with a spectral index (γ)≈−4.65. Next, based on spectral-temporal evolution of the flares we find that the emission in the energy range E=4 – 15 keV is dominated by temperatures of T=12 – 50 MK, while the multi-thermal power-law DEM index (δ) varies in the range of −4.4 and −5.7. The temporal evolution of the X-ray flux F(ε,t) assuming a multi-temperature plasma governed by thermal conduction cooling reveals that the temperature-dependent cooling time varies between 296 and 4640 s and the electron density (n _e) varies in the range of n _e=(1.77 – 29.3)×10¹⁰ cm⁻³. Employing temporal evolution technique in the current study as an alternative method for separating thermal from nonthermal components in the energy spectra, we measure the break-energy point, ranging between 14 and 21±1.0 keV.     

Distinctions between the characteristics of before and after DH CMEs associated flares

A detailed analysis of characteristics of coronal mass ejections and flares associated with deca-hectometer wavelength type-II radio bursts (DH-CMEs and DH-flares) observed in the period 1997–2008 is presented. A sample of 62 limb events is divided into two populations known as after-flare CMEs (AF-CMEs) and before-flare CMEs (BF-CMEs) based on the relative timing of the flare and CME onsets. On average, AF-CMEs (1589 km s⁻¹) have more speed than the BF-CMEs (1226 km s⁻¹) and the difference between mean values are highly significant (P∼2%). The average CME nose height at the time of type-II start is at larger distance for AF-CMEs than the BF-CMEs (4.89 and 3.84 R _o, respectively). We found a good anti-correlation for accelerating (R _a=−0.89) and decelerating (R _d=−0.78) AF-CMEs. In the case of decelerating BF-CMEs, the correlation seems to be similar to that for decelerating AF-CMEs (R _d=−0.83). The number of decelerating AF-CMEs is 51% only; where as, the number of decelerating BF-CMEs is 83%. The flares associated with BF-CMEs have shorter rise and decay times than flares related to AF-CMEs. We found statistically significant differences between the two sets of associated DH-type-II bursts characteristics: starting frequency (P∼4%), drift rate (P∼1%), and ending frequency (P∼6%). The delay time analysis of DH-type-II start and flare onset times shows that the time lags are longer in AF-CME events than in BF-CME events (P≪1%). From the above results, the AF-CMEs which are associated with DH-type-II bursts are found to be more energetic, associated with long duration flares and DH-type-IIs of lower ending frequencies.     

Artificial contradiction between cosmology and particle physics: the Λ problem

It is shown that the usual choice of units obtained by taking G=c=ℏ=1, giving the Planck’s units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with ℏ. We note that the choice of ℏ=1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is ℏ≈1/10¹²², while the choice of ℏ=1 corresponds to the cosmological scale. This is due to the scale factor of 10⁶¹ that converts the Planck scale to the cosmological scale. By choosing the ratio G/c ³=constant=1, which includes the choice G=c=1, and the momentum conservation mc=constant, we preserve the derivation of the Einstein field equations from the action principle. Then the product Gm/c ²=r _g , the gravitational radius of m, is constant. For a quantum black hole we prove that ℏ≈r _g ²≈(mc)². We also prove that the product Λℏ is a general constant of order one, for any scale. The cosmological scale implies Λ≈ℏ≈1, while the Planck scale gives Λ≈1/ℏ≈10¹²². This explains the Λ problem. We get two scales: the cosmological quantum black hole (QBH), size ∼10²⁸ cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size ∼10⁻¹³ cm, as well as the Planck’ scale, size ∼10⁻³³ cm.      

Age and Metallicity Gradients in the Galactic Bulge

We test for age and metallicity gradients in the Galactic Bulgebetween the two low extinction windows Baade's window (l = 1^° .1b=−4^° .8) and Sagittarius-I (l=1^° .3 b=−2^° .7). We derive ametallicity difference of ≤ 0.2 dex between BW andSGR-I window. This corresponds to a metallicity gradient of 1.3 dexkpc^-1. This steep gradient is reconcilable with the existence of ashort scale length inner component to the Bulge, most likely thatprominent in the NIR, which perhaps forms a separate entitysuperimposed on the larger, optical Bulge. Through number counts incolour-magnitude diagram around the turnoff for several fields andclusters, extending over a range in galactic longitude we find no evidencefor a significant young stellar population in the GalacticBulge. Previous suggestions of the existence of a significant youngstellar population have most likely incorrectly identified theforeground disk stars. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the theory of the oblateness of the Sun

In this paper we first emphasize why it is important to know the successive zonal harmonics of the Sun's figure with high accuracy: mainly fundamental astrometry, helioseismology, planetary motions and relativistic effects. Then we briefly comment why the Sun appears oblate, going back to primitive definitions in order to underline some discrepancies in theories and to emphasize again the relevant hypotheses. We propose a new theoretical approach entirely based on an expansion in terms of Legendre's functions, including the differential rotation of the Sun at the surface. This permits linking the two first spherical harmonic coefficients (J ₂ and J ₄) with the geometric parameters that can be measured on the Sun (equatorial and polar radii). We emphasize the difficulties in inferring gravitational oblateness from visual measurements of the geometric oblateness, and more generally a dynamical flattening. Results are given for different observed rotational laws. It is shown that the surface oblateness is surely upper bounded by 11 milliarcsecond. As a consequence of the observed surface and sub-surface differential rotation laws, we deduce a measure of the two first gravitational harmonics, the quadrupole and the octopole moment of the Sun: J ₂=−(6.13±2.52)×10⁻⁷ if all observed data are taken into account, and respectively, J ₂=−(6.84±3.75)×10⁻⁷ if only sunspot data are considered, and J ₂=−(3.49±1.86)×10⁻⁷ in the case of helioseismic data alone. The value deduced from all available data for the octopole is: J ₄=(2.8±2.1)×10⁻¹². These values are compared to some others found in the literature. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005238718479     

Flare Plasma Cooling from 30 MK down to 1 MK modeled from Yohkoh,GOES, and TRACE observations during the Bastille Day Event (14 July 2000)

We present an analysis of the evolution of the thermal flare plasma during the 14 July 2000, 10 UT, Bastille Day flare event, using spacecraft data from Yohkoh/HXT, Yohkoh/SXT, GOES, and TRACE. The spatial structure of this double-ribbon flare consists of a curved arcade with some 100 post-flare loops which brighten up in a sequential manner from highly-sheared low-lying to less-sheared higher-lying bipolar loops. We reconstruct an instrument-combined, average differential emission measure distribution dEM(T)/dT that ranges from T=1 MK to 40 MK and peaks at T ₀=10.9 MK. We find that the time profiles of the different instrument fluxes peak sequentially over 7 minutes with decreasing temperatures from T≈30 MK to 1 MK, indicating the systematic cooling of the flare plasma. From these temperature-dependent relative peak times t _peak(T) we reconstruct the average plasma cooling function T(t) for loops observed near the flare peak time, and find that their temperature decrease is initially controlled by conductive cooling during the first 188 s, T(t)∼[1+(t/τ_cond)]^−2/7, and then by radiative cooling during the next 592 s, T(t)∼[1−(t/τ_rad)]^3/5. From the radiative cooling phase we infer an average electron density of n _e=4.2×10¹¹ cm⁻³, which implies a filling factor near 100% for the brightest observed 23 loops with diameters of ∼1.8 Mm that appear simultaneously over the flare peak time and are fully resolved with TRACE. We reproduce the time delays and fluxes of the observed time profiles near the flare peak self-consistently with a forward-fitting method of a fully analytical model. The total integrated thermal energy of this flare amounts to E _thermal=2.6×10³¹ erg. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014257826116     

Stokes Diagnostics of 2D MHD-Simulated Solar Magnetogranulation

The properties of solar magnetic fields on scales less than the spatial resolution of solar telescopes are studied. A synthetic infrared spectropolarimetric diagnostic based on a 2D MHD simulation of magnetoconvection is used for this. Analyzed are two time sequences of snapshots that likely represent two regions of the network fields with their immediate surroundings on the solar surface with unsigned magnetic flux densities of 300 and 140 G. In the first region from the probability density functions of the magnetic field strength it is found that the most probable field strength at log τ ₅=0 is equal to 250 G. Weak fields (B<500 G) occupy about 70% of the surface, whereas stronger fields (B>1000 G) occupy only 9.7% of the surface. The magnetic flux is −28 G and its imbalance is −0.04. In the second region, these parameters are correspondingly equal to 150 G, 93.3%, 0.3%, −40 G, and −0.10. The distribution of line-of-sight velocities on the surface of log τ ₅=−1 is estimated. The mean velocity is equal to 0.4 km s⁻¹ in the first simulated region. The average velocity in the granules is −1.2 km s⁻¹ and in the intergranules it is 2.5 km s⁻¹. In the second region, the corresponding values of the mean velocities are equal to 0, −1.8, and 1.5 km s⁻¹. In addition the asymmetry of synthetic Stokes V profiles of the Fe i 1564.8 nm line is analyzed. The mean values of the amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude asymmetry is increased to 10% whereas the area asymmetry is only slightly varied.     

How we can learn from studies of wide binary statistics

Summary We present a versatile technique for comparing wide binary observations with theoretical semi-major axis distributions. To illustrate this technique, the theoretical implications of the recent Lathamet al. (1984) data on wide binaries are examined. We conclude that power law models for the underlying distribution are consistent with observations, implying no sharp cut-offs in the semi-major axis distribution. We argue that the detection of 6 wide binaries by Lathamet al. would require an uncomfortably large local density of wide binaries (semi-major axesa≳10⁻³ pc) for a broad range of theoretical models. Motivated by the apparent high number density of wide binaries implied by the Lathamet al. sample, we define a criterion for selecting candidate wide binaries form theYale Bright Star Catalog. The candidate list is used to determine an upper bound for wide binary density ofn _WB=4×10⁻³ pc⁻³. Although the actual value is somewhat uncertain, there is no difficulty in principle in reconciling this result with the local stellar number density.     

Optical imaging and spectroscopic observation of the galactic supernova remnant G85.9-0.6

Optical CCD imaging with Hα and [SII] filters and spectroscopic observations of the galactic supernova remnant G85.9-0.6 have been performed for the first time. The CCD image data are taken with the 1.5 m Russian-Turkish Telescope (RTT150) at TüBİTAK National Observatory (TUG) and spectral data are taken with the Bok 2.3 m telescope on Kitt Peak, AZ. The images are taken with narrow-band interference filters Hα, [SII] and their continuum. [SII]/Hα ratio image is performed. The ratio obtained from [SII]/Hα is found to be ∼0.42, indicating that the remnant interacts with HII regions. G85.9-0.6 shows diffuse-shell morphology. [SII]λ λ6716/6731 average flux ratio is calculated from the spectra, and the electron density N _e is obtained to be 395 cm⁻³. From [OIII]/Hβ ratio, shock velocity has been estimated, pre-shock density of n _c =14 cm⁻³, explosion energy of E=9.2×10⁵⁰ ergs, interstellar extinction of E(B−V)=0.28, and neutral hydrogen column density of N(HI)=1.53×10²¹ cm⁻² are reported.     

Parameters of the local warp of the stellar-gaseous galactic disk from the kinematics of Tycho-2 nearby red giant clump stars

We analyze the three-dimensional kinematics of about 82 000 Tycho-2 stars belonging to the red giant clump (RGC). First, based on all of the currently available data, we have determined new, most probable components of the residual rotation vector of the optical realization of the ICRS/HIPPARCOS system relative to an inertial frame of reference, (ω _x , ω _y , ω _z ) = (−0.11, 0.24, −0.52) ± (0.14, 0.10, 0.16) mas yr⁻¹. The stellar proper motions in the form μ_α cos δ have then be corrected by applying the correction ω _z = −0.52 mas yr⁻¹. We show that, apart from their involvement in the general Galactic rotation described by the Oort constants A = 15.82 ± 0.21 km s⁻¹ kpc⁻¹ and B = −10.87 ± 0.15 km s⁻¹ kpc⁻¹, the RGC stars have kinematic peculiarities in the Galactic yz plane related to the kinematics of the warped stellar-gaseous Galactic disk. We show that the parameters of the linear Ogorodnikov-Milne model that describe the kinematics of RGC stars in the zx plane do not differ significantly from zero. The situation in the yz plane is different. For example, the component of the solid-body rotation vector of the local solar neighborhood around the Galactic x axis is M ₃₂⁻ = −2.6 ± 0.2 km s⁻¹ kpc⁻¹. Two parameters of the deformation tensor in this plane, namely M ₂₃⁺ = 1.0 ± 0.2 km s⁻¹ kpc⁻¹ and M ₃₃ − M ₂₂ = −1.3 ± 0.4 km s⁻¹ kpc⁻¹, also differ significantly from zero. On the whole, the kinematics of the warped stellar-gaseous Galactic disk in the local solar neighborhood can be described as a rotation around the Galactic x axis (close to the line of nodes of this structure) with an angular velocity −3.1 ± 0.5 km s⁻¹ kpc⁻¹ ≤ Ω_W ≤ −4.4 ± 0.5 km s⁻¹ kpc⁻¹.     

Large-scale periodicity in the distribution of QSO absorption-line systems

The spatial-temporal distribution of absorption-line systems (ALSs) observed in QSO spectra within the cosmological redshift interval z=0.0–4.3 is investigated on the base of our updated catalog of absorption systems. We consider so-called metallic systems including basically lines of heavy elements. The sample of the data displays regular variations (with amplitudes ∼15–20%) in the z-distribution of ALSs as well as in the η-distribution, where η is a dimensionless line-of-sight comoving distance, relatively to smoother dependences. The η-distribution reveals the periodicity with period Δη=0.036±0.002, which corresponds to a spatial characteristic scale (108±6)h ⁻¹ Mpc or (alternatively) a temporal interval (350±20)h ⁻¹ Myr for the ΛCDM cosmological model. We discuss the possibility of a spatial interpretation of the results, treating the pattern obtained as a trace of an order imprinted on the galaxy clustering in the early Universe.     

Astronomical constraints on properties of sterile neutrino dark matter

We consider sterile neutrinos as a component of dark matter in the Milky Way and clusters, and compare their rest mass, decay rate and the mixing angle. A radiative decaying rate of order Γ∼10⁻¹⁹ s⁻¹ for sterile neutrino rest mass m _s =18–19 keV can satisfactorily account for the cooling flow problem and heating source in Milky Way center simultaneously. Also, these ranges of decay rate and rest mass match the prediction of the mixing angle sin ²2θ∼10⁻³ with a low reheating temperature in the inflation model, which enables the sterile-active neutrino oscillation to be visible in future experiments. However, decaying sterile neutrinos have to be ruled out as a major component of dark matter because of the high decay rate.     

The kinematics of Trapezium-type systems

Summary In this paper the results of the research of the stars proper motions Trapezium components are reported. They are: the galactic coordinates of the solar aprx and the Sun velocity (L _⊙=43±18°,B _⊙=+28±13°,V _⊙=13±4 km s⁻¹), the dispersion of peculiar velocities in the direction of the galactic coordinates for the above mentioned stars (σ _l =±11 km s⁻¹, σ _b =±7 km s⁻¹).The attained accuracy of the proper motions (±0.005″ yr⁻¹) is shown to be insufficient to the study of internal space motions in these systems. At present the work to increase the relative proper motions accuracy for multiple system components and to improve reductions from the relative to absolute proper motions, is being carried out in the Main Astronomical Observatory (Academy of Sciences of the Ukrainian SSR). The new catalogue of the AGK3 stars is composed now in the vicinity of the galactic equator in order to improve reductions from the relative to absolute proper motions. The r.m.s. errors of the proper motions, obtained in the AGK3 system, are ±0.005″ yr⁻¹.