Neutrino energy loss on nuclides 56Fe, 56Co, 56Ni, 56Mn, 56Cr, and 56V by electron capture in magnetars

Based on the theory of relativity, the assumption of a superstrong magnetic field (SMF), and the shell model, the neutrino energy loss (NEL) rates of nuclides ⁵⁶Fe, ⁵⁶Co, ⁵⁶Ni, ⁵⁶Mn, ⁵⁶Cr, and ⁵⁶V by electron capture are investigated in the range of magnetic fields from 10¹³ G to 10¹⁸ G in magnetars. We also discuss the rates of change of the electron fraction (RCEF) in SMF and compare our results in SMF with those of FFN and Nabi, which is for the case without SMF. The results show that the NEL rates are increased greatly and even exceed by eight orders of magnitude in SMF. The RCEF are decreased largely and even exceed by seven orders of magnitude in SMF. On the other hand, our calculated NEL rates with SMF are larger by seven orders of magnitude than FFN’s at B=10¹⁸ G, and even by eight orders of magnitude compared to Nabi’s.     

The effect of dense cores on the structure and evolution of Jupiter and Saturn

We have calculated evolutionary and static models of Jupiter and Saturn with homogeneous solar composition mantles and dense cores of material consisting of solar abundances of SiO₂, MgO, Fe, and Ni. Evolutionary sequences for Jupiter were calculated with cores of mass 2, 4, 6, and 8% of the Jovian mass. Evolutionary sequences for Saturn were calculated with cores of mass 16, 18, 20, and 22% of total mass. Two envelope mixtures, representative of the solar abundances were used: X (mass fraction of hydrogen) = 0.74, Y (mass fraction of helium) = 0.24 and X = 0.77 and Y = 0.21. For Jupiter, the observations of the temperature at 1 bar pressure (T_1bar), radius and internal luminosity were best fit by evolutionary models with a core mass of ～6.5% and chemical composition of X = 0.77, Y = 0.21. The calculated cooling time for Jupiter is approximately 4.9 × 10⁹ years, which is consistent, within our error bars, with the known age of the solar system. For Saturn, the observations of the radius, internal luminosity and T_1BAR can be best fit by evolutionary models with a core mass of ～21% and chemical composition of X = 0.77, Y = 0.21. The cooling time calculated for Saturn is approximately 2.6 × 10⁹ years, almost a factor 2 less than the present age of the solar system. Static models of Jupiter and Saturn were calculated for the above chemical compositions in order to investigate the sensitivity of the calculated gravitational moments, J₂ and J₄, to the mass of the dense core, T_1BAR and hydrogen/helium ratio. We find for Jupiter that a model having a core mass of approximately 7% gives values of J₂, J₄, and T_1BAR that are within observational limits, for the mixture X = 0.77, Y = 0.21. The static Jupiter models are completely consistent with the evolutionary results. For Saturn, the quantities J₂, J₄, and J₆ determined from the static models with the most probable T_1BAR of 140°K, using modeling procedures which result in consistent models for Jupiter, are considerably below the observed values.     

Variable cosmological “constant” and motion of a test particle in a cloud of dust

We find that Einstein’s like field equations with coordinate-dependent cosmological “constant” Λ(x ⁱ ) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter (“dust”). The deviation from the geodesic law depends on the derivatives ?Λ/? x ⁱ and, in the weak field approximation, causes an anomalous acceleration A～(Vc ²/γ ρ)?Λ/? t+(c ⁴/γ ρ)?Λ/? r where V=dr/dt, c=the speed of light, γ=8π G with G=the gravitational coupling, ρ=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Λ=Λ(t) give A<10^?8 cm/s² when ρ>10^?29 g/cm³ i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological “constant” coupled to matter.     

The Ursa Major supercluster of galaxies: II. The structure and peculiar velocities

Kormendy’s relation (μ_e-logR _e) is used to investigate the structure of the compact Ursa Major supercluster of galaxies (11^h30^m+55°, cz=18 000 km s^?1); this relation allows the distances of early-type galaxies to be estimated. The relative distances of 13 clusters in the supercluster and their peculiar velocities are determined with a mean statistical accuracy of 6%. In general, the supercluster obeys the Hubble relation between radial velocity and distance. However, there is reason to suggest that the supercluster consists of two subsystems with mean radial velocities of 16 200 and 19 700 km s^?1. For a velocity dispersion in the subsystems of ～1100 km s^?1, the fact that each of them is gravitationally bound is not ruled out.     

The Substellar Population in the Young σ Orionis Cluster, Spatial Distribution

We review different surveys, in the optical and infrared, conducted in the very young (age 1–8 Myr), nearby (d ～ 350 pc) σ Orionis cluster aimed to characterize the substellar population. We describe spectral characteristics of very low mass stars, brown dwarfs and planetary mass objects in the cluster with spectral types from K7 to T6. We study the spatial distribution of the substellar population detected in a IZJ survey covering an area of 1.12 deg.² We find that the radial distribution of substellar objects can be well fitted by an exponential law (ρ = ρ_o e ^?r/ro ), with a central density (ρ _o ) of 0.26 ± 0.03 objects/arcmin² and a characteristic radius (r _o) of 8.8 arcmin ± 0.6 (equivalent to 0.90 ± 0.06 pc at the distance of the cluster). We discuss the presence of possible inhomogeneities in this distribution due to the existence of subclustering. We also compare the spatial distribution of the substellar population with previously known stars in the cluster. We report the initial mass spectrum in the substellar domain.     

Do the fundamental constants vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio μ = m _p/m _e was estimated by measuring the H₂ wavelengths in the spectra of distant quasars. We analyze high-resolution (FWHM≈7 km s^?1) spectra of the two damped Lyman-α systems at redshifts z _abs=2.3377 and 3.0249 observed in the spectra of the quasars Q 1232+082 and Q 0347?382, respectively. Our analysis yielded the most conservative estimate for the possible variation of μ in the past ～ 10 Gyr, Δμ/μ = (5.7 ± 3.8) × 10^?5. Since the significance of this result does not exceed 1.5σ, further observations are needed to increase the statistical significance. This is the most stringent limit on the possible cosmological variation of μ to date.     

Spectrographic study of the eclipsing binary system SZ Camelopardalis

Thirteen high-dispersion spectrographs of the eclipsing binary star SZ Cam have been studied with a view of determining more accurate information on: (i) the spectral type and luminosity classifications, (ii) absolute parameters for the component stars, (iii) the stellar environment of SZ Cam. The main results in these categories are as follows: (i) O9.5 Vnk, (ii)m _g=19±2M _⊙,m _s=6.5±1M _⊙;r _g=9.7±3.6R _⊙,r _s=4.8±1.7R _⊙;T _e～30000 K,T _e～23000 K; (iii) there is a local concentration of absorbing material which may reach a density of 2M _⊙ pc^?3, and the distance of the star is found to be 600±150 pc. The determined overluminosity of the secondary star and the local concentration of absorbing material are two topics which provide the basis for a discussion section.     

Recombination of electrons with H3+ and H5+ ions

The dissociative recombination coefficients α for capture of electrons by H₃⁺ and H₅⁺ ions have been determined as a function of electron temperature T_e using a microwave afterglow-mass spectrometer apparatus. At ion and neutral temperatures T_u+ = T_n = 240 K, the coefficient α (H₃⁺) is found to vary slowly with T_e at first, decreasing from 1.6 × 10^?7 cm³/s at T_e = 240 K to 1.2 × 10^?7 cm³/s at T_e = 500 K, thereafter falling as T_e^?1 over the range 500 K ? T_e, ? 3000 K. These results, which have a ± 20% uncertainty, agree satisfactorily over the common energy range (0.03–0.36 eV) with the recombination cross sections determined in merged beam measurements by Auerbach et al. At T₊ = T_n = 128 K, the coefficient α(H₅⁺) is found to be (1.8 ± 0.3) × 10^?6 [T_e(K)/300]^?0.69 cm³/s over the range 128 K ? T_e ? 3000 K, with a more rapid decrease, as T_e^?1, between 3000 K and 5500 K. The implications of these results for modelling planetary atmospheres and interstellar clouds are briefly touched on.     

Stellar structures with constant local adiabatic index under extreme relativistic conditions

Stellar structures with a constant local adiabatic index Γ have been discussed under the extreme relativistic condition (dP/dρ=1, at the center of the configuration). The equation of state,Pαρ^Γ, where ρ _r is the rest-mass density leads to the relations, (i)ρ=AP ^1/Γ?P/(Γ?1) between energy density and pressure, and (ii)e=NP between internal energy density and pressure, where the constantN may be called local polytropic index. The local adiabatic index, Γ, is found to be related to the adiabatic index, γ, through a simple relation, Γ=γ(1+P/ρ). The maximum value of surface redshift comes out to be 0.614 when σ=(P/ρ)₀=0.6. The structure are bound for σ≤0.83 and the maximum value of the binding coefficient is 0.181 at σ=0.4. For bound structures the central redshift z₀≤8.24. The maximum mass of neutron star based upon such a model comes out to be 2.39M _⊙ (for σ=0.4) and the maximum size comes out to be 13.7 km (for σ=0.2).     

A well-behaved class of charged analogue of Durgapal solution

We present a well behaved class of charged analogue of M.C. Durgapal (J. Phys. A, Math. Gen. 15:2637, 1982) solution. This solution describes charged fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. This solution gives us wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling of super dense stars. Keeping in view of well behaved nature of this solution, one new class of solution is being studied extensively. Moreover, this class of solution gives us wide range of constant K (0≤K≤2.2) for which the solution is well behaved hence, suitable for modeling of super dense stars like strange quark stars, neutron stars and pulsars. For this class of solution the mass of a star is maximized with all degree of suitability, compatible with quark stars, neutron stars and pulsars. By assuming the surface density ρ _b =2×10¹⁴ g/cm³ (like, Brecher and Capocaso, Nature 259:377, 1976), corresponding to K=0 with X=0..235, the resulting well behaved model has the mass M=4.03M _Θ , radius r _b =19.53 km and moment of inertia I=1.213×10⁴⁶ g?cm²; for K=1.5 with X=0.235, the resulting well behaved model has the mass M=4.43M _Θ , radius r _b =18.04 km and moment of inertia I=1.136×10⁴⁶ g?cm²; for K=2.2 with X=0.235, the resulting well behaved model has the mass M=4.56M _Θ , radius r _b =17.30 km and moment of inertia I=1.076×10⁴⁶ g?cm². These values of masses and moment of inertia are found to be consistent with the crab pulsars.     

Studies of galaxies with peculiar nuclei

Photometric, morphological and spectral grounds suggest that the peculiar nuclei regions of NGC 1097, 1672, 2997, 5236, and 7552 are composed basically of a normal nucleus surrounded by several large but otherwise normal (T _e ～8000 K,N _e ～1000/cm³) H II regions. The stellar components are also normal although in some cases (NGC 1097, 1672, 1808 and 7552) there is a larger contribution of late type stars.     

The effects of ultra-strong magnetic fields on electron capture rates for iron group nuclei in the outer crust of magnetars

Based on the work of Wang et al. (Chin. Phys. Lett. 29:049701, 2012), we re-investigated electron capture on iron group nuclei in the outer crust of magnetars and studied magnetar evolution. Effects of ultra-strong magnetic field on electron capture rates for ⁵⁷Co have been analyzed in the nuclear shell model and under the Landau-level-quantization approximation, and the electron capture rates and the neutrino energy loss rates on iron group nuclei in the outer crust of magnetar have been calculated. The results show that electron capture rates on ⁵⁷Co are increase greatly in the ultra-strong magnetic field, and above 3 orders of magnitude generally; and the neutrino energy loss rates by electron capture on iron group nuclei increase above 3 orders of magnitude in the range from B=4.414×10¹³ G to B=4.414×10¹⁵ G. These conclusions play an important role in future studying the evolution of magnetar. Furthermore, we modify the expressions of the electron chemical potential (Fermi energy) and phase space factor by introducing Dirac δ-function, and select appropriate parameters of temperature T, magnetic field B and matter density ρ in the our crust, thus our results will be reliable than those of Wang et al.     

On the structure of Mars' atmosphere at 120–220 km

Altitude dependences of [CO₂] and [CO₂⁺] are deduced from Mariner 6 and 7 CO₂⁺ airglow measurements. CO₂ densities are also obtained from n_e radio occultation measurements. Both [CO₂] profiles are similar and correspond to the model atmosphere of Barth et al. (1972) at 120 km, but at higher altitudes they diverge and at 200–220 km the obtained [CO₂] values are three times less the model. Both the airglow and radio occultation observations show that a correction factor of 2.5 should be included into the values for solar ionization flux given by Hinteregger (1970). The ratio of [CO₂⁺]/n_e is 0.15–0.2 and, hence, [O]/[CO₂] is ～3% at 135 km. An atmospheric and ionospheric model is developed for 120–220 km. The calculated temperature profile is characterized by a value of T ≈ 370°K at h ? 220 km, a steep gradient (～2°/km) at 200-160 km, a bend in the profile at 160 km, a small gradient (～0.7°/km) below and a value of T ≈ 250°K at 120 km. The upper point agrees well with the results of the Lyman-α measurements; the steep gradient may be explained by molecular viscosity dissipation of gravity and acoustical waves (the corresponding energy flux is 4 × 10^?2 erg cm^?2sec^?1 at 180 km). The bend at 160 km may be caused by a sharp decrease of the eddy diffusion coefficient and defines K ≈ 2 × 10⁸cm²sec^?1; and the low gradient gives an estimate of the efficiency of the atmosphere heating by the solar radiation as ? ≈ 0.1.     

A family of exact solutions of Einstein-Maxwell field equations in isotropic coordinates: an application to optimization of quark star mass

In the present paper, we have obtained a class of charged super dense star models, starting with a static spherically symmetric metric in isotropic coordinates for perfect fluid by considering Hajj-Boutros (in J. Math. Phys. 27:1363, 1986) type metric potential and a specific choice of electrical intensity which involves a parameter K. The resulting solutions represent charged fluid spheres joining smoothly with the Reissner-Nordstrom metric at the pressure free interface. The solutions so obtained are utilized to construct the models for super-dense star like neutron stars (ρ _b =2 and 2.7×10¹⁴ g/cm³) and Quark stars (ρ _b =4.6888×10¹⁴ g/cm³). Our solution is well behaved for all values of n satisfying the inequalities \(4 < n \le4(4 + \sqrt{2} )\) and K satisfying the inequalities 0≤K≤0.24988, depending upon the value of n. Corresponding to n=4.001 and K=0.24988, we observe that the maximum mass of quark star M=2.335M _⊙ and radius R=10.04 km. Further, this maximum mass limit of quark star is in the order of maximum mass of stable Strange Quark Star established by Dong et al. (in arXiv:1207.0429v3, 2013). The robustness of our results is that the models are alike with the recent discoveries.     

Electron capture strength on odd-A nucleus 59Co in explosive astrophysical environment

The Gamow-Teller (GT) transitions within massive stars play sumptuous role in the dynamics of core collapse supernovae. GT strength distributions and electron capture rates have been calculated for odd-A nucleus ⁵⁹Co within the proton-neutron quasiparticles random phase approximation (pn-QRPA) formalism. The pn-QRPA results are compared with other model calculations and (n,p) reaction experiment carried out at TRIUMF charge-exchange facility. The pn-QRPA calculated a total B(GT ₊) strength of 3.3 for ⁵⁹Co to be compared with the shell model value of 2.5 and the 1.9±0.1 in the (n,p) charge-exchange reaction. Aufderheide et al. (1993) extracted total strength equaling 2.4±0.3. The placement of GT centroid at 5.6 MeV by the pn-QRPA model is in reasonable agreement with the shell model centroid at 5.1 MeV whereas the measured GT centroid was placed at 4.4±0.3 MeV in the (n,p) experiment. Fuller, Fowler and Newman (FFN) (1980, 1982a, 1982b), placed the GT centroid at too low excitation energy of 2.0 MeV in the daughter nucleus ⁵⁹Fe, and this misplacement led to the enhancement of FFN rates. The suppressed pn-QRPA and shell model electron capture rates are in good agreement with each other. The rates are suggestive of higher value of Y _e (electron-to-baryon ratio) and may contribute to a more massive homologously collapsing core resulting in a more energetic shock. It might be interesting for the simulators to check the effect of these suppressed rates on the fine-tuning of the time rate of Y _e , the concomitant heavy element nucleosynthesis, and, on the energetics of the subsequent shock wave.     

A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity

This paper presents a new family of interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of charge distribution. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a star is maximized with all degree of suitability by assuming the surface density equal to normal nuclear density, ρ _nm=2.5×10¹⁷ kg?m^?3. By this model we obtain the mass of the Crab pulsar, M _Crab, 1.36M _⊙ and radius 13.21 km, constraining the moment of inertia >?1.61×10³⁸ kg?m² for the conservative estimate of Crab nebula mass 2M _⊙. And M _Crab=1.96M _⊙ with radius R _Crab=14.38 km constraining the moment of inertia >?3.04×10³⁸ kg?m² for the newest estimate of Crab nebula mass, 4.6M _⊙. These results are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields moments of inertia for PSR J0737-3039A and PSR J0737-3039B, I _A =1.4285×10³⁸ kg?m² and I _B =1.3647×10³⁸ kg?m² respectively. It has been observed that under well behaved conditions this class of solutions gives us the overall maximum gravitational mass of super dense object, M _G(max)=4.7487M _⊙ with radius $R_{M_{\max}}=15.24~\mathrm{km}$ , surface redshift 0.9878, charge 7.47×10²⁰ C, and central density 4.31ρ _nm.     

Current problems on horizontal branch stars

Expected characteristics of RR Lyrae stars as a function of the evolutive parameters are reported. Results from both evolutionary and pulsational investigations are collected in a suitable form, to show the general constraints to any interpretative analysis of the observations. It is shown that the spread in luminosity among the RR Lyrae stars results a function of the original chemical composition. On this basis a set of independent indications is found, suggesting that the globular cluster ω Cen is more He-rich than M 3; agreement with the whole observational frame is attained ifY _ωCen～0.35,Z _ωCen～5×10^?4 andY _M3～0.25,Z _M3～10^?3. No mass loss is needed to account for the RR Lyrae stars observed in ω Cen. The results are discussed, and it is shown that M 13-type clusters can be just characterized by a larger value ofZ in comparison with ω Cen. It is suggested that variations in the original helium content of the order of ΔY～0.1 and a correlationZ=Z(t) can account for some well-observed galactic globular clusters, without allowing for mass loss in the redder HB stars belonging to each cluster.     

A new well behaved class of charge analogue of Adler’s relativistic exact solution

The paper presents a new class of parametric interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of electric field intensity. This solution gives us wide range of parameter, K (0.69≤K≤7.1), for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a superdense object is maximized with all degree of suitability by assuming the surface density of the star equal to the normal nuclear density ρ _nm=2.5×10¹⁷kg?m^?3. By this model we obtain the mass of the Crab pulsar M _Crab=1.401M _⊙ and the radius, R _Crab=12.98 km constraining the moment of inertia I _NS,38>1.61 for the conservative estimate of Crab nebula mass 2M _⊙ and M _Crab=2.0156M _⊙ with radius, R _Crab=14.07 km constraining the moment of inertia I _NS,38>3.04 for the newest estimate of Crab nebula mass 4.6M _⊙ which are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields the moments of inertia for PSR J0737-3039A and PSR J0737-3039B are I _A,38=1.4624 and I _B,38=1.2689 respectively. It has been observed that under well behaved conditions this class of parametric solution gives us the maximum gravitational mass of causal superdense object 2.8020M _⊙ with radius 14.49 km, surface redshift z _R =0.4319, charge Q=4.67×10²⁰ C, and central density ρ _c =2.68ρ _nm.     

Main sequence models for massive Zero-metal stars

Zero-age main-sequence models for stars of 20, 10, 5 and 2M _⊙ with no heavy elements are constructed for three different possible primordial helium abundances:Y=0.00,Y=0.23, andY=0.30. The latter two values ofY bracket the range of primordial helium abundances cited by Wagoner. With the exceptions of the two 20M _⊙ models that contain helium, these models are found to be self-consistent in the sense that the formation of carbon through the triple-alpha process during pre-main sequence contraction is not sufficient to bring the CN cycle into competition with the proton-proton chain on the ZAMS. The zero-metal models of the present study have higher surface and central temperatures, higher central densities, smaller radii, and smaller convective cores than do the population I models with the same masses. If galaxies containing the zero-metal stars were formed as recently as one third the Hubble time, they would likely appear very blue today — perhaps bluer even that most known quasars — and their redshifted effective temperatures could range as high as 3×10⁴ K to 4×10⁴ K.     

The Gas to Dust Ratio in Three Star Forming Regionstwo

Gas to Dust Ratio (GDR) indicates the mass ratio of interstellar gas to dust. It is widely adopted that the GDR in our Galaxy is 100～150. We choose three typical star forming regions to study the GDR: the Orion molecular cloud — a massive star forming region, the Taurus molecular cloud — a low-mass star forming region, and the Polaris molecular cloud — a region with no or very few star formation activities. The mass of gas only takes account of the neutral gas, i.e. only the atomic and molecular hydrogen, because the amount of ionized gas is very small in a molecular cloud. The column density of atomic hydrogen is taken from the high-resolution and high-sensitivity all-sky survey EBHIS (Effelsberg-Bonn HI Survey). The CO J = 1 →0 line is used to trace the molecular hydrogen, since the spectral lines of molecular hydrogen which can be detected are rare. The intensity of CO J = 1 →0 line is taken from the Planck all-sky survey. The mass of dust is traced by the interstellar extinction based on the 2MASS (Two Micron All Sky Survey) photometric database in the direction of anti-Galactic center. Adopting a constant conversion coefficient from the integrated intensity of the CO line to the column density of molecular hydrogen, X_CO = 2.0 × 10²⁰ cm^?2 · (K · km/s)^?1, the gas to dust ratio N(H)/A_V is calculated, which is 25, 38, and 55 (in units of 10²⁰ cm^?2 · mag^?1) for the Orion, Taurus, and Polaris molecular clouds, respectively. These values are significantly higher than the previously obtained average value of the Galaxy. Adopting the WD01 interstellar dust model (when the V-band selective extinction ratio is R_V = 3.1), the derived GDRs are 160, 243, and 354 for the Orion, Taurus, and Polaris molecular clouds, respectively, which are apparently higher than 100～150, the commonly accepted GDR of the diffuse interstellar medium. The high N(H)/A_V values in the star forming regions may be explained by the growth of dust in the molecular clouds because of either the particle collision or accretion, which can lead to the reduction of extinction efficiency per unit mass in the V band, rather than the increase of the GDR itself.