Cosmic microwave background power spectrum estimation with non-circular beam and incomplete sky coverage

Over the last decade, measurements of the cosmic microwave background (CMB) anisotropy have spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic effects in the increasingly sensitive, high-resolution, 'full' sky measurements from different CMB experiments poses a stiff challenge. The analysis techniques must not only be computationally fast to contend with the huge size of the data, but the higher sensitivity also limits the simplifying assumptions which can then be invoked to achieve the desired speed without compromising the final precision goals. While maximum likelihood is desirable, the enormous computational cost makes the suboptimal method of power spectrum estimation using pseudo-C _l unavoidable for high-resolution data. The debiasing of the pseudo-C _l needs account for non-circular beams, together with non-uniform sky coverage. We provide a (semi)analytic framework to estimate bias in the power spectrum due to the effect of beam non-circularity and non-uniform sky coverage, including incomplete/masked sky maps and scan strategy. The approach is perturbative in the distortion of the beam from non-circularity, allowing for rapid computations when the beam is mildly non-circular. We advocate that it is computationally advantageous to employ 'soft' azimuthally apodized masks whose spherical harmonic transform die down fast with m . We numerically implement our method for non-rotating beams . We present preliminary estimates of the computational cost to evaluate the bias for the upcoming CMB anisotropy probes  ( l _max∼ 3000)  , with angular resolution comparable to the Planck surveyor mission. We further show that this implementation and estimate are applicable for rotating beams on equal declination scans, and can possibly be extended to simple approximations to other scan strategies.     

Geochemical identification of impactor for Lonar crater,India

Abstract— The only well‐known terrestrial analogue of impact craters in basaltic crusts of the rocky planets is the Lonar crater, India. For the first time, evidence of the impactor that formed the crater has been identified within the impact spherules, which are ?0.3 to 1 mm in size and of different aerodynamic shapes including spheres, teardrops, cylinders, dumbbells and spindles. They were found in ejecta on the rim of the crater. The spherules have high magnetic susceptibility (from 0.31 to 0.02 SI‐mass) and natural remanent magnetization (NRM) intensity. Both NRM and saturation isothermal remanent magnetization (SIRM) intensity are ?2 Am²/Kg. Demagnetization response by the NRM suggests a complicated history of remanence acquisition. The spherules show schlieren structure described by chains of tiny dendritic and octahedral‐shaped magnetite crystals indicating their quenching from liquid droplets. Microprobe analyses show that, relative to the target basalt compositions, the spherules have relatively high average Fe₂O₃ (by ?1.5 wt%), MgO (?1 wt%), Mn (?200 ppm), Cr (?200 ppm), Co (?50 ppm), Ni (?1000 ppm) and Zn (?70 ppm), and low Na₂O (?1 wt%) and P₂O₅ (?0.2 wt%). Very high Ni contents, up to 14 times the average content of Lonar basalt, require the presence of a meteoritic component in these spherules. We interpret the high Ni, Cr, and Co abundances in these spherules to indicate that the impactor of the Lonar crater was a chondrite, which is present in abundances of 12 to 20 percent by weight in these impact spherules. Relatively high Zn yet low Na₂O and P₂O₅ contents of these spherules indicate exchange of volatiles between the quenching spherule droplets and the impact plume.     

Heating of the solar chromosphere and corona

The generalized inhomogeneous wave equation that governs magnetoacoustic, vortical and thermal motions in compressible fluids and that thus is applicable to the problem of the heating of the solar chromosphere and corona is obtained. The effects of kinematic and bulk viscosity, heat conduction, Joule dissipation and magnetic diffusivity are included. Under the usual assumptions, the generalized wave equation reduces to the well-known equations of Lighthill, Kulsrud, Phillips and others. The major problems encountered in applying Lighthill's mechanism to sound generation in turbulent media are reviewed for both the subsonic and supersonic cases.     

Rapidly rotating supermassive stars in the first post-Newtonian approximation to general relativity

The structure and stability of rapidly uniformly rotating supermassive stars is investigated using the full post-Newtonian equations of hydrodynamics. The standard model of a supermassive star, a polytrope of index three, is adopted. All rotation terms up to and including those of order ⁴, where is the angular velocity, are retained. The effects of rotation and post-Newtonian gravitation on the classical configuration are explicitly evaluated and shown to be very small. The dynamical stability of the model is treated by using the binding energy approach. The most massive objects are found to be dynamically unstable when =1/c ².p _c / _c 2.2 × 10^–3, wherep _c and _c are the central pressure and density, respectively. Hence, the higher-order terms considered in this analysis do not appreciably alter the previously known stability limits.The maximum mass that can be stabilized by uniform rotation in the hydrogen-burning phase is found to be 2.9×10⁶ M , whereM is the solar mass. The corresponding nuclear-generated luminosity of 6×10⁴⁴ erg/sec^–1 is too small for the model to be applicable to the quasi-stellar objects. The maximum kinetic energy of a uniformly rotating supermassive star is found to be 3×10^–5 Mc ², whereM is the mass of the star. Masses in excess of 10¹⁰ M are required if an adequate store of kinetic energy is to be made available to a pulsar like QSO. However such large masses have rotation periods in excess of 100 yr and thus could not account for any short term periodic variability. It is concluded then that the uniformly rotating supermassive star does not provide a suitable base for a model of a QSO.     

The equilibrium and stability of magnetopolytropes

The theory of the oscillations of axisymmetric gaseous configurations with a prevalent magnetic field is presented. The virial tensor method is used to obtain the nine second harmonic modes of oscillations of the system. It is found that out of the nine modes, three are neutral, four are non-radial, and two are coupled. For the Prendergast spherical model it is found that one of the coupled modes is radial and the other non-radial. Both the radial and the non-radial modes obtained in this case agree with the corresponding formulae obtained byChandrasekhar andLimber (1954) andWoltjer (1962).The equilibrium structure of gaseous polytropes with toroidal magnetic fields is also investigated in detail for values of the polytropic indexn=1, 1.5, 2, 3 and 3.5. For this model the components of the moment of intertia and potential energy tensors together with the non-zero components of the supermatrix potential are obtained. The final results in terms of the effect of weak toroidal magnetic fields on the characteristic frequencies of distorted polytropes are presented in the form of tables.     

Calibrations for benthic foraminiferal Mg/Ca paleothermometry and the carbonate ion hypothesis

Benthic foraminiferal magnesium/calcium ratios were determined on one hundred and forty core-top samples from the Atlantic Ocean, the Norwegian Sea, the Indian Ocean, the Arabian Sea and the Pacific Ocean, mostly at sites with bottom water temperatures below 5 °C. Mg/Ca ratios are consistently lower, by  0.2 mmol/mol, in samples cleaned using oxidative and reductive steps than using oxidative cleaning. Differences between Cibicidoides species have been identified: Mg/Ca of Cibicidoides robertsonianus > Cibicidoides kullenbergi > Cibicidoides wuellerstorfi. Comparison with bottom water temperatures support observations of lowered Mg/Ca of C. wuellerstorfi at temperature below  3 °C compared with values predicted by published calibrations and from other Cibicidoides species. Hydrographic data shows that carbonate ion saturation (Δ[CO₃²⁻]) decreases rapidly below this temperature. An empirical sensitivity of Δ[CO₃²⁻] on Mg/Ca has been established for C. wuellerstorfi of 0.0086 ± 0.0006 mmol/mol/μmol/kg. A novel application using modern temperatures and Last Glacial Maximum temperatures derived via pore fluid modelling supports a carbonate ion saturation state effect on Mg incorporation. This may significantly affect calculated δ¹⁸O_seawater obtained from foraminiferal δ¹⁸O and Mg/Ca temperature.     

Analysis of magnetic anomalies due to some two-dimensional bodies using the Mellin transform

An interpretation technique using the Mellin transform is suggested for the analysis of magnetic anomalies due to some two-dimensional structures namely (i) a vertical sheet of both finite and infinite depth extent, (ii) a thick dyke and (iii) a horizontal circular cylinder. The Mellin transformed magnetic anomalies resemble gamma functions which are amenable to an easy interpretation. This procedure is illustrated with a small number of synthetic examples in each case. The practicality of the method is exemplified with the well-known vertical magnetic anomalies of Kursk (USSR) in the case of an infinite sheet model and Karimnagar magnetic anomaly (India) in the case of a horizontal circular cylinder. The results are compared with the techniques already available and found to be reliable.     

Models of rapidly rotating white dwarfs

Numerical solutions of the structural equations for rapidly rotating white dwarfs are tabulated for values of the central density parametery ^–2 _o ranging from 0.0001 to 0.80. The physical parameters of white dwarfs rotating at the break-up velocity are also tabulated. Further, the massradius relations for both the equatorial and the polar radii are derived. These two relations are found to differ from other recent theoretical calculations by less than 10 and 4%, respectively. The use of uniformly rotating white dwarf models to account for the observational data on Sirius B is discussed. It is concluded that Sirius B may be rotating rapidly and near its break-up velocity. Further it is suggested that the radius and Einstein red shift for this star are 0.01135 R and 59 km/sec.     

The structure of rapidly rotating relaxed globular clusters

A model of rapidly rotating globular clusters is constructed assuming uniform angular velocity and a truncated Maxwellian distribution in the stellar velocities. Since the first-order theory developed by Woolley and Dickens becomes inaccurate for rapid rotation, a small-mass envelope is fitted to their models by the method of Monaghan and Roxburgh. A comparison is made of the critical values derived by the two methods.     

Locating oceanic Tuna resources in the Eastern Arabian sea using remote sensing

Tuna fishery resources are currently under exploited. The resource potential of tunas in the Indian Exclusive Economic Zone (EEZ) beyond 50 m depths is around 2.09 lakh tonnes as estimated by Fishery Survey of India. The distribution and availability of the tuna are governed by environmental factors like temperature, thermocline depth, availability of prey, visibility etc. Remote sensing provides synoptic information on productivity in terms of chlorophyll and Sea Surface Temperature (SST). In the present paper, satellite remote sensing data from Indian Remote Sensing Satellite IRS- P4 Ocean Colour Monitor (OCM) sensor for chlorophyll-a and diffuse attenuation coefficient (K) and National Oceanic and Atmospheric Administration (NOAA) - Advanced Very High Resolution Radiometer (AVHRR) sensor data for sea surface temperature were analysed and correlated within situ catch data of oceanic tunas, Skipjack(Katsuwonus pelamis) and Yellowfin tuna(Thunnus albacares), off Maharashtra coast. Higher catches were found to be associated with moderate to good primary productivity and in the vicinity of thermal fronts. Relationship between Hooking rate and SST has shown that SST of 28–30°C range is optimum for skipjack and 28–31°C for yellowfin tuna. Besides satellite derived chlorophyll and SST for identification of potential tuna fishing zones, role of diffuse attenuation coefficient (K) for visibility factor is also discussed.