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Register a new userNew values of gravitational moments J2 and J4 deduced from helioseismology
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Mecheri Redouane
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By applying the theory of slowly rotating stars to the Sun, the solar quadrupole and octopole moments J2 and J4 were computed using a solar model obtained from CESAM stellar evolution code (Morel, 1997) combined with a recent model of solar differential rotation deduced from helioseismology (Corbard et al., 2002). This model takes into account a near-surface radial gradient of rotation which was inferred and quantified from MDI f-mode observations by Corbard and Thompson (2002). The effect of this observational near-surface gradient on the theoretical values of the surface parameters J2, J4 is investigated. The results show that the octopole moment J4 is much more sensitive than the quadrupole moment J2 to the subsurface radial gradient of rotation.
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We have investigated the toroidal analog of ellipsoidal shells of matter, which are of great significance in Astrophysics. The exact formula for the gravitational potential $Psi(R,Z)$ of a shell with a circular section at the pole of toroidal coordinates is first established. It depends on the mass of the shell, its main radius and axis-ratio $e$ (i.e. core-to-main radius ratio), and involves the product of the complete elliptic integrals of the first and second kinds. Next, we show that successive partial derivatives $partial^{n +m} Psi/partial_{R^n} partial_{Z^m}$ are also accessible by analytical means at that singular point, thereby enabling the expansion of the interior potential as a bivariate series. Then, we have generated approximations at orders $0$, $1$, $2$ and $3$, corresponding to increasing accuracy. Numerical experiments confirm the great reliability of the approach, in particular for small-to-moderate axis ratios ($e^2 lesssim 0.1$ typically). In contrast with the ellipsoidal case (Newtons theorem), the potential is not uniform inside the shell cavity as a consequence of the curvature. We explain how to construct the interior potential of toroidal shells with a thick edge (i.e. tubes), and how a core stratification can be accounted for. This is a new step towards the full description of the gravitating potential and forces of tori and rings. Applications also concern electrically-charged systems, and thus go beyond the context of gravitation.
The solar gravitational moments $J_{2n}$ are important astronomical quantities whose precise determination is relevant for solar physics, gravitational theory and high precision astrometry and celestial mechanics. Accordingly, we propose in the present work to calculate new values of $J_{2n}$ (for $n$=1,2,3,4 and 5) using recent two-dimensional rotation rates inferred from the high resolution SDO/HMI helioseismic data spanning the whole solar activity cycle 24. To this aim, a general integral equation relating $J_{2n}$ to the solar internal density and rotation is derived from the structure equations governing the equilibrium of slowly rotating stars. For comparison purpose, the calculations are also performed using rotation rates obtained from a recently improved analysis of SoHO/MDI heliseismic data for solar cycle 23. In agreement with earlier findings, the results confirmed the sensitivity of high order moments ($n>1$) to the radial and latitudinal distribution of rotation in the convective zone. The computed value of the quadrupole moment $J_{2}$ ($n=1$) is in accordance with recent measurements of the precession of Mercurys perihelion deduced from high precision ranging data of the MESSENGER spacecraft. The theoretical estimate of the related solar oblateness $Delta_{odot}$ is consistent with the most accurate space-based determinations, particularly the one from RHESSI/SAS.
Solar supergranulation remains a mystery in spite of decades of intensive studies. Most of the papers about supergranulation deal with its surface properties. Local helioseismology provides an opportunity to look below the surface and see the vertical structure of this convective structure. We present a concept of a (3+1)-D segmentation algorithm capable of recognising individual supergranules in a sequence of helioseismic 3-D flow maps. As an example, we applied this method to the state-of-the-art data and derived descriptive statistical properties of segmented supergranules -- typical size of 20--30 Mm, characteristic lifetime of 18.7 hours, and estimated depth of 15--20 Mm. We present preliminary results obtained on the topic of the three-dimensional structure and evolution of supergranulation. The method has a great potential in analysing the better data expected from the helioseismic
item[Background] Ground-state spins and magnetic moments are sensitive to the nuclear wave function, thus they are powerful probes to study the nuclear structure of isotopes far from stability. item[Purpose] Extend our knowledge about the evolution of the $1/2^+$ and $3/2^+$ states for K isotopes beyond the $N = 28$ shell gap. item[Method] High-resolution collinear laser spectroscopy on bunched atomic beams. item[Results] From measured hyperfine structure spectra of K isotopes, nuclear spins and magnetic moments of the ground states were obtained for isotopes from $N = 19$ up to $N = 32$. In order to draw conclusions about the composition of the wave functions and the occupation of the levels, the experimental data were compared to shell-model calculations using SDPF-NR and SDPF-U effective interactions. In addition, a detailed discussion about the evolution of the gap between proton $1d_{3/2}$ and $2s_{1/2}$ in the shell model and {it{ab initio}} framework is also presented. item[Conclusions] The dominant component of the wave function for the odd-$A$ isotopes up to $^{45}$K is a $pi 1d_{3/2}^{-1}$ hole. For $^{47,49}$K, the main component originates from a $pi 2s_{1/2}^{-1}$ hole configuration and it inverts back to the $pi 1d_{3/2}^{-1}$ in $^{51}$K. For all even-$A$ isotopes, the dominant configuration arises from a $pi 1d_{3/2}^{-1}$ hole coupled to a neutron in the $ u 1f_{7/2}$ or $ u 2p_{3/2}$ orbitals. Only for $^{48}$K, a significant amount of mixing with $pi 2s_{1/2}^{-1} otimes u (pf)$ is observed leading to a $I^{pi}=1^{-}$ ground state. For $^{50}$K, the ground-state spin-parity is $0^-$ with leading configuration $pi 1d_{3/2}^{-1} otimes u 2p_{3/2}^{-1}$.
Analysis of pulsar timing data-sets may provide the first direct detection of gravitational waves. This paper, the third in a series describing the mathematical framework implemented into the tempo2 pulsar timing package, reports on using tempo2 to simulate the timing residuals induced by gravitational waves. The tempo2 simulations can be used to provide upper bounds on the amplitude of an isotropic, stochastic, gravitational wave background in our Galaxy and to determine the sensitivity of a given pulsar timing experiment to individual, supermassive, binary black hole systems.
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