Intensity of radiation reflected by a vertically inhomogeneous medium through multiple scattering

To facilitate the computation of the radiative intensity reflected, upon multiple scattering, by a vertically inhomogeneous medium, an implicit formula for integrating the invariant imbedding equation for Fourier-decomposed reflection function is derived starting with the formal solution: the height variations of the single-scattering albedo and the phase function characterizing the degree of inhomogeneity are thereby approximated by piece-wise, but continuous, linear functions of optical height , while the reflection function is approximated by a piece-wise quadratic polynomial in over each integration step. Using these approximations, the integration involved in the formal solution is then carried out analytically, yielding a correctortype formula for finding the reflection function at each step of . It is expected that this formula is capable of handling general cases of inhomogeneous media where both single-scattering albedo and phase function are allowed to vary continuously with height.Similar, but explicit expressions are also derived for the single and the second-order scattering solutions, with which the higher-order Fourier terms of reflection function are to be approximated, thereby enabling us to avoid the iterative process.     

A direct numerical approach to the Chandrasekhar'sH-functions for arbitrary characteristic functions

The purpose of this paper is to present a numerical technique to directly compute the Chandrasekhar'sH ()-function for anisotropic scattering in terms of the roots of the characteristic equations as well as the quadrature points of a certain degreen employed to approximate the definite integral involved in the basic equation. The principal feature of the algorithm proposed here is a compact computer code to enumerate _n C _m combinations ofn distinct integers {1,...,n} takenm at a time. With these quantities available, the coefficients of the polynomial equation of the characteristics equation can be readily computed for any given characteristic function, so that a standard technique such as the Laguerre method can be applied to find all the roots.It is shown that the results obtained for some representativeH()-functions using the present technique with relatively low-order formula (e.g.,n=7) are sufficiently accurate for all practical purposes.     

Rising motion of a behind-the-limb flare at 35 GHz

Interferometer observation of a behind-the-limb flare on 7 September, 1977, at 35 GHz ( = 8.6 mm) shows that the microwave non-thermal radio source of the burst is located in the coronal region at the height higher than 7000 km above the photosphere and rises gradually with the velocity of about 30 km s^-1.     

15-digit accuracy calculations of Ambartsumian-Chandrasekhar’s $$-functions for four-term phase functions with the double-exponential formula

We have established an iterative scheme to calculate with 15-digit accuracy the numerical values of Ambartsumian-Chandrasekhar’s \(H\)-functions for anisotropic scattering characterized by the four-term phase function: the method incorporates some advantageous features of the iterative procedure of Kawabata (Astrophys. Space Sci. 358:32, 2015) and the double-exponential integration formula (DE-formula) of Takahashi and Mori (Publ. Res. Inst. Math. Sci. Kyoto Univ. 9:721, 1974), which proved highly effective in Kawabata (Astrophys. Space Sci. 361:373, 2016). Actual calculations of the \(H\)-functions have been carried out employing 27 selected cases of the phase function, 56 values of the single scattering albedo \(\varpi_{0}\), and 36 values of an angular variable \(\mu(= \cos\theta)\), with \(\theta\) being the zenith angle specifying the direction of incidence and/or emergence of radiation. Partial results obtained for conservative isotropic scattering, Rayleigh scattering, and anisotropic scattering due to a full four-term phase function are presented. They indicate that it is important to simultaneously verify accuracy of the numerical values of the \(H\)-functions for \(\mu<0.05\), the domain often neglected in tabulation. As a sample application of the isotropic scattering \(H\)-function, an attempt is made in Appendix to simulate by iteratively solving the Ambartsumian equation the values of the plane and spherical albedos of a semi-infinite, homogeneous atmosphere calculated by Rogovtsov and Borovik (J. Quant. Spectrosc. Radiat. Transf. 183:128, 2016), who employed their analytical representations for these quantities and the single-term and two-term Henyey-Greenstein phase functions of appreciably high degrees of anisotropy. While our results are in satisfactory agreement with theirs, our procedure is in need of a faster algorithm to routinely deal with problems involving highly anisotropic phase functions giving rise to near-conservative scattering.     

A spectroscopic study of Epsilon Aurigae

Epsilon Aurigae has been observed during ingress and totality between 1982 and 1983 at Okayama. Analyses of profiles of H line and of radial velocities of neutral hydrogen and metals show that the secondary component consists of at least three parts in structure.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.     

Evolution of West Rota Volcano, an extinct submarine volcano in the southern Mariana Arc: Evidence from sea floor morphology, remotely operated vehicle observations and 40Ar–39Ar geochronological studies

Abstract West Rota Volcano (WRV) is a recently discovered extinct submarine volcano in the southern Mariana Arc. It is large (25 km diameter base), shallow (up to 300 m below sealevel), and contains a large caldera (6 × 10 km, with up to 1 km relief). The WRV lies near the northern termination of a major NNE‐trending normal fault. This and a second, parallel fault just west of the volcano separate uplifted, thick frontal arc crust to the east from subsiding, thin back‐arc basin crust to the west. The WRV is distinct from other Mariana Arc volcanoes: (i) it consists of a lower, predominantly andesite section overlain by a bimodal rhyolite‐basalt layered sequence; (ii) andesitic rocks are locally intensely altered and mineralized; (iii) it has a large caldera; and (iv) WRV is built on a major fault. Submarine felsic calderas are common in the Izu and Kermadec Arcs but are otherwise unknown from the Marianas and other primitive, intraoceanic arcs. ⁴⁰Ar–³⁹Ar dating indicates that andesitic volcanism comprising the lower volcanic section occurred 0.33–0.55 my ago, whereas eruption of the upper rhyolites and basalts occurred 37–51 thousand years ago. Four sequences of rhyolite pyroclastics each are 20–75 m thick, unwelded and show reverse grading, indicating submarine eruption. The youngest unit consists of 1–2 m diameter spheroids of rhyolite pumice, interpreted as magmatic balloons, formed by relatively quiet effusion and inflation of rhyolite into the overlying seawater. Geochemical studies indicate that felsic magmas were generated by anatexis of amphibolite‐facies meta‐andesites, perhaps in the middle arc crust. The presence of a large felsic volcano and caldera in the southern Marianas might indicate interaction of large normal faults with a mid‐crustal magma body at depth, providing a way for viscous felsic melts to reach the surface.     

Spatial periodicity of galaxy number counts, CMB anisotropy, and SNIa Hubble diagram based on the universe accompanied by a non-minimally coupled scalar field

We have succeeded in establishing a cosmological model with a non-minimally coupled scalar field φ that can account not only for the spatial periodicity or the picket-fence structure exhibited by the galaxy N-z relation of the 2dF survey but also for the spatial power spectrum of the cosmic microwave background radiation (CMB) temperature anisotropy observed by the WMAP satellite. The Hubble diagram of our model also compares well with the observation of Type Ia supernovae. The scalar field of our model universe starts from an extremely small value at around the nucleosynthesis epoch, remains in that state for sufficiently long periods, allowing sufficient time for the CMB temperature anisotropy to form, and then starts to grow in magnitude at the redshift z of ～1, followed by a damping oscillation which is required to reproduce the observed picket-fence structure of the N-z relation. To realize such behavior of the scalar field, we have found it necessary to introduce a new form of potential V(φ)∝ φ ²exp?(?q φ ²), with q being a constant. Through this parameter q, we can control the epoch at which the scalar field starts growing.