Constraining dark matter properties with SPI

Using the high-resolution spectrometer SPI on board the International Gamma-Ray Astrophysics Laboratory ( INTEGRAL ), we search for a spectral line produced by a dark matter (DM) particle with a mass in the range  40 keV < M _DM < 14 MeV  , decaying in the DM halo of the Milky Way. To distinguish the DM decay line from numerous instrumental lines found in the SPI background spectrum, we study the dependence of the intensity of the line signal on the offset of the SPI pointing from the direction toward the Galactic Centre. After a critical analysis of the uncertainties of the DM density profile in the inner Galaxy, we find that the intensity of the DM decay line should decrease by at least a factor of 3 when the offset from the Galactic Centre increases from 0° to 180°. We find that such a pronounced variation of the line flux across the sky is not observed for any line, detected with a significance higher than 3σ in the SPI background spectrum. Possible DM decay origin is not ruled out only for the unidentified spectral lines, having low (∼3σ) significance or coinciding in position with the instrumental ones. In the energy interval from 20 keV to 7 MeV, we derive restrictions on the DM decay line flux, implied by the (non-)detection of the DM decay line. For a particular DM candidate, the sterile neutrino of mass M _DM, we derive a bound on the mixing angle.     

Constraints on decaying dark matter from XMM–Newton observations of M31

We derive constraints on the parameters of the radiatively decaying dark matter (DM) particle, using the XMM–Newton EPIC spectra of the Andromeda galaxy (M31). Using the observations of the outer (5–13 arcmin) parts of M31, we improve the existing constraints. For the case of sterile neutrino DM, combining our constraints with the latest computation of abundances of sterile neutrinos in the Dodelson–Widrow (DW) scenario, we obtain the lower mass limit   m _s < 4 keV  , which is stronger than the previous one   m _s < 6 keV  , obtained recently by Asaka, Laine & Shaposhnikov. Comparing this limit with the most recent results on Lyman α forest analysis of Viel et al.  ( m _s > 5.6 keV  ), we argue that the scenario in which all the DM is produced via the DW mechanism is ruled out. We discuss, however, other production mechanisms and note that the sterile neutrino remains a viable candidate for DM, either warm or cold.     

The offset‐midpoint travel‐time pyramid for P‐wave in 2D transversely isotropic media with a tilted symmetry axis

For pre‐stack phase‐shift migration in homogeneous isotropic media, the offset‐midpoint travel time is represented by the double‐square‐root equation. The travel time as a function of offset and midpoint resembles the shape of Cheops’ pyramid. This is also valid for transversely isotropic media with a vertical symmetry axis. In this study, we extend the offset‐midpoint travel‐time pyramid to the case of 2D transversely isotropic media with a tilted symmetry axis. The P‐wave analytical travel‐time pyramid is derived under the assumption of weak anelliptical property of the tilted transverse isotropy media. The travel‐time equation for the dip‐constrained transversely isotropic model is obtained from the depth‐domain travel‐time pyramid. The potential applications of the derived offset‐midpoint travel‐time equation include pre‐stack Kirchhoff migration, anisotropic parameter estimation, and travel‐time calculation in transversely isotropic media with a tilted symmetry axis.     

On shear‐wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axis

The presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The traveltime curve becomes multi‐valued and the geometrical spreading correction factor tends to zero due to energy focusing. We analyse the conditions for the qSV‐wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis. The proposed technique can easily be extended to the case of horizontally layered vertical symmetry axis medium. We show that the triplications of the qSV‐wave in a multilayered medium imply certain algebra. We illustrate this algebra on a two‐layer vertical symmetry axis model.     

Applied Mathematics in EM Studies with Special Emphasis on an Uncertainty Quantification and 3-D Integral Equation Modelling

Despite impressive progress in the development and application of electromagnetic (EM) deterministic inverse schemes to map the 3-D distribution of electrical conductivity within the Earth, there is one question which remains poorly addressed—uncertainty quantification of the recovered conductivity models. Apparently, only an inversion based on a statistical approach provides a systematic framework to quantify such uncertainties. The Metropolis–Hastings (M–H) algorithm is the most popular technique for sampling the posterior probability distribution that describes the solution of the statistical inverse problem. However, all statistical inverse schemes require an enormous amount of forward simulations and thus appear to be extremely demanding computationally, if not prohibitive, if a 3-D set up is invoked. This urges development of fast and scalable 3-D modelling codes which can run large-scale 3-D models of practical interest for fractions of a second on high-performance multi-core platforms. But, even with these codes, the challenge for M–H methods is to construct proposal functions that simultaneously provide a good approximation of the target density function while being inexpensive to be sampled. In this paper we address both of these issues. First we introduce a variant of the M–H method which uses information about the local gradient and Hessian of the penalty function. This, in particular, allows us to exploit adjoint-based machinery that has been instrumental for the fast solution of deterministic inverse problems. We explain why this modification of M–H significantly accelerates sampling of the posterior probability distribution. In addition we show how Hessian handling (inverse, square root) can be made practicable by a low-rank approximation using the Lanczos algorithm. Ultimately we discuss uncertainty analysis based on stochastic inversion results. In addition, we demonstrate how this analysis can be performed within a deterministic approach. In the second part, we summarize modern trends in the development of efficient 3-D EM forward modelling schemes with special emphasis on recent advances in the integral equation approach.     

The proportion of hot and cold regions in the polar solar corona during 1957–2002

Occultation observations of the intensity of the FeXIV 530.3 nm and FeX 637.4 nm forbidden lines detected at the Kislovodsk Mountain Station during 1957–2002, indicate long-term changes in the structure of the solar corona. The monthly average intensities of green (KI_530.3) and red (KI_637.4) spectral lines are calculated for all latitudes (0°–90°) and for a high-latitude zone (45°–90°). A strong correlation (r = 0.91) between the green KI_530.3 line intensity and the Wolf numbers is found and used to fill gaps in the observations. The ratio KI_637.4/KI_530.3 takes on its maximum value at the solar minimum. The KI _637.4 ^p /KI _530.3 ^p ratio in the high-latitude solar zone (45°–90°) increased by more than a factor of two during 1957–2002. This means that the fraction of cool regions in the polar corona has more than doubled over these years. We suggest that this increase in the number of cool regions is related to an increase in the area of the polar solar zones occupied by magnetic field of a single polarity at the solar minimum, and possibly to an increase in the area occupied by polar coronal holes. This is associated with long-term variations in the internal structure of the Sun.     

Intracontinental mountain building in Central Asia as inferred from satellite geodetic data

The results of longstanding GPS measurements in the northwestern part of Central Asia are discussed. These results impose certain constraints for modeling of intraplate tectonic processes. In the territory covered by observations, the velocity vectors of recent motions of the Earth’s surface relative to the stable portion of Eurasia decrease northward. The plane field of velocities, which rules out the development of extension zones, indicates the impossibility of the mountain building driven by ascending mantle flows beneath the lithosphere of these regions. The nonuniform spatial distribution of the motions is suggestive of the discrete character of the Earth’s crust and its deformation. The crust is brittle, at least in its upper part, and capable of breaking into blocks. The blocks, which move at different velocities, interact with one another and change their original orientation and position, while experiencing independent deformations. This phenomenon has been exemplified in the Tarim Block and the Tien Shan. Within the limits of the constraints imposed by the GPS measurements, the mechanism of intracontinental mountain building related to the lateral flow of asthenospheric material and to the drag of the overlying lithospheric layers is discussed. This mechanism springs from Argand’s ideas [2, 29] and the plate tectonic concept [10, 23]. The upper-mantle convective flow in the direction of the Indian Plate’s motion was the main cause of the crustal deformation. The detachment of the lithospheric mantle from the Indian Plate approximately 25 Ma ago and its subduction beneath the Himalayas and Tibet, along with simultaneous ascent of the remaining crust and uplift of the Tibetan Plateau, allowed the mantle flow to spread far northward beneath the Asian continent. This process is accompanied by consecutive separation and sinking of the cooling asthenospheric material over the entire area from the Himalayas to Siberia as the subcrustal material cools. As a result, the flow velocity decreases, the roof of the active flow plunges, and the lithosphere becomes thicker. The motion and deformation of the lithospheric layers dragged by deep flow cannot follow the asthenospheric flow strictly, owing to the rigidity of the layers. Therefore, a difference of tangential velocities originates between the flow and the lithosphere, thus giving rise to horizontal shear stresses. These stresses affect the overlying lithospheric layers, including the crustal ones, and bring about their drag and tectonic delamination. Simultaneously, the decreasing velocity in the direction of the mantle flow results in bending of the lithospheric layers that is accompanied by local warping of the crust and its stacking and fragmentation into blocks. The different velocities of block motions lead to their mechanical interactions. This scenario of intracontinental mountain building allows an explanation of the many specific features of tectonic processes and orogeny in within-plate mountainous regions.