The Theory of Gamma-Ray Bursts

This chapter gives a brief review on the theory of gamma-ray bursts (GRBs), including the models of multi-messengers (e.g., prompt multiwavelength electromagnetic emissions, high-energy neutrinos, ultra-high-energy cosmic rays, and gravitational waves) and central engines (in particular, mergers of binary neutron stars for short GRBs). For detailed reviews, please see (Piran in Phys. Rep. 314:575, 1999; Rev. Mod. Phys. 76:1143, 2004; Mészáros in Annu. Rev. Astron. Astrophys. 40:137, 2002; Rep. Prog. Phys. 69:2259, 2006; Zhang and Mészáros in Int. J. Mod. Phys. A 19:2385, 2004; Zhang in Chin. J. Astron. Astrophys. 7:1, 2007; Nakar in Phys. Rep. 442:166, 2007; Kumar and Zhang in Phys. Rep. 561:1, 2015).     

Interplanetary Origin of Intense,Superintense and Extreme Geomagnetic Storms

We present a review on the interplanetary causes of intense geomagnetic storms (Dst≤−100 nT), that occurred during solar cycle 23 (1997–2005). It was reported that the most common interplanetary structures leading to the development of intense storms were: magnetic clouds, sheath fields, sheath fields followed by a magnetic cloud and corotating interaction regions at the leading fronts of high speed streams. However, the relative importance of each of those driving structures has been shown to vary with the solar cycle phase. Superintense storms (Dst≤−250 nT) have been also studied in more detail for solar cycle 23, confirming initial studies done about their main interplanetary causes. The storms are associated with magnetic clouds and sheath fields following interplanetary shocks, although they frequently involve consecutive and complex ICME structures. Concerning extreme storms (Dst≤−400 nT), due to the poor statistics of their occurrence during the space era, only some indications about their main interplanetary causes are known. For the most extreme events, we review the Carrington event and also discuss the distribution of historical and space era extreme events in the context of the sunspot and Gleissberg solar activity cycles, highlighting a discussion about the eventual occurrence of more Carrington-type storms.     

Long-Term Evolution of the Martian Crust-Mantle System

Lacking plate tectonics and crustal recycling, the long-term evolution of the crust-mantle system of Mars is driven by mantle convection, partial melting, and silicate differentiation. Volcanic landforms such as lava flows, shield volcanoes, volcanic cones, pyroclastic deposits, and dikes are observed on the martian surface, and while activity was widespread during the late Noachian and Hesperian, volcanism became more and more restricted to the Tharsis and Elysium provinces in the Amazonian period. Martian igneous rocks are predominantly basaltic in composition, and remote sensing data, in-situ data, and analysis of the SNC meteorites indicate that magma source regions were located at depths between 80 and 150 km, with degrees of partial melting ranging from 5 to 15 %. Furthermore, magma storage at depth appears to be of limited importance, and secular cooling rates of 30 to 40 K?Gyr^?1 were derived from surface chemistry for the Hesperian and Amazonian periods. These estimates are in general agreement with numerical models of the thermo-chemical evolution of Mars, which predict source region depths of 100 to 200 km, degrees of partial melting between 5 and 20 %, and secular cooling rates of 40 to 50 K?Gyr^?1. In addition, these model predictions largely agree with elastic lithosphere thickness estimates derived from gravity and topography data. Major unknowns related to the evolution of the crust-mantle system are the age of the shergottites, the planet’s initial bulk mantle water content, and its average crustal thickness. Analysis of the SNC meteorites, estimates of the elastic lithosphere thickness, as well as the fact that tidal dissipation takes place in the martian mantle indicate that rheologically significant amounts of water of a few tens of ppm are still present in the interior. However, the exact amount is controversial and estimates range from only a few to more than 200 ppm. Owing to the uncertain formation age of the shergottites it is unclear whether these water contents correspond to the ancient or present mantle. It therefore remains to be investigated whether petrologically significant amounts of water of more than 100 ppm are or have been present in the deep interior. Although models suggest that about 50 % of the incompatible species (H₂O, K, Th, U) have been removed from the mantle, the amount of mantle differentiation remains uncertain because the average crustal thickness is merely constrained to within a factor of two.     

On the Detectability and Use of Normal Modes for Determining Interior Structure of Mars

The InSight mission to Mars is well underway and will be the first mission to acquire seismic data from a planet other than Earth. In order to maximise the science return of the InSight data, a multifaceted approach will be needed that seeks to investigate the seismic data from a series of different frequency windows, including body waves, surface waves, and normal modes. Here, we present a methodology based on globally-averaged models that employs the long-period information encoded in the seismic data by looking for fundamental-mode spheroidal oscillations. From a preliminary analysis of the expected signal-to-noise ratio, we find that normal modes should be detectable during nighttime in the frequency range 5–15 mHz. For improved picking of (fundamental) normal modes, we show first that those are equally spaced between 5–15 mHz and then show how this spectral spacing, obtained through autocorrelation of the Fourier-transformed time series can be further employed to select normal mode peaks more consistently. Based on this set of normal-mode spectral frequencies, we proceed to show how this data set can be inverted for globally-averaged models of interior structure (to a depth of \(\sim 250~\mbox{km}\)), while simultaneously using the resultant synthetically-approximated normal mode peaks to verify the initial peak selection. This procedure can be applied iteratively to produce a “cleaned-up” set of spectral peaks that are ultimately inverted for a “final” interior-structure model. To investigate the effect of three-dimensional (3D) structure on normal mode spectra, we constructed a 3D model of Mars that includes variations in surface and Moho topography and lateral variations in mantle structure and employed this model to compute full 3D waveforms. The resultant time series are converted to spectra and the inter-station variation hereof is compared to the variation in spectra computed using different 1D models. The comparison shows that 3D effects are less significant than the variation incurred by the difference in radial models, which suggests that our 1D approach represents an adequate approximation of the global average structure of Mars.     

A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.     

Prediction of Boundary Layer Transition Based on Modeling of Laminar Fluctuations Using RANS Approach

This article presents a linear eddy-viscosity turbulence model for predicting bypass and natural transition in boundary layers by using Reynolds-averaged Navier-Stokes (RANS) equations. The model includes three transport equations, separately, to compute laminar kinetic energy, turbulent kinetic energy, and dissipation rate in a flow field. It needs neither correlations of intermittency factors nor knowledge of the transition onset. Two transition tests are carried out: flat plate boundary layer under zero ...