Reionization by Hard Photons: I. X-rays from the First Star Clusters

Observations of the Ly-alpha forest at z~3 reveal an average metallicity Z~0.01 Z_solar. The high-redshift supernovae that polluted the IGM also accelerated relativistic electrons. Since the energy density of the CMB scales as (1+z)^4, at high redshift these electrons cool via inverse Compton scattering. Thus, the first star clusters emit X-rays. Unlike stellar UV ionizing photons, these X-rays can escape easily from their host galaxies. This has a number of important physical consequences: (i) Due to their large mean free path, these X-rays can quickly establish a universal ionizing background and partially reionize the universe in a gradual, homogeneous fashion. If X-rays formed the dominant ionizing background, the universe would have more closely resembled a single-phase medium, rather than a two-phase medium. (ii) X-rays can reheat the universe to higher temperatures than possible with UV radiation. (iii) X-rays counter the tendency of UV radiation to photo-dissociate H2, an important coolant in the early universe, by promoting gas phase H2 formation. The X-ray production efficiency is calibrated to local observations of starburst galaxies, which imply that ~10% of the supernova energy is converted to X-rays. While direct detection of sources in X-ray emission is difficult, the presence of relativistic electrons at high redshift and thus a minimal level of X-ray emission may be inferred by synchrotron emission observations with the Square Kilometer Array. These sources may constitute a significant fraction of the unresolved hard X-ray background, and can account for both the shape and amplitude of the gamma-ray background. This paper discusses the existence and observability of high-redshift X-ray sources, while a companion paper models the detailed reionization physics and chemistry.Comment: Final version accepted by ApJ. 32 pages, 3 figure

Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained

Testing and finding the generating functions of an option pricing mechanism through market data

We study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g-expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricing mechanism. We are mainly concerned with two types of pricing mechanisms in an option market: the market pricing mechanism through which the market prices of options are produced, and the ask-bid pricing mechanism operated through the system of market makers. The later one is a typical nonlinear pricing mechanism. Data of prices produced by these two pricing mechanisms are usually quoted in an option market. We introduce a criteria to test if a dynamic pricing mechanism under investigation is a g-pricing mechanism. This domination condition was statistically tested using CME data documents. The result of test is significantly positive. We also provide some useful characterizations of a pricing mechanism by its generating function

Surface friction of rock in terrestrial and simulated lunar environments

The conventional probe-on-the rotating-disk concept was used to determine the surface friction in mineral probe/specimen interfaces. Nine rocks or minerals and two stainless steels were tested in both new (NT) and same track (ST) tests under three different pressure environments-atmospheric, UHV, and dry nitrogen. Each environment was further subdivided into two testing conditions, that is, ambient and elevated (135 C) temperatures. In NT tests, friction was the lowest in an atmospheric pressure condition for all rock types and increased to the largest in UHV ambient condition except for pyroxene and stainless steel. Friction values measured in dry nitrogen ambient condition lie between the two extremes. Heating tends to increase friction in atmospheric and dry nitrogen environment but decreases in UHV environment with the exception of stainless steel, basalt, and pyroxene. In ST tests, friction was the lowest in the first run and increased in subsequent runs except for stainless steel where the reverse was true. The increases leveled off after a few runs ranging from the second to the seventh depending on rock types

A general comparison theorem for 1-dimensional anticipated BSDEs

Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for 1-dimensional ABSDEs with the generators depending on the anticipated term of $Z$.Comment: 8 page