A completely monotonic function involving the tri- and tetra-gamma functions

The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $\Gamma(x)$ is the gamma function. In this paper we prove that a function involving the difference between $[\psi'(x)]^2+\psi''(x)$ and a proper fraction of $x$ is completely monotonic on $(0,\infty)$.Comment: 10 page

Sub-second variations of high energy ( 300 keV) hard X-ray emission from solar flares

Subsecond variations of hard X-ray emission from solar flares were first observed with a balloon-borne detector. With the launch of the Solar Maximum Mission (SMM), it is now well known that subsecond variations of hard X-ray emission occur quite frequently. Such rapid variations give constraints on the modeling of electron energization. Such rapid variations reported until now, however, were observed at relatively low energies. Fast mode data obtained by the Hard X-ray Burst Spectrometer (HXRBS) has time resolution of approximately 1 ms but has no energy resolution. Therefore, rapid fluctuations observed in the fast-mode HXRBS data are dominated by the low energy hard X-rays. It is of interest to know whether rapid fluctuations are observed in high-energy X-rays. The highest energy band at which subsecond variations were observed is 223 to 1057 keV. Subsecond variations observed with HXRBS at energies greater than 300 keV are reported, and the implications discussed

Generation and recovery of strain in (28)Si-implanted pseudomorphic GeSi films on Si(100)

Effects of ion implantation of 320 keV Si-28 at room temperature in pseudomorphic metastable GexSi1-x (x almost-equal-to 0.04, 0.09, 0.13) layers approximately 170 nm thick grown on Si(100) wafers were characterized by x-ray double-crystal diffractometry and MeV He-4 channeling spectrometry. The damage induced by implantation produces additional compressive strain in the GexSi1-x layers, superimposed on the intrinsic compressive strain of the heterostructures. This strain rises with the dose proportionally for doses below several times 10(14) Si-28/cm2. Furthermore, for a given dose, the strain increases with the Ge content in the layer. Upon thermal processing, the damage anneals out and the strain recovers to the value before implantation. Amorphized samples (doses of greater than 2 x 10(15) Si-28/cm2) regrow poorly

Super active regions and production of major solar flares

The success of imaging detectors with small fields of veiw such as HXIS or P/OF (Pinhole/Occulter Facility) depends heavily on pointing to the right place at the right time. During the solar maximum years many active regions coexist on the solar disk. Therefore, in order to point the imaging detector to the right place, it is important to know which active region is most likely to produce major flares. This knowledge is also important for flare prediction. As a first step toward this goal active regions have been identified which produced major flares observed by HXRBS (Hard X-Ray Burst Spectrometer) on SMM during February 1980 through December 1983. For this study the HXRBS Event List, an updated flare list compiled by the HXRBS group, and the Comprehensive Reports of the Solar Geophysical Data were used. During this period, HXRBS detected hard X-rays from approx 7000 solar flares, out of which only 441 flares produced X-rays with peak count rates exceeding 1000 counts/s. Flares with such high peak count rates are major flares. During the same time period about 2100 active regions passed across the solar disk, out of which only 153 were observed to produce major flares. (Some active regions are known to persist for several solar rotations, but at each passage new active region numbers are assigned and the estimate is based on active region numbers.) Out of these 153 active regions, 25 were observed to produce 5 or more major flares. Considering their high productivity of major flares, we may call these active regions super active regions. These 25 super active regions produced 209 major flares, accounting for 51% of all the major flares with identified active regions

Geometry Diagnostics of a Stellar Flare from Fluorescent X-rays

We present evidence of Fe fluorescent emission in the Chandra HETGS spectrum of the single G-type giant HR 9024 during a large flare. In analogy to solar X-ray observations, we interpret the observed Fe K$\alpha$ line as being produced by illumination of the photosphere by ionizing coronal X-rays, in which case, for a given Fe photospheric abundance, its intensity depends on the height of the X-ray source. The HETGS observations, together with 3D Monte Carlo calculations to model the fluorescence emission, are used to obtain a direct geometric constraint on the scale height of the flaring coronal plasma. We compute the Fe fluorescent emission induced by the emission of a single flaring coronal loop which well reproduces the observed X-ray temporal and spectral properties according to a detailed hydrodynamic modeling. The predicted Fe fluorescent emission is in good agreement with the observed value within observational uncertainties, pointing to a scale height $\lesssim 0.3$\rstar. Comparison of the HR 9024 flare with that recently observed on II Peg by Swift indicates the latter is consistent with excitation by X-ray photoionization.Comment: accepted for publication on the Astrophysical Journal Letter

The Solar Photospheric-to-Coronal Fe abundance from X-ray Fluorescence Lines

The ratio of the Fe abundance in the photosphere to that in coronal flare plasmas is determined by X-ray lines within the complex at 6.7~keV (1.9~\AA) emitted during flares. The line complex includes the He-like Fe (\fexxv) resonance line $w$ (6.70~keV) and Fe K$\alpha$ lines (6.39, 6.40~keV), the latter being primarily formed by the fluorescence of photospheric material by X-rays from the hot flare plasma. The ratio of the Fe K$\alpha$ lines to the \fexxv\ $w$ depends on the ratio of the photospheric-to-flare Fe abundance, heliocentric angle $\theta$ of the flare, and the temperature $T_e$ of the flaring plasma. Using high-resolution spectra from X-ray spectrometers on the {\em P78-1} and {\em Solar Maximum Mission} spacecraft, the Fe abundance in flares is estimated to be $1.6\pm 0.5$ and $2.0 \pm 0.3$ times the photospheric Fe abundance, the {\em P78-1} value being preferred as it is more directly determined. This enhancement is consistent with results from X-ray spectra from the {\em RHESSI} spacecraft, but is significantly less than a factor 4 as in previous work.Comment: Accepted for publication by MNRA

Solar coronal non-thermal processes (Solar Maximum Mission)

The Solar Maximum Mission was used to study solar coronal phenomena in hard X-radiation, since its instrument complement included the first solar hard X-ray telescope. Phenomena related to those discovered from OSO-5 and OSO-7 observations were emphasized