Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio

Extreme Ultra-Violet Spectroscopy of the Lower Solar Atmosphere During Solar Flares

The extreme ultraviolet portion of the solar spectrum contains a wealth of diagnostic tools for probing the lower solar atmosphere in response to an injection of energy, particularly during the impulsive phase of solar flares. These include temperature and density sensitive line ratios, Doppler shifted emission lines and nonthermal broadening, abundance measurements, differential emission measure profiles, and continuum temperatures and energetics, among others. In this paper I shall review some of the advances made in recent years using these techniques, focusing primarily on studies that have utilized data from Hinode/EIS and SDO/EVE, while also providing some historical background and a summary of future spectroscopic instrumentation.Comment: 34 pages, 8 figures. Submitted to Solar Physics as part of the Topical Issue on Solar and Stellar Flare

Approximate gravitational field of a rotating deformed mass

A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters representing the quadrupole and the angular momentum respectively. The main feature of the solution is a suitable description of small deviations from spherical symmetry through perturbations of the static configuration and the massive multipole structure by using those parameters. This quality of the solution might eventually provide relevant differences with respect to the description provided by the Kerr solution.Comment: 16 pages. Latex. To appear in General Relativity and Gravitatio

New Insights into White-Light Flare Emission from Radiative-Hydrodynamic Modeling of a Chromospheric Condensation

(abridged) The heating mechanism at high densities during M dwarf flares is poorly understood. Spectra of M dwarf flares in the optical and near-ultraviolet wavelength regimes have revealed three continuum components during the impulsive phase: 1) an energetically dominant blackbody component with a color temperature of T $\sim$ 10,000 K in the blue-optical, 2) a smaller amount of Balmer continuum emission in the near-ultraviolet at lambda $<$ 3646 Angstroms and 3) an apparent pseudo-continuum of blended high-order Balmer lines. These properties are not reproduced by models that employ a typical "solar-type" flare heating level in nonthermal electrons, and therefore our understanding of these spectra is limited to a phenomenological interpretation. We present a new 1D radiative-hydrodynamic model of an M dwarf flare from precipitating nonthermal electrons with a large energy flux of $10^{13}$ erg cm$^{-2}$ s$^{-1}$. The simulation produces bright continuum emission from a dense, hot chromospheric condensation. For the first time, the observed color temperature and Balmer jump ratio are produced self-consistently in a radiative-hydrodynamic flare model. We find that a T $\sim$ 10,000 K blackbody-like continuum component and a small Balmer jump ratio result from optically thick Balmer and Paschen recombination radiation, and thus the properties of the flux spectrum are caused by blue light escaping over a larger physical depth range compared to red and near-ultraviolet light. To model the near-ultraviolet pseudo-continuum previously attributed to overlapping Balmer lines, we include the extra Balmer continuum opacity from Landau-Zener transitions that result from merged, high order energy levels of hydrogen in a dense, partially ionized atmosphere. This reveals a new diagnostic of ambient charge density in the densest regions of the atmosphere that are heated during dMe and solar flares.Comment: 50 pages, 2 tables, 13 figures. Accepted for publication in the Solar Physics Topical Issue, "Solar and Stellar Flares". Version 2 (June 22, 2015): updated to include comments by Guest Editor. The final publication is available at Springer via http://dx.doi.org/10.1007/s11207-015-0708-

The Epidemiology of Ankle Sprains In United States High School Sports, 2011/12-2018/19 Academic Years

Context:Continued monitoring of ankle sprain rates and distributions is needed to assess temporal patterns and gauge how changes in incidence may be associated with prevention efforts. Objective:Describe the epidemiology of ankle sprains in 15 high school sports during the 2011/12–2018/19 school years. Study Design: Descriptive epidemiology study. Setting: Online injury surveillance from high school sports. Patients:High school athletes who participated in practices and competitions during the 2011/12–2018/19 school years. Methods: A convenience sample of high school athletic trainers (ATs) provided injury and athlete-exposure (AE) data to the National High School Sports-Related Injury Surveillance Study (HS RIOTM). Ankle sprain rates per 10,000AE with 95% confidence intervals (CI) and distributions were calculated. Yearly rates were examined overall, by event type, injury mechanism, and recurrence. Results: Overall, 9,320 ankle sprains were reported (overall rate=2.95/10,000AE; 95%CI: 2.89–3.01). The highest sport-specific rates were reported in girls\u27 basketball (5.32/10,000AE), boys\u27 basketball (5.13/10,000AE), girls\u27 soccer (4.96/10,000AE), and boys\u27 football (4.55/10,000AE). Most ankle sprains occurred during competition (54.3%) and were due to contact with another person (39.5%) and non-contact (35.0%). Also, 14.5% of injuries were noted as recurrent. Across the included academic years, ankle sprain rates generally increased. Compared to the 2011/12 academic year, rates in the 2018/19 academic year overall were 22% higher; non-contact-related and recurrent ankle sprain rates also generally increased, with 91% and 29% increases, respectively. Conclusions:: Time trends suggest ankle sprain rates have increased across the past decade, particularly among those with non-contact-related mechanisms; this contrasts previous research suggesting decreases in incidence. Findings may pinpoint specific etiological factors that should direct prevention efforts. This includes considering both person-contact and non-contact mechanisms through mitigating illegal contact through rule changes and enforcement, alongside bracing and proprioceptive and balance training programs