Supernovae driven turbulence in the interstellar medium

PhD ThesisI model the multi-phase interstellar medium (ISM) randomly heated and shocked by supernovae (SN), with gravity, differential rotation and other parameters we understand to be typical of the solar neighbourhood. The simulations are in a 3D domain extending horizontally 1 1 kpc2 and vertically 2 kpc, symmetric about the galactic mid-plane. They routinely span gas number densities 105–102 cm3, temperatures 10–108 K, speeds up to 103 km s1 and Mach number up to 25. Radiative cooling is applied from two widely adopted parameterizations, and compared directly to assess the sensitivity of the results to cooling. There is strong evidence to describe the ISM as comprising well defined cold, warm and hot regions, typified by T 102 ; 104 and 106 K, which are statistically close to thermal and total pressure equilibrium. This result is not sensitive to the choice of parameters considered here. The distribution of the gas density within each can be robustly modelled as lognormal. Appropriate distinction is required between the properties of the gases in the supernova active mid-plane and the more homogeneous phases outside this region. The connection between the fractional volume of a phase and its various proxies is clarified. An exact relation is then derived between the fractional volume and the filling factors defined in terms of the volume and probabilistic averages. These results are discussed in both observational and computational contexts. The correlation scale of the random flows is calculated from the velocity autocorrelation function; it is of order 100 pc and tends to grow with distance from the mid-plane. The origin and structure of the magnetic fields in the ISM is also investigated in nonideal MHD simulations. A seed magnetic field, with volume average of roughly 4 nG, grows exponentially to reach a statistically steady state within 1.6 Gyr. Following Germano (1992), volume averaging is applied with a Gaussian kernel to separate magnetic field into a mean field and fluctuations. Such averaging does not satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The mean field thus obtained varies in both space and time. Growth rates differ for the mean-field and fluctuating field and there is clear scale separation between the two elements, whose integral scales are about 0:7 kpc and 0:3 kpc, respectively. Analysis of the dependence of the dynamo on rotation, shear and SN rate is used to clarify its mean and fluctuating contributions. The resulting magnetic field is quadrupolar, symmetric about the mid-plane, with strong positive azimuthal and weak negative radial orientation. Contrary to conventional wisdom, the mean field strength increases away from the mid-plane, peaking outside the SN active region at jzj ' 300 pc. The strength of the field is strongly dependent on density, and in particular the mean field is mainly organised in the warm gas, locally very strong in the cold gas, but almost absent in the hot gas. The field in the hot gas is weak and dominated by fluctuations

Magnetohydrostatic equilibrium. I: Three-dimensional open magnetic flux tube in the stratified solar atmosphere

A single open magnetic flux tube spanning the solar photosphere (solar radius R) and the lower corona (R + 10 Mm) is modelled in magnetohydrostatic equilibrium within a realistic stratified atmosphere subject to solar gravity. Such flux tubes are observed to remain relatively stable for up to a day or more, and it is our aim to apply the model as the background condition for numerical studies of energy transport mechanisms from the surface to the corona. We solve analytically an axially symmetric 3D structure for the model, with magnetic field strength, plasma density, pressure and temperature all consistent with observational and theoretical estimates. The self similar construction ensures the magnetic field is divergence free. The equation of pressure balance for this particular set of flux tubes can be integrated analytically to find the pressure and density corrections required to preserve the magnetohydrostatic equilibrium. The model includes a number of free parameters, which makes the solution applicable to a variety of other physical problems and it may therefore be of more general interest.Comment: 9 pages, 8 figure

Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)