Magnetically driven accretion in protoplanetary discs

We characterize magnetically driven accretion at radii between 1 au and 100 au in protoplanetary discs, using a series of local non-ideal magnetohydrodynamic (MHD) simulations. The simulations assume a Minimum Mass Solar Nebula (MMSN) disc that is threaded by a net vertical magnetic field of specified strength. Confirming previous results, we find that the Hall effect has only a modest impact on accretion at 30 au, and essentially none at 100 au. At 1-10 au the Hall effect introduces a pronounced bi-modality in the accretion process, with vertical magnetic fields aligned to the disc rotation supporting a strong laminar Maxwell stress that is absent if the field is anti-aligned. In the anti-aligned case, we instead find evidence for bursts of turbulent stress at 5-10 au, which we tentatively identify with the non-axisymmetric Hall-shear instability. The presence or absence of these bursts depends upon the details of the adopted chemical model, which suggests that appreciable regions of actual protoplanetary discs might lie close to the borderline between laminar and turbulent behaviour. Given the number of important control parameters that have already been identified in MHD models, quantitative predictions for disc structure in terms of only radius and accretion rate appear to be difficult. Instead, we identify robust qualitative tests of magnetically driven accretion. These include the presence of turbulence in the outer disc, independent of the orientation of the vertical magnetic fields, and a Hall-mediated bi-modality in turbulent properties extending from the region of thermal ionization to 10 au.Comment: accepted to MNRAS after very minor revision

Resonant state expansion applied to planar waveguides

The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation

Evidence for universality in the initial planetesimal mass function

Planetesimals may form from the gravitational collapse of dense particle clumps initiated by the streaming instability. We use simulations of aerodynamically coupled gas-particle mixtures to investigate whether the properties of planetesimals formed in this way depend upon the sizes of the particles that participate in the instability. Based on three high resolution simulations that span a range of dimensionless stopping time $6 \times 10^{-3} \leq \tau \leq 2$ no statistically significant differences in the initial planetesimal mass function are found. The mass functions are fit by a power-law, ${\rm d}N / {\rm d}M_p \propto M_p^{-p}$, with $p=1.5-1.7$ and errors of $\Delta p \approx 0.1$. Comparing the particle density fields prior to collapse, we find that the high wavenumber power spectra are similarly indistinguishable, though the large-scale geometry of structures induced via the streaming instability is significantly different between all three cases. We interpret the results as evidence for a near-universal slope to the mass function, arising from the small-scale structure of streaming-induced turbulence.Comment: 7 pages, 4 figures, accepted to ApJ Letters after minor modifications, including two new figures and some new text that better clarify our result

Lifetime cost effectiveness of simvastatin in a range of risk groups and age groups derived from a randomised trial of 20,536 people

<i>Objectives</i>: To evaluate the cost effectiveness of 40 mg simvastatin daily continued for life in people of different ages with differing risks of vascular disease. Design A model developed from a randomised trial was used to estimate lifetime risks of vascular events and costs of treatment and hospital admissions in the United Kingdom. <i>Setting</i>: 69 hospitals in the UK. <i>Participants</i>: 20 536 men and women (aged 40-80) with coronary disease, other occlusive arterial disease, or diabetes. <i>Interventions</i>: 40 mg simvastatin daily versus placebo for an average of 5 years. <i>Main</i> <i>outcome</i> <i>measures</i>: Cost effectiveness of 40 mg simvastatin daily expressed as additional cost per life year gained. Major vascular event defined as non-fatal myocardial infarction or death from coronary disease, any stroke, or revascularisation procedure. Results were extrapolated to younger and older age groups at lower risk of vascular disease than were studied directly, as well as to lifetime treatment. <i>Results</i>: At the April 2005 UK price of £4.87 (€7; $9) per 28 day pack of generic 40 mg simvastatin, lifetime treatment was cost saving in most age groups and vascular disease risk groups studied directly. Gains in life expectancy and cost savings decreased with increasing age and with decreasing risk of vascular disease. People aged 40-49 with 5 year risks of major vascular events of 42% and 12% at start of treatment gained 2.49 and 1.67 life years, respectively. Treatment with statins remained cost saving or cost less than £2500 per life year gained in people as young as 35 years or as old as 85 with 5 year risks of a major vascular event as low as 5% at the start of treatment. <i>Conclusions</i>: Treatment with statins is cost effective in a wider population than is routinely treated at present