It is now accepted that accretion on to classical T Tauri stars is controlled by the stellar magnetosphere, yet to date most accretion models have assumed that their magnetic fields are dipolar. By considering a simple steady state accretion model with both dipolar and complex magnetic fields, we find a correlation between mass accretion rate and stellar mass of the form , with our results consistent within observed scatter. For any particular stellar mass there can be several orders of magnitude difference in the mass accretion rate, with accretion filling factors of a few per cent. We demonstrate that the field geometry has a significant effect in controlling the location and distribution of hotspots, formed on the stellar surface from the high velocity impact of accreting material. We find that hotspots are often at mid to low latitudes, in contrast to what is expected for accretion to dipolar fields, and that particularly for higher mass stars, the accretion flow is predominantly carried by open field lines
Summary. A method is described for numerical integ.ration over a semiinfinite interval using a Gaussian formula, with the corresponding set of orthogonal polynomials constructed from a lognormal weight function.The lognormal weight function and hence the coefficients of the polynomials are functions of two arbitrary parameters; the mean and the logarithmic variance. The method is found to be of particular use for integration of "bell-shaped" or "sharply spiked" functions. Rapidly convergent results can be obtained in these cases, since the lognormat distribution can be used to provide a good approximation to the actual function to be integrated, by suitable choice of the two arbitrary parameters. Two examples are given for integrals with known solutions.Subject Classifications. ANS(MOS): 65D30; CR: 5.16.
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