We probe the geometry of magnetospheric accretion in classical T Tauri stars by modeling red absorption at He I 10830 via scattering of the stellar and veiling continua. Under the assumptions that the accretion flow is an azimuthally symmetric dipole and helium is sufficiently optically thick that all incident 1-micron radiation is scattered, we illustrate the sensitivity of He I 10830 red absorption to both the size of the magnetosphere and the filling factor of the hot accretion shock. We compare model profiles to those observed in 21 CTTS with subcontinuum redshifted absorption at He I 10830 and find that about half of the stars have red absorptions and 1-micron veilings that are consistent with dipole flows of moderate width with accretion shock filling factors matching the size of the magnetospheric footpoints. However, the remaining 50% of the profiles, with a combination of broad, deep absorption and low 1-micron veiling, require very wide flows where magnetic footpoints are distributed over 10-20% of the stellar surface but accretion shock filling factors are < 1%. We model these profiles by invoking large magnetospheres dilutely filled with accreting gas, leaving the disk over a range of radii in many narrow streamlets that fill only a small fraction of the entire infall region. In some cases accreting streamlets need to originate in the disk between several stellar radii and at least the corotation radius. A few stars have such deep absorption at velocities greater than half the stellar escape velocity that flows near the star with less curvature than a dipole trajectory seem to be required.
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