The spin of accreting stars: dependence on magnetic coupling to the disc
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abstract
We formulate a general, steady-state model for the torque on a magnetized
star from a surrounding accretion disc. For the first time, we include the
opening of dipolar magnetic field lines due to the differential rotation
between the star and disc, so the magnetic topology then depends on the
strength of the magnetic coupling to the disc. This coupling is determined by
the effective slip rate of magnetic field lines that penetrate the diffusive
disc. Stronger coupling (i.e., lower slip rate) leads to a more open topology
and thus to a weaker magnetic torque on the star from the disc. In the expected
strong coupling regime, we find that the spin-down torque on the star is more
than an order of magnitude smaller than calculated by previous models. We also
use our general approach to examine the equilibrium (`disc-locked') state, in
which the net torque on the star is zero. In this state, we show that the
stellar spin rate is roughly an order of magnitude faster than predicted by
previous models. This challenges the idea that slowly-rotating, accreting
protostars are disc locked. Furthermore, when the field is sufficiently open
(e.g., for mass accretion rates > 5 x 10^{-9} M_sun / yr, for typical accreting
protostars), the star will receive no magnetic spin-down torque from the disc
at all. We therefore conclude that protostars must experience a spin-down
torque from a source that has not yet been considered in the star-disc torque
models--possibly from a stellar wind along the open field lines.