  Recurring outbursts associated with matter flowing onto compact stellar
remnants (black-holes, neutron stars, white dwarfs) in close binary systems,
provide strong test beds for constraining the poorly understood accretion
process. The efficiency of angular momentum (and thus mass) transport in
accretion discs, which has traditionally been encoded in the $\alpha$-viscosity
parameter, shapes the light-curves of these outbursts. Numerical simulations of
the magneto-rotational instability that is believed to be the physical
mechanism behind this transport find values of $\alpha \sim 0.1-0.2$ as
required from observations of accreting white dwarfs. Equivalent
$\alpha$-viscosity parameters have never been estimated in discs around neutron
stars or black holes. Here we report the results of an analysis of archival
X-ray light-curves of twenty-one black hole X-ray binary outbursts. Applying a
Bayesian approach for a model of accretion allows us to determine corresponding
$\alpha$-viscosity parameters, directly from the light curves, to be $\alpha
\sim$0.2--1. This result may be interpreted either as a strong intrinsic rate
of angular momentum transport in the disc, which can only be sustained by the
magneto-rotational instability if a large-scale magnetic field threads the
disc, or as a direct indication that mass is being lost from the disc through
substantial mass outflows strongly shaping the X-ray binary outburst.
Furthermore, the lack of correlation between our estimates of
$\alpha$-viscosity and accretion state implies that such outflows can remove a
significant fraction of disc mass in all black hole X-ray binary accretion
states, favouring magnetically-driven winds over thermally-driven winds that
require specific radiative conditions.
