Star Formation Efficiency and Dispersal of Giant Molecular Clouds with
  UV Radiation Feedback: Dependence on Gravitational Boundedness and Magnetic
  Fields
  Molecular clouds are supported by turbulence and magnetic fields, but
quantifying their influence on cloud lifecycle and star formation efficiency
(SFE) remains an open question. We perform radiation MHD simulations of
star-forming giant molecular clouds (GMCs) with UV radiation feedback, in which
the propagation of UV radiation via ray-tracing is coupled to hydrogen
photochemistry. We consider 10 GMC models that vary in either initial virial
parameter ($1\le\alpha_{v,0}\le 5$) or dimensionless mass-to-magnetic flux
ratio (0.5-8 and $\infty$); the initial mass $10^5M_{\odot}$ and radius 20pc
are fixed. Each model is run with five different initial turbulence
realizations. In most models, the duration of star formation and the timescale
for molecular gas removal (primarily by photoevaporation) are 4-8Myr. Both the
final SFE ($\epsilon_*$) and time-averaged SFE per freefall time
($\epsilon_{ff}$) are reduced by strong turbulence and magnetic fields. The
median $\epsilon_*$ ranges between 2.1% and 9.5%. The median $\epsilon_{ff}$
ranges between 1.0% and 8.0% and anticorrelates with $\alpha_{v,0}$, in
qualitative agreement with previous analytic theory and simulations. However,
the time-dependent $\alpha_{v}(t)$ and $\epsilon_{ff,obs}(t)$ based on
instantaneous gas properties and cluster luminosity are positively correlated
due to rapid evolution, making observational validation of star formation
theory difficult. Our median $\epsilon_{ff,obs}(t)\approx$ 2% is similar to
observed values. We show that the traditional virial parameter estimates the
true gravitational boundedness within a factor of 2 on average, but neglect of
magnetic support and velocity anisotropy can sometimes produce large
departures. Magnetically subcritical GMCs are unlikely to represent sites of
massive star formation given their unrealistic columnar outflows, prolonged
lifetime, and low escape fraction of radiation.
