  We investigate the compact, early-type galaxy NGC 1281 with integral field
unit observations to map the stellar LOSVD out to 5 effective radii and
construct orbit-based dynamical models to constrain its dark and luminous
matter content. Under the assumption of mass-follows-light, the H-band stellar
mass-to-light ratio (M/L) is {\Upsilon} = 2.7(+-0.1) {\Upsilon}_{sun}, higher
than expected from our stellar population synthesis fits with either a
canonical Kroupa ({\Upsilon} = 1.3 {\Upsilon}_{sun}) or Salpeter ({\Upsilon} =
1.7 {\Upsilon}_{sun}) stellar initial mass function. Such models also cannot
reproduce the details of the LOSVD. Models with a dark halo recover the
kinematics well and indicate that NGC 1281 is dark matter dominated, making up
~ 90 per cent of the total enclosed mass within the kinematic bounds.
Parameterised as a spherical NFW profile, the dark halo mass is 11.5 <
log(M_{DM}/M_{sun}) < 11.8 and the stellar M/L is 0.6 < {\Upsilon} < 1.1.
However, this stellar M/L is lower than predicted by its old stellar
population. Moreover, the halo mass within the kinematic extent is ten times
larger than expected based on {\Lambda}CDM predictions, and an extrapolation
yields cluster sized dark halo masses. Adopting {\Upsilon} = 1.7
{\Upsilon}_{sun} yields more moderate dark halo virial masses, but these models
fit the kinematics worse. A non-NFW model might solve the discrepancy between
the unphysical consequences of the best-fitting dynamical models and models
based on more reasonable assumptions for the dark halo and stellar
mass-to-light ratio, which are disfavoured according to our parameter
estimation.
