Lagrangian approach to super-sample effects on biased tracers at field
  level: galaxy density fields and intrinsic alignments
  It has been recognized that the observables of large-scale structure (LSS) is
susceptible to long-wavelength density and tidal fluctuations whose wavelengths
exceed the accessible scale of a finite-volume observation, referred to as the
super-sample modes. The super-sample modes modulate the growth and expansion
rate of local structures, thus affecting the cosmological information encoded
in the statistics of galaxy clustering data. In this paper, based on the
Lagrangian perturbation theory, we develop a new formalism to systematically
compute the response of a biased tracer of LSS, which is expressed
perturbatively in terms of the matter density field of sub-survey modes, to the
super-sample modes at the field level. The formalism presented here reproduces
the power spectrum responses that have been previously derived, and provides an
alternative way to compute statistical quantities with super-sample modes. As
an application, we consider the statistics of the intrinsic alignments of
galaxies and halos, and derive the field response of the galaxy/halo shape bias
to the super-sample modes. Possible impacts of the long-mode contributions on
the covariance of the three-dimensional power spectra of the intrinsic
alignment are also discussed, and the signal-to-noise ratios are estimated.
