It has been recognized that the observed galaxy distribution 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 matter distribution to the super-sample modes at the field level. The formalism presented here reproduces the power spectrum responses that have been previously derived, and beyond the leading order, it also enables us to proceed to a higher-order calculation. As an application, we consider the statistics of the intrinsic alignments of galaxies and halos, and derive the field response of the galaxy/halo ellipticity to the super-sample modes. Possible impacts of the long-mode contributions on the covariance of the power spectra are also discussed, and the signal-to-noise ratios are estimated.
Download