Local Primordial Non-Gaussianities and Super-Sample Variance
  Fluctuations with wavelengths larger than the volume of a galaxy survey
affect the measurement of the galaxy power spectrum within the survey itself.
In the presence of local Primordial Non- Gaussianities (PNG), in addition to
the super-sample matter density and tidal fluctuations, the large-scale
gravitational potential also induces a modulation of the observed power
spectrum. In this work we investigate this modulation by computing for the
first time the response of the redshift-space galaxy power spectrum to the
presence of a long wavelength gravitational potential, fully accounting for the
stochastic contributions. For biased tracers new response functions arise due
to couplings between the small-scale fluctuations in the density, velocity and
gravitational fields, the latter through scale dependent bias operators, and
the large-scale gravitational potential. We study the impact of the
super-sample modes on the measurement of the amplitude of the primordial
bispectrum of the local-shape, $f_{\rm NL}^{\rm loc}$, accounting for
modulations of both the signal and the covariance of the galaxy power spectrum
by the long modes. Considering DESI-like survey specifications, we show that in
most cases super-sample modes cause little or no degradation of the
constraints, and could actually reduce the errorbars on $f_{\rm NL}^{\rm loc}$
by (10 - 30)\%, if external information on the bias parameters is available.
