A Quasar-Anchored Protocluster at z=6.6 in the ASPIRE Survey: II. An Environmental Analysis of Galaxy Properties in an Overdense Structure

We present paper II comprising a 35 arcmin$^2$ \textit{JWST}/NIRCam imaging and wide-field slitless spectroscopy mosaic centered on J0305$-$3150, a luminous quasar at $z=6.61$. The F356W grism data reveals 124 [OIII]+H$\beta$ emitters at $5.3<z<7$, 53 of which constitute a protocluster spanning (10 cMpc)$^2$ across $6.5<z<6.8$. We find no evidence of any broad-line AGN in individual galaxies or stacking, reporting a median H$\beta$ FWHM of 585 $\pm$ 152 km s$^{-1}$; however, the mass-excitation diagram and ``little red dot" color and compactness criteria suggest that there are a few AGN candidates on the outskirts of the protocluster. We fit the spectral energy distributions (SEDs) of the [OIII] emitters with \texttt{Prospector} and \texttt{Bagpipes}, and find that none of the SED-derived properties (stellar mass, age, or star formation rate) correlates with proximity to the quasar. While there is no correlation between galaxy age and local galaxy density, we find modest correlations between local galaxy density with increasing stellar mass, decreasing 10-to-100 Myr star formation rate ratios and decreasing nebular line equivalent widths. We further find that the protocluster galaxies are consistent with being more massive, older, and hosting higher star formation rates than the field sample at the 3$\sigma$ level, distributed in a filamentary structure which supports inside-out formation of the protocluster. There is modest evidence that galaxy evolution proceeds differently as a function of the density of local environment within protoclusters during the epoch of reionization, and the central quasar has little effect on the galaxy properties of the surrounding structure.