Euclid: Data Release 1 (DR1) - First NISP emission-line maps: Methodology, validation, and applications to galaxy evolution

We demonstrate the capability of the slitless spectroscopic mode of the Euclid Near-Infrared Spectrometer and Photometer (NISP) to produce emission-line maps analogous to narrow-band images with user-defined central wavelengths. We present the first such maps of galaxies at $0.4 < z < 0.9$, constructed from blue-grism exposures obtained during the Euclid performance-verification observations of the Cosmic Evolution Survey (COSMOS) field in November 2023. We demonstrate the use of these maps for identifying star-forming clumps, measuring radial star-formation profiles, detecting projected internal velocity gradients, deblending the H$α$--[N II] complex, and assessing spectroscopic redshift measurements. As a first statistical application, we reconstruct the galaxy mass--metallicity relation for 885 galaxies observed with the blue grism at $0.4 < z < 0.9$ by deblending the H$α$--[N II] complex in the emission-line maps, and measure stacked H$α$ radial profiles for 2634 galaxies over the same redshift range. The mass--metallicity relation is consistent with that obtained from the Euclid 1D spectroscopic measurements, demonstrating overall agreement between the two deblending approaches. The recovered H$α$ radial profiles broadly follow the YE stellar continuum but remain modestly more extended after matching the YE images to the H$α$ PSF, consistent with previous results in the literature. Across the four YE size bins, we measure a mean R50,Hα/R_50,YE=1.15.