NGDEEP: A New Non-Parametric Measure of Local Star-Formation and Attenuation at Cosmic Noon

We introduce a new non-parametric technique to quantify the spatially-resolved relationship between the local star-formation rate (SFR) and dust attenuation. We then apply it to 14 star-forming galaxies at $1.0<z<2.5$ using JWST/NIRISS slitless spectroscopy from the NGDEEP survey. First, we construct spatially resolved (~1~kpc per pixel) Balmer decrement ($Hα/Hβ$) maps of these galaxies and derive their corresponding dust attenuation and intrinsic SFR maps. We then rank-order the map pixels by attenuation and construct a cumulative distribution curve of the total SFR as a function of increasing attenuation. We define ASFR10%, ASFR50%, and ASFR90% as the dust attenuation levels behind which 10%, 50%, and 90% of the total integrated SFR is screened, respectively. These metrics quantify the probability that a given star-forming region lies behind a given level of attenuation. Across the full sample, 50% of the local star formation occurs behind an attenuation of 3.41 mag or higher (ASFR50%). This indicates that the bulk of star formation in these galaxies is significantly attenuated by dust. The value of ASFR10% equals 1.45 for the average profile, indicating that even the least attenuated star-forming regions are still highly attenuated. The globally measured attenuation more closely matches ASFR10% than ASFR50%. This suggests that the global value is weighted toward the least dust-obscured star-forming regions and significantly underestimates the typical attenuation a star-forming region encounters. Our results demonstrate a new approach for understanding the extremely dusty local conditions of the star-forming interstellar medium in SF galaxies at cosmic noon.