An empirical calibration of the spectral resolution of JWST NIRSpec PRISM

Abstract

We present an empirical calibration of the effective spectral resolution of the JWST NIRSpec PRISM disperser based on a large sample of galaxies drawn from archival observations. Our sample spans a wide redshift range, $0.5 \lesssim z \lesssim 10$, enabling a wavelength-dependent characterization of the PRISM resolving power across the full bandpass using the [O III]$\lambda\lambda4959,5007$ doublets. To ensure robust measurements, we impose strict signal-to-noise requirements on both continuum and emission-line detections. Emission-line profiles are fitted with multi-Gaussian models, and the full width at half maximum (FWHM) is measured for each source. The derived empirical resolution curve shows a systematic offset from the nominal pre-launch estimate, lying between the tabulated instrumental resolution and the point-source shutter limit. We also discuss how source size affects the final spectral resolution, and provide an analytical formula that combines wavelength and morphology dependence in a root-sum-square framework. This work delivers a population-averaged, statistically robust calibration of the effective PRISM spectral resolution for typical galaxy observations. The resulting calibration is directly applicable to statistical analyses of galaxy spectra obtained with NIRSpec PRISM. Our empirical calibration exceeds the pre-launch JDox values by a factor of 1.03 to 1.63, depending on source morphology, and provides the first wavelength and morphology dependent calibration of the NIRSpec PRISM spectral resolution.