© The Authors 2025

1. Introduction

The JWST Near Infrared Spectrograph (NIRSpec; Böker et al. 2023) has enabled IR spectroscopy with an unprecedented combination of redshift reach, signal-to-noise ratio, and spatial resolution. One of its key applications is the study of stellar or gas kinematics in distant galaxies (e.g., de Graaff et al. 2024; Xu et al. 2024; Newman et al. 2025), which help us to understand their formation and evolution, the properties of gas outflows, and the impact of black hole and baryonic feedback (D’Eugenio et al. 2024). Furthermore, accurate measurement of the stellar velocity dispersion of lensing galaxies also enables high-precision measurement of the Hubble constant and other cosmological parameters through the method of time-delay cosmography (Shajib et al. 2025; TDCOSMO Collaboration 2025).

Accurate measurement of the line spread function (LSF) or the spectral resolution R ≡ Δλ/λ, where Δλ is the full width at half maximum (FWHM), is a prerequisite to robustly measuring the velocity dispersion σ_⋆. The LSF induces additional broadening in the observed lines, which can be parameterized with σ_inst assuming a Gaussian LSF. The accuracy requirement on σ_inst to achieve a desired level of accuracy on σ_⋆ can be estimated using the relation (Knabel et al. 2025)

$$\begin{array}{c}\hfill \frac{\delta {\sigma }_{\star }}{{\sigma }_{\star }}\approx \frac{\delta {\sigma }_{\mathrm{inst}}}{{\sigma }_{\mathrm{inst}}}{\left(\frac{{\sigma }_{\mathrm{inst}}}{{\sigma }_{\star }}\right)}^2.\end{array}$$(1)

Therefore, achieving a 1% accuracy in the velocity dispersion, as desirable for precision cosmology (Knabel et al. 2025), requires an estimate of NIRSpec’s medium-resolution σ_inst accurate to 1.3% and 5.5% for σ_⋆ = 150 km s⁻¹ and 300 km s⁻¹, respectively, for example.

NIRSpec’s LSF in the fixed-slit (FS) mode was previously measured from the narrow emission lines of the planetary nebula (PN) SMP LMC 58 (Isobe et al. 2023). These authors find that the resolution is higher by ∼10–20% than the pre-launch estimates provided by the JWST User Documentation (JDox)¹. These authors assumed that the intrinsic expansion velocity of the PN is negligible. However, if the true expansion velocity is near the upper limit of typical values (i.e, ≲30 km s⁻¹; Jacob et al. 2013), its impact may not be non-negligible, especially for the high-resolution grating (R ∼ 2700), which would require a ∼19% correction (∼2.7% for medium resolution with R ∼ 1000). Nidever et al. (2024) find the resolution in the multi-object spectroscopy (MOS) mode’s G140H/F100LP configuration to be ∼50–85% higher than the JDox estimates, using narrow absorption lines in red giant stars. Through modeling with simulated data in the MOS mode, de Graaff et al. (2024) attribute the discrepancy between direct measurements and JDox estimates to differences in the source morphology. These authors demonstrate that a point source would lead to a ∼50–90% higher resolution in the MOS G395H/F290LP configuration than the JDox estimates, which are based on uniformly illuminated slits. However, the predicted resolution by de Graaff et al. (2024) did not account for the additional broadening introduced by the data reduction procedure. Hence, this value is not directly applicable to the reduced data, and a direct measurement from real data remains indispensable.

In this letter we provide a wavelength-dependent parameterization of NIRSpec’s resolution for multiple disperser–filter combinations for all of its FS, integral field spectroscopy (IFS), and MOS modes. We measured the resolutions by fitting prominent H and He emission lines for the PN SMP LMC 58 using datasets from JWST calibration programs, which were specifically obtained for wavelength and LSF calibrations. Isobe et al. (2023) also used a subset of this dataset for their LSF measurements. The same PN was also targeted by Jones et al. (2023) to measure the LSF for JWST’s Mid-Infrared Instrument (MIRI). Most of the fitted H lines have nearby weaker He multiplets, which are partially or fully blended and need to be accounted for to obtain an accurate characterization of the LSF. As a significant improvement over previous studies, we account for all the blended lines. We simultaneously fit the medium- and high-resolution spectra, thereby allowing lines that are deblended in the high-resolution spectrum to inform their relative strengths when fitting the medium-resolution spectrum. Furthermore, we corrected for the PN’s expansion velocity after directly measuring it from a higher-resolution (R ∼ 6500) spectrum of the same PN obtained using the Very Large Telescope’s (VLT) X-shooter instrument (Vernet et al. 2011).

This letter is organized as follows. In Sect. 2 we describe the JWST and X-shooter datasets we used. We describe our measurement method and provide the mesured values in Sect. 3, and then conclude the letter in Sect. 4. The code scripts and notebooks used in this analysis are publicly available on GitHub².

2. Datasets

We describe the NIRSpec dataset used to measure the spectral resolutions in Sect. 2.1 and the VLT X-shooter spectra used to measure the PN’s expansion velocity in Sect. 2.2.

2.1. NIRSpec spectra

To provide instrument calibrations for the NIRSpec, the planetary nebula SMP LMC 58 (also known as IRAS 05248−7007) was observed with the calibration program CAL-1492 (PI: T. Beck). We utilized the FS and IFS mode spectra from this program³. The FS mode used the S200A1 slit with 0$\stackrel{″}{.}$2 width, while including two primary dither positions with spectral subpixel dithers to improve the sampling. The IFS observations included a four-point nod to improve sampling and enable background subtraction. We obtained the reduced Level 3 spectra from the Mikulski Archive for Space Telescopes (MAST) archive, which had been reduced with the default JWST pipeline v1.18.0 (Bushouse et al. 2023) with CRDS context jwst_1364.pmap. Thus, the reduced and stacked data followed the standard steps in the pipeline.

The FS mode data were already extracted in the form of 1D spectra. For the IFS mode, we summed the spaxels within a circular aperture of radius 0$\stackrel{″}{.}$55, centered on the PN to obtain the corresponding 1D spectra.

2.2. VLT X-shooter specrum

The VLT X-shooter spectrum of the PN was obtained as part of an Euclid-preparation program (program ID 110.23Q7.001; Euclid Collaboration: Paterson et al. 2023). The spectrum was obtained with the VIS arm (covering 550–1020 nm) using a 1$\stackrel{″}{.}$2 slit, which has a nominal resolution of R ∼ 6500⁴. We obtained the observed raw dataset from the European Southern Observatory (ESO) Science Portal⁵, along with the calibration files. We reduced the dataset to produce an extracted 1D spectrum using ESO’s X-shooter data reduction pipeline v3.8.1 (Modigliani et al. 2010) with ESOREFLEX v2.11.5.

3. Measurement of the NIRSpec resolution

We adopted the Gaussian profile to characterize the NIRSpec LSF. By testing on a single emission line (Paα) that is not blended with other lines in both high and medium resolutions, we find that the LSF can be well fit with either a Gaussian or a Voigt profile. The Voigt profile provides a better fit, due to one additional degree of freedom; the Lorentzian profile yields a significantly worse fit. We chose the Gaussian profile also because it is ubiquitously used to account for instrumental resolution in measurements of kinematics, for example, with the software program PPXF (Cappellari 2017, 2023). The resolution parameter R ≡ λ/Δλ relates to the associated instrumental dispersion σ_inst as R = c/(2.355σ_inst), where c is the speed of light. We parameterize the wavelength dependence of σ_inst(λ) = [σ_inst′(λ)² − σ_PN²]^1/2 as

$$\begin{array}{c}\hfill {\sigma }_{\mathrm{inst}}(\lambda )={[{\left\{\frac{{\sigma }_{\mathrm{piv}}^{\prime }}{1+\alpha (\lambda -{\lambda }_{\mathrm{piv}})/[1\mathrm{\mu }\mathrm{m}]}\right\}}^2-{\sigma }_{\mathrm{PN}}^2]}^{1/2},\end{array}$$(2)

where σ_inst′(λ) is the instrumental dispersion not corrected for the PN’s expansion velocity σ_PN, σ_piv′ is the uncorrected instrumental dispersion at the pivot wavelength λ_piv, and α is the coefficient in the inverse-linear dependence on wavelength. We chose the inverse-linear λ-dependence for σ_inst′ because the resolution R ∝ 1/σ_inst is found approximately linear in λ from the pre-launch estimates, given that Δλ tends to be approximately constant in wavelength units. We describe our measurement process for σ_inst′(λ) in Sect. 3.1 and for σ_PN in Sect. 3.2.

3.1. Emission line fitting from the NIRSpec spectra

We fitted the spectra in wavelength slices around several prominent H and He emission lines. The details of the fitted wavelength ranges and the lists of lines within them are provided in Appendix A. Prominent H lines are often accompanied by He lines in proximity, due to the resemblance in their atomic structures. Furthermore, He lines are usually multiplets. These lines are partially or fully blended, especially in the medium resolution. For a given combination of mode, disperser, and filter, we simultaneously fitted all the lines within the chosen wavelength slices both in the high- and medium-resolution spectra, while individually constraining σ_piv′ and α for both gratings. The emission lines were fitted with post-pixelized (i.e., integrated within a pixel) Gaussian LSFs. The advantage of fitting all the lines together is that the information from all of them was aggregated to alleviate the issue that the LSF in most configurations is not critically sampled according to the Nyquist sampling theorem. The advantage of fitting both gratings together is that the relative line strengths could first be robustly constrained from the high-resolution spectrum, where they are less blended, which were then fixed while fitting the blended lines in the medium resolution (see Fig. 1). We also fit for the PN’s relative motion v_PN (previously measured as 295 ± 23 km s⁻¹; Reid & Parker 2006) without any dependence on the wavelength. We allowed the PN velocity to be independent between the medium- and high-resolution spectra to account for any residual offset in the wavelength calibration. In each wavelength slice, we fitted the continuum level with a linear function. We additionally allowed a Gaussian intrinsic scatter δ_intr in the σ_inst fitted to each line group around the mean relation of Eq. (2). Furthermore, we accounted for potential underestimation in the pipeline-produced uncertainties by allowing a systematic uncertainty floor ε_syst to vary freely for each resolution. Thus, we have ten nonlinear parameters characterizing the global properties of our generative model: σ_piv′, α, v_PN, δ_intr, and ε_syst for each resolution. The amplitudes of the line profiles and the continuum levels were solved through linear inversion. We obtained the posteriors of the nonlinear parameters (provided in Table 1) using the NAUTILUS sampler (Lange 2023).

Fig. 1. Post-pixelized Gaussian profile fits (orange) to prominent emission-line groups (black) in the NIRSpec IFS spectra of the PN SMP LMC 58. The IFS mode G140 disperser is illustrated here as an example among the nine combinations analyzed in this letter. The top row corresponds to the G140M/F100LP configuration (i.e., medium resolution), and the bottom row to G140H/F100LP (i.e., high resolution). The principal line within each group is annotated in the corresponding panel. The individual line wavelengths fitted in each group are marked with dashed blue lines. All of these lines are fitted simultaneously to directly constrain the parameters in σinst′(λ) from Eq. (2).

3.2. Measurement of the PN expansion velocity

To measure the expansion velocity of the PN from the X-shooter spectrum, we require a precise measurement of the spectral resolution of the X-shooter itself. We used the arc-lamp spectrum that was taken for wavelength calibration to obtain a wavelength-dependent estimate of X-shooter’s spectral resolution. We used the PYPEIT software program (Prochaska et al. 2020) to measure the FWHMs of the arc-lamp lines in 15 wavelength bins within the covered wavelength range of 550–1020 nm (Fig. 2). The uncertainty of the binned measurement was derived from the scatter in the individual-line measurements within each bin. The extent of the variation in the measured resolutions across the wavelength is qualitatively similar to that measured by Gonneau et al. (2020). We fit a quadratic function R_xsh(λ) to the measured points. We also simultaneously fit a post-pixelized Gaussian function to the Hα line, which is the most prominent H line within the covered wavelengths. Although a few He lines also fall within the covered wavelength range, they do not significantly add to the constraining power, due to their line strengths being smaller by 1.5 orders of magnitude or more. We parameterized the Hα line’s Gaussian profile with a standard deviation [σ_PN² + c²/{2.355R_xsh(λ_Hα)}²]^−1/2, while allowing the peak position to vary to account for the PN’s relative motion. We constrained the PN’s expansion velocity to σ_PN = 6.90  ±  0.49 km s⁻¹.

Fig. 2. Measurement of the PN’s expansion velocity. Left panel: Measurement of the X-shooter resolution (black points with error bars) from arc-lamp lines with the wavelength dependence modeled with a quadratic function (blue line, with the shaded region showing 1σ uncertainty). Right panel: The Hα line of the PN in the X-shooter spectra (emerald points). The error bars are too small to be seen here. The best-fit post-pixelized Gaussian profile is shown in red, while the width of the X-shooter LSF, as determined by the best fit in the left panel, is shown in blue for comparison. Both sets of illustrated datapoints are simultaneously fit to infer the PN’s expansion velocity σPN = 6.90 ± 0.49 km s−1.

We illustrate the measured resolution curves for all the mode–disperser combinations in Fig. 3 and compare them to the corresponding pre-launch estimates provided by JDox. The resolutions in the IFS mode across the covered wavelengths are higher by ∼1–24% than the pre-launch estimates, whereas the resolutions in the FS mode are ∼11–53% higher.

Fig. 3. Comparison of our measured resolution curves in the FS (emerald) and IFS (orange) modes with the pre-launch estimates from JDox (dashed gray lines). The shaded region around each resolution curve signifies the 1σ credible region. The in-flight resolutions are 11–53% higher than the pre-launch estimates in the FS mode, and 1–24% higher in the IFS mode (across the covered wavelengths).

4. Conclusion

In this letter we measured NIRSpec’s spectral resolution in multiple configurations in the FS and IFS modes. Due to the similarity in slit dimensions, the FS mode resolution can be used as a reasonable proxy for the MOS mode. We provided a wavelength-dependent parameterization of the spectral resolution in terms of the instrumental dispersion σ_inst by fitting multiple H and He emission lines across the observed wavelength range in the PN SMP LMC 58. We incorporated a correction for the intrinsic width of the PN’s lines, which we measured using a higher-resolution X-shooter spectrum of the same PN. Our measured resolutions are directly applicable for point source spectra; however, caution is advised when using them for extended sources.

The measured resolutions increase with wavelength in all configurations, as expected from the pre-launch estimates provided by JDox. For the FS mode, our measured resolution values extend up to 20% higher than those found by Isobe et al. (2023), potentially due to our methodology allowing multiple lines to be fitted within a blended line group. Our measured resolution in the G140H/F100LP configuration is smaller than that found by Nidever et al. (2024), which may be a difference between single-exposure and stacked spectra. Therefore, caution is advised when applying our measured value for datasets with drastically different dithering procedures from CAL-1492.

The parametric wavelength-dependent functions we provide will enable accurate measurements of kinematics from the NIRSpec data, as performed by TDCOSMO Collaboration (2025) and Shajib et al. (2025), among others. Although we do not provide directly measured LSFs in the MOS mode, the FS mode values can be used as a substitute, following Isobe et al. (2023), as the slit width for the analyzed data in the FS mode is the same as that of the multi-shutter-array slitlets.

Acknowledgments

We thank David Nidever for helpful comments as the referee, which improved this manuscript. We thank Hsiao-Wen Chen, Danial Rangavar Langeroodi, Mark Morris, and Stefan Noll for useful discussions. This work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with programs #1125 and 1492. The specific observations analyzed can be accessed via https://dx.doi.org/10.17909/m3c0-3t58. AJS and TT acknowledge support from NASA through STScI grants JWST-GO-2974, HST-GO-16773, and JWST-GO-1794. This research made use of NUMPY (Oliphant 2015), SCIPY (Jones et al. 2001), ASTROPY (Astropy Collaboration 2013, 2018), JUPYTER (Kluyver et al. 2016), MATPLOTLIB (Hunter 2007), SEABORN (Waskom et al. 2014), and NAUTILUS (Lange 2023).

References

Appendix A: Fitted line lists

In this appendix we provide the list of fitted lines within the chosen wavelength ranges in Tables A.1, A.2, and A.3 for the G140, G235, and G395 dispersers, respectively. We first obtained a comprehensive list of nebular H and He lines from the Atomic Line List database⁶ (van Hoof 2018). We then aggregated the He lines that are close to each other within one-eighth of a pixel size in the corresponding high-resolution spectrum into a single line with an average wavelength weighted by the transition probability (i.e., the Einstein coefficient g_kA_ki). We adopted one-eighth of the pixel size here, as this is one-half of the target threshold for wavelength calibration error (Böker et al. 2023). Thus, lines that are separated more closely can be sufficiently considered indistinguishable in the spectrum. Not all the line groups were fitted in some modes, as those line groups fall fully or partially outside of the covered wavelength range in the particular modes. The tables in this appendix specify the modes for which each line group was fitted.

All Tables

All Figures

Fig. 1. Post-pixelized Gaussian profile fits (orange) to prominent emission-line groups (black) in the NIRSpec IFS spectra of the PN SMP LMC 58. The IFS mode G140 disperser is illustrated here as an example among the nine combinations analyzed in this letter. The top row corresponds to the G140M/F100LP configuration (i.e., medium resolution), and the bottom row to G140H/F100LP (i.e., high resolution). The principal line within each group is annotated in the corresponding panel. The individual line wavelengths fitted in each group are marked with dashed blue lines. All of these lines are fitted simultaneously to directly constrain the parameters in σinst′(λ) from Eq. (2).

In the text

Fig. 2. Measurement of the PN’s expansion velocity. Left panel: Measurement of the X-shooter resolution (black points with error bars) from arc-lamp lines with the wavelength dependence modeled with a quadratic function (blue line, with the shaded region showing 1σ uncertainty). Right panel: The Hα line of the PN in the X-shooter spectra (emerald points). The error bars are too small to be seen here. The best-fit post-pixelized Gaussian profile is shown in red, while the width of the X-shooter LSF, as determined by the best fit in the left panel, is shown in blue for comparison. Both sets of illustrated datapoints are simultaneously fit to infer the PN’s expansion velocity σPN = 6.90 ± 0.49 km s−1.

In the text

	Fig. 3. Comparison of our measured resolution curves in the FS (emerald) and IFS (orange) modes with the pre-launch estimates from JDox (dashed gray lines). The shaded region around each resolution curve signifies the 1σ credible region. The in-flight resolutions are 11–53% higher than the pre-launch estimates in the FS mode, and 1–24% higher in the IFS mode (across the covered wavelengths).
In the text