tokens: dispersion as a Doppler shift; Huang et al. 2018 ). Battye et al. ( 2020 ), however, suggested that the line width is dominated by the neutron star’s spinning magnetosphere. We adopt this spinning-mirror model that produces, on average, a bandwidth Δ f / f ≃ Ω r c / c , where Ω is the rotation angular frequency and r c is the axion–photon conversion radius. Hook et al. ( 2018 ) showed that r c depends on the neutron star’s radius r 0 , magnetic field B 0 , angular frequency, polar orientation angle θ , and magnetic axis offset angle θ m :where . For now, we assume that θ = π /2 and θ m = 0 (we deal appropriately with these angles in Section 5 ) to obtain the expected line width:(4.1 μ eV corresponds to 1 GHz as observed). PSR J1745−2900 has a 3.76 s rotation period (Kennea et al. 2013 ) and a magnetic field of 1.6 × 10 14 G (Mori et al. 2013 ). The expected axion–photon conversion line width is thus . This corresponds to 2500 km s −1 at 1 GHz and 215 km s −1 at 40 GHz, which is generally broader than the expected dark matter dispersion, ∼300 km s −1 , except at the highest observed frequencies. Spectra have flagged channels due to RFI and due to spectral window edges that lack the signal-to-noise for calibration. Flagged channels are much narrower than the expected line width, so we interpolate across these channels when smoothing using a Gaussian kernel (Price-Whelan et al. 2018 ). In some bands, such as L , S , and K , entire spectral windows can be flagged and all information is lost. RRL emission lines are seen toward the magnetar in X -band (15A-418), Ku 12–13 GHz, Ku 17–18 GHz, and K 26 GHz. To remove RRLs, two 2 MHz channels are flagged per line, and subsequent smoothing interpolates across the flagged channels (the expected axion conversion line width is 18 MHz in X -band and 24 MHz at 26 GHz). We combine spectra obtained from multiple observing sessions using an error-weighted average, and the sky (noise) spectra are combined in quadrature. When different observing programs overlap in frequency, we select the lowest noise observation. This is effectively the same as combining overlapping spectra in quadrature because the less sensitive spectra contribute negligibly to an error-weighted mean. Table 1 lists synthesized beam parameters, channel widths, and spectral rms noise values. Appendix appendix presents the new magnetar flux, noise, and signal-to-noise spectra. 4. Results After smoothing to the expected axion–photon conversion line width, the new spectra show no significant (>3 σ ) single-channel emission features (Appendix appendix ). The exception is a 3.2 σ channel at 2.34 GHz (9.67 μ eV) in an RFI-affected region of S -band (there also two channels at 3.1 σ and 3.5 σ in previous Ka -band spectra; Darling 2020 ). We obtain single-channel 95% confidence limit flux density spectra from the sky noise spectra. Figure 1 shows the combined limits from this work and Darling ( 2020 ). These limits do depend on the assumed line width
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