![Comparison of the projected and angular power spectrum at the mean redshift $\bar{z}=1.4$. Left: the angular autopower spectrum of photometric samples in the photo-z bins zp = [1.4 − Δz/2, 1.4 + Δz/2]. The thick and thin curves show the power spectrum for the bin width of Δzp ≃ 0.365 and 1.05, which corresponds to the width of the comoving radial distance, Δr = 0.5 and 1.5 Gpc h−1, respectively. The solid and dashed curves are the spectra assuming the photo-z accuracies of σz/(1 + z) = 0.05 or 0.3, receptively. Each thin dotted lines show the shot noise level for the photometric samples, which typically have the projected number density more than 104 deg−2 for an imaging survey we are interested in. Middle: similar to the left-hand panel, but for the cross-power spectrum between the spectroscopic and photometric samples, as a function of the transverse comoving separation (equation 7), where the transverse mode k is rescaled to the multipole via the distance to the spectroscopic sample by l = kr(z = 1.4) for an illustrative purpose. The solid and dashed curves are for the photo-z accuracies of the photometric galaxies, as in the left-hand panel. The cross-correlation preserves the BAO wiggles compared to the left-hand panel. Right: the projected autopower spectrum for the spectroscopic samples. The figure shows that, for a spectroscopic survey with a small number density $\bar{n}_{\rm s}<10^{2}\,{\rm deg}^{-2}$, the BAO wiggles in the autospectrum are difficult to measure due to the significant shot noise.](https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/mnras/433/1/10.1093_mnras_stt761/1/stt761fig3.jpeg?Expires=1750257720&Signature=NMd8m9v5qRe1j-nFX8Ms1KHSZd7sc5YiOPsmyY89y0qXcX2ONEAMeVGl3ekfITXv8e5IZmmND8beBi33q5faDMUlFgRb67M84Y~B1j34Kk3-40jE9enQXcFxv2s4lCkb1wvOFxZz3G-y5FiDaPDIuQDE-MjnezMkW7VEh6khf2PCerHLvbGfljxkSSKT2ZJv7lf7nr40iAD06f6wOSWv0FVKZqPP~jwFYy9AwEi12z9uQPrsMhCvBzGpnvihhlcYlXKSJEJc99gxTEQRkiJ33oG1uFamX-2OeQNXUQ8Rh-Rac5xnJ~HbipzMBAZ3Z17U6~ZWFhr1I2crjzvxQ0-m-w__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Comparison of the projected and angular power spectrum at the mean redshift |$\bar{z}=1.4$|. Left: the angular autopower spectrum of photometric samples in the photo-z bins zp = [1.4 − Δz/2, 1.4 + Δz/2]. The thick and thin curves show the power spectrum for the bin width of Δzp ≃ 0.365 and 1.05, which corresponds to the width of the comoving radial distance, Δr = 0.5 and 1.5 Gpc h−1, respectively. The solid and dashed curves are the spectra assuming the photo-z accuracies of σz/(1 + z) = 0.05 or 0.3, receptively. Each thin dotted lines show the shot noise level for the photometric samples, which typically have the projected number density more than 104 deg−2 for an imaging survey we are interested in. Middle: similar to the left-hand panel, but for the cross-power spectrum between the spectroscopic and photometric samples, as a function of the transverse comoving separation (equation 7), where the transverse mode k is rescaled to the multipole via the distance to the spectroscopic sample by l = kr(z = 1.4) for an illustrative purpose. The solid and dashed curves are for the photo-z accuracies of the photometric galaxies, as in the left-hand panel. The cross-correlation preserves the BAO wiggles compared to the left-hand panel. Right: the projected autopower spectrum for the spectroscopic samples. The figure shows that, for a spectroscopic survey with a small number density |$\bar{n}_{\rm s}<10^{2}\,{\rm deg}^{-2}$|, the BAO wiggles in the autospectrum are difficult to measure due to the significant shot noise.
