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Aims.We cross-correlated galaxies from the LOw-Frequency ARray (LOFAR) Two-metre Sky Survey (LoTSS) second data release (DR2) radio source with the extended Baryon Oscillation Spectroscopic Survey (eBOSS) luminous red galaxy (LRG) sample to extract the baryon acoustic oscillation (BAO) signal and constrain the linear clustering bias of radio sources in LoTSS DR2. Methods.In the LoTSS DR2 catalogue, employing a flux density limit of 1.5 mJy at the central LoTSS frequency of 144 MHz and a signal-to-noise ratio (S/N) of 7.5, additionally considering eBOSS LRGs with redshifts between 0.6 and 1, we measured both the angular LoTSS-eBOSS cross-power spectrum and the angular eBOSS auto-power spectrum. These measurements were performed across various eBOSS redshift tomographic bins with a width of Δz = 0.06. By marginalising over the broadband shape of the angular power spectra, we searched for a BAO signal in cross-correlation with radio galaxies, and determine the linear clustering bias of LoTSS radio sources for a constant-bias and an evolving-bias model. Results.Using the cross-correlation, we measured the isotropic BAO dilation parameter asα = 1.01 ± 0.11 atz_eff = 0.63. By combining four redshift slices atz_eff = 0.63, 0.69, 0.75, and 0.81, we determined a more constrained value ofα = 0.968_−0.095^+0.060. For the entire redshift range ofz_eff = 0.715, we measuredb_C = 2.64 ± 0.20 for the constant-bias model,b(z0) =b_C, and thenb_D = 1.80 ± 0.13 for the evolving-bias model,b(z) =b_D/D(z), withD(z) denoting the growth rate of linear structures. Additionally, we measured the clustering bias for individual redshift bins. Conclusions.We detected the cross-correlation of LoTSS radio sources and eBOSS LRGs at a 9.2σstatistical significance for one single redshift bin and at a 14.7σsignificance when the four redshift bins were combined. For the BAO signal, we achieved a significance of 2.2σfor a single redshift bin, 2.7σfor the combined cross-correlation and eBOSS auto-correlation, and 4σfor the combined analysis of four redshift bins in the cross-correlation, when assuming a Gaussian distribution for the BAO dilation parameter. 

ABSTRACT We measure the small-scale clustering of the Data Release 16 extended Baryon Oscillation Spectroscopic Survey Luminous Red Galaxy sample, corrected for fibre-collisions using Pairwise Inverse Probability weights, which give unbiased clustering measurements on all scales. We fit to the monopole and quadrupole moments and to the projected correlation function over the separation range $$7-60\, h^{-1}{\rm Mpc}$$ with a model based on the aemulus cosmological emulator to measure the growth rate of cosmic structure, parametrized by fσ8. We obtain a measurement of fσ8(z = 0.737) = 0.408 ± 0.038, which is 1.4σ lower than the value expected from 2018 Planck data for a flat ΛCDM model, and is more consistent with recent weak-lensing measurements. The level of precision achieved is 1.7 times better than more standard measurements made using only the large-scale modes of the same sample. We also fit to the data using the full range of scales $$0.1\text{--}60\, h^{-1}{\rm Mpc}$$ modelled by the aemulus cosmological emulator and find a 4.5σ tension in the amplitude of the halo velocity field with the Planck + ΛCDM model, driven by a mismatch on the non-linear scales. This may not be cosmological in origin, and could be due to a breakdown in the Halo Occupation Distribution model used in the emulator. Finally, we perform a robust analysis of possible sources of systematics, including the effects of redshift uncertainty and incompleteness due to target selection that were not included in previous analyses fitting to clustering measurements on small scales. 

ABSTRACT We present the joint analysis of Neutral Hydrogen (H i) Intensity Mapping observations with three galaxy samples: the Luminous Red Galaxy (LRG) and Emission Line Galaxy (ELG) samples from the eBOSS survey, and the WiggleZ Dark Energy Survey sample. The H i intensity maps are Green Bank Telescope observations of the redshifted $$21\rm cm$$ emission on $$100 \, {\rm deg}^2$$ covering the redshift range 0.6 < z < 1.0. We process the data by separating and removing the foregrounds present in the radio frequencies with FastI ICA. We verify the quality of the foreground separation with mock realizations, and construct a transfer function to correct for the effects of foreground removal on the H i signal. We cross-correlate the cleaned H i data with the galaxy samples and study the overall amplitude as well as the scale dependence of the power spectrum. We also qualitatively compare our findings with the predictions by a semianalytical galaxy evolution simulation. The cross-correlations constrain the quantity $$\Omega _{\rm {H\,\small {I}}} b_{\rm {H\,\small {I}}} r_{\rm {H\,\small {I}},{\rm opt}}$$ at an effective scale keff, where $$\Omega _\rm {H\,\small {I}}$$ is the H  i density fraction, $$b_\rm {H\,\small {I}}$$ is the H i bias, and $$r_{\rm {H\,\small {I}},{\rm opt}}$$ the galaxy–hydrogen correlation coefficient, which is dependent on the H  i content of the optical galaxy sample. At $$k_{\rm eff}=0.31 \, h\,{\rm Mpc^{-1}}$$ we find $$\Omega _{\rm {H\,\small {I}}} b_{\rm {H\,\small {I}}} r_{\rm {H\,\small {I}},{\rm Wig}} = [0.58 \pm 0.09 \, {\rm (stat) \pm 0.05 \, {\rm (sys)}}] \times 10^{-3}$$ for GBT-WiggleZ, $$\Omega _{\rm {H\,\small {I}}} b_{\rm {H\,\small {I}}} r_{\rm {H\,\small {I}},{\rm ELG}} = [0.40 \pm 0.09 \, {\rm (stat) \pm 0.04 \, {\rm (sys)}}] \times 10^{-3}$$ for GBT-ELG, and $$\Omega _{\rm {H\,\small {I}}} b_{\rm {H\,\small {I}}} r_{\rm {H\,\small {I}},{\rm LRG}} = [0.35 \pm 0.08 \, {\rm (stat) \pm 0.03 \, {\rm (sys)}}] \times 10^{-3}$$ for GBT-LRG, at z ≃ 0.8. We also report results at $$k_{\rm eff}=0.24$$ and $$k_{\rm eff}=0.48 \, h\,{\rm Mpc^{-1}}$$. With little information on H i parameters beyond our local Universe, these are amongst the most precise constraints on neutral hydrogen density fluctuations in an underexplored redshift range.