Unified reconstruction of the Lyman-alpha power spectrum with Hamiltonian Monte Carlo
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912942326284288 |
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| author | Karaçaylı, N. G. Taylor, P. L. |
| author_facet | Karaçaylı, N. G. Taylor, P. L. |
| contents | The complex geometry of the Ly$α$ forest data has motivated the use of various two-point statistics as alternatives to the three-dimensional power spectrum ($P_{\mathrm{3D}}$), which carries cosmological information in Fourier space. On large scales, the three-dimensional correlation function ($ξ_\mathrm{3D}$) has provided robust measurements of the baryon acoustic oscillation (BAO) scale at 150~Mpc. On smaller scales, the one-dimensional power spectrum, $P_{\mathrm{1D}}(k_\|)$, has been the primary tool for extracting information. At the same time, the cross-spectrum, $P_\times(θ, k_\|)$, has been introduced to incorporate angular information without the complications caused by survey window functions. We propose an analytical forward-modeling framework to reconstruct $P_{\mathrm{3D}}$ from all these observables, based on the mathematical relation between them and $P_{\mathrm{3D}}$. We demonstrate the performance of our method using a hypothetical mock data vector representative of future Dark Energy Spectroscopic Instrument (DESI) measurements. We show that the monopole of $P_{\mathrm{3D}}$ can be reconstructed in 25 $k$ bins between $0.07~\mathrm{Mpc}^{-1}$ and $1.8~\mathrm{Mpc}^{-1}$, achieving an average precision of $σ_P/P=13\%$ across the bins. Our method can serve as an intermediary for consistency checks, though it is not intended to replace direct $P_{\mathrm{3D}}$ estimation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_08198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified reconstruction of the Lyman-alpha power spectrum with Hamiltonian Monte Carlo Karaçaylı, N. G. Taylor, P. L. Cosmology and Nongalactic Astrophysics The complex geometry of the Ly$α$ forest data has motivated the use of various two-point statistics as alternatives to the three-dimensional power spectrum ($P_{\mathrm{3D}}$), which carries cosmological information in Fourier space. On large scales, the three-dimensional correlation function ($ξ_\mathrm{3D}$) has provided robust measurements of the baryon acoustic oscillation (BAO) scale at 150~Mpc. On smaller scales, the one-dimensional power spectrum, $P_{\mathrm{1D}}(k_\|)$, has been the primary tool for extracting information. At the same time, the cross-spectrum, $P_\times(θ, k_\|)$, has been introduced to incorporate angular information without the complications caused by survey window functions. We propose an analytical forward-modeling framework to reconstruct $P_{\mathrm{3D}}$ from all these observables, based on the mathematical relation between them and $P_{\mathrm{3D}}$. We demonstrate the performance of our method using a hypothetical mock data vector representative of future Dark Energy Spectroscopic Instrument (DESI) measurements. We show that the monopole of $P_{\mathrm{3D}}$ can be reconstructed in 25 $k$ bins between $0.07~\mathrm{Mpc}^{-1}$ and $1.8~\mathrm{Mpc}^{-1}$, achieving an average precision of $σ_P/P=13\%$ across the bins. Our method can serve as an intermediary for consistency checks, though it is not intended to replace direct $P_{\mathrm{3D}}$ estimation. |
| title | Unified reconstruction of the Lyman-alpha power spectrum with Hamiltonian Monte Carlo |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2506.08198 |