Matrial for 'Unified galaxy power spectrum measurements from 6dFGS, BOSS, and eBOSS' (arXiv:2106.06324)

The products provided here can be handeled using the Python modules provided here. Also see the User guide in Appendix A of arxiv:2106.06324.

Most of the following products use \(\Delta k_{\rm o} = 0.01h/\)Mpc, \(\Delta k_{\rm th} = 0.001h/\)Mpc, meaning the wide-angle transformation matrix, \(\mathbf{M}\), has the shape \(1200 \times 2000\), the window function matrix, \(\mathbf{W}\), has the shape \(200 \times 2000\) and the covariance matrix, \(\mathbf{C}\), has the shape \(200 \times 200\).
Product Size Description
\(\textbf{M}\) \(1200 \times 2000\) Wide-angle transformation matrix: Transforms from 3 multipoles in the k-range \(0 - 0.4h/\)Mpc in bins of \(\Delta k_{\rm th}= 0.001h/\)Mpc to 5 multipoles with the same binning
\(\textbf{W}\) \(200 \times 2000\) Window function matrix: Transforms from 5 multipoles in the k-range \(0 - 0.4h/\)Mpc in bins of \(\Delta k_{\rm th}= 0.001h/\)Mpc to 5 multipoles with binning \(\Delta k_{\rm o}= 0.01h/\)Mpc. This window matrix should be the default choice when convolving a model power spectrum.
\(\textbf{W}\) \(200 \times 200\) Window function matrix: Transforms from 5 multipoles in the k-range \(0 - 0.4h/\)Mpc in bins of \(\Delta k_{\rm th}= 0.01h/\)Mpc to 5 multipoles with binning \(\Delta k_{\rm o}= 0.01h/\)Mpc. This window matrix can be used for deconvolution.
\(\textbf{C}_{\rm conv}\) \(200 \times 200\) Covariance matrix: For 5 multipoles in the k-range \(0 - 0.4h/\)Mpc in bins of \(\Delta k_{\rm o}= 0.01h/\)Mpc
Mock \(\mathbf{P}^{\rm conv}_{\rm o}\) 2000 Mock power spectrum multipoles: Mock power spectrum multipoles in the k-range \(0 - 0.4h/\)Mpc in bins of \(\Delta k = 0.001h/\)Mpc. You need to combine 10 bins so that these power spectra can be used with the other products (see combine_bins parameter in read_power()).
Data \(\mathbf{P}^{\rm conv}_{\rm o}\) 2000 Data power spectrum multipoles: Data power spectrum multipoles in the k-range \(0 - 0.4h/\)Mpc in bins of \(\Delta k = 0.001h/\)Mpc. You need to combine 10 bins so that these power spectra can be used with the other products (see combine_bins parameter in read_power()).
\(\textbf{Q}^{(n)}_{\ell}\) 10000 1D k-space window: Contains the 5 window function multipoles for \(n=[0,1,2]\), where \(n\) is the order of the wide-angle expansion (basically the Fourier transform of eq. 2.6 of arxiv:2106.06324). This quantity is only needed if you want to re-calculate the window matrix \(\textbf{W}\) following eq. (2.5). It needs to be Hankel transformed to get \(\textbf{Q}^{(n)}_{\ell}(s)\) (see eq. 2.9).

To be used as $$ \mathcal{L} \propto \exp\left[-\frac{1}{2}(\mathbf{P}^{\rm conv}_{\rm o} - \mathbf{W}\mathbf{M}\mathbf{P}^{\rm true,flat-sky})^T\mathbf{C}_{\rm conv}^{-1}(\mathbf{P}^{\rm conv}_{\rm o} - \mathbf{W}\mathbf{M}\mathbf{P}^{\rm true,flat-sky})\right]\, , $$ where \(\mathbf{P}^{\rm true,flat-sky}\) is a vector of monopole, quadrupole and hexadecapole models (no wide-angle effects) and \(\mathbf{P}^{\rm conv}_{\rm o}\) is the vector of measured power spectrum monopole, dipole, quadrupole, octopole and hexadecapole. See the user guide in Appendix A of arxiv:2106.06324 for more details.

Downloads

\(\mathbf{M}\) \(\mathbf{W}\) \(\mathbf{W}\) \(\mathbf{C}_{\rm conv}\) Mock \(\mathbf{P}^{\rm conv}_{\rm o}\) Data \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{Q}^{(n)}_{\ell}\)
\(\tiny{1200 \times 2000}\) \(\tiny{200 \times 2000}\) \(\tiny{200 \times 200}\) \(\scriptsize{\text{pre-recon}}\) \(\scriptsize{\text{post-recon}}\) \(\scriptsize{\text{pre-recon}}\) \(\scriptsize{\text{post-recon}}\) \(\scriptsize{\text{pre-recon}}\) \(\scriptsize{\text{post-recon}}\)
6dFGS DR3 M W W \(\mathbf{C}_{\rm conv}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(Q^{(n)}_{\ell}\)
BOSS DR12 NGC z1 M W W \(\mathbf{C}_{\rm conv}\) \(\mathbf{C}_{\rm conv}\) \(\mathbf{P}^{\rm conv}_{\rm o,1}\)\(\mathbf{P}^{\rm conv}_{\rm o,2}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(Q^{(n)}_{\ell}\)
BOSS DR12 SGC z1 M W W \(\mathbf{C}_{\rm conv}\) \(\mathbf{C}_{\rm conv}\) \(\mathbf{P}^{\rm conv}_{\rm o,1}\)\(\mathbf{P}^{\rm conv}_{\rm o,2}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(Q^{(n)}_{\ell}\)
BOSS DR12 NGC z3 M W W \(\mathbf{C}_{\rm conv}\) \(\mathbf{C}_{\rm conv}\) \(\mathbf{P}^{\rm conv}_{\rm o,1}\)\(\mathbf{P}^{\rm conv}_{\rm o,2}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(Q^{(n)}_{\ell}\)
BOSS DR12 SGC z3 M W W \(\mathbf{C}_{\rm conv}\) \(\mathbf{C}_{\rm conv}\) \(\mathbf{P}^{\rm conv}_{\rm o,1}\)\(\mathbf{P}^{\rm conv}_{\rm o,2}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(Q^{(n)}_{\ell}\)
eBOSS DR16 QSO NGC M W W \(\mathbf{C}_{\rm conv}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(Q^{(n)}_{\ell}\)
eBOSS DR16 QSO SGC M W W \(\mathbf{C}_{\rm conv}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(\mathbf{P}^{\rm conv}_{\rm o}\) \(Q^{(n)}_{\ell}\)
DESI DR1 (coming in 2023)
Euclid DR1 (coming in 2024)

References

The products listed above have been derived in arxiv:2106.06324 with the wide-angle formalism suggested by (Beutler, Castorina & Zhang 2019). Please reference both papers when using these products in publications.

- When using any of the products based on the 6dFGS DR3 sample, please cite the corresponding data release paper (Jones et al. MNRAS.399 2009) as well as the papers describing the 6dFGS mock catalogs (Carter et al. MNRAS.481 2018, Koda et al. MNRAS.459 2016).
- Similarly, when using any of the products based on the BOSS DR12 sample, please cite the data release 12 paper (Alam et al. APJ, 219, 12, 2015), the associated catalog paper (Reid et al. MNRAS, 455 2016) and the mock catalog paper (Kitaura et al. MNRAS.456 2016).
- Finally, when using any of the products based on the eBOSS DR16 sample, please cite the data release 16 paper (Ahumada et al., arxiv:1912.02905), the associated catalog paper (Ross et al., arxiv:2007.09000) and the mock catalog paper (Zhao et al. arxiv:2007.08997).