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
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).