A case study for measuring the relativistic dipole of a galaxy cross-correlation with the Dark Energy Spectroscopic Instrument: Data Repository

This repository contains the synthetic catalogue for the DESI Bright Galaxy Survey produced wit the N-body code gevolution, which is analysed in the manuscript "A case study for measuring the relativistic dipole of a galaxy cross-correlation with the Dark Energy Spectroscopic Instrument", as well as the raw data of the analysis results. The catalogue "catalogue.csv.bz2" is in the CSV format and can be directly read using the pandas library of python, for example. The columns in the catalogue contain the following information:

0. Column index
1. Comoving coordinate x (in units of Mpc/h)
2. Comoving coordinate y (in units of Mpc/h)
3. Comoving coordinate z (in units of Mpc/h)
4. Observed redshift
5. Cosine of the observed polar angle measured with respect to the axis pointing in the direction (1,1,1) along the box diagonal (the original comoving coordinate system has been rotated with an intrinsic z-y-z Euler rotation, first rotating along the z-axis with \(\phi_1 = \pi/4\), then rotating along the new y axis with \(\theta_2 = \mathrm{arccos}(1/\sqrt{3})\) and setting the final rotation angle to zero, \(\phi_3 = 0\); hence to get the unperturbed mu and phi coordinates, one needs to rotate the comoving x, y and z coordinates with the corresponding inverse Euler rotation matrix)
6. Observed azimuthal angle phi measured with respect to axis pointing in the direction (1,1,1) along the box diagonal (the original comoving coordinate system has been rotated with an intrinsic z-y-z Euler rotation, first rotating along the z-axis with \(\phi_1 = \pi/4\), then rotating along the new y axis with \(\theta_2 = \mathrm{arccos}(1/\sqrt{3})\) and setting the final rotation angle to zero, \(\phi_3 = 0\); hence to get the unperturbed mu and phi coordinates, one needs to rotate the comoving x, y and z coordinates with the corresponding inverse Euler rotation matrix)
7. Logarithm of the luminosity in units of solar luminosity \(L_\odot\)
8. Observed flux (in units of \(L_\odot/\mathrm{Mpc}^2\))
9. Number of particles in each object, plus a uniform noise between 0 and 1. This quantity is the proxy of the mass that was used to assign luminosity to the objects.
10. Flag that identifies the selected objects within each redshift bin. The Flag is 0 for objects not included in the catalogue, and equal to the mean redshift of the bins \(\bar{z} = 0.25, 0.35, 0.45\) for the selected objects. 
11. Flag that identifies the bright and faint objects for case 1 (50% bright, 50% faint, no flux limit). Flag = 0 for non-selected objects, Flag = 1 for bright objects, Flag = 2 for faint objects.
12. Flag that identifies the bright and faint objects for case 2 (90% bright, 10% faint, no flux limit). Flag = 0 for non-selected objects, Flag = 1 for bright objects, Flag = 2 for faint objects.
13. Flag that identifies the bright and faint objects for case 3 (50% bright, 50% faint, with flux limit). Flag = 0 for non-selected objects, Flag = 1 for bright objects, Flag = 2 for faint objects.
14. Flag that identifies the bright and faint objects for case 4 (90% bright, 10% faint, with flux limit). Flag = 0 for non-selected objects, Flag = 1 for bright objects, Flag = 2 for faint objects.

The example script "example-script.ipynb" demonstrates how to query the catalogue to extract e.g. the redshift distribution of the objects for the different cases considered in Table 4 of the manuscript.

Additionally, the measured dipole data vectors with the jackknife covariance matrices (\(\mathrm{cov}^\mathrm{JK}_{ij}\)), as well as the theoretical data vectors with the theoretical measurement covariance (\(\mathrm{cov}^\mathrm{th}_{ij}\)) and the theoretical prediction covariance (\(\mathrm{cov}^\mathrm{pred}_{ij}\)) are provided within this repository:

In the measurements.tar.gz archive, the measured data for the flux-limited case can be found in the /flux-limit subdirectory, while the data for the case without flux-limit is in /no-flux-limit. The data vectors are named "dipole__<% of bright galaxies>.txt. The first column in each of those files is the separation bin \(d\) in \(\mathrm{Mpc}/h\), the second column is the mean two-point correlation function dipole of the 100 jackknife subsamples, and the third column is the square root of the diagonal part of the jackknife covariance matrix (\(\mathrm{cov}^\mathrm{JK}_{ij}\)). The corresponding jackknife covariance matrices are named "cov__<% of bright galaxies>.txt.

In the theory.tar.gz archive, the theoretical predictions are found in /flux-limit for the case with flux limit and in /no-flux-limit for the case without flux limit. The theoretical data vectors are named "dipole_<% of bright galaxies>B_z_gevol.dat". The first column in each of those files is the separation bin \(d\) in \(\mathrm{Mpc}/h\), the second column the theoretical two-point correlation function dipole and the third column is the square root of the diagonal part of the theoretical prediction covariance matrix (\(\mathrm{cov}^\mathrm{pred}_{ij}\)) . The theoretical measurement covariance matrices are named "covariance_Lp6_<% of bright galaxies>B_z_gevol.dat", and the theoretical prediction covariance matrices are named "covtheo_<% of bright galaxies>B_z_gevol.dat". 

The example script also demonstrates how to use these data files to reproduce plots of the dipole measurement vs the theoretical prediction like in Figures 6, 7, C1 and C2. The archives need to be unpacked before using the example script to access the data.