CORAS

A framework for the fast generation of COnstrained Realizations from All-sky Surveys

Description

CORAS reconstructs the density and velocity fields from a given all-sky redshift survey, using a Wiener filter estimator. By combining this estimator with random log-normal Poisson realizations of the density field and galaxy distribution, constrained realizations can be generated, which sample the space of field realizations compatible with the observed data. By comparing the reconstructed velocities with those obtained from a galaxy distance catalog, CORAS can furthermore infer the normalized growth rate of structures and the external bulk flow contribution from sources beyond the survey volume. As a nuisance parameter, it also fixes the Hubble constant used to translate observed distance moduli to velocities.

Reference

The methodology behind CORAS, its application to the Two-Micron All-Sky Redshift Survey (2MRS), and the comparison to the velocities inferred from the galaxy distance catalog Cosmicflows-3 are described in detail in the following publication:

Robert Lilow & Adi Nusser, MNRAS 507, 1557–1581 (2021)

If you want to use or modify CORAS or any data generated with it, please cite this publication and link to this repository.

Data

Input data

The data directory contains all input data needed to apply CORAS to 2MRS and perform the velocity comparison with Cosmicflows-3.

2MRS is described in

John P. Huchra et al., ApJS 199 (2012) 26
Lucas M. Macri et al., ApJS 245 (2019) 6

the 2MRS group catalog in

R. Brent Tully, AJ 149 (2015) 171

Cosmicflows-3 in

R. Brent Tully et al., AJ 152 (2016) 50

and the power spectrum emulator Cosmic Emu in

Katrin Heitmann et al., AJ 820 (2016) 108

The original 2MRS data are available alongside their publications, the 2MRS group catalog and Cosmicflows-3 are available in the Extragalactic Distance Database, and Cosmic Emu is available in this repository.

Inferred parameters

In addition, the data directory contains the aforementioned inferred parameters: normalized growth rate, external bulk flow contribution and distance catalog Hubble constant. As described in detail in Lilow & Nusser (2021), these have been inferred for different choices of the smoothing scale r_s applied to the reconstructed velocity field and the minimal redshift velocity cz_min considered in the comparison:

5 Mpc/h <= r_s <= 30 Mpc/h
0 km/s <= cz_min <= 2000 km/s

The raw parameter estimates, averaged over 50 constrained realizations and obtained using either observed redshifts in the CMB or Local Group (LG) frame, are listed in parameters_zCMB_CR1-50.dat and parameters_zLG_CR1-50.dat, respectively. These files can also be generated using the estimate_parameters.x executable, as described in more detail below in the section Running the code.

As described in detail in Lilow & Nusser (2021), the raw parameter estimates are subject to an r_s-dependent bias and potentially other systematic errors. These are accounted for by calibrating the raw estimates against a suite of semi-analytic mock galaxy catalogues mimicking the environment of the Local Group. The resulting calibrated parameters are listed in calibrated_parameters_CR1-50.dat.

Reconstructed fields on a grid

The reconstructed normalized density contrast and peculiar velocity fields on a grid, described in Lilow & Nusser (2021), are available in this Dropbox folder. The normalized density contrast is the density contrast divided by sigma_8. The peculiar velocity field is with respect to the CMB frame, and its components point along the Galactic coordinate axes. Both fields have been smoothed with a 5 Mpc/h Gaussian, and were reconstructed using either observed redshifts in the CMB or LG frame (denoted by zCMB and zLG, respectively, in the file name).

They are discretized on a regular $201^{3}$ Cartesian grid in comoving Galactic coordinates, with each coordinate running from -200 Mpc/h to +200 Mpc/h in steps of 2 Mpc/h. The field values at the coordinates (x_i, y_j, z_k) with

x/y/z_i = 2 * (i - 100), 0 <= i <= 200

are written to the line

l = (i * 201 + j) * 201 + k

of the file (excluding the header line and starting at l = 0).

These files can also be generated using the compute_reconstructed_fields_on_cartesian_grid.x executable, as described in more detail below in the section Running the code.

Reconstructed velocities of Cosmicflows-3 galaxies and groups

The reconstructed peculiar velocities at the positions of the Cosmicflows-3 galaxies and their associated groups are available in the Extragalactic Distance Database in the table Lilow-Nusser CF3 Peculiar Velocities. These have been obtained from the velocity field reconstructed using observed redshifts in the LG frame. Both the galaxy and group velocities have been evaluated at the comoving redshift distance to the group. This minimizes the Malmquist bias and reduces the contamination by incoherent small-scale motions (e.g. fingers-of-god). Thus, the only difference between galaxy and group velocities is the angular position at which they have been evaluated. The table also contains the uncertainty in the peculiar velocity components, estimated from the scatter between 50 constrained realizations. This uncertainty is the same for each velocity component and only depends on distance.

Each galaxy has a flag indicating the following:

• flag = -1: The LG-frame redshift of its group is negative. Since the actual distances to these galaxies are small compared to the 5 Mpc/h smoothing scale, their peculiar velocities have simply been evaluated at zero distance.
• flag = 1: The LG-frame redshift distance to its group is beyond the reconstruction boundary of 200 Mpc/h (corresponding to cz = 20,300 km/s). The peculiar velocities of these galaxies can thus not be reconstructed and are set to zero.
• flag = 0: All remaining galaxies.

Of the total 17647 galaxies only 20 have flag = -1 and 76 have flag = 1.

These reconstructed Cosmicflows-3 velocities, errors and flags (as well as those based on the reconstruction using observed redshifts in the CMB frame) can also be generated using the compute_reconstructed_velocities_for_CF3_galaxies.x executable, as described in more detail below in the section Running the code.

Installation

Install dependencies

Before compiling the code, the following dependencies need to be installed:

• GCC
• GNU Make
• GNU Scientific Library (GSL)
• FFTW3

Download and compilation

Clone the repository into the desired location and change into the root directory by running

git clone https://github.com/rlilow/CORAS.git
cd CORAS

If the GSL or FFTW3 are not in the standard paths, specify their include and library paths in the beginning of the Makefile by changing the corresponding variables GSL_INCLUDE_PATH, GSL_LIB_PATH, FFTW3_INCLUDE_PATH and FFTW3_LIB_PATH. Afterwards run

make

This will create a number of executables in the exe directory.

Documentation

If you have Doxygen (https://www.doxygen.nl/index.html) installed, you can build a detailed documentation of the different classes and functions in CORAS by running

make doc

from within the root directory. This will create the directory doc containing the documentation. To view it, open the file doc/documentation.html in the browser.

Running the code

To run CORAS in its default settings, simply execute the desired *.x file in the exe directory, e.g.

exe/compute_reconstructed_fields_on_cartesian_grid.x

By default, all output is written to the data directory.

To change the settings, modify the parameters in configuration.hpp and re-run make before executing a *.x file.

Executables

The different executables in the exe directory can be run independently. They do the following:

• compute_reconstructed_fields_on_cartesian_grid.x
  Compute the reconstructed density and velocity fields for given normalized growth rate and external bulk flow contribution on a Cartesian grid. The reconstructed fields described above in the Data section have been computed with this executable and the default settings.

• analyze_reconstructed_fields.x
  Analyze the reconstructed density and velocity fields for given normalized growth rate and external bulk flow contribution. Among other things, this computes both fields on a slice through the supergalactic plane, and their standard deviations as a function of radius.

• compute_reconstructed_velocities_for_CF3_galaxies.x
  Compute the reconstructed velocities and their errors at the positions of the Cosmicflows-3 galaxies and their associated groups. Precomputed velocity errors are used if this executable is run again or if analyze_reconstructed_fields.x has been run before and if the parameter ANALYSIS_USE_PRECOMPUTED_RECONSTRUCTION_ERRORS in configuration.hpp is set to true. This drastically reduces the execution time, as it avoids generating a set of constrained realizations to re-compute these errors. The reconstructed Cosmicflows-3 velocities described above in the Data section have been computed with this executable and the default settings.

• compare_reconstructed_and_observed_velocities.x
  Compare the reconstructed and observed radial velocities for given normalized growth rate, external bulk flow contribution and distance catalog Hubble constant. This computes the tensor-smoothed values of both velocity fields evaluated at the positions of the Cosmicflows-3 groups as well as their correlation functions. This executable uses the raw parameter estimates listed in the files data/parameters_zCMB_CR1-50.dat and data/parameters_zLG_CR1-50.dat as input. If the settings in configuration.hpp are changed, it is thus necessary to re-run estimate_parameters.x before compare_reconstructed_and_observed_velocities.x.

• estimate_parameters.x
  Compute the normalized growth rate, the external bulk flow contribution and the distance catalog Hubble constant via a maximum-likelihood comparison of the reconstructed and observed radial velocities. The raw parameter estimate files data/parameters_zCMB_CR1-50.dat and data/parameters_zLG_CR1-50.dat described above in the Data section have been computed with this executable and the default settings.

Development and contributing

The Doxygen documentation of the code is still incomplete and will be extended in the near future.

Contributions are very welcome! If you have any suggestions for new features or improvements, or if you encounter any errors, please create a GitHub issue.