GLADE V2 Galaxy Catalogue

• GLADE V2 Galaxy Catalogue is a comprehensive, nearly all-sky resource integrating six major astronomical surveys to provide detailed astrometric, photometric, redshift, and astrophysical parameters for over 22 million galaxies and 750,000 quasars.
• It employs Bayesian corrections for peculiar velocities and standardized magnitudes across multiple bands to ensure accurate distance estimates crucial for gravitational-wave counterpart searches.
• The catalogue assesses completeness through cumulative luminosity metrics and further estimates stellar masses and binary neutron star merger rates to optimize the ranking of host galaxies.

The GLADE V2 Galaxy Catalogue (GLADE⁺) is a homogenized, nearly all-sky catalogue designed for multimessenger astronomy, particularly for targeted follow-up of gravitational-wave detections. GLADE⁺ compiles data from six major astronomical surveys, providing astrometric, photometric, redshift, stellar mass, and compact binary merger-rate information for over 22 million galaxies and approximately 750,000 quasars. Incorporating Bayesian corrections for peculiar velocities, standardized magnitudes across multiple bands, and astrophysical priors such as stellar mass and B-band luminosity, it delivers high completeness out to luminosity distances critical for gravitational-wave counterpart searches (Dálya et al., 2021).

1. Catalogue Construction and Data Sources

GLADE⁺ is assembled by merging six large-scale astronomical catalogues, each offering distinctive contributions in terms of depth, wavelength coverage, or sky coverage:

• GWGC (Gravitational Wave Galaxy Catalogue)
• 2MPZ (2MASS Photometric Redshift)
• 2MASS XSC (Extended Source Catalogue)
• HyperLEDA
• WISExSCOSPZ (WISE×SuperCOSMOS Photometric Redshifts): ~20 million galaxies with W1, W2 mid-infrared photometry, SuperCOSMOS B_J and R_F optical magnitudes, and neural network photometric redshifts (σₙₙₙₙₙₙₙₙ/(1+z) ≃ 0.033)
• SDSS-DR16Q: ~750,000 spectroscopically confirmed quasars, replacing the earlier DR12Q sub-sample

Integration proceeds by spatial cross-matching with 2″ radius for WISExSCOSPZ/GLADE v2.4, and AllWISE data (3″) to fill W1, W2 gaps. Unmatched W1 are approximated using K_s→W1 color-redshift relations from 2MPZ. After all steps, the combined catalogue includes 22,431,348 galaxies and 750,410 quasars, for a total of 23,181,758 objects. More than 21 million galaxies carry W1 photometry, enabling further astrophysical parameter estimates.

2. Redshift Corrections with Bayesian Origin Reconstruction

Observed galaxy redshifts at low redshift ($z \lesssim 0.05$) are contaminated by peculiar velocities, $v_p$, due to local structure. GLADE⁺ compensates these using the BORG (Bayesian Origin Reconstruction from Galaxies) formalism. The method samples the posterior

$$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$

where $\delta$ is the 3D density field and $\theta$ encodes bias/evolution. For each posterior sample, a velocity field $v(x)$ is obtained through Lagrangian particle-mesh combined with the Simplex-in-Cell estimator, yielding a posterior for each galaxy’s radial peculiar velocity $p(v_{p,i}|\text{data})$. The catalogue records both mean and standard deviation of $v_p$ per object; these uncertainties propagate to errors in the CMB-frame redshift $z_{\rm CMB}$.

A small-scale virial component is added in quadrature, with the one-dimensional dispersion for halo of mass $M_h$ given by

$v_p$0

where $v_p$1, $v_p$2, $v_p$3, and $v_p$4. Halo masses are estimated from $v_p$5-band luminosity $v_p$6 via:

$v_p$7

with $v_p$8, $v_p$9, $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$0, $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$1, $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$2, $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$3. The total velocity error is:

$$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$4

This approach yields CMB-frame redshifts corrected for local structure, crucial for accurate distance estimates in the nearby Universe.

3. Completeness Assessment

GLADE⁺ completeness is quantified by cumulative B-band luminosity and inclusion of the most luminous galaxies, relevant for host targeting.

• Cumulative B-band luminosity: Comparing observed $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$5 within a sphere of given luminosity distance $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$6 to expected total from the cosmic luminosity density $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$7, 100% completeness is achieved at $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$8 Mpc.
• Bright-galaxy completeness: Galaxies contributing the top 90% of total $$p(\delta, \theta | \{ z_i, x_i \}) \propto p(\{ z_i \} | \delta, \theta) \, p(\delta) \, p(\theta),$$9- or $\delta$0-band luminosity are included out to $\delta$1 Mpc.

Completeness Metric	Distance Scale (Mpc)	Details
100% $\delta$2 (all galaxies)	$\delta$3	Total expected B-band luminosity covered
90% $\delta$4, $\delta$5-band	$\delta$6	Brightest galaxies within the luminosity budget

This level of completeness is essential for connecting galaxy populations with gravitational-wave event localizations out to relevant distances.

4. Stellar Mass and Compact Binary Merger Rate Estimates

WISE W1 mid-infrared photometry allows GLADE⁺ to estimate stellar masses ($\delta$7) and galaxy-specific BNS merger rates.

• Stellar mass estimation: Galaxies are "passive" if $\delta$8, otherwise "active." Adopted mass-to-light ratios (from Kettlety et al.) are:

$\delta$9

with

$\theta$0

$\theta$1

Only galaxies with $\theta$2 are retained ($\theta$3 completeness).

• Binary neutron star (BNS) merger rates:

For $\theta$4 and $\theta$5, the rate (from Artale et al.) is:

$\theta$6

Rates (with uncertainties) are provided for 3.16 million galaxies.

Parameter	Estimate Method	Coverage/Completeness
Stellar Mass ($\theta$7)	WISE W1 mass-to-light ratio	$\theta$8, $\theta$997%
BNS rate	Artale et al. scaling	For $v(x)$0, $v(x)$1

Uncertainties on stellar mass are typically in the range 30–70%, depending on galaxy type.

5. Ranking and Identification in Gravitational-Wave Follow-Up

GLADE⁺ enables optimized prioritization of host-galaxy candidates for gravitational-wave counterpart searches by associating astrophysical priors with localization volumes. For each candidate, a generic ranking statistic can be constructed:

$v(x)$2

where $v(x)$3 is LIGO/Virgo sky localization probability and $v(x)$4 is an astrophysical weighting, e.g., proportional to $v(x)$5, $v(x)$6, or $v(x)$7. This ranking allows observers to select the most probable galaxies to observe first. Empirical and simulation results indicate that this approach enables recovery of 50–90% of total host probability with substantially fewer telescope pointings than tiling, thus reducing required integration times and increasing rapid counterpart identification probability.

6. Catalogue Content and Distribution

GLADE⁺ provides a unified set of parameters for >22 million galaxies and ~750,000 quasars:

• Coordinates (RA, Dec)
• Redshifts (corrected for peculiar motion, plus errors)
• Magnitudes: $v(x)$8
• Stellar masses $v(x)$9
• Binary neutron star merger rates $p(v_{p,i}|\text{data})$0
• Posterior means and variances of peculiar velocities

This homogenization and broad parameter space make it a powerful resource for multimessenger observational campaigns, especially for gravitational-wave counterpart searches in volumes probed by advanced interferometer networks (Dálya et al., 2021).