CLONEing Galaxy Clusters using Velocity Waves

Title: Distortions of the Hubble diagram: Line-of-sight signatures of local galaxy clusters
Authors: Jenny G. Sorce, Roya Mohayaee, Nabila Aghanim, Klaus Dolag, Nicola Malavasi
First Author’s Institution: Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405, Orsay, France
Status: Accepted to Astronomy & Astrophysics (closed access)

By Catherine Chaison

Catherine is a third year undergraduate student at Texas A&M University, studying both genetics and astrophysics. Her current research focuses on large scale genomic analysis to identify trends in de novo gene formation, where she expands her understanding of how computational approaches can aid research across disciplines. When she is not working, she enjoys playing flute in the TAMU Symphonic Winds, making stained glass, and doing amateur astronomy from her backyard. You can see more from Catherine on LinkedIn or Twitter.

Though the expansion of the universe is largely homogeneous and symmetrical, there is some inconsistency around areas with large gravitational potential. These focal points of mass, locations with large galaxy clusters and oftentimes a high amount of dark matter to increase the mass, create significant velocity waves that show local changes in the rate of expansion of the universe that can be observed and simulated. One such simulation that attempts to predict the location of these mass clusters is CLONE, the Constrained LOcal & Nesting Environment Simulation.

CLONE Parameters

CLONE as a simulation is notable in the constraints it uses for prediction. Though other models also use ΛCDM, a Cosmological model that defines the theoretical basis for the formation of the universe being followed and the parameters used for further study, this model utilizes primarily the peculiar velocities of galaxies to estimate their mass. These peculiar velocities were calculated from the galaxy distance moduli and observed redshifts. The equations to solve for this are shown below, using luminosity distance (1) in the cosmological redshift equation (2) and integrating for the cosmological redshift to finally solve for radial peculiar velocity (3). This model was focused on clusters within the Local Group during the study.

In order to ensure the fit of this model was accurate, it was tested against stacked lensing measurements, other Virial mass estimators, and escape potentials of the cluster. Each of these strategies are limited in how accurate they can be when applied to larger models, but are extremely accurate within their small radius of measurement around clusters. As a result, using them and other proxies, such as infall zone velocity for Virial mass and wave shape for dispersions, as a method of comparison is a good test of how high the resolution of CLONE estimates are or if the model needs to be calibrated further in order to accurately take into account dark energy and dark matter in the Planck cosmology framework and a non-linear state. Testing the model against the dark matter halos and subhalos allow it to be seen that the model, using peculiar velocity and not complete local density and velocity fields, is still able to be accurate without these extra parameters.

Testing the Model

Velocity waves can be visualized using a cylindrical shape around a line of site, comparing a mass halo to the placement of the wave around it to identify the wave’s origin mass without distortion, which other shapes would create.

Interestingly, this model was accurate within a 2-sigma uncertainty for galaxy distance given a simulated dark matter halo within the line of site, and accurately predicted large clusters in the simulated locations. Previous measurements of mass in Hubble diagrams are distorted due, showing the velocity waves as the main cause of their distortion.

When the model was tested using the 2D-Kolmogorov-Smirnov statistic test, it was found to have an insignificant p-value above 0.2. This indicates that the simulated distribution of mass in the cluster was very similar to the actual observed, supporting CLONE as an effective model of galaxy clusters. It must be noted that this variation varied depending on which catalog of galaxies was used to test the model, but this level of accuracy remains promising.

Using Different Wave Properties

The amplitude, height, width, and continuum of velocity waves were checked against mass halos estimated to further tighten estimates of mass. Amplitude is the best out of these as a proxy, as the higher the difference between maximum and minimum peculiar velocity, the stronger the gravitational well when objects are pulled into the cluster. Though the same line of sight simulation was used to line up clusters, just using amplitude as the estimating measure created too much variation to accurately identify galaxy location compared to when using the proper mass. It is also possible that the shape of the well wave amplitudes produce also distorts the data, but further testing would have to be done to investigate this.

Height was not likely to be a better proxy of mass than amplitude, and this expectation was found to be accurate. Though still a similar correlation, more variation was present. This proxy was significant, however, in demonstrating that the velocity waves being used to guide the CLONE model are not symmetrical, and so any assumptions based on this should be reevaluated and the difference in correlation between each half, the positive and negative side, should be studied now that they are known to differ.

Finally, the Gaussian-plus-continuum model combines height, width, and continuum of the positive half of the wave to fit the model against. The Gaussian-plus-continuum model takes a Gaussian and a continuum fit of each dark matter halo and adds the resulting Gaussian amplitude and standard deviation, adjusted to center around 0, to the fitted value from the continuum model according to the equation below in Figure 4. This resulting model had a varying level of uncertainty based on each halo it tested, as illustrated in the rightmost graph below.

Overall, utilizing velocity waves and their peculiar velocity in simulating galaxy cluster mass appears to be an extremely promising approach to applying machine learning to mass and distance analysis across a broader area of galactic clusters. CLONE illustrates one leap into this field by demonstrating the correlation between mass and Gaussian amplitude, most notably. Most importantly, continued use of machine learning models will allow for reduced observational biases within the line of sight, and hopefully continue to become more accurate across farther and farther distances.

Astrobite edited by: Ali Crisp
Featured image credit: NASA/WMAP