Title: The origins of the Bulk Flow 

Authors: Richard Watkins and Hume A. Feldman 

First author institution: Willamette University, Salem, USA  

Status: Available on ArXiv

In our expanding Universe, galaxies all appear to move away from each other like raisins separating in baking raisin bread – at least for the most part. Gravitational interactions can tug on galaxies and pull them towards each other, or allow them to orbit each other or even eventually merge. This motion of galaxies that is separate from space’s expansion is called peculiar motion.

Peculiar motions allow for a test of our understanding of cosmology, which at present is widely seen through the lens of the \(\Lambda\)CDM model. In combination with our understanding of gravity via General Relativity, this model predicts how matter (both the normal and dark matter) is distributed and thus also how galaxies should be moving. The equations governing \(\Lambda\)CDM are also derived under the assumption of the Cosmological Principle, which states on average the Universe is homogeneous (looks pretty much the same wherever you place an observer) and isotropic (the view looks the same in different directions). Various different approaches allow us to test the model. One way we can do this using the motions of galaxies is to measure something called a bulk flow. A bulk flow can be thought of as a measure of the mean peculiar motion of galaxies in a volume of space. If the Cosmological Principle holds, this also suggests the bulk flow will approach very small values on sufficiently large scales, because the mean motion of galaxies should approach zero in a homogeneous volume – the peculiar motions should average to zero. The bulk flow and peculiar motions are also an interesting probe of the nearby structure of the Universe, allowing us to map out the local space.

Interestingly, there have been measurements in the literature that have found just the opposite of this expectation for bulk flows. There has been a consistent trend showing larger than expected bulk flows of galaxies to various degrees of significance, but with increasingly larger flows in larger volumes. This is not expected in the \(\Lambda\)CDM model or even from measurements of the clustering of galaxies on different length scales. In the literature there have been studies to try to understand if this is a consequence of errors in the approach to obtaining peculiar velocity measurements (this process itself could be a discussion of a whole other article) or instead a sign that the \(\Lambda\)CDM model needs to be updated. In the paper we study in today’s bite, the authors take a new approach to try to understand the larger-than-expected bulk flow measurements, using the CosmicFlow-4 (CF4) dataset that consists of around ~50,000 individual measurements of the peculiar motions of galaxies.

Comparing a model to the data

As hinted in the title of the paper, the authors want to study the source of the larger-than-expected bulk flow; does the motion we see in the data originate from a source within the survey volume itself? Or alternatively, is there something beyond what we can see that is creating a huge tug on the motions of galaxies?

The idea is to split the peculiar motion measurements into parts that are ‘internal’ to a volume of space that we can model and parts that are ‘external’. To achieve this, the motion data is compared to a velocity field model for a mass distribution of radius 200 Mpc per little \(h\), that has been constructed using data from just the positions of galaxies (taken from previous work in the literature) and overlaps with the CF4 data. This model is constructed using 2M++ data and has results consistent with the \(\Lambda\)CDM. Ideally, the components of peculiar motion that are sourced from the mass distribution within the \(200h^{-1}\) Mpc radius will be assigned to ‘internal’ and the remaining components of velocity will be called ‘external’ for the purpose of this analysis. To do this, the authors obtain a predicted velocity of each of the galaxies from the CF4 data using the velocity field model. The CF4 data is then averaged in bins according to their predicted velocities from the models. Then, these averages from the CF4 are compared to the averages from the velocity model; in the ideal situation, the model and data would create a one-to-one line. However, the mismatch between the model and data allows one to constrain cosmological parameters. The cosmological parameters are the growth rate of structure (which is related to the energy density of matter and dictate how fast galaxies fall towards each other) and the Hubble parameter (which tells us the current day expansion rate of the Universe).  After this, one can assign the motions of galaxies that are part of the \(200h^{-1}\) Mpc radius mass distribution to an ‘internal’ component of peculiar motion, then subtracting this off to isolate the ‘external’ component of peculiar motion for each galaxy.

Since the model itself depends on cosmological parameters that can only be constrained by data, the best fit values of these parameters to the CF4 data are found by adjusting the model so that the predictions for velocities in the model match the binned velocities of the CF4 data. This is demonstrated in Figure 1 below. They find overall the Hubble parameter is around \(75.9 \pm 0.1\) km/s/Mpc and that the growth rate of structure is around \(0.31 \pm 0.01\) – the Hubble parameter they find is large, but they point out that this analysis doesn’t account for various complicated systematic errors that can affect this value, and this value is best only used for analysis on CF4 data.

Figure 1: A comparison of the binned CF4 galaxy velocities according to their predicted velocities from the velocity field model. By varying the growth rate of structure (in the left panel, Figure 1 in the paper), one can also find the slope with a gradient of unity such that the data and model have a matching growth rate of structure, or vary the Hubble parameter (right panel, Figure 2 in the paper) so that the y-intercept of the slope is zero.

What does this mean for the bulk flow?

Having found a best fit model for the galaxy motions, the ‘external’ component of each galaxy motion (that which is sourced from beyond the radius of the mass distribution in the model) can be isolated. One can also apply algorithms that are used to calculate a bulk flow from galaxy motions, but apply the algorithm in isolation to the external or internal component of galaxy motions. In principle, this lets us understand the bulk flow that arises from only ‘beyond’ the survey volume. Interestingly, the authors find that there is still an increasingly large ‘external’ bulk flow in the data when including data from larger and larger scales. Furthermore, looking at the binned data from the individual galaxy motions in CF4 (the external component of their motions), they find a substantial contribution to the external flow towards the direction of the bulk flow vector. These galaxies are still only those within the volume of the mass distribution accounted for within the velocity model, but the results seem to indicate they have substantial velocities that are sourced from beyond this volume.

The authors suggest this hints that a substantial mass could be present at the edge (but perhaps just outside) of the survey volume, that is sourcing the external bulk flow. Additionally, they point out many authors in the literature tend to model the bulk flow vector from external sources as a ‘uniform’ contribution across the volume of a given survey, which may be a poor assumption that needs revisiting.

Summary

This result suggests more data from peculiar velocity surveys at a greater depth will help us to understand the source of the bulk flow; in this work, the authors have effectively shown that the bulk flow may be sourced by external mass concentrations, which might explain the increasing bulk flow amplitude towards greater survey depths.

This analysis still leaves us with uncertainty on how the observations can be reconciled with \(\Lambda\)CDM, because the required mass concentration for the observed external bulk flow is likely much larger than what we expect within the \(\Lambda\)CDM model. Interestingly, in some literature, the bulk flow is interpreted as an intrinsic ‘dipole’ contribution to the cosmic rest frame (which is generally chosen to be the Cosmic Microwave Background – AKA the CMB – after the dipole motion due to our galaxy moving with respect to this rest frame is subtracted off) that can arise in certain inflationary models. This would perhaps help to explain dipole measurements seen in radio surveys (this ‘intrinsic’ dipole contribution would be something that would be present in CMB temperature maps even when we are at rest with respect to the CMB frame). However, in the case this is true the contribution to the bulk flow would be expected to be uniform across the survey volume, which is not seen in the results of this work.

Edited by: Joe Williams 

Featured image credit: View towards the Great Attractor, by ESO, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons