🔭 astrophysics

The Origins of the Bulk flow

Using the CosmicFlows-4 catalog, this study demonstrates that the observed large-scale bulk flow is primarily driven by external mass concentrations beyond 200 Mpc/h rather than local structures, while simultaneously validating the internal velocity field and challenging the assumption that such external flows are spatially uniform.

Original authors: Richard Watkins, Hume A. Feldman

Published 2026-07-28

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CC BY 4.0

Original authors: Richard Watkins, Hume A. Feldman

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding balloon covered in tiny stickers. As you blow air into the balloon, every sticker moves away from every other sticker. This is the Hubble expansion, the universe's default setting. But sometimes, a sticker doesn't just drift with the wind; it gets pulled by a heavy magnet nearby, or pushed by a gust from a hidden fan. In astronomy, these extra movements are called "peculiar velocities." They are the cosmic equivalent of a leaf swirling in a storm rather than just floating on a calm breeze. Scientists care about these swirls because they act like a map of invisible gravity. By tracking how galaxies move, we can weigh the universe's hidden mass and test if our rules for how the cosmos works are actually correct. For decades, astronomers have been trying to figure out if the whole neighborhood of galaxies is drifting together in a giant, coordinated flow, and if so, what is pushing them.

This paper dives into that mystery using a massive new catalog of galaxy speeds called CosmicFlows-4. The authors, Richard Watkins, Trajan Clark, and Hume A. Feldman, wanted to solve a puzzle: a previous study found that our local universe is moving much faster than the standard model of cosmology predicts. Is this a glitch in the data, a mistake in our math, or is there a massive, invisible monster out there pulling us? To find out, the team broke the problem into two parts. First, they calculated how much the galaxies should move based on the visible matter right around us (like the local neighborhood). Then, they looked at the "leftover" motion to see if it came from something far away.

The team used a clever trick to clean up their data. Because measuring cosmic distances is tricky and often leads to skewed numbers, they grouped thousands of galaxies together and looked at their average speeds. This smoothed out the errors and let them pinpoint two key numbers with high precision: a value called $\beta$ (which tells us how fast structures in the universe are growing) and the Hubble constant ( $H_0$ ), which they found to be $75.9 \pm 0.1$ km s $^{-1}$ Mpc $^{-1}$ for this specific dataset.

Once they had their numbers sorted, they did the real detective work. They subtracted the "local" motion (caused by mass within 200 $h^{-1}$ Mpc) from the total observed motion. What they found was surprising. The huge bulk flow isn't caused by the stuff right next door. Instead, the data shows that the flow is dominated by sources beyond 200 $h^{-1}$ Mpc. Even more interesting, this external flow isn't a uniform push; it gets stronger the closer you get to the edge of the survey in a specific direction. This pattern suggests a single, massive concentration of matter sitting far away, pulling on our local volume like a giant cosmic magnet.

The authors modeled this invisible giant. They calculated that it likely sits just outside the 200 $h^{-1}$ Mpc boundary, in a direction consistent with the flow. Depending on how "clumpy" this mass is, it could be an overdensity of about $2 \times 10^{17}$ or $4 \times 10^{17}$ solar masses. This object is so far away and so hidden behind the dusty plane of our own Milky Way that we haven't seen it in surveys yet. The paper concludes that this massive, distant structure is the most likely culprit for the strange, fast bulk flow we see. It challenges the common assumption that external forces create a uniform, gentle push across our local volume; instead, the universe seems to be tugging us unevenly from a specific, distant point. While this massive object fits the data, the authors note that such a huge structure is rare in our standard model, leaving the door open for either a very lucky cosmic fluke or a need to rethink our understanding of how the universe grows.

Problem Statement
The origin of the large-scale bulk flow—the coherent motion of galaxies relative to the Cosmic Microwave Background (CMB) rest frame—remains a subject of significant debate. Previous analyses using the CosmicFlows-4 (CF4) catalog (Watkins et al. 2023, hereafter W23) reported a bulk flow magnitude of $419 \pm 36$ km/s within a radius of $200h^{-1}$ Mpc, a value in over $4\sigma$ tension with the standard $\Lambda$ CDM cosmological model, which predicts an amplitude of only $\sim 100$ km/s for such volumes. A primary challenge in resolving this tension is distinguishing between "internal" flows, driven by mass fluctuations within the observed volume, and "external" flows, arising from structures beyond the survey boundary. Furthermore, there is a discrepancy between W23 and other recent studies (e.g., Stiskalek et al. 2026) that claim consistency with the standard model; these studies utilize different methodologies, such as modeling external flows as spatially uniform dipoles or using only a subset of the CF4 data. The paper seeks to clarify the physical origin of the observed bulk flow, test the self-consistency of the velocity models, and determine whether the flow is dominated by local mass concentrations or distant external sources.

Methodology
The authors utilize the group version of the CosmicFlows-4 (CF4) catalog, comprising over 23,000 objects with redshifts $cz < 20,000$ km/s. To calculate peculiar velocities, they employ a bias-corrected distance calculation derived from distance moduli and utilize a modified redshift ( $z_{mod}$ ) to account for non-linear Hubble flow effects.

The core methodological innovation is a weighted-average technique designed to test model self-consistency while minimizing the impact of non-Gaussian distance errors. The observed peculiar velocity ( $v_i$ ) is decomposed into:
$v_i = v_{int,i} + v_{ext,i} + \delta_i + \delta_{*,i}$
where $v_{int}$ is the velocity field predicted by mass distributions within $200h^{-1}$ Mpc, $v_{ext}$ is the external contribution, $\delta_i$ is measurement noise, and $\delta_*$ represents the scatter due to galaxies being imperfect tracers of the velocity field.

The authors compare CF4 velocities against two independent internal velocity models:

Carrick et al. (2015): Based on the 2M++ redshift survey.
McAlpine et al. (2025): Based on the same redshift data but incorporating simulations and Bayesian forward modeling.

To test the models, the authors bin the observed velocities based on the predicted internal velocities ( $v_{int}$ ) and calculate weighted averages. They treat the growth rate parameter $\beta = \Omega_m^{0.55}/b$ and the Hubble constant $H_0$ as free parameters to find the best fit where the average observed velocity matches the predicted internal velocity (a line of slope unity and zero intercept).

Finally, the bulk flow is separated into internal and external components using a minimum-variance (MV) formalism. The external component is modeled as a mass concentration at a distance $R_m$ with a specific direction and induced velocity $V_m$ , fitted using Markov Chain Monte Carlo (MCMC) minimization.

Key Results

Model Consistency and Parameters: The CF4 velocities show excellent agreement with the predicted internal fields from both Carrick et al. (2015) and McAlpine et al. (2025). The best-fit parameters derived are:
- Growth rate parameter: $\beta = 0.31 \pm 0.01$ .
- Hubble constant for CF4 peculiar velocity calculations: $H_0 = 75.9 \pm 0.1$ km s $^{-1}$ Mpc $^{-1}$ (consistent with CF4 calibrations).
- The McAlpine et al. (2025) model, which includes non-linear effects, reproduces the data well without adjustable scaling, though it slightly underestimates velocities in the highest bins, likely due to the grouping of galaxies in the CF4 catalog smoothing out infall velocities.
Origin of the Bulk Flow: Using the minimum-variance formalism, the authors find that the observed large-scale bulk flow is dominated by external sources (mass distributions beyond $200h^{-1}$ Mpc). Even within small radii (e.g., $50h^{-1}$ Mpc), the internal contribution is sub-dominant to the external contribution.
Spatial Structure of External Flow: Contrary to the assumption that external mass concentrations induce a spatially uniform flow (a constant dipole) across the local volume, the authors find the external flow is highly non-uniform. The amplitude of the externally driven flow increases monotonically with scale. The contribution to the bulk flow is largest near the edge of the survey volume in the direction of the bulk flow and diminishes toward the Milky Way.
Modeling the External Source: The authors model the external driver as a massive overdensity. The best-fit location is at Galactic coordinates $l \approx 295^\circ, b \approx -3^\circ$ , just outside the $200h^{-1}$ Mpc volume.
- For a density profile falling as $1/r^2$ ( $\alpha=1$ ), the mass concentration is at $R_m \approx 200h^{-1}$ Mpc with an induced velocity $V_m \approx 250$ km/s.
- For a more point-like profile ( $\alpha=2$ ), the mass is similar but slightly further.
- The estimated excess mass is $\delta M \approx 2\text{--}4 \times 10^{17} M_\odot h^{-1}$ .
- Subtracting this modeled external flow from the observations reduces the residual bulk flow within $200h^{-1}$ Mpc to levels consistent with the standard cosmological model.

Significance and Claims
The paper claims that the large bulk flow reported in W23 is not necessarily a failure of the $\Lambda$ CDM model but rather the result of a massive, distant overdensity (potentially in the "zone of avoidance," such as the Vela supercluster region) that has not been fully accounted for in local density reconstructions.

A critical theoretical contribution is the challenge to the common assumption that external mass concentrations induce a spatially uniform flow in the local volume. The authors demonstrate that the flow is strongly non-uniform, peaking near the survey boundary in the direction of the source. This finding suggests that previous analyses modeling external flows as constant dipoles may be insufficient.

The authors conclude that while their results explain the observed bulk flow via a distant massive structure, the required mass and distance push the boundaries of standard expectations. They posit that the situation remains an open question: whether the flow represents a rare statistical fluctuation, an incomplete accounting of the large-scale mass distribution (particularly in obscured regions), or a hint of new physics. They emphasize that future, deeper surveys, particularly in the direction of the bulk flow near the Galactic plane, are necessary to definitively resolve the origin of these motions.

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