Kinematic cosmic dipole from a large sample of strong lenses

This paper proposes using relativistic distortions in the Einstein radii of strong gravitational lenses, particularly when combined with spectroscopic velocity-dispersion measurements, to independently measure the kinematic cosmic dipole and potentially resolve the existing tension between CMB and source number count estimates of the observer's peculiar velocity at a $\sim 4\sigma$ significance level.

The Gist

Imagine you are standing on a moving train, looking out the window. If you hold a perfectly round hula hoop up to the glass, it might look slightly squashed or stretched depending on how fast you're going and which way the train is moving. This isn't because the hula hoop changed shape; it's because you are moving.

This paper is about using that exact same idea to figure out how fast our entire solar system (and the Earth) is moving through the universe.

The Big Mystery: "The Cosmic Speedometer"

Astronomers have two main ways to measure our speed through space:

1. The "Temperature" Method (CMB): By looking at the afterglow of the Big Bang (the Cosmic Microwave Background), we see a slight temperature difference. It's hotter in the direction we are moving toward and cooler in the direction we are moving away from. This tells us we are moving at about 370 km/s.
2. The "Counting" Method: By counting how many distant galaxies or quasars we see in different directions, we should see more in the direction we are moving (because they look brighter and closer). However, recent counts suggest we might be moving three times faster than the temperature method says!

This disagreement is a huge puzzle in physics. Is our speedometer broken? Is there something weird about the universe?

The New Idea: Cosmic "Hula Hoops"

The authors of this paper propose a third, completely independent way to check our speed. They want to use Strong Gravitational Lenses.

What is a gravitational lens?
Imagine a massive galaxy sitting between us and a distant background galaxy. The gravity of the front galaxy acts like a giant magnifying glass, bending the light from the back one. Often, this creates a perfect circle of light around the front galaxy, called an Einstein Ring. Think of it as a cosmic hula hoop made of light.

The Trick:
If we are moving through space, that perfect circle shouldn't look like a circle to us anymore. Just like the hula hoop on the train, the motion of our solar system should squish the ring slightly into an oval.

• Rings in the direction we are moving should look slightly smaller.
• Rings in the opposite direction should look slightly larger.

The authors realized that if we measure the size of thousands of these "cosmic hula hoops" across the sky, we can detect this squishing effect and calculate our speed.

The Problem: A Noisy Room

The authors ran simulations using data expected from the Euclid space telescope (a new telescope that will take pictures of millions of galaxies).

They found a problem: The "hula hoops" aren't all the same size naturally. Some galaxies are heavier than others, making bigger rings. Some are closer, some are farther. This natural variety creates a lot of "noise," like trying to hear a whisper in a crowded, noisy room.

• Result: If they only looked at the shape of the rings, they couldn't tell the difference between our speed and the natural noise. They needed more information.

The Solution: Adding "Kinematic" Clues

To quiet the noise, they added a second layer of data: Stellar Kinematics (how fast the stars inside the lensing galaxy are moving).

Think of it like this:

• Lensing Only: You see a car driving by and guess its speed just by how big it looks. It's hard because cars come in different sizes (trucks vs. motorcycles).
• Lensing + Kinematics: You see the car, and you can hear its engine revving. The engine sound tells you exactly how big and heavy the car is. Now, when you compare the size of the car to the engine sound, you can calculate its speed with incredible precision.

By combining the size of the light ring (from Euclid's camera) with the speed of the stars inside the galaxy (from spectroscopy), they can filter out the natural noise.

The Verdict: Can We Solve the Mystery?

The paper runs the numbers for three scenarios:

1. The "Pessimistic" Scenario: We only have a few extra measurements.
   • Outcome: We can't quite solve the mystery yet. The data is too fuzzy.
2. The "Realistic" Scenario: We get a good amount of extra data from follow-up surveys (like DESI or 4MOST).
   • Outcome: We can likely tell the two theories apart with about 2-sigma confidence (a decent hint, but not a proof).
3. The "Ideal" Scenario: We get a dedicated, massive follow-up campaign to measure the speed of stars in every single lensing galaxy.
   • Outcome: Bingo! We can solve the mystery with 4-sigma confidence. This would be strong enough to tell us definitively if the "Counting Method" is wrong or if the "Temperature Method" is missing something.

Why This Matters

This method is special because it doesn't rely on counting objects or measuring their brightness (which can be tricky due to dust or telescope limits). It relies purely on geometry and angles. It's like measuring speed by looking at the shape of a shadow rather than counting how many people are walking in it.

In short: The authors have proposed a clever new way to use the "squashed" shapes of cosmic light rings to finally figure out how fast we are really moving through the universe, potentially solving one of cosmology's biggest headaches.

Technical Summary

Here is a detailed technical summary of the paper "Kinematic cosmic dipole from a large sample of strong lenses" by Millon et al.

1. Problem Statement

There is a persistent and significant tension in cosmology regarding the measurement of the observer's peculiar velocity ($v_o$) relative to the Cosmic Microwave Background (CMB) rest frame.

• CMB Measurement: The Planck satellite measures a dipole anisotropy in the CMB temperature, inferring a velocity of $v_o \approx 370$ km s$^{-1}$. This is widely accepted as a kinematic effect.
• Source Number Counts: Independent measurements using high-redshift source number counts (e.g., quasars) suggest a significantly larger velocity, often reported at $3\sigma$to$5.7\sigma$ tension with the CMB value.
• The Conflict: While the direction of the dipole is generally consistent, the amplitude differs drastically. Current explanations involve local clustering contamination, source evolution, or intrinsic CMB dipoles, but no consensus exists. There is a critical need for a fully independent method to measure $v_o$ that is immune to the systematics affecting source counts (e.g., flux thresholds and clustering).

2. Methodology

The authors propose a novel method to measure the kinematic cosmic dipole using strong gravitational lenses. The core physical principle is relativistic aberration induced by the observer's motion.

A. Physical Mechanism: Einstein Angle Aberration

• Aberration Effect: An observer moving with velocity $v_o$ sees a distortion in the apparent position of objects. For a strong lens, a perfectly circular Einstein ring (radius $\theta_E$) appears as an ellipse to the moving observer.
• Azimuthal Averaging: While the ring is distorted, the azimuthally averaged Einstein radius $\langle \theta'_E \rangle$ measured by the moving observer is modulated by the angle $\theta'_{cm}$ between the lens and the velocity vector:
  $$\langle \theta'_E(\hat{n}') \rangle = \langle \theta_E \rangle \left( 1 - \frac{v_o}{2c} \cos \theta'_{cm} \right)$$
  This creates a dipolar modulation in the mean Einstein radius across the sky.
• Robustness: Unlike source counts, this observable is derived purely from angular measurements. The authors demonstrate that selection effects (flux and size thresholds) cancel out to a high degree (contamination $< 0.1\%$) because the modulation affects both the number of detected lenses and their mean size in a way that largely cancels in the ratio.

B. Statistical Framework

The authors employ a Bayesian framework to infer $v_o$, its direction $(l_o, b_o)$, and the mean Einstein radius $\langle \theta_E \rangle$.

• Likelihood 1 (Lensing Only): Uses only the measured Einstein radii from imaging. The intrinsic scatter in lens masses and redshifts ($\sigma_{\theta_E}$) acts as significant noise.
• Likelihood 2 (Lensing + Kinematics): Incorporates additional data to constrain the intrinsic mass of each lens, thereby reducing the noise term. Two approaches are modeled:
  1. Spectroscopic Velocity Dispersion ($\sigma_v$): Direct measurement of the lens galaxy's stellar velocity dispersion relates to $\theta_E$ via the Singular Isothermal Sphere (SIS) model.
  2. Fundamental Plane (FP): For lenses without spectroscopy, the FP relation (linking effective radius $R_e$, velocity dispersion, and surface brightness) is used to estimate $\sigma_v$ from photometric data.

C. Simulation and Forecast

• Data Source: The study simulates a sample of $\sim 10^5$ strong lenses expected from the Euclid space mission (Wide Survey).
• Scenarios: They test three scenarios for ancillary data availability:
  1. Pessimistic: Only 5,000 lenses have velocity dispersion measurements; others have photometric redshifts.
  2. Realistic: 10,000 lenses with velocity dispersion; others have spectroscopic or photometric redshifts.
  3. Ideal: A dedicated spectroscopic follow-up yielding 50,000 lenses with velocity dispersion and 50,000 with spectroscopic redshifts.

3. Key Contributions

1. New Observable: Introduction of the Einstein radius dipole as a kinematic probe, distinct from number-count dipoles.
2. Systematic Insensitivity: Rigorous derivation showing that selection biases (flux and size cuts) contribute negligibly ($<0.1\%$) to the dipole measurement, making this method robust against the systematics plaguing source-count analyses.
3. Noise Reduction Strategy: Demonstration that combining lensing with stellar kinematics (via spectroscopy or the Fundamental Plane) drastically reduces the intrinsic scatter noise, transforming the measurement from a detection limit to a precision tool.
4. Euclid Forecasts: Quantitative predictions for the Euclid mission, showing that even with modest spectroscopic follow-up (e.g., from 4MOST or DESI), the method can resolve the CMB vs. Source Count tension.

4. Results

The authors simulated the posterior distributions for $v_o$ under different assumptions:

• Lensing Only (No Kinematics):

  • Even with 400,000 lenses, the intrinsic scatter is too large to distinguish between the CMB value ($370$km s$^{-1}$) and the Source Count value ($\sim 1100$km s$^{-1}$) with high significance. The discrimination power is only$\sim 1.1\sigma$.

• Combined Lensing + Kinematics:

  • Fundamental Plane (Photometric Redshifts): Improves constraints by a factor of $\sim 1.5$.
  • Fundamental Plane (Spectroscopic Redshifts): Improves constraints by a factor of $\sim 3$.
  • Direct Velocity Dispersion (Ideal Scenario): With 50,000 lenses having spectroscopic velocity dispersion, the method achieves a discrimination power of $\sim 4\sigma$ to $5.8\sigma$.
  • Realistic Follow-up (DESI/4MOST): Even in a realistic scenario where only a fraction of lenses have velocity dispersion data, the method can discriminate between the two velocity values at the $\sim 2\sigma$ to $4\sigma$ level.

• Directionality: The method successfully recovers the dipole direction $(l_o, b_o)$ consistent with the true input values in all high-precision scenarios.

5. Significance

• Independent Verification: This method provides a "clean" test of the kinematic dipole that does not rely on flux measurements or source evolution models, addressing the primary criticisms of source-count analyses.
• Resolving the Tension: The results suggest that the tension between CMB and source-count dipoles is likely real and not an artifact of local clustering or selection effects in the lensing method. If the tension persists, it could imply new physics (e.g., a large-scale bulk flow or intrinsic CMB dipole).
• Feasibility: The study proves that the upcoming Euclid mission, combined with existing or planned spectroscopic surveys (DESI, 4MOST), has the statistical power to settle this debate. It transforms strong gravitational lensing from a tool for mass mapping into a precision cosmological probe for observer motion.
• Methodological Advancement: The work highlights the power of combining geometric (lensing) and dynamical (kinematic) observables to break degeneracies and reduce noise in cosmological parameter estimation.