How to Build an Empirical Speed Distribution for Dark Matter in the Solar Neighborhood

This paper proposes and validates a method to reconstruct the local dark matter speed distribution by combining a Maxwell-Boltzmann component for old merger debris with a kinematically boosted stellar tracer for recent massive mergers, demonstrating its application to the Milky Way using Gaia data.

The Gist

Imagine the space around our Sun is filled with invisible "ghosts" called Dark Matter. Scientists want to catch these ghosts in special detectors on Earth, but to know how to build the detector, they need to know how fast these ghosts are moving.

The problem is, we can't see Dark Matter directly. We can only see the stars. For a long time, scientists have guessed the ghosts' speeds by running computer simulations of how galaxies form. But since we can't run a simulation of our own galaxy's exact history, these guesses are just approximations.

This paper proposes a new, more direct way to figure out the speed of these ghosts by looking at the "footprints" they left behind: stars.

Here is the breakdown of their method, using simple analogies:

1. The Two Types of Ghosts

The authors realized that the Dark Matter around us comes from two different sources, like two different types of traffic on a highway:

• The "Old, Calm" Traffic (Untraceable): This is Dark Matter that fell into our galaxy a very long time ago. It has had billions of years to settle down, mix around, and calm its speed. It moves in a predictable, smooth pattern (like a crowd of people walking casually in a park). The authors call this the "Untraceable" part because we can't easily link it to a specific event.
• The "New, Chaotic" Traffic (Traceable): This is Dark Matter that fell in more recently from a massive collision with another galaxy. It hasn't had time to settle. It's still moving in a specific, chaotic pattern, like a group of people running together after a sudden alarm. This is the "Traceable" part because we can see the stars that came with it.

2. The "Star-Shadow" Connection

The big discovery in this paper is the relationship between the stars and the Dark Matter ghosts that fell in together.

Think of a merger between galaxies like a dance troupe (the stars) and their shadow (the Dark Matter).

• When the troupe enters a new city (our galaxy), the shadow gets stripped off first and spreads out faster and wider.
• The dance troupe (stars) stays tighter together and moves a bit slower because they are holding onto each other.

The authors found that if you just look at the stars, you will underestimate how fast the Dark Matter ghosts are moving. The ghosts are always a bit faster and more spread out than their star "shadows."

3. The "Speed Boost" Trick

To fix this, the authors invented a simple math trick they call a "kinematic boost."

Imagine you are trying to guess how fast a car is going by watching a bicycle riding next to it. You know the bicycle is slower. So, you take the bicycle's speed and add a "boost" to it to guess the car's speed.

The authors did this with the stars:

1. They measured the speed of the stars from the recent galaxy crash (the Gaia Sausage–Enceladus merger, or "GSE").
2. They applied a "boost" to make the stars' speed distribution look more like the Dark Matter's.
3. They found that once you add this boost, the stars become a perfect map for the Dark Matter's speed.

4. Putting It All Together

The authors tested this method on 98 computer-simulated galaxies that look like our Milky Way. They found that if you combine:

• The smooth, calm "Old" Dark Matter (which follows a standard speed pattern), and
• The "New" Dark Matter (which you can map by boosting the speed of the crash-related stars),

...you get a very accurate picture of the total speed of Dark Matter around the Sun.

The Result for Our Galaxy

When they applied this to our actual Milky Way using real data from the Gaia satellite:

• They found that the Dark Matter from our galaxy's last big crash (the GSE) is moving slightly slower than the average "background" Dark Matter.
• This changes the "high-speed tail" of the distribution (the fastest ghosts) by about 20%.

In short: Instead of guessing how fast Dark Matter is moving, we can now look at the stars that fell in with it, give their speed a little "boost" to account for the fact that Dark Matter is faster, and get a much clearer, more accurate map of the invisible ghosts surrounding us. This helps scientists build better detectors to catch them.

Technical Summary

Technical Summary: How to Build an Empirical Speed Distribution for Dark Matter in the Solar Neighborhood

Problem Statement
Direct detection experiments searching for dark matter (DM) interactions rely critically on the local speed distribution of DM particles near the Sun. While cosmological simulations of Milky Way (MW)-like galaxies have provided proxies for this distribution, no single simulation captures the specific evolutionary history of the Milky Way. Consequently, there is a need for alternative approaches that infer the local DM speed distribution directly from observations. Previous empirical efforts have utilized the kinematic correlation between accreted stellar debris and their corresponding DM components, but these studies often lacked a comprehensive treatment of "dark accretion" (DM from non-luminous mergers and diffuse accretion) and relied on smaller sample sizes.

Methodology
The authors utilize a sample of 98 MW-analog galaxies from the high-resolution TNG50 cosmological simulation (part of the IllustrisTNG project) to develop and validate a procedure for reconstructing the local DM speed distribution. The methodology proceeds as follows:

1. Region of Interest (ROI): The analysis focuses on a cylindrical shell centered on the Sun's location ($R_\odot \approx 8$ kpc), spanning galactocentric radii $r \in [6, 10]$ kpc and heights $|z| \le 2$ kpc.
2. Particle Tracking and Classification: DM and stellar particles within the ROI are tracked back to their origins using merger trees. The DM population is categorized into three distinct components based on accretion redshift ($z_{acc}$) and merger mass:
   • Traceable: DM from massive mergers ($M_{dyn} \ge 10^9 M_\odot$) with $z_{acc} < 3$ that contribute $>10\%$ of the local DM. These events leave significant stellar debris.
   • Young Untraceable: DM from late-time accretion ($z_{acc} < 3$) that does not meet the Traceable criteria, originating from low-mass mergers or dark accretion.
   • Old Untraceable: DM from early accretion ($z_{acc} > 3$), including early luminous mergers and dark accretion, which has had sufficient time to virialize.
3. Modeling the Untraceable Component: The combined "Untraceable" population (Old + Young) is modeled using a standard Maxwell–Boltzmann distribution (Standard Halo Model, SHM) centered at the local standard-of-rest velocity ($v_0$), derived from the enclosed mass at the solar radius.
4. Modeling the Traceable Component: For the Traceable component, the authors investigate the kinematic correlation between the DM and its associated stellar debris. They find that stellar debris systematically underestimates the velocity dispersion of the corresponding DM. To correct this, they apply a kinematic "boost" to the stellar velocities, increasing the dispersion by a constant offset ($\Delta\sigma$) while preserving the mean velocity.
5. Reconstruction: The total local DM speed distribution is reconstructed as a weighted sum of the SHM (representing the Untraceable background) and the boosted stellar distribution (representing the Traceable component).

Key Results

• Untraceable DM: The combined Untraceable component (Old and Young) is well-described by a Maxwell–Boltzmann distribution. While the Young Untraceable component alone exhibits significant variance and bias toward higher speeds, its small fractional contribution in most MW analogs means the total Untraceable distribution remains close to the SHM (Earth Mover's Distance, EMD $\approx 13$ km s$^{-1}$).
• Traceable DM and Stellar Boost: There is a systematic offset where DM from massive mergers has higher velocity dispersions than the associated stars. This is attributed to DM being stripped earlier and deposited at higher orbital energies than the more deeply bound stars. The authors quantify this offset as $\Delta\sigma \approx 34$ km s$^{-1}$ (averaged over components) for general mergers and $\approx 43$ km s$^{-1}$ for GSE-like mergers. Applying this boost to stellar tracers significantly improves the agreement with the true DM speed distribution, reducing the EMD from $\approx 47$ km s$^{-1}$ (uncorrected) to $\approx 10$ km s$^{-1}$.
• Total Reconstruction: Combining the SHM background with the boosted stellar tracer model yields an accurate reconstruction of the total local DM speed distribution. Even when sampling over uncertainties in the relative weighting ($w_{tr}$) and the boost factor ($\Delta\sigma$), the reconstructed distributions match the exact simulation data with a median EMD of $11^{+6}_{-4}$ km s$^{-1}$.
• Application to the Milky Way: Applying this framework to the Milky Way using Gaia data for the Gaia Sausage–Enceladus (GSE) merger, the authors find that the GSE-contributed DM is modestly slower than the local standard-of-rest speed. The resulting speed distribution has a mode $11$ km s$^{-1}$ slower than a pure Maxwell–Boltzmann model, leading to an $\sim 20\%$ suppression of the high-speed tail.

Significance and Claims
The paper claims to establish a practical framework for building a complete empirical speed distribution for local DM by combining a Maxwell–Boltzmann model for the background (including dark accretion) with a stellar-informed model for recent massive mergers.

• First Treatment of Dark Accretion: This is the first study to explicitly account for the contribution of dark accretion to the solar neighborhood, demonstrating that this component, along with early luminous mergers, can be effectively modeled as a Maxwellian.
• Validation of Stellar Tracers: The work validates that stellar debris from massive mergers can trace the corresponding DM speed distribution, provided a systematic kinematic boost is applied to correct for the velocity dispersion offset.
• Empirical Application: The authors demonstrate the utility of this procedure by updating empirical distributions for the local DM, specifically quantifying the impact of the GSE merger. They find that while the GSE modifies the high-speed tail, the overall distribution remains reasonably approximated by the SHM, though with specific, measurable deviations.

The authors note that their results are consistent with prior work using FIRE-2 simulations regarding the Maxwellian nature of the Untraceable component, though they observe a larger dispersion offset between stars and DM compared to FIRE-2 results. They attribute these differences to numerical resolution and physical environmental factors (e.g., cluster proximity in TNG50 vs. isolated zoom-ins in FIRE-2). The paper concludes that this methodology provides a robust, observationally motivated tool for direct detection experiments, while acknowledging that future higher-resolution simulations and observational surveys (e.g., 4MOST, WEAVE, LSST) will further refine these empirical models.