Probing the Warm Dark Matter mass with [C II] intensity mapping

This paper forecasts the potential of [C II] line-intensity mapping surveys to constrain the mass of Warm Dark Matter particles, demonstrating that while current and near-future surveys can set lower limits on the particle mass, achieving competitive constraints comparable to other methods will require combining multiple redshifts and emission lines with advanced survey capabilities.

The Gist

Here is an explanation of the paper, translated from "astrophysicist" to "everyday human," using some creative analogies.

The Big Mystery: What is Dark Matter?

Imagine the universe is a giant, invisible ocean. We can see the islands (stars and galaxies) floating on it, but we can't see the water itself. We know the water is there because the islands move in specific ways, but we don't know what the water is made of.

For decades, scientists have assumed the water is made of "Cold Dark Matter" (CDM). Think of this like heavy, slow-moving boulders at the bottom of the ocean. They clump together easily, forming big islands and tiny pebbles (small galaxies) everywhere.

But, there's a problem. When we look at the tiny pebbles (dwarf galaxies), there seem to be fewer of them than our "boulder" theory predicts. This has led to a new theory: Warm Dark Matter (WDM).

If CDM is heavy boulders, WDM is like swimming fish. They are lighter and move faster. Because they zip around so quickly, they can't clump together to form the tiniest pebbles. They only form the bigger islands. If WDM is real, the universe should be missing a lot of tiny galaxies.

The Detective Tool: The [C ii] Flashlight

How do we test if the universe is made of boulders or fish? We need a flashlight that can see the tiny pebbles.

The paper proposes using a new kind of telescope survey called Line-Intensity Mapping (LIM). Instead of taking a picture of one galaxy at a time (which is like trying to count individual grains of sand on a beach by looking at one grain), this method takes a "blurry" photo of the whole beach at once.

Specifically, they are looking for a specific color of light emitted by Carbon atoms, called [C ii].

• The Analogy: Imagine the tiny pebbles (small galaxies) are actually glowing fireflies. In a "Cold" universe, there are millions of tiny fireflies. In a "Warm" universe, the tiny fireflies are missing; only the big, bright ones remain.
• By measuring the "flicker" or pattern of this light across the sky, scientists can count how many tiny fireflies are there. If the pattern shows a lack of tiny flickers, it proves the "Warm Fish" theory is correct.

The Experiment: The FYST Telescope

The authors are planning to use a future telescope called FYST (Fred Young Submillimeter Telescope) to do this counting. They are looking at a specific time in the universe's history (about 11 billion years ago, or redshift $z \approx 3.6$).

They ran a massive computer simulation to ask: "If we point this telescope at the sky, how well can we tell the difference between Boulders (CDM) and Fish (WDM)?"

The Results: Good News and Bad News

The paper found two main things:

1. The "Heavy" Problem (The Bad News)
The [C ii] light they are looking for mostly comes from medium-sized galaxies (the size of a large city), not the tiny dwarf galaxies (the size of a small village).

• The Analogy: Imagine you are trying to prove that tiny fireflies are missing. But your flashlight is so bright that it only lights up the big, loud crickets. The tiny fireflies are there, but your light is too "loud" to see them.
• Because the signal is dominated by the big galaxies, the "missing tiny galaxies" signal is very weak. Even with a great telescope, it's hard to prove the fish theory just by looking at this specific light.

2. The "Super-Telescope" Solution (The Good News)
However, the paper says that if we build bigger, better, and sharper versions of this survey, we can solve the mystery.

• Bigger Sky: Looking at more of the sky gives us more data points.
• Sharper Focus: Improving the "spectral resolution" (making the telescope's focus sharper) helps separate the signal from the noise.
• The Result: With a "dream team" setup (looking at half the sky with a super-sensitive telescope), they could potentially rule out "Warm Dark Matter" particles that are lighter than about 6 keV. If the particles are heavier than that, they act just like the "boulders" (Cold Dark Matter).

The "What If" Scenario

The authors also asked: "What if the universe IS actually made of Warm Dark Matter (with a mass of 3 keV)?"

• The Answer: With current or near-future plans, we might not be able to prove it. The data would still look a lot like the "Cold" theory.
• The Catch: We would need the "Dream Team" setup (huge sky coverage + super sensitivity) to finally say, "Aha! We found the missing fish!"

The Bottom Line

This paper is a reality check for astronomers.

• It says: "Using the [C ii] light to find Warm Dark Matter is a great idea, but it's harder than we thought because the light comes from the wrong size of galaxies."
• It concludes: "We can't do it with just one survey. We need to combine many surveys, look at different colors of light, and build much bigger telescopes to finally solve the Dark Matter mystery."

In short: We are trying to find out if the universe is made of slow boulders or fast fish. We have a new flashlight, but it's currently too focused on the big rocks to see the tiny fish. We need to build a better flashlight to catch them!

Technical Summary

Here is a detailed technical summary of the paper "Probing the Warm Dark Matter mass with [C ii] intensity mapping" by Marcuzzo et al.

1. Problem Statement

The nature of Dark Matter (DM) remains a central open question in cosmology. While the Cold Dark Matter (CDM) paradigm is the standard model, it faces small-scale tensions (e.g., the "missing satellites" problem). Warm Dark Matter (WDM), composed of thermal relics with masses in the keV range, offers a solution by suppressing the formation of low-mass halos due to free-streaming effects.

Current constraints on WDM particle mass ($m_{\text{WDM}}$) primarily come from the Lyman-$\alpha$ forest and dwarf galaxy counts, typically setting lower limits of a few keV. However, these probes have limitations in redshift coverage and sensitivity to specific halo mass ranges. Line-Intensity Mapping (LIM) offers a novel approach to probe the large-scale distribution of matter and galaxy properties across cosmic time. This paper investigates whether future LIM surveys targeting the [C ii] 158 $\mu$m fine-structure line can provide competitive constraints on $m_{\text{WDM}}$, specifically by detecting the suppression of small-scale power in the matter distribution.

2. Methodology

Theoretical Framework

• Halo Model Formalism: The authors model the [C ii] power spectrum (PS) using the halo model, decomposing the signal into clustering ($P_{\text{clust}}$) and shot-noise ($P_{\text{shot}}$) components.
• Cosmological Models: They compare CDM against WDM scenarios. The WDM linear matter power spectrum is derived using a transfer function $T(k)$ that introduces a cutoff at small scales. They also consider Fuzzy Dark Matter (FDM) as an alternative, converting constraints via matching half-mode wavenumbers.
• Luminosity Function (LF) & Abundance Matching: A critical component is the connection between halo mass ($M$) and [C ii] luminosity ($L$). The authors use abundance matching to assign luminosities to halos, ensuring the model reproduces the observed bright end of the [C ii] LF.
  • They adopt two parameterizations for the LF based on existing data (ALPINE survey and multi-wavelength fits): an optimistic (high normalization) and a pessimistic (low normalization) scenario, both with a faint-end slope $\alpha = -1.1$.
  • They also test steeper slopes ($\alpha = -1.9$) to maximize the contribution of low-mass halos.
• Survey Simulation: The analysis focuses on the Deep Spectroscopic Survey (DSS) planned for the Fred Young Submillimeter Telescope (FYST) at redshift $z \simeq 3.6$. They simulate various survey configurations varying:
  • Sky coverage ($16$to$1600$deg$^2$ and half-sky).
  • Sensitivity (noise levels).
  • Spectral resolution ($R=100$ vs. $R=500$).

Statistical Analysis

• Bayesian Inference: The authors perform a Bayesian analysis on mock data generated under both CDM and WDM ($m_{\text{WDM}} = 3$ keV) assumptions.
• Parameters: The inference targets the WDM particle mass ($m_{\text{WDM}}$) and the line-of-sight displacement parameter ($\sigma$), which encapsulates Redshift-Space Distortions (RSDs).
• Priors: They explore various priors for $m_{\text{WDM}}$ (uniform in mass, uniform in inverse mass $w=1/m_{\text{WDM}}$, and Jeffreys priors) to assess robustness, noting that uniform priors in mass can artificially shift lower bounds depending on the upper cutoff.

3. Key Contributions

1. First Forecasts for [C ii] LIM on WDM: This is the first study to provide quantitative forecasts for constraining WDM mass using the [C ii] power spectrum from future ground-based telescopes like FYST.
2. Handling LF Uncertainties: The paper rigorously addresses the uncertainty in the [C ii] luminosity function by comparing optimistic and pessimistic models and testing the impact of the faint-end slope ($\alpha$).
3. Degeneracy Analysis: The authors identify and analyze a significant degeneracy between $m_{\text{WDM}}$ and the RSD parameter $\sigma$. In standard setups, the suppression of power by WDM can be mimicked by increasing the velocity dispersion ($\sigma$), making it difficult to distinguish the two effects without high spectral resolution.
4. Halo Mass Dominance: A key finding is that the [C ii] LIM signal is dominated by halos of mass $M \sim 10^{11} - 10^{12} h^{-1} M_\odot$, rather than the low-mass halos where WDM and CDM diverge most significantly. This limits the constraining power of [C ii] compared to tracers that might be more sensitive to smaller scales.

4. Results

Constraints on $m_{\text{WDM}}$ (CDM Universe)

Assuming the true universe is CDM, the study forecasts the lower limits on $m_{\text{WDM}}$ at 95% credibility level (CL):

• Reference Setup (FYST DSS, $16$deg$^2$,$R=100$):
  • Optimistic LF: 1.10 keV
  • Pessimistic LF: 0.58 keV
• Ambitious Future Surveys (Half-sky, $\sqrt{10}$ better sensitivity):
  • Optimistic LF: 5.82 keV
  • Pessimistic LF: 1.90 keV
• Impact of Spectral Resolution: Increasing resolution from $R=100$ to $R=500$ breaks the $m_{\text{WDM}}$-$\sigma$ degeneracy, tightening constraints by a factor of up to 1.8 in favorable setups.

Recovery of True Mass

When generating mock data with a true $m_{\text{WDM}} = 3$ keV:

• Standard setups (CDM-like noise) fail to rule out CDM ($m_{\text{WDM}} \to \infty$) at 95% CL.
• Only in highly ideal setups (e.g., $1600$deg$^2$,$R=500$, high sensitivity) can the true mass be recovered with both upper and lower bounds (e.g.,$2.62 < m_{\text{WDM}} < 4.54$ keV).

Impact of Faint-End Slope

• For the standard slope ($\alpha = -1.1$), low-mass halos contribute negligibly to the signal.
• Adopting a steeper slope ($\alpha = -1.9$) increases the contribution of low-mass halos. This reverses the degeneracy direction (both $m_{\text{WDM}}$ and $\sigma$ suppress power) and improves constraints, particularly in future, larger surveys.

5. Significance and Conclusions

• Potential and Limitations: While [C ii] LIM is a promising probe, its constraining power on WDM is currently limited because the signal is dominated by massive halos ($10^{11}-10^{12} M_\odot$) where the difference between CDM and WDM is small. The suppression of low-mass halos (the primary WDM signature) contributes little to the total [C ii] power spectrum.
• Path Forward: To achieve competitive constraints (comparable to Lyman-$\alpha$ forest limits), future surveys require:
  1. Large Sky Coverage: Moving from $16$deg$^2$to$>1000$deg$^2$.
  2. High Spectral Resolution: To disentangle RSD effects from WDM damping.
  3. Multi-line/Multi-redshift: Combining [C ii] with other tracers (CO, Ly-$\alpha$, H$\alpha$) across different redshifts will probe a wider range of halo masses and break degeneracies, offering the most robust path to determining the nature of Dark Matter.

In summary, the paper demonstrates that while current-generation LIM surveys will provide only modest lower limits on WDM mass, next-generation, wide-area, high-resolution surveys could significantly tighten these constraints, potentially ruling out keV-scale WDM or detecting deviations from CDM.