Constraining the mass of the M31 ionized baryon Halo using CHIME/FRB Catalog 2

Using dispersion measures from 171 Fast Radio Bursts intersecting the Andromeda galaxy's halo compared to a control sample, this study constrains the mass of M31's ionized circumgalactic medium to approximately $1.86 \times 10^{11} M_\odot$, demonstrating the efficacy of FRBs as a tool for probing the baryon content of galactic halos.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Great Cosmic "Missing Person" Case

Imagine you are looking at a massive, invisible cloud of gas surrounding a city. You know the city exists, and you know the laws of physics say there should be a certain amount of gas floating around it to balance the books. But when you try to weigh that gas, it's nowhere to be found.

This is the "Missing Baryon Problem." In astronomy, "baryons" are just the normal stuff that makes up stars, planets, and us (protons and neutrons). Scientists know how much of this stuff the universe should have based on the Big Bang. But when they look at galaxies like our neighbor, Andromeda (M31), they can only find about 20–30% of the expected gas in the stars and the immediate neighborhood.

Where is the other 70%? The leading theory is that it's hiding in the Circumgalactic Medium (CGM)—a vast, hot, diffuse fog of ionized gas surrounding the galaxy. The problem is, this fog is so thin and hot that it's incredibly hard to see with traditional telescopes. It's like trying to see a ghost in a room full of fog; you know it's there, but you can't get a clear picture.

The New Detective: Fast Radio Bursts (FRBs)

Enter the Fast Radio Bursts (FRBs). These are like cosmic lighthouses. They are incredibly bright, millisecond-long flashes of radio waves coming from deep space.

Think of an FRB as a flash of light from a distant lighthouse shining through a thick, invisible fog.

• If the air is clear, the light arrives instantly.
• If the air is thick with fog (ionized gas), the light gets "stuck" for a tiny fraction of a second. The lower frequencies get delayed more than the higher frequencies.

Astronomers call this delay the Dispersion Measure (DM). By measuring how much the light is delayed, they can calculate exactly how much "fog" (electrons) the light passed through, even if they can't see the fog itself.

The Experiment: The "M31 Halo" Test

The authors of this paper decided to use FRBs as a way to "weigh" the fog around the Andromeda galaxy (M31).

1. The Setup: They used data from the CHIME telescope in Canada, which acts like a giant radio net catching these flashes. They found 171 FRBs whose light paths happened to pass right through Andromeda's halo (the foggy region around the galaxy).
2. The Control Group: To make sure the delay wasn't just caused by fog in our own galaxy (the Milky Way) or random space dust, they picked 684 other FRBs that didn't pass through Andromeda. These were the "control group."
3. The Comparison: They compared the "delay" of the Andromeda FRBs against the control group.

The Analogy: Imagine you are timing how long it takes for a runner to finish a race.

• Group A runs through a muddy field (Andromeda's halo).
• Group B runs on a dry track (Control group).
• If Group A takes significantly longer, you know the mud slowed them down. You can then calculate how deep the mud was.

The Results: We Found the Fog!

The team found that the FRBs passing through Andromeda were indeed delayed more than the control group. This confirmed that there is a significant amount of ionized gas in Andromeda's halo.

They calculated the mass of this gas and found:

• The Amount: The halo contains about 186 billion times the mass of our Sun in gas.
• The Implication: This is a huge deal. It suggests that Andromeda might actually hold onto almost 100% of the gas it was supposed to have from the beginning of the universe.

Why is this surprising?
Usually, galaxies are messy. They blow gas out into space with supernova explosions, or they lose it to the vacuum of space. Most models suggest galaxies should have lost a lot of their gas. But Andromeda seems to be a "hoarder," keeping almost all its cosmic gas budget locked up in this invisible halo.

The "Closure Radius" Mystery

The paper also tried to figure out how far out this gas extends. They used a mathematical model to guess the size of the "fog bank."

• They found the gas likely extends out to a distance called the closure radius, which is about 9 times the size of the galaxy's main body.
• Think of it like a city: The "city limits" are the visible stars. But the "fog" (the gas) extends 9 times further out than the city limits, filling the entire region between the city and the next town over.

Why This Matters

This paper is a game-changer for two reasons:

1. It solves a mystery: It provides strong evidence that the "missing" gas in galaxies isn't actually missing; it's just hiding in a hot, invisible fog that we couldn't see before.
2. It proves a new tool works: It shows that FRBs are the perfect tool for this job. Traditional telescopes need bright background stars to see gas (like looking for a stain on a white shirt by shining a light through it). FRBs are so bright and numerous that they act like thousands of flashlights shining through the fog, allowing us to map the gas statistically without needing a single bright star behind it.

The Bottom Line

The universe is full of invisible gas. By using cosmic "flashes" (FRBs) as flashlights, astronomers have finally weighed the invisible fog around our neighbor galaxy, Andromeda. They found that Andromeda is holding onto almost all of its gas, solving a major piece of the puzzle regarding how galaxies grow and evolve.

In short: We used cosmic lightning bolts to weigh the invisible air around a giant galaxy, and we found out that the galaxy is much "fuller" of gas than we thought it was.

Technical Summary

Here is a detailed technical summary of the paper "Constraining the mass of the M31 ionized baryon Halo using CHIME/FRB Catalog 2."

1. Problem Statement

The Circumgalactic Medium (CGM) is a diffuse, multiphase gas reservoir surrounding galaxies, believed to contain a significant fraction of the "missing baryons" predicted by cosmological models ($\Omega_b/\Omega_m \approx 0.158$). While the stellar and interstellar medium (ISM) components of galaxies like the Andromeda Galaxy (M31) are well-mapped, the total mass and distribution of ionized gas in their halos remain poorly constrained.

• The Challenge: Traditional methods (absorption-line spectroscopy of background quasars, X-ray emission, and Sunyaev-Zel'dovich effect) suffer from limitations such as sparse sightlines, dependence on metallicity assumptions, and difficulty detecting hot, diffuse gas ($T > 10^6$ K).
• The Goal: To statistically constrain the total mass and radial distribution of ionized baryons in M31's halo using a novel probe: Fast Radio Bursts (FRBs).

2. Methodology

Data Selection

• Source: The study utilizes CHIME/FRB Catalog 2, containing 3,641 unique FRB sources.
• Target Sample: 171 FRBs whose sightlines intersect the M31 halo within its virial radius ($r_{vir} = 302$ kpc, corresponding to an angular radius of $\approx 23^\circ$).
• Control Sample: 684 FRBs located outside the M31 virial radius.
• Matching Strategy: To minimize systematic errors from the Milky Way's interstellar medium (ISM) and halo, the control sample is strictly matched to the M31 sample based on:
  • Galactic latitude ($|b|$).
  • Milky Way Dispersion Measure ($DM_{MW,ISM}$) within $\pm 3$ pc cm$^{-3}$.
  • This differential approach isolates the excess Dispersion Measure (DM) attributable specifically to M31.

Modeling Framework

The authors employ a Generalized Halo Model to describe the CGM density profile:

• Base Profile: A modified Navarro-Frenk-White (mNFW) profile.
• Modulation: A hyperbolic tangent function, $g(y) = \tanh(y/y_{out})$, is applied to the enclosed baryon mass. This function enforces the cosmic baryon fraction ($\Omega_b/\Omega_m$) at large radii while allowing for baryon depletion in the inner halo due to feedback.
• Key Parameter: The closure radius ($r_{close} = k \cdot r_{vir}$), representing the radius at which the enclosed baryon fraction reaches the cosmic mean. This parameter $k$ is the primary variable to be constrained.
• DM Calculation: The predicted DM contribution ($DM_{M31,halo}$) is calculated by integrating the electron density along the line of sight, assuming full ionization and primordial helium abundance.

Analysis Techniques

1. Weighted Estimator ($\delta DM$): To mitigate the influence of high-DM FRBs (which likely contain large contributions from the cosmic web or host galaxies), the authors use a weighted mean difference between the M31 and control samples:
   $$\delta DM = \sum_{i \in M31} DM_i \hat{w}(DM_i) - \sum_{i \in CS} DM_i \hat{w}(DM_i)$$
   The weighting function $w(DM) = e^{-(DM/\alpha)^\beta}$ downweights high-DM events. The study fixes $\beta=1$ (unbiased estimator) and optimizes $\alpha$ (fiducial value $300$pc cm$^{-3}$) to minimize variance while retaining signal.
2. Validation: The methodology was validated using "sandbox" mock FRB samples (up to 500,000 FRBs) with injected halo signals. Both non-parametric (binned) and parametric ($\chi^2$ fitting) approaches were tested to ensure the recovery of injected signals.

3. Key Contributions

• First Statistical Constraint on M31 CGM via FRBs: This is the first study to use a large sample of FRBs to statistically measure the ionized baryon mass of M31, moving beyond single sightline measurements.
• Differential Control Strategy: The rigorous matching of control sightlines to M31 sightlines in $DM_{MW,ISM}$ and Galactic latitude effectively removes the dominant source of noise (Milky Way structure), allowing for the detection of a subtle excess signal.
• Generalized Halo Model Application: The paper introduces and applies a physically motivated model that links the radial distribution of baryons to the cosmic baryon fraction, constrained by the parameter $r_{close}$.

4. Key Results

Dispersion Measure Excess

The analysis reveals a statistically significant excess in DM for sightlines passing through M31 compared to the control sample:

• **Inner Halo ($0 - 0.5 r_{vir}$):**$\delta DM = 5.9 - 59.6$pc cm$^{-3}$(Signal-to-Noise Ratio$\approx 1.2$).
• **Outer Halo ($0.5 - 1.0 r_{vir}$):**$\delta DM = 25.7 - 64.6$pc cm$^{-3}$(Signal-to-Noise Ratio$\approx 2.3$).
• The results are consistent with independent measurements from localized FRBs (Anna-Thomas et al. 2025) and previous statistical studies of galaxy halos.

Mass Constraints

Using the parametric $\chi^2$ framework to fit the generalized halo model to the observed $\delta DM$:

• Best-fit Closure Radius: $r_{close} = 9.2^{+19.2}_{-4.9} r_{vir}$ (1$\sigma$).
  • Note: The distribution is asymmetric; the data strongly disfavors very concentrated halos ($r_{close} < 4.3 r_{vir}$) but allows for highly extended halos.
• Total CGM Mass: The best-fit model corresponds to a total ionized baryon mass within the virial radius of:
  $$M_{b,halo} = 18.6^{+7.9}_{-8.4} \times 10^{10} M_\odot$$
• Baryon Budget: This mass represents approximately **$100^{+22}{-35}%$** of the expected cosmic baryon fraction ($M{b,cosmic} \approx 2.4 \times 10^{11} M_\odot$) for a halo of M31's mass ($1.5 \times 10^{12} M_\odot$). When combined with the stellar disk mass, the total baryonic content may slightly exceed the cosmic expectation, suggesting M31 is highly efficient at retaining baryons or that ongoing accretion is occurring.

5. Significance and Implications

• Resolving the Missing Baryon Problem: The results suggest that M31 harbors a substantial fraction of its missing baryons in a diffuse, ionized gas phase extending well beyond the virial radius. This supports the hypothesis that "missing" baryons in $L^*$ galaxies reside in the hot/warm-hot CGM.
• Validation of FRBs as Probes: The study demonstrates that FRBs are a powerful, redshift-independent tool for mapping diffuse baryons in nearby galaxies, complementary to absorption-line and X-ray methods.
• Future Prospects: The authors estimate that a sample of $\sim 20,000$ FRBs (achievable with current and next-generation telescopes like CHORD, BURSTT, and DSA-2000) would allow for high-resolution radial profiling of the CGM, breaking current degeneracies in the halo structure.
• Systematics: The paper carefully addresses potential systematics, including the "Local Hot Bridge" between the Milky Way and M31 and variations in CHIME sensitivity, concluding that the differential method robustly isolates the M31 signal.

In summary, this work provides the first direct, statistically robust evidence that the M31 halo contains a massive reservoir of ionized gas, potentially accounting for the galaxy's entire cosmic baryon budget, and establishes FRBs as a premier tool for future CGM studies.