The contribution to Galactic Centre {\gamma}-ray excess from cluster-born millisecond pulsars. Constraints from direct N-body simulations

Using high-resolution direct N-body simulations to track neutron stars from both surviving and disrupted globular clusters, this study demonstrates that the resulting population of millisecond pulsars can fully reproduce the observed Galactic Centre gamma-ray excess, thereby favoring an astrophysical origin over dark matter annihilation.

The Gist

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

The Cosmic Mystery: A Glowing Ghost in the Center of Our Galaxy

Imagine looking up at the night sky and seeing a giant, glowing cloud of invisible energy (gamma rays) right in the center of our Milky Way galaxy. Astronomers call this the Galactic Center Gamma-Ray Excess (GCE).

For years, scientists have been arguing about what causes this glow. There are two main suspects:

1. The "Dark Matter" Suspect: Invisible, mysterious particles crashing into each other and exploding.
2. The "Pulsar" Suspect: A massive crowd of dead, spinning stars (called Millisecond Pulsars) that are too small and faint to see individually, but together they create a bright glow.

This new paper is a detective story that investigates the second suspect: The Pulsars.

The Theory: The "Cosmic Bus" Analogy

The authors propose a specific way these pulsars got to the center. They didn't just form there; they were delivered.

Think of Globular Clusters (GCs) as giant, crowded buses full of stars. These buses have been driving around the galaxy for billions of years.

• The Passengers: Inside these buses are neutron stars (the dead cores of exploded stars).
• The Route: As these buses drive close to the center of the galaxy (the Galactic Center), the gravity of the galaxy acts like a giant hand. It shakes the bus, and some passengers fall out.
• The Destination: These fallen passengers (neutron stars) get stuck in the center of the galaxy. Over time, some of them get "recycled" into super-fast spinning pulsars, which start shooting out beams of gamma rays.

The paper asks: Did enough passengers fall out of enough buses to create the giant glow we see?

The Investigation: A High-Speed Simulation

To answer this, the scientists didn't just guess; they built a massive, high-speed computer simulation.

1. The Setup: They took 12 real, existing globular clusters (the "buses" that are still around today) and created a set of "ghost buses" (clusters that existed long ago but were completely destroyed).
2. The Movie: They ran a movie of the last 8 billion years. They watched how these clusters moved, how the galaxy's gravity tugged on them, and exactly how many neutron stars fell out of each cluster and landed in the central region.
3. The Count: They counted every single neutron star that ended up in the center.

The Big Reveal: The "Ghost Bus" Contribution

Here is what they found:

• The Real Buses: The clusters we can see today are already dropping off enough neutron stars to create a significant amount of the glow.
• The Ghost Buses: However, the real clusters alone aren't quite enough to explain the entire brightness of the glow.
• The Missing Piece: The scientists realized that if we assume there were twice as many "ghost buses" (clusters that were destroyed long ago) as we currently think, the math works perfectly. The debris from these ancient, destroyed clusters would have dumped a huge number of pulsars into the center, creating the exact amount of gamma-ray light we observe.

The Shape of the Glow

The simulation also predicted what this glow should look like.

• The Disk: The pulsars from the destroyed clusters form a flat, pancake-like shape (like a disk) in the middle of the galaxy.
• The Bulge: There is also a puffier, rounder shape sticking up and down from the disk.

This matches what the Fermi telescope actually sees! The glow isn't just a perfect sphere; it has a flat, disk-like structure, which strongly suggests it's made of stars (pulsars) rather than dark matter (which would likely form a perfect sphere).

The Verdict: Not Dark Matter, But Dead Stars

The authors conclude that the "Dark Matter" suspect is likely innocent. The evidence points strongly to the "Pulsar" suspect.

Why?
Because when you combine the pulsars from the clusters we see today plus the pulsars from the ancient, destroyed clusters, the result perfectly matches the brightness, the shape, and the location of the gamma-ray glow.

In a Nutshell

The mystery of the glowing center of our galaxy is likely solved. It's not a collision of invisible dark matter particles. Instead, it's the collective glow of millions of tiny, spinning, dead stars that were kicked out of ancient star clusters and dumped into the galaxy's center billions of years ago. It's a cosmic graveyard that is still shining bright.

Technical Summary

Here is a detailed technical summary of the paper "The contribution to Galactic Centre γ-ray excess from cluster-born millisecond pulsars: Constraints from direct N-body simulations."

1. Problem Statement

The Galactic Centre (GalC) exhibits a GeV γ-ray excess (GCE) that is spatially extended around Sagittarius A* and exceeds predictions from standard cosmic-ray interactions. The origin of this signal is debated between two primary hypotheses:

1. Dark Matter (DM) Annihilation: Weakly Interacting Massive Particles (WIMPs) annihilating in the dense DM halo.
2. Astrophysical Sources: An unresolved population of millisecond pulsars (MSPs).

While previous studies suggested MSPs could explain the GCE, there was a lack of fully dynamical models tracing how neutron stars (NSs) formed in globular clusters (GCs) are stripped and deposited into the central kiloparsec. Specifically, the contribution from destroyed (disrupted) GCs, whose debris was accreted into the bulge over cosmic time, had not been rigorously quantified using high-resolution simulations.

2. Methodology

The authors employed a fully dynamical approach using high-resolution direct N-body simulations to model the evolution of GCs within a time-varying Milky Way potential.

• Simulation Code: Used $\phi$-GPU, a high-order parallel code implementing a fourth-order Hermite integration scheme with individual block time steps. It includes updated stellar evolution libraries (Banerjee et al. 2020; Kamlah et al. 2022b) accounting for mass loss, supernovae, natal kicks, and binary evolution.
• Initial Conditions:
  • Surviving GCs: 12 real, present-day MW GCs (e.g., Terzan 5, NGC 6642) were initialized using King models with parameters fitted to current observations. Their orbits were integrated backward 8 Gyr.
  • Destroyed GCs: A theoretical population of 54 early GCs (50 with $6 \times 10^4 M_\odot$and 4 with$1.8 \times 10^5 M_\odot$) was simulated. These were initialized with specific binding energies and angular momenta to represent clusters that were fully disrupted within the last 5 Gyr, depositing their debris into the inner Galaxy.
• Milky Way Potential: A time-variable, MW-like potential derived from the IllustrisTNG-100 simulation was used to capture external tidal forces.
• NS Tracking: The simulations tracked the 6D phase-space distribution of all NSs formed. NSs were classified as "bound" if their binding energy to the cluster nucleus was negative and they remained within the tidal (Jacobi) radius.
• MSP Conversion: Since the simulations do not model binary recycling (NS $\to$ MSP), the authors applied an empirically calibrated MSP-to-NS ratio ($k$).
  • They calculated the ratio of observed/predicted MSPs to bound NSs for real clusters.
  • Derived a median coefficient: $k \approx 0.0114$ (with a range of $\sim 0.001$ to $0.029$).
  • Applied this coefficient to the stripped NS populations from both surviving and destroyed clusters to estimate the total MSP count.
• Flux Calculation: Mock sky maps and cumulative flux profiles were generated assuming representative per-pulsar luminosities ($\langle L \rangle$) of $1, 4,$and$8 \times 10^{33}$erg s$^{-1}$.

3. Key Contributions

• Dual-Channel Modeling: The study is the first to simultaneously model the contribution of MSPs from surviving GCs (via tidal stripping) and destroyed GCs (via accretion of debris) to the GalC using direct N-body dynamics.
• Dynamical Retention: Unlike previous works that assumed a fixed retention fraction (e.g., 10%), this study dynamically computed the retention of NSs based on individual natal kicks and orbital evolution, finding a lower retention rate ($\sim 6\%$ within 1 kpc).
• Morphological Prediction: The simulations predict specific spatial morphologies for the MSP population, including axisymmetric over-densities in the Galactic plane and perpendicular to it.

4. Key Results

• NS Distribution:
  • Most NSs from surviving GCs are found in massive clusters like Terzan 5, NGC 7078, and NGC 6642.
  • NSs from destroyed clusters are heavily concentrated in the central region ($<1$ kpc), forming a distinct, axisymmetric distribution with a pronounced over-density in the Galactic disk plane.
• MSP Population:
  • Using the median coefficient $k \approx 0.0114$, the surviving GCs alone provide a substantial γ-ray signal.
  • Including the contribution from destroyed clusters significantly increases both the amplitude and the central concentration of the signal.
• Reproducing the GCE:
  • High Luminosity Scenario: Assuming an average MSP luminosity of $\langle L \rangle \approx 8 \times 10^{33}$ erg s$^{-1}$, the combined contribution from surviving and destroyed clusters reproduces the observed GCE amplitude and spatial profile very well.
  • Enhancement Factor: To achieve a near-perfect match with observations (after subtracting the SMBH component), the contribution from destroyed clusters needed to be enhanced by a factor of $\sim 2$, suggesting the initial population of disrupted clusters might be larger than modeled or that dynamical friction was more efficient.
  • Low Luminosity Scenario: Lower luminosities ($1-4 \times 10^{33}$erg s$^{-1}$) result in a flux deficit, implying that either the number of early GCs was higher, or in-situ MSP formation in the bulge is required.
• Morphology: The simulated MSP distribution exhibits an axisymmetric morphology with over-densities in the Galactic plane, qualitatively consistent with recent reports of similar structures in the GCE.

5. Significance and Conclusions

• Favoring MSP Origin: The results strongly favor the MSP origin of the GCE over dark matter annihilation. The combined contribution of MSPs from surviving and disrupted GCs naturally reproduces the observed signal's amplitude, spectrum, and concentration under reasonable physical assumptions.
• Dynamical Validation: The study validates the hypothesis that GC disruption is a major mechanism for populating the Galactic bulge with compact objects.
• Future Directions: The authors suggest that future observations (e.g., FAST, SKA, CTA) targeting the predicted over-densities in the Galactic plane could confirm the MSP population. They also note that future models should incorporate binary evolution directly into the N-body code and refine the treatment of dynamical friction to reduce uncertainties in the disrupted cluster contribution.

In summary, this paper provides a robust, dynamically consistent framework demonstrating that cluster-born MSPs are a viable and likely dominant source of the Galactic Centre γ-ray excess.