🔭 astrophysics

Gamma-ray and radio populations of millisecond pulsars in globular clusters

By comparing two luminosity models for millisecond pulsars in globular clusters, this study demonstrates that a lognormal distribution model predicts a significantly larger population of intrinsically fainter pulsars consistent with recent radio observations, whereas a fundamental plane model implies an unrealistic, brighter population.

Original authors: Hannah Lawson, Duncan R. Lorimer

Published 2026-08-05

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CC BY 4.0

Original authors: Hannah Lawson, Duncan R. Lorimer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Milky Way not just as a flat disk of stars, but as a bustling city where some neighborhoods are incredibly crowded. In these crowded districts, called globular clusters, stars are packed so tightly that they constantly bump into one another. When a dense, dead star called a neutron star happens to be in one of these clusters, it can get a "second wind." It steals material from a nearby companion star, which acts like a cosmic turbocharger, spinning the neutron star up to incredible speeds—hundreds of times per second. These super-fast spinners are called millisecond pulsars. They are like lighthouses in the dark, beaming out pulses of radio waves and high-energy gamma rays. Astronomers care about counting them because their numbers and brightness tell us how these stellar "recycling plants" work and how stars evolve in the most crowded parts of our galaxy.

Now, picture trying to count how many of these cosmic lighthouses exist in these crowded neighborhoods. The problem is, we can't see them all. Some are too faint, and some are beaming their light away from Earth, making them invisible to our telescopes. This is where a team of researchers, led by Hannah Lawson and Duncan Lorimer, stepped in with a digital detective story. They didn't just look at the stars; they built a massive computer simulation to guess how many pulsars are hiding in the shadows of 118 globular clusters.

The team set up two different "rulebooks" for how bright these pulsars should be. The first rulebook (Model A) suggested that pulsars are generally quite bright and powerful. The second rulebook (Model B) suggested that most pulsars are actually quite dim, with only a few being super-bright. They ran their simulation 1,000 times for each rulebook to see which one matched the gamma-ray signals actually detected by the Fermi space telescope.

The results were a tale of two very different crowds. If the first rulebook were true, there would be about 770 millisecond pulsars across all these clusters. But if the second rulebook were true, there would be a staggering 5,150 pulsars! That's a difference of about six to seven times. Why? Because in the second scenario, the individual pulsars are much fainter on average, so you need a much larger crowd of them to create the same total amount of light that Fermi sees.

The researchers then checked their work against what we know about radio waves. They found that the "faint crowd" theory (Model B) fits the data much better. It suggests that the hidden population of pulsars is mostly made up of dim, quiet objects that are fainter than the typical pulsars we see in the rest of the galaxy. This aligns with a growing idea that these pulsars aren't actually weak; they just happen to be pointing their beams away from us, or their geometry makes them look faint. In contrast, the "bright crowd" theory (Model A) would require these pulsars to be intrinsically super-bright, which doesn't make much sense given what we know about how they work.

So, what's the verdict? The paper suggests that the universe is likely hiding a vast, silent army of about 5,000 faint millisecond pulsars in these star clusters, rather than a smaller group of super-bright ones. While the simulation can't tell us exactly which specific cluster holds a single super-bright pulsar that dominates the light (though it predicts there are about three such cases in total), it strongly points toward a future where our telescopes need to get much more sensitive to find this hidden majority. The authors conclude that Model B, the one predicting a larger population of fainter stars, is the more natural and likely description of our galaxy's hidden pulsar population.

Technical Summary: Gamma-ray and radio populations of millisecond pulsars in globular clusters

Problem Statement
Millisecond pulsars (MSPs) in globular clusters (GCs) serve as critical diagnostics for neutron star evolution in dense stellar environments. While radio surveys have established that MSP abundance scales with the stellar encounter rate ( $\Gamma$ ), current samples are often insufficient to robustly constrain the total population across the Galactic GC system. Radio observations are subject to selection effects and may miss faint sources. Conversely, gamma-ray observations by the Fermi Large Area Telescope (LAT) offer a potential probe of the total MSP content, as collective gamma-ray emission from unresolved MSPs can dominate the flux from GCs. However, the underlying gamma-ray luminosity function ( $L_\gamma$ ) of GC MSPs remains uncertain. This paper addresses the question of how different assumptions regarding the $L_\gamma$ distribution affect estimates of the total MSP population and the consistency of these estimates with observed radio properties.

Methodology
The authors performed Monte Carlo simulations on a sample of 118 Galactic GCs to estimate the number of gamma-ray MSPs required to match observed Fermi LAT fluxes or upper limits. The simulation framework involved:

Input Data: Utilizing stellar encounter rates ( $\Gamma$ ) from Bahramian et al. [5], distances from Baumgardt and Vasiliev [8], and Fermi LAT flux measurements or sensitivity-based upper limits from the 4FGL-DR4 catalog.
Luminosity Models: Two distinct models for the gamma-ray luminosity function were tested:
- Model A (3D Fundamental Plane): Based on Kalapotharakos et al. [27], this model correlates $L_\gamma$ with dipole magnetic field strength ( $B$ ), spin-down luminosity ( $\dot{E}$ ), and spectral cutoff energy ( $\epsilon_{cut}$ ). Parameters were generated by simulating MSP spin-down evolution over 0–5 Gyr.
- Model B (Lognormal Distribution): Based on Holst and Hooper [23], this model assumes $L_\gamma$ follows a lognormal distribution with a mean of $5.9 \times 10^{25}$ W and a standard deviation of 2.3.
Simulation Process: For each GC, MSPs were generated iteratively until their summed gamma-ray flux matched the Fermi measurement or upper limit. This was repeated 1,000 times per GC to derive median population estimates and 90% confidence intervals.
Radio Consistency Check: To distinguish between the models, the authors applied a radio-to-gamma-ray luminosity scaling ( $L_r \approx \eta L_\gamma$ ) to predict the number of observable radio MSPs. They compared these predictions against known radio pulsar counts and minimum detectable flux densities ( $S_{min}$ ) for 45 GCs with radio detections.

Key Results

Population Estimates: Both models successfully reproduce the observed gamma-ray fluxes and the established scaling law of abundance with stellar encounter rate ( $N \propto \Gamma^{2/3}$ ). However, they yield fundamentally different total population estimates. Model A predicts a total population of $770 \pm 60$ MSPs across the 118 GCs. In contrast, Model B, due to its lower average gamma-ray luminosity, predicts a population 6–7 times larger: $5150^{+720}_{-710}$ MSPs.
Scaling Laws: The derived abundance models ( $N = \alpha \Gamma^{2/3}$ ) confirm the scaling found in previous studies. The best-fit coefficients are $\alpha_A = 0.29$ and $\alpha_B = 1.62$ . The models predict that roughly three clusters in the sample should have aggregate gamma-ray emission dominated by a single bright MSP, consistent with observations of NGC 6624, NGC 6626, and NGC 6652.
Radio Pseudoluminosity: When applying a radio-to-gamma scaling factor of $\eta \sim 3.5 \times 10^{-7}$ $η \sim 3.5 \times 1 0^{- 7}$ , the models diverge significantly in their implications for radio luminosity:
- Model A implies an intrinsically bright population with a mean radio pseudoluminosity of $\log L_{pseudo} \sim -0.3$ . This suggests MSPs are brighter than canonical pulsars, a result the authors note lacks a clear physical basis and contradicts recent findings by Karastergiou et al. [28].
- Model B predicts a mean radio pseudoluminosity of $\log L_{pseudo} \sim -1.6$ . This is fainter than the canonical pulsar mean ( $\sim -1.1$ ) and aligns with recent evidence suggesting that the apparent faintness of Galactic MSPs is due to geometric effects rather than intrinsic luminosity differences.
Exceptions: While both models generally track observed radio counts, Model A fails to account for the high number of radio pulsars in dense clusters like 47 Tucanae (NGC 104) and Omega Centauri (NGC 5139), whereas Model B's larger underlying population accommodates these observations more naturally.

Significance and Claims
The paper concludes that while both luminosity models are statistically consistent with current Fermi gamma-ray data, Model B (the lognormal distribution) provides a more physically plausible description of the underlying MSP population. Model B's prediction of a vast population of faint MSPs is consistent with the geometric interpretation of MSP radio faintness and successfully explains the high radio pulsar counts in the most massive clusters.

The authors assert that the larger population of faint MSPs predicted by Model B represents a testable hypothesis. They state that future deep radio surveys with emerging facilities—specifically the Deep Synoptic Array, the Square Kilometre Array, MeerKAT, and FAST—are required to probe this low-luminosity regime. Detecting this faint population would provide definitive support for the lognormal model and further constrain the evolutionary pathways of MSPs in dense stellar environments. The study does not claim to have definitively proven Model B over Model A but argues that Model B offers a more natural alignment with multi-wavelength constraints and recent geometric analyses of the Galactic MSP population.

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