# Millisecond Pulsars and Black Holes in Globular Clusters

## TL;DR

This study uses advanced N-body simulations to explore how millisecond pulsars form and distribute in globular clusters, revealing their relationship with black hole populations and providing insights into their observable properties.

## Contribution

The paper introduces realistic N-body simulations to model MSP formation in GCs, highlighting the impact of dynamical interactions and black hole populations.

## Key findings

- MSPs can be formed via electron-capture supernovae and accretion in GCs.
- Number of MSPs correlates with cluster mass and anti-correlates with black hole retention.
- MSPs are more centrally concentrated in clusters with fewer black holes.

## Abstract

Over a hundred millisecond radio pulsars (MSPs) have been observed in globular clusters (GCs), motivating theoretical studies of the formation and evolution of these sources through stellar evolution coupled to stellar dynamics. Here we study MSPs in GCs using realistic $N$-body simulations with our Cluster Monte Carlo code. We show that neutron stars (NSs) formed in electron-capture supernovae (including both accretion-induced and merger-induced collapse of white dwarfs) can be spun up through mass transfer to form MSPs. Both NS formation and spin-up through accretion are greatly enhanced through dynamical interaction processes. We find that our models for average GCs at the present day with masses $\approx 2 \times 10^5\,M_\odot$ can produce up to $10-20$ MSPs, while a very massive GC model with mass $\approx 10^6\,M_\odot$ can produce close to $100$. We show that the number of MSPs is anti-correlated with the total number of stellar-mass black holes (BHs) retained in the host cluster. The radial distributions are also affected: MSPs are more concentrated towards the center in a host cluster with a smaller number of retained BHs. As a result, the number of MSPs in a GC could be used to place constraints on its BH population. Some intrinsic properties of MSP systems in our models (such as the magnetic fields and spin periods) are in good overall agreement with observations, while others (such as the distribution of binary companion types) less so, and we discuss the possible reasons for such discrepancies. Interestingly, our models also demonstrate the possibility of dynamically forming NS--NS and NS--BH binaries in GCs, although the predicted numbers are very small.