Calibration of neutron star natal kick velocities to isolated pulsar observations

🌌 Neutron star kicks and the MM20 model

Supernovae can impart a “kick” to neutron stars, influencing their trajectories and fate in binary systems.

The Mandel & Müller (2020) (MM20) model represents a significant advancement in our understanding of supernova kicks and their impact on neutron star dynamics. Unlike other analytic models such as the Maxwellian model, which relies on a simplistic assumption of kick velocity distributions, the MM20 model incorporates recent simulation data and a more nuanced approach to account for asymmetries in supernova explosions. This enhancement allows for a more accurate depiction of how neutron stars acquire kicks during supernova events, leading to improved predictions of their behavior in binary systems.

📈 Constraining the MM20 model using pulsar observations

The MM20 model contains 2 free parameters: v_ns and σ_ns. To validate and constrain the MM20 model, we turned to a state-of-the-art dataset of observed single pulsar velocities. By comparing the model's predictions with real-world pulsar data using Bayesian inference, we can identify the most likely configurations of the kick model.

We simulated a population of stars in COMPAS, an open source population synthesis software, where we evolved the stars until they experience a supernova explosion, get kicked in accordance with the MM20 model at a given configuration, and formed single pulsars. After repeating this process for a range of parameter configurations, we can compute the relative likelihoods over the parameter space.

Fun fact: We simulated populations of stars in isolation as well as in binaries, and found that the evolutionary histories of the progenitor stars had a surprisingly minimal impact on the final isolated neutron star velocity distributions! This finding suggests that the dynamics of the supernova kicks are more influential than the specific evolutionary pathways taken by stars for determining the final velocities.

📊 Are the models any good?

In order to verify that the models were sensible, we must compare the predicted neutron star velocity distributions against the observed data. For this, we used the followinf statistical tools:

• Bootstrapping: Used to generate hundreds realizaitions of predicted velocity distributions, and thus capture their inherent uncertainty.
• Kolmogorov-Smirnov Test: Statistical comparison of two given data sets to determine whether they are mutually compatible.

The KS tests showed that the predicted velocity distributions are compatible with observations!

🧩Binary Neutron Star (BNS) Simulation: The Impact of Model Evolution

To further investigate the implications of the new model, we conducted simulations of binary neutron star (BNS) populations. The results indicated a notable difference between the BNS event rates predicted by the MM20 model and those from the Maxwellian model. Specifically, the MM20 model predicts a more accurate representation of the expected detection rates, demonstrating its efficacy in predicting the behavior of neutron stars formed in binary systems. This highlights the importance of incorporating realistic kick models in astrophysical simulations, ultimately improving our understanding of neutron star populations and their role in the universe.