A team of astronomers from the Institute of Space Sciences (ICE-CSIC) and the University of Hertfordshire have combined pulsar population synthesis with a novel deep learning technique to model the birth properties and evolution of neutron stars. The team found that long-term magnetic field decay is crucial to explain the observed population of pulsars, confirming previous results, and were able to provide realistic constraints for this process for the first time. These findings provide new insights into the distribution and evolution of pulsar properties in a study recently published in The Astrophysical Journal.
Neutron stars are the remains of the cores of massive stars, once they have exploded. Their main physical properties are their high density, their fast rotation (or spin) and their strong magnetic field. According to these properties, there are different kinds of neutron stars. Pulsars are those neutron stars that generate regular pulses of electromagnetic radiation due to their fast spins and strong magnetic fields.
Researchers have combined pulsar population synthesis with a novel deep learning technique called ‘simulation-based inference’ based on neural networks to constrain the magneto-rotational properties of Galactic radio pulsars. The team modelled the birth properties and evolution of neutron stars and consider realistic magnetic field decay from state-of-the-art magneto-thermal simulations, which were performed at ICE-CSIC.
Additionally, the team shows that it is crucial to include magnetic field decay to explain the observed pulsar population. For the first time, the team also imposed constraints on the late-time magnetic field decay beyond 1 million years that have the potential to shed light on how the magnetic field evolves in neutron star cores. Magnetic field evolution in the neutron star interior is highly uncertain and the older the star gets, the further we see into its interior. This work enhances the understanding of neutron star physics and serves as a foundation for future multi-wavelength analyses of Galactic pulsars.
The team, including ICE-CSIC researchers Michele Ronchi, Celsa Pardo-Araujo and Nanda Rea, took advantage of the ATNF Pulsar Catalogue, which contains a wealth of information on radio pulsars including data recorded with Murriyang, CSIRO’s Parkes radio telescope. In particular, the study combines data from three radio surveys, including the data from the High Time Resolution Universe (HTRU) survey, an all-sky survey for pulsars and radio transients at a frequency of 1400 MHz. The HTRU survey was used for the first time to perform parameter inference on complex physical models of neutron star birth properties and evolution.
Also for the first time, the team applied a deep learning technique called ‘neural posterior estimation’ to perform robust statistical inference for pulsar population synthesis. To date, this was not possible because simulating realistic neutron stars and comparing them to the observed population is too computationally expensive for traditional inference methods. The team thus demonstrated that simulation-based inference with deep neural networks is a powerful tool for parameter inference in pulsar population synthesis.
“The most surprising outcome to me is how well this simulation-based inference method that was not developed for astronomy but computational neurosciences, performs in our astrophysical context. There was no guarantee that this would work but it turned out that this method is incredibly useful to us”, says Vanessa Graber, first author of the study and Senior Lecturer in Data Science at the University of Hertfordshire, formerly a postdoctoral researcher at ICE-CSIC.
Next steps
Currently, the researchers are working to make their new software public so that the neutron star community can use it as well for their research. The team is also expanding their simulations to also include X-ray and gamma-ray pulsars to better constrain the birth properties of the entire Galactic neutron-star population. This will help astronomers to explain the evolutionary links between different neutron-star classes in a unified scenario which is required by theoretical models of neutron star formation.
As this will increase the complexity of their theoretical models, the team is currently also looking into more sophisticated simulation-based inference approaches. They are working to implement a sequential neural posterior estimation which will allow them to constrain additional physical parameters, such as the unknown radio luminosity function of neutron stars, with reduced computational costs.
The deep learning methods applied to this data are of interest in many other fields that involve simulating real-world problems and performing parameter estimation. They were originally developed in the field of computational neuroscience. So, by testing and further developing these tools in the field of astrophysics, researchers in other areas could also benefit from this work.
