Isolated pulsar population synthesis with simulation-based inference
Vanessa Graber Michele Ronchi Celsa Pardo-Araujo Nanda Rea
We combine pulsar population synthesis with simulation-based inference to
constrain the magneto-rotational properties of isolated Galactic radio pulsars.
We first develop a flexible framework to model neutron-star birth properties
and evolution, focusing on their dynamical, rotational and magnetic
characteristics. In particular, we sample initial magnetic-field strengths,
$B$, and spin periods, $P$, from log-normal distributions and capture the
late-time magnetic-field decay with a power law. Each log-normal is described
by a mean, $\mu_{\log B}, \mu_{\log P}$, and standard deviation, $\sigma_{\log
B}, \sigma_{\log P}$, while the power law is characterized by the index,
$a_{\rm late}$, resulting in five free parameters. We subsequently model the
stars' radio emission and observational biases to mimic detections with three
radio surveys, and produce a large database of synthetic $P$-$\dot{P}$ diagrams
by varying our input parameters. We then follow a simulation-based inference
approach that focuses on neural posterior estimation and employ this database
to train deep neural networks to directly infer the posterior distributions of
the five model parameters. After successfully validating these individual
neural density estimators on simulated data, we use an ensemble of networks to
infer the posterior distributions for the observed pulsar population. We obtain
$\mu_{\log B} = 13.10^{+0.08}_{-0.10}$, $\sigma_{\log B} =
0.45^{+0.05}_{-0.05}$ and $\mu_{\log P} = -1.00^{+0.26}_{-0.21}$, $\sigma_{\log
P} = 0.38^{+0.33}_{-0.18}$ for the log-normal distributions, and $a_{\rm late}
= -1.80^{+0.65}_{-0.61}$ for the power law at $95\%$ credible interval. Our
approach represents a crucial step towards robust statistical inference for
complex population-synthesis frameworks and forms the basis for future
multi-wavelength analyses of Galactic pulsars.