Utilizing cosmic-ray positron and electron observations to probe the averaged properties of Milky Way pulsars

Pulsars have long been studied in the electromagnetic spectrum. Their environments are rich in high-energy cosmic-ray electrons and positrons likely enriching the interstellar medium with such particles. In this work we use recent cosmic-ray observations from the AMS-02, CALET and DAMPE collaborations to study the averaged properties of the local Milky Way pulsar population. We perform simulations of the local Milky Way pulsar population, for interstellar medium assumptions in agreement with a range of cosmic-ray nuclei measurements. Each such simulation contains $\sim 10^{4}$ pulsars of unique age, location, initial spin-down power and cosmic-ray electron/positron spectra. We produce more than $7\times 10^{3}$ such Milky Way pulsar simulations. We account for and study i) the pulsars' birth rates and the stochastic nature of their birth, ii) their initial spin-down power distribution, iii) their time evolution in terms of their braking index and characteristic spin-down timescale, iv) the fraction of spin-down power going to cosmic-ray electrons and positrons and v) their propagation through the interstellar medium and the Heliosphere. We find that pulsars of ages $\sim 10^{5}-10^{7}$ yr, have a braking index that on average has to be 3 or larger. Given that electromagnetic spectrum observations of young pulsars find braking indices lower than 3, our work provides strong hints that pulsars' braking index increases on average as they age, allowing them to retain some of their rotational energy. Moreover, we find that pulsars have relatively uniform properties as sources of cosmic-ray electrons and positrons in terms of the spectra they produce and likely release O($10\%$) of their rotational energy to cosmic-rays in the ISM. Finally, we find at $\simeq$12 GeV positrons a spectral feature that suggests a new subpopulation of positron sources contributing at these energies.