A Method to Estimate the Cooling Time of Ultra-Relativistic Electrons in Pulsar Wind Nebulae

Abstract

Pulsar is a highly magnetized rotating neutron star. It continuously emits a wind of relativistic electrons and positrons. This wind creates an electron-positron-cloud around the pulsar. This cloud, which is full of relativistic electrons and positrons, is called a Pulsar Wind Nebula (PWN). As of 2014, 33 Pulsar Wind Nebulae (PWNe) have been detected in the TeV energy band. Current understanding is, these TeV photons are produced from up-scattering low-energy photons to high-energies by ultra-relativistic electrons and positrons in PWNe, which is a non-thermal process. This process is known as inverse-Compton scattering. During inverse-Compton scattering, ultra-relativistic electrons lose their energy and cool-down to low-energies. The average time that an ultra-relativistic electron takes to cool-down by inverse-Compton scattering is called the cooling time. Estimation of cooling time is important to understand how the luminosity of a PWN changes with time. This paper describes a statistical method developed for estimating the cooling time of ultra-relativistic electrons in a given PWN. This new method is a model independent technique. Cooling time was estimated as a function of two parameters: k and γ. Here k is the high-energy electron fraction in PWN at a given time and γ is the Average Bulk Lorentz Factor of electrons in the PWN. The estimated cooling time is proportional to k and inversely proportional to γ. The developed method was applied to four PWNe: MSH 15-52, HESS J1420-607, HESS J1825-137 and HESS J1837-069. The estimated cooling times vary between 1.56 kyr to 1000 kyr for MSH 15-52, 13 kyr to 8000 kyr for HESS J1420-607, 21.4 kyr to 10000 kyr for HESS J1825-137 and 22.7 kyr to 15000 kyr for HESS J1837-069.