On the second derivatives of periods and braking indices in radio pulsars

TL;DR

This paper investigates the second derivatives of pulsar periods and their impact on braking indices, revealing that current calculation methods may need correction for certain pulsars with long periods.

Contribution

It introduces a correction approach for braking index calculations by analyzing second derivatives, challenging the assumption of constant pulsar parameters.

Findings

Second derivatives of pulsar periods can be positive, affecting braking index calculations.

Corrections to braking indices are significant for pulsars with long periods and small derivatives.

Current methods often assume constant pulsar parameters, which may be inaccurate.

Abstract

The analysis of some braking mechanisms for neutron stars was carried out to determine the sign of the second derivative of the pulsar period. This quantity is the important parameter for calculations of the braking index n. It is shown that this derivative can be positive and lead to decreasing of n. It is necessary to correct the methods of calculations of n used this moment because they are based as a rule on the suggestion on the constancy of pulsar parameters (magnetic fields, angles between some axes and so on). The estimations of corrections to braking indices are obtained. It is shown that these corrections can be marked for pulsars with long periods and their small derivatives.