Dynamical determination of the quadrupole mass moment of a white dwarf

TL;DR

This paper dynamically determines the quadrupole mass moment of a white dwarf by analyzing the orbital period of a nearby brown dwarf, using a Newtonian model and considering observational uncertainties.

Contribution

It introduces a method to estimate the quadrupole mass moment of a white dwarf from orbital data, accounting for observational accuracy and inclination effects.

Findings

Quadrupole mass moment Q = (-1.4615 ± 0.9004) x 10^47 kg m^2.

Newtonian model suffices given current orbital parameter accuracy.

Results accommodate a 3-sigma discrepancy in orbital period measurements.

Abstract

In this letter we dynamically determine the quadrupole mass moment Q of the magnetic white dwarf WD 0137-349 by analyzing the period of the recently discovered brown dwarf moving around it in a close 2-hr orbit. It turns out that a purely Newtonian model for the orbit of WD 0137-349B, assumed circular and equatorial, is adequate, given the present-day accuracy in knowing the orbital parameters of such a binary system. Our result is Q=(-1.4615 +/- 0.9004) 10^47 kg m^2 for i=35 deg. It is able to accommodate the 3-sigma significant discrepancy of (1.0 +/- 0.3) 10^-8 s^-2 between the inverse square of the phenomenologically determined orbital period and the inverse square of the calculated Keplerian one. The impact of i, for which a range Delta i of possible values close to 35 deg is considered, is investigated as well.