Stability of the r-modes in white dwarf stars

TL;DR

This paper investigates the stability of r-modes in white dwarf stars, concluding that the gravitational radiation driven instability is unlikely to be significant in most observed white dwarfs due to long growth times and specific conditions required.

Contribution

It provides improved estimates of r-mode growth times and demonstrates that the instability is only relevant in a small subset of very hot, massive, and rapidly rotating white dwarfs.

Findings

R-mode instability growth times exceed 6 billion years.

Instability is only excited in very hot, massive, and rapidly rotating white dwarfs.

Long growth times make the instability unlikely to affect real white dwarf stars.

Abstract

Stability of the r-modes in rapidly rotating white dwarf stars is investigated. Improved estimates of the growth times of the gravitational-radiation driven instability in the r-modes of the observed DQ Her objects are found to be longer (probably considerably longer) than 6x10^9y. This rules out the possibility that the r-modes in these objects are emitting gravitational radiation at levels that could be detectable by LISA. More generally it is shown that the r-mode instability can only be excited in a very small subset of very hot (T>10^6K), rather massive (M>0.9M_sun) and very rapidly rotating (P_min<P<1.2P_min) white dwarf stars. Further, the growth times of this instability are so long that these conditions must persist for a very long time (t>10^9y) to allow the amplitude to grow to a dynamically significant level. This makes it extremely unlikely that the r-mode instability plays a significant role in any real white dwarf stars.