Eccentric millisecond pulsars by resonant convection

Abstract

Eccentric millisecond pulsars (eMSPs) with white dwarf companions exhibit orbital eccentricities orders of magnitude larger than predicted by turbulent convection in the white dwarfs' red giant progenitors. The orbital periods of eMSPs cluster around $P=20-30$ d, remarkably close to the red giant convective eddy turnover time $t_{\rm eddy}$. We propose that the anomalously large eccentricities are resonantly driven by convective flows somehow made coherent when the turnover time matches the tidally locked red giant's spin period, which is also the tidal forcing period. Numerical simulations of rotating red giants and magnetic field studies of stars show some evidence for especially ordered flow patterns when the convective Rossby number $P/t_{\rm eddy}$ is of order unity. We show that resonant convection boosts eccentricities by a factor of $(t_{\rm nuc}/P)^{1/2}\approx 3\times 10^3$ over the random-walk values that characterize conventional MSPs, in good agreement with observations ($t_{\rm nuc}$ is the giant's nuclear burning time-scale). We also show how variations in the eddy turnover time arising from red giant metallicity variations can reproduce the observed effective width of the resonance, $\Delta P/P\approx 0.4$.