A Search for Radio Millisecond Pulsar Companions around Extremely Low-mass White Dwarfs with Ellipsoidal Variability
Extremely low-mass white dwarfs (ELM WDs) are helium-core white dwarfs with masses less than 0.3 $M_{\odot}$. Short-period ELM WD binaries that exhibit ellipsoidal variations may harbor heavier companions, either massive white dwarfs or millisecond pulsars (MSPs). In this study, we selected $\sim$ 12,000 ELM WDs or their candidates, and searched for ellipsoidal-like lightcurves with orbital periods shorter than one day, by using the public data from Zwicky Transient Facility. Finally 23 such systems were found, with 17 being newly discovered. We selected nine high-priority targets likely to evolve from the Roche-lobe overflow channel and estimated their companion masses from the extracted ellipsoidal variation amplitude. Among them, the four targets have companion masses exceeding 1 $M_{\odot}$. We performed a search for radio pulsations from six of these targets by using Five-hundred-meter Aperture Spherical radio Telescope. However, no convincing radio pulsed signals were found, resulting in upper limits for the radio flux at around 8 $μ$Jy. Given the non-detection of radio pulsations from a total of 11 similar systems, the fraction of ellipsoidal ELM WDs around MSPs is estimated to be below 15$^{+6}_{-3}$%. We anticipate that multi-wavelength studies of more ellipsoidal-like ELM WDs will further constrain the fraction.