Studying the black widow pulsars PSR J0312$-$0921 and PSR J1627$+$3219 in the optical and X-rays

Abstract

Context. PSR J0312$-$0921 and PSR J1627$+$3219 are black widow pulsars with orbital periods of 2.34 and 3.98 hours. They were recently detected in the radio and $\gamma$-rays. Aims. Our goals are to estimate the fundamental parameters of both binary systems and their components. Methods. We performed first phase-resolved multi-band photometry of both objects with the 10.4-m Gran Telescopio Canarias and fitted the obtained light curves with a model assuming direct heating of the companion by the pulsar. Archival X-ray data obtained with the Swift and XMM-Newton observatories were also analysed. Results. For the first time, we firmly identified both systems in the optical. Their optical light curves show a rather symmetric single peak per orbital period and a peak-to-peak amplitude of $\gtrsim$2 mag. We also identified the X-ray counterpart to J1627$+$3219, while for J0312$-$0921 we set an upper limit on the X-ray flux. Conclusions. We estimated the masses of the pulsars, companion temperatures and masses, Roche lobe filling factors, orbital inclinations, and the distances to both systems. PSR J0312$-$0921 has a very light ($\approx$0.02 M$_\odot$) companion which possibly has one of the lowest ($\approx$1600 K) `night-side' temperatures among the known black widow systems. We found that the distances to J0312$-$0921 and J1627$+$3219 are about 2.5 and 4.6 kpc, respectively. This likely explains their faintness in X-rays. The X-ray spectrum of PSR J1627$+$3219 can be described by the power-law model, and its parameters are compatible with those obtained for other black widows.