Timing of PSR J2055+3829, an eclipsing black widow pulsar discovered with the Nan\c{c}ay Radio Telescope

We report on the timing observations of the millisecond pulsar PSR J2055+3829 originally discovered as part of the SPAN512 survey conducted with the Nan\c{c}ay Radio Telescope. The pulsar has a rotational period of 2.089 ms, and is in a tight 3.1 hr orbit around a very low mass ($0.023 \leq m_c \lesssim 0.053$ M$_\odot$, 90\% c.l.) companion. Our 1.4 GHz observations reveal the presence of eclipses of the pulsar's radio signal caused by the outflow of material from the companion, for a few minutes around superior conjunction of the pulsar. The very low companion mass, the observation of radio eclipses, and the detection of time variations of the orbital period establish PSR J2055+3829 as a `black widow' (BW) pulsar. Inspection of the radio signal from the pulsar during ingress and egress phases shows that the eclipses in PSR J2055+3829 are asymmetric and variable, as is commonly observed in other similar systems. More generally, the orbital properties of the new pulsar are found to be very similar to those of other known eclipsing BW pulsars. No gamma-ray source is detected at the location of the pulsar in recent \textit{Fermi}-LAT source catalogs. We used the timing ephemeris to search ten years of \textit{Fermi} Large Area Telescope (LAT) data for gamma-ray pulsations, but were unable to detect any, possibly because of the pulsar's large distance. We finally compared the mass functions of eclipsing and non-eclipsing BW pulsars and confirmed previous findings that eclipsing BWs have higher mass functions than their non-eclipsing counterparts. Larger inclinations could explain the higher mass functions of eclipsing BWs. On the other hand, the mass function distributions of Galactic disk and globular cluster BWs appear to be consistent, suggesting, despite the very different environments, the existence of common mechanisms taking place in the last stages of evolution of BWs.