Millisecond pulsars (MSPs) and normal non-recycled pulsars are both detected in $gamma$-rays. However, it appears that a much larger fraction of known energetic and nearby MSPs are detected in $gamma$-rays, in comparison with normal pulsars, thereby
making undetected $gamma$-ray MSPs exceptions. In this paper, we demonstrate that the viewing angles (i.e. between the pulsar spin axis and the line of sight) are well described by the orbital inclination angles which, for binary MSPs with helium white dwarf companions, can be determined using the relationship between the orbital period and the white dwarf mass. We use the predicted viewing angles, in complement with values obtained from other constraints when available, to identify the causes of non-detection of energetic and nearby MSPs from the point of view of beaming geometry and orientation. We find evidence for slightly different viewing angle distributions, and postulate that energetic and nearby MSPs are mainly undetected in $gamma$-rays simply because they are seen under unfavourable (i.e. small) viewing angles. We finally discuss the magnetic fields of $gamma$-ray detected pulsars and show that pulsars which are efficient at converting their rotational energy into $gamma$-ray emission may have overestimated dipolar magnetic field strengths.
We report on timing observations of the recently discovered binary pulsar PSR J1952+2630 using the Arecibo Observatory. The mildly recycled 20.7-ms pulsar is in a 9.4-hr orbit with a massive, M_WD > 0.93 M_sun, white dwarf (WD) companion. We present,
for the first time, a phase-coherent timing solution, with precise spin, astrometric, and Keplerian orbital parameters. This shows that the characteristic age of PSR J1952+2630 is 77 Myr, younger by one order of magnitude than any other recycled pulsar-massive WD system. We derive an upper limit on the true age of the system of 50 Myr. We investigate the formation of PSR J1952+2630 using detailed modelling of the mass-transfer process from a naked helium star on to the neutron star following a common-envelope phase (Case BB Roche-lobe overflow). From our modelling of the progenitor system, we constrain the accretion efficiency of the neutron star, which suggests a value between 100 and 300% of the Eddington accretion limit. We present numerical models of the chemical structure of a possible oxygen-neon-magnesium WD companion. Furthermore, we calculate the past and the future spin evolution of PSR J1952+2630, until the system merges in about 3.4 Gyr due to gravitational wave emission. Although we detect no relativistic effects in our timing analysis we show that several such effects will become measurable with continued observations over the next 10 years; thus PSR J1952+2630 has potential as a testbed for gravitational theories.
