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The pulsar PSR J1756$-$2251 resides in a relativistic double neutron star(DNS) binary system with a 7.67-hr orbit. We have conducted long-term precisiontiming on more than 9 years of data acquired from five telescopes, measuringfive post-Keplerian parameters. This has led to several independent tests ofgeneral relativity (GR), the most constraining of which shows agreement withthe prediction of GR at the 4% level. Our measurement of the orbital decay ratedisagrees with that predicted by GR, likely due to systematic observationalbiases. We have derived the pulsar distance from parallax and orbital decaymeasurements to be 0.73$_{-0.24}^{+0.60}$ kpc (68%) and < 1.2 kpc (95% upperlimit), respectively; these are significantly discrepant from the distanceestimated using Galactic electron density models. We have found the pulsar massto be 1.341$\pm$0.007 M$_\odot$, and a low neutron star (NS) companion mass of1.230$\pm$0.007 M$_\odot$. We also determined an upper limit to the spin-orbitmisalignment angle of 34{\deg} (95%) based on a system geometry fit tolong-term profile width measurements. These and other observed properties haveled us to hypothesize an evolution involving a low mass loss, symmetricsupernova progenitor to the second-formed NS companion, as is thought to be thecase for the double pulsar system PSR J0737$-$3039A/B. This would make PSRJ1756$-$2251 the second compact binary system providing concrete evidence forthis type of NS formation channel.

PSR J1756$-$2251: a pulsar with a low-mass neutron star companion