Basically, pulsar timing provides the following Keplerian orbital parameters of the binary system: the binary orbital period as measured from periodic Doppler variations of the pulsar spin, the projected semimajor axis as measured from the semiamplitude of the pulsar radial velocity curve ( is the binary inclination angle defined such that for faceon systems), the orbital eccentricity as measured from the shape of the pulsar radial velocity curve, and the longitude of periastron at a particular epoch . The first two parameters allow one to construct the mass function of the secondary companion,
In this expression, is measured in lightseconds, , and and denote masses of the pulsar and its companion, respectively. This function gives the strict lower limit on the mass of the unseen companion. However, assuming the pulsar mass to have the typical value of a NS mass (for example, confined between the lowest measured NS mass for PSR J0737–3039B [241] and the maximum measured NS mass of in the NS–WD binary PSR J0751+1807 [291]), one can estimate the mass of the secondary star even without knowing the binary inclination angle .Longterm pulsar timing allows measurements of several relativistic phenomena: the advance of periastron , the redshift parameter , the Shapiro delay within the binary system qualified through postKeplerian parameters , , and the binary orbit decay . From the postKeplerian parameters the individual masses , and the binary inclination angle can be calculated [46].
Of the postKeplerian parameters of binary pulsars, the periastron advance rate is usually measured most readily. Assuming it to be entirely due to general relativity, the total mass of the system can be evaluated:
High values of the derived total mass of the system () suggests the presence of another NS or even BH^{2}.If the individual masses, binary period, and eccentricity of a compact binary system are known, it is easy to calculate the time it takes for the binary companions to coalesce due to GW emission using the quadrupole formula for GW emission [309] (see Section 3.1.4 for more detail):
Here the reduced mass of the binary. Some observed and derived parameters of known compact binaries with NSs are collected in Tables 2 and 3.
















PSR  Ref.  
[ms]  [d]  [lts]  [deg yr^{–1}]  [× 10^{–12}]  








J0737–3039A  22.70  0.102  1.42  0.088  16.88  –1.24  [49] 
J0737–3039B  2773  —  —  —  —  —  [241] 
J1518+4904  40.93  8.634  20.04  0.249  0.011  ?  [290] 
B1534+12  37.90  0.421  3.73  0.274  1.756  –0.138  [455, 388] 
J1756–2251  28.46  0.320  2.75  0.181  2.585  ?  [98] 
J1811–1736  104.18  18.779  34.78  0.828  0.009  < 30  [242] 
J1906+0746  144.07  0.116  1.42  0.085  7.57  ?  [239] 
B1913+16  59.03  0.323  2.34  0.617  4.227  –2.428  [155] 
B2127+11C  30.53  0.335  2.52  0.681  4.457  –3.937  [7, 333] 


























PSR  
[]  []  [Myr]  [Myr]  





J0737–3039A  0.29  2.58  210  87 
J0737–3039B  —  —  50  — 
J1518+4904  0.12  2.62  9.6 × 10^{6}  
B1534+12  0.31  2.75  248  2690 
J1756–2251  0.22  2.57  444  1690 
J1811–1736  0.13  2.6  1.7 × 10^{6}  
J1906+0746  0.11  2.61  0.112  300 
B1913+16  0.13  2.83  108  310 
B2127+11C  0.15  2.71  969  220 










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