Post-Keplerian timing parameters

4.1 Post-Keplerian timing parameters

In any given theory of gravity, the post-Keplerian (PK) parameters can be written as functions of the pulsar and companion star masses and the Keplerian parameters. As the two stellar masses are the only unknowns in the description of the orbit, it follows that measurement of any two PK parameters will yield the two masses, and that measurement of three or more PK parameters will over-determine the problem and allow for self-consistency checks. It is this test for internal consistency among the PK parameters that forms the basis of the classic tests of strong-field gravity. It should be noted that the basic Keplerian orbital parameters are well-measured and can effectively be treated as constants here.

In general relativity, the equations describing the PK parameters in terms of the stellar masses are (see [35 , 132 , 45 ]):

( ) −5∕3 ˙ω = 3 Pb- (T M )2∕3(1 − e2)−1, (31 ) 2π ⊙ (P )1∕3 γ = e --b T⊙2∕3M −4∕3m2 (m1 + 2m2 ), (32 ) 2 π ˙ 192-π (Pb-)− 5∕3 ( 73- 2 37-4) 2− 7∕2 5∕3 −1∕3 Pb = − 5 2π 1 + 24 e + 96e (1 − e) T ⊙ m1m2 M , (33 ) r = T ⊙m2, (34 ) ( Pb) −2∕3 −1∕3 2∕3 −1 s = x 2π T⊙ M m 2 . (35 )

where $s ≡ sin i$ , $M = m1 + m2$ and $3 T ⊙ ≡ GM ⊙∕c = 4.925490947 μs$ . Other theories of gravity, such as those with one or more scalar parameters in addition to a tensor component, will have somewhat different mass dependencies for these parameters. Some specific examples will be discussed in Section 4.4 below.