Analytical effective one-body formalism for extreme-mass-ratio inspirals with eccentric orbits

Chen Zhang,Wen-Biao Han,Shu-Cheng Yang

Table 2. Relative differences in the orbital frequencies Ωr, Ωφ between the EOB model with small mass ratios and the test-particle approximation.

a/M p/M e Test-particle ν = 10−2 ν = 10−3 ν = 10−4 ν = 10−5 ν = 10−6 $\tfrac{{\rm{\Delta }}\omega }{\omega }(/\nu )$ 0.99 5 0.1 Ωr 0.050841032 0.052967383 0.051054792 0.050862411 0.050843170 0.050841250 4.2 Ωφ 0.081375480 0.080796016 0.081318545 0.081369800 0.081374912 0.081375431 0.70 0.99 10 0.1 Ωr 0.023863900 0.023996289 0.023876964 0.023865208 0.023864071 0.023863903 0.55 Ωφ 0.030284712 0.030221400 0.030278593 0.030284103 0.030284660 0.030284683 0.20 0.99 5 0.6 Ωr 0.031648541 0.032582060 0.031743453 0.031658044 0.031649491 0.031648640 3.0 Ωφ 0.051669258 0.050254323 0.051523452 0.051654638 0.051667794 0.051669119 2.8 0.99 20 0.6 Ωr 0.0052501837 0.0052537928 0.0052505388 0.0052502166 0.0052501873 0.0052501841 0.07 Ωφ 0.0059449013 0.0059371561 0.0059441512 0.0059448231 0.0059448938 0.0059449005 0.13 0.5 5 0.1 Ωr 0.030270602 0.032859397 0.030538233 0.030297445 0.030273290 0.030270870 8.9 Ωφ 0.085402159 0.084958240 0.085355747 0.085397498 0.085401693 0.085402113 0.55