The luminosity function of Fast Radio Bursts ( FRBs ) , defined as the event rate per unit cosmic co-moving volume per unit luminosity , may help to reveal the possible origins of FRBs and design the optimal searching strategy .
With the Bayesian modelling , we measure the FRB luminosity function using 46 known FRBs .
Our Bayesian framework self-consistently models the selection effects , including the survey sensitivity , the telescope beam response , and the electron distributions from Milky Way / the host galaxy / local environment of FRBs .
Different from the previous companion paper , we pay attention to the FRB event rate density and model the event counts of FRB surveys based on the Poisson statistics .
Assuming a Schechter luminosity function form , we infer ( at the 95 % confidence level ) that the characteristic FRB event rate density at the upper cut-off luminosity L ^ { * } = 2.9 _ { -1.7 } ^ { +11.9 } \times 10 ^ { 44 } \mathrm { erg } \mathrm { s } ^ { -1 } is \phi ^ { * } = 339 _ { -313 } ^ { +1074 } \mathrm { Gpc } ^ { -3 } \mathrm { yr } ^ { -1 } , the power-law index is \alpha = -1.79 _ { -0.35 } ^ { +0.31 } , and the lower cut-off luminosity is L _ { 0 } \leq 9.1 \times 10 ^ { 41 } \mathrm { erg } \mathrm { s } ^ { -1 } .
The event rate density of FRBs is found to be 3.5 _ { -2.4 } ^ { +5.7 } \times 10 ^ { 4 } \mathrm { Gpc } ^ { -3 } \mathrm { yr } ^ { -1 } above 10 ^ { 42 } \mathrm { erg } \mathrm { s } ^ { -1 } , 5.0 _ { -2.3 } ^ { +3.2 } \times 10 ^ { 3 } \mathrm { Gpc } ^ { -3 } \mathrm { yr } ^ { -1 } above 10 ^ { 43 } \mathrm { erg } \mathrm { s } ^ { -1 } , and 3.7 _ { -2.0 } ^ { +3.5 } \times 10 ^ { 2 } \mathrm { Gpc } ^ { -3 } \mathrm { yr } ^ { -1 } above 10 ^ { 44 } \mathrm { erg } \mathrm { s } ^ { -1 } .
As a result , we find that , for searches conducted at 1.4 GHz , the optimal diameter of single-dish radio telescopes to detect FRBs is 30–40 m. The possible astrophysical implications of the measured event rate density are also discussed in the current paper .