We consider a sample of $82$ non-repeating FRBs detected at Parkes, ASKAP,
CHIME and UTMOST each of which operates over a different frequency range and
has a different detection criteria. Using simulations, we perform a maximum
likelihood analysis to determine the FRB population model which best fits this
data. Our analysis shows that models where the pulse scatter broadening
increases moderately with redshift ($z$) are preferred over those where this
increases very sharply or where scattering is absent. Further, models where the
comoving event rate density is constant over $z$ are preferred over those where
it follows the cosmological star formation rate. Two models for the host
dispersion measure ($DM_host$) distribution (a fixed and a random
$DM_host$) are found to predict comparable results. We obtain the best
fit parameter values $\alpha=-1.53^+0.29_-0.19$,
$E_33=1.55^+0.26_-0.22$ and $\gamma=0.770.24$. Here
$\alpha$ is the spectral index, $\gamma$ is the exponent of the Schechter
luminosity function and $E_33$ is the mean FRB energy in units of
$10^33 \, J$ across $2128 - 2848\; MHz$ in the FRB rest frame.
Description
A maximum likelihood estimate of the parameters of the FRB population
%0 Generic
%1 bhattacharyya2021maximum
%A Bhattacharyya, Siddhartha
%A Tiwari, Himanshu
%A Bharadwaj, Somnath
%A Majumdar, Suman
%D 2021
%K library
%T A maximum likelihood estimate of the parameters of the FRB population
%U http://arxiv.org/abs/2109.06785
%X We consider a sample of $82$ non-repeating FRBs detected at Parkes, ASKAP,
CHIME and UTMOST each of which operates over a different frequency range and
has a different detection criteria. Using simulations, we perform a maximum
likelihood analysis to determine the FRB population model which best fits this
data. Our analysis shows that models where the pulse scatter broadening
increases moderately with redshift ($z$) are preferred over those where this
increases very sharply or where scattering is absent. Further, models where the
comoving event rate density is constant over $z$ are preferred over those where
it follows the cosmological star formation rate. Two models for the host
dispersion measure ($DM_host$) distribution (a fixed and a random
$DM_host$) are found to predict comparable results. We obtain the best
fit parameter values $\alpha=-1.53^+0.29_-0.19$,
$E_33=1.55^+0.26_-0.22$ and $\gamma=0.770.24$. Here
$\alpha$ is the spectral index, $\gamma$ is the exponent of the Schechter
luminosity function and $E_33$ is the mean FRB energy in units of
$10^33 \, J$ across $2128 - 2848\; MHz$ in the FRB rest frame.
@misc{bhattacharyya2021maximum,
abstract = {We consider a sample of $82$ non-repeating FRBs detected at Parkes, ASKAP,
CHIME and UTMOST each of which operates over a different frequency range and
has a different detection criteria. Using simulations, we perform a maximum
likelihood analysis to determine the FRB population model which best fits this
data. Our analysis shows that models where the pulse scatter broadening
increases moderately with redshift ($z$) are preferred over those where this
increases very sharply or where scattering is absent. Further, models where the
comoving event rate density is constant over $z$ are preferred over those where
it follows the cosmological star formation rate. Two models for the host
dispersion measure ($DM_{\rm host}$) distribution (a fixed and a random
$DM_{\rm host}$) are found to predict comparable results. We obtain the best
fit parameter values $\alpha=-1.53^{+0.29}_{-0.19}$,
$\overline{E}_{33}=1.55^{+0.26}_{-0.22}$ and $\gamma=0.77\pm 0.24$. Here
$\alpha$ is the spectral index, $\gamma$ is the exponent of the Schechter
luminosity function and $\overline{E}_{33}$ is the mean FRB energy in units of
$10^{33} \, {\rm J}$ across $2128 - 2848\; {\rm MHz}$ in the FRB rest frame.},
added-at = {2021-09-15T15:12:21.000+0200},
author = {Bhattacharyya, Siddhartha and Tiwari, Himanshu and Bharadwaj, Somnath and Majumdar, Suman},
biburl = {https://www.bibsonomy.org/bibtex/24e92c3c6c7e283f411d07cabcebddcab/gpkulkarni},
description = {A maximum likelihood estimate of the parameters of the FRB population},
interhash = {b818abdf7b0df5d754a6dc57c113fc70},
intrahash = {4e92c3c6c7e283f411d07cabcebddcab},
keywords = {library},
note = {cite arxiv:2109.06785Comment: 5 pages, 3 figures, Accepted for Publication in the MNRAS Letter},
timestamp = {2021-09-15T15:12:21.000+0200},
title = {A maximum likelihood estimate of the parameters of the FRB population},
url = {http://arxiv.org/abs/2109.06785},
year = 2021
}