%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 }