Comparison of Burst Properties between FRB 20190520B and FRB 20121102A

A comparative analysis of the individual bursts between FRB 20190520B and FRB 20121102A is presented by compiling a sample of bursts in multiple wavelengths. It is found that the peak frequency ($\nu_p$) distribution of the bursts of FRB 20190520B illustrates four discrete peaks in $\sim1-6$ GHz and their spectral width distribution can be fitted with a log-normal function peaking at 0.35 GHz. The discrete $\nu_p$ distribution and the narrow-banded spectral feature are analogous to FRB 20121102A. The burst duration of FRB 20190520B in the rest frame averages 10.72 ms, longer than that of FRB 20121102A by a factor 3. The specific energy ($E_{\rm \mu_{\rm c}}$) at 1.25 GHz of FRB 20190520B observed with the FAST telescope narrowly ranges in $[0.4, 1]\times 10^{38}$ erg, different from the bimodal $E_{\rm \mu_{\rm c}}$ distribution of FRB 20121102A. Assuming a Gaussian spectral profile of the bursts, our Monte Carlo simulation analysis suggests that a power-law (PL) or a cutoff power-law (CPL) energy function can comparably reproduce the $E_{\rm \mu_{\rm c}}$ distribution of FRB 20190520B. The derived energy function index of the PL model is $4.46\pm 0.17$, much steeper than that of FRB 20121102A ($1.82^{+0.10}_{-0.30}$). For the CPL model, we obtain an index of $0.47$ and a cutoff energy of $7.4\times 10^{37}$ erg. Regarding the predicted $\nu_p$ distribution in 1-2 GHz, the CPL model is more preferred than the PL model. These results indicate that FRB 20190520B and FRB 20121102A shares similar spectral properties, but their energy functions are intrinsically different.