We constrain the photon mass from well-localized fast radio bursts (FRBs) using Bayes inference method. The probability distributions of dispersion measures (DM) of host galaxy and intergalactic medium are properly taken into account. The photon mass is tightly constrained from 17 well-localized FRBs in the redshift range 0 < z < 0.66. Assuming that there is no redshift evolution of host DM, the 1σ and 2σ upper limits of photon mass are constrained to be mγ < 4.8 × 10−51 kg and mγ < 7.1 × 10−51 kg, respectively. Monte Carlo simulations show that, even enlarging the FRB sample to 200 and extending the redshift range to 0 < z < 3 couldn’t significantly improve the constraining ability on photon mass. This is because of the large uncertainty on the DM of intergalactic medium.

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We investigate the fraction of baryon mass in intergalactic medium (fIGM), using 18 well-localized FRBs in the redshift range z ∈ (0.0039, 0.66). We construct a five-parameter Bayesian inference model, with the probability distributions of dispersion measures (DM) of IGM and host galaxy properly taken into account. To check the possible redshift evolution, we parameterize fIGM as a mildly evolving function of redshift, fIGM = fIGM, 0[1 + αz/(1 + z)]. By simultaneously constraining five parameters, we get $f_\mathrm{IGM,0} = 0.92^{+0.06}_{-0.12}$ and $\alpha = 0.49^{+0.59}_{-0.47}$, and the median value of DM of host galaxy is $\exp (\mu )=72.49^{+33.31}_{-25.62}~{\rm pc ~ cm ^ {-3}}$. By fixing two parameters which can be constrained independently with other observations, we obtain $\alpha =0.11^{+0.24}_{-0.27}$ in the three-parameter fit, which is consistent with zero within 1σ uncertainty. Monte Carlo simulations show that even 300 FRBs are not enough to tightly constrain five parameters simultaneously. This is mainly caused by the correlation between parameters. Only if two parameters are fixed, 100 FRBs are necessary to achieve unbiased constraints on the remaining parameters.