New constraints on the dust and gas distribution in the LkCa 15 disk from ALMA

We search a large parameter space of the LkCa 15's disk density profile to fit its observed radial intensity profile of $^{12}$CO (J = 3-2) obtained from ALMA. The best-fit model within the parameter space has a disk mass of 0.1 $M_{\odot}$ (using an abundance ratio of $^{12}$CO/H$_2$ $=$ 1.4 $\times 10^{-4}$ in mass), an inner cavity of 45 AU in radius, an outer edge at $\sim$ 600 AU, and a disk surface density profile follows a power-law of the form $\rho_r \propto r^{-4}$. For the disk density profiles that can lead to a small reduced $\chi^2$ of goodness-of-fit, we find that there is a clear linear correlation between the disk mass and the power-law index $\gamma$ in the equation of disk density profile. This suggests that the $^{12}$CO disk of LkCa 15 is optically thick and we can fit its $^{12}$CO radial intensity profile using either a lower disk mass with a smaller $\gamma$ or a higher disk mass with a bigger $\gamma$. By comparing the $^{12}$CO channel maps of the best-fit model with disk models with higher or lower masses, we find that a disk mass of $\sim$ 0.1 $M_{\odot}$ can best reproduce the observed morphology of the $^{12}$CO channel maps. The dust continuum map at 0.87 mm of the LkCa 15 disk shows an inner cavity of the similar size of the best-fit gas model, but its out edge is at $\sim$ 200 AU, much smaller than the fitted gas disk. Such a discrepancy between the outer edges of the gas and dust disks is consistent with dust drifting and trapping models.