We present approximate models for the solution of the Helmholtz equation set in a domain which represents the sun and its atmosphere. This problem involves a large parameter $\alpha$ which corresponds to the exponential decay rate of the radial density inside the atmosphere. We derive equivalent boundary conditions up to the fourth order of approximation with respect to the parameter $\alpha^{-1}$ for the exact solution $\mathsf{u}$ and we prove error estimates. This approach leads to solve only equations set in a subdomain which represents the sun. The construction of equivalent conditions is based on a multiscale asymptotic expansion in power series of $\alpha^{-1}$ for $\mathsf{u}$. We present numerical results to illustrate the accuracy of the asymptotic models.