What can we learn from the radiative decays of the $D_{s1}(2460)$ meson?

We study the radiative decays $D_{s1}(2460)\to \gamma D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)\to \gamma D^0{K}^{+}\mathrm{/}\gamma D^{+}{K}^0$ and argue that their simultaneous experimental measurement, or at least a constraint on the ratio of the corresponding branching fractions, can allow one to probe the nature of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ mesons.