Sterile Neutrinos as the Warm Dark Matter in the Type II Seesaw Model

In the framework of type II seesaw mechanism we discuss the number of sterile right-handed Majorana neutrinos being the warm dark matter (WDM). When the type II seesaw mass term $M_ u ^{II}$ is far less than the type I seesaw mass term $M_ u ^{I}$, only one of three sterile neutrinos may be the WDM particle. On the contrary, the WDM particles may contain all sterile neutrinos. If $M_ u ^{II} sim M_ u ^{I}$, the allowed number is not more than $N - 1$ for $N$ sterile neutrinos. It is worthwhile to stress that three different types of neutrino mass spectrum are permitted when $M_ u ^{II} gg M_ u ^{I}$ and $M_ u ^{II} sim M_ u ^{I}$.