The 6.7 GHz methanol maser emission , a tracer of forming massive stars , sometimes shows enigmatic periodic flux variations over several 10 - 100 days .
In this Letter , we propose that this periodic variations could be explained by the pulsation of massive protostars growing under rapid mass accretion with rates of \dot { M } _ { \ast } \gtrsim 10 ^ { -3 } ~ { } { M } _ { \sun } ~ { } { yr } ^ { -1 } .
Our stellar evolution calculations predict that the massive protostars have very large radius exceeding 100 ~ { } R _ { \sun } at maximum , and we here study the pulsational stability of such the bloated protostars by way of the linear stability analysis .
We show that the protostar becomes pulsationally unstable with various periods of several 10 - 100 days , depending on different accretion rates .
With the fact that the stellar luminosity when the star is pulsationally unstable also depends on the accretion rate , we derive the period-luminosity relation \log ( L / { L } _ { \sun } ) = 4.62 + 0.98 \log ( P / 100 ~ { } { day } ) , which is testable with future observations .
Our models further show that the radius and mass of the pulsating massive protostar should also depend on the period .
It would be possible to infer such protostellar properties and the accretion rate with the observed period .
Measuring the maser periods enables a direct diagnosis of the structure of accreting massive protostars , which are deeply embedded in dense gas and inaccessible with other observations .