Upper stellar mass limit by radiative feedback at low-metallicities: metallicity and accretion rate dependence

We investigate the upper stellar mass limit set by radiative feedback by the forming star with various accretion rates and metallicities. To this end, we numerically solve the structures of both a protostar and its surrounding accretion envelope assuming a spherical symmetric and steady flow. The optical depth of the dust cocoon, a dusty part of the accretion envelope, differs among the direct light from the stellar photosphere and the diffuse light re-emitted as dust thermal emission. As a result, varying the metallicity qualitatively changes the way that the radiative feedback suppresses the accretion flow. With a fixed accretion rate of $10^{-3}M_{\odot} {\rm yr^{-1}}$, the both direct and diffuse lights jointly operate to prevent the mass accretion at $Z \gtrsim 10^{-1}Z_{\odot}$. At $Z \lesssim 10^{-1}Z_{\odot}$, the diffuse light is no longer effective, and the direct light solely limits the mass accretion. At $Z \lesssim 10^{-3}Z_{\odot}$, the HII region formation plays an important role in terminating the accretion. The resultant upper mass limit increases with decreasing metallicity, from a few $\times~10~M_\odot$ to $\sim 10^3~M_\odot$ over $Z = 1Z_{\odot} - 10^{-4}~Z_\odot$. We also illustrate how the radiation spectrum of massive star-forming cores changes with decreasing metallicity. First, the peak wavelength of the spectrum, which is located around $30 \mu {\rm m}$ at $1Z_{\odot}$, shifts to $< 3 \mu {\rm m}$ at $Z \lesssim 0.1 Z_\odot$. Second, a characteristic feature at $10 \mu \rm{m}$ due to the amorphous silicate band appears as a dip at $1Z_{\odot}$, but changes to a bump at $Z \lesssim 0.1 Z_{\odot}$. Using these spectral signatures, we can search massive accreting protostars in nearby low-metallicity environments with up-coming observations.