Based on a three-dimensional model of an early star-forming galaxy , we explore the evolution of the sub-millimeter brightness .
The model galaxy is employed from an ultra-high-resolution chemodynamic simulation of a primordial galaxy by Mori & Umemura , where the star formation rate ( SFR ) is \sim 10 { M _ { \odot } yr ^ { -1 } } at t _ { age } \lesssim 0.3 Gyr and several { M _ { \odot } yr ^ { -1 } } at t _ { age } > 0.3 Gyr .
The former phase well reproduces the observed properties of Lyman alpha emitters ( LAEs ) and the latter does Lyman break galaxies ( LBGs ) .
We solve the three-dimensional radiative transfer in the clumpy interstellar media in this model galaxy , taking the size distributions of dust grains into account , and calculate the dust temperature as a function of galactic evolutionary time .
We find that the clumpiness of interstellar media plays an important role for the sub-millimeter brightness .
In the LAE phase , dust grains are concentrated on clumpy star-forming regions that are distributed all over the galaxy , and the grains can effectively absorb UV radiation from stars .
As a result , the dust is heated up to T _ { dust } \gtrsim 35 K. In the LBG phase , the continuous supernovae drive dust grains far away from star-forming regions .
Then , the grains can not absorb much radiation from stars , and becomes into a cold state close to the CMB temperature .
Consequently , the dust temperature decreases with the evolutionary time , where the mass-weighted mean temperature is T _ { dust } = 26 ~ { } K at t _ { age } = 0.1 Gyr and T _ { dust } = 21 ~ { } K at t _ { age } = 1.0 Gyr .
By this analysis , it turns out that the sub-millimeter brightness is higher in the LAE phase than that in the LBG phase , although the dust-to-gas ratio increases monotonically as a function of time .
We derive the spectral energy distributions by placing the model galaxy at a given redshift .
The peak flux at 850 \mu m is found to be S _ { 850 } \sim 0.2 - 0.9 mJy if the model galaxy is placed at 6 \geq z \geq 2 .
This means that ALMA can detect an early star-forming galaxy with SFR of \sim 10 { M _ { \odot } yr ^ { -1 } } by less than one hour integration with 16 antennas .