We present CO J = 4 - 3 line and 3 mm dust continuum observations of a 100 kpc-scale filamentary Ly \alpha nebula ( SSA22 LAB18 ) at z = 3.1 using the Atacama Large Millimeter/submillimeter Array ( ALMA ) .
We detected the CO J = 4 - 3 line at a systemic z _ { CO } = 3.093 \pm 0.001 at 11 \sigma from one of the ALMA continuum sources associated with the Ly \alpha filament .
We estimated the CO J = 4 - 3 luminosity of L ^ { \prime } _ { CO ( 4 - 3 ) } = ( 2.3 \pm 0.2 ) \times 10 ^ { 9 } K km s ^ { -1 } pc ^ { 2 } for this CO source , which is one order of magnitude smaller than those of typical z > 1 dusty star-forming galaxies ( DSFGs ) of similar far-infrared luminosity L _ { IR } \sim 10 ^ { 12 } L _ { \odot } .
We derived a molecular gas mass of M _ { gas } = ( 4.4 ^ { +0.9 } _ { -0.6 } ) \times 10 ^ { 9 } M _ { \odot } and a star-formation rate of SFR = 270 \pm 160 M _ { \odot } yr ^ { -1 } .
We also estimated a gas depletion time of \tau _ { dep } = 17 \pm 10 Myr , being shorter than those of typical DSFGs .
It is suggested that this source is in a transition phase from DSFG to a gas-poor , early-type galaxy .
From ALMA to Herschel multi-band dust continuum observations , we measured a dust emissivity index \beta = 2.3 \pm 0.2 , which is similar to those of local gas-poor , early-type galaxies .
Such a high \beta can be reproduced by specific chemical compositions for interstellar dust at the submillimeter wavelengths from recent laboratory experiments .
ALMA CO and multi-band dust continuum observations can constrain the evolutionary stage of high-redshift galaxies through \tau _ { dep } and \beta , and thus we can investigate dust chemical compositions even in the early Universe .