We report a Plateau de Bure interferometer search for C ii -158 \mu m emission from HCM 6A , a lensed Lyman- \alpha emitter ( LAE ) at z = 6.56 .
Our non-detections of C ii -158 \mu m line emission and 1.2 mm radio continuum emission yield 3 \sigma limits of L _ { CII } < 6.4 \times 10 ^ { 7 } \times ( \Delta V / 100 kms ^ { -1 } ) ^ { 1 / 2 } L _ { \odot } on the C ii -158 \mu m line luminosity and S _ { 1.2 mm } < 0.68 mJy on the 1.2 mm flux density .
The local conversion factor between L _ { CII } and star formation rate ( SFR ) yields an SFR < 4.7 M _ { \odot } yr ^ { -1 } , \approx 2 times lower than that inferred from the ultraviolet ( UV ) continuum , suggesting that the local factor may not be applicable in high- z LAEs .
The non-detection of 1.2 mm continuum emission yields a total SFR < 28 M _ { \odot } yr ^ { -1 } ; any obscured star formation is thus within a factor of two of the visible star formation .
Our best-fit model to the rest-frame UV/optical spectral energy distribution of HCM 6A yields a stellar mass of 1.3 \times 10 ^ { 9 } M _ { \odot } and an SFR of \approx 10 M _ { \odot } yr ^ { -1 } , with negligible dust obscuration .
We fortuitously detect CO J = 3 - 2 emission from a z = 0.375 galaxy in the foreground cluster Abell 370 , obtaining a CO line luminosity of L ^ { \prime } ( { CO } ) > ( 8.95 \pm 0.79 ) \times 10 ^ { 8 } K km s ^ { -1 } pc ^ { 2 } , and a molecular gas mass of M ( { H _ { 2 } } ) > ( 4.12 \pm 0.36 ) \times 10 ^ { 9 } M _ { \odot } , for a CO-to-H _ { 2 } conversion factor of 4.6 M _ { \odot } ( K km s ^ { -1 } pc ^ { 2 } ) ^ { -1 } .