The mechanisms governing the stellar mass assembly and star formation history of brightest cluster galaxies ( BCGs ) are still being debated .
By means of new and archival molecular gas observations we investigate the role of dense megaparsec-scale environments in regulating the fueling of star formation in distant BCGs , through cosmic time .
We observed in CO with the IRAM 30m telescope two star-forming BCGs belonging to SpARCS clusters , namely , 3C 244.1 ( z = 0.4 ) and SDSS J161112.65+550823.5 ( z = 0.9 ) , and compared their molecular gas and star formation properties with those of a compilation of \sim 100 distant cluster galaxies from the literature , including nine additional distant BCGs at { z \sim 0.4 - 3.5 } .
We set robust upper limits of M _ { { H } _ { 2 } } < 1.0 \times 10 ^ { 10 } ~ { } M _ { \odot } and < 2.8 \times 10 ^ { 10 } ~ { } M _ { \odot } to their molecular gas content , respectively , and to the ratio of molecular gas to stellar mass M ( { H } _ { 2 } ) / M _ { \star } \lesssim 0.2 and depletion time \tau _ { dep } \lesssim 40 Myr of the two targeted BCGs .
They are thus among the distant cluster galaxies with the lowest gas fractions and shortest depletion times .
The majority ( 64 \% \pm 15 \% and 73 \% \pm 18 \% ) of the 11 BCGs with observations in CO have lower M ( { H } _ { 2 } ) / M _ { \star } values and \tau _ { dep } , respectively , than those estimated for main sequence galaxies .
Statistical analysis also tentatively suggests that the values of M ( { H } _ { 2 } ) / M _ { \star } and \tau _ { dep } for the 11 BCGs deviates , with a significance of \sim 2 \sigma , from those of the comparison sample of cluster galaxies .
A morphological analysis for a subsample of seven BCGs with archival HST observations reveals that 71 \% \pm 17 \% of the BCGs are compact or show star-forming components or substructures .
Our results suggest a scenario where distant star-forming BCGs assemble a significant fraction \sim 16 \% of their stellar mass on the relatively short timescale \sim \tau _ { dep } , while environmental mechanisms might prevent the replenishment of gas feeding the star formation .
We speculate that compact components also favor the rapid exhaustion of molecular gas and ultimately help to quench the BCGs .
Distant star-forming BCGs are excellent targets for ALMA and for next-generation telescopes such as the James Webb Space Telescope .