Physical properties and chemical composition of the cores in the California molecular cloud

We aim to reveal the physical properties and chemical composition of the cores in the California molecular cloud (CMC), so as to better understand the initial conditions of star formation. We made a high-resolution column density map (18.2") with Herschel data, and extracted a complete sample of the cores in the CMC with the \textsl{fellwalker} algorithm. We performed new single-pointing observations of molecular lines near 90 GHz with the IRAM 30m telescope along the main filament of the CMC. In addition, we also performed a numerical modeling of chemical evolution for the cores under the physical conditions. We extracted 300 cores, of which 33 are protostellar and 267 are starless cores. About 51\% (137 of 267) of the starless cores are prestellar cores. Three cores have the potential to evolve into high-mass stars. The prestellar core mass function (CMF) can be well fit by a log-normal form. The high-mass end of the prestellar CMF shows a power-law form with an index $\alpha=-0.9\pm 0.1$ that is shallower than that of the Galactic field stellar mass function. Combining the mass transformation efficiency ($\varepsilon$) from the prestellar core to the star of $15\pm 1\%$ and the core formation efficiency (CFE) of 5.5\%, we suggest an overall star formation efficiency of about 1\% in the CMC. In the single-pointing observations with the IRAM 30m telescope, we find that 6 cores show blue-skewed profile, while 4 cores show red-skewed profile. [$\rm {HCO}^{+}$]/[HNC] and [$\rm {HCO}^{+}$]/$\rm [N_{2}H^{+}]$ in protostellar cores are higher than those in prestellar cores; this can be used as chemical clocks. The best-fit chemical age of the cores with line observations is $\sim 5\times 10^4$~years.