A scaling relation in [C ii]-detected galaxies and its likely application in cosmology

Abstract

ABSTRACT We identify and investigate a possible correlation between the $\rm {[C\,II]} \,158{-}{\mu }m$ luminosity and linewidth in the $\rm {[C\,II]}$-detected galaxies. Observationally, the strength of the $\rm {[C\,II]}\, 158{-}{\mu }m$ emission line is usually stronger than that of the carbon monoxide (CO) emission line and this $\rm {[C\,II]}$ line has been used as another tracer of the galactic characteristics. Moreover, many $\rm {[C\,II]}$-detected galaxies are identified in z > 4. Motivated by previous studies of the CO luminosity–full width at half-maximum correlation relation (LFR) and the available new $\rm {[C\,II]}$ measurements, we compile samples of the $\rm {[C\,II]}$-detected galaxies in the literature and perform the linear regression analysis. The $\rm {[C\,II]}$ LFR is confirmed at a robust level. We also demonstrate the possible application of the $\rm {[C\,II]}$ LFR by utilizing it on the distance measurement of the high-z galaxy. As a result, we extend the cosmic spatial scale beyond the redshift z of 7. With the outcome of the distance measurement, we constrain the cosmology parameters in the Chevallier–Polarski–Linder model, which considers the evolution of dark energy. Consequently, the uncertainties of the w0 and wa are reduced significantly when the measured distance data of the $\rm {[C\,II]}$-detected galaxies are included in the cosmological parameter constraint, exemplifying the potential of using the $\rm {[C\,II]}$-detected galaxies as a tracer to constrain the cosmological parameters.