Carbon stars as standard candles -- III. Un-binned maximum likelihood fitting and comparison with TRGB estimations

Understand

In the second paper of this series, we developed a new distance determination method using the median $J$ magnitude of carbon-rich asymptotic giant branch stars (CS) as standard candles and the Magellanic Clouds as the fundamental calibrators.

• The $J$-band CS luminosity function was modeled using a modified Lorentzian distribution whose parameters were used to determined whether the LMC or SMC was the most suitable calibrator.
• In this third paper of the series, we expand our sample of galaxies and introduce a more robust method to determine the parameters of the Lorentzian model.
• The new fitting method uses an un-binned maximum likelihood estimator to determine the parameters of the Lorentzian model resulting in parameter errors that are significantly smaller compared to the second paper.