Galaxy clusters are the most massive gravitationally bound objects in the universe, forming the nodes of the cosmic web. The imprint of structure formation is carried by the galaxy cluster number density and spatial distributions of galaxy clusters. Hence, these cluster properties are sensitive to the underlying cosmological model. Specifically, the abundance of galaxy clusters with mass and redshift is a well-known cosmological probe. With the successful launch of eROSITA, which is to conduct a deep all sky X-ray survey out to redshift ∼1.5 and is expected to detect ∼100,000 clusters, the constraints on cosmology using galaxy clusters are expected to be more precise. To this end, better understanding of the associated biases, selection effects, and scaling relations is very important.
The cluster mass is a key parameter for studies that aim to constrain cosmological parameters using galaxy clusters. It is therefore critical to understand and properly calibrate scaling relations between observables like the cluster X-ray temperature and the mass of the cluster. The parameters of the underlying scaling relation model can be fit directly to the observed data but, they need to be simultaneously fit together with parameters describing the cosmological model. Here, we use simulations to create samples of clusters with associated observables like the X-ray photon counts, temperature, and luminosity in a given energy band in the observer frame. We then try to find an optimal observable for calibration of the observable-mass scaling relation. Establishing the scaling relation also provides a way to constrain the cosmological parameters like the matter density parameter. This improved observable will be useful for getting more accurate results and understanding better, the large-scale properties of clusters and their use in cosmology.