Abstract Galaxy clusters present unique advantages for cosmological study. Here we collect a new sample of 10 lensing galaxy clusters with X-ray observations to constrain cosmological parameters. The redshifts of the lensing clusters lie between 0.1 and 0.6, and the redshift range of their arcs is from 0.4 to 4.9. These clusters are selected carefully from strong gravitational lensing systems which have both X-ray satellite observations and optical giant luminous arcs with known redshifts. Giant arcs usually appear in the central region of clusters, where mass can be traced with luminosity quite well. Based on gravitational lensing theory and a cluster mass distribution model, we can derive a ratio using two angular diameter distances. One is the distance between lensing sources and the other is that between the deflector and the source. Since angular diameter distance relies heavily on cosmological geometry, we can use these ratios to constrain cosmological models. Moreover, X-ray gas fractions of galaxy clusters can also be a cosmological probe. Because there are a dozen parameters to be fitted, we introduce a new analytic algorithm, Powell’s UOBYQA (Unconstrained Optimization By Quadratic Approximation), to accelerate our calculation. Our result demonstrates that this algorithm is an effective fitting method for such a continuous multi-parameter constraint. We find an interesting fact that these two approaches are separately sensitive to ΩΛ and ΩM . By combining them, we can get reasonable fitting values of basic cosmological parameters: ΩM = 0.26+0.04−0.04, and ΩΛ = 0.82+0.14−0.16.

Keywords X-rays: galaxies: clusters — gravitational lensing — cosmological parameters

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