SIMBAD references

The concentration-mass (c-M) relation encodes key information about the assembly history of dark matter halos. However, its behavior at the high mass end has not been measured precisely in observations yet. In this paper, we report the measurement of the halo c-M relation with the galaxy-galaxy lensing method, using the shear catalog of the Dark Energy Camera Legacy Survey (DECaLS) Data Release 8, which covers a sky area of 9500 deg². The foreground lenses are selected from the redMaPPer, LOWZ, and CMASS catalogs, with halo masses ranging from 10¹³ to 10¹⁵ M_☉ and redshifts ranging from z = 0.08 to z = 0.65. We find that the concentration decreases with the halo mass from 10¹³ to 10¹⁴ M_☉, but shows a trend of upturn after the pivot point of ∼10¹⁴ M_☉. We fit the measured c-M relation with the concentration model c(M)=C₀(M/(10¹²M_☉/h))^-γ[1+(M/M₀)^0.4], and we get the values (C₀, γ, log₁₀(M₀)) = (5.119_–0.185^0.183, 0.205_–0.010^0.010, 14.083_–0.133^0.130) and (4.875_–0.208^0.209, 0.221_–0.010^0.010, 13.750_–0.141^0.142) for halos with 0.08 <= z < 0.35 and 0.35 <= z < 0.65, respectively. We also show that the model including an upturn is favored over a simple power-law model. Our measurement provides important information for the recent argument over the massive cluster formation process.