Abell 2163: Temperature, Mass, and Hydrostatic Equilibrium

Abstract

Using ASCA data, we have measured the electron temperature in Abell 2163 out to 1.5 h<SUP>-1</SUP> Mpc (¾ of the virial radius, or 10a<SUB>x</SUB>, where a<SUB>x</SUB> is the X-ray core-radius) from the center, in three radial bins. The obtained temperatures are 12.2<SUP>+1.9</SUP><SUB>-1.2</SUB> keV, 11.5<SUP>+2.7</SUP><SUB>-2.9</SUB> keV, and 3.8<SUP>+1.1</SUP><SUB>-0.9</SUB> keV in the 0-3a<SUB>x</SUB> (0-3'.5), 3-6a<SUB>x</SUB> and 6-13a<SUB>x</SUB> spherical shells, respectively. [Errors are 90% throughout the paper unless otherwise stated and h = H<SUB>0</SUB>(100 km s<SUP>-1</SUP> Mpc<SUP>-1</SUP>)<SUP>-1</SUP>.] Formally applying the hydrostatic equilibrium and spherical symmetry assumptions and using these data together with the Ginga spectral and the ROSAT imaging data, we were able to severely limit the possible binding mass distribution of the generic form ρ = ρ<SUB>0</SUB>(1 + r<SUP>2</SUP>/a<SUP>2</SUP><SUB>b</SUB>)<SUP>-n/2</SUP>. All the allowed binding mass profiles are steeper than the gas density profiles, and mass profiles with the same slope as gas are excluded at a greater than 99% confidence. The total mass inside 0.5 h<SUP>-1</SUP> Mpc is 4.3±0.5 × 10<SUP>14</SUP> h<SUP>-1</SUP> M<SUB>sun</SUB>, of which 0.074h<SUP>-3/2</SUP> is gas, while inside 1.5h<SUP>-1</SUP> Mpc, the mass is 1.07±0.13 × 10<SUP>15</SUP> h<SUP>-1</SUP> M<SUB>sun</SUB>. <P />The strongest constraint on the mass profile is the observed quick drop of the temperature at large radii, which can be reconciled only marginally with the ROSAT detection of gas at an even greater radius. We note that in the outer part of this cluster, which is likely to be a recent merger, the timescale for reaching electron- ion temperature equality via collisions is comparable to the merger timescale, so the measured electron temperature may give an underestimate of the gas pressure there. Otherwise, if our low value is indeed representative of the gas temperature in the outer shell, the cluster atmosphere should be convectionally unstable, and gas turbulence should exist. Bulk motions of the gas are also expected during the merger. Their existence would increase the total gas pressure above that indicated by the observed temperature. Thus, failure of the model in which dark matter and gas have the same distribution at the radii of interest, which is favored by hydrodynamic simulations, may be due to the neglect of these phenomena, which leads to an underestimate of the total density and an overestimate of the baryonic fraction at large radii. The mass estimate at the smaller radius, where there is no evidence of departing from equilibrium, is likely to be correct. <P />Our measured electron temperatures, combined with the previously reported Sunyaev-Zeldovich decrement toward this cluster and the ROSAT gas density profile, under the assumption of spherical symmetry, are consistent with a Hubble constant between 42 and 110 km s<SUP>-1</SUP> Mpc<SUP>-1</SUP> (68% interval), where the uncertainty is dominated by that of the available SZ measurement.