Context. The second release of Gaia data (Gaia DR2) contains the astrometric parameters for more than half a million quasars. This set defines a kinematically non-rotating reference frame in the optical domain. A subset of these quasars have accurate VLBI positions that allow the axes of the reference frame to be aligned with the International Celestial Reference System (ICRF) radio frame. Aims. We describe the astrometric and photometric properties of the quasars that were selected to represent the celestial reference frame of Gaia DR2 (Gaia-CRF2), and to compare the optical and radio positions for sources with accurate VLBI positions. Methods. Descriptive statistics are used to characterise the overall properties of the quasar sample. Residual rotation and orientation errors and large-scale systematics are quantified by means of expansions in vector spherical harmonics. Positional differences are calculated relative to a prototype version of the forthcoming ICRF3. Results. Gaia-CRF2 consists of the positions of a sample of 556 869 sources in Gaia DR2, obtained from a positional cross-match with the ICRF3-prototype and AllWISE AGN catalogues. The sample constitutes a clean, dense, and homogeneous set of extragalactic point sources in the magnitude range G ≈ 16 to 21 mag with accurately known optical positions. The median positional uncertainty is 0.12 mas for G < 18 mag and 0.5 mas at G = mag. Large-scale systematics are estimated to be in the range 20 to 30 μas. The accuracy claims are supported by the parallaxes and proper motions of the quasars in Gaia DR2. The optical positions for a subset of 2820 sources in common with the ICRF3-prototype show very good overall agreement with the radio positions, but several tens of sources have significantly discrepant positions. Conclusions. Based on less than 40% of the data expected from the nominal Gaia mission, Gaia-CRF2 is the first realisation of a non-rotating global optical reference frame that meets the ICRS prescriptions, meaning that it is built only on extragalactic sources. Its accuracy matches the current radio frame of the ICRF, but the density of sources in all parts of the sky is much higher, except along the Galactic equator.
Gaia Data Release 2: The celestial reference frame (Gaia -CRF2)
	
	
	
		
		
		
		
		
	
	
	
	
	
	
	
	
		
		
		
		
		
			
			
			
		
		
		
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
							
						
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
							
						
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
							
						
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
							
						
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
			
			
				
				
					
					
					
					
						
						
							
							
						
					
				
				
				
				
				
				
				
				
				
				
				
			
			
		
		
		
		
	
Lanzafame, A. C.Membro del Collaboration Group
;Becciani, U.Membro del Collaboration Group
;Brugaletta, E.Membro del Collaboration Group
;Leccia, S.Membro del Collaboration Group
;
	
		
		
	
			2018-01-01
Abstract
Context. The second release of Gaia data (Gaia DR2) contains the astrometric parameters for more than half a million quasars. This set defines a kinematically non-rotating reference frame in the optical domain. A subset of these quasars have accurate VLBI positions that allow the axes of the reference frame to be aligned with the International Celestial Reference System (ICRF) radio frame. Aims. We describe the astrometric and photometric properties of the quasars that were selected to represent the celestial reference frame of Gaia DR2 (Gaia-CRF2), and to compare the optical and radio positions for sources with accurate VLBI positions. Methods. Descriptive statistics are used to characterise the overall properties of the quasar sample. Residual rotation and orientation errors and large-scale systematics are quantified by means of expansions in vector spherical harmonics. Positional differences are calculated relative to a prototype version of the forthcoming ICRF3. Results. Gaia-CRF2 consists of the positions of a sample of 556 869 sources in Gaia DR2, obtained from a positional cross-match with the ICRF3-prototype and AllWISE AGN catalogues. The sample constitutes a clean, dense, and homogeneous set of extragalactic point sources in the magnitude range G ≈ 16 to 21 mag with accurately known optical positions. The median positional uncertainty is 0.12 mas for G < 18 mag and 0.5 mas at G = mag. Large-scale systematics are estimated to be in the range 20 to 30 μas. The accuracy claims are supported by the parallaxes and proper motions of the quasars in Gaia DR2. The optical positions for a subset of 2820 sources in common with the ICRF3-prototype show very good overall agreement with the radio positions, but several tens of sources have significantly discrepant positions. Conclusions. Based on less than 40% of the data expected from the nominal Gaia mission, Gaia-CRF2 is the first realisation of a non-rotating global optical reference frame that meets the ICRS prescriptions, meaning that it is built only on extragalactic sources. Its accuracy matches the current radio frame of the ICRF, but the density of sources in all parts of the sky is much higher, except along the Galactic equator.| File | Dimensione | Formato | |
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											aa32916-18.pdf
										
																				
									
										
											 accesso aperto 
											Descrizione: Articolo principale
										 
									
									
									
										
											Tipologia:
											Versione Editoriale (PDF)
										 
									
									
									
									
									
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										5.23 MB
									 
									
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								5.23 MB | Adobe PDF | Visualizza/Apri | 
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