We report the detection of a dark substructure – undetected in the HST-ACS F814W image – in the gravitational lens galaxy SDSSJ0946+1006 ( the “ Double Einstein Ring ” ) , through direct gravitational imaging .
The lens galaxy is of particular interest because of its relative high inferred fraction of dark matter inside the effective radius .
The detection is based on a Bayesian grid reconstruction of the two-dimensional surface density of the galaxy inside an annulus around its Einstein radius .
The detection of a small mass concentration in the surface density maps has a strong statistical significance .
We confirm this detection by modeling the substructure with a tidally truncated pseudo-Jaffe density profile ; in that case the substructure mass is M _ { sub } = ( 3.51 \pm 0.15 ) \times 10 ^ { 9 } M _ { \odot } , located at ( -0.651 \pm 0.038 , 1.040 \pm 0.034 ) ” , precisely where also the surface density map shows a strong convergence peak ( Bayes factor \Delta \log { \cal { E } } = -128.0 ; equivalent to a \sim 16– \sigma detection ) .
We set a lower limit of { ( M / L ) } _ { { V } , \odot } \ga 120 \leavevmode \nobreak M _ { \odot } / { L } _ { { V% } , \odot } ( 3– \sigma ) inside a sphere of 0.3 kpc centred on the substructure ( r _ { tidal } =1.1 kpc ) .
The result is robust under substantial changes in the model and the data-set ( e.g. PSF , pixel number and scale , source and potential regularization , rotations and galaxy subtraction ) .
It can therefore not be attributed to obvious systematic effects .
Our detection implies a dark matter mass fraction at the radius of the inner Einstein ring of f _ { CDM } = 2.15 ^ { +2.05 } _ { -1.25 } percent ( 68 % C.L ) in the mass range 4 \times 10 ^ { 6 } M _ { \odot } to 4 \times 10 ^ { 9 } M _ { \odot } assuming \alpha = 1.9 \pm 0.1 ( with dN / dm \propto m ^ { - \alpha } ) .
Assuming a flat prior on \alpha , between 1.0 and 3.0 , increases this to f _ { CDM } = 2.56 ^ { +3.26 } _ { -1.50 } percent ( 68 % C.L ) .
The likelihood ratio is 0.51 between our best value ( f _ { CDM } = 0.0215 ) and that from simulations ( f _ { sim } \approx 0.003 ) .
Hence the inferred mass fraction , admittedly based on a single lens system , is large but still consistent with predictions .
We expect to further tighten the substructure mass function ( both fraction and slope ) , using the large number of systems found by SLACS and other surveys .